Working Fluid Characterization

**Chapter 1**

**Abstract**

**1. Introduction**

fluid screening."

**3**

A Predictive Equation of State to

Perform an Extending Screening

of Working Fluids for Power and

*Silvia Lasala, Andrés-Piña Martinez and Jean-Noël Jaubert*

This chapter presents the features of the *Enhanced*-*Predictive*-PR78 equation of state (E-PPR78), a model highly suitable to perform "physical fluid screening" in power and refrigeration cycles. It enables, in fact, the accurate and predictive (i.e., without the need for its preliminary optimization by the user) determination of the thermodynamic properties of pure and multicomponent fluids usable in power and refrigeration cycles: hydrocarbons (alkanes, alkenes, alkynes, cycloalkane, naphthenic compounds, and so on), permanent gases (such as CO2, N2, H2, He, Ar, O2, NH3, NO2/N2O4, and so on), mercaptans, fluorocompounds, and water. The E-PPR78 equation of state is a developed form of the Peng-Robinson equation of state, which enables both the predictive determination of binary interaction parameters and the accurate calculation of pure fluid and mixture thermodynamic properties

(saturation properties, enthalpies, heat capacities, volumes, and so on).

Performance and design of closed power and refrigeration cycles are basically driven by the thermodynamic properties of their working fluids. This is the reason why, since the early 1900s, many researchers have been stressing over the importance of optimizing the working fluid of these cycles and of selecting a proper

Two approaches are currently applied to seek the optimal working fluid. The first strategy consists in considering a limited number of existing pure fluids, the "physical fluid screening." Alternatively, authors apply a *product design* approach, consisting in considering the molecular parameters of the working fluid as optimization variables; the resulting optimal fluid is thus fictive and is named here "fictive

The application of the "physical fluid screening" is preferably associated with the use of equations of state whose accuracy has been properly validated over experimental data of the considered set of existing fluids (see, e.g., [1–5]). The preferred modeling option lies in the use of multi-parameter equations of state such

**Keywords:** thermodynamic cycle, pure working fluid, mixture,

thermodynamic model to accurately calculate their properties.

thermodynamic models, translated-E-PPR78

Refrigeration Cycles

#### **Chapter 1**

## A Predictive Equation of State to Perform an Extending Screening of Working Fluids for Power and Refrigeration Cycles

*Silvia Lasala, Andrés-Piña Martinez and Jean-Noël Jaubert*

#### **Abstract**

This chapter presents the features of the *Enhanced*-*Predictive*-PR78 equation of state (E-PPR78), a model highly suitable to perform "physical fluid screening" in power and refrigeration cycles. It enables, in fact, the accurate and predictive (i.e., without the need for its preliminary optimization by the user) determination of the thermodynamic properties of pure and multicomponent fluids usable in power and refrigeration cycles: hydrocarbons (alkanes, alkenes, alkynes, cycloalkane, naphthenic compounds, and so on), permanent gases (such as CO2, N2, H2, He, Ar, O2, NH3, NO2/N2O4, and so on), mercaptans, fluorocompounds, and water. The E-PPR78 equation of state is a developed form of the Peng-Robinson equation of state, which enables both the predictive determination of binary interaction parameters and the accurate calculation of pure fluid and mixture thermodynamic properties (saturation properties, enthalpies, heat capacities, volumes, and so on).

**Keywords:** thermodynamic cycle, pure working fluid, mixture, thermodynamic models, translated-E-PPR78

#### **1. Introduction**

Performance and design of closed power and refrigeration cycles are basically driven by the thermodynamic properties of their working fluids. This is the reason why, since the early 1900s, many researchers have been stressing over the importance of optimizing the working fluid of these cycles and of selecting a proper thermodynamic model to accurately calculate their properties.

Two approaches are currently applied to seek the optimal working fluid. The first strategy consists in considering a limited number of existing pure fluids, the "physical fluid screening." Alternatively, authors apply a *product design* approach, consisting in considering the molecular parameters of the working fluid as optimization variables; the resulting optimal fluid is thus fictive and is named here "fictive fluid screening."

The application of the "physical fluid screening" is preferably associated with the use of equations of state whose accuracy has been properly validated over experimental data of the considered set of existing fluids (see, e.g., [1–5]). The preferred modeling option lies in the use of multi-parameter equations of state such as Helmholtz energy-based equations of state optimized by NIST (e.g., the GERG [6], the Span and Wagner [7], and so on), m-Benedict-Webb-Rubin (BWR) [8], Bender [9], and so on. Despite being highly accurate, these equations of state require the availability of a huge number of fluid-specific parameters, and their optimal values are thus provided by the model developer. An interesting chapter [10] has been recently published by Bell and Lemmon to spread the use of multiparameter equations of state in the ORC community. However, at their current state of development, these models are thus not sufficiently flexible to be used in a screening approach extended to a population of hundreds of existing pure fluids and mixtures. For the same reason, the use of these multi-parameter models in a "fictive fluid screening" approach is inappropriate. To provide the reader with an order of magnitude, more than 1000 of fluids could be considered in this physical fluid screening procedure. The Design Institute for Physical Properties (DIPPR) currently provides accurate experimental data in a database (DIPPR 801) for 2330 pure fluids. Refprop 10.0 (NIST) [11] currently allows for the accurate representation of only 147 fluids.

developed to allow for the accurate and predictive (i.e., without the need for its optimization over experimental data) application of the Peng-Robinson equation of state to multi-component mixtures. We thus start with introducing the forerunner

*A Predictive Equation of State to Perform an Extending Screening of Working Fluids for Power…*

*<sup>v</sup>* � *<sup>b</sup>* � *<sup>a</sup>*

When applied to the *i*th pure component, *a* in Eq. (1) corresponds to the purecomponent cohesive parameter, *ai*, and *b* to its co-volume, *bi*. We will refer to *a* and *b* to indicate the mixture cohesive and co-volume parameters. We will detail in the following section how to calculate pure fluid *ai* and *bi* (Section 2.1) and mixture *a* and *b* (Section 2.2). Before continuing, it is worth warning the reader of the fact that the original *E*-PPR78 model degenerates into the standard PR78 equation of state

When applied to pure fluids, the standard Peng-Robinson equation of state requires the definition of parameters *ai* and *bi*, calculated as reported in the

� 0*:*253076587

*<sup>α</sup>i*ð Þ *<sup>T</sup>* is the so‐called *<sup>α</sup>* � function

The standard Peng-Robinson equation of state incorporates the Soave α-function

However, in the last 4 years, two improved (i.e., thermodynamically consistent

� exp *Li* <sup>1</sup> � *<sup>T</sup>*

*Tc*,*<sup>i</sup>* � �*MiNi* " # ! <sup>2</sup>

and <sup>Ω</sup>*<sup>a</sup>* <sup>¼</sup> 8 5ð Þ *<sup>X</sup>* <sup>þ</sup> <sup>1</sup>

<sup>49</sup> � <sup>37</sup>*<sup>X</sup>* � <sup>0</sup>*:*<sup>457235529</sup>

*i*

*<sup>i</sup>* <sup>þ</sup> <sup>0</sup>*:*016666*ω*<sup>3</sup>

(2)

*i*

(3)

(4)

*v v*ð Þþ <sup>þ</sup> *<sup>b</sup> b v*ð Þ ‐*<sup>b</sup>* (1)

*<sup>P</sup>* <sup>¼</sup> *RT*

PR78 equation of state:

when considering pure fluids.

*<sup>R</sup>* <sup>¼</sup> <sup>8</sup>*:*<sup>314472</sup> *J mol*�<sup>1</sup>

*RTc*,*<sup>i</sup> Pc*,*<sup>i</sup>*

*ai*ð Þ¼ *T ac*,*<sup>i</sup>αi*ð Þ *T* with

*αi*ð Þ¼ *T* 1 þ *mi* 1 �

[46] for 1721 molecules):

following:

8

>>>>>>>>>>>><

>>>>>>>>>>>>:

[19, 47]:

8 >><

>>:

**5**

*X* ¼ 1 þ

*bi* ¼ Ω*<sup>b</sup>*

**2.1 PR78: the application to pure fluids**

*DOI: http://dx.doi.org/10.5772/intechopen.92173*

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>4</sup> � <sup>2</sup> ffiffi 2 <sup>p</sup><sup>3</sup> <sup>p</sup> <sup>þ</sup>

*K*�<sup>1</sup>

h i p<sup>3</sup> p �<sup>1</sup>

with: <sup>Ω</sup>*<sup>b</sup>* <sup>¼</sup> *<sup>X</sup>*

8 ><

>:

ffiffiffiffiffi *T Tc*,*<sup>i</sup>*

if *<sup>ω</sup><sup>i</sup>* <sup>≤</sup>0*:*491 then *mi* <sup>¼</sup> <sup>0</sup>*:*<sup>37464</sup> <sup>þ</sup> <sup>1</sup>*:*54226*ω<sup>i</sup>* � <sup>0</sup>*:*26992*ω*<sup>2</sup>

if *<sup>ω</sup><sup>i</sup>* <sup>&</sup>gt;0*:*491 then *mi* <sup>¼</sup> <sup>0</sup>*:*<sup>379642</sup> <sup>þ</sup> <sup>1</sup>*:*48503*ω<sup>i</sup>* � <sup>0</sup>*:*164423*ω*<sup>2</sup>

[42, 48] and very accurate) α-functions have been developed and published [44, 46]: a fluid-specific α-function and a generalized one, respectively, based on the model Twu91 [49] and Twu88 [50]. The application of the fluid-specific αfunction Twu91 optimized in [46] guarantees the highest accuracy and requires three parameters (L, M, and N) for each pure fluid (reported by Pina-Martinez et al.

h i � � q <sup>2</sup>

*<sup>α</sup>i*ð Þ¼ *<sup>T</sup> <sup>T</sup>*

*Tc*,*<sup>i</sup>*

� �*Ni*ð Þ *Mi*�<sup>1</sup>

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>4</sup> <sup>þ</sup> <sup>2</sup> ffiffi 2

*ac*,*<sup>i</sup>* ¼ Ω*<sup>a</sup>*

*<sup>X</sup>* <sup>þ</sup> <sup>3</sup> � <sup>0</sup>*:*<sup>07780</sup>

*R*2 *T*2 *c*,*i Pc*,*<sup>i</sup>*

To extend the range of considered fluids, studies present in the literature also consider the use of more flexible equations of state, that is, models characterized by a low number of parameters. If we focus on studies about closed power cycles, the equations of state, which have mainly been applied, are as follows: PC-SAFT-based model [12, 13] (which requires three molecule-specific parameters) in [14–16], BACKONE equation of state [17] (with four molecule-specific parameters) in [18], and the standard Peng-Robinson equations of state [19, 20] (with three parameters for each pure fluid) in [21–23]. These authors considered a different number of fluids. The one counting the highest considered number of fluids is the study by Drescher and Brüggemann [21], with 700 pure fluids. To our knowledge, all the other studies count less than 100 fluids (generally between 10 and 30). Peng-Robinson equation of state is currently the most flexible model to perform an extensive "physical fluid screening" of power and refrigeration working fluids. One of the main conclusions of authors who applied and compared different thermodynamic models (which is, unfortunately, rarely the case—we just found one study) is that the use of the Peng-Robinson equation of state is reliable in comparison with more accurate—but less flexible—multi-parameter equations of state [23].

Since 2004, Jaubert and co-workers have started publishing an improved version of the Peng-Robinson equation of state (version of the year 1978, PR78), the "Enhanced-Predictive-Peng-Robinson-78" (*E*-PPR78) [24–40]. Differently from PR78, this model is entirely able to **predict** the properties of mixtures *without the need for its preliminary calibration* over experimental data; moreover, the adjective *enhanced* has been juxtaposed to its previous name (PPR78) in 2011 [41] to highlight the **improved accuracy** in calculating **mixing enthalpies and heat capacities** (with respect to the original PPR78 model).

This model is widely used in the Chemical Engineering community but, inexplicably, remains unknown in the Energy Engineering one. The aims of this chapter are thus to present this model, to outline the proper way to apply it according to the latest advancements over pure fluid modeling [42–46], and to perform the screening of pure and/or multicomponent working fluids for power and refrigeration cycles.

#### **2. From Peng-Robinson to E-PPR78 equation of state**

The E-PPR78 model is an improved version of the equation of state published in 1978 by Peng and Robinson, the PR78 equation of state. This model has been

*A Predictive Equation of State to Perform an Extending Screening of Working Fluids for Power… DOI: http://dx.doi.org/10.5772/intechopen.92173*

developed to allow for the accurate and predictive (i.e., without the need for its optimization over experimental data) application of the Peng-Robinson equation of state to multi-component mixtures. We thus start with introducing the forerunner PR78 equation of state:

$$P = \frac{RT}{v - b} - \frac{a}{v(v + b) + b(v \cdot b)}\tag{1}$$

When applied to the *i*th pure component, *a* in Eq. (1) corresponds to the purecomponent cohesive parameter, *ai*, and *b* to its co-volume, *bi*. We will refer to *a* and *b* to indicate the mixture cohesive and co-volume parameters. We will detail in the following section how to calculate pure fluid *ai* and *bi* (Section 2.1) and mixture *a* and *b* (Section 2.2). Before continuing, it is worth warning the reader of the fact that the original *E*-PPR78 model degenerates into the standard PR78 equation of state when considering pure fluids.

#### **2.1 PR78: the application to pure fluids**

as Helmholtz energy-based equations of state optimized by NIST (e.g., the GERG [6], the Span and Wagner [7], and so on), m-Benedict-Webb-Rubin (BWR) [8], Bender [9], and so on. Despite being highly accurate, these equations of state require the availability of a huge number of fluid-specific parameters, and their optimal values are thus provided by the model developer. An interesting chapter [10] has been recently published by Bell and Lemmon to spread the use of multiparameter equations of state in the ORC community. However, at their current state of development, these models are thus not sufficiently flexible to be used in a screening approach extended to a population of hundreds of existing pure fluids and mixtures. For the same reason, the use of these multi-parameter models in a "fictive fluid screening" approach is inappropriate. To provide the reader with an order of magnitude, more than 1000 of fluids could be considered in this physical fluid screening procedure. The Design Institute for Physical Properties (DIPPR) currently provides accurate experimental data in a database (DIPPR 801) for 2330

*Organic Rankine Cycles for Waste Heat Recovery - Analysis and Applications*

pure fluids. Refprop 10.0 (NIST) [11] currently allows for the accurate

To extend the range of considered fluids, studies present in the literature also consider the use of more flexible equations of state, that is, models characterized by a low number of parameters. If we focus on studies about closed power cycles, the equations of state, which have mainly been applied, are as follows: PC-SAFT-based model [12, 13] (which requires three molecule-specific parameters) in [14–16], BACKONE equation of state [17] (with four molecule-specific parameters) in [18], and the standard Peng-Robinson equations of state [19, 20] (with three parameters for each pure fluid) in [21–23]. These authors considered a different number of fluids. The one counting the highest considered number of fluids is the study by Drescher and Brüggemann [21], with 700 pure fluids. To our knowledge, all the other studies count less than 100 fluids (generally between 10 and 30). Peng-Robinson equation of state is currently the most flexible model to perform an extensive "physical fluid screening" of power and refrigeration working fluids. One of the main conclusions of authors who applied and compared different thermodynamic models (which is, unfortunately, rarely the case—we just found one study) is that the use of the Peng-Robinson equation of state is reliable in comparison with more accurate—but less flexible—multi-parameter equations of state [23].

Since 2004, Jaubert and co-workers have started publishing an improved version

This model is widely used in the Chemical Engineering community but, inexplicably, remains unknown in the Energy Engineering one. The aims of this chapter are thus to present this model, to outline the proper way to apply it according to the latest advancements over pure fluid modeling [42–46], and to perform the screening of pure and/or multicomponent working fluids for power and refrigera-

The E-PPR78 model is an improved version of the equation of state published in

1978 by Peng and Robinson, the PR78 equation of state. This model has been

of the Peng-Robinson equation of state (version of the year 1978, PR78), the "Enhanced-Predictive-Peng-Robinson-78" (*E*-PPR78) [24–40]. Differently from PR78, this model is entirely able to **predict** the properties of mixtures *without the need for its preliminary calibration* over experimental data; moreover, the adjective *enhanced* has been juxtaposed to its previous name (PPR78) in 2011 [41] to highlight the **improved accuracy** in calculating **mixing enthalpies and heat capacities**

representation of only 147 fluids.

(with respect to the original PPR78 model).

**2. From Peng-Robinson to E-PPR78 equation of state**

tion cycles.

**4**

When applied to pure fluids, the standard Peng-Robinson equation of state requires the definition of parameters *ai* and *bi*, calculated as reported in the following:

$$\begin{cases} R = 8.314472 \int \operatorname{mol}^{-1} K^{-1} \\ X = \left[ 1 + \sqrt[3]{4 - 2\sqrt{2}} + \sqrt[3]{4 + 2\sqrt{2}} \right]^{-1} \sim 0.253076587 \\\ b\_i = \Omega\_b \frac{RT\_{c,i}}{P\_{c,i}} \text{ with: } \Omega\_b = \frac{X}{X + 3} \sim 0.07780 \\\ a\_i(T) = a\_{c,i} a\_i(T) \text{ with } \begin{cases} a\_{c,i} = \Omega\_a \frac{R^2 T\_{c,i}^2}{P\_{c,i}} \text{ and } \Omega\_a = \frac{8(5X + 1)}{49 - 37X} \sim 0.457235529 \\\ a\_i(T) \text{ is the so-called } a - \text{function} \end{cases} \end{cases} \tag{2}$$

The standard Peng-Robinson equation of state incorporates the Soave α-function [19, 47]:

$$\begin{cases} \boldsymbol{a}\_{i}(T) = \left[1 + m\_{i}\left(1 - \sqrt{\frac{T}{T\_{ci}}}\right)\right]^{2} \\ \text{if } \boldsymbol{w}\_{i} \le 0.491 \text{ then } \boldsymbol{m}\_{i} = 0.37464 + 1.54226\boldsymbol{\omega}\_{i} - 0.26992\boldsymbol{\omega}\_{i}^{2} \\ \text{if } \boldsymbol{w}\_{i} > 0.491 \text{ then } \boldsymbol{m}\_{i} = 0.379642 + 1.48503\boldsymbol{\omega}\_{i} - 0.164423\boldsymbol{\omega}\_{i}^{2} + 0.016666\boldsymbol{\omega}\_{i}^{3} \end{cases} \tag{3}$$

However, in the last 4 years, two improved (i.e., thermodynamically consistent [42, 48] and very accurate) α-functions have been developed and published [44, 46]: a fluid-specific α-function and a generalized one, respectively, based on the model Twu91 [49] and Twu88 [50]. The application of the fluid-specific αfunction Twu91 optimized in [46] guarantees the highest accuracy and requires three parameters (L, M, and N) for each pure fluid (reported by Pina-Martinez et al. [46] for 1721 molecules):

$$a\_i(T) = \left(\frac{T}{T\_{c,i}}\right)^{N\_i(M\_i - 1)} \cdot \exp\left[L\_i \left(1 - \left(\frac{T}{T\_{c,i}}\right)^{M\_i N\_i}\right)\right]^2\tag{4}$$

The generalized version of Twu88 [46] requires, similar to the Soave α-function, the knowledge of the acentric factor of each pure fluid and takes the following form:

$$\begin{cases} a\_i(T) = \left(\frac{T}{T\_{\epsilon i}}\right)^{2(M\_i - 1)} \cdot \exp\left[L\_i \left(1 - \left(\frac{T}{T\_{\epsilon i}}\right)^{2M\_i}\right)\right]^2\\ L\_i(o\_i) = 0.0925o\_i^2 + 0.6693o\_i + 0.0728\\ M\_i(o\_i) = 0.1695o\_i^2 - 0.2258o\_i + 0.8788 \end{cases} \tag{5}$$

interaction parameters of PR-78 equation of state, and its use is extremely recommended to predictively calculate thermodynamic properties of multicomponent mixtures. The expression provided by this model to predictively calcu-

*A Predictive Equation of State to Perform an Extending Screening of Working Fluids for Power…*

*<sup>l</sup>*¼<sup>1</sup> *<sup>α</sup>ik* � *<sup>α</sup>jk* � � *<sup>α</sup>il* � *<sup>α</sup>jl* � �*Akl* <sup>298</sup>*:*<sup>15</sup>

2

where *ai* and *bi* are the energy and co-volume parameters of the *i*th molecule, given in Eq. (2); *Ng* is the number of different groups defined by the method; and *αik* is the fraction of molecule *i* occupied by group *k* (occurrence of group *k* in molecule *i* divided by the total number of groups present in molecule *i*). *Akl* and *Bkl*, the group-interaction parameters, are symmetric, *Akl* = *Alk* and *Bkl* = *Blk* (where *k* and *l* are two different groups), and empirically determined by correlating experimental data. Also, *Akk* = *Bkk* = 0. The inclusion of this predictive expression for *kij* in

It is worth recalling the historical development of the process of optimization of *Akl* and *Bkl* provided by the model developers. These parameters have initially been optimized over only vapor-liquid equilibrium data of binary mixtures. The model resulting from the use of these so-optimized group contribution parameters is called PPR78 (Predictive-Peng-Robinson equation of state). Lately, authors recognized that the inclusion of enthalpy and heat capacity data in the optimization process does not affect the accuracy in modeling VLE properties but improves extraordinarily the accuracy in calculating enthalpies and heat capacities of mixtures. So, starting from the year 2011 [41], published *Akl* and *Bkl* have been obtained by minimizing the errors between model calculations and experimental data relative to VLE, mixing enthalpy and heat capacity properties. The model resulting from the inclusion of these group contribution parameters is called **Enhanced-Predictive-PR78 equation of state (E-PPR78)**. The last optimized values of *Akl* and of *Bkl* are reported in Table S1 of Supplementary Material of [39]

The optimization of these parameters has been performed over more than 150,000 experimental data and developed over more than 15 years. Even if preferable, that would be quite time-expensive if there was the need to re-optimize these group contribution parameters when changing any feature of the cubic equation of state (e.g., the α-function) or the cubic equation of state itself. Thankfully, it has been demonstrated [52] that it is possible to rigorously determine *kij* of any equation of state, knowing those of the original E-PPR78. In particular, it is possible to easily

replace the Soave α-function, originally present in E-PPR78, with one of the improved functions presented in Section 2.1 (Eqs. **(4)** and **(5)**) and to use *Akl* and *Bkl* parameters of the Soave-based E-PPR78 by applying, instead of Eq. (7):

*<sup>l</sup>*¼<sup>1</sup> *<sup>α</sup>ik* � *<sup>α</sup>jk* � � *<sup>α</sup>il* � *<sup>α</sup>jl* � �*Akl* <sup>298</sup>*:*<sup>15</sup>

2

p

2 � �

*T=K* � � *Bkl*

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *a*mod *<sup>i</sup>* ð Þ *<sup>T</sup> <sup>a</sup>*mod *<sup>j</sup>* ð Þ *T*

*bibj*

*Akl*�<sup>1</sup>

3 5 �

ffiffiffiffiffiffiffiffiffiffiffiffi *a*mod *<sup>i</sup>* ð Þ *<sup>T</sup>* <sup>p</sup> *bi* �

� �<sup>2</sup>

ffiffiffiffiffiffiffiffiffiffiffiffi *a*mod *<sup>j</sup>* ð Þ *T* p *bj*

(8)

2 � �

the PR78 equation of state results in the **Predictive-PR78 (PPR78)**.

