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Thermodynamic analysis of an adsorption-based desalination cycle
chemical engineering research and design 8 8 ( 2 0 1 0 ) 1541–1547
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Chemical Engineering Research and Design journal homepage: www.elsevier.com/locate/cherd
Thermodynamic analysis of an adsorption-based desalination cycle Jun W. Wu a,1 , Mark J. Biggs b,1 , Eric J. Hu a,∗,1 a b
School of Mechanical Engineering, University of Adelaide, SA 5005, Australia School of Chemical Engineering, University of Adelaide, SA 5005, Australia
a b s t r a c t Adsorption-based desalination (AD) is attracting increasing attention because of its ability to co-generate doubledistilled fresh water and cooling. In this paper, a thermodynamic model has been developed in order to study the factors that influence the fresh water production rate (FWPR) and energy consumption of an adsorption-based desalination system. Water adsorption on the silica gel adsorbent is modelled using a Langmuir isotherm and the factors studied are the silica gel adsorption equilibrium constant and the temperatures of the hot and cooling water which supply and extract heat from the silica gel respectively. © 2010 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. Keywords: Adsorption desalination; Silica gel-water; Isotherms; Adsorption chiller
1.
Introduction
Rising water scarcity due to climate change and overexploitation of traditional water resources is of increasing concern across the world, both because of its economic implications as well as the continued habitability of long-standing communities. One solution to this issue is desalination of saline or brackish water, which has long been used in regions that have traditionally faced water shortages such as the Middle East. There are several ways in which desalination – which is defined as separation of excess salt and other minerals from water molecules – is carried out, including multi-effect, multi-stage flash and membrane-based reverse osmosis (RO) desalination, which are all exploited commercially (Zejli et al., 2004; Mosry et al., 1994; Awerbuch et al., 1989; Wazzan and AlModaf, 2001; Bruggen and Vandecasteele, 2002; Al-Shammiri and Safar, 1999; Buckley et al., 1993). Adsorption-based desalination (AD) uses low temperature waste heat to inexpensively desalinate saline and brackish water to produce potable water for both industrial and residential applications (Wang and Ng, 2005). There are five significant advantages of the AD compared with more traditional desalination techniques (Wang and Ng, 2005; ElSharkawy et al., 2007 Wang et al., 2007): (1) fewer moving parts, which reduces maintenance costs, (2) reduced fouling and cor-
∗
rosion due to the low operating temperature and confinement of the saline/brackish solution to a fraction of the total system, (3) ability to co-generate potable water and cooling, (4) double distillation – the desalination process minimizes the possibility of so-called ‘(bio) gen-contamination’, and (5) ability to treat/desalinate saline water containing organic compounds. Adsorption-based desalination has received very little attention in the literature despite its considerable advantages. Ng and co-workers (Wang and Ng, 2005; Wang et al., 2007; Thua et al., 2009; Ng et al., 2009) have investigated in detail the performance of a pilot scale adsorption-based desalination system as a function of system configuration and operating parameters. This group (Chua et al., 1999, 2004) and others (Wang et al., 2005; Wang and Chua, 2007) have also developed and used a lumped dynamic model of adsorption desalination to study the dynamic behaviour of adsorption desalination systems as a function of operating parameters such as the cycle time. In order to more fully probe the effect that thermal parameters and adsorbent properties have on the performance of adsorption-based desalination, we have undertaken a comprehensive thermodynamic analysis of an AD cycle based on a silica gel adsorbent. The paper first outlines in detail the thermodynamic model along with details of the adsorbent and other conditions used in the study. Results obtained from the model are
Corresponding author. Tel.: +61 83130545. E-mail address: [email protected] (E.J. Hu). Received 9 September 2009; Received in revised form 15 February 2010; Accepted 4 April 2010 1 Equal contributor. 0263-8762/$ – see front matter © 2010 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.cherd.2010.04.004
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Nomenclature C h K0I ka kd m ˙ m P X
X0
Q Qst R T H EC
specific heat (kJ/(kg K)) enthalpy (J/kg) adsorption equilibrium constant adsorption rate constant desorption rate constant mass (kg) mass flow rate (kg/s) pressure (Pa) fraction of amount adsorbate adsorbed by the adsorbent at equilibrium condition (kg/kg dry adsorbent) fraction of amount adsorbate which can be adsorbed by the adsorbent under equilibrium condition (kg/kg dry adsorbent) heat of desorption (kJ/kg) isosteric heat of adsorption (kJ/kg) universal gas constant (kJ/(kg K)) temperature (◦ C) standard enthalpy change (kJ/kg) energy consumption for 1 kg water (kJ/kg)
Superscripts/subscripts ads adsorption bed adsorption or desorption bed chilled chilled water cond condenser des desorption evap evaporator fg enthalpy change heating(bed) bed heating capacity cooling(bed) bed cooling capacity hot hot water in inlet out outlet sg silica gel water water 1→2 state 1 to state 2 2→3 state 2 to state 3 3→4 state 3 to state 4 4→1 state 4 to state 1
then presented, including the effect the silica gel adsorption equilibrium constant and the temperatures of the hot and cool water (which supply and extract heat from the silica gel respectively) have on the fresh water production rate (FWPR) and energy consumption of AD under the equilibrium assumption. We conclude with a comment about future work.
2.
