Modelling of osmotic energy from natural salt gradients dueto pressure retarded osmosis: Effects of detrimental factorsand flow schemes

Wei He, Yang Wang, Mohammad Hasan Shaheed n

School of Engineering and Materials Science, Queen Mary University of London, London E1 4NS, United Kingdom

a r t i c l e i n f o

Article history:Received 19 March 2014Received in revised form30 July 2014Accepted 3 August 2014Available online 11 August 2014

Keywords:Pressure retarded osmosisDetrimental effectsMembrane areaCo-current cross-flowCounter-current cross-flow

a b s t r a c t

In this investigation, a simplified pressure retarded osmosis (PRO) model incorporating the detrimentaleffects of internal polarization concentration (ICP), external polarization concentration (ECP) and reversesalt permeation (RSP) is proposed and verified using published data. The results demonstrate theaccuracy of the model to address decreased water flux and power density due to the performancelimiting effects. Based on the model, the discharge behaviour of a PRO process is reported with respect todifferent applied pressures on the draw solution and two flow schemes, co-current and counter-currentflows. In the co-current flow PRO process, from the flow profiles in the draw and feed channels, it isfound that the adverse effects on the process dynamics, such as water flux and power density, andrequired membrane area, can be regarded as a further retardation by applying ‘an extra applied pressure’on the draw solution. In addition, the capacity of extractable energy of the full scale PRO discharge issignificantly reduced due to the ICP, ECP and RSP effects. Furthermore, the termination conditions of thePRO discharge and its effects on the dynamics of the PRO process are also investigated in the case of thecounter-current flow PRO process.

Crown Copyright & 2014 Published by Elsevier B.V. All rights reserved.

1. Introduction

Osmotic energy from natural salinities has been identified as oneof the major renewable energy sources (RES) since the 1950s [1].Compared with other RES, it is, in fact, less periodic and has nosignificant operational hazards. In addition, the osmotic powerproduction process is eco-friendly with no significant emission ofgreenhouse gases. It offers a huge potential energy capacity, esti-mated to be 2 TW, which is about 13% of the current world energyconsumption [2]. Research groups worldwide investigated the feasi-bility of capturing energy from the mixture of freshwater andseawater [3,4]. In this regard, pressure retarded osmosis (PRO) isone of the most explored technologies [5]. It is an osmotic drivenmembrane process that takes advantage of hydraulic pressureapplied to the draw solution and conversion of osmotic energy intoelectricity by hydro-turbine [6]. Following rapid developments in thefield over the last decade, the technology is now in operational use.In 2009, the world's first PRO plant was launched in Norway with a4 kW capacity.

However, theoretical estimation of potential power generationfrom natural salinities was based on conditions that are not realistictoday, mainly due to the formidable challenges of developing mem-branes providing sufficient specific power density [7]. There is a needfor further optimization of membrane properties such as higher waterpermeability (A), lower salt permeability (B), and smaller structuralparameter (S). Although the current best commercial RO membranescan be used in the PRO process to produce energy, the higherstructural parameter results in a serious performance decrease [8].In addition, the hydraulic pressure applied makes the forward osmosis(FO) membrane, another osmotic-driven membrane, more likely to bedeformed [9]. Therefore, a new membrane specifically for PRO needsto be developed.

Prior investigations to improve the performance of PRO mem-branes have been focused on quantifying, elucidating and thenminimizing the performance limiting phenomena, namely the internalconcentration polarization (ICP) inside the porous support layer,external concentration polarization (ECP) on the draw solution sidenear the membrane surface, and the reverse salt permeation (RSP)across the membrane from the draw solution side to the feed side.In order to minimize these detrimental effects, different membranetypes [10], properties [11,12] and orientations [13], as well as opera-tional conditions have been investigated [14]. It was found that theeffect of ICP, resulting from an asymmetric membrane structure,

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Journal of Membrane Science

http://dx.doi.org/10.1016/j.memsci.2014.08.0020376-7388/Crown Copyright & 2014 Published by Elsevier B.V. All rights reserved.

n Corresponding author. Tel.:þ44 20 7882 3774.E-mail addresses: w.he@qmul.ac.uk (W. He), yang.wang@qmul.ac.uk (Y. Wang),

m.h.shaheed@qmul.ac.uk (M.H. Shaheed).

Journal of Membrane Science 471 (2014) 247–257

becomes severe with higher difference of concentration [12]. The ECPeffect can be reduced with higher cross-flow velocities [15] andspacers in the flow channels [16]. Moreover, several mathematicalmodels have been developed and verified with experiments todescribe the effects on power generation [3,11,13,17–19]. Accordingly,based on these models, many studies have been carried out toinvestigate the PRO process through numerical simulation [20–24].However, only a few investigations have addressed the dynamics ofthe PRO discharge behaviour considering the dilution of the drawsolution and the concentration of the feed solution [25,26].

In the current study, by investigating the two fundamentalinfluencing factors, detrimental effects and flow schemes, theirimpact on the water flux, power density and extractable energy forthe PRO process have been numerically evaluated based on dis-charge behaviour. First, membrane parameters and flow schemeswere derived. Then, two PRO models with and without the limitingeffects were introduced. For the purpose of simplifying calculations,a simplified PRO model is also proposed to approximate the waterflux considering the effects of the ICP, ECP and RSP and verifiedusing both a classic PRO model and experimental data. Besides, onthe basis of the PRO models, the framework of modelling the PROdischarge is provided, and the discharge behaviour of PRO ispresented with respect to different hydraulic pressures applied onthe draw solution and two flow schemes, the co-current andcounter-current cross-flows. Finally, water flux, power density andconcentration profiles have been derived.

