**Table 1.**

**2.1 Case study**

streams to recover energy.

substances.

**Figure 5.**

**460**

**2.2 Energy integration of the process**

*Solar Cells - Theory, Materials and Recent Advances*

and determine the optimal *ΔTmin*.

The case study is a dairy process described in the literature [12]. It operates on batch and the required heat utility is from 8:00 h to 13:00 h (five hours), enough to carry out pasteurisation of milk at 85 °C. Hot water is needful to curd the milk from 8:30 h to 13:00 h (4.5 hours) at 40 °C; more hot water is required at 62 °C to clean the equipment during a period of 2 hours (16:00 h – 18:00 h). **Figure 4** represents

In **Figure 5** the periods of demand for thermal energy of the main operations of the process are shown (squares) and the period of solar energy production is also displayed (parabolic line). **Figure 5** shows the pairing periods, and this allows to determine if the heat supply is direct from the solar collector network or if requires storage, it also helps to define the possible heat exchanges between the process

Next, Pinch Analysis is used to carry out the integration of solar thermal energy

The Composite Curves provide a scheme of pure countercurrent heat transfer of the process streams for a chosen *ΔTmin*. They are used to determine the minimum heating and cooling requirements of the process and this allows the calculation of the minimum transfer area prior to the detailed design of the heat transfer network. In **Figure 6** we have the Composite Curves for a *ΔTmin* of 10 °C where the minimum utilities are determined, which are 294.78 and 260.68 kW of heating and cooling, respectively. It is observed that the thermal load and the temperature level

Determination of the minimum area assumes that there is vertical heat exchange between the Composite Curves throughout the entire enthalpy range. In the graph of the Composite Curves, we can read the amount of heat that will be transferred

Dairy process stream data is shown in **Table 1** including inlet and outlet temperatures and heat capacity. From the data of the currents, the Composite Curves are constructed and determine the minimum hot and cold utilities, and thus the process-process heat exchanges. To deliver the thermal load required by the process, a boiler that produces hot water at 95 °C for 5 hours is used, providing a thermal load of 4,401.01 kWh. The heat transfer coefficients used are 0.8 kW/m2 °C

for water and slightly viscous substances and 0.3 kW/m<sup>2</sup> °C for viscous

of the hot utility can be supplied by solar thermal energy.

*Pairing between major process operations and available irradiance in a day.*

the diverse production stages in a dairy plant at required temperatures.

*Stream data for dairy process*

**Figure 6.** *Composite curves for a ΔTmin of 10 °C.*

between the streams, as well as the values of the outlet and inlet temperatures (at that interval) of the hot streams, like so the values of the outlet temperatures and entry of cold currents. So if the curves, both for hot and cold currents, correspond to only one of them, as happens between an exchange of process current - auxiliary service, we can estimate the necessary area of heat exchange given by Eq. (1) known as the Bath equation, which is based on the countercurrent heat exchange assumption implicit in the compound curves and this leads to the minimum area, only if the global heat transfer coefficients are equal for all exchanges [13].

$$A\_{HRN} = \sum\_{k}^{k \text{ intervals}} \frac{\mathbf{1}}{\Delta T\_{ML}} \left( \sum\_{i}^{\text{hot } i} \frac{q\_i}{h\_i} + \sum\_{j}^{col \, j} \frac{q\_j}{h\_j} \right) \tag{1}$$

The estimate of the total *AHRN* area is obtained by adding the area of each interval (m<sup>2</sup> ), *qi* and *qj* are the thermal exchange loads obtained from the enthalpies in the Composite Curves (kW). *hi* and *h*j are the individual transfer coefficients (kW/m<sup>2</sup> °C). The subscripts *k*, *i* and *j*.

The calculated minimum area is used to determine the cost of the heat recovery network, *CHRN* (USD), of the process based on Eq. (2).

$$\mathbf{C}\_{HRN} = \mathbf{N}\_{\varepsilon} \left[ 26600 + 6500 \left( \frac{A\_{HRN}}{N\_{\varepsilon}} \right)^{0.9} \right] \tag{2}$$

Where *Ne* is the number of equipment, *AHRN* is the area of the heat recovery network (m<sup>2</sup> ) this value corresponds to the exchange area [14]. To determine the cost of auxiliary services, *CAS*, Eq. (3), reported by [15].

$$\mathbf{C}\_{\rm AS} = \mathbf{Q}\_{\rm h} \mathbf{C}\_{\rm ST} + \mathbf{Q}\_{\rm c} \mathbf{C}\_{\rm CO} \tag{3}$$

In Eq. (3) *Qh* and *Qc* are the minimum requirements for heating and cooling the process (kW), while *CST* and *CCO* are the costs associated with steam and cooling water, respectively (USD/kW year). In this study, the cost of heating services is proposed to be 150 USD/kW year and cooling services 35 USD/kW year.

