**Adsorption Cycle and Its Hybrid with Multi-Effect Desalination**

Muhammad Wakil Shahzad, Kyaw Thu, Ang Li, Azhar Bin Ismail and Kim Choon Ng

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/60400

#### **Abstract**

Ishak, Development of low NOx liquid fuel burner, Faculty of Mechanical Engineer‐ ing, Universiti Teknologi Malaysia 2005, http://eprints.utm.my/539/1/LAPOR‐

[19] AP 42, Fifth Edition, Volume I, Chapter 3: Stationary Internal Combustion Sources, Stationary Gas Turbines, http://www.epa.gov/ttn/chief/ap42/ch03/final/c03s01.pdf

[20] Ueli Honegger, Gas turbine combustion modeling for a parametric emissions moni‐ toring system, M.Sc. thesis, Kansas State University, 2007, https://krex.k-state.edu/

[21] Bassam G. Jabboury and Mohamed A. Darwish, Performance of gas turbine co-gen‐ eration power desalting plants under varying operating conditions in Kuwait, Heat

[22] Bassam G. Jabboury and Mohamed A. Darwish, The effect of the operating parame‐ ters of heat recovery steam generators on combined cycle/sea-water desalination plant performance, Heat Recover)' Systems & CHP, Vol. 10, No. 3, pp. 255-267, 1990

[23] J. Dastych, Pickhardt, H.Unbehauen, Control schemes of cogenerating power plants for desalination, in Process Instrumentation, Control and Automation, from Encyclopedia of Desalination and Water Resources, Eolss Publishers, Paris, France, [http://

[24] Steam turbine technology HEATs up, Power Engineering International, http:// www.powerengineeringint.com/articles/print/volume-11/issue-3/features/steam-tur‐

[25] M. Boss, Steam turbines for STAG combined-cycle power systems, http://site.ge-ener‐

[26] SSS CLUTCH, Key to combined cycle flexibility, http://www.sssclutch.com/power‐

[27] R.W. Smith, P. Polukort, C.E. Maslak, C.M. Jones, B.D. Gardiner, Advanced Technol‐ ogy Combined Cycles, http://site.ge-energy.com/prod\_serv/products/tech\_docs/en/

[28] J.P. Ninan and B. Khan, SPECIAL DESIGN ASPECTS OF CO-GENERATION UNITS, in Thermal Power Plants and Co-generation Planning, from Encyclopedia of Desalina‐ tion and Water Resources, Eolss Publishers, Paris, France, [http://www.desware.net]

[29] G. Volpi, G. Silva, R. Piasente, Ansaldo Caldaie experience in HRSG design develop‐ ments. http://www.ansaldoboiler.it/prodotti/generatori-di-vapore-a-recupero/

[30] M.A. Darwish, Anwar Bin Amer, Cost allocation in cogeneration power–desalina‐ tionplant utilising gas/steam combined cycle (GTCC) in Kuwait, *Int. J. Exergy, Vol. 14,*

gy.com/prod\_serv/products/tech\_docs/en/downloads/ger3582e.pdf

generation/combinedcycle/attachments/NR9905\_2.pdf

dspace/bitstream/handle/2097/371/UeliHonegger2007.pdf?sequence=1

Recover), Systems & CHP Vol. 10, No. 3, pp. 243-253, 1990

www.desware.net] [Retrieved January 5, 2015]

bine-technology-heats-up.html

downloads/ger3936a.pdf

[Retrieved January 5, 2015]

%3Faid%3D747%26sa%3D1

*No. 3, 2014* 275

AN\_AKHIR\_IRPA\_74069.pdf

184 Desalination Updates

Adsorption (AD) cycle is recently pioneered for cooling and desalination applications. For water treatment, the cycle can be used to treat highly concentrated feed water, ranging from seawater, ground water, and chemically laden waste water. This chapter presents a review of the recent development of AD cycle and its hybridization with known conventional cycles such as the MED and MSF. We begin by looking at the basic sorption theory for different adsorbent–adsorbate pairs, namely the silica gel– water and the zeolite–water pairs. Under the IUPAC categorization, there are six types of isotherm behavior that capture almost all types of adsorbent–adsorbate behaviors and many isotherm correlations have been developed to described their uptake patterns, namely the Henry, Langmuir, Toth, etc. We have recently developed a correlation that can universally capture all six types of isotherms of IUPAC and it requires only four regression coefficients.