Fig. 1 – Schematic of a two-bed adsorption desalination system. Refer to text for a description of its operation. closed and valve 2 is opened. At the same time, the circulating water in bed 1 is switched to hot water. The hot water drives off the water adsorbed on (i.e. regenerates) the silica gel to the condenser where it is finally condensed and harvested as pure water. Once the temperature of bed 1 peaks, the silica gel regeneration process ceases and the cycle for the bed is ready to re-start. Beds 1 and 2 are operated alternatively in this way to produce fresh water (and cooling capacity from the evaporator) in a continuous manner. It should be noted that the fresh water is distilled twice (i.e. double-distilled). At the same time, a cooling effect is created by the evaporator, which can be used for air conditioning purposes as in a normal adsorption chiller, or be fed back to the bed or condenser. In other words, the adsorption desalination system has the ability to perform as a chiller and doubledistilling desalinator simultaneously. Silica gel is a popular adsorbent because it is able to take-up significant levels of water (up to 40% by mass) (Ng et al., 2001) without significant structural or volume change and readily release it under mild heating (Chakraborty et al., 2009). To improve energy efficiency, in practice systems with two or more beds are used (Chua et al., 1999). However, in this study, consideration will be restricted to a single-bed system for simplicity sake. The P–T–X diagram on ln P vs. −1/T coordinates (where X is the amount of adsorbate adsorbed by the adsorbent at equilibrium conditions, kg adsorbate/kg adsorbent), is a convenient way to describe and model the thermodynamic cycle of an AD desalinator. Theoretically the cycle consists of two isosters and two isobars, as shown in Fig. 2.
Working principle
Fig. 1 shows a schematic of a two-bed adsorption-based desalinator, which is the most basic form of such a system. This system consists of three major components: the condenser, the (silica gel) beds, and the evaporator. After the whole system is degassed and the saline/source water is charged into the evaporator, with valve 1 open, the source water evaporates and travels from the evaporator into bed 1 where it is adsorbed by the silica gel as the heat liberated by the adsorption is removed by the cooling water circulating in the manifold of bed 1. Once bed 1 is saturated with water vapour, valve 1 is
Fig. 2 – P–T–X diagram of the cyclic steady-state condition of the bed cycle. See text for a description of each process.
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2.1.
Process 1 → 2
Assume the process starts at point 1 where the silica gel is at its maximum temperature of about 90 ◦ C and the amount of adsorbed water is at a minimum, X1 . After the cooling water starts to circulate through the bed that is isolated from the evaporator and condenser, the temperature of the silica gel decreases at fixed X until point 2 where the bed pressure is P2 , the saturated pressure of pure water at the evaporator temperature. At point 2, the bed temperature will be at about 60–70 ◦ C.
2.2.
Process 2 → 3
Fig. 3 – P–X diagram at absolute temperatures.
Once the process reaches point 2, the valve between the bed and the evaporator is opened while the cooling water continues to circulate through the bed. The source water in the evaporator begins to evaporate and the vapour travels to the bed and is adsorbed by the silica gel. During this process, the pressure in the bed and evaporator remains constant (i.e. P2 = P3 ) but the temperature of the bed continues to decrease to T3 that is determined by the cooling water supply temperature. At point 3, the concentration of the water in the silica gel reaches the maximum (i.e. X3 = Xmax .).
2.3.
Process 3 → 4
Modelling
For a given adsorbative–adsorbent pair (water–silica gel in the present case), the adsorption equilibrium can be described by X = f (P, T)
KP 1 + KP
(2)
where (=X/X0 ) is the fractional coverage of the micropore surface, X is the amount of adsorbate at the pressure P, X0 is the amount of adsorbate when the adsorbent is saturated, and K (=ka /kd ) is the adsorption equilibrium constant where ka and kd are the adsorption and desorption constants respectively. Henry’s law is approached for the low adsorbate concentrations (i.e. X X0 ) (Ng et al., 2001), which is expressed as: X = KP X0
(3)
The heat released during adsorption, which is equal to the isosteric heat of adsorption, Qst , is related to the adsorption isotherms at various temperatures by the van’t Hoff equation (Atkins and Paula, 2006): d ln K −Qst = dT RT 2
(4)
where K is the equilibrium constant, and R is the universal gas constant. By integrating Eq. (4), we get:
Process 4 → 1
At point 4, the valve between the bed and the condenser is opened and the water vapour starts to be desorbed from the silica gel and pass into the condenser due to the heat from the hot water being circulated through the bed. As the cooling water is circulated through the condenser, the vapour condenses in the condenser and the pressure in the bed and condenser is fixed until the bed reaches its maximum temperature and the adsorbed water a minimum, X1 . This process can also be called silica gel regeneration or condensing process, while it is also the fresh water production process.
3.
=
=
Once the process reaches point 3, the valve between the bed and the evaporator is closed, and the circulation of the cooling water is stopped. Hot water is then circulated through the bed to increase its temperature and pressure along the constant concentration line (i.e. X3 = X4 ). This process continues until it reaches point 4 whose pressure, P4 , is determined by the saturation pressure of water at the condenser temperature (which is slightly greater than the cooling water temperature).
2.4.
