Desalination

Article pubs.acs.org/IECR

Optimization of Multitrain Brackish Water Reverse Osmosis (BWRO) Desalination Mingheng Li*,† †

Department of Chemical and Materials Engineering, California State Polytechnic University, Pomona, California 91768, United States ABSTRACT: This work focuses on optimal operation of brackish water reverse osmosis (BWRO) plants employing multitrains which have different service times and membrane permeability parameters. A nonlinear optimization problem, based on a previously developed comprehensive RO model that accounts for characteristic curves of booster pumps driving the RO trains and pressure drop along each RO train, is formulated and solved to minimize the overall specific energy consumption (SEC) while maintaining the same overall water production. A 16−17% reduction in SEC is possible by optimizing production allocations among all trains as well as operating conditions within the normal pump operating range in each train. It is shown that optimizing each train individually (without optimizing production allocations) could yield a higher SEC.

parameter γ = ALpΔπ0/Qf (where A is the membrane area, Lp is the hydraulic permeability, Δπ0 is the feed osmotic pressure, and Qf is the feed rate) that describes the dimensionless membrane capacity. γ determines the best achievable NSEC. Under optimized conditions, the higher the γ, the lower the NSEC. When γ is sufficiently large, the RO is operated near the thermodynamic limit, and the optimal NSEC approaches its global minimum (e.g., 4 for single stage RO without ERD). In order to achieve the optimal NSEC, the applied pressure should be determined based on the value of γ, and charts are available. 22 The theoretical analysis also shows that increasing number of stages with interstage pumps may also improve NSEC to a limited extent. However, it is desirable for a high water recovery.23 Employing an ERD can significantly reduce NSEC, while the optimal condition tends to have a low water recovery if no constraint is applied.22,23 It is therefore recommended to combine all these methods (a sufficiently large γ, multistage with interstage pumps, and an ERD) to reduce NSEC and to maintain a high recovery at the same time. For example, an NSEC around 2.5−2.8 with an 80% water recovery may be possible using 3−5 RO stages operated at a γtotal about 3−5 (or Qf = 0.2−0.3 AtotalLpΔπ0, where Atotal is the total membrane area in all stages) assuming a 90% ERD efficiency.23 This is lower than the theoretical minimum of a single-stage RO without ERD. The optimization framework also provides analytical solutions to RO desalination with/without minimum recovery constraints at the theoretical thermodynamic limit, where γ approaches infinity.23 The author’s most recent work focuses on operation of a single BWRO train where the pump, train configurations, and membrane elements are

1. INTRODUCTION Reverse osmosis (RO) membrane separation is a proven desalination technology to make clean and drinking water. Energy consumption is considered to be a very important issue in RO desalination.1,2 To reduce specific energy consumption (SEC), or energy cost per unit volume of permeate flow, research efforts have been made including development of high permeability membranes,3,4 utilization of energy recovery devices,4,5 and alternative energy sources to subsidize electricity consumption,6 as well as first-principles based analysis and optimization of RO configurations and operating conditions.7,8 It is reported that implementation of energy-efficient ideas is able to make the RO desalination technology more competitive with alternatives.9,10 In the area of model-based approach, it has been shown that operating RO near the thermodynamic limit (where the applied pressure is slightly above the concentrate osmotic pressure) significantly reduces the SEC.11,12 Recent research has been focused on a formal mathematical framework to provide a clear evaluation of production cost by studying the effect of RO configuration, applied pressure, water recovery, pump efficiency, membrane cost, ERD, stream mixing, and brine disposal cost.3,13−16 Using model-based control, a reduction of SEC in an pilot-scale RO experimental system has been demonstrated.17,18 It is acknowledged that energy consumption of booster pumps to drive the RO membrane elements accounts for a major portion of the total cost of water desalination.19−21 In a series of previous papers, 22−24 the author provided a comprehensive analysis of NSEC (SEC normalized by the feed osmotic pressure) of the pump in RO desalination. A dimensionless characteristic equation, based on the assumption of negligible pressure drop along the RO train, was derived to reveal the coupled relationship between RO configuration, feed conditions, membrane performance, and operating conditions.22 The equation involves an important dimensionless © 2012 American Chemical Society

Received: Revised: Accepted: Published: 3732

November 30, 2011 January 24, 2012 February 8, 2012 February 8, 2012 dx.doi.org/10.1021/ie202796u | Ind. Eng. Chem. Res. 2012, 51, 3732−3739

Industrial & Engineering Chemistry Research

Article

Figure 1. Schematic of an industrial multitrain RO water desalination process.

