Two-Step Optimization of Pressure and Recovery of Reverse Osmosis

Apr 2, 2009 - Driving pressure and recovery are two primary design variables of a reverse osmosis process that largely determine the total cost of sea...
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Environ. Sci. Technol. 2009, 43, 3272–3277

Two-Step Optimization of Pressure and Recovery of Reverse Osmosis Desalination Process SHUANG LIANG,† CUI LIU,‡ AND L I A N F A S O N G * ,‡ College of Environmental Science and Engineering; Shandong University 27 Shanda Nanlu, Jinan, Shandong 250100, China, and Department of Civil and Environmental Engineering, Texas Tech University, 10th and Akron, Lubbock, Texas 79409-1023, Phone: (806) 742-3598, Fax: (806) 742-3449

Received December 29, 2008. Revised manuscript received March 11, 2009. Accepted March 12, 2009.

Driving pressure and recovery are two primary design variables of a reverse osmosis process that largely determine the total cost of seawater and brackish water desalination. A two-step optimization procedure was developed in this paper to determine the values of driving pressure and recovery that minimize the total cost of RO desalination. It was demonstrated that the optimal net driving pressure is solely determined by the electricity price and the membrane price index, which is a lumped parameter to collectively reflect membrane price, resistance, and service time. On the other hand, the optimal recovery is determined by the electricity price, initial osmotic pressure, and costs for pretreatment of raw water and handling of retentate. Concise equations were derived for the optimal net driving pressure and recovery. The dependences of the optimal net driving pressure and recovery on the electricity price, membrane price, and costs for raw water pretreatment and retentate handling were discussed.

Introduction Reverse osmosis (RO) is an advanced water treatment technology that is able to produce high quality water from unconventional water sources, such as seawater, brackish water, and treated wastewater (1-3). However, the cost of water treatment by RO is usually higher than those of the conventional water treatment processes. Although the higher cost of RO is reasonably justifiable because the raw waters treated by RO are often of low qualities that cannot be adequately treated to the required quality by the conventional treatments, it is still a restraint for more widespread applications of the technology (4, 5). Therefore, there have been intensive efforts to reduce the cost of RO desalination to make it a more affordable means of sustainable water supply (5-7). Energy consumption in RO desalination is a major constituent of the total cost of water treatment because a large amount of energy is needed to push water through RO membranes under high pressure. Substantial reductions in energy consumption in RO processes have been obtained in the last two decades mainly due to the emergence of the highly permeable RO membranes and the installations of * Corresponding author e-mail: [email protected]. † Shandong University. ‡ Texas Tech University. 3272

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energy recovery devices in the retentate stream (3). The permeability of current RO membranes is at least one order higher than that of RO membranes about 20 years ago (8). As a result, the required permeate flux of a RO process can be obtained at a lower driving pressure. The widespread applications of energy recovery devices in seawater desalination cut energy consumption about to a half because the energy in the retentate stream, which is about 60% of the feed flow, can be recovered at high efficiencies greater than 95% (7, 9). Apart from the dependence on the hardware, the energy consumption and cost of RO desalination are also tightly related to the design and operation of the process. Driving pressure and process recovery are the two primary variables of a RO process that largely determine the energy consumption and total cost of water production (7, 10). Many studies can be found in the literature on qualitative or quantitative analyses of the optimal values of the two variables. However, most of the studies only involve comparisons of a few alternatives of particular cases and selections of the alternative that results in the lowest total cost among them. A general theoretical procedure to optimize the two variables is still unavailable. In this paper, a systematic procedure was attempted for determining the optimal driving pressure and recovery to minimize the total cost of RO desalination. These two design variables were linked to the cost components of RO process with concise expressions. The procedure was demonstrated and discussed for typical cases in seawater and brackish water desalination.

Decoupling between Pressure and Recovery Most of the previous optimization studies consider driving pressure and recovery of a RO process simultaneously. It makes the problem a very challenging task and sometimes elusive. It will be shown in the following analysis that the net driving pressure and recovery of the RO process can be treated separately and optimized in a two-step procedure. The average permeate flux and recovery are two related but different performance parameters of a RO process. The average permeate flux is the production rate of permeate by a unit membrane area, determined by v)

∆P - ∆πa ∆Pnet ) Rm Rm

(1)

where v is the permeate flux (m3/m2h or m/h), ∆P is the driving pressure (Pa), ∆πa is the average osmotic pressure of water in the membrane channel (Pa), Rm is the membrane resistance (Pam2h/m3 or Pah/m), and ∆Pnet ()∆P - ∆πa) is the net driving pressure. The average osmotic pressure is determined by ∆πa )

