Operating Energy Consumption Analysis of RO Desalting System

Article pubs.acs.org/IECR

Operating Energy Consumption Analysis of RO Desalting System: Effect of Membrane Process and Energy Recovery Device (ERD) Performance Variables Bingwei Qi, Yue Wang,* Shichang Xu, Zhaocheng Wang, and Shichang Wang Chemical Engineering Research Center, School of Chemical Engineering and Technology, Tianjin Key Laboratory of Membrane Science and Desalination Technology, Tianjin University, Tianjin 300072, People's Republic of China ABSTRACT: Significant improvement in reverse osmosis (RO) membrane permeability makes the emergence of thermodynamic restriction in desalting process. Due to the filtration flux, both the accumulation of rejected solute and the subsequent concentration polarization layer contribute to the transmembrane osmotic pressure difference that needs to be overcome by the applied pressure. A theoretically derived formula predicting the permeate flux accounting for pressure drop, effect of applied pressure on solute rejection and concentration polarization is presented, and the obtained average rejection is used to calculate the operating energy consumption of RO process more accurately. On the basis of theoretical considerations, at the limit imposed by thermodynamic restriction, an energy consuming analysis model of RO process was developed to study the effects of RO operating parameters (e.g., recovery rate), energy recovery devices (ERDs) performance variables (efficiency and leakage ratio), and pump efficiencies on the specific energy consumption (SEC).

1. INTRODUCTION Reverse osmosis (RO) technology has been accepted worldwide as a reliable way to produce potable and industrial water of specific requirements. However, there are still many constraints that prevent it from increasing deployment, especially the high operating energy consumption. Generally, the total cost of RO desalting process consists of pretreatment of raw seawater, capital cost (typically including membrane and pump), maintenance of equipment, energy required (i.e., operating cost), and brine disposal cost. Actually, operating cost is the major part of the total cost of RO desalting process and can reach as high as 45% of the product charges,1,2 which is largely due to the high pressure required to overcome the transmembrane osmotic pressure (up to about 1000 psi for seawater and in the range 200−600 psi for brackish water desalting).3,4 Due to its especial importance, the operating energy consumption analysis of RO process is the main topic of the present study. The permeate flux is a major concern in both RO system design and analysis of energy consumption. The permeate flux is dependent on the net driving force (pressure difference between the applied transmembrane pressure and real osmotic pressure) and the membrane resistance. As filtration proceeds, the rejected solute accumulates near the membrane surface and forms a layer with higher solute concentration than the bulk field. This phenomenon is called concentration polarization.5−7 Clearly, an additional osmotic pressure would be generated due to the concentration polarization layer and reduce the net driving force of RO process. It has been reported that the concentration polarization would be significant for highly permeable membranes under high solute concentrations and high applied pressures.8 Meanwhile, it is also claimed that the rapid increment of osmotic pressure, due to high permeate flux, which could be considered as “concentration polarization in the longitudinal direction”, would make it possible to approach the applied transmembrane pressure.9−12 This phenomenon is called © 2012 American Chemical Society

thermodynamic restriction. Even though it is indicated that the concentration polarization is usually weaker than the thermodynamic limit for highly permeable membranes in previous work,13 the locally varying rejection mainly due to concentration polarization is derived to estimate the operating energy consumption of RO process more accurately. As known, the concentration polarization was investigated relatively completely, but few publications referring to the operating energy consumption analysis of RO accounted for this phenomenon. Therefore, with continuous improvement of membrane permeability, it is indeed needed to study the operating energy consumption of RO process at the thermodynamic limit with taking concentration polarization into consideration. In addition, the average solute rejection was obtained by integrating the locally varying solute rejection from the inlet to the exact point of RO channel. Besides the membrane process mentioned above, there are other factors affecting the operating energy consumption of RO process. To reduce the energy consumption of RO desalting process, considerable efforts have been made from several points of view: the hydraulic permeability improvement of RO membranes, optimization of the configurations of RO arrays, and employment of energy recovery devices (ERDs). Zhu14 proposed that apparent reduction in the cost of RO water desalination was less likely to arise from the development of significantly more permeable membranes. The second viewpoint, configurations optimization of RO arrays, was extensively studied in previous works.15−19 The focus was mainly put on the constructure improvement of RO module (e.g., high hydraulic performance, feed channel height, etc.) and arrangement of the Received: Revised: Accepted: Published: 14135