*T=K* � � *Bkl*

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *ai*ð Þ *<sup>T</sup> aj*ð Þ *<sup>T</sup>* <sup>p</sup> *bibj*

*Akl*�<sup>1</sup>

3 5 �

ffiffiffiffiffiffiffiffi *ai*ð Þ *<sup>T</sup>* <sup>p</sup> *bi* �

� �<sup>2</sup>

ffiffiffiffiffiffiffiffi *aj*ð Þ *<sup>T</sup>* <sup>p</sup> *bj*

(7)

late the binary interaction parameter is as follows:

*DOI: http://dx.doi.org/10.5772/intechopen.92173*

*kij*ð Þ¼ *T*

� 1 2

4

for 40 molecular groups.

*kij*ð Þ¼ *T*

**7**

� 1 2 P*Ng k*¼1 P*Ng*

4

P*Ng k*¼1 P*Ng*

The alternative use of the three α-functions recalled above leads to different accuracies in the calculation of thermodynamic properties. A comparison is reported in **Table 1** between the PR equation of state incorporating the three different α-functions and pseudo-experimental data made available by DIPPR [51]. Piña-Martinez et al. also showed [46] that the modification of the α-function affects in a very negligible way the accuracy on volume calculations. To improve volumes, a further modification is required, as explained in Section 2.3.

#### **2.2 From PR78 to E-PPR78: the application to mixtures**

The application of the PR equation of state to a mixture requires the selection of mixing rules for calculating mixture cohesive and co-volume parameters, *a* and *b*. Classical Van der Waals one-fluid mixing rules are used in the original PR78 model:

$$\begin{cases} a(T, \mathbf{z}) = \sum\_{i=1}^{N} \sum\_{j=1}^{N} z\_i \mathbf{z}\_j \sqrt{a\_i(T) a\_j(T)} \left(\mathbf{1} - k\_{\mathrm{ij}}\right) \\\\ b(\mathbf{z}) = \sum\_{i=1}^{N} z\_i b\_i \end{cases} \tag{6}$$

The *kij* parameter is the so-called binary interaction parameter characterizing the molecular interactions between molecules *i* and *j*. The most accurate application of the original PR78 model requires the empirical optimization of the *kij* parameter over, at least, vapor-liquid equilibrium experimental data.

In 2004, Jaubert and Mutelet [24] proposed a model to *predictively* calculate the *kij* parameter by means of the application of a group contribution method. This method allows to estimate and predict the *kij* parameter by combining the molecular characteristics of elementary groups in which each molecule can be subdivided. This model is the most physically grounded model to determine the *kij* binary


#### **Table 1.**

*Comparison of the mean average percentage errors (MAPEs) calculated with PR incorporating either the Soave α-function or the generalized Twu88 α-function or fluid-specific Twu91 α-function.*

*A Predictive Equation of State to Perform an Extending Screening of Working Fluids for Power… DOI: http://dx.doi.org/10.5772/intechopen.92173*

interaction parameters of PR-78 equation of state, and its use is extremely recommended to predictively calculate thermodynamic properties of multicomponent mixtures. The expression provided by this model to predictively calculate the binary interaction parameter is as follows:

$$k\_{\vec{q}}(T) = \frac{-\frac{1}{2} \left[ \sum\_{k=1}^{N\_{\vec{x}}} \sum\_{l=1}^{N\_{\vec{x}}} \left( a\_{ik} - a\_{jk} \right) \left( a\_{il} - a\_{jl} \right) A\_{kl} \left( \frac{298.15}{T/K} \right)^{\left( \frac{R\_{\vec{q}l}}{A\_{kl}} - 1 \right)} \right] - \left( \frac{\sqrt{a\_{i}(T)}}{b\_{i}} - \frac{\sqrt{a\_{i}(T)}}{b\_{\vec{q}}} \right)^{2}}{2 \frac{\sqrt{a\_{i}(T) a\_{j}(T)}}{b\_{i} b\_{j}}} \tag{7}$$

where *ai* and *bi* are the energy and co-volume parameters of the *i*th molecule, given in Eq. (2); *Ng* is the number of different groups defined by the method; and *αik* is the fraction of molecule *i* occupied by group *k* (occurrence of group *k* in molecule *i* divided by the total number of groups present in molecule *i*). *Akl* and *Bkl*, the group-interaction parameters, are symmetric, *Akl* = *Alk* and *Bkl* = *Blk* (where *k* and *l* are two different groups), and empirically determined by correlating experimental data. Also, *Akk* = *Bkk* = 0. The inclusion of this predictive expression for *kij* in the PR78 equation of state results in the **Predictive-PR78 (PPR78)**.

It is worth recalling the historical development of the process of optimization of *Akl* and *Bkl* provided by the model developers. These parameters have initially been optimized over only vapor-liquid equilibrium data of binary mixtures. The model resulting from the use of these so-optimized group contribution parameters is called PPR78 (Predictive-Peng-Robinson equation of state). Lately, authors recognized that the inclusion of enthalpy and heat capacity data in the optimization process does not affect the accuracy in modeling VLE properties but improves extraordinarily the accuracy in calculating enthalpies and heat capacities of mixtures. So, starting from the year 2011 [41], published *Akl* and *Bkl* have been obtained by minimizing the errors between model calculations and experimental data relative to VLE, mixing enthalpy and heat capacity properties. The model resulting from the inclusion of these group contribution parameters is called **Enhanced-Predictive-PR78 equation of state (E-PPR78)**. The last optimized values of *Akl* and of *Bkl* are reported in Table S1 of Supplementary Material of [39] for 40 molecular groups.

The optimization of these parameters has been performed over more than 150,000 experimental data and developed over more than 15 years. Even if preferable, that would be quite time-expensive if there was the need to re-optimize these group contribution parameters when changing any feature of the cubic equation of state (e.g., the α-function) or the cubic equation of state itself. Thankfully, it has been demonstrated [52] that it is possible to rigorously determine *kij* of any equation of state, knowing those of the original E-PPR78. In particular, it is possible to easily replace the Soave α-function, originally present in E-PPR78, with one of the improved functions presented in Section 2.1 (Eqs. **(4)** and **(5)**) and to use *Akl* and *Bkl* parameters of the Soave-based E-PPR78 by applying, instead of Eq. (7):

$$k\_{\vec{\eta}}(T) = \frac{-\frac{1}{2} \left[ \sum\_{k=1}^{N\_t} \sum\_{l=1}^{N\_t} \left( a\_{\vec{a}l} - a\_{\vec{j}k} \right) \left( a\_{\vec{l}l} - a\_{\vec{j}l} \right) A\_{\vec{k}l} \left( \frac{298.15}{T/K} \right)^{\left( \frac{b\_{\vec{a}l}}{b\_{\vec{l}l}} - 1 \right)} \right] - \left( \frac{\sqrt{a\_{\vec{a}l}^{\text{mid}}(T)} - \sqrt{a\_{\vec{j}}^{\text{mid}}(T)}}{b\_{\vec{l}}} \right)^2}{2 \frac{\sqrt{a\_{\vec{a}}^{\text{mid}}(T) a\_{\vec{j}}^{\text{mid}}(T)}}{b\_{\vec{l}} b\_{\vec{l}}}}$$

(8)

The generalized version of Twu88 [46] requires, similar to the Soave α-function, the knowledge of the acentric factor of each pure fluid and takes the following form:

The alternative use of the three α-functions recalled above leads to different accuracies in the calculation of thermodynamic properties. A comparison is reported in **Table 1** between the PR equation of state incorporating the three different α-functions and pseudo-experimental data made available by DIPPR [51]. Piña-Martinez et al. also showed [46] that the modification of the α-function affects in a very negligible way the accuracy on volume calculations. To improve volumes,

The application of the PR equation of state to a mixture requires the selection of mixing rules for calculating mixture cohesive and co-volume parameters, *a* and *b*. Classical Van der Waals one-fluid mixing rules are used in the original PR78 model:

The *kij* parameter is the so-called binary interaction parameter characterizing the molecular interactions between molecules *i* and *j*. The most accurate application of the original PR78 model requires the empirical optimization of the *kij* parameter

In 2004, Jaubert and Mutelet [24] proposed a model to *predictively* calculate the *kij* parameter by means of the application of a group contribution method. This method allows to estimate and predict the *kij* parameter by combining the molecular characteristics of elementary groups in which each molecule can be subdivided. This model is the most physically grounded model to determine the *kij* binary

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *ai*ð Þ *<sup>T</sup> aj*ð Þ *<sup>T</sup>* <sup>p</sup> <sup>1</sup> � *<sup>k</sup>*ij

**Generalized Twu88, Eq. (5)**

3.1% 2.7% 2.9%

7.1% 4.1% 2.0%

� �

� exp *Li* <sup>1</sup> � *<sup>T</sup>*

*<sup>i</sup>* þ 0*:*6693*ω<sup>i</sup>* þ 0*:*0728

*<sup>i</sup>* � 0*:*2258*ω<sup>i</sup>* þ 0*:*8788

*Tc*,*<sup>i</sup>* � �2*Mi* � � � � <sup>2</sup>

(5)

(6)

**Fluid-specific Twu91, Eq. (4)**

*<sup>α</sup>i*ð Þ¼ *<sup>T</sup> <sup>T</sup>*

8 >>><

>>>:

*Tc*,*<sup>i</sup>* � �2ð Þ *Mi*�<sup>1</sup>

*Organic Rankine Cycles for Waste Heat Recovery - Analysis and Applications*

*Li*ð Þ¼ *<sup>ω</sup><sup>i</sup>* <sup>0</sup>*:*0925*ω*<sup>2</sup>

*<sup>Μ</sup>i*ð Þ¼ *<sup>ω</sup><sup>i</sup>* <sup>0</sup>*:*1695*ω*<sup>2</sup>

a further modification is required, as explained in Section 2.3.

**2.2 From PR78 to E-PPR78: the application to mixtures**

*a T*ð Þ¼ , **<sup>z</sup>** <sup>P</sup>

8 >>><

>>>:

**α-Function Soave,**

sat, liquid (829

MAPE on ΔvapH (1453 compounds)

*Data have been collected from [46].*

MAPE on cp

compounds)

**Table 1.**

**6**

*<sup>b</sup>*ð Þ¼ **<sup>z</sup>** <sup>P</sup> *N i*¼1 *zibi*

over, at least, vapor-liquid equilibrium experimental data.

**Eq. (3)**

*α-function or the generalized Twu88 α-function or fluid-specific Twu91 α-function.*

MAPE on Psat (1721 compounds) 2.8% 1.8% 1.0%

*Comparison of the mean average percentage errors (MAPEs) calculated with PR incorporating either the Soave*

*N i*¼1 P *N j*¼1 *zizj*

#### *Organic Rankine Cycles for Waste Heat Recovery - Analysis and Applications*

With respect to Eq. (7), this expression incorporates the pure component energy parameters calculated from the modified α-function. If we consider Twu α-function, we will thus use *a*mod *<sup>i</sup>* given by:

$$a\_i^{\text{mod}}(T) = a\_{c,i} a\_i^{\text{mod}}(T) \tag{9}$$

closed power cycle working fluids and refrigerants (see the examples reported in

*Isothermal VLE diagrams of the benzene (1)–cyclohexane (2) system, at 298.15 K. Lines represent calculations with standard E-PPR78 (a) and E-PPR78 with Twu91 alpha-function, Eq. (4) (b). Bubble points are indicated in red, dew points in blue. Green points represent calculated pure components saturation pressures.*

*A Predictive Equation of State to Perform an Extending Screening of Working Fluids for Power…*

However, there are systems for which the Soave model is very inaccurate and the use of Twu α-function with Soave-based E-PPR78 *Akl* and *Bkl* parameters highly improves results. By way of example, we present a pivotal binary mixture, benzenecyclohexane, for which the standard PR equation of state (i.e., with the Soave αfunction) does predict in a very inaccurate way of pure component saturation pressures. The original *E*-PPR78 equation of state, based on standard PR, is thus not very accurate in predictively modeling mixture saturation pressures because of the basic incapacity of the PR equation of state in modeling pure fluid properties (see in **Figure 2a**). However, if the Soave α-function is replaced with a more accurate αfunction (given, e.g., by Eq. (4)) and if we then use Eq. (8) (with the Soave-based E-PPR78 *Akl* and *Bkl* parameters reported in [39]) to represent benzene (formed by six groups CHaro) and cyclohexane (formed by six groups CH2,cyclic), we obtain the graph as shown in **Figure 2b**. The accuracy is thus strongly improved without the

Considering the above remarks, we suggest the replacement of the Soave αfunction with the Twu one, in E-PPR78, thus applying Eq. (8) and Soave-based E-

It is well known that one of the main limitations of cubic equations of state is their inaccuracy in high predicting liquid densities. Péneloux et al. [53] showed that it was possible to come up with this problem by adding a *translation term to the volume*. This translation consists in correcting the volume resulting from the reso-

*<sup>i</sup>*ð Þ¼ *T*, *P vi*ð Þ� *T*, *P ci* (10)

(11)

**Figure 1**).

**Figure 2.**

need of re-optimizing any parameter.

*DOI: http://dx.doi.org/10.5772/intechopen.92173*

**2.3 Volume correction**

• In case of pure fluids:

• In case of mixtures:

**9**

PPR78 group contribution *Akl* and *Bkl* parameters.

lution of the cubic equation of state (Eq. (1)) as follows:

*vt*

8 ><

>:

*<sup>c</sup>* <sup>¼</sup> <sup>P</sup> *Nc i*

*vt*

ð Þ¼ *T*, *P*, *z v T*ð Þ� , *P*, *z c*

*ci* � *zi* ð Þ linear mixing rule for *c*

It is worth observing that for the systems for which the Soave α-function is already very accurate (i.e., *mean average percentage errors* of the order of 1% for saturation pressures and of 2% for vaporization enthalpies and liquid heat capacities), the *kij* in Eq. (7) (i.e., the standard *E*-PPR78 model, with the Soave function) is able to provide the best reproduction of mixture data. The alternative use of a more accurate *α-function* (which thus improves pure fluid calculations) and Eq. (8), to enable the use of original *Akl* and *Bkl* group contribution parameters optimized with the original Soave-based *E*-PPR78, slightly deteriorates the results on mixtures (e.g., in the case of mixtures of alkanes). Clearly, the best would consist in re-optimizing all group contribution parameters using the best α-function directly in Eq. (7) instead of using the less-time-consuming Eq. (8) to derive the modified *kij*(T) parameters. However, even adopting the simplified approach consisting in using Eq. (8), the predictive capability of this model remains very accurate for modeling

#### **Figure 1.**

*Isobar vapor-liquid equilibrium phase diagrams for the system n-butane (1)–n-hexane (2) (a) and isothermal vapor-liquid equilibrium phase diagrams for the system 1-butene (1)-R610 (2) (b), CO2 (1)-R134a (2) (c), R116 (1)-ethylene (2) (d). Lines represent calculations with E-PPR78 with Twu91 alpha-function, Eq. (4) (b). Bubble points are indicated in red, dew points in blue. Black points represent calculated pure component saturation pressures. (a)* P *(bar) = 10.132 (continuous line), 25.855 (long-dashed line), 32.75 (long- and short-dashed line), and 37.921 (short-dashed line); (b)* T *(K) = 312.92 (continuous line), 327.93 (longdashed line), and 342.93 (short-dashed line); (c)* T *(K) = 252.95 (continuous line), 329.60 (long-dashed line), 339.10 (long- and short-dashed line), and 354.00 (short-dashed line); and (d)* T *(K) = 251.00 (continuous line) and 275.00 (short-dashed line).*

*A Predictive Equation of State to Perform an Extending Screening of Working Fluids for Power… DOI: http://dx.doi.org/10.5772/intechopen.92173*

#### **Figure 2.**

With respect to Eq. (7), this expression incorporates the pure component energy

*<sup>i</sup>* ð Þ *T* (9)

parameters calculated from the modified α-function. If we consider Twu

*<sup>i</sup>* given by:

*<sup>i</sup>* ð Þ¼ *<sup>T</sup> ac*,*iα*mod

It is worth observing that for the systems for which the Soave α-function is already very accurate (i.e., *mean average percentage errors* of the order of 1% for saturation pressures and of 2% for vaporization enthalpies and liquid heat capacities), the *kij* in Eq. (7) (i.e., the standard *E*-PPR78 model, with the Soave function) is able to provide the best reproduction of mixture data. The alternative use of a more accurate *α-function* (which thus improves pure fluid calculations) and Eq. (8), to enable the use of original *Akl* and *Bkl* group contribution parameters optimized with the original Soave-based *E*-PPR78, slightly deteriorates the results on mixtures (e.g., in the case of mixtures of alkanes). Clearly, the best would consist in re-optimizing all group contribution parameters using the best α-function directly in Eq. (7) instead of using the less-time-consuming Eq. (8) to derive the modified *kij*(T) parameters. However, even adopting the simplified approach consisting in using Eq. (8), the predictive capability of this model remains very accurate for modeling

*Isobar vapor-liquid equilibrium phase diagrams for the system n-butane (1)–n-hexane (2) (a) and isothermal vapor-liquid equilibrium phase diagrams for the system 1-butene (1)-R610 (2) (b), CO2 (1)-R134a (2) (c), R116 (1)-ethylene (2) (d). Lines represent calculations with E-PPR78 with Twu91 alpha-function, Eq. (4) (b). Bubble points are indicated in red, dew points in blue. Black points represent calculated pure component saturation pressures. (a)* P *(bar) = 10.132 (continuous line), 25.855 (long-dashed line), 32.75 (long- and short-dashed line), and 37.921 (short-dashed line); (b)* T *(K) = 312.92 (continuous line), 327.93 (longdashed line), and 342.93 (short-dashed line); (c)* T *(K) = 252.95 (continuous line), 329.60 (long-dashed line), 339.10 (long- and short-dashed line), and 354.00 (short-dashed line); and (d)* T *(K) = 251.00*

*a*mod

*Organic Rankine Cycles for Waste Heat Recovery - Analysis and Applications*

α-function, we will thus use *a*mod

**Figure 1.**

**8**

*(continuous line) and 275.00 (short-dashed line).*

*Isothermal VLE diagrams of the benzene (1)–cyclohexane (2) system, at 298.15 K. Lines represent calculations with standard E-PPR78 (a) and E-PPR78 with Twu91 alpha-function, Eq. (4) (b). Bubble points are indicated in red, dew points in blue. Green points represent calculated pure components saturation pressures.*

closed power cycle working fluids and refrigerants (see the examples reported in **Figure 1**).

However, there are systems for which the Soave model is very inaccurate and the use of Twu α-function with Soave-based E-PPR78 *Akl* and *Bkl* parameters highly improves results. By way of example, we present a pivotal binary mixture, benzenecyclohexane, for which the standard PR equation of state (i.e., with the Soave αfunction) does predict in a very inaccurate way of pure component saturation pressures. The original *E*-PPR78 equation of state, based on standard PR, is thus not very accurate in predictively modeling mixture saturation pressures because of the basic incapacity of the PR equation of state in modeling pure fluid properties (see in **Figure 2a**). However, if the Soave α-function is replaced with a more accurate αfunction (given, e.g., by Eq. (4)) and if we then use Eq. (8) (with the Soave-based E-PPR78 *Akl* and *Bkl* parameters reported in [39]) to represent benzene (formed by six groups CHaro) and cyclohexane (formed by six groups CH2,cyclic), we obtain the graph as shown in **Figure 2b**. The accuracy is thus strongly improved without the need of re-optimizing any parameter.

Considering the above remarks, we suggest the replacement of the Soave αfunction with the Twu one, in E-PPR78, thus applying Eq. (8) and Soave-based E-PPR78 group contribution *Akl* and *Bkl* parameters.

#### **2.3 Volume correction**

It is well known that one of the main limitations of cubic equations of state is their inaccuracy in high predicting liquid densities. Péneloux et al. [53] showed that it was possible to come up with this problem by adding a *translation term to the volume*. This translation consists in correcting the volume resulting from the resolution of the cubic equation of state (Eq. (1)) as follows:

• In case of pure fluids:

$$\upsilon\_i^t(T, P) = \upsilon\_i(T, P) - \varepsilon\_i \tag{10}$$

• In case of mixtures:

$$\begin{cases} v^t(T, P, \mathbf{z}) = v(T, P, \mathbf{z}) - \mathbf{c} \\ \mathbf{c} = \sum\_{i}^{N\_c} \mathbf{c}\_i \cdot \mathbf{z}\_i \quad (\text{linear mixing rule for } \mathbf{c}) \end{cases} \tag{11}$$

In a recent publication, some accurate generalized (i.e., predictive) expressions for the translation term are optimized over 475 compounds, available in the DIPPR. For the Peng-Robinson equation of state, it is provided as follows:

$$\boldsymbol{c}\_{i} = \frac{\boldsymbol{R}\boldsymbol{T}\_{c,i}}{\boldsymbol{P}\_{c,i}} (\boldsymbol{0}.1975 - \boldsymbol{0}.7325 \cdot \boldsymbol{z}\_{\mathbb{R}\boldsymbol{A},i}) \tag{12}$$

determined with the translated cubic equation of state, *wt*, and the one calculated

*A Predictive Equation of State to Perform an Extending Screening of Working Fluids for Power…*

r

which generally varies between 0.990 and 1.020 for liquid systems and is equal to 1.000 for vapor systems. These quantifications have been performed considering

Despite its simplicity and flexibility, E-PPR78 is a model that guarantees one of the most reliable predictive determinations of the thermodynamic properties of working fluids for power and refrigeration cycles. Being by definition a predictive model, its use is highly suggested to look for the best working fluid candidate over

In this chapter, we presented the model and suggested to modify the Soavebased-original-*E*-PPR78 model by using the Twu α-function, to allow for the more precise representation of systems for which the Soave one is not sufficiently accurate. Finally, we recalled that the inclusion of a volume translation term in the E-PPR78 model highly improves the errors in the calculation of densities without

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>1</sup> � *<sup>c</sup> v T*ð Þ , *P*

(15)

*wt*ð Þ *T*, *P <sup>w</sup>*0ð Þ *<sup>T</sup>*, *<sup>P</sup>* <sup>¼</sup>

with the nontranslated EoS, *w0*, is given by:

*DOI: http://dx.doi.org/10.5772/intechopen.92173*

toluene, R134a, butane, propane, and ammonia.

thousands of pure and multi-component fluids.

affecting the rest of the, already accurate, properties.

Silvia Lasala\*, Andrés-Piña Martinez and Jean-Noël Jaubert Université de Lorraine, CNRS, LRGP, Nancy, France

\*Address all correspondence to: silvia.lasala@univ-lorraine.fr

provided the original work is properly cited.

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

**3. Conclusion**

**Author details**

**11**

A databank of Rackett compressibility factors, zRA, for 1489 components is available in Supplementary Material of [46]. The application of this translation has been observed to greatly improve the mean average percentage errors on calculated volumes. Considering the same 1489 pure fluids, the authors attested, in the same work, that the error in calculating the volume of the liquid phase at saturation condition is reduced from 8.7% (PR without translation) to 2.2% (PR with translation in Eq. (12)). If zRA is not available, authors suggested the use of the following expression, where the translation term is only a function of the acentric factor.

$$c\_i = \frac{RT\_{c,i}}{P\_{c,i}}(0.0096 + 0.0049 \cdot o\_i) \tag{13}$$

Jaubert et al. [45] were able to demonstrate that entropy (*s*), internal energy (*u*), Helmholtz energy (*a*), constant pressure and constant volume heat capacity (*cp* and *cv*), vapor pressure (*Psat*), and all properties change of vaporization (*ΔvapH*, *ΔvapS*, *ΔvapU*, *ΔvapA*, *ΔvapCp*, and *ΔvapCv*) of pure fluid properties are not influenced by a temperature-independent volume translation.

