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Desalination 293 (212) 61 68 Contents lists available at SciVerse ScienceDirect Desalination journal homepage: www.elsevier.com/locate/desal Optimal plant operation of brackish water reverse osmosis (BWRO) desalination Mingheng Li Department of Chemical and Materials Engineering, California State Polytechnic University, Pomona, CA 91768, USA article info abstract Article history: Received 9 January 212 Received in revised form 17 February 212 Accepted 19 February 212 Available online 17 March 212 Keywords: Brackish water reverse osmosis Specific energy consumption Nonlinear optimization Pump characteristic map Plant operation Optimal plant operation of brackish water reverse osmosis (BWRO) desalination is studied in this work to reduce specific energy consumption (SEC). A comprehensive first-principles based mathematical model, which explicitly accounts for membrane area and hydraulic permeability, pump characteristic curves, and pressure drops along the RO train, is developed and validated by plant data. A constrained nonlinear optimization is formulated and solved for two RO trains with different service times. It is shown that a 16% reduction in SEC is possible by optimizing operating conditions within the normal operating range of the pump while maintaining the same permeate rate. Results are discussed using dimensionless parameters derived in the author's previous work. Suggestions are made to further reduce SEC in BWRO plant operation. 212 Elsevier B.V. All rights reserved. 1. Introduction Reverse osmosis (RO) membrane separation is an important desalination technology to produce drinking water. The applied pressure reach 1 6 psi and 1 1 psi to provide sufficient driving force across the membrane for industrial production from brackish water and seawater, respectively [1]. The energy consumption of booster pumps to drive the membrane module accounts for a major portion of the total cost of water desalination [2 4]. Therefore, reducing specific energy consumption (SEC), or the energy cost per volume of produced permeate, has been an important topic in RO research and development. Interested readers may refer to Ref. [5] and references therein for a review and perspective of energy issues in desalination processes. Reducing SEC in RO processes may be achieved using highly permeable membrane materials [6 8], employing an energy recovery device (ERD) to drive an auxiliary pump pressurizing the feed [9 11], using renewable energy resources to subsidize the electricity energy demand [12,13], and using intermediate chemical demineralization (ICD) at high recoveries [14]. It has been shown that operating the RO near the thermodynamic limit (where the applied pressure is slightly above the concentrate osmotic pressure) significantly reduces the SEC [6,7,15,16]. The development and implementation of efficient methods have led to a reduction in energy consumption of several industrial RO processes [17,18]. Model-based optimization and control is another approach to reduce SEC in RO desalination. For example, energy reduction has been done by Tel.: +1 99 869 3668; fax: +1 99 869 692. E-mail address: minghengli@csupomona.edu. optimizing RO configurations and operating conditions [19,2]. Using simplified or first-principles based models, it is also possible to account for capital cost, feed intake and pretreatment, and cleaning and maintenance cost in the optimization framework [21 23]. Recent research efforts have been focused on a formal mathematical approach to provide a clear evaluation of minimization of the production cost by studying the effect of applied pressure, water recovery, pump efficiency, membrane cost, ERD, and brine disposal cost [8,24 26]. Using model-based control, reduction of SEC in an pilot-scale RO experimental system has been demonstrated [27,28]. In two previous papers [1,29], the author provided a comprehensive analysis of single- and multi-stage RO with/without ERD from firstprinciples. With the assumption of negligible pressure drop along the membrane channel, the author derived a dimensionless characteristic equation to unambiguously reveal the coupled relationship between RO configuration, feed conditions, membrane performance, and operating conditions. The equation has the following form: γ ¼ α Y þ α ln 1 α 1 Y α where α= /ΔP, Y= /Q f,andγ=al p /Q f. is osmotic pressure in the feed, ΔP is the pressure across the membrane, is the permeate flow rate, Q f is the feed rate, A is the membrane area, and L P is the hydraulic permeability. The physical meanings of these dimensionless parameters are as follows: α 1 is the dimensionless applied pressure, Y is the dimensionless fractional recovery, and γ is the dimensionless membrane capacity. Moreover, β 1 =Y/γ= /AL p may be defined as the dimensionless average flux or average driving force. Note that α and β are defined in such away for a better presentation of results in equations and/or figures [1,29]. Based on the characteristic RO equation, ð1þ 11-9164/$ see front matter 212 Elsevier B.V. All rights reserved. doi:1.116/j.desal.212.2.24