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⎛ R c w = cb + Cw = cb⎜1 + 2t j(x)2 Dγ ⎝

RO vessels. The third point refers to the ERDs, which can extract the energy from the high pressure retentate brine and transfer it to the raw seawater efficiently (up to 98%),20 therefore significantly reducing the energy consumption of RO process. The investigations of effect of ERDs on energy consumption of RO desalting process date back to the 1960s.21,22 In our earlier works,23,24 an innovative positive displacement (PD) type of energy recovery device called FS-ERD was introduced and tested. In this paper, we extend our earlier work to study the effect of ERD performance variables (efficiency and leakage ratio) on the SEC of RO process at the thermodynamic limit for both single-stage and two-stage crossflow RO processes, with taking pressure drop in the feed channel, locally varying rejection along the RO channel and concentration polarization into account. In addition, the effect of pump efficiency is also discussed and analyzed.

j( x ) =

∞

γyC dy = R tcb

R tcb 2

Dγ

j(x)2

∫0

(6)

ΔP − Δπm Δπm

(6a)

1/3 R m ⎛ D2 γ ⎞ M= ⎟ ⎜ Δπm ⎝ L ⎠

(6b)

F=

and N = 1 + 6F 2X /M3

(6c)

Here, X (defined as x/L) is the longitudinal distance in dimensionless form. Equation 6 is a fundamental relationship between the local permeate flux and the exact location point in longitudinal direction taking concentration polarization into consideration. Inspections of eqs 4 and 6 suggest how the wall concentration cw varies along the membrane channel, and further, the corresponding local osmotic pressure (ϕcw) is obtained to estimate the effective driving force of RO process accurately. The model developed in this section is featured with progressive derivations in theoretical development and is later used to properly calculate the energy consumption of RO process. 2.2. Effect of Transmembrane Pressure Difference (ΔP) on Solute Rejection. Generally, the investigation of solute rejection refers to specific membrane, solute component, and operating conditions. Specially, the driving forces for both the solute and water increase with increasing applied pressure, which further results in the variation of rejection. An analytical model presented by Song8 indicates that the solute rejection is a performance variable of the RO process subject to transmembrane pressure differences and concentrations. Although

(2)

x

j(x′) dx′

(5)

with

where γ is the shear rate (1/s), and Rt (i.e., 1 − cp/cb) is the observed rejection. x′ is the dummy integration variable. cp is the permeate concentration. By solving eqs 1 and 2, the locally varying wall concentration of retained solute in terms of local permeate flux can be expressed by Cw =

ΔP − (Δπm + Δπa) Rm

− ( 1/N + 4 − 2)1/3 ]

x

j(x′) dx′

(4)

⎛ D2γ ⎞1/3 F /M × [( 1/N + 4 + 2)1/3 j( x ) = ⎜ ⎟ ⎝ L ⎠ N1/3

(1)

∫0

⎞ j(x′) dx′⎟ ⎠

Here, ΔP is the applied pressure difference between the feed and permeate sides of membrane. Δπm = ϕ(cb − cp) is the original osmotic pressure difference without concentration polarization (also called observed osmotic pressure difference), ϕ is the osmotic pressure coefficient. Δπa = ϕC is the additional osmotic pressure difference due to concentration polarization. Rm is the membrane resistance to pure water. Using eqs 1, 2, and 5, the local permeate flux could be described by

with the boundary conditions y = 0 ⇒ C = Cw; y = δ ⇒ C = Cb. Where x and y are the longitudinal and transverse coordinates, respectively. j(x) represents the local permeate flux at x. D is the solute diffusion rate. C indicates the concentration of retained solute (the actual solute concentration in the polarization layer is cb + C; cb is the concentration of bulk retentate brine). δ is the thickness of concentration polarization layer. At steady state, the longitudinal solute flux at any point x along the channel should equal to the total amount of solute rejected by the membrane from the inlet to the location x, that is,25,26