is:
(1)
where X is the amount of adsorbate at equilibrium in kg of adsorbate per kg of adsorbent, and P and T are the bed partial pressure and temperature respectively. The Langmuir isotherm is often used to represent the adsorption of water on silica gel (Liu, 2006). Its common form
K = K0 exp
Q st
(5)
RT
where K0 is a constant. Using this in Eq. (3), we obtain a more practical form of the P–T–X relationship of Ng et al. (2001): X = PK0I exp
Q st
(6)
RT
K0I (=K0 X0 ) is the adsorption constant. Once Qst and K0I are known for a particular adsorbative–adsorbent pair (e.g. from experiment), then the P–T–X relationship is known and the analysis of the AD cycle can be undertaken. In order to determine Qst and K0I from the experimental data (e.g. in the form of isotherms or isosters), the van’t Hoff equation (Atkins and Paula, 2006) is used once again by integrating Eq. (4) at a constant concentration, X, to get: ln
P 2
P1
=
−Qst R
1 T2
−
1 T1
(7)
If two isotherms at different temperatures are available as shown in Fig. 3, for example, Qst can be determined for a silica gel by using Eq. (7). Once the value of the isosteric heat of adsorption is determined, K0I can be determined by taking the log of both sides of
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Similarly, the cooling requirement of a single cycle, Qcooling(bed) , for the bed can be expressed as
Eq. (6) and rearranging to obtain
ln X = ln P + ln K0I +
Qst RT
(8)
As this is a linear relationship between ln X and ln P, ln K0I can be calculated from the y-intersect given the alreadydetermined value of Qst . Alternatively, Eq. (8) can be rearranged to get: ln P =
Qst R
1 −
T
Qcooling(bed) = Q1→2 + Q2→3
(15)
where Q1→2 and Q2→3 are the heat to be removed (by the cooling water) from state 1 to state 2 and from state 2 to state 3 respectively, and their corresponding expressions are Q1→2 = (X1 msg Cwater + msg Csg )(T1 − T2 )
+ ln
X
(16)
(9)
K0I
and
This expression reveals the linear relationship between ln P and −1/T, which explains the linear processes in the cycle diagram of Fig. 2. Based on the cycle diagram shown in Fig. 2, the mass of fresh water generated in a single cycle from one bed (i.e. water productivity) can be expressed as mwater = m4–1 = m4 − m1 = X4 msg − X1 msg
(10)
where msg is the mass of the silica gel in one bed, m4→1 is the mass change of the water adsorbed in the silica gel between state 4 and state 1, X1 and X4 are the adsorbed phase concentration at equilibrium for state 1 and 4, which can be calculated by using Eq. (8). Here, the water productivity is of key interest as it is also used to calculate the system energy consumption, EC. The total heating requirement of a single cycle, Qheating(bed) , is the sum of heat in processes of 3 to 4 and 4 to 1, i.e. Qheating(bed) = Q3→4 + Q4→1
Q2→3 = msg Csg +
X + X 2 3 2
msg Cwater (T2 − T3 )
+ (X3 − X2 )msg Qads
(17)
where T1 , T2 and T3 are the corresponding temperatures at each state, X2 and X3 are the adsorbed phase concentration at equilibrium for state 2 and 3, and Qads is the amount of heat needs to be released for the adsorption process of 1 kg of water. In this study, Qads is assumed to be equal to Qdes and Qst . Similar to Eq. (13), Eq. (17) describes the heat to be removed from process 2 to 3, which consists of two parts, namely the heat input to increase the temperature of the adsorbent and the water adsorbed within the adsorbent (i.e. silica gel), and the latent heat required to drive the water evaporating from liquid form to vapour form. Substitute Eqs. (16) and (17) into Eq. (15) leads to Qcooling(bed) = (X1 msg Cwater + msg Csg )(T1 − T2 )
+ msg Csg +
(11)
X + X 2 3 2
+ (X3 − X2 )msg Qads
msg Cwater (T2 − T3 ) (18)
where Q3→4 and Q4→1 are: Q3→4 = (X3 msg Cwater + msg Csg )(T4 − T3 )
(12)
The cooling requirement of the condenser can also be expressed as Qcooling(cond) = msg (X4 − X1 )h1fg
and
Q4→1 = msg Csg +
X + X 4 1 2
msg Cwater (T1 − T4 )
+ (X4 − X1 )msg Qdes
(13)
where T1 , T3 and T4 are the corresponding temperatures at each state, X1 and X4 are the adsorbed phase concentration at equilibrium for state 1 and 4, Cwater is the water specific heat, Csg is the average silica gel specific heat, and Qdes is the amount of heat that 1 kg of water is required for the desorption process. Eq. (13) describes the heat required from process 4 to 1, which consists of two part of heat, namely the heat input to increase the temperature of the adsorbent and the water adsorbed within the adsorbent (i.e. silica gel), and the latent/desorption heat required to drive the water out of the silica gel. Using Eqs. (12) and (13) in Eq. (11) leads to Qheating(bed) = (X3 msg Cwater + msg Csg )(T4 − T3 )
+ msg Csg +
X + X 4 1 2
+ (X4 − X1 )msg Qdes
msg Cwater (T1 − T4 ) (14)
(19)
where h1fg is the specific enthalpy of phase change at the condenser pressure determined by the cooling water temperature. Similarly, the cooling effect in the evaporator, which is a benefit in the chiller mode, can be expressed as Qevap = msg (X3 − X2 )h2fg
(20)
where h2fg is the specific phase change enthalpy at the evaporator pressure. In order to have a clear view of energy consumption of the system per cycle, the energy required per kilogram of water produced, EC, is required. This may be evaluated using EC =
Qheating(bed) mwater
(21)
where mwater and Qheating(bed) are from Eq. (10) and Eq. (14) respectively. It should be noted that this definition of energy required per kilogram of water desalinated does not consider any energy recovery measures and the cooling benefit produced. The following assumptions are used in the study:
chemical engineering research and design 8 8 ( 2 0 1 0 ) 1541–1547
Fig. 4 – The effect of varying hot water inlet temperature on the fresh water production rate and energy requirement per kilogram water produced for two different cooling water temperatures at 20 ◦ C and 30 ◦ C. (1) Temperature difference for heat transfer is 5 ◦ C. (2) Structure mass is ignored. (3) The porous properties of Type RD Fuji Davison silica gel–water system are used, where K0I = 5.5 × 10−12 Pa−1 and Qst = 2370 kJ/kg (Ng et al., 2001). (4) Qads = Qdes = Qst for all Xs .
4.
Results and discussions
4.1.
Effects of hot water temperature
Fig. 4 shows the water productivity and energy consumption versus the heat source temperature when the cooling water is fixed at Tcoolingwater = 20 ◦ C or 30 ◦ C and K0I = 5.5 × 10−12 Pa−1 (Ng et al., 2001). For 20 ◦ C cooling water, the system uses the lowest energy to produce a unit mass of fresh water when the hot water temperature is about 65 ◦ C. The energy cost increases if higher grade energy is used, although the quantity of silica gel required per unit mass of water produced would decrease, thus reducing the costs associated with the adsorbent. The reason of such concave shape of the energy consumption curves (in Fig. 4) is thought to be that the specific adsorptive properties of the particular silica gel chosen makes the increase rate of water production gradually flat out when the (hot source) temperature is 70 ◦ C, while the total energy consumption for the cycle does not vary much with the (heat source) temperature. Therefore, the energy consumption per unit mass of water produced has such trend as shown in Fig. 4.