2. Preliminary concepts and theories

2.1. Membrane parameters

Thin-film composite (TFC) polyamide membranes are widelyutilized in separating and salt-rejecting membrane processes [27].In general, with a given structural parameter, increasing themembrane water permeability and decreasing the salt permeabil-ity will increase the specific power density [23]. However, achiev-ing high performance is limited by the permeability-selectivity

trade-off relationship of the TFC polyamide membrane [28,29],such that an increase in the membrane water permeability, A, iscommonly accompanied by a corresponding increase in saltpermeability, B. The trade-off relationship between the perme-ability and selectivity can be approximated by a non-linearempirical relation proposed by Yip and Elimelech [29]. In addition,the range of the values of the structural parameter, S, is alsorestricted by the types and functions of the membrane. Thestructural parameter usually ranges from 10 to 10,000 mm, includ-ing conventional TFC reverse osmosis membranes (S¼ 10000 μm)[11], hollow fibre membranes (S¼ 600�1400 μm) [30], hand-castflat sheet membranes (S¼ 300�3000 μm) [31] and nano-fibrecomposite membranes (S¼ 80�110 μm) [32]. Some current mem-brane properties from selected publications are listed in Table 1.

2.2. Flow parameters

The geometry of the simple cross-flow chamber model used inthis study is shown in Fig. 1. A feed solution with low saltconcentration flows through a channel with a PRO membraneside wall. On the other side of the semi-permeable membrane,a draw solution with higher salinity flows in the same direction(co-current scheme in Fig. 1(a)) or in the opposite direction(counter-current scheme in Fig. 1(b)).

The flow parameters are determined by local water conditionsthat comprise concentration and mass flow rates of both the highand low concentration solutions. In the context of natural sali-nities, seawater and brackish water could be used as the drawsolution. The low concentration water from river, sewage, indus-trial wastewater and private effluent can be used as feed water.Furthermore, if high concentration brine water is available, brack-ish water and seawater can also be regarded as potential feedwater. However, the water needs to be pre-treated for thepurposes of preventing membrane fouling. In this study, the drawsolution was selected with a concentration of 35 g/kg and the feedsolution, fresh water, with a concentration of 0.1 g/kg. Bothsolutions are hypothetically considered as ideal based on the fact

Table 1Membrane properties selected from the literature.

No Reference Water permeability,A (L m�2 h�1 bar�1)

Salt permeability,B (L m�2 h�1 � )

Structural parameter,S, (mm)

1 [33] 0.44 0.27 4812 [13] 0.74 0.63 4803 [11] 1.74 0.16 3074 [34] 1.90 0.48 7765 [35] 3.32 0.14 4606 [36] 4.02 1.65 3507 [11] 5.81 0.88 3708 [11] 7.55 5.45 327

Fig. 1. Illustrative flow schemes of a PRO chamber in co-current cross-flow (a) and counter-current cross-flow (b). In the figure, c0F and c0D represent the initial concentrationsof the feed and draw solutions, respectively, q0F and q0D represent the initial mass flow rates of the feed and draw solutions, respectively. And cOUTD and cOUTF are the finalconcentrations of the draw and feed solutions at the outlets, respectively, and qOUTD and qOUTF are the final mass flow rates of the draw and feed solutions at the outlets,respectively.

W. He et al. / Journal of Membrane Science 471 (2014) 247–257248

that they obey the van't Hoff law [37]. Mass flow rates of the twosolutions are described by a dimensionless ratio, ϕ, defined as theratio of the initial mass flow rate of the feed solution to the sum ofthe initial mass flow rates of both feed and draw solutions whichcan be represented as

ϕ¼ q0Fq0F þq0D

ð1Þ

where q0F and q0D are the initial flow rates of the draw and feedsolutions, respectively. In this study, a ratio of 0.5 was assumed bydefault. For simplicity, the initial flow rate of the feed solution isassumed to be 1 kg h�1.

2.3. Mathematical models of a PRO process

The power density of a PRO membrane unit can be representedas

_W ¼ JWΔP ð2Þwhere water flux, JW , across the membrane is determined by

JW ¼ AðΔπm�ΔPÞ ð3Þwhere A is the membrane water permeability, Δπm and ΔP arerespectively the osmotic pressure difference and the appliedpressure difference between the two sides of the membrane.Furthermore, according to van't Hoff's law [38], the osmoticpressure difference can be represented as

Δπm ¼ CosðcD;m�cF ;mÞ ð4Þwhere Cos is the van't Hoff coefficient, cD;m and cF;m are theconcentrations of the draw solution and the feed solution on thetwo sides of the membrane, respectively. The van't Hoff law isrestricted to use on dilute, ideal solutions [39,40]. In the salinityrange of 0–70 g/kg, the linear osmotic pressure approximation isvalidated and the maximum deviation is 6.8% [38,41]. Since thisstudy aims to address the overall effect of ICP, ECP and RSP on thePRO process dynamics by comparing the difference between thetwo models, at the first stage, the linear van't Hoff law is used inapproximating the osmotic pressure.