∫0

x

Inspection of eq 4 suggests that diffusion rate and shear rate help reducing the wall concentration, while higher rejection and permeate flux facilitate the development of concentration polarization layer. Until now, the major parameters relevant to eqs 1−4 are known for specific operating conditions with exception of j(x). Hence, an explicit formulation of j(x) is desired to obtain. When concentration polarization is significantly developed, the effective driving force is ΔP − (Δπm + Δπa), as a consequence, locally varying permeate flux could be expressed as

2. THEORETICAL CONSIDERATIONS 2.1. Development of Concentration Polarization. Concentration polarization in RO process is a mass transfer problem controlled by convection and diffusion of the solute. Due to the filtration flux, the retained solute accumulates near the membrane surface and a concentration polarization layer develops gradually along the RO channel. The concentration polarization layer results in an additional osmotic pressure, and therefore, the effective driving force of RO process as well as the filtration flux and solute rejection are reduced correspondingly. To give an accurate prediction of the net driving force and solute rejection, which will be desirable in RO energy consumption estimation, a new numerical model accounting for the impact of concentration polarization is presented. The model captures the fundamental interplay between locally varying filtration flux along the cross-flow RO channel and concentration polarization layer development using the concept of “retained solute”. At steady state, the increment rate of retained solute is equal to its diffusion rate. So we get dC j( x ) C + D =0 dy

∫0

(3)

The actual wall concentration is therefore estimated from 14136

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featured by theoretical derivations, the main drawback of this model is the requirement of iterative calculation, which makes it inconvenient in process design. H. Al-Zoubi proposed that,27 as long as high concentration differences between the retentate and the permeate develop, the following expression (i.e., the Spiegler−Kedem model12) of varying rejection related to permeate flux will be true. Rw =

σ(1 − U ) (1 − σU )

Table 1. Parameters Used in the Simulation

(7)

with ⎛ (1 − σ ) ⎞ j(x )⎟ U = exp⎜ − Ps ⎝ ⎠

(8)

where σ is the reflection coefficient, which indicates the fraction of solute reflected by the membrane in convective flow and ranges from 0 (no rejection of solutes) to 1 (no passage of solutes); Ps is the solute permeability representing the effective diffusivity of a solute inside a pore. Rw = 1 − cp/cw is the real rejection. Referring to the so-called concentration polarization equation8 ⎛ j( x ) ⎞ = exp⎜ ⎟ ⎝ k ⎠ cb − c p

(9)

Here, k is the mass transfer coefficient in the boundary layer, which could be calculated by28 kdH = 0.2Re 0.57Sc 0.40 D

(10)

dH is the radius of the stirred cell base. Sc is the Schmidt number expressed by Grover equation.29 Referring to eq 9, the observed rejection Rt = 1 − cp/cb could be expressed by

Q f c f = Q p c p + Q b cb

Rw

Rt = exp

( ) ( ( ) ) j(x) k

− exp

j(x) k

− 1 Rw

ΔL

= − f1 Re−f2

U 2ρ d

(13)

where Qf represents the flow rate of raw seawater and Qb is the volumetric retentate brine flow rate. c f , c p and cb are the average salt concentration of raw seawater, permeate product, and retentate brine, respectively. Noting that π = ϕc, R t = 1 − c p/ cb, and Qb = (1 − Y)Qf, the osmotic pressure difference at the exit of membrane module (i.e., Δπexit) is therefore approximated by

(11)

