Multi-physics Simulation Of Salinity Gradient Power Generation Using Reverse Electrodialysis

Reverse electrodialysis（RED）is a promising technology that directly converts salinity gradient energy into electrical energy through the selective permeation of the ion exchange membranes（IEMs）.The RED power generation is a complex multi-physics coupling process involving solution flow,ion transport,and electrical phenomena.When developing a RED model,these multi-physical phenomena need to be described as comprehensively and accurately as possible.In this work,a two-dimensional RED model based on the Nernst-Planck framework was developed.The fluid dynamics,ion transport and electrical phenomena were modelled in a full-length cell pair domain by employing the continuity,Navier-Stokes and Nernst-Planck equations complemented by the Donnan equilibrium and local electroneutrality.The ion diffusion coefficient in the IEM is a very important physical property that is difficult to obtain through experiment.In this paper,it was determined theoretically by combining the tortuosity model and the Manning counter-ion condensation theory.A numerical simulation was carried out using the developed model.The velocity field,concentration field electric field and ion flux distribution were obtained and the characteristics of ion transport were analyzed.Also,the effects of solution inlet velocity,IEM fixed charge concentration and cell pair length on the RED stack performance were investigated and the mechanisms governing the variations of performance parameters were revealed based on ion transport.In addition,the characteristics of ion transport when using NaCl+Mg Cl₂solution under different Mg Cl₂molar fraction were compared,and the influence of divalent ion(Mg²⁺)on the resistance,open circuit voltage and power density of the cell pair was analyzed.The results of using pure NaCl solution show that:increasing the inlet velocity of the solution will increase the cell pair resistance,the open circuit voltage and the maximum power density.For the case of IEM fixed charge concentration of 5M and cell pair length of10cm,when the solution inlet velocity increases from 0.25 to 1.5cm/s,the maximum power density increases by 27.5%.Increasing the IEM fixed charge concentration will significantly reduce the resistance of the IEM,but will increase the open circuit voltage,short circuit current and maximum power density.Under the conditions of inlet velocity of 1.0cm/s and cell pair length of 10cm,when the IEM fixed charge concentration increases from 2 to 6M,the maximum power density increases by 26.4%.When the inlet velocity is 1.0cm/s and the IEM fixed charge concentration is 5M,if the cell pair length is increased from 10 to 50cm,the maximum power density will be reduced from 1.4 to 0.87W/m²,a decrease of about 37.9%.The results of using the solution of NaCl+Mg Cl₂show that:divalent ion(Mg²⁺)will adversely affects the power generation performance of the cell pair.Increasing the molar fraction of Mg²⁺will cause the decrease of the cell pair electromotive force and the increase of cell pair resistance,thus reducing the power density of the cell pair.Compared with the cell pair using pure NaCl solution,the open circuit voltage of the cell pair using the50%NaCl+50%Mg Cl₂solution is reduced by about 25%,and the maximum power density is reduced by about 18.2%.This model is able to explore the relationship between RED ion transport behavior and stack performance,as well as the transport behavior of multivalent ions in RED stack and its influence on RED power generation performance.At the same time,it can also be used to optimize the design of the stack.