2.3.1. Two PRO modelsIdeally, without any consideration of concentration polarization

effects, the concentration of the solution near the membranesurface is equivalent to the concentration of the bulk flow. In thiscase, the concentration of the solutions near the membrane can beapproximated as

cD;m ¼ cD;b; cF;m ¼ cF ;b ð5Þin which cD;b and cF ;b represent the concentrations of the bulk flowof the draw and feed solutions.

However, the ideal condition cannot be ensured because of theexistence of ICP, ECP, and RSP. Due to these detrimental effects theosmotic driving force is lower than the osmotic pressure differencebetween the bulk draw and feed solutions. Several mathematicalmodels have been developed to represent the concentration differ-ence between the two sides of the membrane in terms of bulkconcentrations. One of these models, which was developed byMcCutcheon and Elimelech [17,18], was for osmotic flux and incor-porated a dense, symmetric membrane. Elsewhere, the effect of drawsolution concentration, draw solution flow rate, feed water flow rate,and membrane orientation on PRO water flux performance andderived PRO water flux equations combining the ICP effect wasstudied by Xu et al. [12]. Recently, a derivation of the complete waterflux equation for the PRO process, taking all ICP, ECP and RSP effectsinto consideration was presented by Yip et al. [11]. According to their[11] study, when the solute permeability is much less than the

permeate flux, the concentration difference between the two sides ofthe membrane can be represented as

cD;m�cF;m ¼ cD;bexpð� JW=kÞ�cF;bexpðJWS=DÞ1þ B

JW½expðJWS=DÞ�expð� JW=kÞ� ð6Þ

where D is the bulk diffusion coefficient, k¼D=δ is the boundarylayer mass transfer coefficient in which δ is the boundary layerthickness, and S¼ tsτ=ε is the support layer structural parameter inwhich ts is the thickness of the porous layer, τ and ε are thetortuosity and porosity of the support layer of the membrane,respectively. In Eq. (6), the effects of ECP and ICP are described bythe first and the second terms of the numerator on the right handside, whilst the denominator accounts for the effect of RSP at themembrane interface [29].

In the current study, two kinds of PRO models are used toinvestigate the different flow schemes of the PRO process. They arethe ideal PRO (I-PRO) model and the PRO model with detrimentaleffects (D-PRO). The water flux, JW , based on the two models wasobtained. The I-PRO model can be represented as

JI�PROW ¼ AðCosðcD;b�cF;bÞ�ΔPÞ ð7Þ

Whilst the D-PRO model can be expressed as

JD�PROW ¼ A Cos

cD;bexpð� JD�PROW =kÞ�cF;bexpðJD�PRO

W S=DÞ1þðB=JD�PRO

W ÞðexpðJD�PROW S=DÞ�expð� JD�PRO

W =kÞÞ

!�ΔP

!

ð8Þ

In addition, when the RSP effect is considered, the reversesolute flux, JS, is also included

JS ¼ BðcD;m�cF;mÞ ¼ BcD;bexpð� JD�PRO

W =kÞ�cF ;bexpðJD�PROW S=DÞ

1þ BJD�PROW

ðexpðJD�PROW S=DÞ�expð� JD�PRO

W =kÞÞ

0@

1Að9Þ

2.3.2. Discharge behaviour of the PRO processWater flux is, in fact, the velocity of the permeated mass flow

per unit area of membrane. From this view point, at the steady-state, the water flux can be expressed as

dðΔqPÞ ¼ ρF JwdðAmÞ ð10Þwhere ΔqP is the mass rate of permeated water, ρF is the densityof permeating water, and Am is the area of the membrane. Inaddition, when RSP effect is included in the modelling, thetransporting rate of the reverse solute permeation is also crucialand can be expressed as

dðΔSÞ ¼ ρDJSdðAmÞ ð11Þwhere ρD is the density of the draw solution, and ΔS is the massrate of the reverse solute.

Based on the I-PRO model, if the water flux is expressed interms of the permeated mass of water, Eq. (10) can be solved withrespect to mass rate of permeated water. Therefore, in accordancewith mass balance, the concentration of the bulk solutions can beexpressed in terms of their initial conditions [26]

cD;b ¼1�ϕ

1�ϕð1�ðΔqP=q0F ÞÞc0D;b; cF ;b ¼

11�ðΔqP=q0F Þ

c0F ;b ð12Þ

where c0D;b and c0F ;b are the initial concentrations of the bulk drawand feed solutions. However, when the RSP effect is considered,the mass balance will be changed to

cD;b ¼c0D;bq

0D�ΔS

q0DþΔqP¼c0D;bð1�ϕÞ�ϕΔS=q0F1�ϕð1�ΔqP=q0F Þ

;

W. He et al. / Journal of Membrane Science 471 (2014) 247–257 249

cF;b ¼c0F;bq

0F þΔS

q0F �ΔqP¼c0F ;bþΔS=q0F1�ΔqP=q0F

ð13Þ

2.3.3. The approximated D-PRO (AD-PRO) modelDue to the high non-linear relation of the D-PRO model repre-

sented by Eq. (8), it is difficult to solve the ODE of permeated watermass transfer rate based on the D-PROmodel. An equation such as thisusually needs to use iterative methods to solve a non-linear equationin each position along the membrane channel to get the changingwater flux. In order to reduce the computational effort, the water fluxrepresented by Eq. (8) can be simplified by using the first order Taylorseries which means that Eq. (8) can then be written as