Equation 11 suggests the locally varying observed rejection along the membrane channel with the permeate flux j(x) as an intermediate variable, and more concretely, the rejection decreases with decreasing permeate flux. The variables involved in eq 8, Ps increases with solute concentration due to high quantity of salt passing through the membrane and σ decreases slightly because of reduction of rejection. However, to simplify the energy consumption analysis, these two parameters were assumed constant. This closed-form formulation of rejection is used to calculate the operating energy consumption of RO in this work. To analyze the operating energy numerically, parameters of special conditions are listed Table 1. Additionally, the pressure of permeate product is assumed to be normal atmosphere, and the targeted recovery rate is 45%. 2.3. Pressure Drop along the Membrane Channel. Although not completely realistic, for a cross-flow membrane module, each of the feed and permeate side flows can be treated as a flow between two parallel plates. The pressure drop (Δpf) in the retentate channel can be estimated as follows:30,31 Δpf

value 8.314 × 103 298 5 × 10−4 6 1.5 × 1011 0.98 3.5 × 10−9 0.59 (35 000 ppm) 6 × 106 3.2 × 10−5 1.35 × 10−9 0.15 0.85 U/D Re0.49 (ref 28)

where Re is defined as Re = dU(μ/ρ). ρ and μ are the fluid density and viscosity, respectively. p and d represent the retentate channel pressure and spacer filament diameter, respectively. The coefficients f1 and f 2 depend on the spacer geometry (pitch to diameter ratio H/d and filament crossing angle β) and on the flow incidence angle θ. In general, f1 and f 2 could be obtained by computational fluid dynamics (CFD) simulations.31 In fact, there is also small pressure drop in the permeate side, which was discussed in detail in recent studies.30,31 However, for the sake of topic-prominence (i.e., operating energy analysis of RO desalting process), this small pressure drop in the permeate side was not taken into account. 2.4. Energy Consumption of RO Process. According to the salt mass balance law, the mass of salt in the feed solution equals to the mass of salt in the retentate brine plus that in the permeate product, which can be expressed as

c w − cp

Sh =

param. universal gas constant, J/mol·K temp., K feed channel height, m length of membrane vessel, m membrane resistance, Pa·s/m reflection coefficient pure water permeability constant, kg/m2·s·Pa salt concn, mol/L applied pressure, Pa solute permeability constant, kg/m2·s solute diffusion coefficient, m2/s cross-flow velocity, m/s shear rate, 1/s

Δπexit = Δπm,exit + Δπa,exit =

π0 R t + Δπa,exit 1 − YR t

(14)

Here, π0 is the osmotic pressure of raw seawater, Y = Qp/Qf is the targeted recovery rate. To ensure that the entire membrane area is used to produce water, the pressure of seawater into the module should not lower than the osmotic pressure difference at the exit of membrane module. ΔP − ΔPf ≥ Δπexit =

π0 R t + Δπa,exit 1 − YR t

(15)

Here, the average rejection is defined as R t = ∫ 0LRt dx/L. Equation 15 is the so-called thermodynamic limit for crossflow RO process. Inspection of eq 15 suggests that Δπexit would increase rapidly at high target recovery rates and so is the required applied pressure. It is important to note that the partial recovery rate Yx is defined as

(12) 14137

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∫0

Yx = Y

x

j(x ) d x /

∫0

Article

In this work, the SEC normalized by π0 (i.e., nondimensional form) is used to illustrate the approach of analysis. The normalized SEC could be expressed by

L

j (x ) d x

(16)

Equation 16 is used to express the partial recovery rate from the inlet to the location x. Substituting eq 16 into eq 15 gives the variations of osmotic pressure difference without concentration polarization (i.e., Δπm) with respect to the location x. Finally, the rate of pump work or operating energy consumption of RO process is normally calculate by W=

Q × ΔP η

‐ stage = SECsingle norm

Rt ηHPYt(1 − R tYt)

(22)

Under the conditions listed in Table 1, the observed rejection varies from 97.96% to 94.98%, and the average rejection R t is 95.91% by integration method. The optimal recovery rate can be single‑stage worked out by setting ∂(SECnorm )/∂Yt|ηHP = 0. It is convenient to solve the equation and find that Yt = 1/(1 + Rt) = 51.04% with corresponding SECsingle‑stage = 3.6811/ηHP. Too norm high (>51.04%) or too low (98%).