It can be thus deduced that the addition of a translation term and the modification of the α-function have unlinked effects: the utilization of a volume translation improves volume calculations without affecting the abovementioned thermodynamic properties, while the use of an improved α-function improves subcritical and supercritical properties without deteriorating density calculations (see Conclusion reported in Section 2.1).

The application of both the consistent-Twu α-function (either Eq. (4) or Eq. (5)) and the volume translation in Eq. (12) results in the most accurate generalized cubic equation of state available in the literature.

For completeness, we would like to observe that, other than volume, also enthalpy and speed of sound are affected by the inclusion of a temperatureindependent volume translation term (see [45]). However, the impact of such a translation on the calculation of enthalpy differences and of speed of sound is really negligible. In fact, it can be mathematically demonstrated from the use of relations presented in [45] that the enthalpy variation calculated with the translated cubic equation of state, Δht, and the one calculated with the nontranslated form, Δh0, are related by the following relation:

$$\underbrace{\frac{\Delta h\_t}{h\_t(T\_1, P\_1) - h\_t(T\_2, P\_2)}}\_{\Delta h\_0} = 1 - \frac{c\_i \cdot (P\_1 - P\_2)}{\Delta h\_0} \tag{14}$$

So, first, it can be observed that isobar enthalpy variations are not affected by the inclusion of a volume translation term. Moreover, it can be shown that, in general, for temperature and pressure conditions relevant for power and refrigeration cycle applications, the term *ci* � ð Þ *P*<sup>1</sup> � *P*<sup>2</sup> *=Δh*<sup>0</sup> is much lower than 0.001 for gaseous systems and lower than 0.005 for liquid systems. As regards the speed of sound, it can be mathematically derived that ratio between the speed of sound

*A Predictive Equation of State to Perform an Extending Screening of Working Fluids for Power… DOI: http://dx.doi.org/10.5772/intechopen.92173*

determined with the translated cubic equation of state, *wt*, and the one calculated with the nontranslated EoS, *w0*, is given by:

$$\frac{w\_t(T, P)}{w\_0(T, P)} = \sqrt{1 - \frac{c}{v(T, P)}}\tag{15}$$

which generally varies between 0.990 and 1.020 for liquid systems and is equal to 1.000 for vapor systems. These quantifications have been performed considering toluene, R134a, butane, propane, and ammonia.

#### **3. Conclusion**

In a recent publication, some accurate generalized (i.e., predictive) expressions for the translation term are optimized over 475 compounds, available in the DIPPR.

A databank of Rackett compressibility factors, zRA, for 1489 components is available in Supplementary Material of [46]. The application of this translation has been observed to greatly improve the mean average percentage errors on calculated volumes. Considering the same 1489 pure fluids, the authors attested, in the same work, that the error in calculating the volume of the liquid phase at saturation condition is reduced from 8.7% (PR without translation) to 2.2% (PR with translation in Eq. (12)). If zRA is not available, authors suggested the use of the following expression, where the translation term is only a function of the acentric factor.

Jaubert et al. [45] were able to demonstrate that entropy (*s*), internal energy (*u*), Helmholtz energy (*a*), constant pressure and constant volume heat capacity (*cp* and *cv*), vapor pressure (*Psat*), and all properties change of vaporization (*ΔvapH*, *ΔvapS*, *ΔvapU*, *ΔvapA*, *ΔvapCp*, and *ΔvapCv*) of pure fluid properties are not influenced by a

It can be thus deduced that the addition of a translation term and the modification of the α-function have unlinked effects: the utilization of a volume translation improves volume calculations without affecting the abovementioned thermodynamic properties, while the use of an improved α-function improves subcritical and supercritical properties without deteriorating density calculations (see Conclusion

The application of both the consistent-Twu α-function (either Eq. (4) or Eq. (5)) and the volume translation in Eq. (12) results in the most accurate generalized cubic

> <sup>¼</sup> <sup>1</sup> � *ci* � ð Þ *<sup>P</sup>*<sup>1</sup> � *<sup>P</sup>*<sup>2</sup> *Δh*<sup>0</sup>

(14)

For completeness, we would like to observe that, other than volume, also enthalpy and speed of sound are affected by the inclusion of a temperatureindependent volume translation term (see [45]). However, the impact of such a translation on the calculation of enthalpy differences and of speed of sound is really negligible. In fact, it can be mathematically demonstrated from the use of relations presented in [45] that the enthalpy variation calculated with the translated cubic equation of state, Δht, and the one calculated with the nontranslated form, Δh0, are

So, first, it can be observed that isobar enthalpy variations are not affected by the inclusion of a volume translation term. Moreover, it can be shown that, in general, for temperature and pressure conditions relevant for power and refrigeration cycle applications, the term *ci* � ð Þ *P*<sup>1</sup> � *P*<sup>2</sup> *=Δh*<sup>0</sup> is much lower than 0.001 for gaseous systems and lower than 0.005 for liquid systems. As regards the speed of sound, it can be mathematically derived that ratio between the speed of sound

*ht*ð Þ� *T*1, *P*<sup>1</sup> *ht*ð Þ *T*2, *P*<sup>2</sup> *h*0ð Þ� *T*1, *P*<sup>1</sup> *h*0ð Þ *T*2, *P*<sup>2</sup> |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} *Δh*<sup>0</sup>

zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{ *Δht*

ð Þ 0*:*1975 � 0*:*7325 � *zRA*,*<sup>i</sup>* (12)

ð Þ 0*:*0096 þ 0*:*0049 � *ω<sup>i</sup>* (13)

For the Peng-Robinson equation of state, it is provided as follows:

*Organic Rankine Cycles for Waste Heat Recovery - Analysis and Applications*

*ci* <sup>¼</sup> *RTc*,*<sup>i</sup> Pc*,*<sup>i</sup>*

*ci* <sup>¼</sup> *RTc*,*<sup>i</sup> Pc*,*<sup>i</sup>*

temperature-independent volume translation.

equation of state available in the literature.

related by the following relation:

**10**

reported in Section 2.1).

Despite its simplicity and flexibility, E-PPR78 is a model that guarantees one of the most reliable predictive determinations of the thermodynamic properties of working fluids for power and refrigeration cycles. Being by definition a predictive model, its use is highly suggested to look for the best working fluid candidate over thousands of pure and multi-component fluids.

In this chapter, we presented the model and suggested to modify the Soavebased-original-*E*-PPR78 model by using the Twu α-function, to allow for the more precise representation of systems for which the Soave one is not sufficiently accurate. Finally, we recalled that the inclusion of a volume translation term in the E-PPR78 model highly improves the errors in the calculation of densities without affecting the rest of the, already accurate, properties.

#### **Author details**

Silvia Lasala\*, Andrés-Piña Martinez and Jean-Noël Jaubert Université de Lorraine, CNRS, LRGP, Nancy, France

\*Address all correspondence to: silvia.lasala@univ-lorraine.fr

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

### **References**

[1] Dai Y, Wang J, Gao L. Parametric optimization and comparative study of organic Rankine cycle (ORC) for low grade waste heat recovery. Energy Convers Manag. 2009;**50**(3):576-582

[2] Schuster A, Karellas S, Aumann R. Efficiency optimization potential in supercritical organic Rankine cycles. Energy. 2010;**35**(2):1033-1099

[3] Martelli E, Capra F, Consonni S. Numerical optimization of combined heat and power organic Rankine cycles— Part A: Design optimization. Energy. 2015;**90**(P1):310-328

[4] Astolfi M, Alfani D, Lasala S, Macchi E. Comparison between ORC and CO2 power systems for the exploitation of low-medium temperature heat sources. Energy. 2018;**161**:1250-1261

[5] Walraven D, Laenen B, D'haeseleer W. Comparison of thermodynamic cycles for power production from low-temperature geothermal heat sources. Energy Conversion and Management. 2013;**66**: 220-233

[6] Kunz O, Klimeck R, Wagner W, Jaeschke M. The GERG-2004 Wide-Range Equation of State for Natural Gases and Other Mixtures [Internet]. 2007. pp. 1–555. Disponible sur: http:// www.gerg.eu/publications/technicalmonographs

[7] Span R, Wagner W. A new equation of state for carbon dioxide covering the fluid region from the triple-point temperature to 1100 K at pressures up to 800 MPa. Journal of Physical and Chemical Reference Data. 1996;**25**(6): 1509-1596

[8] Benedict M, Webb GB, Rubin LC. An empirical equation for thermodynamic properties of light hydrocarbons and their mixtures II. Mixtures of methane, ethane, propane, and n-butane. The

Journal of Chemical Physics. 1942; **10**(12):747-758

optimization of working fluid and process for organic Rankine cycles using PC-SAFT. Industrial and Engineering Chemistry Research. 2014;**53**(21):

*DOI: http://dx.doi.org/10.5772/intechopen.92173*

turbine efficiency. Frontiers in Energy

[24] Jaubert J-N, Mutelet F. VLE predictions with the Peng-Robinson equation of state and temperaturedependent kij calculated through a group contribution method. Fluid Phase

Equilibria. 2004;**224**(2):285-304

[25] Jaubert J-N, Vitu S, Mutelet F, Corriou J-P. Extension of the PPR78 model (predictive 1978, Peng–Robinson EOS with temperature dependent kij calculated through a group contribution method) to systems containing aromatic compounds. Fluid Phase Equilibria.

[26] Vitu S, Privat R, Jaubert J-N, Mutelet F. Predicting the phase

[27] Vitu S, Jaubert J-N, Mutelet F. Extension of the PPR78 model (predictive 1978, Peng-Robinson EoS with temperature-dependent kij

method) to systems containing naphtenic compounds. Fluid Phase Equilibria. 2006;**243**(1–2):9-28

2008;**47**(6):2033-2048

calculated through a group contribution

[28] Privat R, Jaubert J-N, Mutelet F. Addition of the nitrogen group to the PPR78 model (predictive 1978, Peng Robinson EOS with temperaturedependent kij calculated through a group contribution method). Industrial and Engineering Chemistry Research.

[29] Privat R, Mutelet F, Jaubert J-N. Addition of the hydrogen sulfide group to the PPR78 model (predictive 1978, Peng-Robinson equation of state with temperature dependent k(ij) calculated through a group contribution method). Industrial and Engineering Chemistry Research. 2008;**47**(24):10041-10052

equilibria of CO2 + hydrocarbon systems with the PPR78 model (PR EoS and kij calculated through a group contribution method). Journal of Supercritical Fluids.

Research. 2019;**7**:50

*A Predictive Equation of State to Perform an Extending Screening of Working Fluids for Power…*

2005;**237**(1):193-211

2008;**45**(1):1-26

[16] White MT, Oyewunmi OA, Chatzopoulou MA, Pantaleo AM, Haslam AJ, Markides CN. Computer-

[17] Müller A, Winkelmann J, Fischer J. Backone family of equations of state: 1. Nonpolar and polar pure fluids. AIChE

[18] Saleh B, Koglbauer G, Wendland M, Fischer J. Working fluids for lowtemperature organic Rankine cycles. Energy. 2007;**32**(7):1210-1121

[19] Peng D-Y, Robinson DB. A new two-constant equation of state. Industrial and Engineering Chemistry Fundamentals. 1976;**15**(1):59-64

[20] Peng D-Y, Robinson DB. The Characterization of the Heptanes and Heavier Fractions for the GPA Peng-Robinson Programs. Gas Processors Association. Edmonton, Alberta, Canada: University of Alberta; 1978

[21] Drescher U, Brüggemann D. Fluid selection for the Organic Rankine Cycle (ORC) in biomass power and heat plants. Applied Thermal Engineering.

[22] Invernizzi C, Iora P, Silva P. Bottoming micro-Rankine cycles for micro-gas turbines. Applied Thermal Engineering. 2007;**27**(1):100-110

[23] White MT, Sayma AI. Simultaneous cycle optimization and fluid selection for ORC systems accounting for the effect of the operating conditions on

2007;**27**(1):223-228

**13**

aided working-fluid design, thermodynamic optimisation and thermoeconomic assessment of ORC systems for waste-heat recovery. Energy. 2018;**161**:1181-1198

Journal. 1996;**42**(4):1116-1126

8821-8830

[9] Bender E. The calculation of phase equilibria from a thermal equation of state (Engl. Transl.) [PhD thesis]. Bochum: Ruhr University; 1971

[10] Bell IH, Lemmon EW. Organic fluids for organic Rankine cycle systems: Classification and calculation of thermodynamic and transport properties. In: Organic Rankine Cycle (ORC) Power Systems: Technologies and Applications. Woodhead Publishing; 2016. pp. 91-119

[11] Lemmon EW, Huber ML, Bell IH, McLinden MO. NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, Version 10.0. Standard Reference Data Program. Gaithersburg: National Institute of Standards and Technology; 2018

[12] Gross J, Sadowski G. Perturbedchain SAFT: An equation of state based on a perturbation theory for chain molecules. Industrial and Engineering Chemistry Research. 2001;**40**(4): 1244-1260

[13] Papaioannou V, Lafitte T, Avendaño C, Adjiman CS, Jackson G, Müller EA, et al. Group contribution methodology based on the statistical associating fluid theory for heteronuclear molecules formed from Mie segments. Journal of Chemical Physics. 2014;**140**(5):054107

[14] Hattiangadi A. Working Fluid Design for Organic Rankine Cycle (ORC) Systems. 2013. Disponible sur: https://repository.tudelft.nl/islandora/ object/uuid%3A492ce6c0-ab22-42d0 ba00-3cf3702eb873

[15] Lampe M, Stavrou M, Buecker HM, Gross J, Bardow A. Simultaneous

*A Predictive Equation of State to Perform an Extending Screening of Working Fluids for Power… DOI: http://dx.doi.org/10.5772/intechopen.92173*

optimization of working fluid and process for organic Rankine cycles using PC-SAFT. Industrial and Engineering Chemistry Research. 2014;**53**(21): 8821-8830

**References**

[1] Dai Y, Wang J, Gao L. Parametric optimization and comparative study of organic Rankine cycle (ORC) for low grade waste heat recovery. Energy Convers Manag. 2009;**50**(3):576-582

*Organic Rankine Cycles for Waste Heat Recovery - Analysis and Applications*

Journal of Chemical Physics. 1942;

[9] Bender E. The calculation of phase equilibria from a thermal equation of state (Engl. Transl.) [PhD thesis]. Bochum: Ruhr University; 1971

[10] Bell IH, Lemmon EW. Organic fluids for organic Rankine cycle systems:

Classification and calculation of thermodynamic and transport properties. In: Organic Rankine Cycle (ORC) Power Systems: Technologies

and Applications. Woodhead Publishing; 2016. pp. 91-119

[11] Lemmon EW, Huber ML, Bell IH, McLinden MO. NIST Standard

Reference Database 23: Reference Fluid

[12] Gross J, Sadowski G. Perturbedchain SAFT: An equation of state based on a perturbation theory for chain molecules. Industrial and Engineering Chemistry Research. 2001;**40**(4):

[13] Papaioannou V, Lafitte T,

associating fluid theory for

ba00-3cf3702eb873

Avendaño C, Adjiman CS, Jackson G, Müller EA, et al. Group contribution methodology based on the statistical

heteronuclear molecules formed from Mie segments. Journal of Chemical Physics. 2014;**140**(5):054107

[14] Hattiangadi A. Working Fluid Design for Organic Rankine Cycle (ORC) Systems. 2013. Disponible sur: https://repository.tudelft.nl/islandora/ object/uuid%3A492ce6c0-ab22-42d0-

[15] Lampe M, Stavrou M, Buecker HM, Gross J, Bardow A. Simultaneous

1244-1260

Thermodynamic and Transport Properties—REFPROP, Version 10.0. Standard Reference Data Program. Gaithersburg: National Institute of Standards and Technology; 2018

**10**(12):747-758

[2] Schuster A, Karellas S, Aumann R. Efficiency optimization potential in supercritical organic Rankine cycles. Energy. 2010;**35**(2):1033-1099

[3] Martelli E, Capra F, Consonni S. Numerical optimization of combined heat and power organic Rankine cycles— Part A: Design optimization. Energy.

[4] Astolfi M, Alfani D, Lasala S,

geothermal heat sources. Energy Conversion and Management. 2013;**66**:

[6] Kunz O, Klimeck R, Wagner W, Jaeschke M. The GERG-2004 Wide-Range Equation of State for Natural Gases and Other Mixtures [Internet]. 2007. pp. 1–555. Disponible sur: http:// www.gerg.eu/publications/technical-

[7] Span R, Wagner W. A new equation of state for carbon dioxide covering the fluid region from the triple-point temperature to 1100 K at pressures up to 800 MPa. Journal of Physical and Chemical Reference Data. 1996;**25**(6):

[8] Benedict M, Webb GB, Rubin LC. An empirical equation for thermodynamic properties of light hydrocarbons and their mixtures II. Mixtures of methane, ethane, propane, and n-butane. The

220-233

monographs

1509-1596

**12**

Macchi E. Comparison between ORC and CO2 power systems for the exploitation of low-medium temperature heat sources. Energy. 2018;**161**:1250-1261

[5] Walraven D, Laenen B, D'haeseleer W. Comparison of thermodynamic cycles for power production from low-temperature

2015;**90**(P1):310-328

[16] White MT, Oyewunmi OA, Chatzopoulou MA, Pantaleo AM, Haslam AJ, Markides CN. Computeraided working-fluid design, thermodynamic optimisation and thermoeconomic assessment of ORC systems for waste-heat recovery. Energy. 2018;**161**:1181-1198

[17] Müller A, Winkelmann J, Fischer J. Backone family of equations of state: 1. Nonpolar and polar pure fluids. AIChE Journal. 1996;**42**(4):1116-1126

[18] Saleh B, Koglbauer G, Wendland M, Fischer J. Working fluids for lowtemperature organic Rankine cycles. Energy. 2007;**32**(7):1210-1121

[19] Peng D-Y, Robinson DB. A new two-constant equation of state. Industrial and Engineering Chemistry Fundamentals. 1976;**15**(1):59-64

[20] Peng D-Y, Robinson DB. The Characterization of the Heptanes and Heavier Fractions for the GPA Peng-Robinson Programs. Gas Processors Association. Edmonton, Alberta, Canada: University of Alberta; 1978

[21] Drescher U, Brüggemann D. Fluid selection for the Organic Rankine Cycle (ORC) in biomass power and heat plants. Applied Thermal Engineering. 2007;**27**(1):223-228

[22] Invernizzi C, Iora P, Silva P. Bottoming micro-Rankine cycles for micro-gas turbines. Applied Thermal Engineering. 2007;**27**(1):100-110

[23] White MT, Sayma AI. Simultaneous cycle optimization and fluid selection for ORC systems accounting for the effect of the operating conditions on

turbine efficiency. Frontiers in Energy Research. 2019;**7**:50

[24] Jaubert J-N, Mutelet F. VLE predictions with the Peng-Robinson equation of state and temperaturedependent kij calculated through a group contribution method. Fluid Phase Equilibria. 2004;**224**(2):285-304

[25] Jaubert J-N, Vitu S, Mutelet F, Corriou J-P. Extension of the PPR78 model (predictive 1978, Peng–Robinson EOS with temperature dependent kij calculated through a group contribution method) to systems containing aromatic compounds. Fluid Phase Equilibria. 2005;**237**(1):193-211

[26] Vitu S, Privat R, Jaubert J-N, Mutelet F. Predicting the phase equilibria of CO2 + hydrocarbon systems with the PPR78 model (PR EoS and kij calculated through a group contribution method). Journal of Supercritical Fluids. 2008;**45**(1):1-26

[27] Vitu S, Jaubert J-N, Mutelet F. Extension of the PPR78 model (predictive 1978, Peng-Robinson EoS with temperature-dependent kij calculated through a group contribution method) to systems containing naphtenic compounds. Fluid Phase Equilibria. 2006;**243**(1–2):9-28

[28] Privat R, Jaubert J-N, Mutelet F. Addition of the nitrogen group to the PPR78 model (predictive 1978, Peng Robinson EOS with temperaturedependent kij calculated through a group contribution method). Industrial and Engineering Chemistry Research. 2008;**47**(6):2033-2048

[29] Privat R, Mutelet F, Jaubert J-N. Addition of the hydrogen sulfide group to the PPR78 model (predictive 1978, Peng-Robinson equation of state with temperature dependent k(ij) calculated through a group contribution method). Industrial and Engineering Chemistry Research. 2008;**47**(24):10041-10052

[30] Privat R, Jaubert J-N, Mutelet F. Addition of the sulfhydryl group (SH) to the PPR78 model (predictive 1978, Peng-Robinson EoS with temperaturedependent kij calculated through a group contribution method). The Journal of Chemical Thermodynamics. 2008;**40**(9):1331-1341

[31] Privat R, Jaubert J-N. Addition of the sulfhydryl group (SH) to the PPR78 model: Estimation of missing groupinteraction parameters for systems containing mercaptans and carbon dioxide or nitrogen or methane, from newly published data. Fluid Phase Equilibria. 2012;**334**:197-203

[32] Qian J-W, Privat R, Jaubert J-N. Predicting the phase equilibria, critical phenomena, and mixing enthalpies of binary aqueous systems containing alkanes, cycloalkanes, aromatics, alkenes, and gases (N2, CO2, H2S, H2) with the PPR78 equation of state. Industrial and Engineering Chemistry Research. 2013;**52**(46):16457-16490

[33] Qian J-W, Jaubert J-N, Privat R. Prediction of the phase behavior of alkene-containing binary systems with the PPR78 model. Fluid Phase Equilibria. 2013;**354**:212-235

[34] Qian J-W, Jaubert J-N, Privat R. Phase equilibria in hydrogen-containing binary systems modeled with the Peng-Robinson equation of state and temperature-dependent binary interaction parameters calculated through a group-contribution method. Journal of Supercritical Fluids. 2013;**75**: 58-71

[35] Qian J-W, Privat R, Jaubert J-N, Coquelet C, Ramjugernath D. Fluidphase-equilibrium prediction of fluorocompound-containing binary systems with the predictive *E*-PPR78 model [Prévision en matière d'équilibre des phases de fluide des systèmes binaires contenant des fluorocomposés avec le modèle prédictif *E*-PPR78].

International Journal of Refrigeration. 2017;**73**:65-90

α-functions of cubic equations of state. Fluid Phase Equilibria. 2016;**427**:513-538

*DOI: http://dx.doi.org/10.5772/intechopen.92173*

rule. Fluid Phase Equilibria. 1991;**69**:

[50] Twu CH. A modified Redlich-Kwong equation of state for highly polar, supercritical systems. In: International Symposium on Thermodynamics in Chemical Engineering and Industry. 1988

[51] DIPPR 801 Database [Internet]. Disponible sur: https://www.aiche.org/ dippr/events-products/801-database

[52] Jaubert J-N, Privat R. Relationship between the binary interaction

parameters (kij) of the Peng–Robinson and those of the Soave–Redlich–Kwong equations of state: Application to the definition of the PR2SRK model. Fluid Phase Equilibria. 2010;**295**(1):26-37

[53] Péneloux A, Rauzy E, Fréze R. A consistent correction for Redlich-Kwong-Soave volumes. Fluid Phase

Equilibria. 1982;**8**(1):7-23

33-50

*A Predictive Equation of State to Perform an Extending Screening of Working Fluids for Power…*

[43] Le Guennec Y, Privat R, Lasala S, Jaubert JN. On the imperative need to use a consistent α-function for the prediction of pure-compound supercritical properties with a cubic equation of state. Fluid Phase Equilibria.

[44] Le Guennec Y, Privat R, Jaubert J-N.