4.2.
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Fig. 5 – The effect of varying temperature of the cooling water entering both the bed and condenser on the fresh water production rate and energy consumption per kilogram water produced for two different heat source temperature at 75 ◦ C and 90 ◦ C. contrary to the trend for the hot water temperature (Fig. 4), lower cooling water temperature always gives a better outcome: higher fresh water production rate and lower energy consumption rate. In addition, changing the cooling water temperature has a greater impact on the water productivity and energy consumption. For example, reduction of the cooling water temperature by 20 ◦ C (from 25 ◦ C to 5 ◦ C) would lead to a water productivity and energy consumption increase and decrease of 314% and 10.5% respectively, while increasing the hot water temperature by the same amount (from 65 ◦ C to 85 ◦ C) would lead to a productivity increase of just 33.3% along with a small (1.5%) increase in the energy consumption rate. Figs. 6 and 7 show the impact when just one stream of cooling water temperature changes. The latter figure suggests the temperature of the cooling water entering the condenser has little impact on water productivity. Fig. 6 shows, the temperature of cooling water entering the bed has, on the other hand, a more significant impact on the system performance. These
Effects of cooling water temperature
There are cooling water streams: one that cools the beds and a second to the condenser. Figs. 5–7 depict the effects of varying the cooling temperatures on the fresh water production rate and energy consumption per kilogram of water produced. The hot water temperature Thotwater = 90 ◦ C is fixed and K0I = 5.5 × 10−12 Pa−1 (Ng et al., 2001) in this study. Fig. 5 shows the impact of varying simultaneously the temperatures of the cooling water entering the bed and the condenser on the water productivity and energy consumption for two different temperatures of heat source, Thotwater = 75 ◦ C and Thotwater = 90 ◦ C. It can be seen from Fig. 5 that, the change of heat source temperature from 75 ◦ C to 90 ◦ C does not have major effect on either the water productivity or energy consumption. Also,
Fig. 6 – The change of water production rate and system energy consumption on different cooling source temperatures entering the bed, while the cooling water entering condenser temperature is fixed at 20 ◦ C.
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chemical engineering research and design 8 8 ( 2 0 1 0 ) 1541–1547
Fig. 7 – The change of water production rate and system energy consumption on different cooling water temperatures entering condenser, while the cooling water entering bed temperature is fixed at 20 ◦ C. results also indicate an air cooled condenser may be suitable. The results in Figs. 5–7, also suggest that any energy recovery effort (to improve energy efficiency of the system) should be on the cooling water side, especially the stream of the cooling water entering the bed rather than the one entering the condenser. For example, the effort should be put into recovering extra cooling generated (in the evaporator) to cool down further the cooling water entering the bed if no external cooling demand (e.g. air conditioning) is required. This would be more effective than recycling the cooling to the stream entering the bed.
4.3. Effects of silica gel adsorption equilibrium constant The value of the silica gel adsorption equilibrium constant, K0I , is determined by the silica gel adsorptive properties. Fig. 8 shows the effect of modifying K0I on the fresh water productivity and energy consumption rate. The determination of K0I
range for the study is based on the consideration that the value of K0I is typically less than 23.7 × 10−12 Pa−1 , which is calculated from the model with the limit of X (i.e. X ≤ 1). There is a linear increase of the fresh water production rate with K0I . In other words, the bigger K0I the better the performance (i.e. increase in water production and decrease in energy consumption). Some surface treatment technologies can improve the K0I value for silica gel. The K0I value has been improved from 2.0 × 10−12 Pa−1 to 5.5 × 10−12 Pa−1 for specific types of silica gel since 1992 (Ng et al., 2001; Wang and Chua, 2007). As the water productivity increases with K0I , the quantity of silica gel required per unit mass of water produced is reduced and, hence, the sensible energy part of the total energy consumption also decreases. However, as the sensible heat component of the energy accounts for just a small fraction (about 17%) of the total energy consumption, K0I only marginally affects the energy consumption as shown in Fig. 8.
5.
Conclusions and future developments
In this study, the working principle and thermodynamic cycle of AD desalinator has been described and its performance evaluated under equilibrium conditions. The analysis shows that there is an optimum hot water temperature existing for the minimum energy consumption of per unit mass fresh water produced. The optimum temperature depends on the cooling water temperatures and other operating parameters of the system. The temperature of the cooling water entering the bed during the adsorption process has significant impact on both the water productivity and energy consumption: the lower the better. Therefore any effort to improve the system performance and reduce costs should be put into the cooling water entering the bed (e.g. recycle the cooling effect from the evaporator). These results also indicate an air cooled condenser may be suitable for the cooling water entering the condenser. The results also show that silica gel adsorption equilibrium constant (K0I ) and the fresh water productivity are linearly related. K0I has little impact on the energy consumption. The use of the equilibrium thermodynamic model here allows rapid calculation and, therefore, consideration of many combinations of system parameters with modest resource. It is, however, recognised that the equilibrium assumption means the results here can only be used as a guide. The model also does not give any information about the dynamic behaviour of AD systems. Both these issues may be overcome by adopting lumped dynamic models such as done by some (Chua et al., 1999, 2004; Wang et al., 2005; Wang and Chua, 2007) or even one- or higher-dimensional dynamic models that allow adsorptive dispersion and bed geometry to be included. Development and application of such models is currently underway in our laboratory and will be reported on in the near future.