(27)

4. SEC ANALYSIS FOR TWO-STAGE RO DESALTING PROCESS 4.1. SEC of Two-Stage RO Desalting Process without ERDs. Figure 4 illustrates a simple two-stage RO desalting

By combining eqs 23−25, the SEC of single-stage RO process in the presence of ERDs can be evaluated by ‐ stage SECsingle = ERD

+

(Q p + Q l)ΔP WHP + WBP = ηHPQ p Qp

(Q b − Q l)(Pf − PE) ηBPQ p

(28)

The SEC normalized by π0 of single-stage RO process in the presence of ERDs can be expressed as ‐ stage SECsingle norm,ERD =

Yt + β(1 − Yt) Rt Yt(1 − R tYt)ηHP +

(1 − ηE)(1 − β)(1 − Yt) Yt(1 − R tYt)ηBP

Figure 4. Schematic of a simple two-stage RO process without ERDs.

Rt

(29)

process without ERDs; the retentate brine of the first stage is pumped to the second stage, and the final product is the permeate mixture of the two stages. With respect to the two-stage RO process, a major problem is that how the individual permeate flow should be assigned to the two stages for given total permeate flow rate. In another words, for a given target recovery rate Yt, it is needed to optimize the individual recovery rate of Y1 (recovery rate of first stage) and Y2 (recovery rate of second stage) to minimize the SEC of two-stage RO process. Similarly, the rate of HP pump work and BP pump work could be evaluated by eq 30 and eq 31, respectively.

It is noticed that, for given pump efficiency and ERD efficiency, SECsingle‑stage norm,ERD is dependent on the targeted recovery rate Yt and initial leakage ratio β. Therefore, for the simplicity of SEC analysis, without a loss of generality, the focus is first put on the effect of ERDs performance variables (i.e., efficiency and leakage ratio) on the SECsingle‑stage norm,ERD with the pump efficiencies assumed to be 100%. Then, the effect of pump efficiency on the SEC is specially studied in section 6. Based on eq 29, Figure 3 illustrates the relationship between the normalized SEC of single-stage RO process SECsingle‑stage norm,ERD and

WHP =

WBP =

Q f,1(Pf,1 − P0) ηHP

(30)

Q b,1(Pf,2 − Pf,1) ηBP

(31)

With respect to the first stage, the pressure difference of HP pump can be calculated by ΔP1 = Pf ,1 − P0 =

π0 R t 1 − R tY1

(32)

For the second stage, the pressure difference of BP pump can be calculated by ΔP2 = Pf,2 − Pf,1 =

Figure 3. Variation of SECsingle‑stage norm,ERD with target recovery rate (Yt) at different ERD efficiencies and leakage ratios.

=

Pf,1R t 1 − R tY2

− Pf,1

π0 R t( R tY2 + R t − 1) (1 − R tY1)(1 − R tY2)

(33)

By combining eqs 30−33, the SEC of two-stage RO process normalized by π0 in the absence of ERDs can be expressed as

the target recovery rate Yt with ERD efficiency and leakage ratio as parameters. When both the ERD efficiency and the leakage ratio are zero (i.e., in the absence of ERDs), the minimum value of SECsingle‑stage norm,ERD is 3.6811 at recovery rate of 51.04%, which has been explained in section 3.1. As the ERD is employed, the global optimized recovery rate shifts to lower values. For example, at ERD efficiency of 80% and leakage ratio of 4%, the minimum value of SECsingle‑stage norm,ERD is approximately 2.064 at recovery rate of 34%. For given ERD efficiency, the lower of the leakage ratio, the lower of the global optimized recovery rate. As the ERD efficiency increases, SECsingle‑stage norm,ERD becomes more sensitive to the leakage ratio, which shows the necessity of controlling leakage.