We present also the basic AD cycle for seawater desalination as well as its hybridiza‐ tion with known conventional thermally driven cycles. We present the performances of the AD pilot which was powered by renewable solar thermal input. Owing to thermodynamic synergy between the thermally driven cycles, the AD cycle is combined with the robust multi-effect distillation cycle to improve the water production yields. The hybrid cycle is called the "MED+AD" or MEDAD in short. With hybridization, it allows the bottom-brine temperature of the MED to operate below ambient temperature, as low as 5°C, in contrast to the conventional MED which is limited by the ambient, resulting in a quantum increase of distillate production by two to three times. We demonstrate this efficiency improvement in a pilot comprising

© 2015 The Author(s). Licensee InTech. 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.

a three-stage MED and AD plant and the top-brine temperature is maintained at 70°C. Lastly, we present the concept of exergy to apportion the operating cost of fuel input in a cogeneration plant where both electricity and water are being produced, and this concept gives an operating cost of fuel input to be lower than the conventional enthalpic approach. approach. Keywords: Thermal Desalination, Adsorption Desalination (AD), Exergy Analysis, Multi-Effect Distillation (MED), Hybrid Cycles.

this concept gives an operating cost of fuel input to be lower than the conventional enthalpic

Desalination Updates (ISBN 978-953-51-4239-3)

2

**Keywords:** Thermal Desalination, Adsorption Desalination (AD), Exergy Analysis, Multi-Effect Distillation (MED), Hybrid Cycles 1- Introduction

Fresh water is a precious entity which is needed for economic development of every sector of a country such as agriculture, industrial, and domestic sectors. The persistent quest of

the water demand which is projected to grow annually at a rate of 3–4% [1–3]. Even though

#### **1. Introduction** economic development and exponential population growth in many countries has intensified

Fresh water is a precious entity which is needed for economic development of every sector of a country such as agriculture, industrial, and domestic sectors. The persistent quest of economic development and exponential population growth in many countries has intensified the water demand which is projected to grow annually at a rate of 3–4% [1–3]. Even though 70% of the earth is covered by water, most of the part is in nonpotable state due to its salinity, either in the form of brackish, waste, and seawater [3–7]. About 20% of the world population is living below the acute water poverty level of 500 m3 per capita per year [8], risking their health due to poor water quality and substandard sanitation. The demand for fresh water in 2030 is expected to increase up to 6,900 billion cubic meters (Bm3 ), as compared to total available water resources of 4,500 Bm3 [9]. The fresh water supply and demand scenario is shown in Figure 1, and it is predicted that the sustainable natural water cycle of our earth cannot meet the projected future water demand. 70% of the earth is covered by water,most of the part is in nonpotable state due to its salinity, either in the form of brackish, waste, and seawater [3–7]. About 20% of the world population is living below the acute water poverty level of 500 m<sup>3</sup> per capita per year [8], risking their health due to poor water quality and substandard sanitation. The demand for fresh water in 2030 is expected to increase up to 6,900 billion cubic meters (Bm<sup>3</sup> ), as compared to total available water resources of 4,500 Bm<sup>3</sup> [9]. The fresh water supply and demand scenario is shown in Figure 1, and it is predicted that the sustainable natural water cycle of our earth cannot meet the projected future water demand.

Figure 1: Fresh water supply demand gap: current and future estimates

**Figure 1.** Fresh water supply demand gap: current and future estimates

In 2012, installed desalinated water capacity was 72 Mm3 /day (mcmd) and it is estimated to increase to 98 mcmd by 2015 as reported in the literature [10]. Almost half of total desalination capacity is installed in the Gulf Cooperation Council (GCC) countries. In the 1960s and 1970s, many GCC countries relied heavily on the ground water supply for all sectors such as agriculture, industrial, and domestic sectors. However, the ground water resource in these countries has depleted rapidly over the decades due to excessive water extraction and insufficient aquifer recharge. Despite a higher desalination market share in GCC, the fresh water availability is dropping rapidly to below the acute water poverty level of 500 m3 per capital per year, caused by an exponential population growth and higher GDP thrust.

**Figure 2.** Fresh water availability per capita in GCC countries

a three-stage MED and AD plant and the top-brine temperature is maintained at 70°C. Lastly, we present the concept of exergy to apportion the operating cost of fuel input in a cogeneration plant where both electricity and water are being produced, and this concept gives an operating cost of fuel input to be lower than the conventional

this concept gives an operating cost of fuel input to be lower than the conventional enthalpic

Keywords: Thermal Desalination, Adsorption Desalination (AD), Exergy Analysis, Multi-

**Keywords:** Thermal Desalination, Adsorption Desalination (AD), Exergy Analysis,

Fresh water is a precious entity which is needed for economic development of every sector of a country such as agriculture, industrial, and domestic sectors. The persistent quest of economic development and exponential population growth in many countries has intensified the water demand which is projected to grow annually at a rate of 3–4% [1–3]. Even though 70% of the earth is covered by water,most of the part is in nonpotable state due to its salinity, either in the form of brackish, waste, and seawater [3–7]. About 20% of the world population

