Effectiveness-mass transfer units (ε-MTU) model of a reverse osmosis membrane mass exchanger

Abstract A strong analogy exists between heat exchangers and osmotic mass exchangers. The effectiveness-number of transfer units (e-NTU) method is well-known for the sizing and rating of heat exchangers. A similar method, called the effectiveness-mass transfer units (e-MTU) method, is developed for reverse osmosis (RO) mass exchangers. Governing equations for an RO mass exchanger are nondimensionalized assuming ideal membrane characteristics and a linearized form of the osmotic pressure function for seawater. A closed form solution is found which relates three dimensionless groups: the number of mass transfer units, which is an effective size of the exchanger; a pressure ratio, which relates osmotic and hydraulic pressures; and the recovery ratio, which is the ratio of permeate to inlet feed flow rates. A novel performance parameter, the effectiveness of an RO exchanger, is defined as a ratio of the recovery ratio to the maximum recovery ratio. A one-dimensional numerical model is developed to correct for the effects of feed-side external concentration polarization and nonlinearities in osmotic pressure as a function of salinity. A comparison of model results to experimental data found in the literature resulted in an average error of less than 7.8%. The analytical e-MTU model can be used for design or performance evaluation of RO membrane mass exchangers.

[1]  Chad Knutson.  Discussion of “Second law analysis of reverse osmosis desalination plants: An alternative design using pressure retarded osmosis” [Energy (2011) 36: 6617–6626] , 2012 .

[2]  S. Prabhakar,et al.  A new concept of mass transfer coefficient in reverse osmosis — practical applications , 1994 .

[3]  G. Srinivasan,et al.  Reprint of: “An analytical model for spiral wound reverse osmosis membrane modules: Part II — Experimental validation” , 2011 .

[4]  Kwee Guan Tay,et al.  Performance prediction of a long crossflow reverse osmosis membrane channel , 2006 .

[5]  Abhijit Chatterjee,et al.  Modeling of a radial flow hollow fiber module and estimation of model parameters using numerical techniques , 2004 .

[6]  Bélafi-Bakó Katalin.  Membrane separation processes , 2000 .

[7]  C. S. Slater,et al.  Modeling of small scale reverse osmosis systems , 1985 .

[8]  M. Sorin,et al.  On maximum power of reverse osmosis separation processes , 2006 .

[9]  Shyam S. Sablani,et al.  Concentration polarization in ultrafiltration and reverse osmosis: a critical review , 2001 .

[10]  Yoram Cohen,et al.  Numerical study of concentration polarization in a rectangular reverse osmosis membrane channel: Permeate flux variation and hydrodynamic end effects , 2007 .

[11]  H. K. Lonsdale,et al.  The growth of membrane technology , 1982 .

[12]  G. Schock,et al.  Mass transfer and pressure loss in spiral wound modules , 1987 .

[13]  S. S. Wang,et al.  A critical review of fouling of reverse osmosis membranes , 1981 .

[14]  A. Katchalsky,et al.  Thermodynamic analysis of the permeability of biological membranes to non-electrolytes. , 1958, Biochimica et biophysica acta.

[15]  S. Sundaramoorthy,et al.  An analytical model for spiral wound reverse osmosis membrane modules: Part I — Model development and parameter estimation , 2011 .

[16]  Panagiotis D. Christofides,et al.  On RO membrane and energy costs and associated incentives for future enhancements of membrane permeability , 2009 .

[17]  P. Christofides,et al.  Minimization of energy consumption for a two-pass membrane desalination: Effect of energy recovery, membrane rejection and retentate recycling , 2009 .

[18]  Thomas K. Sherwood,et al.  Desalination by Reverse Osmosis , 1967 .

[19]  John H. Lienhard,et al.  Second law analysis of reverse osmosis desalination plants: An alternative design using pressure retarded osmosis , 2011 .

[20]  R. Shah,et al.  Compact Heat Exchangers , 1990 .

[21]  A. Katchalsky,et al.  Thermodynamics of flow processes in biological systems. , 1962, Biophysical journal.

[22]  R. L. Riley,et al.  Transport properties of cellulose acetate osmotic membranes , 1965 .

