A UNIFIED MODEL-BASED ANALYSIS AND

OPTIMIZATION OF SPECIFIC ENERGY

CONSUMPTION IN BWRO AND SWRO

Mingheng Li

Department of Chemical and Materials Engineering

California State Polytechnic University, Pomona

AIChE Annual Meeting

San Francisco, CA

November 2013

MOTIVATION OF THIS WORK

• Reverse osmosis is the most common method of water

desalination.

• Energy consumption in reverse osmosis membrane module

accounts for a major portion (up to 45%) of the total cost of

water desalination (Manth et al., 2003; Busch and Mickols, 2004;

Wilf and Bartels, 2005).

• There is no rigorous theoretical framework for minimization of

specific energy consumption (SEC) in reverse osmosis (Zhu,

2012).

• Assumptions of negligible retentate pressure drop and

thermodynamic limit are often made.

OUTLINE OF PRESENTATION

(Li, Ind. Eng. Chem. Res., 2013, accepted)

• A unified dimensionless model for both BWRO and SWRO

⋄ Different operation regions in γ v.s. κ map

• Analysis and optimization of SEC in BWRO and SWRO

⋄ Recovery

⋄ RO configuration (one-stage, two-stage, two-stage with booster pump)

⋄ Brine recirculation

• Implications to operation

MATHEMATICAL MODEL FOR REVERSE OSMOSIS

• Spiral wound reverse osmosis module

• Mathematical model'

&

$

%

−dQ(x)

dx= A · Lp ·

(∆P − Q0

Q∆π0

)d(∆P (x))

dx= −k ·Q2

Q(x) = Q0 @x = 0

∆P (x) = ∆P0 @x = 0

DIMENSIONLESS FORM OF RO MODEL

• Dimensionless parameters��

� α =

∆π0

∆P0, γ =

ALp∆π0

Q0, κ =

kQ20

∆π0, q =

Q

Q0, p =

∆P

∆P0

α: Osmotic hydraulic pressure ratio

γ: Membrane demand capacity ratio

κ: Retentate pressure drop ratio

• Dimensionless RO model'

&

$

%

dp(x)

dx= −καq2(x)

dq(x)

dx= −γ

(p(x)

α− 1

q(x)

)p(x) = 1, @x = 0

q(x) = 1, @x = 0

MULTI-STAGE RO NETWORK

• Model '

&

$

%

dpi(x)

dx= −κiαiq

2i (x), i = 1, 2, ..., N

dqi(x)

dx= −γi

(pi(x)

αi− 1

qi(x)

), i = 1, 2, ..., N

pi(x) = 1, @x = i− 1, i = 1, 2, ..., N

qi(x) = 1, @x = i− 1, i = 1, 2, ..., N

• Relationship between stage level and system level#

"

!p(x) = pi(x)

i−1∏k=0

pk(k), i− 1 < x ≤ i, i = 1, 2, ..., N

q(x) = qi(x)i−1∏k=0

qk(k), i− 1 < x ≤ i, i = 1, 2, ..., N

• System recovery ��

� Y = 1−

N∏i=1

qi(i)

OPTIMIZATION OF NSEC IN RO DESALINATION

• Normalized Specific Energy Consumption (NSEC)��

� NSEC =

Q0∆Ppump/ηpump

(Y Q0)∆π0

• Optimization model (no ERD, no booster pump)'

&

$

%

minα1

J =1/α1

ηpump

(1−

N∏i=1

qi(i)

)s.t.

dpi(x)

dx= −κiαiq

2i (x), i = 1, 2, ..., N

dqi(x)

dx= −γi

(pi(x)

αi− 1

qi(x)

), i = 1, 2, ..., N

pi(x) = 1, @x = i− 1, i = 1, 2, ..., N

qi(x) = 1, @x = i− 1, i = 1, 2, ..., N

OPTIMIZATION OF NSEC IN TWO-STAGE RO WITH

INTER-STAGE BOOSTER PUMP'

&

$

%

minα1,α2

J =1/α1 + 1/α2 − p1(1)q1(1)

1− q1(1)q2(2)dpi(x)

dx= −κiαiq

2i (x), i = 1, 2

dqi(x)

dx= −γi

(pi(x)

αi− 1

qi(x)

), i = 1, 2

pi(x) = 1, @x = i− 1, i = 1, 2

qi(x) = 1, @x = i− 1, i = 1, 2

γ1 = (2/3)γtotal

γ2 = γ1/2/q21(1)

κ2 = 4κ1q31(1)

α2 ≤ α1/p1(1)/q1(1)

−αi ≤ 0, i = 1, 2

αi ≤ 1, i = 1, 2

MAP OF γ v.s. κ CORRELATED FROM INDUSTRIAL BWRO

AND SWRO PLANTS WORLDWIDE

0 0.5 1 1.50

1

2

3

4

5

6

γ1

κ 1

SWROBWRO

Recall that γ =ALp∆π0

Q0, κ =

kQ20

∆π0

∆π0 = 390 psi for seawater and 10-20 psi for brackish water

OPTIMIZATION RESULTS OF SINGLE-STAGE RO

• Effect of γ and κ on optimization results

0 0.5 1 1.5 210

0

101

102

103

γ

NS

EC

opt

κ = 0κ = 0.05κ = 0.1κ = 1κ = 5

0 0.5 1 1.5 20

0.1

0.2

0.3

0.4

0.5

γ

α opt

κ = 0κ = 0.05κ = 0.1κ = 1κ = 5

0 0.5 1 1.5 20.5

0.6

0.7

0.8

0.9

γ

Yop

t

κ = 0κ = 0.05κ = 0.1κ = 1κ = 5

• Comparison between SWRO and BRWO

RO Type γ κ αopt NSECopt Yoptp(0)

α-

1

q(0)

p(1)

α-

1

q(1)

BWRO 0.05 1 0.059 22.9 0.75 16.1 12.7

SWRO 1 0.1 0.438 4.2 0.54 1.28 0.05

Thermodynamic Limit ∞ 0 0.5 4 0.5 1 0

EFFECT OF PRESSURE DROP IN BWRO

• Dimensionless Q and ∆P in an industrial two-stage BWRO

without interstage booster pump (Li, Desalination, 2012)

0 1 20

0.2

0.4

0.6

0.8

1

x

p an

d q

p, κ = 0q, κ = 0p, κ = 5.5q, κ = 5.5

• Ignoring pressure drop leads to 12% over-prediction of recovery.