62 M. Li / Desalination 293 (212) 61 68 a nonlinear optimization problem was formulated and solved neglecting the effect of pump efficiency. The optimization indicated that reducing NSEC (SEC normalized by the feed pressure ) can be pursued using one or more of the following three independent methods: (1) increasing γ (i.e., increasing AL p and/or reducing Q f ), (2) increasing number of stages with inter-stage pump, and (3) using an ERD. When γ increases, the feed rate is adversely affected and NSEC reduces but flattens out eventually. Using more stages with interstage pumps not only reduces NSEC but also improves water recovery. However, the NSEC flattens out when the number of stages increases and ROs with more than five stages are not recommended. Close to the thermodynamic limit where γ is sufficiently large, the NSEC of ROs up to five stages approaches 4, 3.6, 3.45, 3.38 and 3.33 respectively. The ERD can significantly reduce the NSEC, theoretically to 1, while the corresponding recovery approaches zero. The NSEC becomes larger when the required water recovery increases. It is found that a combination of all three methods can significantly reduce the NSEC while maintaining a high recovery and a reasonable feed or permeate rate. An NSEC around 2.5 2.8 with an 8% water recovery may be possible using 3 5 RO stagesoperated at a γ about 3 5 (orq f =.2.3 A total L p )assuminga9%erd efficiency. Analytical solutions to RO operation at the theoretical thermodynamic limit (where γ is sufficiently large) are also provided [1]. It is worth noting that the developed optimization results depend on two important assumptions: (1) the pump is sized such that the optimal solution matches the Best Efficiency Point (BEP) of the pump, and (2) the retentate stream has negligible pressure drop along the RO train. However, if a pump is fixed in plant operation, changing flow rate and/or applied pressure would shift the operation point on the characteristic map of the pump, resulting in a change in pump efficiency. Moreover, because several RO elements are used in series in a pressure vessel in industrial applications, it is observed a fair amount of pressure drop in each stage of RO plant operation. The pressure drop along the membrane channel reduces the driving force and thus, affecting water recovery. Therefore, explicitly accounting for the pump characteristic curve and pressure drops along the RO train would provide more accurate results to guide the operation of RO desalination. 2. Formulation of model-based optimization problem of RO desalination In this section, the model-based analysis and optimization of RO plant operation will be presented using an industrial desalter in Inland Empire Utility Agency (IEUA), Chino, California. The developed methodology, however, might be readily applied to other BWRO processes with different configurations. The IEUA desalination plant has four RO trains with an overall production of 6.7 MGD (or mega gallons per day). Each train has two stages with no interstage pump (see Fig. 1). Feedwater from underground wells is sent to the RO plant and is split into four streams. Each RO train has a dedicated booster pump to elevate the feed pressure in order to maintain sufficient driving force across the membrane. Each RO feed pump is equipped with a variable frequency drive (VFD)to change the rotational speed of the pump, which in turn, varies both the flow rate and the pressure of incoming stream to the RO train. A control valve is installed in each concentrate line which also affects the flow rate and the pressure. The desalination operation is controlled by a RO programmable logic controller (PLC). Based on the set points of permeate flow and water recovery, the PLC automatically adjusts the speed of the RO train feed pump and the position of the concentrate control valve. Each RO train consists of pressure vessels in a two-stage array (see Fig. 2). The first stage has 28 pressure vessels operated in parallel. The second stage has only 14 pressure vessels in parallel because of significantly smaller volumetric flow rate due to water recovery in the first stage. There are 7 RO elements in series in each pressure vessel. The concentrate streams from the first stage pressure vessels are combined and fed to the second stage pressure vessels. The concentrate from the second stage, or brine, is piped to a well