JAD�PROW ¼ AðCosðcD;b�cF ;bÞ=ð1þBS=DþB=kÞ�ΔPÞ

1þACosðcD;b=kþcF ;bS=DÞ=ð1þBS=DþB=kÞ ð14Þ

3. Simulation and results

Based on the models, the simulation of the two flow schemeswas carried out with the following assumptions:

(i) Pressure drop through the flow channel is negligible in thecase of both feed and draw solutions of the both flowchannels. A constant hydraulic pressure is applied on thedraw solution, and no pressure is applied on the feed solution.

(ii) Osmotic pressure is linearly proportional to the concentrationdifference based on the van't Hoff law [39] in the range of saltconcentrations used in this study.

(iii) Mass flow rates are averaged in the cross-section area of thetwo flow channels. Accordingly, it becomes a one dimensionalproblem in each flow channel, and the mass transfer coeffi-cient is constant when the effect of ECP is considered.

(iv) Membrane fouling does not occur.

3.1. AD-PRO model verification

On the basis of the permeability-selectivity trade-off and themembrane properties discussed earlier (Section 2.1), three mem-branes from Table 1 are selected for the verification of theproposed AD-PRO model (membranes 3, 5, 7) representing a lowpermeability (LP) PRO membrane, a medium permeability (MP)PRO membrane and a high permeability (HP) PRO membrane,respectively. The parameters used in the calculation are: tempera-ture 298 K, mass transfer coefficient 138.6 L m�2 h�1 [11], diffu-sion coefficient 1.49�10�9 m2 s�1 [3], and van't Hoff coefficient0.7345 bar kg g�1 [38]. Empirical expression for the changingdensity (in kg L�3) of both draw and feed solutions is [42]

ρ¼ 0:9971þ0:694c1000

ð15Þ

where c is the solution concentration on the surface of themembrane, such as cD;m and cb;m. The water flux and powerdensity of the three membranes based on the I-PRO, D-PRO andAD-PRO model are shown in Fig. 2.

Because the D-PRO model has been verified using experimentaldata with satisfactory consistency [11], the effects of ICP, ECP andRSP can be estimated by the difference between the solid and

Fig. 2. Modelled water flux and power density as a function of applied hydraulic pressure based on I-PRO, D-PRO and AD-PRO models. The results of the LP, MP and HPmembranes are shown in (a), (b) and (c), respectively. The water flux is the transient value based on the infinitesimal membrane area. The draw solution is seawater (35 g/kg), and the feed solution is fresh water (0.1 g/kg).

W. He et al. / Journal of Membrane Science 471 (2014) 247–257250

dashed curves in Fig. 2 representing water flux and powerdensities, respectively. It is observed from Fig. 2 that the waterflux and power density of the PRO process with detrimental effectsare significantly reduced compared with the ideal water flux for allthe LP, MP and HP membranes selected. In addition, the differencein water flux and power density between the I-PRO and D-PROmodels increases with the membrane of higher water permeabil-ity. According to Eq. (8), this is due to more severe ICP, ECP and RSPeffects caused by the increased water flux.

From the results, it can be concluded that a linearized AD-PROmodel can be used to describe the water flux and power density ofthe LP membrane with very high accuracy, and the accuracydecreases with more severe effects of the ICP, ECP and RSP inthe cases of high water permeability membranes. In Fig. 2(a), thecircled line is almost overlapped by the dashed line for all theapplied hydraulic pressure. This is the same as the situation in themodelling of power density of the LP membrane in Fig. 2(a). Inaddition, in Fig. 2(b) and (c), although the water flux and powerdensity based on the AD-PRO model are higher than the values onD-PRO model, the water flux and power density based on the AD-PRO model still address the significant decrease caused by theeffects of ICP, ECP and RSP. Therefore, in the later investigation, theAD-PRO model was used to address the three detrimental effectsin simulating the PRO processes. The LP membrane was selected tofurther study the discharge behaviour of the PRO process due to itshigh accuracy.

In addition to the comparison with existing D-PRO model, theAD model is also verified with experimental data. The results areshown in Fig. 3 in which the water flux and power densitybased on the AD-PRO model are validated using experimentaldata [43]. The membrane parameters listed in this study werewater permeability, A, 1.35 L m�2 h�1 bar�1, salt permeability,B, 0.28 L m�2 h�1, and structure parameter, S, 149 mm. The resultsshow satisfactory agreement between the model and experimen-tal data in the case of both the mixture of seawater and brackishwater, and the mixture of the seawater and river water.