Fresh water is a precious entity which is needed for economic development of every sector of a country such as agriculture, industrial, and domestic sectors. The persistent quest of economic development and exponential population growth in many countries has intensified the water demand which is projected to grow annually at a rate of 3–4% [1–3]. Even though 70% of the earth is covered by water, most of the part is in nonpotable state due to its salinity, either in the form of brackish, waste, and seawater [3–7]. About 20% of the world population

health due to poor water quality and substandard sanitation. The demand for fresh water in

health due to poor water quality and substandard sanitation. The demand for fresh water in

water resources of 4,500 Bm3 [9]. The fresh water supply and demand scenario is shown in Figure 1, and it is predicted that the sustainable natural water cycle of our earth cannot meet

Figure 1: Fresh water supply demand gap: current and future estimates

shown in Figure 1, and it is predicted that the sustainable natural water cycle of our earth

per capita per year [8], risking their

[9]. The fresh water supply and demand scenario is

per capita per year [8], risking their

Desalination Updates (ISBN 978-953-51-4239-3)

), as compared to total available

), as compared to total

2

enthalpic approach.

1- Introduction

Effect Distillation (MED), Hybrid Cycles.

**1. Introduction**

approach.

186 Desalination Updates

Multi-Effect Distillation (MED), Hybrid Cycles

is living below the acute water poverty level of 500 m3

**Figure 1.** Fresh water supply demand gap: current and future estimates

is living below the acute water poverty level of 500 m<sup>3</sup>

the projected future water demand.

available water resources of 4,500 Bm<sup>3</sup>

cannot meet the projected future water demand.

2030 is expected to increase up to 6,900 billion cubic meters (Bm3

2030 is expected to increase up to 6,900 billion cubic meters (Bm<sup>3</sup>

GCC countries population, fresh water availability, and desalination scenario are shown in Figure 2, spanning from the early decades in 1950 to the future years up to 2025 [11–17]. Seawater desalination was started in GCC countries in the 1960s, but significantly desalinated water supply was observed in the past two decades, contributing to the overall water con‐ sumption share. Increasing trend of desalination capacities has resulted in higher energy consumption, more than 25% of total energy production in GCC countries. It is estimated that, with contracted desalination facilities, the total primary energy requirement will grow up to 255.45 GWh in 2025 with 55% increment as compared to 112.47 GWh in 2000 and CO2 emission will be doubled in 2025 as compared to 60 ktonne/year in 2000 as shown in Table 1. The income loss attributed to desalination was 3.6 billion USD in 2000 and this loss is expected to rise to 31 billion USD in 2025 as calculated by considering yearly fuel price in terms of US\$/bbl as shown in Table 1.


**Table 1.** Specific energy consumed and CO2 footprint in GCC countries due to desalination processes

Water production by desalination processes has significant effect on the energy requirement and environment. The intricate nexus between water, energy, and environment has encour‐ aged scientists and engineers to innovate desalination methods with better energy efficiency and environment-friendly processes. Although RO processes are energy-efficient and domi‐ nantly used, they have certain limitations with respect to local conditions. For example, the frequent maintenance issues from high operating pressure; water quality problems in term of residuals of boron, chlorides, and bromides; and severe fluctuations in the seawater intake quality are some of the challenges faced by the RO membranes. In the GCC region, frequent occurrence of harmful algae blooms (HABs) that may contain neuroparalytic and diarrhetic toxins which can pass through the pores of membranes lead to health problems. Large fluctuations in the feed water quality have direct implication to the operation and maintenance costs of RO plants [18–20]. Owing to the uncertainty of RO operation, thermal desalination methods are deemed as the dominant processes employed in desalination market in the Middle East countries, more than 65% of installed capacities.

An innovative solution to strengthen the thermally driven and yet robust multi-effect desali‐ nation (MED) is its integration with the heat-driven adsorption desalination (AD) cycle. AD cycle is an emerging low-cost desalination system that requires only low temperature waste heat or solar energy to operate the cycle. The hybridization of both cycles, called MEDAD, extend the range of downstream (last stage) temperature of conventional MED system typically from 40o C to 5o C. The additional number of stages enhances the water production of the MED cycle by 2 - 3 fold at the same top-brine temperatures. In addition, AD integration cycle has the following advantages: (i) it increases inter-stage temperature differential of each MED stages due to the lowering of the bottom-brine temperature; (ii) it helps to scavenge the ambient energy in last part of the MED stages where the latent energy is further recycled; (iii) the AD cycle utilizes only low temperature waste heat; (iv) it has almost no major moving parts; (v) it reduces the chances of corrosion and fouling due to high concentration exposed to low temperature (5o C) in the last stages; (vi) it produces additional cooling effect from last stages of MED operating below ambient temperature; and (vii) significant increase in system performance. The basics of adsorption phenomenon, AD cycle, and its hybrids and desalina‐ tion processes economics are presented in detail in this chapter.

