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System-Level Analysis and Optimization of Pressure ...minghengli/pdfs/AIChE15Presentation.pdfNSEP...
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System-Level Analysis and Optimization of Pressure Retarded Osmosis for Power Generation Mingheng Li Department of Chemical and Materials Engineering California State Polytechnic University, Pomona [email protected] Nov. 12, 2015 Mingheng Li AIChE Annual Meeting Nov. 12, 2015 1 / 21
Transcript of System-Level Analysis and Optimization of Pressure ...minghengli/pdfs/AIChE15Presentation.pdfNSEP...
System-Level Analysis and Optimization of PressureRetarded Osmosis for Power Generation
Mingheng Li
Department of Chemical and Materials Engineering
California State Polytechnic University, Pomona
Nov. 12, 2015
Mingheng Li AIChE Annual Meeting Nov. 12, 2015 1 / 21
OUTLINE
1 Motivation
2 Simple Analysis in Literature
3 Analysis and Optimization Accounting for Flux ProfileBasic definitionswithout Concentration Polarizationwith Concentration Polarization
4 Concluding Remarks
Mingheng Li AIChE Annual Meeting Nov. 12, 2015 2 / 21
MOTIVATION OF THIS WORK
Pressure retarded osmosis is one of the promising “green” energytechniques that produces power from salinity gradient.
There is a lack of computational framework to address scale-up issuesin PRO
◮ Optimal applied pressure much lower than ∆π/2 is observed in someexperiments (Xu et al., JMS, 2009; She et al., JMS, 2012; Sharif et al.,Membranes, 2014).
◮ Power generation in PRO is much lower than theoretical prediction.
Mathematical models helps elucidate the understanding of energyissues in PRO.
◮ Power density
◮ Specific Energy Production (SEP)
◮ Efficiency of osmotic to hydraulic energy
Mingheng Li AIChE Annual Meeting Nov. 12, 2015 3 / 21
SIMPLE ANALYSIS BASED ON CONSTANT FLUX
(see, e.g. Review by Helfer et al. JMS, 2014)
π0D
Q0
)
0
qdQ0
Q0(1−q
d
PRO
PUMP
TURBINE
FS
DS
πF
Constant water flux along membrane✞✝ ☎✆Jw = dQ/dA = Lp(∆π −∆P )
Power Density (PD)✞✝ ☎✆PD = Jw∆P = Lp(∆π −∆P )∆P✞✝ ☎✆∆Popt = ∆π/2
This may be true for short membranes (i.e. under lab-scaleexperimental conditions)
Mingheng Li AIChE Annual Meeting Nov. 12, 2015 4 / 21
BASIC DEFINITIONS IN PRO
π0D
Q0
)
0
qdQ0
Q0(1−q
d
PRO
PUMP
TURBINE
FS
DS
πF
Specific Energy Production (SEP)✞✝ ☎✆SEP = Q0(qd − 1)∆P/Q0 = (qd − 1)∆P
qd: dilution ratio at the end of the membrane∆P : applied pressure
Normalized SEP or Osmotic to Hydraulic Efficiency✞✝ ☎✆NSEP = SEP/πD0
= (Q0SEP )/(Q0πD0) = ηO2H
Power Density (PD)✞✝ ☎✆PD = (NSEP )(Q0/A)πD0
Mingheng Li AIChE Annual Meeting Nov. 12, 2015 5 / 21
1D MATHEMATICAL MODEL WITHOUT CP
Local water flux (assuming πF = πF0)✎
✍☞✌
dQ
dA= Lp(∆π −∆P ) = Lp(π
D0
Q0
Q− πF
0 −∆P )
Dimensionless form ✎✍
☞✌
dq
dx= γ
(
1
q− θ
)
✞✝ ☎✆q = Q/Q0, θ = (∆P + πF0)/πD
0, γ = ALpπ
D0/Q0
Solution (Li, AIChE J., 2015)✓✒
✏✑γ =
1
θ
[
1− qd +1
θln
1− θ
1− qdθ
]
qd: dilution ratio at the end of the membrane
Mingheng Li AIChE Annual Meeting Nov. 12, 2015 6 / 21
SOLUTION TO qd AND NSEP
Profiles of qd and NSEP
0
5
10
0
0.5
11
2
3
4
5
γθ
q d
0
5
10
0
0.5
10
0.2
0.4
0.6
0.8
γθ
NS
EP
Observations
◮ qd increases as ∆P reduces and/or γ increases.
