Systematic Analysis and Optimization of Power Generation in Pressure Retarded Osmosis: Effect of Multi-Stage Design

Transcription

1 Systematic Analysis and Optimization of Power Generation in Pressure Retarded Osmosis: Effect of Multi-Stage Design Mingheng Li Department of Chemical and Materials Engineering California State Polytechnic University, Pomona November 2, 2017 Mingheng Li Multi-stage PRO AICHE / 24

2 Outline 1 Motivation 2 Methodology 3 Results and Discussion 4 Conclusions Mingheng Li Multi-stage PRO AICHE / 24

3 Motivation Mingheng Li Multi-stage PRO AICHE / 24

4 Global Grand Challenges in Energy and Water Humanity s Top Ten Problems for next 50 years 1. ENERGY 2. WATER 3. FOOD 4. ENVIRONMENT 5. POVERTY 6. TERRORISM & WAR 7. DISEASE 8. EDUCATION 9. DEMOCRACY 10. POPULATION Billion People Billion People 1 Professor Richard Smalley, Nobel Laureate Mingheng Li Multi-stage PRO AICHE / 24

5 Membrane-Based Processes Reverse Osmosis (RO) Feed Pump Valve Brine Permeate Membrane RO Module Pressure Retarded Osmosis (PRO) Draw Solution Pump Turbine Feed Water PRO Module 1 Mingheng Li Multi-stage PRO AICHE / 24

6 Need for System-Level Understanding of PRO There is a lack of computational framework to address scale-up issues in PRO Optimal applied pressure much lower than π/2 is observed in some experiments (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 energy issues in PRO. Mingheng Li Multi-stage PRO AICHE / 24

7 Methodology Mingheng Li Multi-stage PRO AICHE / 24

8 Characteristic Equation of RO and PRO Q0 π 0 P Q0 π 0 P dq(x) dx RO PRO α = π 0 /P γ = AL p π 0 / Q 0 = A L p Q 1 π 1 P Q 1 π 1 P ( P Q0 Q π0 ) Y = 1 Q 1 /Q 0 q = Q 1 /Q 0 Assumptions: Negligible pressure drop Negligible concentration polarization Perfect transverse mixing of salt [ γ = α 1 q +αln α 1 ] α q γ: Dimensionless membrane area Design parameter α 1 : Dimensionless applied pressure Operating parameter q: Dimensionless flow rate (Y = 1 q) Performance parmater 1 Li, IECR, 2010; AIChE J., 2015 Mingheng Li Multi-stage PRO AICHE / 24

9 Model Accounting for PRO Efficiency Detrimental Effects in PRO External Concentration Polarization (ECP) Internal Concentration Polarization (ICP) Reverse Salt Leakage Equation accounting for PRO efficiency γ = α [ ] 1 q ideal α 1 +αln α q ideal q 1 = η PRO (q ideal 1) 1 Wang, Ong, and Chung, IECR, Li, AIChE J., 2017 Mingheng Li Multi-stage PRO AICHE / 24

10 Energy Production in PRO PUMP PRO 1 Turbine PRO 2 Turbine PRO 3 Turbine Low salinity water Seawater Energy Management Normalized Specific Energy Production (NSEP) in PRO NSEP = W turb W pump Q 0 π 0 NSEP in Single- or Multi-stage PRO N NSEP = η turb j=1 q j 1 α j + 1 α 1 ( 1 1 η turb η pump ) 1 Li, AIChE J., 2017 Mingheng Li Multi-stage PRO AICHE / 24

11 Optimization Model for PRO max α j,γ j,q j NSEP = η turb [ N j=1 0 = γ j α j [ q j ( 1 α j α 1 1 q ideal j +α j ln 1 ) ] η turb η pump ] α j 1, j = 1,...,N α j qj ideal 0 = (q j 1) η PRO (qj ideal 1), j = 1,...,N [ ] j 1 N 0 = γ tot γ 1 + γ j j=2 k=1 q 2 k 0 α j+1q j α j, j = 1,...,N 1 0 γ j, j = 1,...,N 0 α j 1, j = 1,...,N 0 q j 1, j = 1,...,N 1 Li, AIChE J, 2017 Mingheng Li Multi-stage PRO AICHE / 24

12 Results & Discussion Mingheng Li Multi-stage PRO AICHE / 24

13 Results of NSEP in PRO Single stage PRO Two stage PRO Three stage PRO Single stage PRO Two stage PRO Three stage PRO NSEP = Power/(Q 0 π 0 ) q tot γ =A L π /Q tot tot p γ tot =A tot L p π 0 /Q 0 The increased volume gain is not the sole cause to the boosted power generation in multi-stage design. NSEP = k j=1 (q j 1)/α j (if ignoring equipment efficiencies), implying pressure profile has a contribution to NSEP as well. Mingheng Li Multi-stage PRO AICHE / 24