#### **2. Basic adsorption phenomena**

with contracted desalination facilities, the total primary energy requirement will grow up to 255.45 GWh in 2025 with 55% increment as compared to 112.47 GWh in 2000 and CO2 emission will be doubled in 2025 as compared to 60 ktonne/year in 2000 as shown in Table 1. The income loss attributed to desalination was 3.6 billion USD in 2000 and this loss is expected to rise to 31 billion USD in 2025 as calculated by considering yearly fuel price in terms of US\$/bbl as

> **CO2 production on the basis of fuel (0.527 tonne/MWh ) (ktonne/yr)**

 6.32 3.3 517.2 25.19 13.3 2066.0 62.29 32.8 5107.6 92.79 48.9 5103.7 98.26 51.8 3930.6 109.92 57.9 2748.0 112.47 59.3 3598.9 131.93 69.5 7256.2 163.96 86.4 13116.6 191.21 100.8 21989.5 221.97 117.0 26636.7 255.45 134.6 31164.5

**Table 1.** Specific energy consumed and CO2 footprint in GCC countries due to desalination processes

Water production by desalination processes has significant effect on the energy requirement and environment. The intricate nexus between water, energy, and environment has encour‐ aged scientists and engineers to innovate desalination methods with better energy efficiency and environment-friendly processes. Although RO processes are energy-efficient and domi‐ nantly used, they have certain limitations with respect to local conditions. For example, the frequent maintenance issues from high operating pressure; water quality problems in term of residuals of boron, chlorides, and bromides; and severe fluctuations in the seawater intake quality are some of the challenges faced by the RO membranes. In the GCC region, frequent occurrence of harmful algae blooms (HABs) that may contain neuroparalytic and diarrhetic toxins which can pass through the pores of membranes lead to health problems. Large fluctuations in the feed water quality have direct implication to the operation and maintenance costs of RO plants [18–20]. Owing to the uncertainty of RO operation, thermal desalination

**Displaced income due to desalination (1 bbl = 1628kWh), (million USD)**

shown in Table 1.

188 Desalination Updates

**Year**

**Specific energy utilization for desalination (GWh\_pe)**

> The understanding of an AD cycle is predicated on the availability of basic equilibria–vapor uptake or isotherms of an adsorbent–adsorbate pair at assorted pressures and temperatures. From literature, all isotherms of adsorbent–adsorbate pairs can be categorized into six types (IUPAC) and they are described by many types of empirical and semi-empirical models. The simplest adsorption isotherm model is the classical Langmuir model [21] where it assumes a homogeneous surface with a monolayer vapor uptake where all adsorbent surfaces contain a uniform charged energy. Each pore vacant site is assumed to be filled by a single vapor molecule, forming a single sorption event. Invoking the rate of gas molecules filling the adsorption sites ( <sup>d</sup>*<sup>θ</sup>* <sup>d</sup>*<sup>t</sup>* ), as given by Ward and co-workers [22–25], the expression of the Langmuir isotherm model can be derived as follows:

$$\frac{\text{d}\,\theta}{\text{d}t} = K' \left[ \exp\left(\frac{\mu\_\text{g} - \mu\_a}{RT}\right) - \exp\left(\frac{\mu\_a - \mu\_\text{g}}{RT}\right) \right] \tag{1}$$

where *μ* is the chemical potential in kJ/mol and subscripts g and a are the gaseous and adsorbed phases, *T* is the absolute temperature, and *K*′ is the dimensionless constant. The isotherm, *θ*, can be obtained by integrating the rate equation over the energy level from *E*c to infinity and in this simple case, when →0 then *θ* →0, and as *P* is large, *θ* approaches 1.

$$\theta = \frac{K \exp\left(\frac{\mathcal{E}}{RT}\right)P}{1 + K \exp\left(\frac{\mathcal{E}}{RT}\right)P} \tag{2}$$

A real solid surface of an adsorbent contains geometrical roughness that is formed during its formation or activation process and the energetic heterogeneity has to be accounted for. The gas molecules experienced varying potential at adsorption sites of uneven energy levels and the surfaces are subdivided into infinitesimal pieces. Thus, the total adsorption of a heteroge‐ neous surface is the sum of the product of the sorption event or surface coverage, *θ*˜(*ε<sup>i</sup>* ) and its probability energy distribution, *χ*(*ε<sup>i</sup>* ), i.e.,

$$\theta = \sum\_{i} \mathcal{X}(\varepsilon\_{i}) \cdot \tilde{\theta}(\varepsilon\_{i}) = \int\_{0}^{\varkappa} \mathcal{X}(\varepsilon) \cdot \tilde{\theta}(\varepsilon) \, \mathrm{d}\varepsilon \tag{3}$$

where the Langmuir model can be applied with a probability function over the entire surface being summed to unity, i.e.,

$$\int\_0^\infty \mathcal{X}\left(\varepsilon\right) \cdot \mathbf{d}\varepsilon = 1 \tag{4}$$