bypass equalization basin. Permeate streams from each of the pressure vessels are collected and piped to decarbonators for further processing. The RO elements use Dow FILMTEC membranes (Model No. BW3-4) which has a permeability around.1 gfd/psi, or gallon per day per square foot per psi (according to the Dow FILMTEC Reverse Osmosis Membranes Technical Manual [3], its membranes cover a flux performance range from.4 to.55 gfd/psi. A permeability of.11 gfd/psi was reported in literature for the BW3-4 membrane [31]). The plant is operated at a recovery about 8% in order to meet the production need ( 6.7 MGD) and brine discharge requirement ( 2 MGD). The following assumptions and simplifications are made in deriving the mathematical model of the RO train: (1) negligible salinity in the permeate as compared to the one in the retentate because the average salt rejection of Dow Filmtec membrane is about 99.5%, (2) linear relationship between osmotic pressure and salt concentration [32], (3) negligible pressure drop along the permeate stream as suggested by operation data, and (4) retentate pressure drop in proportion to the square of flow velocity as suggested by plant test data and literature [33]. Moreover, the effect of concentration polarization is not included. Such a simplification has been made by others for analysis of energy consumption in RO desalination (e.g., [16,24]). However, accounting for this factor could further improve modeling accuracy and will be considered in future work. Based on these, a set of one-dimensional differential equations are derived to describe the coupled behavior of retentate flow and pressure drop along the pressure vessel in each stage of the RO train: dqx ðþ dx ¼ ¼ A L p ðδp Þ Q f Q dðδpðþ xþ ¼ k Q 2 dx Qx ðþ ¼ Q f @x ¼ ΔPðÞ x ¼ P þ ΔP pump P p @x ¼ ð2þ P b, Q b, C b P f, Q f, C f P, Q f, C f P p,, C p Fig. 1. Schematic of an industrial two-stage RO water desalination train without inter-stage pump.

M. Li / Desalination 293 (212) 61 68 63 2nd stage feed Retentate RO feed Retentate RO feed Permeate Fig. 2. Array of pressure vessels in an industrial two-stage RO water desalination train. where dq is the flow rate of water across the membrane of area da (da=a dx and x is dimensionless number with 1 and 1 2 representing the first and second stage, respectively), L P is the membrane hydraulic permeability, ΔP and are the differences in the system pressure and osmotic pressure across the membrane, respectively. Q is the flow rate in the retentate and Q f is the feed flow rate. A is the total area of all RO elements in each stage. is at the entrance of the membrane channel. P is the feed pressure before the pump. ΔP pump is the pressure increase across the pump. k is a coefficient describing the pressure drop along the pressure vessel in the retentate stream. It is important to note that the flow area is reduced by a half in the second stage, therefore k is four times of the one in the first stage. As mentioned earlier, the energy cost in the context of RO water desalination process is typically described using SEC, or the electrical energy demand per cubic meter of permeate [8,24 26]. For singlestage RO or multi-stage RO without interstage pump, it is readily derived that: SEC ¼ Q f ΔP η pump η moter where η pump and η moter are pump and motor efficiencies, respectively. Typically, η moter is close to 1 and varies little with load or speed. However, pump efficiency changes with flow rate and pressure increase across the pump [34]. The IEUA desalter employs a Johnston 12GHC 9-stage pump. The design point of the pump is 145 GPM and 625 feet. Its characteristic curves are plotted in Fig. 3 [35]. Fig. 3 ð3þ provides the relationship between intake flow and pump head at different pump speeds. The iso-bhp (brake horsepower) lines are also plotted using dash-dot lines. The BHP as a function of pump speed and intake flow is shown in Fig. 3. From the pump characteristic map, any two known parameters in flow rate, pump head and pump speed would uniquely determine the rest one using interpolation, after which the pump efficiency and BHP can be calculated accordingly. If assuming η motor =1%, the minimization of NSEC of a RO train accounting for pump efficiency is formulated as follows: Q f ΔP pump min NSEC ¼ Q f ;Y η pump s:t: η pump ¼ η pump ðq f ; HÞ dqðþ x ¼ A L dx p ΔP Q f Q dðδpðþ xþ ¼ k Q 2 dx Qx ðþ ¼ Q f @x ¼ Px ðþ ¼ ΔP þ ΔP pump P p @x ¼ ΔP pump ¼ :4327 H ¼ Q f Qð2Þ Y ¼ Q f Y Y max Y Y min g pump ðq f ; HÞ ð4þ 9 η=.49 3 n=177 Pump head (ft) 8 7 6 5 4 3 η=.676 η=.785 η=.819 η=.89 η=.794 η=.747 n=177 n=1645 n=1466 BHP (hp) 25 15 1 n=1645 n=1466 n=1287 n=1287 4 8 1 16 24 Flow (gpm) 5 4 8 1 16 24 Flow (gpm) Fig. 3. Characteristic curves of the Johnston 12GHC 9-stage pump.