3.2. Co-current flow scheme

In the co-current flow scheme, the two respective streams ofthe draw and feed solutions, c0D and c0F , are in the same directionwith mass flow rates of q0D and q0F , respectively. Here, a dimension-less water flux is defined for the use of inlet and outlet conditions

in all cases. The dimensionless water flux, JnW is represented as

JnW ¼ JWJMAXW

¼ JWACosðc0D�c0F Þ

ð16Þ

where JMAXW is the maximum water flux in PRO with zero hydraulic

pressure difference. Therefore, the inlet condition and outletcondition can be expressed as

Jn;INW ¼ JINWJMAXW

¼ c0D;m�c0F ;m�ΔP=ðCosÞc0D�c0F

;

Jn;OUTW ¼ JOUTW

JMAXW

; ð17Þ

where JINW and JOUTW represent the water fluxes at the inlet andoutlet, respectively. Theoretically, for a full scale PRO discharge,the water flux reduces to zero at the outlet. However, it is verydifficult to reach absolute zero flux numerically, especially whenthe salt concentration of the feed solution is zero or very diluted.Thus, Jn;OUTW ¼ 0:01 is used as the outlet condition for a full scalePRO discharge (actual water flux is approximately 0.5 L m�2 h�1

with the given initial condition of the salinities).

3.2.1. Water flux and power densityBy updating the salt concentration of the draw and feed

solutions represented by Eqs. (12) and (13) into permeated watermass flow rate expressed by Eq. (10), an ODE describing permeatedwater flux based on the I-PRO model can be obtained. When thedetrimental effects are included, considering the reverse solute fluxrepresented by Eq. (9), a system of ODEs on mass rate of permeatedwater and mass rate of reverse solute permeation can also beobtained. Moreover, with the inlet and outlet conditions of the co-current flow PRO discharge, the ODEs can be solved and water fluxand power density can be obtained. The flowchart of simulating thePRO discharge is illustrated in Fig. 4. The stopping condition of thecalculation is satisfied when the outlet condition is reached.The water flux and power density with three different appliedhydraulic pressures are shown in Figs. 5 and 6, respectively.

The difference between the water flux shown in Fig. 2 and thewater flux profiles shown in Fig. 5 is that the results presented inFig. 2 are the transient water flux for the membrane areaapproaching zero, while Fig. 5 shows the profiles of water fluxalong the channel with enough membrane area during thedischarge of the PRO process. First of all, with increased appliedhydraulic pressure, less deviation between the two profiles of

Fig. 3. Verification of the AD-PRO model with the experimental data. Circle symbols in (a) and (b) are the experimental results of the mixture of the seawater brine and riverwater, respectively. Square symbols in (a) and (b) are the experimental results of the mixture of the seawater brine and brackish water, respectively.

W. He et al. / Journal of Membrane Science 471 (2014) 247–257 251

water flux with and without consideration of ICP, ECP and RSPeffects is obtained. As illustrated in Fig. 5(a), with 20 bar appliedon the draw solution, the two profiles are overlapping over most ofthe membrane area. The insignificant reduction on the water fluxis a result of the lower water flux caused by the higher appliedpressure. In addition, for operation with different hydraulic pres-sures, the highest transient water flux is observed at the inlets.This causes a larger deviation of the AD-PRO process from theI-PRO process. With the water flux decreasing along the mem-brane channel, the deviation also decreases. Actually, the overallperformance limiting effects are reflected by the reduction on the

net driving force. In this context, the water flux can be expressedas

JD�PROW ¼ AðΔπm�ΔPÞ ¼ A½Δπb�ðΔPþΔπb�ΔπmÞ� ð18Þwhere Δπb is the osmotic pressure difference of the bulk solu-tions. The performance limiting effects on the water flux can beregarded as the effect of ‘an extra applied pressure’ to furtherretard the water transportation across the membrane. As such, inFig. 5(a), all the dashed curves representing the water fluxconsidering detrimental effects start at a lower value and behavesimilarly as the profiles of water flux with a higher hydraulic

Fig. 4. Flowchart of the PRO discharge modelling.

Fig. 5. Water flux along the membrane during the steady-state co-current cross-flow PRO discharge with different applied hydraulic pressures in (a) and the approximateddecreased water flux by ‘an extra applied pressure’ in (b). The dimensionless flow ratio is 0.5. The draw solution is seawater (35 g/kg), and the feed solution is fresh water(0.1 g/kg). In (a), ΔP¼7, 12.5, and 20 bar increasing in the direction of the arrow.

W. He et al. / Journal of Membrane Science 471 (2014) 247–257252

pressure applied on the draw in the I-PRO process. Although the‘extra applied pressure’, Δπb�Δπm, varies along the membranechannel, an averaged pressure can be implemented on the drawsolution of the I-PRO process to approximate the profile. This is incomparison with Fig. 5(b) where the detrimental effects can beapproximated by applying a constant ‘extra pressure’ on the I-PROmodel. In Fig. 5(b), the water flux based on the I-PRO model withΔP ¼ 9 bar is relatively closer to the profile of water flux consider-ing the detrimental effects.

It is seen from Fig. 6 that the power density also changes withdifferent applied pressures, a result of water flux change based onEq. (2). In addition, the effects of ICP, ECP and RSP also lower thepower density at the start. Moreover, the ‘extra pressure approx-imation’ of the performance limiting is still validated in the powerdensity due to the close relation between the water flux and thepower density.