Applying a condensation approximation at moderate temperature, the local surface coverage can be simplified to a step-like dirac-delta function as shown in Figure 3, and expressed below;

$$\lim\_{T \to 0} \tilde{\theta} \left( \varepsilon \right) = \begin{cases} 0 \text{ for } \varepsilon < \varepsilon\_c \\ 1 \text{ for } \varepsilon \ge \varepsilon\_c \end{cases} \tag{5}$$

where, *εc* relates to the adsorption energy in equilibrium conditions. Hence, Equation 3 can be simplified to

$$\begin{aligned} \theta &= \int\_0^{\varepsilon\_c} 0 \cdot \mathcal{X}\left(\varepsilon\right) d\varepsilon + \int\_{\varepsilon\_c}^\kappa 1 \cdot \mathcal{X}\left(\varepsilon\right) d\varepsilon \\ &= \int\_{\varepsilon\_c}^\kappa \mathcal{X}\left(\varepsilon\right) d\varepsilon \end{aligned} \tag{6}$$

A solution of *χ*(*ε*) to represent the site energy allocation for a real adsorbent surface is obtained by approximating it to a continuous probability distribution function. Depending on the adsorbent surface energy characteristics during adsorption interactions, symmetrical or asymmetrical Gaussian functions are usually assumed, as illustrated in Figure 4.

**Figure 3.** Step-like profile yielded from Equation 5 at moderate temperatures

*K P RT*

exp

è ø <sup>=</sup> æ ö + ç ÷ è ø

neous surface is the sum of the product of the sorption event or surface coverage, *θ*˜(*ε<sup>i</sup>*

( *i i* ) ( ) ( ) ( )

where the Langmuir model can be applied with a probability function over the entire surface

 ed 1 ¥

Applying a condensation approximation at moderate temperature, the local surface coverage can be simplified to a step-like dirac-delta function as shown in Figure 3, and expressed below;

> ( ) *<sup>c</sup> <sup>T</sup> <sup>c</sup>* <sup>0</sup> 0 for lim

ìï <sup>&</sup>lt; <sup>=</sup> <sup>í</sup> ï ³ î

e e

e e

1 for

where, *εc* relates to the adsorption energy in equilibrium conditions. Hence, Equation 3 can be

( ) ( )

A solution of *χ*(*ε*) to represent the site energy allocation for a real adsorbent surface is obtained by approximating it to a continuous probability distribution function. Depending on the adsorbent surface energy characteristics during adsorption interactions, symmetrical or

*c*

¥

e

*d d*

 ce e

 ce qe e

<sup>d</sup> ¥

= ×= × å ò % % (3)

× = ò (4)

% (5)

<sup>ò</sup> (6)

), i.e.,

*<sup>i</sup>* <sup>0</sup>

( ) <sup>0</sup> ce

q e ®

( )

ce e

 ce e

*d*

asymmetrical Gaussian functions are usually assumed, as illustrated in Figure 4.

<sup>0</sup> 0 1

= × +×

ò ò

*c*

e

q

*c*

¥

e

=

1 exp

q

probability energy distribution, *χ*(*ε<sup>i</sup>*

190 Desalination Updates

being summed to unity, i.e.,

simplified to

q

 ce qe

*K P RT*

A real solid surface of an adsorbent contains geometrical roughness that is formed during its formation or activation process and the energetic heterogeneity has to be accounted for. The gas molecules experienced varying potential at adsorption sites of uneven energy levels and the surfaces are subdivided into infinitesimal pieces. Thus, the total adsorption of a heteroge‐

e

(2)

) and its

e

æ ö ç ÷

**Figure 4.** An illustration of symmetrical or asymmetrical Gaussian function to represent the adsorption site energy dis‐ tribution for classical isotherm models

The details of EDFs, *χ*(*ε*), for the classic Langmuir–Freundlich [26], Dubinin–Astakhov [27], Dubinin–Raduskevich [28], and Tóth isotherm models are outlined in Table 2, and integrating EDFs from the cut-off energy *εc* to *∞*, the exact correlation of these isotherm models can be obtained.