64 M. Li / Desalination 293 (212) 61 68 Table 1 RO plant operation data. Parameter Number of pressure vessels per train 42 42 Number of 1st stage pressure vessels 28 28 Number of 2nd stage pressure vessels 14 14 Number of membrane elements per vessel 7 7 Area per element, ft 2 4 4 Feed pressure, P, psi 4.6 4.6 Feed osmotic pressure,, psi 9 9 Feed flow, Q f, gpm 1,525 1,56 Permeate pressure, P P, psi 16.4 16.8 Permeate flow,, gpm 1,234 1,179, Y, % 8.9 78.3 Retentate pressure drop in 1st stage, ΔP r1, psi 24.9 25.8 Retentate pressure drop in 2nd stage, ΔP r2, psi 18.2 19.3 Pump head, H, ft 36 513 Table 2 Parameters used in the mathematical model. Parameter k in 1st stage, psi/gpm 2 2.1 1 5 2.1 1 5 k in 2nd stage, psi/gpm 2 8.4 1 5 8.4 1 5 L p, gfd/psi.11.7 where H is the pump head (ft). η pump (Q f, H) is the reading from the pump characteristic curve. Y is the water recovery. Y max and Y min are the upper and lower limits of water recovery. Y min is set to be 5% in all cases. The inequality constraint g pump (Q f, H) is to guarantee that the RO process is operated within the normal range of the pump. ΔP pump =.4327 H is the conversion of pump head (ft) to pressure increase (psi) for water. 3. Results and discussion Operation data from two BWRO trains (trains A and D) with different service times (the membrane in train A is newer than that in D) shown in Table 1 are used to validate the mathematical model. The parameters used in the simulation (k and L P ) are shown in Table 2. Note that a unit conversion of gfd/psi to gpm/psi/ft 2 is necessary when calculate the product of A and L P. These parameters are derived using optimization to best fit the experimental data following a similar approach in the author's previous work [36]. It is worth noting that the values of derived L P are consistent with those reported in literature [31,37]. Fig. 4 shows the simulated pressure differences across the membrane (system pressure and osmotic pressure) as well as flows (permeate and retentate) along the pressure vessel in both the first and the second stages. As expected, the hydraulic pressure difference reduces, and the osmotic pressure difference increases along the pressure vessel. The reduced driving force results in a slight decrease in permeate flux in each stage. Between stages, there is a substantial difference in water production rate due to different membrane areas. However, the difference in pressure drops is not very significant because the second stage has reduced flow area, even though its inlet flow is smaller. The measured values of brine flow and the pressures at exit of first and second stages are marked with circles in Fig. 4 for a comparison. A nearly perfect match between measurement and model prediction is 16 14 Q r 16 14 Q r 1 1 Flows (gpm) 1 8 6 Flows (gpm) 1 8 6 4 4 1 2 1 2 (c) Pressures (psi) 18 16 14 12 1 8 6 4 2 ΔP 1 2 (d) Pressures (psi) 25 15 1 5 ΔP 1 2 Fig. 4. Profiles of simulated flow rates (a, b) and pressure differences across the membrane (c, d) along two RO trains (train A: a and c; train D: b and d) with different service times.