3.2.2. Extractable energyThe extractable energy of a PRO plant is assessed from the view

of the full scale discharge. The extractable energy of the PROprocess can be obtained as [26]

E¼ΔVPΔP ð19Þwhere ΔVP is the volumetric flow rate of the permeated water.It can be obtained using the permeating water density where

ΔVP ¼RJWdAM . Based on the full scale PRO discharge behaviour,

the extractable energy of the PRO process considering ICP, ECP andRSP is shown in Fig. 7 in which three dimensionless flow ratios of0.2, 0.5 and 0.8 are studied to represent the different volumes ofsalinities available worldwide. For the purpose of comparison, theextractable energy profiles of the three conditions in the I-PROprocess are also presented.

The results clearly indicate the significant reduction on theextractable energy capacity of the full scale PRO discharge on allexamined flow ratios. With the constant hydraulic pressure on thedraw solution, the ICP, ECP and RSP effects on the process-basedextractable energy are determined only by the reduced mass rateof permeated water as presented in Fig. 7(b). The decrease is aresult of an accumulating effect of the reduced water flux alongthe membrane caused by the overall effect of ICP, ECP and RSP.

3.2.3. Required membrane area for PRO dischargeThe water flux and power density obtained above in Fig. 2

reveal the change of profiles with different hydraulic pressuresapplied on the draw solution. It is also observed that the detri-mental effects drive the water flux and power density away fromthe ideal behaviour of the PRO process. But the required mem-brane area of the PRO process cannot be easily differentiated in thecases of 12.5 and 20 bars as demonstrated in Figs. 5 and 6. Thus,the change on required membrane area of the PRO process isneeded to be studied further. The concept is to describe theminimum area required to reach the predefined outlet condition.By rearranging Eq. (10), the required membrane area can beexpressed as

AM ¼Z

1ρJW

dΔqP ð20Þ

Previously, in Section 3.2.1, it has been shown that the waterflux keeps decreasing after entering in the co-current PRO process.Therefore, the required membrane area of a full scale PROdischarge used is the minimum area that allows the dimensionlesswater flux to be reduced to 0.01. The required membrane area of afull PRO discharge is shown in Fig. 8.

Theoretically, if there is no RSP and with a zero salt concentra-tion in the feed solution, the permeated flux will never reach zero,except for infinite membrane area, because the driving force onthe feed solution side will not vanish when the water is permeat-ing. In Fig. 8(a), with a zero salt concentration feed solution (DIwater in practice), huge amount of the area is required at lowerrange of the hydraulic pressure even to reach the “pseudo zerowater flux” (Jn;OUTW ¼ 0:01 ). With a non-zero salt concentration(0.1 g/kg illustrated in Fig. 8(a)) in the feed solution, the hypotheticinfinite membrane area of the I-PRO process without RSP is notneeded.

Comparing the two PRO models in the modelling of requiredmembrane area, it is found that the curve of the area representingthe full scale AD-PRO discharge can be approximated by atranslational curve of area representing the full scale I-PRO processtowards the lower hydraulic pressure. It is a demonstration of the‘extra pressure approximation’ of the overall effects of ICP, ECP andRSP on the dynamics of the PRO. Because in the I-PRO process,with respect to the range of the available lower hydraulic pressure,and with the increase on the pressure, more membrane area isrequired for a full scale discharge. Thus, for the AD-PRO processapproximated by applying ‘an extra pressure’ on the draw solutionin the I-PRO process, more area is required in the lower range ofthe hydraulic pressure. Conversely, less area is required for theoperations in the higher range of applied pressure. Furthermore,the deviation of the area required in the different PRO operationsbetween the two processes also varies because of the differentmagnitude of water flux. When water flux is lower, the

Fig. 6. Power density along the membrane during the steady-state co-currentcross-flow PRO discharge with different applied hydraulic pressures. The dimen-sionless flow ratio is 0.5. The draw solution is seawater (35 g/kg), and the feedsolution is fresh water (0.1 g/kg).

W. He et al. / Journal of Membrane Science 471 (2014) 247–257 253

detrimental effects are insignificant. As shown in Fig. 8(a), the twocurves of area are almost overlapping when the applied pressure islarger than 20 bar.

In addition, the required area of different scale of PRO dischargeis also evaluated. In Fig. 8(b), the outlet condition is 0.2 dimension-less water flux (approximate 10 L m�2 h�1). The results demon-strate that the overall detrimental effects on the required area aresignificant in all the operations. It is also clear from the results thatthe approximation of the AD-PRO by applying ‘an extra pressure’on draw solution of the I-PRO is more feasible.

3.2.4. Salinity concentration and driving force profileAn average salinity concentration variation along the membrane

can be also obtained according to mass balance. Besides, if theconcept of osmotic driving force of each solution on the two sides ofthe membrane is defined as the difference between the osmoticpressure and the hydraulic pressure, then the driving force of waterflux across the membrane is the difference of the driving forcebetween the membrane surfaces in the two solution channels.

Fig. 7. Effects of ICP, ECP and RSP on the extractable energy capacity of the full scale PRO discharge. (a) Three dimensionless flow ratios (0.2, 0.5 and 0.8) of salinity gradientsare investigated. (b) The accumulated permeated flow rates of three conditions considering the detrimental effects are shown. The draw solution is seawater (35 g/kg), andthe feed solution is fresh water (0.1 g/kg). In both (a) and (b), ϕ¼0.8, 0.5 and 0.2 decreasing in the direction of the arrow. The flow rate of the feed solution is 1 kg/h.