**Table 2.** Assorted forms of adsorption site energy distribution functions (EDF) for the Langmuir-Freundlich, Dubinin-Astakhov (DA), Dubinin-Raduskevich (DR) and Tóth isotherm models

#### **2.1. Universal site-Energy probability Distribution Function (EDF)**

In the recent development of adsorption isotherm theory, Li [29] proposed a universal model that was able to fit all types of isotherms, as specified in Equation 7. Type I to V patterns at various temperatures could be directly captured by the equation with four regression param‐ eters.

$$\frac{q}{q\_0} = \frac{A\phi \exp\left(\beta \frac{P}{P\_s}\right) \frac{P}{P\_s} + C \frac{P}{P\_s}}{\left\{1 + \phi \exp\left(\beta \frac{P}{P\_s}\right) \frac{P}{P\_s}\right\}^t} \tag{7}$$

and,

$$\beta = \exp\left(\frac{E\_c}{RT}\right) \tag{8}$$

#### Adsorption Cycle and Its Hybrid with Multi-Effect Desalination http://dx.doi.org/10.5772/60400 193

$$A = \frac{\left[1 + \phi \exp(\beta)\right]^\ast - \mathcal{C}}{\phi \exp(\beta)}\tag{9}$$

where the alphabet *ϕ*, *C* are constants, *t* is surface heterogeneity factor, and *Ec* denotes the characteristic energy of the adsorbent–adsorbate pair. These four parameters are required to calculate in the regression process. The rest of the letters have their usual means.

EDFs from the cut-off energy *εc* to *∞*, the exact correlation of these isotherm models can be

*<sup>c</sup>* ) <sup>2</sup> *<sup>θ</sup>* <sup>=</sup>

*KP*exp( *<sup>ε</sup>*<sup>0</sup>

1 + *KP*exp( *<sup>ε</sup>*<sup>0</sup>

*r*(*ε* −*ε*1)*<sup>r</sup>*−<sup>1</sup>

*<sup>θ</sup>* =exp <sup>−</sup>( *RT*

*<sup>θ</sup>* =exp <sup>−</sup>( *RT*

*χ*(*ε*)=

*θ* =

*RT* ) *RT c*

*<sup>E</sup> <sup>r</sup>* exp <sup>−</sup>( *<sup>ε</sup>* <sup>−</sup>*ε*<sup>1</sup>

*<sup>E</sup>* ln *P*0 *P* ) *r*

*<sup>E</sup>* ln *P*0 *P* ) 2

> *RT* ) *<sup>t</sup>* } 1 *t*

> > (7)

*KP*exp( *<sup>ε</sup>*<sup>3</sup> *RT* )

{1 + *KP*exp( *<sup>ε</sup>*<sup>3</sup>

è ø (8)

*RT* ) *RT c*

> *<sup>E</sup>* ) *r*

**Model Name Adsorption Site Energy Distribution** *χ***(***ε***) Isotherm Equation**

1 *<sup>c</sup>* exp( *<sup>ε</sup>* <sup>−</sup>*ε*<sup>0</sup> *<sup>c</sup>* )

2(*ε* −*ε*1)

1 *RT* exp( *<sup>ε</sup>* <sup>−</sup>*ε*<sup>3</sup>

Astakhov (DA), Dubinin-Raduskevich (DR) and Tóth isotherm models

{1 + exp( *<sup>ε</sup>* <sup>−</sup>*ε*<sup>3</sup>

**2.1. Universal site-Energy probability Distribution Function (EDF)**

0

1 + exp( *<sup>ε</sup>* <sup>−</sup>*ε*<sup>0</sup>

*<sup>E</sup>* <sup>2</sup> exp <sup>−</sup>( *<sup>ε</sup>* <sup>−</sup>*ε*<sup>2</sup>

*<sup>E</sup>* ) 2

**Table 2.** Assorted forms of adsorption site energy distribution functions (EDF) for the Langmuir-Freundlich, Dubinin-

In the recent development of adsorption isotherm theory, Li [29] proposed a universal model that was able to fit all types of isotherms, as specified in Equation 7. Type I to V patterns at various temperatures could be directly captured by the equation with four regression param‐

> *PP P A C q PP P <sup>q</sup> P P*

æ ö ç ÷ +

> b

*c E RT*

ì ü ï ï æ ö í ý <sup>+</sup> ç ÷ ï ï î þ è ø

 b

exp

f

b exp æ ö <sup>=</sup> ç ÷

1 exp

f

è ø <sup>=</sup>

*ss s t*

*s s*

*P P*

*RT* ) *<sup>t</sup>*

*RT* ) *<sup>t</sup>* } *t* +1 *t*

obtained.