COMPARISON BETWEEN ONE-STAGE AND TWO-STAGE

DESIGNS IN BWRO

• Dimensionless Q and ∆P in BWRO

0 1 20.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Stage number

p an

d q

p, 1−stageq, 1−stagep, 2−stageq, 2−stage

0 1 20

5

10

15

20

25

Stage numberp/

α an

d 1/

q

p/α, 1−stage1/q, 1−stagep/α, 2−stage1/q, 2−stage

• For BWRO, one-stage has a higher recovery (or lower NSEC)

due to reduced κ.

DETAILED COMPARISON OF RO CONFIGURATIONS

• Three different configurations

(c)

(a)

(b)

• Comparison basis

⋄ The same total area, or γtotal

⋄ The same flow characteristics (note that κ would be different)

DETAILED COMPARISON RESULTS FOR BWRO

• Results using κ = 1 (based on the first-stage in a two-stage RO)

0 0.02 0.04 0.06 0.08 0.110

1

102

103

γtotal

NS

EC

opt

one−stagetwo−stagetwo−stage with booster pump

0 0.02 0.04 0.06 0.08 0.10.6

0.7

0.8

γtotal

Yop

t

one−stagetwo−stagetwo−stage with booster pump

• Observations from simulation

⋄ One-stage is better due to reduced retentate pressure drop.

⋄ Using booster pump does not reduce NSEC under optimal conditions.

DETAILED COMPARISON RESULTS FOR SWRO

• Results using κ = 0.1 (based on the first-stage in a two-stage RO)

0.5 1 1.53.8

4

4.2

4.4

4.6

4.8

5

γtotal

NS

EC

opt

one−stagetwo−stagetwo−stage with booster pump

0.5 1 1.50.5

0.6

0.7

γtotal

Yop

t

one−stagetwo−stagetwo−stage with booster pump

• Observations from simulation

⋄ Two-stage with booster pump could be better if γ is sufficiently large.

⋄ Using booster pump does reduce NSEC under optimal conditions.

EFFECT OF BRINE RECIRCULATION ON NSEC

• Brine recirculation

C

ERD

ROE

B H

G

F

D

A 0 10

0.2

0.4

0.6

0.8

1

Stage Number

p an

d q

p, with PXq, with PXp, without PXq, without PX

with PX A B C D E F G H

Flow (gpm) 1,774 250 1,524 775 2,299 1,500 799 274

Pressure (psi) 25 25 241 221 241 5 231 10

TDS (mg/l) 2,000 2,000 2,000 10,563 4,886 92 14,000 14,000

without PX A B C D E F G H

Flow (gpm) 1,774 - 1,774 - 1,774 1,604 170 170

Pressure (psi) 25 - 241 - 241 5 237 237

TDS (mg/l) 2,000 - 2,000 - 2,000 92 20,000 20,000

• Brine recirculation does not reduce NSEC in BWRO.

SUMMARY

• A unified dimensionless model for both SWRO and BWRO

⋄ γ = ALp∆π0/Q0

⋄ κ = kQ20/∆π0

• Model-based analysis and optimization of NSEC in RO

⋄ For single-stage, SWRO is near thermodynamic limit while BWRO is

far away from it.

⋄ For BWRO, single-stage is better than two-stage in terms of NSEC.

Using booster pump does not improve NSEC under optimal conditions.

⋄ For SWRO, two-stage with booster pump could be better than

one-stage in terms of NSEC if γ is sufficiently large. Using booster

pump does improve NSEC under optimal conditions.

⋄ Brine recirculation does not improve NSEC in BWRO due to increase in

feed salinity and retentate pressure drop.

• Ongoing work includes further model-based optimization and

implementation in a water desalter plants in Southern California.

RELATED PUBLICATIONS• Li, M. “Energy Consumption in Spiral Wound Seawater Reverse Osmosis

at the Thermodynamic Limit,” Desalination, Ind. Eng. Chem. Res., 53,

3293-3299, 2014.

• Li, M. “A Unified Model-Based Analysis and Optimization of Specific

Energy Consumption in BWRO and SWRO,” Ind. Eng. Chem. Res., 52,

17241-17248, 2014.

• Li, M.; Noh, B. “Validation of Model-Based Optimization of Reverse

Osmosis (RO) Plant Operation,” Desalination, 304, 20-24, 2012.

• Li, M. “Optimization of Multitrain Brackish Water Reverse Osmosis

(BWRO) Desalination,” Ind. Eng. Chem. Res., 51, 3732-3739, 2012.

• Li, M. “Optimal Plant Operation of Brackish Water Reverse Osmosis

Water Desalination,” Desalination, 293, 61-68, 2012.

• Li, M. “Reducing Specific Energy Consumption in Reverse Osmosis Water

Desalination: An Analysis from First Principles,”Desalination, 276,

128-135, 2011.

• Li, M. “Minimization of Energy in Reverse Osmosis Water Desalination

using Constrained Nonlinear Optimization,” Ind. Eng. Chem. Res., 49,

1822-1831, 2010.