Figure 2. Array of pressure vessels in an industrial two-stage RO water desalination train without interstage pump.

fixed.24 The model-based optimization explicitly accounts for the effects of pressure drop along the RO train and pump characteristic curves, thus improving the accuracy of previous works.22,23 It is shown that the NSEC can be reduced by shifting the operation point on the pump characteristic map while maintaining the same permeate production rate.24

As a continuation of the above efforts, this work focuses on optimal operation of BWRO plants employing multitrains, which has not been addressed previously.24 A modern RO plant typically utilizes several trains which could have different service times and different permeability parameters. Therefore, allocation of production rates among all trains may also have an effect on NSEC. 3733

dx.doi.org/10.1021/ie202796u | Ind. Eng. Chem. Res. 2012, 51, 3732−3739


Article

2. PROBLEM FORMULATION OF MULTITRAIN RO OPTIMIZATION

optimization problem of multitrain RO operation accounting for pump efficiency is formulated as follows

In this section, the optimization methodology of multitrain RO desalination will be illustrated using an industrial desalination plant in Chino, California. This facility has four RO trains with an overall production about 7 mega gallon per day (MGD), as shown in Figure 1. Each RO train has two stages with no interstage pump. Please note that this is different from brine staged operation with additional pumps.13 A dedicated booster pump equipped with a variable frequency drive (VFD) is used to provide adequate feed pressure in an energy-efficient manner. A control valve is installed in each concentrate line. The permeate flow and water recovery are controlled by manipulating pump speed and concentrate valve position using a RO programmable logic controller (PLC). Each RO train consists of pressure vessels in a two-stage array (see Figure 2). The first stage has 28 pressure vessels operated in parallel. The number of pressure vessels in the second stage is only a half of the one in the first stage because of a significantly smaller volumetric flow rate. Each pressure vessel contains 7 RO elements in series. The concentrate streams from the first stage pressure vessels are combined and fed to the second stage pressure vessels. The plant is operated at a recovery around 80% in order to meet the minimum production and the maximum brine discharge requirements. In the author’s previous work,24 a comprehensive model was developed to explicitly account for the effects of pressure drop along each RO train as well as pump characteristic curves. Specifically, the RO model mathematical model has the following form24

min NSEC

dQ (x) dx

−

d(ΔP(x)) =−k·Q 2 dx

Q (x )

=Q f

ΔP(x)

=P0 + ΔPpump − Pp

Qp

total

Δπ 0

s.t . =ηpump(Q f , Hi),

ηpump

i = 1, ..., Ntrain

i

i

⎛ ⎞ Qf i =− A ·L p ·⎜⎜ΔPi − Δπ 0⎟⎟, i Qi ⎝ ⎠

dQ i(x) dx d(ΔPi(x)) dx

=− k i·Q i2 ,

Q i(x)

=Q f i

ΔPi(x)

=P0i +ΔPpump − Pp

@x = 0,

i = 1, ..., Ntrain i

@x = 0,

ΔPpump

=0.4327·Hi ,

Qp

=Q f − Q i(2), i

∑ Q pi

=Q p

Yi

=

Yi

≤Ymax ,

i = 1, ..., Ntrain

Yi

≥Ymin ,

i = 1, ..., Ntrain

i

total

i

Qp

i

Qf i

gpump(Q f , Hi) ≤0, i

,

i = 1, ..., Ntrain

i = 1, ..., Ntrain

i

i

i = 1, ..., Ntrain

i = 1, ..., Ntrain i = 1, ..., Ntrain

i = 1, ..., Ntrain

i = 1, ..., Ntrain

,

i = 1, ..., Ntrain (2)

where Ntrain is the number of RO trains. H is the pump head in feet. ΔPpump is the pressure increase across the pump. ηpump(Qf,H) is the efficiency based on the pump characteristic map. Y is the water recovery, and Ymax and Ymin are its upper and lower limits. Qp is the permeate flow rate at the exit of the RO train. The inequity constraint gpump(Qf,H) ≤ 0 is to guarantee that each RO train is operated within the normal range of the booster pump. ΔPpump = 0.4327 · H is the conversion of pump head (ft) to pressure increase (psi) for water.