∆π0 + ∆πr 2

(2)

where ∆π0 is the initial osmotic pressure of the raw feedwater, and ∆πr is the osmotic pressure of the retentate. The recovery of a RO channel or process is defined as the ratio of the permeate flow rate to the feed flow rate of a RO channel or process, R) 10.1021/es803692h CCC: $40.75

Q Qf

(3)  2009 American Chemical Society

Published on Web 04/02/2009

TABLE 1. Calculation of Membrane Price Index membrane element

FIGURE 1. Schematic of a cross-flow RO channel. where Qf is the feed flow rate (m3/h). The permeate flux and recovery of a RO channel or process are related for a required permeate flow rate: Q ) vA ) RQf

(4)

where Q is the permeate flow rate (m3/h) and A is the total membrane area of the membrane channel (m2). From eqs 1 and 4, it can be seen that the mass conservation principle mandates an upper limit of QfRm/A on the net pressure. Otherwise more permeate than feed would be produced by the RO process. The net driving pressure can be freely manipulated to obtain the required average permeate flux under this upper limit. Equation 4 shows the permeate flow rate of a RO process is related to two independent groups of variables. There is not a fixed relationship between permeate flux and the system recovery unless both membrane area and feed flow rate are fixed, which usually is not the case in the RO process design. The average permeate flux only affects the membrane area but has nothing to do with the recovery. Similarly, the recovery only affects the feed flow rate but not the average permeate flux. Because the average permeate flux is determined by the net driving pressure as indicated by eq 1, the net driving pressure and process recovery are independent from each other. The decoupling of the net driving pressure and recovery is the theoretical basis for the two-step optimization of the RO process.

Optimization of the Net Driving Pressure Combined Cost of Energy and Membrane. The commonly used cross-flow RO as schematically shown in Figure 1 will be considered in this paper. A pressure exchanger is installed to recover the energy in the retentate stream. For a required permeate flow rate Q, the feed flow rate and retentate flow rate are Q/R and Q(1 - R)/R, respectively, where the recovery R can take an arbitrary value. The question here is to determine the optimal net pressure and required membrane area to produce the designed permeate flow rate at the lowest cost. With the assumption that energy in the retentate stream is assumed to be fully recovered, the energy cost of the RO process is ME ) 2.78 × 10-7aQ(∆Pnet + ∆πa)t

(5)

where ME is the monetary cost of the energy ($), a is the price of electricity ($/kWh), and t is the service time (h). The leading coefficient in eq 5 is the conversion factor of energy unit of Joule to kilowatt-hour (kWh). It is worthy to point out that the average osmotic pressure is a fixed value for a given recovery and is independent from the net driving pressure. Equation 5 indicates that the energy consumption of the RO process is linearly related to the net driving pressure ∆Pnet. It is obvious that a RO system operated at a lower net pressure will reduce energy consumption and the associated cost. According to eqs 1 and 4, the membrane area required to produce a required permeate flow rate is QRm/∆Pnet.

size element price ($) typical total area (m2) service time (yr) annual membrane price ($/m2 · yr)

8” × 40” 600 37 5 4.05

pressure vessel size vessel price ($) number of elements service time (yr) additional annual price ($/m2 · yr)

8m 2,000 8 20 0.34

total annual price ($/m2 · yr) membrane resistance (mpa · hr · m2/m3) membrane price index ($ · MPa/m3)

4.39 100 4.09 × 10-2

Therefore the membrane cost can be written as Mm ) b

QRm ∆Pnet

(6)

where Mm is the monetary membrane cost ($) and b is the membrane price per unit area ($/m2). Equation 6 shows that the membrane cost increases with the decreasing net driving pressure. The total combined cost of energy and membrane for a RO process to produce permeate flux Q over the lifetime of membranes will be ME-M ) ME + Mm ) 2.78 × 10-7a(∆Pnet + ∆πa)Qt + QRm b (7) ∆Pnet where ME-M is the combined cost ($) for energy and membrane. To consider the membrane cost appropriately, t is selected to be the service life of the RO membranes in eq 7 and thereafter. The combined cost of a unit volume of permeate can be determined from eq 7 as CE-M )