◮ At a fixed γ, there is an optimal ∆P corresponding the maximumNSEP.
Mingheng Li AIChE Annual Meeting Nov. 12, 2015 7 / 21
CONSTRAINED NONLINEAR OPTIMIZATION
Optimization model to determine optimal NSEP and ∆P✬
✫
✩
✪
maxα,z
NSEP = (qd − 1)
(
1
α− r
)
s.t.qd = α− (α− 1)e−z
γ = α(1− qd + αz)
1− α ≤ 0
1− qd ≤ 0
Optimization of PD and optimization NSEP are essentially equivalentif Q0/A and πD
0are given, since PD = (NSEP )(Q0/A)π
D0.
Mingheng Li AIChE Annual Meeting Nov. 12, 2015 8 / 21
CONSTRAINED NONLINEAR OPTIMIZATION OF NSEP
Optimization results
10−1
100
101
102
0.1
0.2
0.3
0.4
0.5
γ
(∆P
/∆π 0) op
t
r = 0r = 0.1r = 0.2r = 0.4
10−1
100
101
102
1
2
3
4
5
6
7
γ
q d opt
r = 0r = 0.1r = 0.2r = 0.4
10−1
100
101
102
0
0.2
0.4
0.6
0.8
1
γ
NS
EP
opt
r = 0r = 0.1r = 0.2r = 0.4
Observations
◮ The optimal ∆P shifts away from ∆π0/2 as γ = ALpπD0/Q0 increases.
◮ An increase in r (r = πF0/πD
0) significantly reduces qd and NSEP.
◮ When r = 0 (or fresh water is used as feed solution), the largest NSEPoccurs at forward osmosis conditions, i.e., ∆Popt = 0.
Mingheng Li AIChE Annual Meeting Nov. 12, 2015 9 / 21
OPTIMAL DRIVING FORCE IN PRO
Optimal dimensionless driving force ζ = (∆π −∆P )/πD0
10−1
100
101
102
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
γ
ζ opt
InletOutletAverage
10−1
100
101
102
0
0.1
0.2
0.3
0.4
0.5
γ
ζ−
opt
r = 0r = 0.1r = 0.2r = 0.4
Inlet Outlet Average (ζ)
1− θ 1/qd − θ (qd − 1)/γ
Similarity between RO and PRO◮ A larger γ allows the PRO to be operated closer to its thermodynamic
limit, thus improving SEP.
◮ A larger γ allows the RO to be operated closer to its thermodynamiclimit, thus improving SEC (Li, IECR, 2010; Li, Desalination, 2012, Li,IECR, 2013).
Mingheng Li AIChE Annual Meeting Nov. 12, 2015 10 / 21
NONLINEARITIES IN PRO
Profiles of power efficiency and density when FS is fresh water
A
η O2H
Lp
η O2H
∆π0
η O2H
Q0
η O2H
A
PD
Lp
PD
∆π0
PD
Q0
PD
Power density reduces as membrane areas increases. Therefore, itsvalue in plant operation might be smaller than the one measuredunder lab-scale experimental conditions even if the same type ofmembrane is used.
Mingheng Li AIChE Annual Meeting Nov. 12, 2015 11 / 21
PRO MODEL ACCOUNTING FOR CP
Water flux accounting for concentration polarization (Achilli et al.,JMS, 2009, Xu et al., JMS, 2010)★
✧
✥
✦Jw = Lp
πDb exp(− Jw
km)1−
πF
b
πD
b
exp(JwK) exp( Jwkm
)
1 + BJw
[exp(JwK)− 1]−∆P
dQ
dA= Jw
Power Density ✓✒
✏✑PD =
∆P
∫ A
0
JwdA
A
Jw is in implicit form. Intensive computation is required to directlysolve optimal ∆P .