M. Li / Desalination 293 (212) 61 68 65 Table 3 A comparison between current and optimized operating conditions. Parameter A, optimal D, optimal Feed, Q f, gpm 1525 1334 156 1256 Pump head, H, ft 36 367 513 521 Pump efficiency, η pump, % 74.9 79.8 8.4 81.9, Y, % 8.9 92.5 78.3 93.9 NSEC 28.4 23.9 39.2 32.6 Potential energy saving, % 16 17 obtained. It is noticed that even though these two RO trains have different service times, the parameter k does not change, or the relationship between pressure drop along the vessel and retentate flow remains the same. However, a significant change in L P is observed, implying that the RO hydraulic performance is degrading. As a result, a larger pump head is required to obtain a similar amount of permeate flow and water recovery. Tests done at Orange County Water District using the same type of membrane also indicate a decay of permeability from.11 gfd/psi to.5 gfd/psi during a certain period of operation [37]. Based on the parameters determined in the mathematical model, the optimization problem described by Eq. (4) is solved using standard optimization packages in Matlab. The objective is to reduce the SEC while maintaining the same amount of permeate flow rates (i.e., 1234 gpm for train A and 1179 gpm for train B). The optimal results by setting Y max =1% and the current operation conditions are shown in Table 3. It is seen that by optimizing operating conditions, the NSEC can be reduced by 16 17% in both trains. Several additional optimization studies were done by including an equality constraint of recovery in each case (Y=78%, 8%,, 96%) and the results are plotted in Fig. 5. The optimal solutions shown in Table 3 (without the equality constraint of recovery) are marked by stars. It is shown that the optimal solution may not be corresponding to the best efficiency or the lowest/ highest feed flow or pump head. It is actually a tradeoff among all these factors. Generally speaking, the brine pressure increases as the recovery increases, indicating that the pressure drop across the concentrate valve increases. This fact confirms the strategy of using concentrate valve to control water recovery currently used in IEUA. Another observation is that the NSEC curve follows a very similar trend as the pump speed curve. The solved results are also plotted in the pump characteristic maps, as shown in Fig. 6. The current operating conditions are marked by circles and squares and the model-derived optimal operating conditions are marked by stars. Because these points share the same permeate flow rate within the same train, they may be connected to form iso-permeate lines. It is apparent that both trains (A and D) have very similar iso-permeate lines. The location and curvature on the pump characteristic maps are a little different due to different membrane properties and different specified permeate flows. One can reduce NSEC by increasing pump head and reducing feed following the isopermeate trajectory or vice versa, depending on the location of the original operating point. The usefulness of the optimization framework is to guarantee that the move is in the right direction and that the operation is always within the normal range of the pump. It is also worth noting that the steady-state pump head and feed flow are shared by both the characteristic curve of the pump and the pipe curve according to the pump operation theory [34]. Applying this to Fig. 6 it is known that when the operating points moves from right to left (as water recovery increases), the flow resistance is increasing (or the concentrate control valve is gradually closing), and the pump speed reduces and then increases. These are consistent with Fig. 5. The pressures and flows along the RO train under three different conditions (current operating conditions, conditions with 96% recovery, and optimal operating conditions) are shown in Fig. 7. As compared to the current conditions, more water is recovered in the first stage in the optimal case. This is due to an elevated applied pressure. However, the driving force in the second stage is smaller and less water is recovered. When the water recovery is specified as high as 96%, the water production mainly occurs in the first stage. The osmotic pressure in the