ME-m b Rm ) 2.78 × 10-7a(∆Pnet + ∆πa) + Qt t ∆Pnet (8)

where CE-M is the combined cost of energy and membrane per unit volume of permeate. The first term on the righthand side of eq 8 is the energy cost and the second term is the membrane cost. The term of Rmb/t collectively reflects the contribution of membranes to the combined cost for permeate production, which is named the membrane price index. The membrane price index can also be expressed with the membrane permeability l ()1/Rm) as b/lt. The energy cost, membrane cost, and the combined cost of a seawater RO process are presented as functions of the net driving pressure in Figure 2. Table 1 shows the basic information and calculation of the annual membrane cost and membrane price index for the common 8” seawater membrane element. The resulted overall annual cost of membrane is $4.39/m2 and the membrane price index is $4.09 × 104Pa/m3. These values include about 10% additional cost for the pressure vessel. Other information of the RO process is given in the caption of the figure. It can be seen from the figure that the energy cost increases linearly with the net driving pressure and is the dominant cost component in most of the pressure domain except for the very low net driving pressure. On the contrary, the VOL. 43, NO. 9, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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TABLE 2. The Net Driving Pressure, MPa (psi) membrane price index (Rmb/t) (unit: $Pa/m3) energy cost ($/kWH) 4.00 × 104 3.00 × 104 2.00 × 104 1.00 × 104 0.50 × 104 0.05 0.10 0.15 0.20

1.70 (246) 1.20 (174) 0.98 (142) 0.85 (123)

1.47 (213) 1.04 (151) 0.85 (123) 0.74 (107)

1.20 (174) 0.85 (123) 0.69 (100) 0.60 (87)

0.85 (123) 0.60 (87) 0.49 (71) 0.42 (62)

0.60 (87) 0.42 (62) 0.35 (50) 0.30 (44)

permeate flux at the optimal net driving pressure increases to 2.47 × 10-2m3/m2h. Optimal Net Pressure and Permeate Flux. Taking derivative of the combined cost in eq 8 with respect to the net driving pressure and letting it equal to zero, one has dCE-M b Rm ) 2.78 × 10-7a )0 d∆Pnet t ∆P2

(9)

net

FIGURE 2. The combined cost of energy and membrane and the average flux of a RO process at different pressure. Conditions: salt concentration ) 34 500 mg/L, recovery ) 40%, electricity price ) $0.10/kWh, membrane annual cost ) $4.39/m2, and membrane price index ) $4.09 × 104Pa/m3.

The optimal net pressure to minimize the combined cost can be determined from eq 9 as ∆Pnet ) 1896.6



Rmb/t a

(10)

The net driving pressure is solely determined by the membrane price index (Rmb/t) and the electricity price a. The driving pressure can be determined from the net driving pressure by adding the average osmotic pressure. After the net driving pressure is determined, the optimal permeate flux can then be determined with eq 1 as v ) 1896.6



b/t Rma

(11)

The required membrane area can be calculated with eq 4. Alternatively, the channel length to produce the required permeate flow rate is L)

FIGURE 3. The combined cost of energy and membrane and the average flux of a RO process at different pressure. Conditions: salt concentration ) 5000 mg/L, recovery ) 50%, electricity price ) $0.10/kWh, annual membrane cost ) $2.70/m2, and membrane price index is $6.79 × 103 Pa/m3. membrane is the minor cost component for most net driving pressures. But it increases rapidly and overtakes the energy to become the dominant cost component as the net driving pressure diminishes to zero. The combined cost has a minimum of $0.16/m3 at net driving pressure of about 1.2 MPa. At this net driving pressure, the average permeate flux is 1.21 × 10-2m3/m2h. The brackish RO membrane is cheaper in cost and smaller in resistance. Following the same procedure for the seawater RO membrane, the annual membrane cost and membrane price index are determined as $2.70/m2 and $6.79 × 103 Pa/m3, respectively. Figure 3 shows the energy cost, membrane cost, and combined cost for the brackish membrane process and similar behaviors as for seawater membrane process are observed. However, the minimum combined cost and optimal net driving pressure reduce to $0.043/m3 and 0.5 MPa, respectively. The average 3274

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QRm A ) W W∆Pnet

(12)

where W is the width of the membrane channel. For the common membrane elements of one meter long, the width of the channel is equal to the membrane area of the element in value. The optimal net driving pressures to minimize the combined cost of energy and membrane are calculated for various combinations of electricity price and membrane price index and the results are presented in Table 2. It is clear that the optimal net driving pressure decreases with the increasing electricity price and the decreasing membrane price index.