[45] Jaubert JN, Privat R, Le Guennec Y, Coniglio L. Note on the properties altered by application of a Pénelouxtype volume translation to an equation of state. Fluid Phase Equilibria. 2016;

[46] Pina-Martinez A, Le Guennec Y, Privat R, Jaubert J-N, Mathias PM. Analysis of the combinations of

property data that are suitable for a safe estimation of consistent Twu α-function parameters: Updated parameter values for the translated-consistent *tc*-PR and *tc*-RK cubic equations of state. Journal of Chemical Engineering Data. 2018;

[47] Soave G. Equilibrium constants from a modified Redlich-Kwong

Science. 1972;**27**(6):1197-1203

equation of state. Chemical Engineering

[48] Lasala S. Advanced cubic equations of state for accurate modelling of fluid mixtures. In: Application to CO2 Capture Systems. Italy: Politecnico di

[49] Twu CH, Bluck D, Cunningham JR, Coon JE. A cubic equation of state with a new alpha function and a new mixing

Development of the translatedconsistent tc-PR and tc-RK cubic equations of state for a safe and accurate prediction of volumetric, energetic and

saturation properties of pure compounds in the sub- and supercritical domains. Fluid Phase Equilibria.

2017;**445**:45-53

2016;**429**:301-312

**63**(10):3980-3988

Milano; 2016

**15**

**419**:88-95

[36] Plee V, Jaubert J-N, Privat R, Arpentinier P. Extension of the *E*-PPR78 equation of state to predict fluid phase equilibria of natural gases containing carbon monoxide, helium-4 and argon. Journal of Petroleum Science and Engineering. 2015;**133**:744-770

[37] Xu X, Privat R, Jaubert J-N. Addition of the sulfur dioxide group (SO2), the oxygen group (O2) and the nitric oxide group (NO) to the *E*-PPR78 model. Industrial and Engineering Chemistry Research. 2015;**54**(38): 9494-9504

[38] Xu X, Lasala S, Privat R, Jaubert J-N. E-PPR78: A proper cubic EoS for modeling fluids involved in the design and operation of carbon dioxide capture and storage (CCS) processes. International Journal of Greenhouse Gas Control. 2017;**56**:126-154

[39] Xu X, Jaubert J-N, Privat R, Arpentinier P. Prediction of thermodynamic properties of alkynecontaining mixtures with the *E*-PPR78 model. Industrial and Engineering Chemistry Research. 2017;**56**(28): 8143-8157

[40] Qian JW, Privat R, Jaubert JN, Duchet-Suchaux P. Enthalpy and heat capacity changes on mixing: Fundamental aspects and prediction by means of the PPR78 cubic equation of state. Energy & Fuels. 2013;**27**(11): 7150-7178

[41] Qian J. Développement du modèle *E*-PPR78 pour prédire les équilibres de phases et les grandeurs de mélange de systèmes complexes d'intérêt pétrolier sur de larges gammes de températures et de pressions. Nancy: Institut National Polytechnique de Lorraine; 2011

[42] Le Guennec Y, Lasala S, Privat R, Jaubert J-N. A consistency test for

*A Predictive Equation of State to Perform an Extending Screening of Working Fluids for Power… DOI: http://dx.doi.org/10.5772/intechopen.92173*

α-functions of cubic equations of state. Fluid Phase Equilibria. 2016;**427**:513-538

[30] Privat R, Jaubert J-N, Mutelet F. Addition of the sulfhydryl group (SH) to the PPR78 model (predictive 1978, Peng-Robinson EoS with temperaturedependent kij calculated through a group contribution method). The Journal of Chemical Thermodynamics.

*Organic Rankine Cycles for Waste Heat Recovery - Analysis and Applications*

International Journal of Refrigeration.

[36] Plee V, Jaubert J-N, Privat R, Arpentinier P. Extension of the *E*-PPR78 equation of state to predict fluid phase equilibria of natural gases containing carbon monoxide, helium-4 and argon. Journal of Petroleum Science and Engineering. 2015;**133**:744-770

[37] Xu X, Privat R, Jaubert J-N. Addition of the sulfur dioxide group (SO2), the oxygen group (O2) and the nitric oxide group (NO) to the *E*-PPR78 model. Industrial and Engineering Chemistry Research. 2015;**54**(38):

[38] Xu X, Lasala S, Privat R, Jaubert J-N.

International Journal of Greenhouse Gas

E-PPR78: A proper cubic EoS for modeling fluids involved in the design and operation of carbon dioxide capture

and storage (CCS) processes.

[39] Xu X, Jaubert J-N, Privat R, Arpentinier P. Prediction of

thermodynamic properties of alkynecontaining mixtures with the *E*-PPR78 model. Industrial and Engineering Chemistry Research. 2017;**56**(28):

[40] Qian JW, Privat R, Jaubert JN, Duchet-Suchaux P. Enthalpy and heat

Fundamental aspects and prediction by means of the PPR78 cubic equation of state. Energy & Fuels. 2013;**27**(11):

[41] Qian J. Développement du modèle *E*-PPR78 pour prédire les équilibres de phases et les grandeurs de mélange de systèmes complexes d'intérêt pétrolier sur de larges gammes de températures et de pressions. Nancy: Institut National Polytechnique de Lorraine; 2011

[42] Le Guennec Y, Lasala S, Privat R, Jaubert J-N. A consistency test for

capacity changes on mixing:

Control. 2017;**56**:126-154

2017;**73**:65-90

9494-9504

8143-8157

7150-7178

[31] Privat R, Jaubert J-N. Addition of the sulfhydryl group (SH) to the PPR78 model: Estimation of missing groupinteraction parameters for systems containing mercaptans and carbon dioxide or nitrogen or methane, from newly published data. Fluid Phase Equilibria. 2012;**334**:197-203

[32] Qian J-W, Privat R, Jaubert J-N. Predicting the phase equilibria, critical phenomena, and mixing enthalpies of binary aqueous systems containing alkanes, cycloalkanes, aromatics, alkenes, and gases (N2, CO2, H2S, H2) with the PPR78 equation of state. Industrial and Engineering Chemistry Research. 2013;**52**(46):16457-16490

[33] Qian J-W, Jaubert J-N, Privat R. Prediction of the phase behavior of alkene-containing binary systems with

[34] Qian J-W, Jaubert J-N, Privat R. Phase equilibria in hydrogen-containing binary systems modeled with the Peng-

[35] Qian J-W, Privat R, Jaubert J-N, Coquelet C, Ramjugernath D. Fluidphase-equilibrium prediction of fluorocompound-containing binary systems with the predictive *E*-PPR78 model [Prévision en matière d'équilibre des phases de fluide des systèmes binaires contenant des fluorocomposés avec le modèle prédictif *E*-PPR78].

the PPR78 model. Fluid Phase Equilibria. 2013;**354**:212-235

Robinson equation of state and temperature-dependent binary interaction parameters calculated through a group-contribution method. Journal of Supercritical Fluids. 2013;**75**:

58-71

**14**

2008;**40**(9):1331-1341

[43] Le Guennec Y, Privat R, Lasala S, Jaubert JN. On the imperative need to use a consistent α-function for the prediction of pure-compound supercritical properties with a cubic equation of state. Fluid Phase Equilibria. 2017;**445**:45-53

[44] Le Guennec Y, Privat R, Jaubert J-N. Development of the translatedconsistent tc-PR and tc-RK cubic equations of state for a safe and accurate prediction of volumetric, energetic and saturation properties of pure compounds in the sub- and supercritical domains. Fluid Phase Equilibria. 2016;**429**:301-312

[45] Jaubert JN, Privat R, Le Guennec Y, Coniglio L. Note on the properties altered by application of a Pénelouxtype volume translation to an equation of state. Fluid Phase Equilibria. 2016; **419**:88-95

[46] Pina-Martinez A, Le Guennec Y, Privat R, Jaubert J-N, Mathias PM. Analysis of the combinations of property data that are suitable for a safe estimation of consistent Twu α-function parameters: Updated parameter values for the translated-consistent *tc*-PR and *tc*-RK cubic equations of state. Journal of Chemical Engineering Data. 2018; **63**(10):3980-3988

[47] Soave G. Equilibrium constants from a modified Redlich-Kwong equation of state. Chemical Engineering Science. 1972;**27**(6):1197-1203

[48] Lasala S. Advanced cubic equations of state for accurate modelling of fluid mixtures. In: Application to CO2 Capture Systems. Italy: Politecnico di Milano; 2016

[49] Twu CH, Bluck D, Cunningham JR, Coon JE. A cubic equation of state with a new alpha function and a new mixing

rule. Fluid Phase Equilibria. 1991;**69**: 33-50

[50] Twu CH. A modified Redlich-Kwong equation of state for highly polar, supercritical systems. In: International Symposium on Thermodynamics in Chemical Engineering and Industry. 1988

[51] DIPPR 801 Database [Internet]. Disponible sur: https://www.aiche.org/ dippr/events-products/801-database

[52] Jaubert J-N, Privat R. Relationship between the binary interaction parameters (kij) of the Peng–Robinson and those of the Soave–Redlich–Kwong equations of state: Application to the definition of the PR2SRK model. Fluid Phase Equilibria. 2010;**295**(1):26-37

[53] Péneloux A, Rauzy E, Fréze R. A consistent correction for Redlich-Kwong-Soave volumes. Fluid Phase Equilibria. 1982;**8**(1):7-23

**Chapter 2**

**Abstract**

**1. Introduction**

**17**

Applications

Experimental Determination of

*Christophe Coquelet, Alain Valtz and Pascal Théveneau*

The design and optimization of Organic Rankine Cycle (ORC) require knowledge concerning the thermophysical properties of the working fluids: pure components or mixtures. These properties are generally calculated by thermodynamic and transport property models (thermodynamic or equation of state or correlations). The parameters of these models are adjusted on accurate experimental data. The main experimental data of interest concern phase equilibrium properties (noncritical and critical data), volumetric properties (density and speed of sound), energetic properties (enthalpy, heat capacity), and transport properties (dynamic viscosity and thermal conductivity). In this chapter, some experimental techniques frequently used to obtain the experimental data are presented. Also, we will present some models frequently used to correlate the data and some results (comparison between experimental data and model predictions).

**Keywords:** working fluid design, experimental techniques, transport properties,

The utilization of energy available at low, average, and high temperature can be one solution to reduce the energy consumption particularly the fossil energy and to reduce emission of CO2 in the atmosphere. Closed power cycle (Brayton cycle and ORC) proves to be the solution to convert heat sources into energy. Heat source can come from geothermal, solar, and biomass energy or from processes and energy systems. In general, the conditions of the heat source are fixed, and a temperature glide may be observed. In consequence, it is necessary to design the most suitable cycle architecture and to select the best working fluid in order to obtain the best performance and design of each component of the system. The selection of fluid requires thermodynamic models, and these models currently need experimental data in order to optimize their parameters. The knowledge of experimental techniques is very important to measure the thermophysical properties and to estimate their experimental uncertainties. The choice of the most suitable technique depends on the type of data to be determined, the range of pressure and temperature, the precision required, and the composition of the mixture if necessary.

thermodynamic properties, equations of state

Thermophysical Properties of

Working Fluids for ORC

#### **Chapter 2**

## Experimental Determination of Thermophysical Properties of Working Fluids for ORC Applications

*Christophe Coquelet, Alain Valtz and Pascal Théveneau*

### **Abstract**

The design and optimization of Organic Rankine Cycle (ORC) require knowledge concerning the thermophysical properties of the working fluids: pure components or mixtures. These properties are generally calculated by thermodynamic and transport property models (thermodynamic or equation of state or correlations). The parameters of these models are adjusted on accurate experimental data. The main experimental data of interest concern phase equilibrium properties (noncritical and critical data), volumetric properties (density and speed of sound), energetic properties (enthalpy, heat capacity), and transport properties (dynamic viscosity and thermal conductivity). In this chapter, some experimental techniques frequently used to obtain the experimental data are presented. Also, we will present some models frequently used to correlate the data and some results (comparison between experimental data and model predictions).

**Keywords:** working fluid design, experimental techniques, transport properties, thermodynamic properties, equations of state

#### **1. Introduction**

The utilization of energy available at low, average, and high temperature can be one solution to reduce the energy consumption particularly the fossil energy and to reduce emission of CO2 in the atmosphere. Closed power cycle (Brayton cycle and ORC) proves to be the solution to convert heat sources into energy. Heat source can come from geothermal, solar, and biomass energy or from processes and energy systems. In general, the conditions of the heat source are fixed, and a temperature glide may be observed. In consequence, it is necessary to design the most suitable cycle architecture and to select the best working fluid in order to obtain the best performance and design of each component of the system. The selection of fluid requires thermodynamic models, and these models currently need experimental data in order to optimize their parameters. The knowledge of experimental techniques is very important to measure the thermophysical properties and to estimate their experimental uncertainties. The choice of the most suitable technique depends on the type of data to be determined, the range of pressure and temperature, the precision required, and the composition of the mixture if necessary.

In the literature several studies published concerning the investigation of working fluid for ORC applications exist. We will not present and described all the working fluid investigation. In 1985, Badr et al. [1] have examined around 68 pure working fluids (including natural fluid and hydrofluorocarbons) and given the main characteristic of the working fluids and their impacts on heat exchangers and turbine design. We can notice that in 1985, chlorofluorocarbon were not definitively banned. More recently, Saleh et al. [2] made a screening of 31 pure working fluids. They concluded that the thermal efficiency is better if the critical temperature of the working fluid is higher as possible. To increase the performance of heat exchangers and so reduce their size, Maizza and Maizza [3] suggest to use fluid with high density and high heat of vaporization. In 2012, Liu et al. [4], in the context of power generation, presented a two-stage Rankine cycle for electricity power plants. Ten pure working fluids from different chemical families (aromatics, hydrofluoroolefin, hydrofluorocarbons, hydrocarbons, ammonia) were tested. They concluded that the performance was not affected by the fluid selected. They concluded that selection would be realized on installation volume, size of the different components in the cycle, environmental protection, and operator safety. In 2017, Rahbar et al. [5] published a complete review of ORC for small-scale applications. In their paper, they present some main characteristic of the working fluid.

**3. Working fluid selection: characteristics**

*DOI: http://dx.doi.org/10.5772/intechopen.87113*

working fluids impact strongly on component's size.

necessary to add a superheating equipment.

working fluid.

**19**

**Figure 2.**

*cooling medium.*

**3.1 Chemical properties**

temperature of the heat source.

The choice of a working fluid is very crucial in the ORC systems. The working fluid should guarantee the cycle performance and system efficiency and must be adapted to the operating conditions of the system (temperature, pressure). Also hygiene, safety, and environment (HSE) aspects of the fluid have to be taken into account: the working fluid should satisfy the environment protection standards and ensure the safety of the operators. Moreover, the thermophysical properties of the

*Temperature-entropy diagram of the simple ORC. In green, working fluid; in red, heating medium; in blue,*

*Experimental Determination of Thermophysical Properties of Working Fluids for ORC…*

As the efficiency of the cycle is better for fluids with high critical temperature value [6], the working fluids are often heavy compounds with important molecular weight and low boiling point. Three types of organic fluids exist: dry, isentropic, and wet fluids. **Figure 3** presents the T-S diagrams of these fluids. For dry fluid, dT/ dS > 0, and for isentropic fluid, dT/dS = 0. It signifies that during expansion, there is no formation of liquid droplet. For wet fluid, dT/dS < 0 (like water). During expansion, liquid droplets are formed and can damage the equipment. So, it can be

In general, fluorinated components are used as working fluids. It is important to note that in 2014, European F-gas directive plans the prohibition of fluorinated working fluids with GWP of 2500 or more from 2020. The 2009 F-gas regulation fixes the limits of GWP for each year (Bolaji [7]). In 2018, the objective was to use fluids with GWP < 1300 close to the GWP of R134A (GWP = 1300). In 2020, the objective is to use fluids with GWP < 1000. In order to reach the objectives in terms of GWP, two solutions exist: the first one consists of the development of new fluids with low GWP values, such as hydrofluoroolefins (HFOs). The second one consists in developing new blends of refrigerants, less than four components [6]. With the existing equipment retrofit aspects are also very important. For all the cases, it is important to consider the thermophysical properties for the selection of the organic

**Critical temperature:** In order to guarantee ORC efficiency, the critical temperature of the chosen fluid should be as high as possible and close to the maximum

#### **2. Description of Organic Rankine Cycle**

An Organic Rankine Cycle is composed of a boiler/evaporator, a condenser, a pump, and a turbine (expander). The main application of ORC concerns the transformation/utilization of heat source at low or intermediate temperature (around 80°C). **Figure 1** reminds the schematic diagram of ORC. The pump compresses the liquid state working fluid until its desired pressure (and so temperature). The liquid is heated and vaporized in the boiler/evaporator which is also called the generator of vapor (the heat source). The vapor state working fluid is expanded in the turbine. During this operation electricity can be produced thanks to a generator. At low pressure, the working fluid is cooled in the condenser.

The cycle performance depends on the architecture of the system but also on the chosen working fluid and the operating conditions. The **Figure 2** presents a typical T-s diagram of an ORC with a heating and cooling medium.

**Figure 1.** *Schematic diagram of ORC.*

*Experimental Determination of Thermophysical Properties of Working Fluids for ORC… DOI: http://dx.doi.org/10.5772/intechopen.87113*

**Figure 2.**

In the literature several studies published concerning the investigation of working fluid for ORC applications exist. We will not present and described all the working fluid investigation. In 1985, Badr et al. [1] have examined around 68 pure working fluids (including natural fluid and hydrofluorocarbons) and given the main characteristic of the working fluids and their impacts on heat exchangers and turbine design. We can notice that in 1985, chlorofluorocarbon were not definitively banned. More recently, Saleh et al. [2] made a screening of 31 pure working fluids. They concluded that the thermal efficiency is better if the critical temperature of the working fluid is higher as possible. To increase the performance of heat exchangers and so reduce their size, Maizza and Maizza [3] suggest to use fluid with high density and high heat of vaporization. In 2012, Liu et al. [4], in the context of power generation, presented a two-stage Rankine cycle for electricity power plants.

*Organic Rankine Cycles for Waste Heat Recovery - Analysis and Applications*

Ten pure working fluids from different chemical families (aromatics,

the working fluid.

**Figure 1.**

**18**

*Schematic diagram of ORC.*

**2. Description of Organic Rankine Cycle**

pressure, the working fluid is cooled in the condenser.

T-s diagram of an ORC with a heating and cooling medium.

hydrofluoroolefin, hydrofluorocarbons, hydrocarbons, ammonia) were tested. They concluded that the performance was not affected by the fluid selected. They concluded that selection would be realized on installation volume, size of the different components in the cycle, environmental protection, and operator safety. In 2017, Rahbar et al. [5] published a complete review of ORC for

small-scale applications. In their paper, they present some main characteristic of

An Organic Rankine Cycle is composed of a boiler/evaporator, a condenser, a pump, and a turbine (expander). The main application of ORC concerns the transformation/utilization of heat source at low or intermediate temperature (around 80°C). **Figure 1** reminds the schematic diagram of ORC. The pump compresses the liquid state working fluid until its desired pressure (and so temperature). The liquid is heated and vaporized in the boiler/evaporator which is also called the generator of vapor (the heat source). The vapor state working fluid is expanded in the turbine. During this operation electricity can be produced thanks to a generator. At low

The cycle performance depends on the architecture of the system but also on the chosen working fluid and the operating conditions. The **Figure 2** presents a typical

*Temperature-entropy diagram of the simple ORC. In green, working fluid; in red, heating medium; in blue, cooling medium.*

#### **3. Working fluid selection: characteristics**

The choice of a working fluid is very crucial in the ORC systems. The working fluid should guarantee the cycle performance and system efficiency and must be adapted to the operating conditions of the system (temperature, pressure). Also hygiene, safety, and environment (HSE) aspects of the fluid have to be taken into account: the working fluid should satisfy the environment protection standards and ensure the safety of the operators. Moreover, the thermophysical properties of the working fluids impact strongly on component's size.

As the efficiency of the cycle is better for fluids with high critical temperature value [6], the working fluids are often heavy compounds with important molecular weight and low boiling point. Three types of organic fluids exist: dry, isentropic, and wet fluids. **Figure 3** presents the T-S diagrams of these fluids. For dry fluid, dT/ dS > 0, and for isentropic fluid, dT/dS = 0. It signifies that during expansion, there is no formation of liquid droplet. For wet fluid, dT/dS < 0 (like water). During expansion, liquid droplets are formed and can damage the equipment. So, it can be necessary to add a superheating equipment.

In general, fluorinated components are used as working fluids. It is important to note that in 2014, European F-gas directive plans the prohibition of fluorinated working fluids with GWP of 2500 or more from 2020. The 2009 F-gas regulation fixes the limits of GWP for each year (Bolaji [7]). In 2018, the objective was to use fluids with GWP < 1300 close to the GWP of R134A (GWP = 1300). In 2020, the objective is to use fluids with GWP < 1000. In order to reach the objectives in terms of GWP, two solutions exist: the first one consists of the development of new fluids with low GWP values, such as hydrofluoroolefins (HFOs). The second one consists in developing new blends of refrigerants, less than four components [6]. With the existing equipment retrofit aspects are also very important. For all the cases, it is important to consider the thermophysical properties for the selection of the organic working fluid.

#### **3.1 Chemical properties**

**Critical temperature:** In order to guarantee ORC efficiency, the critical temperature of the chosen fluid should be as high as possible and close to the maximum temperature of the heat source.

should have zero ozone depletion potential (ODP), minimal global warming poten-

*Experimental Determination of Thermophysical Properties of Working Fluids for ORC…*

**Material compatibility:** The working fluid should be non-corrosive and should have a non-eroding characteristic in order to guarantee the integrity of the compo-

**Phase diagram:** The knowledge of pure component phase diagram (mainly the pure component vapor pressure) is very important in order to know the physical state of the fluid. Concerning mixtures, the phase diagrams are more complex. Recently, Privat and Jaubert [8] have revisited the Scott and van Konynenburg [9] (**Figure 4**) classification of binary systems. Depending on the temperature and pressures conditions, vapor-liquid equilibrium but also vapor-liquid-liquid equilib-

**Density and specific volume:** Working fluids with low specific volume lead to low volume flow rates and so have a non-negligible impact on the sizing of heat

**Latent heat:** In general, a working fluid with high heat of vaporization is preferable as more heat is absorbed during the evaporation step. But in case of the

tial (GWP), and low atmospheric lifetime (ALT).

*DOI: http://dx.doi.org/10.5772/intechopen.87113*

rium (VLLE) and liquid-liquid equilibrium (LLE) can appear.

exchangers and expanders (low volume of vapor at the outlet).

nents of the ORC.

**Figure 4.**

**21**

*Scott and van Konynenburg classification [9].*

**3.2 Thermodynamic properties**

**Figure 3.** *Types of organic fluids (dry, isentropic, and wet) (Liu [6]).*

**Triple point temperature:** As low as possible, the working fluid should not be freezing in ORC under low temperature condition (cold source).

**Molecular weight:** The larger is the molecular weight, the smaller is the specific enthalpy drop, and the lower is the number of stages required for the expander.

**Thermal stability:** The working fluid should not have the possibility to decompose itself under high pressure and high temperature conditions.

**Safety and environment impacts:** Nontoxic and non-flammable organic fluid is required to protect the personnel in case of fluid leakage. Also, the working fluid

#### *Experimental Determination of Thermophysical Properties of Working Fluids for ORC… DOI: http://dx.doi.org/10.5772/intechopen.87113*

should have zero ozone depletion potential (ODP), minimal global warming potential (GWP), and low atmospheric lifetime (ALT).

**Material compatibility:** The working fluid should be non-corrosive and should have a non-eroding characteristic in order to guarantee the integrity of the components of the ORC.

