Specific Energy Consumption in Spiral Wound Reverse
Osmosis Water Desalination
Mingheng Li
Department of Chemical and Materials Engineering
California State Polytechnic University, Pomona
[email protected]
Nov. 16, 2014
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1 / 23
OUTLINE
1
Motivation
2
Introduction
Definition of Normalized Specific Energy Consumption (NSEC)
Mathematical model
Differences between SWRO and BWRO
3
NSEC in RO
Review of NSEC in thermodynamically reversible RO
Theorems of NSEC in SWRO
Analysis of NSEC in BWRO
4
Concluding Remarks
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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; Zhu et al., 2009).
There is a huge gap between specific energy consumption in RO
plants and its theoretical minimum.
Mathematical models helps elucidate the understanding of energy
issues in RO.
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DEFINITION OF SEC AND NSEC IN RO
Schematic of RO
Feed
Brine
Valve
Pump
Permeate
RO Module
Membrane
✎
Specific Energy Consumption (SEC)
SEC
✎
✍
=
∆Ppump Q0
Qp
☞
✌
Normalized Specific Energy Consumption (NSEC)
NSEC
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✍
=
NSEC
∆π0
=
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∆Ppump 1
∆π0 Y
☞
✌
Nov. 16, 2014
4 / 23
MATHEMATICAL MODEL FOR RO
Spiral wound reverse osmosis module
Mathematical ✬
model (Li, Desalination, 2012)
✩
dQ(x)
Q0
−
= A · Lp · ∆P −
∆π0
dx
Q
d(∆P(x))
= −k · Q 2
dx
Q(x) = Q0 @x = 0
∆P(x) = ∆P0 @x = 0
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✫
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✪
Nov. 16, 2014
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DIMENSIONLESS RO MODEL
Dimensionless
✎ parameters
☞
ALp ∆π0
kQ02
Q
∆P
∆π0
,γ =
,κ =
,q =
,p =
α=
∆P0
Q0
∆π0
Q0
∆P0 ✌
✍
α:
γ:
κ:
Osmotic hydraulic pressure ratio
Membrane demand capacity ratio
Retentate pressure drop ratio
Dimensionless RO model
✬
✩
dp(x)
2
= −καq (x)
dx
p(x)
1
dq(x)
= −γ
−
dx
α
q(x)
p(x) = 1, @x = 0
q(x) = 1, @x = 0
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✫
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✪
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DIFFERENCES BETWEEN SWRO AND BWRO
Plant data and optimization (Li, IECR, 2013)
3
10
2
10
0.8
0.3
αopt
3
0.7
0.2
1
2
10
κ=0
κ = 0.05
κ = 0.1
κ=1
κ=5
0.1
1
0
0
κ=0
κ = 0.05
κ = 0.1
κ=1
κ=5
0.4
NSECopt
κ1
4
0.9
0.5
κ=0
κ = 0.05
κ = 0.1
κ=1
κ=5
opt
SWRO
BWRO
5
Y
6
0
0.5
γ1
1
1.5
10
0
0.5
1
γ
1.5
2
0
0
0.5
1
γ
1.5
0.6
2
0.5
0
0.5
1
γ
1.5
2
Difference is due to ∆π0 (390 psi for seawater and 10-20 psi for
brackish water)
☞
✎
kQ02
ALp ∆π0
, κ =
γ =
Q0
∆π0 ✌
✍
SWRO is operated near thermodynamic limit
BWRO is operated far away from thermodynamic limit
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NSEC OF FULLY REVERSIBLE RO
☛
✟
Schematic of an ideal, thermodynamically reversible RO
✡
∆P ≡
∆π0
1−Y
✠
Force
Permeate
Membrane
NSEC of a fully reversible RO
✩
✬
Z Yo
∆π0
· 1 · dY
1−Y
0
NSEC =
(1 · Yo ) · ∆π0
5
✫
=
Mingheng Li
NSEC
4
− ln(1 − Yo )
Yo
3
✪
2
(Spiegler, 1977)
1
0
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0.2
0.4
0.6
Recovery
0.8
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1
8 / 23
NSEC OF MULTI-STAGE SWRO WITH ERD
Schematic of a generic multi-stage RO with interstage booster pumps
and ERD
ERD
NSEC (Li, Desalination,
2011)
✤
NSEC
✣
=
N−1
X
Yj
1
ηerd (1 − YN )
+
−
αj
αN
αN
j=1
h
i
Q
1− N
(1
−
Y
)
j
j=1
Pressure drop is ignored
αj , Yj are based on each stage
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✜
✢
Nov. 16, 2014
9 / 23
NSEC IN SWRO AT THERMODYNAMIC LIMIT
Theorem 1
The minimum of NSEC for a single- or multi-stage RO with/without ERD
at the thermodynamic
limit is: NSEC = N (1 − Yo )−1/N − 1 + (1 − ηerd ) /Yo , where Yo is system
level water recovery, N is number of stages (N ≥ 1) and ηerd is energy
recovery efficiency of ERD (0 ≤ ηerd ≤ 1).