Optimization of the Recovery In the previous section, it was shown that the optimal net driving pressure can be determined by minimizing the combined cost of energy consumption and membrane. The factors that affect the optimal net driving pressure are the electricity price and the membrane price index. As a second step of process optimization, the optimal recovery of a crossflow RO process is determined in this section. Total Cost of Water Desalination. As indicated by eq 4, the recovery of a RO process to produce the required permeate flow rate will affect the feed flow rate. The flow rate of retentate is also a function of recovery. Therefore, the costs associated with pretreatment of the raw feedwater and the handling and disposal of the retentate will contribute to the determination of the optimal recovery that minimize the total cost of permeate production. As shown in Figure 4, the

FIGURE 4. Schematic of cost components in RO desalination.

FIGURE 5. The total cost for RO desalination of seawater with salt concentration of 34 500 mg/L at different pretreatments and recoveries. The combined cost of the net driving pressure and membrane is calculated with the data from Figure 2. The cost for retentate handling is $0.05/m3 and the pretreatment costs for 1 m3 feedwater are assumed (1) $0.05, (2) $0.10, (3) $0.20, (4) $0.30, (5) $0.40, and (6) $0.50. total cost of a RO desalination process can be divided into premembrane, membrane, and postmembrane components. The premembrane cost is for the intake, transmission, and pretreatment of raw water. The membrane cost can be also viewed as permeate production cost that is for energy, membrane and post-treatment of permeate. The postmembrane cost includes those associated to handling and disposal of the retentate. All three cost components are tightly linked to the process recovery. Although the net driving pressure and the membrane area are unaffected by the recovery, the osmotic pressure of the retentate is related to the recovery by ∆π0/(1-R). As a result, eq 2 can be rewritten as ∆π0 2 - R ∆πa ) 2 1-R Substituting eq 13 into eq 8 results in

(13)

FIGURE 6. The total cost for RO desalination of brackish water with salt concentration of 5000 mg/L at different pretreatments and recoveries. The combined cost of the net driving pressure and membrane is calculated with the data from Figure 3. The cost for pretreatment is $0.05/m3 and the handling and disposal costs for 1 m3 retentate are assumed (1) $0.05, (2) $0.10, (3) $0.20, (4) $0.40, (5) $0.80, and (6) $1.60.

(

CE-M ) 2.78 × 10-7a ∆Pnet + ) 2.78 × 10-7a

)

∆π0 2 - R b Rm + 2 1-R t ∆Pnet

∆π0 2 - R + C0 2 1-R

(14)

where C0 is the combined cost of the net driving pressure and membrane ($/m3) defined as C0 ) 2.78 × 10-7a∆Pnet +

b Rm t ∆Pnet

(15)

C0 is a parameter that is independent from the process recovery. The RO systems operated at high recoveries are usually susceptible to stronger scaling that might shorten the service time of the membranes. In this paper, C0 is kept independent from the recovery with the assumption that VOL. 43, NO. 9, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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costs change moderately. It can also be seen that the higher cost for pretreatment shifts the lowest total cost to the right (higher recovery). Figure 6 presents the total cost of brackish water desalination as functions of the recovery with different costs for retentate handling and disposal. It is clear that the minimum total costs occur all at recoveries greater than 80%. When high cost is involved in retentate handling and disposal, a recovery greater than 90% is usually required to minimize the total cost. Determination of the Optimal Recovery. Taking derivative of the total cost in eq 17 with respect to recovery and letting it equal zero, one has ∆π0 1 1 dC - (c + d) 2 ) 0 (18) ) 2.78 × 10-7a dR 2 (1 - R)2 R Solving eq 18 for the optimal recovery that minimizes the total cost yields R) FIGURE 7. The optimal recoveries for different costs of pretreatment at various salt concentration of the feedwater. The pretreatment costs for 1 m3 of raw water are (1) $0.05, (2) $0.10, (3) $0.15, (4) $0.20, (5) $0.25, and (6) $0.30. the adequate pretreatment would be provided at any recoveries to the warranted service time of the membranes. Equation 14 shows that the initial osmotic pressure and the recovery are factors to the combined cost of energy and membrane even though they have no impact in the determination of the optimal net driving pressure. The volumes of raw water and the retentate to produce 1 unit volume of permeate are 1/R and (1-R)/R, respectively. The additional cost per unit volume of permeate for raw water pretreatment and retentate handling can be determined as Cad ) c