14 Pressure Profile γ tot = 4 (top) and 10 (bottom) π/π 0 and P/π Single stage π Single stage P Two stage π Two stage P Three stage π Three stage P (π P)/π Single stage Two stage Three stage π/π 0 and P/π Fraction of membrane Single stage π Single stage P Two stage π Two stage P Three stage π Three stage P Fraction of membrane (π P)/π Fraction of membrane Single stage Two stage Three stage Fraction of membrane Mingheng Li Multi-stage PRO AICHE / 24

15 Power Density Relationships between NSEP and Power Density (PD) PD = (NSEP)(Q 0 /A tot )π 0 = (NSEP/γ tot )L p π0 2 = (NSEPγ tot )(Q 0 /A tot ) 2 /L p PD vs L p PD vs π 0 PD vs Q 0 /A Single stage PRO Single stage PRO Two stage PRO Two stage PRO Three stage PRO 6 Three stage PRO 0.16 PD/(Q 0 /A tot )/π 0 = NSEP L p *π 0 /(Q 0 /A tot ) = γ tot PD*L p /(Q 0 /A tot ) 2 = NSEP*γ tot π 0 *L p /(Q 0 /A tot ) = γ tot PD/(L p π 0 2 ) = NSEP/γtot Single stage PRO 0.06 Two stage PRO Three stage PRO (Q 0 /A tot )/(L p π 0 ) = 1/γ tot Mingheng Li Multi-stage PRO AICHE / 24

16 Optimization at the Thermodynamic Limit As γ j, driving force 0. i.e. α j = q j Optimization model Solution maxnsep = α j,q j N j=1 q j 1 α j 0 = q j α j, j = 1,...,N N 0 = q tot q j j=1 q j = q 1/N tot, j = 1,...,N ( ) NSEP = N 1 q 1/N tot Mingheng Li Multi-stage PRO AICHE / 24

17 Optimization at the Thermodynamic Limit N=1 N=2 N=3 N= NSEP = Power/(Q 0 π 0 ) q = Q /Q tot N 0 Mingheng Li Multi-stage PRO AICHE / 24

18 Infinite Stages at the Thermodynamic Limit Infinite PRO stages at the thermodynamic limit ( lim NSEP = lim N N N 1 qtot x x 0 = lim x 1 q 1/N tot = lim x 0 1 e x lnqtot x ) Fully reversible PRO NSEP rev = = lnq tot qtot 1 π 0 q 1 dq 1 π 0 = lnq tot Mingheng Li Multi-stage PRO AICHE / 24

19 How Far from the Thermodynamic Limit γ tot =4 Single-Stage Two-Stage Three-Stage q tot NSEP NSEP (eq) NSEP(γ tot =4)/NSEP(eq) 80% 74% 71% γ tot =10 Single-Stage Two-Stage Three-Stage q tot NSEP NSEP (eq) NSEP(γ tot =10)/NSEP(eq) 88% 82% 78% Mingheng Li Multi-stage PRO AICHE / 24

20 Optimization Accounting for Process Efficiencies η PRO = 80%, η turb = 80%, and η pump = 80% NSEP = Power/(Q 0 π 0 ) Single stage, ideal Single stage, real Two stage PRO, ideal Two stage PRO, real Three stage PRO, ideal Three stage PRO, real γ =A L π /Q tot tot p 0 0 Mingheng Li Multi-stage PRO AICHE / 24

21 Conclusions Mingheng Li Multi-stage PRO AICHE / 24

22 Conclusions NSEP increases with number of stages and γ tot = A tot L p π 0 /Q 0. Multistage not only improves volume gain ratio, but also allows a stage-dependent, progressively decreasing pressure, both enhancing power production. At the thermodynamic limit where γ tot goes to infinity, ( the theoretical ) maximum NSEP by an N-stage PRO system is N 1 q 1/N tot. For one stage, NSEP is no more than 1. For infinite number of stages, the NSEP at the theoretical limit becomes lnq tot, which is equivalent to that of a fully reversible PRO. Process efficiencies have a significant effect on NSEP. Mingheng Li Multi-stage PRO AICHE / 24

23 Acknowledgment and References Acknowledgement American Chemical Society Petroleum Research Fund (No UR9) References Li, M. Systematic Analysis and Optimization of Power Generation in Pressure Retarded Osmosis: Effect of Multi-Stage Design, AIChE Journal, in press, Li, M. Reducing Energy Consumption of Seawater Desalination: Staged RO or RO-PRO? Desalination, 422, , Li, M. Analysis and Optimization of Pressure Retarded Osmosis for Power Generation, AIChE Journal, 61, , Mingheng Li Multi-stage PRO AICHE / 24

24 Mingheng Li Multi-stage PRO AICHE / 24