✛
Proof
✘
minNSEC
αj
Yo = 1 −
Solution: ✓
✚
αj + Yj
= 1
QN
j=1 (1
− Yj )
✙
α1 = α2 = ... = αN = α = (1 − Yo )1/N
NSEC = N (1 − Yo )−1/N − 1 + (1 − ηerd ) /Yo
✒
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✏
✑
Nov. 16, 2014
10 / 23
NSEC IN SWRO AT THERMODYNAMIC LIMIT
Theorem 2
For single- or multi-stage RO, the reduction in NSEC due to an ERD at
the thermodynamic limit is ηerd /Yo . The reduction in NSEC increases as
ηerd increases. The reduction in NSEC is more significant at low recoveries.
✬
Proof
or,
✎
✩
N (1 − Yo )−1/N − 1 + (1 − ηerd )
∆erd =
−
Yo N (1 − Yo )−1/N − 1 + 1
Yo
ηerd
= −
Yo
✫
✪
∆erd
✍
Mingheng Li
ηerd [Q0 (1 − Yo )][∆π0 /(1 − Yo )]
= −
(Q0 Yo )∆π0
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ηerd
= −
Yo
☞
✌
Nov. 16, 2014
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NSEC IN SWRO AT THERMODYNAMIC LIMIT
Theorem 3
− ln(1 − Yo ) + (1 − ηerd )
at the
Yo
= 100%, it is equivalent to a fully reversible
For infinite number of stages, NSEC =
thermodynamic limit. If ηerd
RO process.
Proof
✬
lim NSEC
N→∞
=
=
=
✫
Mingheng Li
=
✩
N (1 − Yo )−1/N − 1 + (1 − ηerd )
lim
N→∞
Yo
(1 − Yo )−x − 1 + (1 − ηerd )x
1
lim
Yo x→0
x
−x
ln(1−Y
o)
1
e
− 1 + (1 − ηerd )x
lim
Yo x→0
x
− ln(1 − Yo ) + (1 − ηerd )
Yo
✪
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EFFECT OF ERD AND MULTI-STAGE IN SWRO
2
10
NSEC
single stage, without ERD
single stage, with 100% ERD
infinite stages, without ERD
infinite stages, with 100% ERD
1
10
0
10
0
Mingheng Li
0.2
0.4
0.6
Overall Recovery
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0.8
1
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NSEC IN SWRO AT THERMODYNAMIC LIMIT
Theorem 4
With/without ERD, the NSEC at the thermodynamic limit reduces
monotonically as the number of stages N increases. However, the
reduction in NSEC due to N is less significant as N becomes larger.
Multi-stage design works better at high recoveries.
✞
Proof (see Li, IECR, 2014 for details)
✝
∆N
= NSECN+1 − NSECN
✞
✝
∆N−1 < ∆N
✞
✝
< 0
∆′N (Yo ) < 0
☎
✆
< 0
☎
✆
☎
✆
For high-recovery design, it is motivated to employ multi-stage
configuration.
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NSEC IN SWRO AT THERMODYNAMIC LIMIT
Theorem 5
Without ERD, as the number of stages increases from 1 to ∞, the
corresponding optimal Yo monotonically increases from 0.5 to 0.6822, and
the minimum of NSEC monotonically reduces from 4 to 3.1462.
✞
Proof (see Li, IECR, 2014 for details)
✞✝
✝
(1 − N)(1 − Yo
)(N+1)/N
+ (N + 1)(1 − Yo ) − 1 = 0
NSECN+1 (YoN+1 ) < NSECN+1 (YoN ) < NSECN (YoN )
N=1
☎
✆☎
N=∞
✆
2(1 − Yo ) = 1
Yo
− 1 + ln(1 − Yo ) = 0
1 − Yo
Yo = 0.5
Yo = 0.6822
NSEC = 4
NSEC = 3.1462
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NSEC IN SWRO AT THERMODYNAMIC LIMIT
Theorem 6
At the thermodynamic limit, when Yo = 0.6822, the NSEC of a
single-stage RO with 100% ERD is equivalent to the one of an
infinite-stage RO without ERD. Below this recovery, a single-stage RO
with 100% ERD has a lower NSEC. Above this recovery, an infinite-stage
RO has a lower NSEC.