References Fig. 8 – The change of fresh water production rate and desalination process energy consumption on different levels of K0I value, when the typical input water temperatures Tcoolingwater = 20 ◦ C and Thotwater = 90 ◦ C are fixed.
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Chemical Engineering Research and Design journal homepage: www.elsevier.com/locate/cherd
Thermodynamic analysis of an adsorption-based desalination cycle Jun W. Wu a,1 , Mark J. Biggs b,1 , Eric J. Hu a,∗,1 a b
School of Mechanical Engineering, University of Adelaide, SA 5005, Australia School of Chemical Engineering, University of Adelaide, SA 5005, Australia
a b s t r a c t Adsorption-based desalination (AD) is attracting increasing attention because of its ability to co-generate doubledistilled fresh water and cooling. In this paper, a thermodynamic model has been developed in order to study the factors that influence the fresh water production rate (FWPR) and energy consumption of an adsorption-based desalination system. Water adsorption on the silica gel adsorbent is modelled using a Langmuir isotherm and the factors studied are the silica gel adsorption equilibrium constant and the temperatures of the hot and cooling water which supply and extract heat from the silica gel respectively. © 2010 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. Keywords: Adsorption desalination; Silica gel-water; Isotherms; Adsorption chiller
1.
Introduction
Rising water scarcity due to climate change and overexploitation of traditional water resources is of increasing concern across the world, both because of its economic implications as well as the continued habitability of long-standing communities. One solution to this issue is desalination of saline or brackish water, which has long been used in regions that have traditionally faced water shortages such as the Middle East. There are several ways in which desalination – which is defined as separation of excess salt and other minerals from water molecules – is carried out, including multi-effect, multi-stage flash and membrane-based reverse osmosis (RO) desalination, which are all exploited commercially (Zejli et al., 2004; Mosry et al., 1994; Awerbuch et al., 1989; Wazzan and AlModaf, 2001; Bruggen and Vandecasteele, 2002; Al-Shammiri and Safar, 1999; Buckley et al., 1993). Adsorption-based desalination (AD) uses low temperature waste heat to inexpensively desalinate saline and brackish water to produce potable water for both industrial and residential applications (Wang and Ng, 2005). There are five significant advantages of the AD compared with more traditional desalination techniques (Wang and Ng, 2005; ElSharkawy et al., 2007 Wang et al., 2007): (1) fewer moving parts, which reduces maintenance costs, (2) reduced fouling and cor-
∗
rosion due to the low operating temperature and confinement of the saline/brackish solution to a fraction of the total system, (3) ability to co-generate potable water and cooling, (4) double distillation – the desalination process minimizes the possibility of so-called ‘(bio) gen-contamination’, and (5) ability to treat/desalinate saline water containing organic compounds. Adsorption-based desalination has received very little attention in the literature despite its considerable advantages. Ng and co-workers (Wang and Ng, 2005; Wang et al., 2007; Thua et al., 2009; Ng et al., 2009) have investigated in detail the performance of a pilot scale adsorption-based desalination system as a function of system configuration and operating parameters. This group (Chua et al., 1999, 2004) and others (Wang et al., 2005; Wang and Chua, 2007) have also developed and used a lumped dynamic model of adsorption desalination to study the dynamic behaviour of adsorption desalination systems as a function of operating parameters such as the cycle time. In order to more fully probe the effect that thermal parameters and adsorbent properties have on the performance of adsorption-based desalination, we have undertaken a comprehensive thermodynamic analysis of an AD cycle based on a silica gel adsorbent. The paper first outlines in detail the thermodynamic model along with details of the adsorbent and other conditions used in the study. Results obtained from the model are
Corresponding author. Tel.: +61 83130545. E-mail address: [email protected] (E.J. Hu). Received 9 September 2009; Received in revised form 15 February 2010; Accepted 4 April 2010 1 Equal contributor. 0263-8762/$ – see front matter © 2010 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.cherd.2010.04.004
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Nomenclature C h K0I ka kd m ˙ m P X
X0
Q Qst R T H EC
specific heat (kJ/(kg K)) enthalpy (J/kg) adsorption equilibrium constant adsorption rate constant desorption rate constant mass (kg) mass flow rate (kg/s) pressure (Pa) fraction of amount adsorbate adsorbed by the adsorbent at equilibrium condition (kg/kg dry adsorbent) fraction of amount adsorbate which can be adsorbed by the adsorbent under equilibrium condition (kg/kg dry adsorbent) heat of desorption (kJ/kg) isosteric heat of adsorption (kJ/kg) universal gas constant (kJ/(kg K)) temperature (◦ C) standard enthalpy change (kJ/kg) energy consumption for 1 kg water (kJ/kg)
Superscripts/subscripts ads adsorption bed adsorption or desorption bed chilled chilled water cond condenser des desorption evap evaporator fg enthalpy change heating(bed) bed heating capacity cooling(bed) bed cooling capacity hot hot water in inlet out outlet sg silica gel water water 1→2 state 1 to state 2 2→3 state 2 to state 3 3→4 state 3 to state 4 4→1 state 4 to state 1
then presented, including the effect the silica gel adsorption equilibrium constant and the temperatures of the hot and cool water (which supply and extract heat from the silica gel respectively) have on the fresh water production rate (FWPR) and energy consumption of AD under the equilibrium assumption. We conclude with a comment about future work.
2.