192 Desalination Updates

**Langmuir–**

**Dubinin–Astakhov**

**Dubinin–**

eters.

and,

**Freundlich** *<sup>χ</sup>*(*ε*)=

**Radushkevich** *<sup>χ</sup>*(*ε*)=

**Tóth** *χ*(*ε*)=

Using the unified adsorption isotherm framework, a universal adsorption site energy distri‐ bution function (EDF) was proposed, which relates directly to their isotherm types, and the proposed EDF fitted well with the statistical rate theory of adsorption. The EDF yielded a single peak asymmetrical distribution for Type I which was similar to that for the classical LF, DA, DR, and Tóth isotherm models. The EDF is given as below;

$$\chi(\varepsilon) = \frac{\boldsymbol{\beta}^{\prime}}{RT} \left[ \boldsymbol{\phi} \exp(\boldsymbol{\beta}^{\prime}) \frac{\boldsymbol{\beta}^{\prime}}{\boldsymbol{\beta}} + 1 \right]^{-t-1} \begin{bmatrix} (\boldsymbol{\beta}^{\prime} + 1) & \boldsymbol{\frac{C}{\boldsymbol{\beta}}} \\ \boldsymbol{1} - \boldsymbol{\phi} \exp(\boldsymbol{\beta}^{\prime}) \frac{\boldsymbol{\beta}^{\prime}}{\boldsymbol{\beta}} (t-1) \\ \boldsymbol{1} - \boldsymbol{\phi} \exp(\boldsymbol{\beta}^{\prime}) \frac{\boldsymbol{\beta}^{\prime}}{\boldsymbol{\beta}} (t-1) \\ - \boldsymbol{C}t \boldsymbol{\phi} \exp(\boldsymbol{\beta}^{\prime}) \left( \frac{\boldsymbol{\beta}^{\prime}}{\boldsymbol{\beta}} \right)^{2} \end{bmatrix} \tag{10}$$

where the variable *β\** is a function of the adsorption site energy *ε* and it is expressed as

$$\boldsymbol{\beta}^\* = \exp\left(\frac{2E\_c - \varepsilon}{RT}\right) \tag{11}$$

From the data available from literature and the proposed Eqs. 9 and 10, the assorted isotherms as categorized by the IUPAC can be successfully captured succinctly by these equations using only four coefficients of regression, and these energy distribution functions and isotherms are depicted in Table 3. For each type of isotherm, the corresponding energy distribution functions (EDFs) have been developed.

The adsorbent–adsorbate interaction is the key in the design of adsorption cycle, which can be functionalized to adopt to warmer ambient temperatures, particularly for operation in the summer period of semi-arid or desert regions. Figures 5(a) and (b) depict two major types of useful adsorbents in water uptake: The former is silica gel Type 3A, suitable for an AD cycle operating below 33<sup>ο</sup> C ambient such as tropical weather conditions. The latter figure depicts the isotherms of zeolite (Z0-alumina phosphate oxide, AlXPhYO.nH2O). It has properties that can be tailored for adsorption/desorption at ambient temperatures up to 50<sup>ο</sup> C (corresponding to desorption at 3.8–4.5 kPa (60<sup>ο</sup> C isotherm) and adsorption at 2–2.8 kPa (40<sup>ο</sup> C isotherm). The thermos-physical properties of both adsorbents are tabulated in Table 4, showing the BET surface-pore areas of 600–800 m2 /g.

11

Desalination Updates (ISBN 978-953-51-4239-3)

pyrrolidone

Type II Water–boehmite

Type II Water–polyvinyl

Lagorsse S, Campo MC, Magalhaes FD, Mendes A. Water adsorption on carbon molecular sieve membranes: experimental data and isotherm

The adsorbent–adsorbate interaction is the key in the design of adsorption cycle, which can

**Table 3.** A summary of the energy distribution functions and isotherms as categorized by the IUPAC

thermos-physical properties of both adsorbents are tabulated in Table 4, showing the BET

**Types of Isotherms (IUPAC Categorization) Adsorbate–Adsorbent Pair / References**

Type I Water–silica gel Type RD Type I Water–silica gel Type A

Type II ⋄ Water–boehmite

NUS

Qiu J. Characterization of silica gel–water vapor adsorption, MEng Thesis, 2004,

Type II *Δ* Water–polyvinyl pyrrolidone 1. Wang, S-L, Johnston CT, David L, White JL, Stanley LH. Watervapor adsorption and surface area measurement of poorly crystalline boehmite. J Colloid Interface Sci 2003;260(1):26–35. 2. Zhang, J, Zografi G. The relationship between "BET" and "free volume"‐ derived parameters for water vapor absorption into amorphous solids. J Pharm Sci 2000;89(8):1063–72. Type III ⋄ Water-sctivated carbon Type III *Δ* Water–carbon S-W nanotube Kim P, Agnihotri S. Application of wateractivated carbon isotherm models to water adsorption isotherms of singlewalled carbon nanotubes. J Colloid Interface Scie 2008;325(1):64–73. Type IV ⋄ Water–boehmite

Type IV *Δ* Water–polyvinyl pyrrolidone

Figure 5(a)

Bansal RC, Dhami TL. Surface characteristics and surface behaviour of polymer carbons—II: adsorption of water vapor. Carbon 1978;16(5):389–95.