1 1-R +d R R

(16)

where Cad is the additional cost per unit volume of permeate for raw water pretreatment and retentate handling ($/m3), c is the pretreatment cost per unit volume of raw water ($/m3), and d is the handling cost per unit volume of retentate ($/m3), respectively. The specific pretreatment cost may increase with increasing recovery because of the need for more effective scaling control. In that case, a variable specific pretreatment cost has to be used in eq 16. Equations 14 and 16 indicate that the combined cost of energy and membrane increases but the additional cost for handling of raw water and retentate decreases with the increasing recovery. The total cost per unit volume of permeate is C ) CE-M + Cad ) 2.78 × 10-7a

∆π0 2 - R 1 + C0 + c + 2 1-R R 1-R d (17) R

The total cost for seawater desalination was calculated and presented in Figure 5 for different pretreatment costs. The cost curves can be basically divided into three segments. The costs drop rapidly with increasing recovery in the low range of recovery. On the other end, the costs increase even more rapidly with recovery when the recovery is greater than 90%. There is a range of medium recovery in which the total 3276

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1 × 1.39 × 10 a∆π0 - (c + d) -7

[√1.39 × 10-7a∆π0(c + d) - (c + d)] (19) It can be seen that the optimal recovery is a function of the electricity price a, salinity ∆π0, pretreatment cost c, and the retentate handling cost d but independent of membrane and net driving pressure. It is also interesting to note that the costs of raw water pretreatment and retentate handling appear in eq 19 at the exact same positions. Therefore, there is no need to distinguish between the costs of raw water pretreatment and retentate handling in the determination of the optimal recovery. The optimal recoveries were calculated with eq 19 for different pretreatment costs and salinities and the results were presented in Figure 7. The graphs show that there are two obvious trends of the recoveries. First, the optimal recovery increases with the cost of pretreatment of the raw water or the handling of the retentate. Second, the optimal recovery decreases with the increasing salinity of the raw water. For example, in the simulated costs of pretreatment or retentate handling, the optimal recoveries of brackish water desalination for salinity smaller than 5000 mg/L are greater than 80%, while the optimal recoveries of seawater desalination for salinity equal to or greater than 34,500 mg/L usually should be smaller than 75%. Finally, it should be pointed out that the simulations and discussions presented in this paper are not intended to reproduce the performance of practical RO processes in seawater and brackish water desalination. For that purpose, details of the RO process under consideration have to be analyzed, such as the process configuration, actual efficiencies of the motors, pumps, and energy recovery devices, pressure loss along the membrane channel, and more. Furthermore, membrane scaling or fouling may not be adequately controlled in some cases that the RO processes have to be operated under suboptimal conditions dependent on feedwater quality. It is our hope that the principles and methodologies developed in this paper will contribute to improving such analysis.

Acknowledgments This work was supported in part by the Texas Tech University in the form of start-up funds to Dr. Lianfa Song.

Literature Cited (1) Kumar, M.; Adham, S. S.; Pearce, W. R. Investigation of seawater reverse osmosis fouling and its relationship to pretreatment type. Environ. Sci. Technol. 2006, 40, 2037–2044.

(2) Rahardianto, A.; Mccool, B. C.; Cohen, Y. Reverse osmosis desalting of inland brackish water of high gypsum scaling propensity: Kinetics and mitigation of membrane mineral scaling. Environ. Sci. Technol. 2008, 42, 4292–4297. (3) Shannon, M. A.; Bohn, P. W.; Elimelech, M.; Georgiadis, J. G.; Marinas, B. J.; Mayes, A. M. Science and technology for water purification in the coming decades. Nature (London) 2008, 452, 301–310. (4) National Research Council of the National Academies, Committee on Advancing Desalination Technology. Desalination: a National Perspective; National Academies Press: Washington, D.C., 2008. (5) Wilf, M.; Bartels, C. Optimization of seawater RO systems design. Desalination 2005, 173, 1–12.

(6) Avlonitis, S. A. Optimization of the design and operation of seawater RO desalination plants. Sep. Sci. Technol. 2005, 40, 2663–2678. (7) Geraldes, V.; Pereira, N. E.; de Pinho, M. N. Simulation and optimization of medium-sized seawater reverse osmosis processes with spiral-wound modules. Ind. Eng. Chem. Res. 2005, 44, 1897–1905. (8) Matsuura, T. Progress in membrane science and technology for seawater desalination - a review. Desalination 2001, 134, 47–54. (9) Stover, R. L. Seawater reverse osmosis with isobaric energy recovery devices. Desalination 2007, 203, 168–175. (10) Wilf, M.; Klinko, K. Optimization of seawater RO systems design. Desalination 2001, 138, 299–306.

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