#### **3.2 Thermodynamic properties**

**Phase diagram:** The knowledge of pure component phase diagram (mainly the pure component vapor pressure) is very important in order to know the physical state of the fluid. Concerning mixtures, the phase diagrams are more complex. Recently, Privat and Jaubert [8] have revisited the Scott and van Konynenburg [9] (**Figure 4**) classification of binary systems. Depending on the temperature and pressures conditions, vapor-liquid equilibrium but also vapor-liquid-liquid equilibrium (VLLE) and liquid-liquid equilibrium (LLE) can appear.

**Density and specific volume:** Working fluids with low specific volume lead to low volume flow rates and so have a non-negligible impact on the sizing of heat exchangers and expanders (low volume of vapor at the outlet).

**Latent heat:** In general, a working fluid with high heat of vaporization is preferable as more heat is absorbed during the evaporation step. But in case of the

**Figure 4.** *Scott and van Konynenburg classification [9].*

**Triple point temperature:** As low as possible, the working fluid should not be

**Molecular weight:** The larger is the molecular weight, the smaller is the specific enthalpy drop, and the lower is the number of stages required for the expander. **Thermal stability:** The working fluid should not have the possibility to decom-

**Safety and environment impacts:** Nontoxic and non-flammable organic fluid is required to protect the personnel in case of fluid leakage. Also, the working fluid

freezing in ORC under low temperature condition (cold source).

*Organic Rankine Cycles for Waste Heat Recovery - Analysis and Applications*

*Types of organic fluids (dry, isentropic, and wet) (Liu [6]).*

**Figure 3.**

**20**

pose itself under high pressure and high temperature conditions.

utilization of low-grade waste heat, it is better to use fluids with low latent heat of vaporization [5].

**Speed of sound:** The speed of the sound of the fluid limits the flow of fluid flowing in the expander. This parameter directly influences the size and therefore the cost of an ORC turbine.

The other thermodynamic properties are also useful but not crucial for the selection for the working fluid (heat capacity, surface tension).

#### **3.3 Transport properties**

**Dynamic viscosity:** Low dynamic viscosity for both liquid and vapor phases is preferable in order to reduce the friction losses and to maximize the heat transfer (reduction of the size of the heat exchangers, particularly heat surface exchange).

**Thermal conductivity:** High values of thermal conductivity are preferable in order to reduce the size of the heat exchangers (mainly surface of exchange).

#### **4. Experimental techniques for the estimation of thermophysical properties**

In this section, we will present several experimental techniques used for the experimental determination of thermodynamic and transport properties. Experimental methods for the investigation of thermophysical properties belong either to closed or open circuit methods.

**Closed circuit methods:** They can be divided into two main classes, depending on the method considered to determine the composition: static-analytic methods and static-synthetic methods. For the analytic methods, the composition of each phase is obtained by analyses after sampling (direct sampling method). For the synthetic methods, the global composition of the mixture is known a priori. No sampling is necessary.

properties (pressure and saturated molar volume) of the mixture are determined through the pressure vs. volume curve recorded that displays a break point. Isochoric method (**Figure 7**) can be used also to measure the dew point of multicomponent system. The components of the mixture are introduced separately, and the composition is known by weighing procedure or after analysis. The mixture is introduced at its vapor state, and then the temperature slowly decreases. The pressure and temperature are recorded. When the first drop of liquid appears, a break in the P-T curve is observed. The break point corresponds to the dew point. This technique is identical to the technique used to determine gas hydrate dissociation points [15]. Concerning critical point measurement, it is necessary to use a special device.

*Schematic diagram of the static-analytic apparatus. EC, equilibrium cell; LV, loading valve; MS, magnetic stirrer; PP, platinum resistance thermometer probe; PT, pressure transducer; RT, temperature regulator; LB, liquid bath; TP, thermal press; C1, more volatile compound; C2, less volatile compound; V, valve; GC, gas chromatograph; LS, liquid sampler; VS, vapor sampler; SC, sample controlling; PC, personal computer; VP,*

*Experimental Determination of Thermophysical Properties of Working Fluids for ORC…*

*DOI: http://dx.doi.org/10.5772/intechopen.87113*

The technique is based on dynamic-synthetic method where the mixture is circulating through the equilibrium cell (**Figure 8**) under specific conditions of temperature and pressure. A critical point can be determined by visually observing the critical opalescence and the simultaneous disappearance and reappearance of the meniscus, i.e., of the liquid-vapor interface from the middle of the view cell.

It is well known that density is required for the development of equations of state and the development of models for mass and heat transfers. Several techniques which can be used to measure the density exist. We can cite the hydrostatic balance densitometer coupling with magnetic suspension (single-sinker method from Wagner et al. [16]), density measurement with vibrating bodies, bellows [17], and

**4.2 Volumetric properties or densities**

**Figure 5.**

*vacuum pump.*

**23**

**Open circuit methods:** There are several different techniques based on this principle. The mixture circulates through an equipment composed of sensitive element where the measurement of the thermophysical properties is realized. We can cite critical point measurement as an example of utilization of this technique. Also the densitometer technique developed by Galicia-Luna et al. [10] and Bouchot and Richon [11] which is a synthetic method can be classified as an open circuit method. A mixture with known composition circulates through a vibrating U-tube. Dynamic viscosity measurement can be also classified in this rubric.

#### **4.1 Equilibrium properties and critical point**

Synthetic or analytic methods can be considered for the determination of equilibrium properties. Vapor-liquid equilibrium properties can be obtained using the "static-analytic" method. Herein, the mixture is enclosed in an equilibrium cell equipped with a mixing mechanism to get fast equilibrium conditions. When the equilibrium is reached, small quantities of the phases are sampled and analyzed through chromatographic analyzers. A complete description of the setup is available in Wang et al.'s [12] paper. The apparatus is similar to the one present on **Figure 5**. Capillary samplers like ROLSI™ (Armines's patent) can be used to take samples.

The variable volume cell technique (**Figure 6**) can be cited as a static-synthetic method [13, 14]. The components of the mixture are introduced separately, and the composition is known by weighing procedure or after analysis. The volume of the cell is modified with a piston to study bubble points. At fixed temperature, saturating

*Experimental Determination of Thermophysical Properties of Working Fluids for ORC… DOI: http://dx.doi.org/10.5772/intechopen.87113*

#### **Figure 5.**

utilization of low-grade waste heat, it is better to use fluids with low latent heat of

**Speed of sound:** The speed of the sound of the fluid limits the flow of fluid flowing in the expander. This parameter directly influences the size and therefore

The other thermodynamic properties are also useful but not crucial for the

**Dynamic viscosity:** Low dynamic viscosity for both liquid and vapor phases is preferable in order to reduce the friction losses and to maximize the heat transfer (reduction of the size of the heat exchangers, particularly heat surface exchange). **Thermal conductivity:** High values of thermal conductivity are preferable in order to reduce the size of the heat exchangers (mainly surface of exchange).

**4. Experimental techniques for the estimation of thermophysical**

In this section, we will present several experimental techniques used for the experimental determination of thermodynamic and transport properties. Experimental methods for the investigation of thermophysical properties belong either to

**Closed circuit methods:** They can be divided into two main classes, depending on the method considered to determine the composition: static-analytic methods and static-synthetic methods. For the analytic methods, the composition of each phase is obtained by analyses after sampling (direct sampling method). For the synthetic methods, the global composition of the mixture is known a priori. No

**Open circuit methods:** There are several different techniques based on this principle. The mixture circulates through an equipment composed of sensitive element where the measurement of the thermophysical properties is realized. We can cite critical point measurement as an example of utilization of this technique. Also the densitometer technique developed by Galicia-Luna et al. [10] and Bouchot and Richon [11] which is a synthetic method can be classified as an open circuit method. A mixture with known composition circulates through a vibrating U-tube.

Synthetic or analytic methods can be considered for the determination of equilibrium properties. Vapor-liquid equilibrium properties can be obtained using the "static-analytic" method. Herein, the mixture is enclosed in an equilibrium cell equipped with a mixing mechanism to get fast equilibrium conditions. When the equilibrium is reached, small quantities of the phases are sampled and analyzed through chromatographic analyzers. A complete description of the setup is available in Wang et al.'s [12] paper. The apparatus is similar to the one present on **Figure 5**. Capillary samplers like ROLSI™ (Armines's patent) can be used to take samples. The variable volume cell technique (**Figure 6**) can be cited as a static-synthetic method [13, 14]. The components of the mixture are introduced separately, and the composition is known by weighing procedure or after analysis. The volume of the cell is modified with a piston to study bubble points. At fixed temperature, saturating

Dynamic viscosity measurement can be also classified in this rubric.

**4.1 Equilibrium properties and critical point**

selection for the working fluid (heat capacity, surface tension).

*Organic Rankine Cycles for Waste Heat Recovery - Analysis and Applications*

vaporization [5].

the cost of an ORC turbine.

**3.3 Transport properties**

**properties**

closed or open circuit methods.

sampling is necessary.

**22**

*Schematic diagram of the static-analytic apparatus. EC, equilibrium cell; LV, loading valve; MS, magnetic stirrer; PP, platinum resistance thermometer probe; PT, pressure transducer; RT, temperature regulator; LB, liquid bath; TP, thermal press; C1, more volatile compound; C2, less volatile compound; V, valve; GC, gas chromatograph; LS, liquid sampler; VS, vapor sampler; SC, sample controlling; PC, personal computer; VP, vacuum pump.*

properties (pressure and saturated molar volume) of the mixture are determined through the pressure vs. volume curve recorded that displays a break point.

Isochoric method (**Figure 7**) can be used also to measure the dew point of multicomponent system. The components of the mixture are introduced separately, and the composition is known by weighing procedure or after analysis. The mixture is introduced at its vapor state, and then the temperature slowly decreases. The pressure and temperature are recorded. When the first drop of liquid appears, a break in the P-T curve is observed. The break point corresponds to the dew point. This technique is identical to the technique used to determine gas hydrate dissociation points [15].

Concerning critical point measurement, it is necessary to use a special device. The technique is based on dynamic-synthetic method where the mixture is circulating through the equilibrium cell (**Figure 8**) under specific conditions of temperature and pressure. A critical point can be determined by visually observing the critical opalescence and the simultaneous disappearance and reappearance of the meniscus, i.e., of the liquid-vapor interface from the middle of the view cell.

#### **4.2 Volumetric properties or densities**

It is well known that density is required for the development of equations of state and the development of models for mass and heat transfers. Several techniques which can be used to measure the density exist. We can cite the hydrostatic balance densitometer coupling with magnetic suspension (single-sinker method from Wagner et al. [16]), density measurement with vibrating bodies, bellows [17], and

#### **Figure 6.**

*Example of equipment which can be used for bubble point measurement. DAU, data acquisition unit; DDD, digital displacement display; DT, displacement transducer; GC, gas cylinder; LB, liquid bath; LVi, loading valve; P, piston; PM, piston monitoring; PN, pressurized nitrogen; PP, platinum probe; PT, pressure transducer; PV (VP), vacuum pump; R, gas reservoir; SD, stirring device; SB, stirring bar; ST, sapphire tube; TR, thermal regulator; Vi, valve; VVCM, variable volume cell.*

isochoric method [18]. More details concerning these techniques of measurements (and others) are detailed in the IUPAC book dedicated to experimental thermodynamics [19]. Herein, we will only describe the technique based on vibrating tube densitometer.

A mixture with known composition can circulate through a vibrating U-tube (static or dynamic mode). Density is deduced from careful calibration using reference fluids. This apparatus can be used to obtain (PρT) data of compressed phases. A complete description of this technique is available in the papers of Coquelet et al. [20]. This technique is not very recommended close to the critical point. In effect, vibration of the tube may provoke a phase transition. Other techniques based on isochoric method can be used also to determine the volumetric properties at the vicinity of the critical point [21] (**Figure 9**).

#### **4.3 Speed of sound**

The speed of sound data is also very important to determine the equation of state, and it is linked to other thermodynamic properties. In effect, the isothermal compressibility κ<sup>T</sup> is related to the isentropic compressibility κ<sup>S</sup> via Maxwell's relations (Eq. (1)):

$$
\kappa\_T = \kappa\_S + a^2 v \frac{T}{C\_p} \tag{1}
$$

ρ [kg/m3

**Figure 7.**

phase via *c* ¼

**4.4 Heat capacity**

released, *<sup>ϕ</sup>* <sup>¼</sup> *<sup>∂</sup><sup>H</sup>*

**25**

*∂t*

ffiffiffiffiffi 1 *κSρ* q

] reached in this work. Indeed, these three properties are linked in the liquid

developed to obtain the value of speed of sound exist. The spherical resonator developed by Mehl and Moldover [22] (with high accuracy in gases), Trusler and Zarari [23], and Benedetto et al. [24] can be cited as example. For liquid and dense fluid, pulse-echo techniques are preferred for measuring the speed of sound particularly at high pressure. More details concerning these techniques of measurements (and others) are detailed in the IUPAC book dedicated to experimental thermodynamics [19]. Herein, we will describe one technique used at Heriot-Watt University [25]. **Figure 10** describes the cell of measurement. A cylindrical acoustic cell with wellknown dimension is considered to measure the sound speed in the fluid using throughtransmission method of ultrasonic testing. In this method, a transducer is located on one side of the cell, and a detector is placed on the opposite side of the acoustic cell (electric signal is converted into ultrasound waves and vice versa). An oscilloscope is used to observe the waves. Speed of sound is obtained by dividing the period of the

*Example of equipment which can be used for dew point measurement. DW, degassed water; DAU, data acquisition unit; EC, equilibrium cell; GC, gas cylinder; LPT, low pressure transducer; LPT, high pressure transducer; LB, liquid bath; PP, platinum probe; SD, stirring device; TR, temperature regulator; VP, vacuum*

*Experimental Determination of Thermophysical Properties of Working Fluids for ORC…*

*DOI: http://dx.doi.org/10.5772/intechopen.87113*

*pump; VVC, variable volume cell; PF, pressurizing fluid; DT, displacement transducer.*

waves by the distance between the speed of sound transducer and detector.

The determination of isobaric heat capacity is done using a differential scanning calorimeter (DSC). The equipment is composed of two cells: one is the measurement cell, and one is the reference cell. A sample is introduced into the measurement cell, and a temperature ramp is applied. Knowing the heat flux transferred (absorbed or

� �) and the ramp, it is possible to estimate the heat capacity (Eq. (2)):

. Like with density measurement, several techniques which were

In Eq. (2), v [m3 /mol] is the molar volume of the compound, Cp is the heat capacity [J/mol], and <sup>κ</sup><sup>S</sup> is the isentropic compressibility *<sup>κ</sup><sup>S</sup>* ¼ � <sup>1</sup> *v ∂v ∂P <sup>S</sup>* [Pa�<sup>1</sup> ] and is determined thanks to the measurements of speed of sound c [m/s] and density

*Experimental Determination of Thermophysical Properties of Working Fluids for ORC… DOI: http://dx.doi.org/10.5772/intechopen.87113*

#### **Figure 7.**

isochoric method [18]. More details concerning these techniques of measurements (and others) are detailed in the IUPAC book dedicated to experimental thermodynamics [19]. Herein, we will only describe the technique based on vibrating tube

*Example of equipment which can be used for bubble point measurement. DAU, data acquisition unit; DDD, digital displacement display; DT, displacement transducer; GC, gas cylinder; LB, liquid bath; LVi, loading valve; P, piston; PM, piston monitoring; PN, pressurized nitrogen; PP, platinum probe; PT, pressure transducer; PV (VP), vacuum pump; R, gas reservoir; SD, stirring device; SB, stirring bar; ST, sapphire tube;*

*Organic Rankine Cycles for Waste Heat Recovery - Analysis and Applications*

A mixture with known composition can circulate through a vibrating U-tube (static or dynamic mode). Density is deduced from careful calibration using reference fluids. This apparatus can be used to obtain (PρT) data of compressed phases. A complete description of this technique is available in the papers of Coquelet et al. [20]. This technique is not very recommended close to the critical point. In effect, vibration of the tube may provoke a phase transition. Other techniques based on isochoric method can be used also to determine the volumetric properties at the

The speed of sound data is also very important to determine the equation of state, and it is linked to other thermodynamic properties. In effect, the isothermal compressibility κ<sup>T</sup> is related to the isentropic compressibility κ<sup>S</sup> via Maxwell's relations (Eq. (1)):

> *v T Cp*

/mol] is the molar volume of the compound, Cp is the heat

*v ∂v ∂P* 

*<sup>S</sup>* [Pa�<sup>1</sup>

(1)

] and is

*<sup>κ</sup><sup>T</sup>* <sup>¼</sup> *<sup>κ</sup><sup>S</sup>* <sup>þ</sup> *<sup>α</sup>*<sup>2</sup>

determined thanks to the measurements of speed of sound c [m/s] and density

capacity [J/mol], and <sup>κ</sup><sup>S</sup> is the isentropic compressibility *<sup>κ</sup><sup>S</sup>* ¼ � <sup>1</sup>

densitometer.

**Figure 6.**

**4.3 Speed of sound**

In Eq. (2), v [m3

**24**

vicinity of the critical point [21] (**Figure 9**).

*TR, thermal regulator; Vi, valve; VVCM, variable volume cell.*

*Example of equipment which can be used for dew point measurement. DW, degassed water; DAU, data acquisition unit; EC, equilibrium cell; GC, gas cylinder; LPT, low pressure transducer; LPT, high pressure transducer; LB, liquid bath; PP, platinum probe; SD, stirring device; TR, temperature regulator; VP, vacuum pump; VVC, variable volume cell; PF, pressurizing fluid; DT, displacement transducer.*

ρ [kg/m3 ] reached in this work. Indeed, these three properties are linked in the liquid phase via *c* ¼ ffiffiffiffiffi 1 *κSρ* q . Like with density measurement, several techniques which were developed to obtain the value of speed of sound exist. The spherical resonator developed by Mehl and Moldover [22] (with high accuracy in gases), Trusler and Zarari [23], and Benedetto et al. [24] can be cited as example. For liquid and dense fluid, pulse-echo techniques are preferred for measuring the speed of sound particularly at high pressure. More details concerning these techniques of measurements (and others) are detailed in the IUPAC book dedicated to experimental thermodynamics [19]. Herein, we will describe one technique used at Heriot-Watt University [25]. **Figure 10** describes the cell of measurement. A cylindrical acoustic cell with wellknown dimension is considered to measure the sound speed in the fluid using throughtransmission method of ultrasonic testing. In this method, a transducer is located on one side of the cell, and a detector is placed on the opposite side of the acoustic cell (electric signal is converted into ultrasound waves and vice versa). An oscilloscope is used to observe the waves. Speed of sound is obtained by dividing the period of the waves by the distance between the speed of sound transducer and detector.

#### **4.4 Heat capacity**

The determination of isobaric heat capacity is done using a differential scanning calorimeter (DSC). The equipment is composed of two cells: one is the measurement cell, and one is the reference cell. A sample is introduced into the measurement cell, and a temperature ramp is applied. Knowing the heat flux transferred (absorbed or released, *<sup>ϕ</sup>* <sup>¼</sup> *<sup>∂</sup><sup>H</sup> ∂t* � �) and the ramp, it is possible to estimate the heat capacity (Eq. (2)):

#### **Figure 8.**

*Schematic diagram of the critical point measurement apparatus. DAU, data acquisition unit; FV, flow regulation valve; HE, heat exchanger; MR, magnetic rode, O, oven; PN, pressurized nitrogen; PP, platinum probe; PT, pressure transducer; ST, sapphire tube; SP, syringe pump; TR, temperature regulator; Vi, valve; VVC, variable volume cell; VP, vacuum pump; W, waste.*

#### **Figure 9.**

*Flow diagram of the vibrating tube densimeter [20]. (1) loading cell, (2a and 2b) regulating and shutoff valves, (3) DMA-512P densimeter, (4) heat exchanger, (5) bursting disk, (6) inlet of the temperature regulating fluid, (7a and 7b) regulating and shutoff valves, (8) pressure transducers, (9) vacuum pump, (10) vent, (11) vibrating cell temperature probe, (12) HP 53131A data acquisition unit, (13) HP34970A data acquisition unit, (14) bath temperature probe, (15) principal liquid bath.*

$$\mathbf{C}\_{P} = \phi \left/ \left(\frac{\partial T}{\partial t}\right)\right. \tag{2}$$

**4.5 Transport properties**

*mixtures from Al Ghafri et al. [26].*

exchangers:

**27**

**Figure 11.**

**Figure 10.**

*4.5.1 Interest of transport properties in engineering*

*View of the acoustic cell of equipment designed by Ahmadi et al. [25].*

*DOI: http://dx.doi.org/10.5772/intechopen.87113*

*Experimental Determination of Thermophysical Properties of Working Fluids for ORC…*

Chemical and mechanical engineers use correlations with nondimensional numbers (Eq. (3)) to estimate heat transfer coefficient (*h*) essential for the estimation of global heat transfer coefficient of the heat exchanger and so the design of heat

*Differential scanning calorimeter used for measurements of the isobaric heat capacities of liquid refrigerant*

*Nu* <sup>¼</sup> *<sup>A</sup>*Re*<sup>α</sup>*Pr*<sup>β</sup>* (3)

In Eq. (4), *H* is the enthalpy,*T* is the temperature, and t is the time. A complete description of this technique is available in the paper of Al Ghafri et al. [26]. **Figure 11** presents a short description of the technique.

*Experimental Determination of Thermophysical Properties of Working Fluids for ORC… DOI: http://dx.doi.org/10.5772/intechopen.87113*

#### **Figure 10.**

*View of the acoustic cell of equipment designed by Ahmadi et al. [25].*

#### **Figure 11.**

*Differential scanning calorimeter used for measurements of the isobaric heat capacities of liquid refrigerant mixtures from Al Ghafri et al. [26].*

#### **4.5 Transport properties**

#### *4.5.1 Interest of transport properties in engineering*

Chemical and mechanical engineers use correlations with nondimensional numbers (Eq. (3)) to estimate heat transfer coefficient (*h*) essential for the estimation of global heat transfer coefficient of the heat exchanger and so the design of heat exchangers:

$$N\mu = A\mathrm{Re}^a \mathrm{Pr}^\beta \tag{3}$$

*CP* ¼ *ϕ*

*Flow diagram of the vibrating tube densimeter [20]. (1) loading cell, (2a and 2b) regulating and shutoff valves, (3) DMA-512P densimeter, (4) heat exchanger, (5) bursting disk, (6) inlet of the temperature regulating fluid, (7a and 7b) regulating and shutoff valves, (8) pressure transducers, (9) vacuum pump, (10) vent, (11) vibrating cell temperature probe, (12) HP 53131A data acquisition unit, (13) HP34970A*

*Schematic diagram of the critical point measurement apparatus. DAU, data acquisition unit; FV, flow regulation valve; HE, heat exchanger; MR, magnetic rode, O, oven; PN, pressurized nitrogen; PP, platinum probe; PT, pressure transducer; ST, sapphire tube; SP, syringe pump; TR, temperature regulator; Vi, valve;*

*Organic Rankine Cycles for Waste Heat Recovery - Analysis and Applications*

*VVC, variable volume cell; VP, vacuum pump; W, waste.*

description of this technique is available in the paper of Al Ghafri et al. [26].