second stage is so high that thermodynamic limit is approaching in the middle or near the end of the second stage. In this sense, one may conclude that the optimization serves to optimally allocate water production in each stage. Apparently, operating near the thermodynamic limit does not always reduce SEC in RO desalination. To explain this, one may use conclusions drawn from the author's previous works [29,1], where a dimensionless parameter γ was used as an indication of the RO operation regime. For a single stage, if γ is sufficiently large (say γ 1.5), the system should be operated near the thermodynamic limit in order to reduce SEC. However, if γ is small (say, γ 1), the RO process is limited by mass transfer. In this case the optimal applied pressure should be a function of γ, which can be read from Fig. 5 in [29] for single-stage RO and Fig. 3 in [1] for multi-stage RO with interstage pumps. Equations are also provided that may handle additional constraints such as minimum water recovery [29,1]. Based on these works, the best expected NSEC is higher if γ is smaller. Table 4 provides the values of γ at each stage based on its definition (γ 1 =A 1 L p /Q f for stage 1 and γ 2 =A 2 L p [ /(1 Y 1 )]/[Q f (1 Y 1 )], where Y 1 is the fractional recovery in stage 1). Detailed expressions of other parameters are provided in the author's previous work [1]. γ is also calculated using Eq. (1), which was derived assuming no pressure drop along the vessel. Since pressure drop is accounted for in this work, the dimensionless applied pressure can be defined using pressure difference at either inlet (α ) or outlet of the stage (α + ). Based on α and α +, γ and γ + are calculated. It is shown that γ is bounded by γ and γ + and they are not very different from each other. In fact, a geometric or arithmetic average of γ and γ + is very close to γ. From Table 4, it is apparent that γ 1 (or the production rate is too much ) in all cases, implying that the RO operation lies in the mass transfer region. Therefore, NSEC is high and operating near the thermodynamic limit may not be energy efficient. It is also noticed that by optimizing the operating conditions, γ becomes greater in each stage, resulting in a reduction in NSEC. This also explains that train A is more energy efficient than train D because of a larger mma in each stage. The author's previous papers [29,1] are consistent with the current work because the pump efficiency varies less than 1% and the pressure drop in each stage is about 1 15% of the inlet pressure. However, explicitly accounting for pump efficiency and pressure drop in this work provides more accurate results. It is worth noting that even though the feed pressure is higher than the permeate pressure in this case study, the optimized NSEC is still about 24 in the RO train with relatively new membranes (or 33 in the other train with older membranes). The value is several times higher than the theoretical minimum for a single-stage RO without ERD, or 4, which occurs at the thermodynamic limit and a recovery of 5% by assuming negligible pressure drop and 1% pump efficiency [1,24,29]. There are several constraints in plant operation that contribute to the gap between theory and practice. Firstly, this RO plant is designed to operate at a recovery around 8% to meet the requirements of water production and brine discharge. Based on the author's previous analysis [1], the theoretical minimum NESC at the thermodynamic limit will be higher than 4 if the recovery is not 5% (e.g., 6.25 for a water recovery of 8%). Secondly, the RO is currently operated far from the thermodynamic limit as implied by the value of γ. As pointed out in the author's previous work [29], the best achievable NSEC is at least 3 times of its theoretical value at the thermodynamic limit if γ becomes less than.1. Thirdly, there is a pressure drop along the RO train which reduces the driving force for permeate flow. However, this effect is usually ignored in theoretical analysis. Lastly, the pump has an efficiency around 8% or even lower, especially if the operating point is far from its Best Efficiency Point (BEP). To further reduce NSEC, the plant might consider increasing the number of pressure vessels in parallel to increase the value of γ so that the operation shifts towards the thermodynamic equilibrium. If