Mingheng Li AIChE Annual Meeting Nov. 12, 2015 12 / 21
FLUX IN EXPLICIT FORM UNDER TWO
ASSUMPTIONS
If Jw/km << 1 (Achilli et al., JMS, 2009) and JwK << 1 (Lee etal., JMS, 1981), Jw may be approximated by (Li, AIChE J., 2015)☛
✡✟✠Jw ≈ L′
p(σ∆π −∆P )
where σ = 1/(1 +BK) and L′
p = Lp/(1 + Lp∆πσ/km).
Under such assumptions an analytical solution in PRO may beobtained (Li, AIChE J., 2015)✓✒
✏✑γ =
1
θ
[
(1− qd) +σ
θln
σ − θ
σ − qdθ
]
where γ = AL′
pQ0/πD0.
Mingheng Li AIChE Annual Meeting Nov. 12, 2015 13 / 21
SHORT-CUT OPTIMIZATION ACCOUNTING FOR CP
Optimization model✬
✫
✩
✪
maxα,z
NSEP = (qd − 1)
(
1
α− r
)
s.t.qd = ασ − (ασ − 1)e−z
γ = α(1− qd + ασz)
1/σ − α ≤ 0
1− qd ≤ 0
It is found that the model provides very accurate solution to ∆Popt.However, flux profile, NSEP and PD may be better calculated usingthe original concentration polarization model and the derived ∆Popt.
Mingheng Li AIChE Annual Meeting Nov. 12, 2015 14 / 21
EFFECT OF ICP IN PRO
10−1
100
101
102
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
γ
θ opt
σ=0.9σ=1
10−1
100
101
102
1
2
3
4
5
6
7
γ
q d opt
σ=0.9σ=1
10−1
100
101
102
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
γ
NS
EP
opt
σ=0.9σ=1
10−1
100
101
102
0
0.1
0.2
0.3
0.4
0.5
γ
ζ−
opt
σ=0.9σ=1
Mingheng Li AIChE Annual Meeting Nov. 12, 2015 15 / 21
CASE STUDIES
Parameters used in the studies (Achilli et al., JMS, 2009)
Parameters Value
km 8.48×10−5 m/sK 4.51×105 s/mB 1.11×10−7 m/sLp 1.87×10−9 m/s/kPa∆π0 2763, 4882 kPa
Four different Q0/A (1, 2, 4, 8 ×10−6 m/s) are considered. Thecorresponding γ are between 0.5-10. These are comparable to thereverse process of industrial SWRO (Li, IECR, 2013).
Mingheng Li AIChE Annual Meeting Nov. 12, 2015 16 / 21
COMPARISON BETWEEN SHORT-CUT AND
RIGOROUS OPTIMIZATION METHODS
Values obtained using the short-cut optimization method, if different fromthe rigorous method, are presented in parenthesis.