Fig. 1 – Schematic of a two-bed adsorption desalination system. Refer to text for a description of its operation. closed and valve 2 is opened. At the same time, the circulating water in bed 1 is switched to hot water. The hot water drives off the water adsorbed on (i.e. regenerates) the silica gel to the condenser where it is finally condensed and harvested as pure water. Once the temperature of bed 1 peaks, the silica gel regeneration process ceases and the cycle for the bed is ready to re-start. Beds 1 and 2 are operated alternatively in this way to produce fresh water (and cooling capacity from the evaporator) in a continuous manner. It should be noted that the fresh water is distilled twice (i.e. double-distilled). At the same time, a cooling effect is created by the evaporator, which can be used for air conditioning purposes as in a normal adsorption chiller, or be fed back to the bed or condenser. In other words, the adsorption desalination system has the ability to perform as a chiller and doubledistilling desalinator simultaneously. Silica gel is a popular adsorbent because it is able to take-up significant levels of water (up to 40% by mass) (Ng et al., 2001) without significant structural or volume change and readily release it under mild heating (Chakraborty et al., 2009). To improve energy efficiency, in practice systems with two or more beds are used (Chua et al., 1999). However, in this study, consideration will be restricted to a single-bed system for simplicity sake. The P–T–X diagram on ln P vs. −1/T coordinates (where X is the amount of adsorbate adsorbed by the adsorbent at equilibrium conditions, kg adsorbate/kg adsorbent), is a convenient way to describe and model the thermodynamic cycle of an AD desalinator. Theoretically the cycle consists of two isosters and two isobars, as shown in Fig. 2.
Working principle
Fig. 1 shows a schematic of a two-bed adsorption-based desalinator, which is the most basic form of such a system. This system consists of three major components: the condenser, the (silica gel) beds, and the evaporator. After the whole system is degassed and the saline/source water is charged into the evaporator, with valve 1 open, the source water evaporates and travels from the evaporator into bed 1 where it is adsorbed by the silica gel as the heat liberated by the adsorption is removed by the cooling water circulating in the manifold of bed 1. Once bed 1 is saturated with water vapour, valve 1 is
Fig. 2 – P–T–X diagram of the cyclic steady-state condition of the bed cycle. See text for a description of each process.
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2.1.
Process 1 → 2
Assume the process starts at point 1 where the silica gel is at its maximum temperature of about 90 ◦ C and the amount of adsorbed water is at a minimum, X1 . After the cooling water starts to circulate through the bed that is isolated from the evaporator and condenser, the temperature of the silica gel decreases at fixed X until point 2 where the bed pressure is P2 , the saturated pressure of pure water at the evaporator temperature. At point 2, the bed temperature will be at about 60–70 ◦ C.
2.2.
Process 2 → 3
Fig. 3 – P–X diagram at absolute temperatures.
Once the process reaches point 2, the valve between the bed and the evaporator is opened while the cooling water continues to circulate through the bed. The source water in the evaporator begins to evaporate and the vapour travels to the bed and is adsorbed by the silica gel. During this process, the pressure in the bed and evaporator remains constant (i.e. P2 = P3 ) but the temperature of the bed continues to decrease to T3 that is determined by the cooling water supply temperature. At point 3, the concentration of the water in the silica gel reaches the maximum (i.e. X3 = Xmax .).
2.3.
Process 3 → 4
Modelling
For a given adsorbative–adsorbent pair (water–silica gel in the present case), the adsorption equilibrium can be described by X = f (P, T)
KP 1 + KP
(2)
where (=X/X0 ) is the fractional coverage of the micropore surface, X is the amount of adsorbate at the pressure P, X0 is the amount of adsorbate when the adsorbent is saturated, and K (=ka /kd ) is the adsorption equilibrium constant where ka and kd are the adsorption and desorption constants respectively. Henry’s law is approached for the low adsorbate concentrations (i.e. X X0 ) (Ng et al., 2001), which is expressed as: X = KP X0
(3)
The heat released during adsorption, which is equal to the isosteric heat of adsorption, Qst , is related to the adsorption isotherms at various temperatures by the van’t Hoff equation (Atkins and Paula, 2006): d ln K −Qst = dT RT 2
(4)
where K is the equilibrium constant, and R is the universal gas constant. By integrating Eq. (4), we get:
Process 4 → 1
At point 4, the valve between the bed and the condenser is opened and the water vapour starts to be desorbed from the silica gel and pass into the condenser due to the heat from the hot water being circulated through the bed. As the cooling water is circulated through the condenser, the vapour condenses in the condenser and the pressure in the bed and condenser is fixed until the bed reaches its maximum temperature and the adsorbed water a minimum, X1 . This process can also be called silica gel regeneration or condensing process, while it is also the fresh water production process.
3.
=
=
Once the process reaches point 3, the valve between the bed and the evaporator is closed, and the circulation of the cooling water is stopped. Hot water is then circulated through the bed to increase its temperature and pressure along the constant concentration line (i.e. X3 = X4 ). This process continues until it reaches point 4 whose pressure, P4 , is determined by the saturation pressure of water at the condenser temperature (which is slightly greater than the cooling water temperature).
2.4.