The total cost of the annualised heat recovery network, *CTA HRN* (USD/year), is obtained by adding the estimated cost of capital (*CHRN*) and the annualised service costs (*CAS*), given by Eq. (4)

$$\mathbf{C}\_{\text{TA\\_HRN}} = f\_A \mathbf{C}\_{\text{HRN}} + f\_A \mathbf{C}\_{\text{AS}} \tag{4}$$

determined since it is influenced by the environmental conditions of the place, this must be evaluated to guarantee the supply of the hot utility. This methodology combines this information to lead to the design of the solar thermal installation to reach the target temperature required by the process and satisfy the thermal requirements of the process with the lowest cost and taking care of the restrictions that the process presents. This must be attractive to compete with fossil fuels.

**ΔTmin (°C)**

**Table 2.**

**463**

*Results of pinch analysis to determine optimal ΔTmin.*

**Qh (kW)**

*Solar Energy in Industrial Processes*

**Qc (kW)**

*DOI: http://dx.doi.org/10.5772/intechopen.97008*

**Ne AHRN (m2 )**

**CHRN (USD) CHRNA**

1 159.69 125.65 17 531.63 3,199,987.73 227,046.99 28,351.41 255,398.40 2 174.70 140.66 17 428.05 2,721,302.35 193,083.09 31,128.26 224,211.35 3 189.71 155.67 17 369.75 2,446,943.96 173,616.69 33,905.11 207,521.80 4 204.72 170.68 17 329.89 2,256,861.40 160,129.86 36,681.96 196,811.82 5 219.73 185.63 17 301.89 2,121,959.05 150,558.21 39,456.78 190,014.99 6 234.74 200.64 17 278.22 2,006,954.08 142,398.32 42,233.63 184,631.95 7 249.75 215.65 17 258.87 1,912,212.04 135,676.14 45,010.48 180,686.62 8 264.76 230.66 17 242.64 1,832,205.01 129,999.45 47,787.33 177,786.78 9 279.77 245.67 17 228.77 1,763,388.35 125,116.74 50,564.18 175,680.92 10 294.78 260.68 17 216.70 1,703,160.69 120,843.44 53,341.03 174,184.47 11 309.79 275.69 17 206.12 1,650,130.10 117,080.79 56,117.88 173,198.67 12 324.80 290.70 17 196.77 1,603,030.89 113,738.98 58,894.73 172,633.71 13 339.81 305.71 17 188.45 1,560,908.19 110,750.27 61,671.58 172,421.85 14 354.82 320.72 17 180.99 1,522,985.26 108,059.55 64,448.43 172,507.98 15 369.83 335.73 17 174.26 1,488,643.65 105,622.92 67,225.28 172,848.20 16 384.84 350.74 17 168.16 1,457,391.84 103,405.53 70,002.13 173,407.66 17 399.85 365.75 17 162.60 1,428,847.98 101,380.28 72,778.98 174,159.26 18 414.86 380.76 17 157.53 1,402,675.38 99,523.27 75,555.83 175,079.10 19 429.87 395.77 17 152.88 1,378,625.23 97,816.85 78,332.68 176,149.53 20 444.88 410.78 17 148.61 1,356,470.80 96,244.94 81,109.53 177,354.47 21 459.89 425.79 17 144.67 1,336,008.06 94,793.05 83,886.38 178,679.43 22 474.90 440.79 17 141.04 1,317,077.19 93,449.86 86,662.92 180,112.78 23 489.91 455.81 17 137.69 1,299,526.66 92,204.61 89,440.08 181,644.69 24 504.92 470.82 17 134.58 1,283,244.98 91,049.38 92,216.93 183,266.31 25 521.52 487.41 18 130.09 1,293,338.46 91,765.54 95,286.82 187,052.36 26 539.17 505.12 18 125.69 1,270,040.65 90,112.50 98,554.10 188,666.60 27 556.82 322.05 19 121.57 1,281,326.20 90,913.24 94,794.15 185,707.39 28 576.80 542.75 18 117.34 1,225,502.94 86,952.45 105,516.39 192,468.84 29 596.01 561.96 18 113.47 1,204,793.70 85,483.07 109,069.50 194,552.57 30 613.66 579.61 18 110.03 1,186,270.01 84,168.77 112,334.75 196,503.52

**(USD/y)**

**CASA (USD/y)** **CTA HRN (USD/y)**

The design of the solar collector network is based on the methodology proposed by Martínez-Rodríguez et al., [16] to supply the thermal load at the required process temperature level. The design variables of the low temperature solar collector

The annualisation factor *fA* is calculated considering an annual interest of 5% for a period of 25 years. In this study, this value is considered as the number of years of useful life of a piece of equipment or a network of equipment. To find the optimal *ΔTmin* it is required to evaluate the total cost associated with each chosen *ΔTmin*. **Table 2** shows the results to determine the optimal *ΔTmin* in an interval from 1 to 30 °C, for each *ΔTmin* the minimum energy requirements, the heat exchange area and the annualised costs of: heat recovery (*CHRNA*), auxiliary services (*CASA*) and the total cost of the heat recovery network (*CTA HRN*).