@x = 0 @x = 0

(∑i Q f ΔPpump /ηpump ) i i i

Hi , Q f i

⎛ ⎞ Qf =A ·Lp ·⎜⎜ΔP − Δπ 0⎟⎟ Q ⎝ ⎠

−

=

(1)

where Q is the retentate flow rate, and ΔP is the pressure difference across the membrane. −dQ is the flow rate of water across the membrane of area dA (dA = A · dx, where A is the total area of all RO elements in each stage and x is dimensionless number with 0−1 and 1−2 representing the first and second stage, respectively). Lp is the membrane hydraulic permeability. Δπ0 is the osmotic pressure difference at the entrance of the membrane channel. Qf is the feed flow rate. P0 is the feed pressure before the pump. ΔPpump 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. The model is based on the assumptions of negligible pressure drop and osmotic pressure in the permeate flow.24 In a previous work, the mathematical model was implemented in a computational framework to optimize operating conditions in a single train.23 Based on this model, the

3. RESULTS AND DISCUSSION 3.1. Model Validation Using Plant Data. The operation data from all trains with different service times (A, B, C, and D) are shown in Table 1). The parameters k and Lp in the mathematical model described in eq 1 are shown in Table 2. These values are determined using nonlinear regression to best fit the plant data. A similar approach was employed in the author’s previous works.24,25 Using these parameters, the profiles of pressure differences across the membrane (system pressure and osmotic pressure) and flows (permeate and retentate) along the RO train are solved and shown in Figure 3. The measured values of feed and brine flows and the pressure differences across the membrane at the exit of the first and the second stages are marked with circles for a comparison. A nearly perfect match between all measurement points is obtained. It is clearly seen a strong correlation between the permeability parameter and the membrane service time, i.e., the longer the service time, the smaller the membrane permeability Lp. It is also 3734



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consistency was found. The solving time is only several seconds using a 2.67 GHz laptop. Two optimization strategies are studied for a comparison. In one optimal case (case ii), eq 2 is solved where not only the operating conditions in each RO train but also the allocation of production rates among all trains are optimized. In the other optimal case (case iii), each RO train is optimized individually, i.e., only the operating conditions are optimized, however, the permeate rate of each train is maintained at current production level.24 Unless mentioned specifically, Ymax = 100% and Ymin = 50% are used for all studies in this work. The operating conditions of these two optimized cases are shown in Table 3, and the profiles of flow rates and pressure differences across the membrane are plotted in Figure 4. As compared to the current operating conditions, both optimized cases suggest higher recoveries in each train to reduce NSEC. To achieve these, all RO trains are operated at smaller feed rates and more closed valve openings in the concentrate lines,24 which helps to maintain a high pressure at the outlet of the second stage and allows the pumps to run in slower speeds. A comparison between cases i and iii also shows a very consistent trend to reduce NSEC at a fixed permeate flow in each train, i.e., a lower feed, a higher pump head, a lower pump speed, and a higher recovery. It is shown that the reduction of NSEC is about 16−17% in both optimized cases. Accounting for permeate allocation in the optimization increases the production in train A (associated with the most permeable membranes) and decreases the production in train C (associated with the least permeable membranes). Even though the NSEC of train A alone is higher, those of other trains are lower. As a result, the overall NSEC is reduced. From a viewpoint of mathematics, fixing permeate production in each train adds constraints to the optimization problem; therefore, the objective function is higher than the one in case ii where the constraints are removed. 3.3. Effect of Recovery on Optimal NSEC. From Table 3 it is known that the best operating conditions have a water recovery around 93−94% in all trains. In this subsection, several additional optimization studies are done by including an additional equality constraint of recovery in each case (Y = 80%, 82%, ..., 96% in each train). These steady-state optimization studies aim to provide trajectories for incremental reduction in NSEC in plant operation. The results are shown in Figure 5. Except for

Table 1. RO Train Configuration and Operation Data parameter

train A

number of pressure vessels per train number of first stage pressure vessels number of second stage pressure vessels number of membrane elements per vessel area per element, ft2 rough service time, days feed flow, Qf, gpm feed pressure before pump, P0, psi pressure after pump, psi pump head, H, ft feed osmotic pressure, Δπ0, psi permeate pressure, Pp, psi retentate pressure drop in first stage, ΔPr1, psi

train B

train C

train D

42 28 14

42 28 14

42 28 14

42 28 14

7

7

7

7

400 500 1,525 40.6 196.5 360 9 16.4 24.9

400 1,000 1,524 40.6 247.9 479 9 16.7 25.3

400 1,700 1,404 40.6 283.8 562 9 16.3 28.6

400 1,300 1,506 40.6 263.2 514 9 16.8 25.8

retentate pressure drop in second stage, ΔPr2, psi

18.2

20.6

17.1

19.3

permeate flow, Qp, gpm recovery, Y, %

1,234 80.9

1,234 81.0

1,131 80.6

1,179 78.3

Table 2. Parameters Used in the Mathematical Model parameter k in first stage, psi/gpm2 Lp, gfd/psi

train A 2.1 × 10

−5

1.1 × 10−1

train B −5

train C

train D

2.2 × 10

−5

2.6 × 10

2.1 × 10−5

8.1 × 10−2

6.2 × 10−2

7.0 × 10−2

noticed that three trains (A, B, D) have almost the same parameter k. However, train C corresponding to the longest service time has a larger k than the rest, impling possible scaling and fouling. 3.2. Effect of Permeate Allocation on Optimal NSEC. The optimization of multitrain RO operation is solved using the parameters determined from the current operating conditions (referred to as case i). The objective is to reduce the NSEC while maintaining the same overall permeate production (i.e., 4,778 gpm). The optimization was done using a nonlinear constrained multivariable optimization package (fmincon) in Matlab. It is not a global optimization solver; however, different initial guesses were used to check the final solutions and