is:
(1)
where X is the amount of adsorbate at equilibrium in kg of adsorbate per kg of adsorbent, and P and T are the bed partial pressure and temperature respectively. The Langmuir isotherm is often used to represent the adsorption of water on silica gel (Liu, 2006). Its common form
K = K0 exp
Q st
(5)
RT
where K0 is a constant. Using this in Eq. (3), we obtain a more practical form of the P–T–X relationship of Ng et al. (2001): X = PK0I exp
Q st
(6)
RT
K0I (=K0 X0 ) is the adsorption constant. Once Qst and K0I are known for a particular adsorbative–adsorbent pair (e.g. from experiment), then the P–T–X relationship is known and the analysis of the AD cycle can be undertaken. In order to determine Qst and K0I from the experimental data (e.g. in the form of isotherms or isosters), the van’t Hoff equation (Atkins and Paula, 2006) is used once again by integrating Eq. (4) at a constant concentration, X, to get: ln
P 2
P1
=
−Qst R
1 T2
−
1 T1
(7)
If two isotherms at different temperatures are available as shown in Fig. 3, for example, Qst can be determined for a silica gel by using Eq. (7). Once the value of the isosteric heat of adsorption is determined, K0I can be determined by taking the log of both sides of
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Similarly, the cooling requirement of a single cycle, Qcooling(bed) , for the bed can be expressed as
Eq. (6) and rearranging to obtain
ln X = ln P + ln K0I +
Qst RT
(8)
As this is a linear relationship between ln X and ln P, ln K0I can be calculated from the y-intersect given the alreadydetermined value of Qst . Alternatively, Eq. (8) can be rearranged to get: ln P =
Qst R
1 −
T
Qcooling(bed) = Q1→2 + Q2→3
(15)
where Q1→2 and Q2→3 are the heat to be removed (by the cooling water) from state 1 to state 2 and from state 2 to state 3 respectively, and their corresponding expressions are Q1→2 = (X1 msg Cwater + msg Csg )(T1 − T2 )
+ ln
X
(16)
(9)
K0I
and
This expression reveals the linear relationship between ln P and −1/T, which explains the linear processes in the cycle diagram of Fig. 2. Based on the cycle diagram shown in Fig. 2, the mass of fresh water generated in a single cycle from one bed (i.e. water productivity) can be expressed as mwater = m4–1 = m4 − m1 = X4 msg − X1 msg
(10)
where msg is the mass of the silica gel in one bed, m4→1 is the mass change of the water adsorbed in the silica gel between state 4 and state 1, X1 and X4 are the adsorbed phase concentration at equilibrium for state 1 and 4, which can be calculated by using Eq. (8). Here, the water productivity is of key interest as it is also used to calculate the system energy consumption, EC. The total heating requirement of a single cycle, Qheating(bed) , is the sum of heat in processes of 3 to 4 and 4 to 1, i.e. Qheating(bed) = Q3→4 + Q4→1
Q2→3 = msg Csg +
X + X 2 3 2
msg Cwater (T2 − T3 )
+ (X3 − X2 )msg Qads
(17)
where T1 , T2 and T3 are the corresponding temperatures at each state, X2 and X3 are the adsorbed phase concentration at equilibrium for state 2 and 3, and Qads is the amount of heat needs to be released for the adsorption process of 1 kg of water. In this study, Qads is assumed to be equal to Qdes and Qst . Similar to Eq. (13), Eq. (17) describes the heat to be removed from process 2 to 3, which consists of two parts, namely the heat input to increase the temperature of the adsorbent and the water adsorbed within the adsorbent (i.e. silica gel), and the latent heat required to drive the water evaporating from liquid form to vapour form. Substitute Eqs. (16) and (17) into Eq. (15) leads to Qcooling(bed) = (X1 msg Cwater + msg Csg )(T1 − T2 )
+ msg Csg +
(11)
X + X 2 3 2
+ (X3 − X2 )msg Qads
msg Cwater (T2 − T3 ) (18)
where Q3→4 and Q4→1 are: Q3→4 = (X3 msg Cwater + msg Csg )(T4 − T3 )
(12)
The cooling requirement of the condenser can also be expressed as Qcooling(cond) = msg (X4 − X1 )h1fg
and
Q4→1 = msg Csg +
X + X 4 1 2
msg Cwater (T1 − T4 )
+ (X4 − X1 )msg Qdes
(13)
where T1 , T3 and T4 are the corresponding temperatures at each state, X1 and X4 are the adsorbed phase concentration at equilibrium for state 1 and 4, Cwater is the water specific heat, Csg is the average silica gel specific heat, and Qdes is the amount of heat that 1 kg of water is required for the desorption process. Eq. (13) describes the heat required from process 4 to 1, which consists of two part of heat, namely the heat input to increase the temperature of the adsorbent and the water adsorbed within the adsorbent (i.e. silica gel), and the latent/desorption heat required to drive the water out of the silica gel. Using Eqs. (12) and (13) in Eq. (11) leads to Qheating(bed) = (X3 msg Cwater + msg Csg )(T4 − T3 )
+ msg Csg +
X + X 4 1 2
+ (X4 − X1 )msg Qdes
msg Cwater (T1 − T4 ) (14)
(19)
where h1fg is the specific enthalpy of phase change at the condenser pressure determined by the cooling water temperature. Similarly, the cooling effect in the evaporator, which is a benefit in the chiller mode, can be expressed as Qevap = msg (X3 − X2 )h2fg
(20)
where h2fg is the specific phase change enthalpy at the evaporator pressure. In order to have a clear view of energy consumption of the system per cycle, the energy required per kilogram of water produced, EC, is required. This may be evaluated using EC =
Qheating(bed) mwater
(21)
where mwater and Qheating(bed) are from Eq. (10) and Eq. (14) respectively. It should be noted that this definition of energy required per kilogram of water desalinated does not consider any energy recovery measures and the cooling benefit produced. The following assumptions are used in the study:
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Fig. 4 – The effect of varying hot water inlet temperature on the fresh water production rate and energy requirement per kilogram water produced for two different cooling water temperatures at 20 ◦ C and 30 ◦ C. (1) Temperature difference for heat transfer is 5 ◦ C. (2) Structure mass is ignored. (3) The porous properties of Type RD Fuji Davison silica gel–water system are used, where K0I = 5.5 × 10−12 Pa−1 and Qst = 2370 kJ/kg (Ng et al., 2001). (4) Qads = Qdes = Qst for all Xs .
4.
Results and discussions
4.1.
Effects of hot water temperature
Fig. 4 shows the water productivity and energy consumption versus the heat source temperature when the cooling water is fixed at Tcoolingwater = 20 ◦ C or 30 ◦ C and K0I = 5.5 × 10−12 Pa−1 (Ng et al., 2001). For 20 ◦ C cooling water, the system uses the lowest energy to produce a unit mass of fresh water when the hot water temperature is about 65 ◦ C. The energy cost increases if higher grade energy is used, although the quantity of silica gel required per unit mass of water produced would decrease, thus reducing the costs associated with the adsorbent. The reason of such concave shape of the energy consumption curves (in Fig. 4) is thought to be that the specific adsorptive properties of the particular silica gel chosen makes the increase rate of water production gradually flat out when the (hot source) temperature is 70 ◦ C, while the total energy consumption for the cycle does not vary much with the (heat source) temperature. Therefore, the energy consumption per unit mass of water produced has such trend as shown in Fig. 4.