**Figure 11** presents a short description of the technique.

*data acquisition unit, (14) bath temperature probe, (15) principal liquid bath.*

**Figure 9.**

**26**

**Figure 8.**

 *∂T ∂t* 

In Eq. (4), *H* is the enthalpy,*T* is the temperature, and t is the time. A complete

(2)

In Eq. (1), Nu is the Nusselt number *Nu* <sup>¼</sup> *hL <sup>λ</sup>* , Re is the Reynolds number Re <sup>¼</sup> *<sup>ρ</sup>vL <sup>μ</sup>* , and Pr is the Prandtl number Pr <sup>¼</sup> *CP<sup>μ</sup> <sup>λ</sup>* with h being the heat transfer coefficient [J.m�<sup>2</sup> ], L a characteristic length [m], λ the thermal conductivity [J. m�<sup>1</sup> ], ρ the density [kg.m<sup>3</sup> ], μ the viscosity [Pa.s], Cp the heat capacity [J.mol�<sup>1</sup> . K�<sup>1</sup> ], and v the speed of the fluid [m.s�<sup>1</sup> ]. The correlation can be modified with the utilization of Weber number (*We* <sup>¼</sup> *<sup>ρ</sup>Lv*<sup>2</sup> *<sup>γ</sup>* , γ is the surface tension) taking into account the effect of interfacial tension during the formation of the bubble of gas in the evaporator or drop of liquids in the condenser.

comprised of two small cylinders connected to each other through a capillary tube and a temperature-dependent calibrated internal diameter. A complete description of this technique is available in the paper of Kashefi et al. [32]. The temperature of the system was set to the desired condition, and the desired pressure was set using the hand pump. Poiseuille equation (Eq. (4)) (in laminar flow conditions) can relate the pressure drop across the capillary tube to the viscosity, tube characteristics, and

*Experimental Determination of Thermophysical Properties of Working Fluids for ORC…*

<sup>Δ</sup>*<sup>P</sup>* <sup>¼</sup> <sup>128</sup>*LQ<sup>μ</sup>*

D refers to the internal diameter of the capillary tube in cm, μ is the dynamic viscosity of the flown fluid in cP, and C is the unit conversion factor equal to

Several techniques exist to measure the thermal conductivity of fluids [33]. Among those methods, the transient hot-wire method is considered to be the most used technique and to be a very accurate and reliable technique to measure this thermophysical property. The basic theory of the transient hot-wire method is presented in Healy's paper [34], and procedure of measurement is fully described in the paper of Marsh et al. [35]. Generally, a transient hot-wire apparatus consists of one highly pure platinum wire, a current source, a voltage meter, a data acquisition system, and a computer (**Figure 13**). The current source provides a constant current for the platinum wire, which is embedded in the tested fluid. Then the temperature of the wire will rise because of the Joule effect. Subsequently, the temperature of the

*View of the thermal conductivity cell (hot-wire method). LB, liquid bath; C, cell; LV, loading valve; M, motor;*

*PW, platinum wire; MR, magnetic rod; SD, stirring device; to SM, to SourceMeter.*

In Eq. (3), ΔP is the differential pressure across the capillary tube viscometer in

*<sup>C</sup>πD*<sup>4</sup> (4)

/sec, L is the length of the capillary tube in cm,

also flow rate for laminar flow:

*DOI: http://dx.doi.org/10.5772/intechopen.87113*

psi, Q represents the flow rate in cm<sup>3</sup>

6,894,757 if the above units are used.

*4.5.3 Thermal conductivity*

**Figure 13.**

**29**

We remind that for a heat exchanger, global heat transfer coefficient (U) depends on the local heat transfers (h) of the two fluids and the thermal conductivity of the material of the heat exchanger.

#### *4.5.2 Dynamic viscosity*

Like density measurements, several techniques to determine viscosity of fluids exist. For example, we can cite the falling ball technique [27], capillary technique, vibration quartz [28], and vibrating bodies [29, 30]. We invite the reader to have a look in the paper from Le Neindre [31] for a complete overview of the techniques of measurement. Herein we will only describe the viscometer used to measure dynamic viscosities using the capillary tube viscosity method. A schematic view of the setup used at Heriot-Watt University is shown in **Figure 12**. The apparatus is

**Figure 12.** *Schematic diagram of the setup used for dynamic viscosity measurement [32].*

*Experimental Determination of Thermophysical Properties of Working Fluids for ORC… DOI: http://dx.doi.org/10.5772/intechopen.87113*

comprised of two small cylinders connected to each other through a capillary tube and a temperature-dependent calibrated internal diameter. A complete description of this technique is available in the paper of Kashefi et al. [32]. The temperature of the system was set to the desired condition, and the desired pressure was set using the hand pump. Poiseuille equation (Eq. (4)) (in laminar flow conditions) can relate the pressure drop across the capillary tube to the viscosity, tube characteristics, and also flow rate for laminar flow:

$$
\Delta P = \frac{128LQ\mu}{C\pi D^4} \tag{4}
$$

In Eq. (3), ΔP is the differential pressure across the capillary tube viscometer in psi, Q represents the flow rate in cm<sup>3</sup> /sec, L is the length of the capillary tube in cm, D refers to the internal diameter of the capillary tube in cm, μ is the dynamic viscosity of the flown fluid in cP, and C is the unit conversion factor equal to 6,894,757 if the above units are used.

#### *4.5.3 Thermal conductivity*

In Eq. (1), Nu is the Nusselt number *Nu* <sup>¼</sup> *hL*

the evaporator or drop of liquids in the condenser.

], and v the speed of the fluid [m.s�<sup>1</sup>

tivity of the material of the heat exchanger.

utilization of Weber number (*We* <sup>¼</sup> *<sup>ρ</sup>Lv*<sup>2</sup>

*<sup>μ</sup>* , and Pr is the Prandtl number Pr <sup>¼</sup> *CP<sup>μ</sup>*

*Organic Rankine Cycles for Waste Heat Recovery - Analysis and Applications*

Re <sup>¼</sup> *<sup>ρ</sup>vL*

**Figure 12.**

**28**

*Schematic diagram of the setup used for dynamic viscosity measurement [32].*

m�<sup>1</sup>

K�<sup>1</sup>

coefficient [J.m�<sup>2</sup>

*4.5.2 Dynamic viscosity*

], ρ the density [kg.m<sup>3</sup>

*<sup>λ</sup>* , Re is the Reynolds number

*<sup>λ</sup>* with h being the heat transfer

]. The correlation can be modified with the

.

], L a characteristic length [m], λ the thermal conductivity [J.

account the effect of interfacial tension during the formation of the bubble of gas in

Like density measurements, several techniques to determine viscosity of fluids exist. For example, we can cite the falling ball technique [27], capillary technique, vibration quartz [28], and vibrating bodies [29, 30]. We invite the reader to have a look in the paper from Le Neindre [31] for a complete overview of the techniques of

measurement. Herein we will only describe the viscometer used to measure dynamic viscosities using the capillary tube viscosity method. A schematic view of the setup used at Heriot-Watt University is shown in **Figure 12**. The apparatus is

We remind that for a heat exchanger, global heat transfer coefficient (U) depends on the local heat transfers (h) of the two fluids and the thermal conduc-

], μ the viscosity [Pa.s], Cp the heat capacity [J.mol�<sup>1</sup>

*<sup>γ</sup>* , γ is the surface tension) taking into

Several techniques exist to measure the thermal conductivity of fluids [33]. Among those methods, the transient hot-wire method is considered to be the most used technique and to be a very accurate and reliable technique to measure this thermophysical property. The basic theory of the transient hot-wire method is presented in Healy's paper [34], and procedure of measurement is fully described in the paper of Marsh et al. [35]. Generally, a transient hot-wire apparatus consists of one highly pure platinum wire, a current source, a voltage meter, a data acquisition system, and a computer (**Figure 13**). The current source provides a constant current for the platinum wire, which is embedded in the tested fluid. Then the temperature of the wire will rise because of the Joule effect. Subsequently, the temperature of the

#### **Figure 13.**

*View of the thermal conductivity cell (hot-wire method). LB, liquid bath; C, cell; LV, loading valve; M, motor; PW, platinum wire; MR, magnetic rod; SD, stirring device; to SM, to SourceMeter.*

fluid will also change as a result of the heat conduction between the wire and the fluid (heat radiation and convection are in general neglected). The temperature rise of the platinum wire as a function of the duration t is given by Eq. (5):

$$
\Delta T = \frac{\mathbf{q}}{4\pi\lambda} \ln\left(\frac{4\kappa t}{r^2 \mathbf{C}}\right) \tag{5}
$$

developed the first EoS SAFT (statistical associating fluid theory) called SAFT-0. Many versions exist today, such as SAFT-VR [37], PC-SAFT [38], and SAFT Mie [39]. The various versions differ mainly in the choice of the reference fluid, the radial distribution function, and explicit expressions of the terms of perturbation. The last type of equation of state which can be used to estimate the thermodynamic properties is based on multi-fluid approximation. It is well known that from the knowledge of Helmholtz energy, all thermodynamic properties can be calculated. This equation of state is explained in terms of reduced molar Helmholtz free energy (Eq. (8)). Temperature and density are expressed in the dimensionless vari-

*Experimental Determination of Thermophysical Properties of Working Fluids for ORC…*

*RT* <sup>¼</sup> *a Tr; <sup>ρ</sup><sup>r</sup>* ð Þ¼ *; <sup>x</sup> <sup>a</sup>id Tr; <sup>ρ</sup><sup>r</sup>* ð Þþ *; <sup>x</sup> <sup>a</sup>res Tr; <sup>ρ</sup><sup>r</sup>* ð Þ *; <sup>x</sup>* (8)

*<sup>j</sup> Tr; <sup>ρ</sup><sup>r</sup>* ð Þþ *ares*

*pq* <sup>¼</sup> <sup>∑</sup>*<sup>p</sup>*¼<sup>1</sup> <sup>∑</sup>*<sup>q</sup>*¼*p*þ<sup>1</sup> *xpxqFpqaE*

*pq* can be considered to be equal to zero [41]:

*<sup>α</sup>kτtk <sup>δ</sup>dk* exp �*γδlk*

*<sup>C</sup>* <sup>¼</sup> <sup>∑</sup>*<sup>p</sup>*¼<sup>1</sup> <sup>∑</sup>*<sup>p</sup>*¼<sup>1</sup> *kT,pqxpxq TCpTCq* <sup>0</sup>*:*<sup>5</sup> and *<sup>v</sup>mix*

where *kT,pq* and *kv,pq* are adjustable

*<sup>j</sup> Tr; <sup>ρ</sup><sup>r</sup>* ð Þ <sup>þ</sup> *xj* ln *xj*

(9)

*pq* is called departure

(10)

*<sup>C</sup>* ¼

In Eq. (8), the exponent "id" stands for the ideal gas contribution, and exponent "res" is the residual contribution. *ρ<sup>r</sup>* and *Tr* are the reduced density and temperature, respectively. Concerning the development of equation of state for the mixtures, the first possibility is to consider mixing rules for each parameter like in the cubic equation of state. The best approach is to consider the multi-fluid approximation. This approach was introduced by Tillner-Roth in 1993 [40]. It applies mixing rules to the Helmholtz free energy of the mixture of components (Eq. (9)):

ables *<sup>δ</sup>* <sup>¼</sup> *<sup>ρ</sup>*

*ρC*

*a Tr; ρ<sup>r</sup>* ð Þ¼ *; x*

and *<sup>τ</sup>* <sup>¼</sup> *<sup>T</sup> TC* :

*A Tr; ρ<sup>r</sup>* ð Þ *; x*

*DOI: http://dx.doi.org/10.5772/intechopen.87113*

*A Tr; ρ<sup>r</sup>* ð Þ *; x*

þ ∑ *p*¼1

deviation from ideal mixture. Δ*ares*

*A Tr; ρ<sup>r</sup>* ð Þ

reduced parameters are used in Eq. (8). For example, we can use *Tmix*

1

*RT* <sup>¼</sup> ln ð Þþ *<sup>δ</sup>* <sup>∑</sup>

<sup>8</sup> *vCp* <sup>1</sup>*=*<sup>3</sup> <sup>þ</sup> *vCq* <sup>1</sup>*=*<sup>3</sup> <sup>3</sup>

properties are available, *a<sup>E</sup>*

γ = 0 and if lk 6¼ 0, then γ =1.

<sup>∑</sup>*<sup>p</sup>*¼<sup>1</sup> <sup>∑</sup>*<sup>p</sup>*¼<sup>1</sup> *kv,pqxpxq*

to fit *kv,pq*.

**31**

*RT* <sup>¼</sup> <sup>∑</sup>

∑ *q*¼*p*þ1 *j*

*xpxqFpqaE*

*xj aid*

*pq*

"j" are the component index. An excess property is defined to calculate the

*i*

Equation (10) contains several adjustable parameters αi, αk, tk, dk, and lk. Experimental data is required to adjust these parameters. Moreover, if lk = 0, then

properties corresponding to the mixture studied (superscript "mix") because

binary interaction parameters. VLE data should be used to fit *kT,pq* parameters, and if experimental data concerning densities of mixture are available, it is possible

In Eq. (9), superscript "E" is for excess properties, and subscripts "p," "q," and

*<sup>α</sup>iτti* <sup>þ</sup> <sup>∑</sup> *k*

With the multi-fluid approximation, it is important to calculate the new critical

function from the ideal solution. It is an empirical function, like Eq. (10), fitted to experimental binary mixture data, mainly densities, speed of sound, or heat of mixing. In this departure function, the Fpq parameters take into account the behavior of one binary pair with another. If only vapor-liquid equilibrium

In Eq. (5), λ is the thermal conductivity of the sample, q is the constant power provided to the wire, W/m. κ is the thermal diffusivity of the fluid, r is the radius of the hot wire, and C is Euler's constant, whose value is 1.781. As the relation between the ΔT and ln(t) can be determined through the experiments, the thermal conductivity of the tested fluid can be calculated using this equation. Compared with other methods, the convenience, accuracy, and the short duration of transient hot-wire method make it a widely used method nowadays.

#### **5. Data treatment**

Process or system simulator required models or correlation in order to define the best operating conditions (T, P, flow, compositions) with the maximum of efficiency and the best coefficient of performance (COP) but also to design each component (heat exchangers, expanders, valves, expander). In this section we will just present few models which can be used with the experimental data in order to predict the phase diagrams and thermodynamic and transport properties.

#### **5.1 Thermodynamic models**

In this section, we propose a presentation of three types of thermodynamic models. These models are briefly described. The main difference concerns the number of parameters we have to adjust and so the quantity and type of experimental data we have to acquire in order to adjust the parameters.

The thermodynamic properties are obtained by using equations of state (EoSs). In the process simulators, the most famous EoSs are of cubic type, such as Eq. (6):

$$P = \frac{RT}{v - b} - \frac{aa(T)}{v^2 + uvb + wb^2} \tag{6}$$

In Eq. (6), R is the ideal gas constant, a and b are the parameters of the EoS calculated using the critical temperature (Tc) and pressure (Pc) of each component, and α(T) is a function of temperature, acentric factor, Tc, and Pc. u and w are other parameters.

Another type of equation of state of the molecular type can be used. The Helmholtz energy is calculated by considering all the molecular interactions like dispersion, polarity, H bonding (association), etc. Equation (7) describes the method of calculation of the Helmholtz energy A:

$$\frac{A}{Nk\_bT} = \frac{A^{\text{Ideal}}}{Nk\_bT} + \frac{A^{\text{Segment}}}{Nk\_bT} + \frac{A^{\text{Chain}}}{Nk\_bT} + \frac{A^{\text{Association}}}{Nk\_bT} \tag{7}$$

In Eq. (7), kb is the Boltzmann constant, T is the temperature, and N is the mole number. The most known molecular EoSs of this type are SAFT type. Based on the Wertheim's statistical theory of associative fluids (1984), Chapman et al. [36]

*Experimental Determination of Thermophysical Properties of Working Fluids for ORC… DOI: http://dx.doi.org/10.5772/intechopen.87113*

developed the first EoS SAFT (statistical associating fluid theory) called SAFT-0. Many versions exist today, such as SAFT-VR [37], PC-SAFT [38], and SAFT Mie [39]. The various versions differ mainly in the choice of the reference fluid, the radial distribution function, and explicit expressions of the terms of perturbation.

The last type of equation of state which can be used to estimate the thermodynamic properties is based on multi-fluid approximation. It is well known that from the knowledge of Helmholtz energy, all thermodynamic properties can be calculated. This equation of state is explained in terms of reduced molar Helmholtz free energy (Eq. (8)). Temperature and density are expressed in the dimensionless variables *<sup>δ</sup>* <sup>¼</sup> *<sup>ρ</sup> ρC* and *<sup>τ</sup>* <sup>¼</sup> *<sup>T</sup> TC* :

$$\frac{A(T\_r, \rho\_r, \overline{\mathfrak{x}})}{RT} = a(T\_r, \rho\_r, \overline{\mathfrak{x}}) = a^{id}(T\_r, \rho\_r, \overline{\mathfrak{x}}) + a^{r\infty}(T\_r, \rho\_r, \overline{\mathfrak{x}}) \tag{8}$$

In Eq. (8), the exponent "id" stands for the ideal gas contribution, and exponent "res" is the residual contribution. *ρ<sup>r</sup>* and *Tr* are the reduced density and temperature, respectively. Concerning the development of equation of state for the mixtures, the first possibility is to consider mixing rules for each parameter like in the cubic equation of state. The best approach is to consider the multi-fluid approximation. This approach was introduced by Tillner-Roth in 1993 [40]. It applies mixing rules to the Helmholtz free energy of the mixture of components (Eq. (9)):

$$\begin{aligned} a(T\_r, \rho\_r, \overline{\mathbf{x}}) &= \frac{A(T\_r, \rho\_r, \overline{\mathbf{x}})}{RT} = \sum\_j \mathbf{x}\_j \left( a\_j^{id}(T\_r, \rho\_r) + a\_j^{rc}(T\_r, \rho\_r) \right) + \mathbf{x}\_j \ln \mathbf{x}\_j \\ &+ \sum\_{p=1} \sum\_{q=p+1} \mathbf{x}\_p \mathbf{x}\_q F\_{pq} a\_{pq}^E \end{aligned} \tag{9}$$

In Eq. (9), superscript "E" is for excess properties, and subscripts "p," "q," and "j" are the component index. An excess property is defined to calculate the deviation from ideal mixture. Δ*ares pq* <sup>¼</sup> <sup>∑</sup>*<sup>p</sup>*¼<sup>1</sup> <sup>∑</sup>*<sup>q</sup>*¼*p*þ<sup>1</sup> *xpxqFpqaE pq* is called departure function from the ideal solution. It is an empirical function, like Eq. (10), fitted to experimental binary mixture data, mainly densities, speed of sound, or heat of mixing. In this departure function, the Fpq parameters take into account the behavior of one binary pair with another. If only vapor-liquid equilibrium properties are available, *a<sup>E</sup> pq* can be considered to be equal to zero [41]:

$$\frac{A(T\_r, \rho\_r)}{RT} = \ln\left(\delta\right) + \sum\_i a\_i \pi^{t\_i} + \sum\_k a\_k \pi^{t\_k} \delta^{d\_k} \exp\left(-\gamma \delta^{l\_k}\right) \tag{10}$$

Equation (10) contains several adjustable parameters αi, αk, tk, dk, and lk. Experimental data is required to adjust these parameters. Moreover, if lk = 0, then γ = 0 and if lk 6¼ 0, then γ =1.

With the multi-fluid approximation, it is important to calculate the new critical properties corresponding to the mixture studied (superscript "mix") because reduced parameters are used in Eq. (8).

For example, we can use *Tmix <sup>C</sup>* <sup>¼</sup> <sup>∑</sup>*<sup>p</sup>*¼<sup>1</sup> <sup>∑</sup>*<sup>p</sup>*¼<sup>1</sup> *kT,pqxpxq TCpTCq* <sup>0</sup>*:*<sup>5</sup> and *<sup>v</sup>mix <sup>C</sup>* ¼ <sup>∑</sup>*<sup>p</sup>*¼<sup>1</sup> <sup>∑</sup>*<sup>p</sup>*¼<sup>1</sup> *kv,pqxpxq* 1 <sup>8</sup> *vCp* <sup>1</sup>*=*<sup>3</sup> <sup>þ</sup> *vCq* <sup>1</sup>*=*<sup>3</sup> <sup>3</sup> where *kT,pq* and *kv,pq* are adjustable binary interaction parameters. VLE data should be used to fit *kT,pq* parameters, and if experimental data concerning densities of mixture are available, it is possible to fit *kv,pq*.

fluid will also change as a result of the heat conduction between the wire and the fluid (heat radiation and convection are in general neglected). The temperature rise

> ln <sup>4</sup>*κ<sup>t</sup> r*2*C*

In Eq. (5), λ is the thermal conductivity of the sample, q is the constant power provided to the wire, W/m. κ is the thermal diffusivity of the fluid, r is the radius of the hot wire, and C is Euler's constant, whose value is 1.781. As the relation between the ΔT and ln(t) can be determined through the experiments, the thermal conductivity of the tested fluid can be calculated using this equation. Compared with other methods, the convenience, accuracy, and the short duration of transient hot-wire

Process or system simulator required models or correlation in order to define the best operating conditions (T, P, flow, compositions) with the maximum of efficiency and the best coefficient of performance (COP) but also to design each component (heat exchangers, expanders, valves, expander). In this section we will just present few models which can be used with the experimental data in order to

predict the phase diagrams and thermodynamic and transport properties.

mental data we have to acquire in order to adjust the parameters.

*<sup>P</sup>* <sup>¼</sup> *RT*

*NkbT* <sup>þ</sup>

In this section, we propose a presentation of three types of thermodynamic models. These models are briefly described. The main difference concerns the number of parameters we have to adjust and so the quantity and type of experi-

The thermodynamic properties are obtained by using equations of state (EoSs). In the process simulators, the most famous EoSs are of cubic type, such as Eq. (6):

*<sup>v</sup>* � *<sup>b</sup>* � *<sup>a</sup>α*ð Þ *<sup>T</sup>*

In Eq. (6), R is the ideal gas constant, a and b are the parameters of the EoS calculated using the critical temperature (Tc) and pressure (Pc) of each component, and α(T) is a function of temperature, acentric factor, Tc, and Pc. u and w are other

Another type of equation of state of the molecular type can be used. The Helmholtz energy is calculated by considering all the molecular interactions like dispersion, polarity, H bonding (association), etc. Equation (7) describes the method of

In Eq. (7), kb is the Boltzmann constant, T is the temperature, and N is the mole number. The most known molecular EoSs of this type are SAFT type. Based on the Wertheim's statistical theory of associative fluids (1984), Chapman et al. [36]

*A*Chain *NkbT* <sup>þ</sup>

*A*Segment *NkbT* <sup>þ</sup>

*<sup>v</sup>*<sup>2</sup> <sup>þ</sup> *uvb* <sup>þ</sup> *wb*<sup>2</sup> (6)

*A*Association

*NkbT* (7)

(5)

of the platinum wire as a function of the duration t is given by Eq. (5):

*Organic Rankine Cycles for Waste Heat Recovery - Analysis and Applications*

<sup>Δ</sup>*<sup>T</sup>* <sup>¼</sup> <sup>q</sup> 4*πλ*

method make it a widely used method nowadays.

**5. Data treatment**

**5.1 Thermodynamic models**

calculation of the Helmholtz energy A:

*A NkbT* <sup>¼</sup> *<sup>A</sup>*Ideal

parameters.

**30**

#### **5.2 Transport property models**

Concerning the transport properties, different approaches exist. One consists in using the corresponding state method. The most famous approach is the TRAPP method developed by the NIST. Huber et al. [42] and Klein et al. [43] have developed a series of equations adapted to the prediction of viscosities and thermal conductivities of pure components and mixtures. The approach consists in modifying the transport properties in the ideal dilute gas state taking into account the molecular interactions (and so the density of the fluid with temperature and pressure).