‐ stage = SECtwo norm

Rt ηHPYt(1 − R tY1) +

R t( R tY2 + R t − 1)(1 − Y1) ηBP(1 − R tY1)(1 − R tY2)Yt

(34)

According to the mass balance raw, the target recovery rate can be expressed as Yt = Y1 + (1 − Y1)Y2 14139

(35)

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Substituting eq 35 into eq 34, one has ‐ stage SECtwo norm

R ⎛ 1 = t⎜ Yt ⎝ (1 − R tY1)

R t(Yt − Y1) + ( R t − 1)(1 − Y1) ⎞ + ⎟ (1 − R tY1)(1 − R t(Yt − Y1)/(1 − Y1)) ⎠

(Y1 < Yt) (36)

The minimum SECtwo‑stage , for specific target recovery rate Yt, norm can be found by setting ∂SECtwo‑stage /∂Y1|Yt = 0. As clearly shown norm decreases with increasing in Figure 5, for given Y1, the SECtwo‑stage norm

Q HP + Q b = Q p,1 + Q b,1 = Q p,1 + Q b,2 + Q p,2

(37)

Q b = Q b,2 − Q l

(38)

Q HP = Q p,1 + Q p,2 + Q l

(39)

Q p = Q p,1 + Q p,2

(40)

Q p = YtQ f,1

(41)

Q p,1 = Y1Q f,1

(42)

Q p,2 = Y2Q b,1 = Y2(1 − Y1)Q f,1

(43)

The rate of pump work consumed in the first stage could be expressed by Pf,1 × Q HP

W1 = WHP =

ηHP

(44)

The rate of pump work consumed in the second stage could be expressed by W2 = WBP =

(Pf,2 − Pf,1) × Q b,1 ηBP

(45)

By combining eq 44 and eq 45, the total energy required to produce specific permeate flow rate for two-stage RO process in the presence of ERD can be evaluated by ‐ stage = SECtwo ERD

Figure 5. Variation of SECtwo‑stage at the limit of thermodynamic norm restriction (in the absence of ERDs and ηp = 1 for all pumps) with respect to recovery rate of stage 1 (Y1) and target recover rate (Yt).

=

Yt first and tends to increase rapidly with continuous increment of Yt after the global optimized values. The main reason is similar to that presented in section 3.2. Especially, when Y1 is zero or equals to Yt (i.e., all the permeate is produced by the second stage or the first stage), the SEC of the two pseudo two-stage, which would have the equivalent values for given Yt, are marked as boundary curves in Figure 5. In addition, the global minimum of SECtwo‑stage is found to be 3.5963 at Yt = 57.4% and Y1 = 34.73% at norm ideal pump efficiency (i.e., ηp = 1). 4.2. SEC of Two-Stage RO Desalting Process with ERDs. Figure 6 illustrates the typical technological process of two-stage RO desalting plant in the presence of ERD. Unlike the RO process shown in Figure 4, the retentate brine discharged out of the second stage RO modules is not wasted but used to pressurize the raw seawater in ERD. The flow rates shown in Figure 6 satisfy the following equations:

W1 + W2 Qp (Pf,1Q HP/ηHP) + ((Pf,2 − Pf,1)Q b,1/ηBP) Qp (46)

The SEC of two-stage RO process normalized by π0 is therefore estimated from ‐ stage SECtwo norm,ERD

⎡ Rt ⎢ Yt + β(1 − Yt) − (1 − Y1) = Yt(1 − Y1R t) ⎢⎢ ⎣

⎤ R t(1 − Y1) ⎥ + (Y − Y ) ⎥ 1 − R t (1t − Y1) ⎥⎦ 1

(Y1 < Yt) (47)