/g.

surface-pore areas of 600–800 m2

194 Desalination Updates

Figures 5: (a) shows the isotherms of water-silica gel Type 3A at four temperatures: **Figure 5.** (a) shows the isotherms of water-silica gel Type 3A at four temperatures: 30o C to 45o C at increasing pressure up to 10 kPa, (b) depicts the isotherms of Zeolite (Z01- Alumina Phosphate Oxide) from 30o C to 60o C.

C to 45o C at increasing pressure up to 10 kPa, (b) depicts the isotherms


**Table 4.** Thermo-physical properties of the silica gel type 3A and Zeolite (Z01)

30o

### **3. Design of AD batch-operated cycle**

There are five main components of AD system namely: (i) evaporator, (ii) adsorption and desorption reactor beds, (iii) condenser, (iv) pumps, and (v) pretreatment facility. The detailed process diagram is shown in Figure 6. For the batch-operated AD cycle, it involves two main processes.

#### **3.1. Adsorption-assisted-evaporation**

In which the vapors generated in AD evaporator are adsorbed on the pore surface area of adsorbent. The heat source is circulated through the tubes of evaporator and seawater is sprayed on the tube bundle. It is observed that the evaporation is initiated by heat source, but during adsorption process the high affinity of water vapor of adsorbent drops the evaporator pressure and contribute in evaporation. The AD evaporator operation temperature can be controlled by heat source temperature that is normally circulated in terms of chilled water. The AD evaporator can operate at a wide range of chilled water temperature varying from 5<sup>ο</sup> C to 30<sup>ο</sup> C to produce the cooling effect as well at low temperature operation. The vapor adsorp‐ tion process continues until the adsorbent bed reaches a saturation state.

**Figure 6.** Detailed schematics of an adsorption desalination cycle. The circle (filled) dots are the vapor valves and the pair of triangles refers to the liquid valves. The range of vapor pressures in evaporator and condenser are 1-2 kPa and 5 to 7 kPa

#### **3.2. Desorption-activated-condensation**

**3. Design of AD batch-operated cycle**

**3.1. Adsorption-assisted-evaporation**

processes.

196 Desalination Updates

to 30<sup>ο</sup>

5 to 7 kPa

There are five main components of AD system namely: (i) evaporator, (ii) adsorption and desorption reactor beds, (iii) condenser, (iv) pumps, and (v) pretreatment facility. The detailed process diagram is shown in Figure 6. For the batch-operated AD cycle, it involves two main

In which the vapors generated in AD evaporator are adsorbed on the pore surface area of adsorbent. The heat source is circulated through the tubes of evaporator and seawater is sprayed on the tube bundle. It is observed that the evaporation is initiated by heat source, but during adsorption process the high affinity of water vapor of adsorbent drops the evaporator pressure and contribute in evaporation. The AD evaporator operation temperature can be controlled by heat source temperature that is normally circulated in terms of chilled water. The AD evaporator can operate at a wide range of chilled water temperature varying from 5<sup>ο</sup>

C to produce the cooling effect as well at low temperature operation. The vapor adsorp‐

**Figure 6.** Detailed schematics of an adsorption desalination cycle. The circle (filled) dots are the vapor valves and the pair of triangles refers to the liquid valves. The range of vapor pressures in evaporator and condenser are 1-2 kPa and

tion process continues until the adsorbent bed reaches a saturation state.

C

In which saturated adsorbent is regenerated using the low-grade industrial waste heat or renewable energy (desorption temperature varies from 55°C to 85°C) and desorbed vapors are condensed in a water-cooled condenser and collected as a distillate water.

It can be seen that two useful effects produced by AD cycle are the cooling effect by the first process "adsorption-assisted-evaporation" and fresh water production by converting the seawater by second process "desorption-activated-condensation". Useful effects which are cooling and water production can be produced simultaneously by introducing the multi-bed technique.

In multi-bed AD system, the operation and switching technique is used. During operation, one or pair of adsorbent reactor beds undergo the adsorption process and at the same time one or pair of adsorbent reactor beds execute the desorption process. The time for adsorbent reactor beds operation, either adsorption or desorption, depends on the heat source temperature and silica gel quantity packed in a bed. Prior to changing the reactor duties, there is a short time interval called switching in which the adsorber bed is preheated whilst the desorber bed is precooled to enhance the performance of cycle. In AD cycles, the operation (adsorption and desorption) and switching processes are controlled by automated control scheme that can open and close the respective bed hot/cold water valves. During switching operation, all vapor valves are closed so that there is no adsorption or desorption taking place.