Figure 3. Simulated profiles of (a) flow rates and (b) pressure differences across the membrane along all RO trains with different service times. Plant data are marked with circles. 3735



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Table 3. Comparison between Current and Optimized Operating Conditions case

train

n

Qf

H

ηpump

Y

Qp

NSEC

i

A B C D overall A B C D overall A B C D overall

1,513 1,639 1,684 1,672

1,525 1,524 1,404 1,506

360 479 562 514

0.754 0.798 0.816 0.804

0.809 0.810 0.806 0.783

1,507 1,557 1,587 1,568

1,418 1,302 1,150 1,230

400 479 544 509

0.795 0.815 0.811 0.819

0.934 0.935 0.941 0.937

1,434 1,571 1,628 1,590

1,334 1,314 1,204 1,256

367 487 567 522

0.798 0.815 0.814 0.819

0.925 0.939 0.939 0.939

1,234 1,234 1,131 1,179 4,778 1,326 1,218 1,082 1,152 4,778 1,234 1,234 1,131 1,179 4,778

28.4 35.6 41.1 39.3 36.0 25.9 30.2 34.2 31.9 30.3 23.9 30.6 35.7 32.7 30.6

ii

iii

Figure 4. Simulated profiles of (a,c) flow rates and (b,d) pressure differences across the membrane along all RO trains (a,b) with and (c,d) without optimal allocation of production rates.

among all trains is very consistent when the recovery is between 84 and 96%. The optimized results are also plotted in the pump characteristic maps, as shown in Figure 6. The current operating conditions are marked by circles, and the optimal operating conditions are marked by diamonds (with optimal allocation of permeate productions) and stars (with fixed allocation of permeate productions). The operating conditions corresponding

train A at recoveries between 80 and 83%, all RO trains follow very similar trends in pump speed, feed flow, pump head, permeate flow, and NSEC. Based on the graphical results, it can be concluded that increasing the recovery (up to 93−94%) can gradually reduce NSEC. However, a further increase in recovery would lead to an increase in the NSEC, primarily because the pump head starts to take off. It is also noticed that the optimal allocation of permeate rates 3736



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Figure 5. Relationship of (a) pump speed, (b) feed flow, (c) pump head, (d) pump efficiency, (e) permeate flow, and (f) NSEC and specified water recovery.

to recoveries from 80 to 96% are also plotted in order to show the optimization trajectory. It is clear that all the results are well within the normal range of the pump. The curve in Figure 6(a) explains why the feed and permeate rates of train A follow a different trend from the rest when the recovery is between 80 and 83% (Figure 5(b) and (e)). In this range, the optimal flow rate and pump head lie on the boundary of the recommended operating

range. If a different pump with a wider operating range is selected, the feed rates in train A could be larger to reduce NSEC. Figure 7 provides a relationship between membrane property and permeate allocation as well as the effect of permeate allocation on overall NSEC of all trains. For a wide range of water recoveries, allocating more productions to RO trains with more permeable membranes would reduce the overall NSEC. 3737



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Figure 6. Trajectories of feed flow and pump head on the pump characteristic map (recovery varies from 80% to 96%).

Figure 7. Effect of permeate allocation on overall NSEC.

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It is worth noting that the current plant does realize this fact, even though it is not done in a systematic way.

4. CONCLUSIONS A 16−17% reduction in NSEC in a multitrain RO desalination process might be possible by optimizing operating conditions within the normal operating range of each pump and production rates allocated among all RO trains. It is shown that RO trains with longer service times (or smaller permeability paraments) should produce less water in order to reduce the overall NSEC. For each train studied in this work, the optimal water recovery is around 93%-94%.

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REFERENCES

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AUTHOR INFORMATION

Corresponding Author

*Phone: +1-909-869-3668. Fax: +1-909-869-6920. E-mail: [email protected]. Notes

The author declares no competing financial interest.

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ACKNOWLEDGMENTS The author would like to thank Brian Noh and Moustafa Aly from Inland Empire Utility Agency for plant tours, operation data, and fruitful discussions. 3738



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