4.2.
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Fig. 5 – The effect of varying temperature of the cooling water entering both the bed and condenser on the fresh water production rate and energy consumption per kilogram water produced for two different heat source temperature at 75 ◦ C and 90 ◦ C. contrary to the trend for the hot water temperature (Fig. 4), lower cooling water temperature always gives a better outcome: higher fresh water production rate and lower energy consumption rate. In addition, changing the cooling water temperature has a greater impact on the water productivity and energy consumption. For example, reduction of the cooling water temperature by 20 ◦ C (from 25 ◦ C to 5 ◦ C) would lead to a water productivity and energy consumption increase and decrease of 314% and 10.5% respectively, while increasing the hot water temperature by the same amount (from 65 ◦ C to 85 ◦ C) would lead to a productivity increase of just 33.3% along with a small (1.5%) increase in the energy consumption rate. Figs. 6 and 7 show the impact when just one stream of cooling water temperature changes. The latter figure suggests the temperature of the cooling water entering the condenser has little impact on water productivity. Fig. 6 shows, the temperature of cooling water entering the bed has, on the other hand, a more significant impact on the system performance. These
Effects of cooling water temperature
There are cooling water streams: one that cools the beds and a second to the condenser. Figs. 5–7 depict the effects of varying the cooling temperatures on the fresh water production rate and energy consumption per kilogram of water produced. The hot water temperature Thotwater = 90 ◦ C is fixed and K0I = 5.5 × 10−12 Pa−1 (Ng et al., 2001) in this study. Fig. 5 shows the impact of varying simultaneously the temperatures of the cooling water entering the bed and the condenser on the water productivity and energy consumption for two different temperatures of heat source, Thotwater = 75 ◦ C and Thotwater = 90 ◦ C. It can be seen from Fig. 5 that, the change of heat source temperature from 75 ◦ C to 90 ◦ C does not have major effect on either the water productivity or energy consumption. Also,
Fig. 6 – The change of water production rate and system energy consumption on different cooling source temperatures entering the bed, while the cooling water entering condenser temperature is fixed at 20 ◦ C.
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Fig. 7 – The change of water production rate and system energy consumption on different cooling water temperatures entering condenser, while the cooling water entering bed temperature is fixed at 20 ◦ C. results also indicate an air cooled condenser may be suitable. The results in Figs. 5–7, also suggest that any energy recovery effort (to improve energy efficiency of the system) should be on the cooling water side, especially the stream of the cooling water entering the bed rather than the one entering the condenser. For example, the effort should be put into recovering extra cooling generated (in the evaporator) to cool down further the cooling water entering the bed if no external cooling demand (e.g. air conditioning) is required. This would be more effective than recycling the cooling to the stream entering the bed.
4.3. Effects of silica gel adsorption equilibrium constant The value of the silica gel adsorption equilibrium constant, K0I , is determined by the silica gel adsorptive properties. Fig. 8 shows the effect of modifying K0I on the fresh water productivity and energy consumption rate. The determination of K0I
range for the study is based on the consideration that the value of K0I is typically less than 23.7 × 10−12 Pa−1 , which is calculated from the model with the limit of X (i.e. X ≤ 1). There is a linear increase of the fresh water production rate with K0I . In other words, the bigger K0I the better the performance (i.e. increase in water production and decrease in energy consumption). Some surface treatment technologies can improve the K0I value for silica gel. The K0I value has been improved from 2.0 × 10−12 Pa−1 to 5.5 × 10−12 Pa−1 for specific types of silica gel since 1992 (Ng et al., 2001; Wang and Chua, 2007). As the water productivity increases with K0I , the quantity of silica gel required per unit mass of water produced is reduced and, hence, the sensible energy part of the total energy consumption also decreases. However, as the sensible heat component of the energy accounts for just a small fraction (about 17%) of the total energy consumption, K0I only marginally affects the energy consumption as shown in Fig. 8.
5.
Conclusions and future developments
In this study, the working principle and thermodynamic cycle of AD desalinator has been described and its performance evaluated under equilibrium conditions. The analysis shows that there is an optimum hot water temperature existing for the minimum energy consumption of per unit mass fresh water produced. The optimum temperature depends on the cooling water temperatures and other operating parameters of the system. The temperature of the cooling water entering the bed during the adsorption process has significant impact on both the water productivity and energy consumption: the lower the better. Therefore any effort to improve the system performance and reduce costs should be put into the cooling water entering the bed (e.g. recycle the cooling effect from the evaporator). These results also indicate an air cooled condenser may be suitable for the cooling water entering the condenser. The results also show that silica gel adsorption equilibrium constant (K0I ) and the fresh water productivity are linearly related. K0I has little impact on the energy consumption. The use of the equilibrium thermodynamic model here allows rapid calculation and, therefore, consideration of many combinations of system parameters with modest resource. It is, however, recognised that the equilibrium assumption means the results here can only be used as a guide. The model also does not give any information about the dynamic behaviour of AD systems. Both these issues may be overcome by adopting lumped dynamic models such as done by some (Chua et al., 1999, 2004; Wang et al., 2005; Wang and Chua, 2007) or even one- or higher-dimensional dynamic models that allow adsorptive dispersion and bed geometry to be included. Development and application of such models is currently underway in our laboratory and will be reported on in the near future.
References Fig. 8 – The change of fresh water production rate and desalination process energy consumption on different levels of K0I value, when the typical input water temperatures Tcoolingwater = 20 ◦ C and Thotwater = 90 ◦ C are fixed.
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