✎
☞
Proof (see Li, IECR, 2014 for details)
∆ = NSECerd − NSEC∞ =
✍
Mingheng Li
✞
✝
✞
✝
1 − ln(1 − Yo )
1
−
1 − Yo
Yo
✌
∆′ (Yo ) > 0
☎
✆
∆(Yo = 0.6822) = 0
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☎
✆
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NSEC IN SWRO AT THERMODYNAMIC LIMIT
Theorem 7
A RO using brine recirculation is equivalent to a RO with ERD in which
feed osmotic pressure difference = ∆π0 /(1 − fYo ), RO recovery =
Yo (1 − f )/(1 − fYo ), and ηerd = f , where f is brine recycle ratio. Using
brine recirculation would not reduce NSEC.
F
E
RO
D
C
B
G
A
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NSEC IN SWRO AT THERMODYNAMIC LIMIT
Proof of Theorem 7
Location
Fresh Feed
no recirculation
Q0
∆π0
Recycled Brine
0
-
RO Inlet
Q0
∆π0
RO Outlet
(1 − Yo )Q0
Product
Yo Q0
Rejected Brine
(1 − Yo )Q0
✎
NSEC br
=
with recirculation
Q0
f
Q0
1−f f
1 + (1 − Yo )
Q0
1−f
1 − Yo
Q0
1−f
Yo Q0
(1 − Yo )
∆π0
1 − Yo
0
∆π0
1 − Yo
(1 − Yo )Q0
∆π0
∆π0
1 − Yo
∆π0
(1 − f ) + f (1 − Yo )
∆π0
1 − Yo
0
∆π0
1 − Yo
☞
N (1 − Yobr )−1/N − 1 + (1 − f ) ∆π0br
Yobr
∆π0
✍
N = 1,
NSEC br
= NSEC
N ≥ 2,
NSEC br
> NSEC (see Li, IECR, 2014 for details)
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✌
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NSEC IN BWRO FAR AWAY FROM THERMODYNAMIC
LIMIT
Small γ, high pressure drop and recovery (Li, IECR, 2013)
ERD may not be so helpful as in SWRO
1
p and q
0.8
Brine energy for ERD:
0.6
Seawater:
(0.5Q0 )(∆P0 ) = 0.50(Q0 ∆P0 )
0.4
0.2
Brackish water:
(0.2Q0 )(0.75∆P0 ) = 0.15(Q0 ∆P0 )
p, κ = 0
q, κ = 0
p, κ = 5.5
q, κ = 5.5
0
0
1
x
2
Brine recirculation will increase NSEC because of increased flow
resistance.
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NSEC IN BWRO FAR AWAY FROM THERMODYNAMIC
LIMIT
One-stage is more energy-efficient than two-stage design. However,
two-stage design with 2:1 array are used in industry due to other
reasons.
For a two-stage design, an interstage booster pump does not reduce
NSEC because of small γ.
3
1
0.8
10
one−stage
two−stage
two−stage with booster pump
0.9
0.8
0.5
opt
0.6
2
10
Y
NSECopt
p and q
0.7
0.7
0.4
0.3
0.2
0.1
0
p, 1−stage
q, 1−stage
p, 2−stage
q, 2−stage
one−stage
two−stage
two−stage with booster pump
1
10
1
Stage number
Mingheng Li
2
0
0.02
0.04
γtotal
0.06
0.08
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0.1
0.6
0
0.02
0.04
γ
0.06
0.08
0.1
total
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CONCLUSIONS
How to approach the theoretical value of NSEC?
Very large γ = ALp ∆π0 /Q0
Very small κ = kQ02 /∆π0
Multiple stages (especially at high recoveries)
ERD
Efficient pump
SWRO (near thermodynamic limit)
Multiple stages and ERD are beneficial
BWRO (far away from thermodynamic limit)
One stage is the best in terms of NSEC
Other factors (e.g., to achieve a more uniform flow) lead to two-stage
designs
Interstage pump is not necessary from a viewpoint of energy saving
ERD in BWRO is not so beneficial as in SWRO
Brine circulation does not help NSEC in SWRO or BWRO
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RELATED PUBLICATIONS
Li, M. “Energy Consumption in Spiral Wound Seawater Reverse Osmosis at the
Thermodynamic Limit,” 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,
2013.
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.
Mingheng Li
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The End
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