The minimum SECtwo‑stage norm,ERD, for specific target recovery rate Yt, can be found by setting ∂SECtwo‑stage norm,ERD/∂Y1|Yt = 0. Figure 7 illustrates the relationship between the optimized Y1 and target recovery rate Yt at different leakage ratios. As Yt is always higher than Y1, the optimized values of Y1 in the range of 0 < Yt < 50% are invalid. While for Yt > 50%, the optimized values of Y1 increase with increasing Yt, for example, the corresponding optimized Y1 are 60% and 70% for target recovery rates of 80% and 90%, respectively. This result suggests that if there is a need to increase the total recovery rate, increment of Y1 always takes precedence due to relatively lower pressure required. In addition, the effect of leakage ratio on the optimized Y1 for given Yt is very little. As predicted by eq 47, Figures 8−10) illustrate the variations of normalized SEC of two-stage RO process SECtwo‑stage norm,ERD with respect to target recovery rate Yt and individual recovery rate of

Figure 6. Schematic of a typical two-stage RO process with ERD. 14140

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Figure 7. Variation of optimized Y1 with target recovery rate Yt at different leakage ratios.

Figure 10. Variation of SECtwo‑stage norm,ERD with target recovery rate Yt and water recovery in the first stage Y1(ηp = 1 for all pumps, ERD efficiency 100%, and leakage ratio of 4%).

e.g., 0. single‑stage Figure 12. SECtwo‑stage norm,ERD-SECnorm,ERD assuming that the leakage ratio is single‑stage 0%. (a) Variation of SECtwo‑stage norm,ERD-SECnorm,ERD at the thermodynamic limit (ηE = 1 and ηp = 1 for all pumps) with respect to recovery rate of first stage (Y1) and target recovery rate (Yt). (b) Subdomain area where single‑stage SECtwo‑stage norm,ERD − SECnorm,ERD > 0.

required to study the effects of actual pump efficiency and ERD efficiency on the SEC of RO desalting process. Referring to eq 47, the normalized SEC of two-stage RO desalting process taking into account the pump and ERD efficiency can be expressed as

desalting process is always less energy efficient than the singlestage, which is clearly shown by the subdomain area where single‑stage SECtwo‑stage norm,ERD − SECnorm,ERD > 0. While the target recovery rate Yt is higher than 50%, in the range Y1 < Yt < 1 − Y1, the two-stage RO desalting process is also less energy efficient compared with the single-stage. However, when Yt is higher than 50% as well as Yt > 1 − Y1, the two-stage RO desalting process is more energy efficient than the single-stage. That is, as suggested previously, only at higher recovery rate can we take the advantage of twostage RO process in the presence of ERDs. The three leakage ratios studied, 0%, 2%, 4%, show nearly the same subdomain area single‑stage where SECtwo‑stage norm,ERD − SECnorm,ERD > 0, from which we can draw the conclusion that the leakage ratio does not affect the operating area for more energy efficient.

‐ stage SECtwo norm,ERD

+

+

⎡ ⎢ Yt + β(1 − Yt) Rt = ⎢ Yt(1 − Y1R t) ⎢ ηHP ⎣

(1 − ηE)(1 − β)(1 − Yt) − (1 − Y1) ηBP R t(1 − Y1)

(

(Y − Y )

ηBP 1 − R t (1t − Y1) 1

)

⎤ ⎥ ⎥ ⎥ ⎦

(48)

Assuming that 80% < ηHP = ηBP < 100%, 90% < ηE < 100%, and Y t = 45%, which is reasonable according to practical experience,32−34 as a demonstration, Figure 15 shows the two‑stage variation of optimized SECnorm,ERD with respect to pump efficiency and ERD efficiency. For given target recovery rate of 45% and ERD leakage ratio 2%, the minimum SECtwo‑stage norm,ERD is 1.6316 when both the pump efficiency and ERD efficiency are 100%. With the pump efficiency and ERD efficiency ranging from 100% to 80% and 90%, respectively, the optimized SECtwo‑stage norm,ERD increases from 1.6316 to 2.305. As known, even