The viscosity of a dilute gas can be determined as a function of temperature by Eq. (11). A dilute gas is composed by noninteractive rigid spheres of diameter σ:

$$\eta^{\sigma} = \mathcal{C} \frac{T^{\ddagger} \mathcal{M}^{\ddagger}}{\sigma^2} \tag{11}$$

*<sup>λ</sup>*ð Þ¼ *<sup>T</sup> <sup>λ</sup>*°ð Þþ *<sup>T</sup> Δλ<sup>R</sup> <sup>T</sup>*

*Experimental Determination of Thermophysical Properties of Working Fluids for ORC…*

1 2*h*�<sup>2</sup> <sup>3</sup> *MR M* <sup>1</sup> 2

In this section, we will present some results obtained for pure component (transport properties) and multicomponent systems (equilibrium properties) on

We will present the results obtained for three binary systems. The first one concerns a mixture of CO2 and R1234ze(e) published by Wang et al. [12]).

**Figure 14** presents the phase diagram. The system presents no azeotropic behavior. We can notice that with the experimental data, we can also predict a critical point using asymptotic laws of behavior [12]. **Figure 15** presents a comparison with the critical point measured by Juntaratchat et al. [50] using a critical point setup similar

The binary system R245fa + isopentane is presented on **Figure 16** at 392.87 K.

Measurement was done using static-analytic method [51]. We have used REFPROP 10.0 to correlate the data (REFPROP 10.0 [52] uses Fundamental Helmholtz equation). We can observe a good agreement between REFPROP prediction and the experimental data (we have one comment concerning this point: the reference of the data used in the data treatment by REFPROP is not

*Pressure as a function of CO2 mole fraction in the CO2. (1)*�*R-1234ze(E) and (2) mixture at different temperatures. <sup>Δ</sup>, 283.32 K; o, 293.15 K;* ⃞*, 298.15 K; ▲, 308.13 K; ●, 318.11 K; ■, 333.01 K;* �*, 353.02 K. Solid lines: calculated with Peng-Robinson EoS [47], Wong-Sandler mixing rules [48], and NRTL [49]*

, and *F<sup>λ</sup>* ¼ *f*

In Eq. (17), *<sup>f</sup>* <sup>¼</sup> *Tc*

*TR c* , *<sup>h</sup>* <sup>¼</sup> *<sup>ρ</sup><sup>R</sup> c ρc*

*DOI: http://dx.doi.org/10.5772/intechopen.87113*

mixing rules have to be considered [46].

**6. Presentation of some results**

working fluids already published.

to the equipment already presented in Section 4.

**6.1 Phase diagram**

clearly mentioned).

**Figure 14.**

**33**

*activity coefficient model [12].*

*<sup>f</sup> ; <sup>ρ</sup><sup>h</sup>*

*<sup>F</sup><sup>λ</sup>* (17)

reduction ratio. For mixtures,

In Eq. (11), T is temperature in K, M is the molar mass in g/mol, σ is the diameter of the rigid sphere in nm, and C is a constant depending of the molecule considered. Chapman-Enskog cited in Poling and Prausnitz [44] have introduced an additional term called "collision integral" which takes into account the collision between the molecules (Eq. (12)):

$$
\eta^{\sigma} = K \frac{T^{\frac{1}{2}} \mathcal{M}^{\frac{1}{2}}}{\sigma^2 \mathcal{Q}} \tag{12}
$$

In Eq. (12), ln ð Þ¼ *<sup>Ω</sup>* <sup>∑</sup>*<sup>i</sup> ai* ln *<sup>T</sup> ϵ k <sup>i</sup>* , and ?/k is an empirical factor link to the potential of interaction.

Concerning thermal conductivity, λ0(T) represents the dilute gas thermal conductivity and can be calculated by Eq. (13):

$$
\lambda\_0 = A\_1 + A\_2(T/T\_C) + A\_3(T/T\_C)^2 \tag{13}
$$

When the pressure and so the density of the fluid increases, molecular interaction between molecules cannot be neglected, and so it is necessary to apply a correction (like a residual term for equation of state). Equations (14) and (15) lead to calculate dynamic viscosity and thermal conductivity:

$$
\eta = \eta^{\sigma} + \Delta \eta \tag{14}
$$

In Eq. (14), *Δη* is the residual viscosity:

$$
\lambda(\rho, T) = \lambda\_0(T) + \Delta\lambda\_r(\rho, T) + \Delta\lambda\_C(\rho, T) \tag{15}
$$

In Eq. (15), Δλ<sup>r</sup> (ρ, T) is the residual thermal conductivity, and ΔλC(ρ, T) is the empirical critical enhancement.

The R134a is the reference fluid for the refrigerants [42], but for the hydrocarbons, it is better to consider propane or methane [45]. The viscosity and thermal conductivity of the other fluids are calculated from the properties of reference fluids. Critical properties of the fluid are required. Equation (16) presents the equation for the dynamic viscosity:

$$\eta(T) = \eta^{\circ}(T) + \Delta \eta^{R} \left(\frac{T}{f}, \rho h\right) F\_{\eta} \tag{16}$$

In Eq. (16),*<sup>f</sup>* <sup>¼</sup> *Tc TR c* , *<sup>h</sup>* <sup>¼</sup> *<sup>ρ</sup><sup>R</sup> c ρc* , and *F<sup>η</sup>* ¼ *f* 1 2*h*�<sup>2</sup> <sup>3</sup> *M MR* <sup>1</sup> 2 reduction ratio. Equation (17) presents the equation for the thermal conductivity:

*Experimental Determination of Thermophysical Properties of Working Fluids for ORC… DOI: http://dx.doi.org/10.5772/intechopen.87113*

$$
\lambda(T) = \lambda^{\bullet}(T) + \Delta\lambda^{R}\left(\frac{T}{f}, \rho h\right) F\_{\lambda} \tag{17}
$$

In Eq. (17), *<sup>f</sup>* <sup>¼</sup> *Tc TR c* , *<sup>h</sup>* <sup>¼</sup> *<sup>ρ</sup><sup>R</sup> c ρc* , and *F<sup>λ</sup>* ¼ *f* 1 2*h*�<sup>2</sup> <sup>3</sup> *MR M* <sup>1</sup> 2 reduction ratio. For mixtures, mixing rules have to be considered [46].

#### **6. Presentation of some results**

In this section, we will present some results obtained for pure component (transport properties) and multicomponent systems (equilibrium properties) on working fluids already published.

#### **6.1 Phase diagram**

**5.2 Transport property models**

between the molecules (Eq. (12)):

In Eq. (12), ln ð Þ¼ *<sup>Ω</sup>* <sup>∑</sup>*<sup>i</sup> ai* ln *<sup>T</sup>*

conductivity and can be calculated by Eq. (13):

In Eq. (14), *Δη* is the residual viscosity:

empirical critical enhancement.

equation for the dynamic viscosity:

*TR c* , *<sup>h</sup>* <sup>¼</sup> *<sup>ρ</sup><sup>R</sup> c ρc*

presents the equation for the thermal conductivity:

In Eq. (16),*<sup>f</sup>* <sup>¼</sup> *Tc*

**32**

to calculate dynamic viscosity and thermal conductivity:

potential of interaction.

Concerning the transport properties, different approaches exist. One consists in using the corresponding state method. The most famous approach is the TRAPP method developed by the NIST. Huber et al. [42] and Klein et al. [43] have developed a series of equations adapted to the prediction of viscosities and thermal conductivities of pure components and mixtures. The approach consists in modifying the transport properties in the ideal dilute gas state taking into account the molecular interactions (and so the density of the fluid with temperature and pressure).

*Organic Rankine Cycles for Waste Heat Recovery - Analysis and Applications*

The viscosity of a dilute gas can be determined as a function of temperature by Eq. (11). A dilute gas is composed by noninteractive rigid spheres of diameter σ:

> 2*M*<sup>1</sup> 2

2*M*<sup>1</sup> 2

*<sup>σ</sup>*<sup>2</sup> (11)

*<sup>σ</sup>*<sup>2</sup>*<sup>Ω</sup>* (12)

<sup>2</sup> (13)

*F<sup>η</sup>* (16)

reduction ratio. Equation (17)

, and ?/k is an empirical factor link to the

*η* ¼ *η*° þ *Δη* (14)

*λ ρ*ð Þ¼ *; T λ*0ð Þþ *T* Δ*λr*ð Þþ *ρ; T* Δ*λC*ð Þ *ρ; T* (15)

*<sup>f</sup> ; <sup>ρ</sup><sup>h</sup>* 

*<sup>η</sup>*° <sup>¼</sup> *<sup>C</sup>T*<sup>1</sup>

In Eq. (11), T is temperature in K, M is the molar mass in g/mol, σ is the diameter of the rigid sphere in nm, and C is a constant depending of the molecule considered. Chapman-Enskog cited in Poling and Prausnitz [44] have introduced an additional term called "collision integral" which takes into account the collision

*<sup>η</sup>*° <sup>¼</sup> *<sup>K</sup> <sup>T</sup>*<sup>1</sup>

Concerning thermal conductivity, λ0(T) represents the dilute gas thermal

*λ*<sup>0</sup> ¼ *A*<sup>1</sup> þ *A*2ð Þþ *T=TC A*3ð Þ *T=TC*

tion between molecules cannot be neglected, and so it is necessary to apply a correction (like a residual term for equation of state). Equations (14) and (15) lead

When the pressure and so the density of the fluid increases, molecular interac-

In Eq. (15), Δλ<sup>r</sup> (ρ, T) is the residual thermal conductivity, and ΔλC(ρ, T) is the

The R134a is the reference fluid for the refrigerants [42], but for the hydrocarbons, it is better to consider propane or methane [45]. The viscosity and thermal conductivity of the other fluids are calculated from the properties of reference fluids. Critical properties of the fluid are required. Equation (16) presents the

*<sup>η</sup>*ð Þ¼ *<sup>T</sup> <sup>η</sup>*°ð Þþ *<sup>T</sup> Δη<sup>R</sup> <sup>T</sup>*

1 2*h*�<sup>2</sup> <sup>3</sup> *M MR* <sup>1</sup> 2

, and *F<sup>η</sup>* ¼ *f*

*ϵ k <sup>i</sup>*

We will present the results obtained for three binary systems. The first one concerns a mixture of CO2 and R1234ze(e) published by Wang et al. [12]). **Figure 14** presents the phase diagram. The system presents no azeotropic behavior. We can notice that with the experimental data, we can also predict a critical point using asymptotic laws of behavior [12]. **Figure 15** presents a comparison with the critical point measured by Juntaratchat et al. [50] using a critical point setup similar to the equipment already presented in Section 4.

The binary system R245fa + isopentane is presented on **Figure 16** at 392.87 K. Measurement was done using static-analytic method [51]. We have used REFPROP 10.0 to correlate the data (REFPROP 10.0 [52] uses Fundamental Helmholtz equation). We can observe a good agreement between REFPROP prediction and the experimental data (we have one comment concerning this point: the reference of the data used in the data treatment by REFPROP is not clearly mentioned).

#### **Figure 14.**

*Pressure as a function of CO2 mole fraction in the CO2. (1)*�*R-1234ze(E) and (2) mixture at different temperatures. <sup>Δ</sup>, 283.32 K; o, 293.15 K;* ⃞*, 298.15 K; ▲, 308.13 K; ●, 318.11 K; ■, 333.01 K;* �*, 353.02 K. Solid lines: calculated with Peng-Robinson EoS [47], Wong-Sandler mixing rules [48], and NRTL [49] activity coefficient model [12].*

#### **Figure 15.**

*Critical pressure of the binary system CO2 (1) +R-1234ze(E) (2) [12]. Solid line: calculated using PR EoS, Wong-Sandler mixing rules, and NRTL activity coefficient model. Δ, experimental data from Juntaratchat et al. [50]; ▲, predicted using power laws with asymptotic behavior at critical point.*

#### **Figure 16.**

*Pressure as a function of CO2 mole fraction in the isopentane. (1) R245fa and (2) mixture at 392.87 K. Comparison between experimental data [51] and modeling using REFPROP 10.0.*

of the critical point was obtained by an isochoric method used by Tanaka and

*saturation; () 362.90 K; (*⋄*) 355.18 K and (*⃞*) 303.28 K; O, critical point [20].*

*Pressure density phase diagram of hexafluoropropene (R1216). (Δ), experimental densities at saturation; out of*

*The system R32 (1) +R290 (2) +R227ea (3) [53]. Pressure versus temperature diagram for each composition. Mixture 1: 1 = 0.322, 2 = 0.123, (□) experimental bubble points. Mixture 2: 1 = 0.135, 2 = 0.174, (○)*

*experimental bubble points. Mixture 3: 1 = 0.493, 2 = 0.127, (Δ) experimental bubble points.*

*Experimental Determination of Thermophysical Properties of Working Fluids for ORC…*

*DOI: http://dx.doi.org/10.5772/intechopen.87113*

ison with prediction using REFPROP 10.0. A good agreement is observed.

Capillary viscometer was used by Laesecke et al. [57] to determine the dynamic viscosity of liquid R245fa at saturation. **Figure 20** presents the results and compar-

Marrucho et al. [58] have used the transient hot-wire technique to measure the thermal conductivity of R365mfc. **Figure 21** presents the results obtained at 336.85

Higashi [21].

**35**

**Figure 18.**

**Figure 17.**

**6.4 Dynamic viscosity**

**6.5 Thermal conductivity**

#### **6.2 Bubble point**

Variable volume cell was used to determine bubble pressure of the ternary system composed with R32 + R290 + R227ea [53]. **Figure 17** presents the results obtained. The data were correlated by a cubic equation of state (Redlich-Kwong-Soave EoS [54], MHV1 [55] mixing rules, and NRTL [49] activity coefficient model).

#### **6.3 Densities**

Vibrating tube densitometer technique was used to measure the densities of the R1216 [20]. The results are presented on **Figure 18**. The same technique is used to obtain density data of R1234yf (**Figure 19**) at saturation [56]. Density at the vicinity *Experimental Determination of Thermophysical Properties of Working Fluids for ORC… DOI: http://dx.doi.org/10.5772/intechopen.87113*

#### **Figure 17.**

*The system R32 (1) +R290 (2) +R227ea (3) [53]. Pressure versus temperature diagram for each composition. Mixture 1: 1 = 0.322, 2 = 0.123, (□) experimental bubble points. Mixture 2: 1 = 0.135, 2 = 0.174, (○) experimental bubble points. Mixture 3: 1 = 0.493, 2 = 0.127, (Δ) experimental bubble points.*

#### **Figure 18.**

**6.2 Bubble point**

model).

**34**

**Figure 16.**

**Figure 15.**

**6.3 Densities**

Variable volume cell was used to determine bubble pressure of the ternary system composed with R32 + R290 + R227ea [53]. **Figure 17** presents the results obtained. The data were correlated by a cubic equation of state (Redlich-Kwong-Soave EoS [54], MHV1 [55] mixing rules, and NRTL [49] activity coefficient

*Pressure as a function of CO2 mole fraction in the isopentane. (1) R245fa and (2) mixture at 392.87 K.*

*Comparison between experimental data [51] and modeling using REFPROP 10.0.*

*Critical pressure of the binary system CO2 (1) +R-1234ze(E) (2) [12]. Solid line: calculated using PR EoS, Wong-Sandler mixing rules, and NRTL activity coefficient model. Δ, experimental data from Juntaratchat*

*et al. [50]; ▲, predicted using power laws with asymptotic behavior at critical point.*

*Organic Rankine Cycles for Waste Heat Recovery - Analysis and Applications*

Vibrating tube densitometer technique was used to measure the densities of the R1216 [20]. The results are presented on **Figure 18**. The same technique is used to obtain density data of R1234yf (**Figure 19**) at saturation [56]. Density at the vicinity

*Pressure density phase diagram of hexafluoropropene (R1216). (Δ), experimental densities at saturation; out of saturation; () 362.90 K; (*⋄*) 355.18 K and (*⃞*) 303.28 K; O, critical point [20].*

of the critical point was obtained by an isochoric method used by Tanaka and Higashi [21].

#### **6.4 Dynamic viscosity**

Capillary viscometer was used by Laesecke et al. [57] to determine the dynamic viscosity of liquid R245fa at saturation. **Figure 20** presents the results and comparison with prediction using REFPROP 10.0. A good agreement is observed.

#### **6.5 Thermal conductivity**

Marrucho et al. [58] have used the transient hot-wire technique to measure the thermal conductivity of R365mfc. **Figure 21** presents the results obtained at 336.85

#### **Figure 19.**

*Pressure density phase diagram of R1234yf at saturation. (Δ) data from Tanaka and Higashi [X], (▲) Coquelet et al. [56], () critical point from REFPROP. Solid line, correlation presented in Coquelet et al. [20]; (—), Peng-Robinson EoS.*

techniques are very accurate, and we recommend to use the experimental technique with which the operator/engineer is the most familiar with. It is obvious to see that we have the capability to determine all the thermophysical properties of interest for the design and optimization of ORC. In our opinion, there are two main challenges for the future. The first one concerns the development of equipment which permits the determination of several thermophysical properties together and particularly thermophysical properties at equilibrium. The second one concerns the development of equipment which require a small quantity of sample and so the utilization of in situ analysis techniques. In effect, it is difficult to have important quantity of new synthesis molecules (with high purity) to realize the measurement of accurate thermophysical properties of pure components and mixtures. The experimental data will be used to adjust parameters on models or correlations. Data acquisition is an essential step for a good working fluid design. In the literature an optimal selection (**Figure 22**) of working fluids as a function of the temperature of the heating medium exists [59]. This classification does not concern mixtures, and in the case of the utilization of mixtures, experimental characterization has to be done.

*Thermal conductivity of R365mfc as a function of pressure. Symbol: experimental data from Marrucho et al.*

*Experimental Determination of Thermophysical Properties of Working Fluids for ORC…*

*DOI: http://dx.doi.org/10.5772/intechopen.87113*

*[58] at (Δ) 336.85 K and (▲) 377.40 K. Solid line: prediction using REFPROP 10.0.*

*Some working fluid for several level of temperature of heating medium [59].*

**Figure 21.**

**Figure 22.**

**37**

#### **Figure 20.**

*Dynamic viscosity of R245fa at saturation. Symbol: experimental data from Laesecke et al. [57]. Solid line: prediction using REFPROP 10.0.*

and 377.4 K for several pressures from 1 to 4.5 bar. Comparison was done with prediction from REFPROP 10.0. A good agreement is observed.

#### **7. Conclusion**

The optimization of ORC depends strongly on the capability of models to predict the thermophysical properties of working fluids for their selection and retrofit in existing ORC equipment. The main thermophysical properties include phase equilibria (and so critical point), densities, speed of sound, dynamic viscosity, and thermal conductivity. Through this book chapter, the reader can easily understand that several experimental techniques developed to measure the thermophysical properties exist. Some of them were presented and described. In general, these

*Experimental Determination of Thermophysical Properties of Working Fluids for ORC… DOI: http://dx.doi.org/10.5772/intechopen.87113*

#### **Figure 21.**

*Thermal conductivity of R365mfc as a function of pressure. Symbol: experimental data from Marrucho et al. [58] at (Δ) 336.85 K and (▲) 377.40 K. Solid line: prediction using REFPROP 10.0.*

techniques are very accurate, and we recommend to use the experimental technique with which the operator/engineer is the most familiar with. It is obvious to see that we have the capability to determine all the thermophysical properties of interest for the design and optimization of ORC. In our opinion, there are two main challenges for the future. The first one concerns the development of equipment which permits the determination of several thermophysical properties together and particularly thermophysical properties at equilibrium. The second one concerns the development of equipment which require a small quantity of sample and so the utilization of in situ analysis techniques. In effect, it is difficult to have important quantity of new synthesis molecules (with high purity) to realize the measurement of accurate thermophysical properties of pure components and mixtures. The experimental data will be used to adjust parameters on models or correlations. Data acquisition is an essential step for a good working fluid design. In the literature an optimal selection (**Figure 22**) of working fluids as a function of the temperature of the heating medium exists [59]. This classification does not concern mixtures, and in the case of the utilization of mixtures, experimental characterization has to be done.


#### **Figure 22.**

and 377.4 K for several pressures from 1 to 4.5 bar. Comparison was done with

*Dynamic viscosity of R245fa at saturation. Symbol: experimental data from Laesecke et al. [57]. Solid line:*

*Pressure density phase diagram of R1234yf at saturation. (Δ) data from Tanaka and Higashi [X], (▲) Coquelet et al. [56], () critical point from REFPROP. Solid line, correlation presented in Coquelet et al. [20];*

*Organic Rankine Cycles for Waste Heat Recovery - Analysis and Applications*

The optimization of ORC depends strongly on the capability of models to predict the thermophysical properties of working fluids for their selection and retrofit in existing ORC equipment. The main thermophysical properties include phase equilibria (and so critical point), densities, speed of sound, dynamic viscosity, and thermal conductivity. Through this book chapter, the reader can easily understand that several experimental techniques developed to measure the thermophysical properties exist. Some of them were presented and described. In general, these

prediction from REFPROP 10.0. A good agreement is observed.

**7. Conclusion**

**36**

*prediction using REFPROP 10.0.*

**Figure 20.**

**Figure 19.**

*(—), Peng-Robinson EoS.*

*Some working fluid for several level of temperature of heating medium [59].*

*Organic Rankine Cycles for Waste Heat Recovery - Analysis and Applications*

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*DOI: http://dx.doi.org/10.5772/intechopen.87113*

*Experimental Determination of Thermophysical Properties of Working Fluids for ORC…*

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#### **Author details**

Christophe Coquelet\*, Alain Valtz and Pascal Théveneau CTP-Centre of Thermodynamics of Processes, Mines ParisTech, PSL University, France

\*Address all correspondence to: christophe.coquelet@mines-paristech.fr

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Experimental Determination of Thermophysical Properties of Working Fluids for ORC… DOI: http://dx.doi.org/10.5772/intechopen.87113*

#### **References**

[1] Badr O, Probert SD, O'Callaghan PW. Selecting a working fluid for a Rankine cycle engine. Applied Energy. 1985;**21**:1-42. DOI: 10.1016/0306-2619 (85)90072-8

[2] Saleh B, Kogalbauer G, Wendland M, Fischer J. Working fluids for low temperature organic Rankine cycles. Energy. 2007;**32**:1210-1221. DOI: 10.1016/j.energy.2006.07.001

[3] Maizza V, Maizza A. Unconventional working fluids in organic Rankine Cycles for waste energy recovery systems. Applied Thermal Engineering. 2001;**21**:381-390. DOI: 10.1016/ S1359-4311(00)00044-2

[4] Liu B, Riviere P, Coquelet C, Gicquel R, David F. Investigation of a two stage Rankine cycle of electricity power plants. Applied Energy. 2012;**100**: 285-294. DOI: 10.1016/j. apenergy.2012.05.044

[5] Rahbar K, Mahmoud S, Al-Dadah RK, Moazami N, Mirhadizadeh SA. Review of organic Rankine cycle for small-scale applications. Energy Conversion and Management. 2017;**134**: 135-155. DOI: 10.1016/j. enconman.2016.12.023

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[12] Wang S, Fauve R, Coquelet C, Valtz A, Houriez C, Artola PA, et al. Vapor– liquid equilibrium and molecular simulation data for carbon dioxide (CO2)+ trans-1, 3, 3, 3-tetrafluoroprop-1-ene (R-1234ze (E)) mixture at temperatures from 283.32 to 353.02 K and pressures up to 7.6 MPa. International Journal of Refrigeration. 2019;**98**:362-371. DOI: 10.1016/j. ijrefrig.2018.10.032

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[14] Fontalba F, Richon D, Renon H. Simultaneous determination of PVT and

**Author details**

France

**38**

Christophe Coquelet\*, Alain Valtz and Pascal Théveneau

*Organic Rankine Cycles for Waste Heat Recovery - Analysis and Applications*

provided the original work is properly cited.