In **Figure 7** the total cost of the heat recovery network is shown, it can be seen the optimal *ΔTmin* is located at 13 °C and the minimum energy requirements are: 339.81 kW and 305.71 kW, corresponding to the minimum services heating and cooling, respectively.

The design of the solar collector network will be carried out considering the optimal *ΔTmin* and its corresponding minimum hot utility (thermal load).

#### **2.3 Solar resource available**

The irradiance data and other environmental variables (ambient temperature and wind speed) were taken from a meteorological station of the Solar Energy Laboratory of the University of Guanajuato, Guanajuato city, Mexico. The geographical location of the meteorological station is latitude of 21°01<sup>0</sup> 0" N, longitude 101°15<sup>0</sup> 24" W, at an average sea level elevation of +2 000 meters, central time zone, UTC � 6 and in summer UTC � 5. **Figure 8** shows the radiation data throughout the year under clear sky.

#### **2.4 Design of the solar collector network**

The integration of solar energy in an industrial process presents a challenge for existing process integration techniques, due to the non-continuous nature of supply, available irradiance levels associated with direct supply time from the solar collector network to the process. The efficiency of solar technologies must be

*Solar Energy in Industrial Processes DOI: http://dx.doi.org/10.5772/intechopen.97008*

The calculated minimum area is used to determine the cost of the heat recovery

� �0*:*<sup>9</sup> " #

) this value corresponds to the exchange area [14]. To determine the

*Ne*

*CAS* ¼ *Qh CST* þ *QcCCO* (3)

*CTA HRN* ¼ *f <sup>A</sup>CHRN* þ *f <sup>A</sup>CAS* (4)

(2)

*CHRN* <sup>¼</sup> *Ne* <sup>26600</sup> <sup>þ</sup> <sup>6500</sup> *AHRN*

Where *Ne* is the number of equipment, *AHRN* is the area of the heat recovery

In Eq. (3) *Qh* and *Qc* are the minimum requirements for heating and cooling the process (kW), while *CST* and *CCO* are the costs associated with steam and cooling water, respectively (USD/kW year). In this study, the cost of heating services is proposed to be 150 USD/kW year and cooling services 35 USD/kW year.

The total cost of the annualised heat recovery network, *CTA HRN* (USD/year), is obtained by adding the estimated cost of capital (*CHRN*) and the annualised service

The annualisation factor *fA* is calculated considering an annual interest of 5% for a period of 25 years. In this study, this value is considered as the number of years of useful life of a piece of equipment or a network of equipment. To find the optimal *ΔTmin* it is required to evaluate the total cost associated with each chosen *ΔTmin*. **Table 2** shows the results to determine the optimal *ΔTmin* in an interval from 1 to 30 °C, for each *ΔTmin* the minimum energy requirements, the heat exchange area and the annualised costs of: heat recovery (*CHRNA*), auxiliary services (*CASA*) and

In **Figure 7** the total cost of the heat recovery network is shown, it can be seen the optimal *ΔTmin* is located at 13 °C and the minimum energy requirements are: 339.81 kW and 305.71 kW, corresponding to the minimum services heating and

The design of the solar collector network will be carried out considering the

The irradiance data and other environmental variables (ambient temperature and wind speed) were taken from a meteorological station of the Solar Energy Laboratory of the University of Guanajuato, Guanajuato city, Mexico. The geographical location of the

The integration of solar energy in an industrial process presents a challenge for existing process integration techniques, due to the non-continuous nature of supply, available irradiance levels associated with direct supply time from the solar collector network to the process. The efficiency of solar technologies must be

sea level elevation of +2 000 meters, central time zone, UTC � 6 and in summer UTC � 5. **Figure 8** shows the radiation data throughout the year under clear sky.

0" N, longitude 101°15<sup>0</sup>

24" W, at an average

optimal *ΔTmin* and its corresponding minimum hot utility (thermal load).

network, *CHRN* (USD), of the process based on Eq. (2).

*Solar Cells - Theory, Materials and Recent Advances*

cost of auxiliary services, *CAS*, Eq. (3), reported by [15].

the total cost of the heat recovery network (*CTA HRN*).

network (m<sup>2</sup>

costs (*CAS*), given by Eq. (4)

cooling, respectively.