Fig. 8. Required membrane area in the PRO discharge. Results in (a) are the required area of the full scale PRO discharge with zero and non-zero (0.1 g/L) feed saltconcentrations modelled by the two PRO models. Results in (b) are the required membrane area of PRO discharge with a non-zero water flux at the outlet. In (b), the outletdimensionless water flux is 0.2. The dimensionless flow ratio is 0.5. The draw solution is seawater (35 g/kg), and the feed solution is fresh water (0.1 g/kg) or DI water(0 g/kg). The flow rate of the feed solution is 1 kg/h.

Fig. 9. The driving forces of the draw and feed solutions along the co-current flowPRO membrane module. The dimensionless flow ratio is 0.5. The draw solution isseawater (35 g/kg), and the feed solution is fresh water (0.1 g/kg).

W. He et al. / Journal of Membrane Science 471 (2014) 247–257254

Therefore, the driving force of a solution is defined as

DFi ¼ πi�Pi ð21Þ

where DFi is the driving force and πi and Pi are the osmotic pressureand hydraulic pressure, respectively. Higher osmotic driving force ineach side allows higher permeating rate of water from the oppositeside of the membrane. Accordingly, the driving forces of the drawand feed solutions along the membrane in the I-PRO process areillustrated in Fig. 9 with three hydraulic conditions. From Fig. 9, it isobserved that during the PRO discharge, the driving force of the drawsolution decreases and the corresponding increase occurs in the feedsolution. Water permeation terminates when the two driving forcesare equalised. In addition, the profiles of the driving force aredifferent with different values of the applied hydraulic pressure.With a lower applied pressure such as 7 bar illustrated in Fig. 9, theterminated driving force at the outlet of the flow channel is aconsequence of the rapidly increasing driving force on the feed sidedue to the lack of the feed solution. In such a case, the variation onthe driving force of the feed solution side dominates the terminationof the PRO discharge. This is also the reason why large membranearea is required when the feed salt concentration is zero in the PROoperations with a lower hydraulic pressure. In contrast, when ahigher hydraulic pressure is applied, the equilibrium of the concen-tration between the two sides across the membrane is mainly aresult of the dilution effect of the draw solution.

3.3. Counter-current flow scheme

In the case of a counter-current flow scheme, the two streamsof the draw and the feed solutions flow in the opposite directions.The inlet and outlet conditions of the two channels should beconsidered separately, and depending on different applied hydrau-lic pressures, the terminated condition of the water flux varies.

Similarly, the initial concentrations of the draw and the feedsolutions are c0D and c0F , respectively, and the mass flow rates are q0Dandq0F , respectively. Because of the different positions of the twostreams' inlets and outlets, from the view of the dimensionlesswater flux, two conditions can be expressed as

condition 1 ðFeed DirectionÞ :

Jn;INW ¼cOUTD;m �c0F;m�ΔP

Cos

c0D�c0F; Jn;OUTW ¼

c0D;m�cOUTF ;m �ΔPCos

c0D�c0F

condition 2 ðDraw DirectionÞ :

Jn;INW ¼c0D;m�cOUTF ;m �ΔP

Cos

c0D�c0F; Jn;OUTW ¼

cOUTD;m �c0F ;m�ΔPCos

c0D�c0Fð22Þ

where cOUTD;m and cOUTF;m are the concentrations of the draw and feedsolutions on the surface of the membrane at their outlets. In thecase of condition 1, the zero water flux is reached at the outlet ofthe feed solution channel. In contrast, the termination of the waterflux happens at the outlet of the draw solution channel in the caseof condition 2. Based on Eq. (12) describing the solute balance inthe I-PRO process and the termination conditions above, theapplied hydraulic pressure is divided into three parts

ΔP0 ¼ Cos½ð1�ϕÞc0D�ϕc0F � condition 1&2

ΔP ¼ΔP1oΔP0 condition 1

ΔP ¼ΔP24ΔP0 condition 2 ð23Þ

where ΔP0 represents the applied hydraulic pressure when bothconditions 1 and 2 are satisfied simultaneously, and ΔP1 and ΔP2

represent the two ranges of hydraulic pressure and conditions1 and 2 are satisfied separately in the I-PRO process.

3.3.1. Water flux and power densitySimilarly, with the inlet and outlet conditions of a counter-

current flow scheme, the ODE describing the water permeationcan be solved and then the water flux and power density can beobtained based on Eqs. (7) and (2) during the steady-statedischarge of the I-PRO process. The resulting water flux and powerdensity are studied. Due to these two conditions, the results ofeach flow with three different applied hydraulic pressures areshown in Fig. 10.