CTP-Centre of Thermodynamics of Processes, Mines ParisTech, PSL University,

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

\*Address all correspondence to: christophe.coquelet@mines-paristech.fr

VLE data of binary mixtures up to 45 MPa and 433 K: A new apparatus without phase sampling and analysis. The Review of Scientific Instruments. 1984;**55**:944-951. DOI: 10.1063/1.1137870

[15] Tzirakis F, Stringari P, Von Solms N, Coquelet C, Kontogeorgis G. Hydrate equilibrium data for the CO2+ N2 system with the use of tetra-n-butylammonium bromide (TBAB), cyclopentane (CP) and their mixture. Fluid Phase Equilibria. 2016;**2016, 408**:240-247. DOI: 10.1016/j.fluid.2015.09.021

[16] Wagner W, Brachthäuser K, Kleinrahm R, Lösch HW. A new, accurate single-sinker densitometer for temperatures from 233 to 523 K at pressures up to 30 MPa. International Journal of Thermophysics. 1995;**16**(2): 399-411. DOI: 10.1007/BF01441906

[17] Bridgman PW. The volume of eighteen liquids as a function of pressure and temperature. Proceedings of the American Academy of Arts and Sciences. 1931;**66**(5):185-233. DOI: 10.2307/20026332

[18] Straty GC, Palavra AMF. Automated high temperature PVT apparatus with data for propane. Journal of Research of the National Bureau of Standards. 1984; **89**(5):375-383

[19] Goodwin ARH, Marsh KN, Wakeham WA. Measurement of the Thermodynamic Properties of Single Phases, Experimental Thermodynamics Vol VI IUPAC. Amsterdam: Elsevier; 2003

[20] Coquelet C, Ramjugernath D, Madani H, Valtz A, Naidoo P, Meniai AH. Experimental measurement of vapor pressures and densities of pure hexafluoropropylene. Journal of Chemical & Engineering Data. 2010;**55**(6): 2093-2099. DOI: 10.1021/je900596d

[21] Tanaka K, Higashi Y. Thermodynamic properties of HFO-1234yf (2, 3, 3, 3tetrafluoropropene). International Journal of Refrigeration. 2010;**33**(3):474-479. DOI: 10.1016/j.ijrefrig.2009.10.003

[28] Daridon JL, Cassiède M, Paillol JH, Pauly J. Viscosity measurements of liquids under pressure by using the quartz crystal resonators. Review of Scientific Instruments. 2011;**82**(9):095114. DOI: 10.1063/

*DOI: http://dx.doi.org/10.5772/intechopen.87113*

[36] Chapman WG, Gubbins KE, Jackson G, Radosz M. SAFT: Equationof-state solution model for associating fluids. Fluid Phase Equilibria. 1989;**52**: 31-38. DOI: 10.1016/0378-3812(89)

[37] Gil-Villegas A, Galindo A, Whitehead PJ, Mills SJ, Jackson G, Burgess AN. Statistical associating fluid theory for chain molecules with attractive potentials of variable range. The Journal of Chemical Physics. 1997;**106**(10):4168-4186. DOI:

[38] Gross J, Sadowski G. Perturbedchain SAFT: An equation of state based on a perturbation theory for chain molecules. Industrial & Engineering Chemistry Research. 2001;**40**(4): 1244-1260. DOI: 10.1021/ie0003887

[39] Lafitte T, Apostolakou A, Avendano C, Galindo A, Adjiman CS, Müller EA, et al. Accurate statistical associating fluid theory for chain molecules formed from Mie segments. The Journal of Chemical Physics. 2013;**139**(15):154504.

thermodynamischen Eigenschaften von R 152a, R 134a and ihren Gemischen-Messungen Und Fundamentalgleichungen PhD. Germany: University of Hannover;

[41] Mac Linden MO, Klein SA. A next generation refrigerant properties database. In: International Refrigeration and Air Conditioning conference 1996:

[42] Huber ML, Laesecke A, Perkins RA. Model for the viscosity and thermal conductivity of refrigerants, including a new correlation for the viscosity of R134a. Industrial & Engineering Chemistry Research. 2003;**42**: 3163-3178. DOI: 10.1021/ie0300880

[43] Klein SA, McLinden MO, Laesecke

A. An improved extended

DOI: 10.1063/1.4819786

[40] Tillner-Roth R. Die

paper 357. pp. 409-414

1993

80308-5

*Experimental Determination of Thermophysical Properties of Working Fluids for ORC…*

10.1063/1.473101

[29] Caudwell D, Goodwin AR, Trusler JM. A robust vibrating wire viscometer for reservoir fluids: results for toluene and n-decane. Journal of Petroleum Science and Engineering. 2004;**44**(3–4): 333-340. DOI: 10.1016/j.petrol.2004.

[30] El Abbadi J. Thermodynamic properties of new refrigerants [thesis].

[31] Le N, Viscosité B. Définitions et dispositifs de mesure. Techniques de l'ingénieur. Constantes physico-

[32] Kashefi K, Chapoy A, Bell K, Tohidi B. Viscosity of binary and multicomponent hydrocarbon fluids at high pressure and high temperature

conditions: Measurements and predictions. Journal of Petroleum Science and Engineering. 2013;**112**: 153-160. DOI: 10.1016/j.petrol.2013.

[33] Tait RWF, Hills BA. Methods for determining liquid thermal conductivities. Industrial and Engineering Chemistry. 1964;

**56**(7):29-35. DOI: 10.1021:ie50655a005

[34] Healy JJ, De Groot JJ, Kestin J. The theory of the hot-wire method for measuring thermal conductivity. Physica C. 1976;**82**(2):392-408. DOI: 10.1016/0378-4363(76)90203-5

[35] Marsh KN, Perkins RA, Ramires MLV. Measurement and correlation from 86 to 600K at pressures to 70 MPa. Journal of Chemical & Engineering Data. 2002;**47**:932-940. DOI: 10.1021/

Mines ParisTech; 2016

chimiques. 2004:3K478

1.3638465

02.019

10.021

je010001m

**41**

[22] Moldover MR, Mehl JB, Greenspan M. Gas-filled spherical resonators: Theory and experiment. The Journal of the Acoustical Society of America. 1986; **79**(2):253-272. DOI: 10.1121/1.393566

[23] Trusler JPM, Zarari M. The speed of sound and derived thermodynamic properties of methane at temperatures between 275 and 375 K and pressures up to 10 MPa. The Journal of Chemical Thermodynamics. 1992;**24**(9): 973-991. DOI: 10.1016/S0021-9614(05) 80008-4

[24] Benedetto G, Gavioso RM, Spagnolo R, Marcarino P, Merlone A. Acoustic measurements of the thermodynamic temperature between the triple point of mercury and 380 K. Metrologia. 2004; **41**(1):74-98

[25] Ahmadi P, Chapoy A, Tohidi B. Density, speed of sound and derived thermodynamic properties of a synthetic natural gas. Journal of Natural Gas Science and Engineering. 2017;**40**: 249-266. DOI: 10.1016/j.jngse.2017.02. 009Get

[26] Al Ghafri SZ, Rowland D, Akhfash M, Arami-Niya A, Khamphasith M, Xiao X, et al. Thermodynamic properties of hydrofluoroolefin (R1234yf and R1234ze (E)) refrigerant mixtures: Density, vapour-liquid equilibrium, and heat capacity data and modelling. International Journal of Refrigeration. 2019;**98**:249-260. DOI: 10.1016/j. ijrefrig.2018.10.027

[27] Calvignac B, Rodier E, Letourneau JJ, Vitoux P, Aymonier C, Fages J. Development of an improved falling ball viscometer for high-pressure measurements with supercritical CO2. The Journal of Supercritical Fluids. 2010;**55**(1):96-106. DOI: 10.1016/j. supflu.2010.07.012

*Experimental Determination of Thermophysical Properties of Working Fluids for ORC… DOI: http://dx.doi.org/10.5772/intechopen.87113*

[28] Daridon JL, Cassiède M, Paillol JH, Pauly J. Viscosity measurements of liquids under pressure by using the quartz crystal resonators. Review of Scientific Instruments. 2011;**82**(9):095114. DOI: 10.1063/ 1.3638465

VLE data of binary mixtures up to 45 MPa and 433 K: A new apparatus without phase sampling and analysis. The Review of Scientific Instruments. 1984;**55**:944-951. DOI: 10.1063/1.1137870

*Organic Rankine Cycles for Waste Heat Recovery - Analysis and Applications*

tetrafluoropropene). International Journal of Refrigeration. 2010;**33**(3):474-479. DOI: 10.1016/j.ijrefrig.2009.10.003

[22] Moldover MR, Mehl JB, Greenspan M. Gas-filled spherical resonators: Theory and experiment. The Journal of the Acoustical Society of America. 1986; **79**(2):253-272. DOI: 10.1121/1.393566

[23] Trusler JPM, Zarari M. The speed of sound and derived thermodynamic properties of methane at temperatures between 275 and 375 K and pressures

Chemical Thermodynamics. 1992;**24**(9): 973-991. DOI: 10.1016/S0021-9614(05)

[24] Benedetto G, Gavioso RM, Spagnolo R, Marcarino P, Merlone A. Acoustic measurements of the thermodynamic temperature between the triple point of mercury and 380 K. Metrologia. 2004;

[25] Ahmadi P, Chapoy A, Tohidi B. Density, speed of sound and derived thermodynamic properties of a

synthetic natural gas. Journal of Natural Gas Science and Engineering. 2017;**40**: 249-266. DOI: 10.1016/j.jngse.2017.02.

[26] Al Ghafri SZ, Rowland D, Akhfash M, Arami-Niya A, Khamphasith M, Xiao X, et al. Thermodynamic properties of hydrofluoroolefin (R1234yf and R1234ze (E)) refrigerant mixtures: Density, vapour-liquid equilibrium, and heat capacity data and modelling. International Journal of Refrigeration. 2019;**98**:249-260. DOI: 10.1016/j.

[27] Calvignac B, Rodier E, Letourneau JJ, Vitoux P, Aymonier C, Fages J. Development of an improved falling ball

measurements with supercritical CO2. The Journal of Supercritical Fluids. 2010;**55**(1):96-106. DOI: 10.1016/j.

viscometer for high-pressure

up to 10 MPa. The Journal of

80008-4

**41**(1):74-98

009Get

ijrefrig.2018.10.027

supflu.2010.07.012

[15] Tzirakis F, Stringari P, Von Solms N, Coquelet C, Kontogeorgis G. Hydrate equilibrium data for the CO2+ N2 system with the use of tetra-n-butylammonium bromide (TBAB), cyclopentane (CP) and their mixture. Fluid Phase Equilibria. 2016;**2016, 408**:240-247. DOI: 10.1016/j.fluid.2015.09.021

[16] Wagner W, Brachthäuser K, Kleinrahm R, Lösch HW. A new, accurate single-sinker densitometer for temperatures from 233 to 523 K at pressures up to 30 MPa. International Journal of Thermophysics. 1995;**16**(2): 399-411. DOI: 10.1007/BF01441906

[17] Bridgman PW. The volume of eighteen liquids as a function of pressure and temperature. Proceedings of the American Academy of Arts and Sciences. 1931;**66**(5):185-233. DOI:

[18] Straty GC, Palavra AMF. Automated high temperature PVT apparatus with data for propane. Journal of Research of the National Bureau of Standards. 1984;

[20] Coquelet C, Ramjugernath D, Madani

hexafluoropropylene. Journal of Chemical

[21] Tanaka K, Higashi Y. Thermodynamic properties of HFO-1234yf (2, 3, 3, 3-

H, Valtz A, Naidoo P, Meniai AH. Experimental measurement of vapor pressures and densities of pure

& Engineering Data. 2010;**55**(6): 2093-2099. DOI: 10.1021/je900596d

[19] Goodwin ARH, Marsh KN, Wakeham WA. Measurement of the Thermodynamic Properties of Single Phases, Experimental Thermodynamics Vol VI IUPAC. Amsterdam: Elsevier;

10.2307/20026332

**89**(5):375-383

2003

**40**

[29] Caudwell D, Goodwin AR, Trusler JM. A robust vibrating wire viscometer for reservoir fluids: results for toluene and n-decane. Journal of Petroleum Science and Engineering. 2004;**44**(3–4): 333-340. DOI: 10.1016/j.petrol.2004. 02.019

[30] El Abbadi J. Thermodynamic properties of new refrigerants [thesis]. Mines ParisTech; 2016

[31] Le N, Viscosité B. Définitions et dispositifs de mesure. Techniques de l'ingénieur. Constantes physicochimiques. 2004:3K478

[32] Kashefi K, Chapoy A, Bell K, Tohidi B. Viscosity of binary and multicomponent hydrocarbon fluids at high pressure and high temperature conditions: Measurements and predictions. Journal of Petroleum Science and Engineering. 2013;**112**: 153-160. DOI: 10.1016/j.petrol.2013. 10.021

[33] Tait RWF, Hills BA. Methods for determining liquid thermal conductivities. Industrial and Engineering Chemistry. 1964; **56**(7):29-35. DOI: 10.1021:ie50655a005

[34] Healy JJ, De Groot JJ, Kestin J. The theory of the hot-wire method for measuring thermal conductivity. Physica C. 1976;**82**(2):392-408. DOI: 10.1016/0378-4363(76)90203-5

[35] Marsh KN, Perkins RA, Ramires MLV. Measurement and correlation from 86 to 600K at pressures to 70 MPa. Journal of Chemical & Engineering Data. 2002;**47**:932-940. DOI: 10.1021/ je010001m

[36] Chapman WG, Gubbins KE, Jackson G, Radosz M. SAFT: Equationof-state solution model for associating fluids. Fluid Phase Equilibria. 1989;**52**: 31-38. DOI: 10.1016/0378-3812(89) 80308-5

[37] Gil-Villegas A, Galindo A, Whitehead PJ, Mills SJ, Jackson G, Burgess AN. Statistical associating fluid theory for chain molecules with attractive potentials of variable range. The Journal of Chemical Physics. 1997;**106**(10):4168-4186. DOI: 10.1063/1.473101

[38] Gross J, Sadowski G. Perturbedchain SAFT: An equation of state based on a perturbation theory for chain molecules. Industrial & Engineering Chemistry Research. 2001;**40**(4): 1244-1260. DOI: 10.1021/ie0003887

[39] Lafitte T, Apostolakou A, Avendano C, Galindo A, Adjiman CS, Müller EA, et al. Accurate statistical associating fluid theory for chain molecules formed from Mie segments. The Journal of Chemical Physics. 2013;**139**(15):154504. DOI: 10.1063/1.4819786

[40] Tillner-Roth R. Die thermodynamischen Eigenschaften von R 152a, R 134a and ihren Gemischen-Messungen Und Fundamentalgleichungen PhD. Germany: University of Hannover; 1993

[41] Mac Linden MO, Klein SA. A next generation refrigerant properties database. In: International Refrigeration and Air Conditioning conference 1996: paper 357. pp. 409-414

[42] Huber ML, Laesecke A, Perkins RA. Model for the viscosity and thermal conductivity of refrigerants, including a new correlation for the viscosity of R134a. Industrial & Engineering Chemistry Research. 2003;**42**: 3163-3178. DOI: 10.1021/ie0300880

[43] Klein SA, McLinden MO, Laesecke A. An improved extended

corresponding states method for estimation of viscosity of pure refrigerants and mixtures. International Journal of Refrigeration. 1997;**20**(3): 208-217. DOI: 10.1016/S0140-7007(96) 00073-4

[44] Poling E, Prausnitz JM. The Properties of Gases and Liquids. McGraw-Hill Professional. New York: Mcgraw-Hill; 2000

[45] Huber ML, Hanley HJM. The Corresponding-States Principle: Dense Fluids. Transport Properties of Fluids. Cambridge University Press, IUPAC; 1996. pp. 283-296

[46] Ely JF, Huber ML. A predictive extended corresponding states model for pure and mixed refrigerants including a new equation of state for R134a. International Journal of Refrigeration. 1994;**17**:18-31. DOI: 10.1016/0140-7007(94)90083-3

[47] Peng DY, Robinson DB. A new twoconstant equation of state. Industrial and Engineering Chemistry Fundamentals. 1976;**15**(1):59-64. DOI: 10.1021:i160057a011

[48] Wong DSH, Sandler SI. A theoretically correct mixing rule for cubic equations of state. AICHE Journal. 1992;**38**(5):671-680. DOI: 10.1002: aic.690380505

[49] Renon H, Prausnitz JM. Local compositions in thermodynamic excess functions for liquid mixtures. AICHE Journal. 1968, 1968;**14**(1):135-144. DOI: 10.1002/aic.690140124

[50] Juntarachat N, Valtz A, Coquelet C, Privat R, Jaubert JN. Experimental mea surements and correlation of vaporliquid equilibrium and critical data for the CO2 + R1234yf and CO2 + R1234ze (E) binary mixtures. International Journal of Refrigeration. 2014;**47**: 141-152. DOI: 10.1016/j.ijrefrig.2014. 09.001

[51] El Ahmar E, Valtz A, Paricaud P, Coquelet C, Abbas L, Rached W. Vapour–liquid equilibrium of binary systems containing pentafluorochemicals from 363 to 413 K: Measurement and modelling with Peng– Robinson and three SAFT-like equations of states. International Journal of Refrigeration. 2012;**35**(8):2297-2310. DOI: 10.1016/j.ijrefrig.2012.05.016

[58] Marrucho IM, Oliveira NS, Dohrn R. Vapor-phase thermal conductivity, vapor pressure, and liquid density of R365mfc. Journal of Chemical & Engineering Data. 2002;**47**(3):554-558.

*DOI: http://dx.doi.org/10.5772/intechopen.87113*

*Experimental Determination of Thermophysical Properties of Working Fluids for ORC…*

[59] Wang D, Ling X, Peng H, Liu L, Tao L. Efficiency and optimal performance evaluation of organic Rankine cycle for low grade waste heat power generation. Energy. 2013;**50**:343-352. DOI: 10.1016/

DOI: 10.1021/je015534

j.energy.2012.11.010

**43**

[52] Lemmon EW, Bell IH, Huber ML, McLinden MO. NIST standard reference database 23: Reference fluid thermodynamic and transport properties-REFPROP (National Institute of Standards and Technology, Boulder, CO) 2018: Version 10.0

[53] Coquelet C, Chareton A, Richon D. Vapour–liquid equilibrium measurements and correlation of the difluoromethane (R32) + propane (R290)+ 1, 1, 1, 2, 3, 3, 3 heptafluoropropane (R227ea) ternary mixture at temperatures from 269.85 to 328.35 K. Fluid Phase Equilibria. 2004; **218**(2):209-214. DOI: 10.1016/j. fluid.2003.12.009

[54] Soave G. Equilibrium constants from a modified Redlich-Kwong equation of state. Chemical Engineering Science. 1972;**27**(6):1197-1203. DOI: 10.1016/0009-2509(72)80096-4

[55] Michelsen ML. A modified Huron-Vidal mixing rule for cubic equations of state. Fluid Phase Equilibria. 1990;**60** (1–2):213-219. DOI: 10.1016/0378-3812 (90)85053-D

[56] Coquelet C, Valtz A, Théveneau P. Personal Communication and Confidential Data

[57] Laesecke A, Hafer RF. Viscosity of fluorinated propane isomers. 2. Measurements of three compounds and model comparisons. Journal of Chemical & Engineering Data. 1998;**43**(1):84-92. DOI: 10.1021/je970186q

*Experimental Determination of Thermophysical Properties of Working Fluids for ORC… DOI: http://dx.doi.org/10.5772/intechopen.87113*

[58] Marrucho IM, Oliveira NS, Dohrn R. Vapor-phase thermal conductivity, vapor pressure, and liquid density of R365mfc. Journal of Chemical & Engineering Data. 2002;**47**(3):554-558. DOI: 10.1021/je015534

corresponding states method for estimation of viscosity of pure

[44] Poling E, Prausnitz JM. The Properties of Gases and Liquids. McGraw-Hill Professional. New York:

[45] Huber ML, Hanley HJM. The Corresponding-States Principle: Dense Fluids. Transport Properties of Fluids. Cambridge University Press, IUPAC;

[46] Ely JF, Huber ML. A predictive extended corresponding states model for pure and mixed refrigerants including a new equation of state for R134a. International Journal of Refrigeration. 1994;**17**:18-31. DOI: 10.1016/0140-7007(94)90083-3

[47] Peng DY, Robinson DB. A new twoconstant equation of state. Industrial

Fundamentals. 1976;**15**(1):59-64. DOI:

and Engineering Chemistry

[48] Wong DSH, Sandler SI. A theoretically correct mixing rule for cubic equations of state. AICHE Journal. 1992;**38**(5):671-680. DOI: 10.1002:

[49] Renon H, Prausnitz JM. Local compositions in thermodynamic excess functions for liquid mixtures. AICHE Journal. 1968, 1968;**14**(1):135-144. DOI:

[50] Juntarachat N, Valtz A, Coquelet C, Privat R, Jaubert JN. Experimental mea surements and correlation of vaporliquid equilibrium and critical data for the CO2 + R1234yf and CO2 + R1234ze (E) binary mixtures. International Journal of Refrigeration. 2014;**47**: 141-152. DOI: 10.1016/j.ijrefrig.2014.

10.1002/aic.690140124

10.1021:i160057a011

aic.690380505

09.001

**42**

Mcgraw-Hill; 2000

1996. pp. 283-296

00073-4

refrigerants and mixtures. International Journal of Refrigeration. 1997;**20**(3): 208-217. DOI: 10.1016/S0140-7007(96)

*Organic Rankine Cycles for Waste Heat Recovery - Analysis and Applications*

[51] El Ahmar E, Valtz A, Paricaud P, Coquelet C, Abbas L, Rached W. Vapour–liquid equilibrium of binary

pentafluorochemicals from 363 to 413 K: Measurement and modelling with Peng– Robinson and three SAFT-like equations of states. International Journal of Refrigeration. 2012;**35**(8):2297-2310. DOI: 10.1016/j.ijrefrig.2012.05.016

[52] Lemmon EW, Bell IH, Huber ML, McLinden MO. NIST standard reference

properties-REFPROP (National Institute of Standards and Technology, Boulder,

[53] Coquelet C, Chareton A, Richon D.

measurements and correlation of the difluoromethane (R32) + propane

heptafluoropropane (R227ea) ternary mixture at temperatures from 269.85 to 328.35 K. Fluid Phase Equilibria. 2004; **218**(2):209-214. DOI: 10.1016/j.

[54] Soave G. Equilibrium constants from a modified Redlich-Kwong

equation of state. Chemical Engineering Science. 1972;**27**(6):1197-1203. DOI: 10.1016/0009-2509(72)80096-4

[55] Michelsen ML. A modified Huron-Vidal mixing rule for cubic equations of state. Fluid Phase Equilibria. 1990;**60** (1–2):213-219. DOI: 10.1016/0378-3812

[56] Coquelet C, Valtz A, Théveneau P.

[57] Laesecke A, Hafer RF. Viscosity of fluorinated propane isomers. 2.

Measurements of three compounds and model comparisons. Journal of Chemical & Engineering Data. 1998;**43**(1):84-92.

Personal Communication and

database 23: Reference fluid thermodynamic and transport

CO) 2018: Version 10.0

Vapour–liquid equilibrium

(R290)+ 1, 1, 1, 2, 3, 3, 3-

fluid.2003.12.009

(90)85053-D

Confidential Data

DOI: 10.1021/je970186q

systems containing

[59] Wang D, Ling X, Peng H, Liu L, Tao L. Efficiency and optimal performance evaluation of organic Rankine cycle for low grade waste heat power generation. Energy. 2013;**50**:343-352. DOI: 10.1016/ j.energy.2012.11.010

Section 2

Applications

**45**