**462**

**2.3 Solar resource available**

meteorological station is latitude of 21°01<sup>0</sup>

**2.4 Design of the solar collector network**


**Table 2.**

*Results of pinch analysis to determine optimal ΔTmin.*

determined since it is influenced by the environmental conditions of the place, this must be evaluated to guarantee the supply of the hot utility. This methodology combines this information to lead to the design of the solar thermal installation to reach the target temperature required by the process and satisfy the thermal requirements of the process with the lowest cost and taking care of the restrictions that the process presents. This must be attractive to compete with fossil fuels.

The design of the solar collector network is based on the methodology proposed by Martínez-Rodríguez et al., [16] to supply the thermal load at the required process temperature level. The design variables of the low temperature solar collector

**Figure 7.** *Annualised total cost from heat recovery network against ΔTmin.*

**Figure 8.** *Irradiance throughout a year for clear sky days.*

network are the operating conditions of the process (temperature and required thermal load), the environmental parameters (irradiance and ambient temperature), geometric dimensions and characteristics of the flate-plate solar materials, the properties of the working fluid, and the network operating conditions (flow and feed temperature).

The minimum number of collectors connected in series can be calculated considering that the minimum difference between the outlet temperature of the fluid from the collector,*T0* (°C), and the temperature of the fluid at the entrance to the collector,*Ti* (°C), is equal to or greater than 1 °C. Generalising this difference for any collector or series have Eq. (5)

$$
\Delta T = T\_o^n - T\_o^{n-1} \tag{5}
$$

Several solar collectors, *Nc*, make up the structure of the solar collector network

*Ns* is the number of series collectors and *Np* is the number of parallel branches. In **Figure 10** the arrangement of a network of 16 collectors in a 4 x 4 arrangement (parallel series) is displayed. Generalising the arrangement for any collector network it can be denoted as *mxn*, where the lines in parallel to be placed (*m*) and the number of collectors connected in series (*n*) are shown. In this way, it is possible to meet the temperature level and the thermal load required for the process, of these, the first is achieved by connecting n collectors in series and the second is

The absorber surface of the solar collector network is calculated from Eq. (8)

Then we proceed to determine the cost of the collector network, *CSCN* (USD),

Where *Nc* is the number of collectors, *At* is the lateral area of the tube, *Nt* is the number of tubes, *d* is the internal diameter of a tube, *W* and *L* are the width and length of a solar collector, *Hb* and *eff* are the load and pump efficiency, respectively.

); 3.52 (USD h m�<sup>1</sup> kg�<sup>1</sup>

collectors, *L* is the length (m), and *W* is the width of the solar collector (m).

*d* � � <sup>þ</sup> *WLγ*<sup>4</sup> <sup>þ</sup> *<sup>γ</sup>*<sup>10</sup>

� �

achieved through the determination of branches given by Eq. (6).

Where *ASCN* is the area of the solar collector network (m<sup>2</sup>

*<sup>π</sup> <sup>γ</sup>*1*<sup>d</sup>* <sup>þ</sup> *<sup>γ</sup>*<sup>2</sup> <sup>þ</sup> *<sup>γ</sup>*<sup>3</sup>

The *γ<sup>i</sup>* terms are as follows: 6,768.82 (USD); 202,822.47 (USD/m<sup>3</sup>

); 1 dimensionless, 0.54 (m) and 261.61 (USD m h2

*Nc* ¼ *NpNs* (7)

*ASCN* ¼ *LWNc* (8)

*mL*\_ *μ πρd*<sup>4</sup>

þ *γ*<sup>5</sup>

), *Nc* is the number of

*mH*\_ *<sup>b</sup> eff* ! (9)

); 0.14 (h2

/kg), respectively.

); �1,576.96 (USD/

/m<sup>5</sup>

); 0.45

as show Eq. (7)

*Structure of a solar collector network with 16 units.*

**Figure 10.**

**Figure 9.** *Series of* n *collectors.*

*Solar Energy in Industrial Processes*

*DOI: http://dx.doi.org/10.5772/intechopen.97008*

using Eq. (9) reported in [17]:

*AtNt*

); 32,576 (USD/m); 994.1 (USD/m<sup>2</sup>

*CSCN* ¼ *Nc γ*<sup>0</sup> þ

m2

**465**

(h/m<sup>2</sup>

Where *n* refers to outlet temperature of the *n-th* element and *n-1* refers to the outlet temperature of one minus to the *n-th* element (°C) (**Figure 9**).

The number of branches or lines in parallel is calculated by Eq. (6)

$$N\_p = \frac{Qi}{Q} \tag{6}$$

*Qi* is the thermal load provided by a series of *n* collectors connected in series (kW) and *Q* is the total thermal load (kW) required by the process, whether to cover partially or totally.