66 M. Li / Desalination 293 (212) 61 68 17 165 155 15 Pump speed (rpm) 16 155 15 Feed (gpm) 145 14 135 13 145 125 (c) 14.78.8.82.84.86.88.9.92.94.96 55 5 (d) 1.78.8.82.84.86.88.9.92.94.96.82.81.8 Pump head (ft) 45 4 Pump efficiency.79.78.77.76 35.78.8.82.84.86.88.9.92.94.96.75.74.78.8.82.84.86.88.9.92.94.96 (e) Brine pressure (psi) 26 24 22 18 16 (f) NSEC 4 38 36 34 32 3 28 26 14 24 12.78.8.82.84.86.88.9.92.94.96 22.78.8.82.84.86.88.9.92.94.96 Fig. 5. Relationship of pump speed, feed flow, (c) pump head, (d) pump efficiency, (e) brine pressure, and (f) NSEC and specified water recovery. the constraint of brine discharge can be relaxed, the plant may also consider increasing number of trains and/or resizing the pumps so that each train has a lower recovery while maintaining the total permeate production. A detailed quantitative analysis of capital investment and annual energy reduction might be necessary to identify the best condition. The usefulness of the model-based approach lies in the fact all coupled design and operating parameters can be integrated in a single mathematical model for optimization. Interested readers are referred to the author's most recent work on modelbased optimization of multi-train RO operation with different service times where permeate allocation can be optimized to reduce the overall NSEC [38]. 4. Conclusions A compressive model-based optimization was carried out for an industrial BWRO desalination process. The model accounted for pressure drop along the RO train, pump map as well as the effect of membrane permeability. Trajectories of optimization curves are also provided if plant operators desire minor changes. It was shown that even though

M. Li / Desalination 293 (212) 61 68 67 8 3 7 η=.785 η=.819 25 Pump head (ft) 6 5 4 η=.89 η=.794 η=.747 n=177 n=1645 BHP (hp) 15 3 n=1466 n=1287 8 1 1 14 16 18 Feed (gpm) 1 5 8 1 1 14 16 18 Flow (gpm) Fig. 6. Iso-permeate lines on the pump characteristic map. both trains studied in this work have different membrane permeability pamperers due to difference service times, they share the same trend on the iso-permeate curve in the pump characteristic curve. By moving the operating point along the iso-permeate line, the NSEC may be reduced by 16% in both RO trains. The optimization framework guarantees that such a move is within the normal operating range of the pump. It is also shown that when the membrane performance decays, the required pump head is higher in order to maintain the same permeate rate. Because the dimensionless membrane capacity (γ) is very small in each stage of both RO trains in this work, a further improvement might be achieved by installing additional vessels in parallel. Future work will report plant operation results. 16 16 Q r Q r 14 14 1 1 Flows (gpm) 1 8 6 Flows (gpm) 1 8 6 4 4 1 2 1 2 (c) 25 ΔP (d) 3 25 ΔP Pressures (psi) 15 1 Pressures (psi) 15 1 5 5 1 2 1 2 Fig. 7. Profiles of (a, b) flow rates and (c, d) pressures along two RO trains (train A: a and c; train D: b and d) with different service times (dash line: current operating conditions; dash dot line: conditions with 96% recovery; solid line: optimized operating conditions).

68 M. Li / Desalination 293 (212) 61 68 Table 4 Stage analysis using dimensionless parameters. Parameter A, optimal D, optimal stage 1: γ 1.35.41.23.27 Y 1.589.7.552.682 α 1.5.49.37.36 + α 1.58.54.41.38 γ 1.32.38.21.26 + γ 1.38.42.24.28 stage 2: γ 2.15.225.57.136 Y 2.536.75.516.83 α 2.141.181.91.121 + α 2.159.186.1.123 γ 2.95.216.54.132.111.228.6.136 γ 1 + Acknowledgements The author would like to thank Brian Noh and Moustafa Aly from Inland Empire Utility Agency for plant tours, operation data and fruitful discussions. References [1] M. Li, Reducing specific energy consumption in reverse osmosis (RO) water desalination: an analysis from first principles, Desalination 276 (211) 128 135. [2] T. Manth, M. Gabor, E. Oklejas, Minimizing RO energy consumption under variable conditions of operation, Desalination 157 (3) 9 21. [3] M. Busch, W.E. Mickols, Reducing energy consumption in seawater desalination, Desalination 165 (4) 299 312. [4] M. Wilf, C. 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