∆π0 = 2763 kPa ∆P , kPa Jw , µm/s PD, W/m2 γ qd ηO2H , %
∆π = ∆π0 1330 (1316) 2.16 (2.18) 2.87 - - -Q0/A = 8µm/s 1300 (1295) 1.78 (1.79) 2.31 0.65 1.22 10.5Q0/A = 4µm/s 1260 (1259) 1.56 (1.56) 1.96 1.29 1.39 17.7Q0/A = 2µm/s 1190 (1186) 1.28 (1.28) 1.52 2.58 1.64 27.6Q0/A = 1µm/s 1070 (1067) 1.00 (1.01) 1.07 5.17 2.01 38.9
∆π0 = 4882 kPa ∆P , kPa Jw , µm/s PD, W/m2 γ qd ηO2H , %
∆π = ∆π0 2390 (2325) 3.38 (3.47) 8.07 - - -Q0/A = 8µm/s 2260 (2244) 2.64 (2.66) 5.97 1.14 1.33 15.3Q0/A = 4µm/s 2140 (2133) 2.24 (2.25) 4.79 2.28 1.56 24.6Q0/A = 2µm/s 1950 (1943) 1.79 (1.80) 3.50 4.56 1.90 35.8Q0/A = 1µm/s 1680 (1685) 1.38 (1.38) 2.32 9.13 2.37 47.4
Mingheng Li AIChE Annual Meeting Nov. 12, 2015 17 / 21
EFFECT OF DILUTION AND CP IN PRO
800 900 1000 1100 1200 1300 1400 1500 16000.5
1
1.5
2
2.5
3
3.5
4 ← ∆π
0/2
∆P (kPa)
PD
(W
/m2 )
rigorousshort−cut
500 1000 1500 2000 2500 30000
2
4
6
8
10
12 ← ∆π
0/2
∆P (kPa)
PD
(W
/m2 )
rigorousshort−cut
0 0.2 0.4 0.6 0.8 10
0.5
1
1.5
2
2.5
3x 10
−6
Fraction of Membrane
J w (
m/s
)
0 0.2 0.4 0.6 0.8 10
0.5
1
1.5
2
2.5
3
3.5
4
4.5x 10
−6
Fraction of Membrane
J w (
m/s
)
Black: ∆π = ∆π0 and no concentration polarization.Red: ∆π = ∆π0 and with concentration polarization.Magenta: Q0/A = 8× 10−6 m/s. Yellow: Q0/A = 4× 10−6 m/s.Blue: Q0/A = 2× 10−6 m/s. Green: Q0/A = 1× 10−6 m/s.
Mingheng Li AIChE Annual Meeting Nov. 12, 2015 18 / 21
CONCLUSIONS
Characteristic equation in PRO to relate membrane properties,operating conditions and performance✓
✒✏✑γ =
1
θ
[
(1− qd) +σ
θln
σ − θ
σ − qdθ
]
where γ = AL′
pQ0/πD0, θ = (∆P + πF
0)/πD
0, σ = 1/(1 +BK).
Short-cut optimization yields essentially the same solution as therigorous solution. Moreover, it provides parameters to explain theeffect of ICP, ECP and dilution in DS.
Shift of optimal ∆P from ∆π0/2.
◮ Dilution effect (i.e. γ is not zero).
◮ Internal concentration polarization (i.e., σ < 1).
Nonlinearities and conflicting power density and efficiency in processscale-up.
Mingheng Li AIChE Annual Meeting Nov. 12, 2015 19 / 21
ACKNOWLEDGEMENT AND RELATED PUBLICATIONS
Financial Support from American Chemical Society Petroleum ResearchFund (No. 55347-UR9) is gratefully acknowledged.
Li, M. “Analysis and Optimization of Pressure Retarded Osmosis for PowerGeneration, ” AIChE Journal, 61, 1233-1241, 2015.Li, M. “Energy Consumption in Spiral Wound Seawater Reverse Osmosis at theThermodynamic Limit,” Ind. Eng. Chem. Res., 53, 3293-3299, 2014.Li, M. “A Unified Model-Based Analysis and Optimization of Specific EnergyConsumption 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 WaterDesalination,” Desalination, 293, 61-68, 2012.Li, M. “Reducing Specific Energy Consumption in Reverse Osmosis WaterDesalination: An Analysis from First Principles,”Desalination, 276, 128-135, 2011.Li, M. “Minimization of Energy in Reverse Osmosis Water Desalination usingConstrained Nonlinear Optimization,” Ind. Eng. Chem. Res., 49, 1822-1831, 2010.
Mingheng Li AIChE Annual Meeting Nov. 12, 2015 20 / 21
Mingheng Li AIChE Annual Meeting Nov. 12, 2015 21 / 21
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