6. EFFECTS OF PUMP EFFICIENCY AND ERD EFFICIENCY ON THE SEC OF TWO-STAGE RO PROCESS In the previous discussions, both the pump efficiency and ERD efficiency were assumed to be ideal (100%). However, it is not the practical case for real pump and ERD. Therefore, it is 14142

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7. CONCLUSIONS Theoretical formulations of locally varying applied pressure, observed osmotic pressure difference (Δπm) as well as the additional pressure difference (Δπa) along the cross-flow RO channel were carefully derived and solved. Due to the filtration flux and the subsequent concentration polarization, the overall osmotic pressure difference increases along the channel, which would affect the required applied pressure and further the relevant pump work consumption for given permeate rate. The theoretical analysis presented in this work contributes to better understanding of effective driving force of RO process. At the thermodynamic limit, the effects of recovery rate, pump efficiency, performance variables of ERDs on the SEC for both the single-stage and two-stage RO desalting process have been discussed systematically in this study. The investigations of this work show that the optimized recovery rate shifts to lower values due to the presence of ERDs and becomes more sensitive to the leakage at higher ERD efficiency. The SEC of RO process is more sensitive to the leakage at lower recovery rates than the higher ones. The analysis of comparison between the single-stage and two-stage RO process helps us to run the system more efficiently. The important effects of pump and ERD efficiency on the SEC are also demonstrated numerically.

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AUTHOR INFORMATION

Corresponding Author

*Tel/Fax: +86 22 27406889. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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single‑stage Figure 14. SECtwo‑stage norm,ERD-SECnorm,ERD assuming that the leakage ratio is two‑stage 4%. (a) Variation of SECnorm,ERD-SECsingle‑stage norm,ERD at the thermodynamic limit (ηE = 1 and ηp = 1 for all pumps) with respect to recovery rate of first stage (Y1) and target recovery rate (Yt). (b) Subdomain area where single‑stage SECtwo‑stage norm,ERD − SECnorm,ERD > 0.

ACKNOWLEDGMENTS This research is supported by the National Key Technologies R&D Program (No. 2006 BAB03A021) and the R&D Programs of Tianjin (10JCYBJC04700 and 10ZCKFSH02100).

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NOMENCLATURE Q = volumetric flow rate, m3/s Lp = membrane hydraulic permeability, m/s·Pa P = pressure, Pa ΔP = transmembrane pressure, Pa c = salt concentration, mol/L d = spacer filament diameter, m Y = recovery rate W = rate of work done by the pump, kWh SEC = specific energy consumption, kWh/m3 ERD = energy recovery device

Greek Symbols

σ = membrane reflection coefficient ϕ = coefficient of osmotic pressure π = osmotic pressure, Pa η = efficiency β = leakage ratio

Figure 15. Variation of SECtwo‑stage norm,ERD with pump efficiency and ERD efficiency (target recovery rate 45% and leakage ratio 2%).

Subscripts

0 = parameter of raw seawater 1 = first-stage 2 = second-stage E = ERD norm = normalized to the feed osmotic pressure HP = high pressure pump BP = booster pump f = feed b = brine

little increment of SEC would result in significant increase of the overall operating cost of a large scale RO plant. The specific case studied quantitatively demonstrates the importance of pump efficiency. For example, every 1 percentage point increase in the pump efficiency would provide SEC savings of approximately 0.0337. Effect of pump and ERD efficiency on SECsingle‑stage norm,ERD can be easily obtained using the approach presented in this work. 14143

dx.doi.org/10.1021/ie300361e | Ind. Eng. Chem. Res. 2012, 51, 14135−14144

Industrial & Engineering Chemistry Research

Article

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p = permeate l = leakage exit = exit of membrane module t = target T = total

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