The positions of the zero water flux are different in the case oftwo termination conditions. According to Eq. (22), withcondition 1 applied, the water flux terminates at the outlet ofthe feed solution. In contrast, condition 2 is reached at the outletof the draw solution. This is illustrated in Fig. 10 where (a) and(b) represent condition 1, and (c) and (d) represent condition 2.The zero points of the area-axis (x-axis) in Fig. 10 represent theinlet of the draw solution. Thus, all the results are presented in thesame x-axis direction of the flow of the draw solution, namelyfrom the left to the right as illustrated in Fig. 1(b). In PROoperations under condition 1, the water flux at the outlet of thefeed solution is always zero for a full scale PRO discharge. As notedin Fig. 10(a), from the inlet of the feed solution, the water fluxstarts at a non-zero value, increases gradually during the PROdischarge until its maximum is reached. Then the water fluxdecreases to zero rapidly before flowing out of the feed channel.In addition, the starting value on the right hand side ofFig. 10(a) decreases with the increase of the applied pressure inthe range of ΔP1. When the value of ΔP1 approaches to ΔP0 (inthis case, ΔP0 ¼ 12:817 bar), the starting water flux also getscloser to zero as illustrated in Fig. 10(a) when 12.5 bar is appliedon the draw solution. In such a case, water flux at both ends isnearly zero. Conversely, in the PRO operations applying hydraulicpressure in the range of ΔP2, the termination of the full scaledischarge occurs at the outlet of the draw channel. The profilesof the water flux in a counter-current scheme (Fig. 10) PRO processare more even comparable to that in co-current flowscheme (Fig. 5) because of the lower maximal value and the largerminimal value. Moreover, according to the findings of Thorsen andHolt[8], the power yielding from a membrane module is similar forco-current and counter-current cross-flows in practice. However,the more evenly distributed water flux of the counter-currentmeans that its maximum water flux is lower than that of the co-current scheme, and therefore, comparatively, it possesses a lowerpossibility to be fouled at the higher water flux. From this point ofview, the counter-current flow scheme is preferred.

3.3.2. Driving force profileThe driving forces of the two solutions along the membrane

were also studied. The results of I-PRO process with two condi-tions are presented in Fig. 11(a) and (b), respectively. Also thedriving force profiles of the counter-current flow PRO process areshown using the same area-axis (x-axis) as Fig. 10.

From Fig. 11, it is evident that the driving forces of the draw andfeed solutions change along the membrane in the same direction,This can be seen where both the driving forces decrease from theleft hand side to the right hand side of the membrane module (flowdirection of the draw solution as illustrated in Fig. 1(b)). Condition 1,as represented by Fig. 11(a), clearly indicates a more retarded waterpermeation due to the reduced net driving force with a higherapplied pressure. Also, the different applied hydraulic conditionsinduce different driving force profiles along the membrane for boththe conditions as represented in Fig. 11(a) and (b). Based on theprofiles of the driving force of the water permeation in the counter-current PRO flow scheme, it is found that the difference betweenthe two termination conditions is due to the disappearance of the

W. He et al. / Journal of Membrane Science 471 (2014) 247–257 255

net driving force for different reasons. Similar to the co-current flowscheme, in the case of condition 1 (lower range of availablehydraulic pressure, ΔP1), the water flux is terminated as a resultof the shortage of the feed solution near the outlet of the feedsolution. The ‘over-permeation’ of the feed solution increases itsconcentration rapidly and terminates the water flux sharply. Con-versely, the dilution of the draw solution reduces the driving forcegradually and terminates the water permeation in condition 2 whenthe applied pressure is in the higher range as denoted by ΔP2.

4. Conclusions

An analysis of the PRO processes for energy production fromnatural salinities has been performed with and without detri-mental effects. The I-PRO and D-PRO models are introduced andan approximated AD-PRO model is proposed and compared withpublished data. Furthermore, water flux and power density of thePRO processes with co-current and counter-current flow schemeshave been studied and analysed. In addition, the driving force

Fig. 10. Water flux and power density along the membrane during the steady-state counter-current cross-flow PRO discharges with different applied hydraulic pressures.The water flux and power density of counter-current flow PRO process in the case of termination condition 1 are shown in (a) and (b), respectively. The water flux and powerdensity of counter-current flow PRO process in the case of termination condition 2 are shown in (c) and (d), respectively. The dimensionless flow ratio is 0.5. The drawsolution is seawater (35 g/kg), and the feed solution is fresh water (0.1 g/kg).

Fig. 11. The driving forces of the draw and feed solutions along the counter-current flow PRO membrane module. The counter-current flow PRO within the terminationconditions 1 and 2 are shown in (a) and (b), respectively. The dimensionless flow ratio is 0.5. The draw solution is seawater (35 g/kg), and the feed solution is fresh water(0.1 g/kg).

W. He et al. / Journal of Membrane Science 471 (2014) 247–257256

profiles along the different membrane modules and operationswith different applied hydraulic pressures are also analysed. Basedon the results of this study, the following conclusions can bedrawn: (1) the proposed AD-PRO model can be used to approx-imate water flux and power density of the PRO process incorpor-ating the effects of ICP, ECP and RSP, especially, for the PRO processwith low water permeability membrane where a very highaccuracy is achieved; (2) during the discharge of a full scale PROprocess, the detrimental effects further retard the water permea-tion and power generation and both water flux and power densitystart at much lower values and behave similar as that with an‘extra pressure’ applied on the draw solution in an ideal PROprocess; (3) the capacity of the extractable energy from a full scalePRO discharge is significantly reduced due to the ICP, ECP and RSPeffects; (4) termination of the water permeation is a result of therun out of the draw solution or the feed solution, determined bythe hydraulic pressure applied on the draw solution in both co-current and counter-current flow PRO processes; and (5) the waterflux of the counter-current flow PRO process varies more evenlyalong the membrane channel compared to that of the flux of theco-current flow PRO process.

Acknowledgments

The authors would like to thank Professor Pankaj Vadgama forhis constructive suggestions to improve the manuscript.

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