[23]  D. Whiffen.  Thermodynamics , 1973, Nature.

[25]  Mostafa H. Sharqawy,et al.  Rebuttal to “Discussion of ‘Second law analysis of reverse osmosis desalination plants: An alternative design using pressure retarded osmosis’ [Energy 2011] 36: 6617–6626]” , 2012 .

[26]  P. Christofides,et al.  Effect of Thermodynamic Restriction on Energy Cost Optimization of RO Membrane Water Desalination , 2009 .

[27]  Thomas Melin,et al.  State-of-the-art of reverse osmosis desalination , 2007 .

[28]  Mingheng Li.  Reducing specific energy consumption in Reverse Osmosis (RO) water desalination: An analysis from first principles , 2011 .

[29]  M. Shimizu.  [Electrolyte solutions]. , 2019, [Kango] Japanese journal of nursing.

[30]  Masaaki Sekino,et al.  Precise analytical model of hollow fiber reverse osmosis modules , 1993 .

[31]  S. Nakao,et al.  Transport equation for a membrane based on a frictional model , 1993 .

[32]  K. S. Spiegler,et al.  Thermodynamics of hyperfiltration (reverse osmosis): criteria for efficient membranes , 1966 .

[33]  J. G. Wijmans,et al.  The solution-diffusion model: a review , 1995 .

[34]  Mingheng Li,et al.  Validation of model-based optimization of brackish water reverse osmosis (BWRO) plant operation , 2012 .

[35]  H. K. Lonsdale,et al.  Statistical-mechanical theory of membrane transport , 1990 .

[36]  Frank J. Millero,et al.  The thermodynamics of seawater at one atmosphere , 1976 .

[37]  J. Baeyens,et al.  Modelling reverse osmosis by irreversible thermodynamics , 1998 .

[38]  E. Nagy.  On Mass Transport Through a Membrane Layer , 2012 .

[39]  Gunnar Eigil Jonsson,et al.  Overview of theories for water and solute transport in9 UF/RO membranes , 1980 .

[40]  John H. Lienhard,et al.  Effectiveness–mass transfer units (ε–MTU) model of an ideal pressure retarded osmosis membrane mass exchanger , 2013 .

[41]  J. Lienhard,et al.  Erratum to Thermophysical properties of seawater: A review of existing correlations and data , 2010 .

[42]  É. Favre,et al.  Dense membrane permeation: From the limitations of the permeability concept back to the solution-diffusion model , 2005 .

[43]  M. Wilf,et al.  Optimization of seawater RO systems design , 2001 .

[44]  K. Gleason,et al.  Random copolymer films as potential antifouling coatings for reverse osmosis membranes , 2011 .

[45]  K. C. Channabasappa.  Status of reverse osmosis desalination technology , 1975 .

[46]  Pio A. Aguirre,et al.  Improvements of a hollow fiber reverse osmosis desalination model: Analysis of numerical results , 2010 .

[47]  H. K. Lonsdale,et al.  Recent advances in reverse osmosis membranes , 1973 .

[48]  Sangho Lee,et al.  A simplified simulation model of RO systems for seawater desalination , 2009 .

[49]  B. Freeman,et al.  Effect of crossflow testing conditions, including feed pH and continuous feed filtration, on commercial reverse osmosis membrane performance , 2009 .

[50]  Mingheng Li,et al.  Optimal plant operation of brackish water reverse osmosis (BWRO) desalination , 2012 .

[51]  Anping Liao,et al.  Optimization design of RO system for water purification , 2012 .

[52]  Andriy Yaroshchuk,et al.  Influence of osmosis on the diffusion from concentrated solutions through composite/asymmetric membranes: Theoretical analysis , 2010 .

[53]  Lianfa Song,et al.  A total salt balance model for concentration polarization in crossflow reverse osmosis channels with shear flow , 2012 .

[54]  J. Lienhard.  A heat transfer textbook , 1981 .

[55]  Donald R Paul,et al.  Reformulation of the solution-diffusion theory of reverse osmosis , 2004 .

[56]  Mohammad Kamil,et al.  Mathematical modeling of reverse osmosis systems , 2004 .