(435d) One and Two-Equation Models to Simulate the Capacitive Deionization Process

Capacitive deionization (CDI) is an electrochemical water treatment process that can be used for treating water and saving energy. A two-equation model is derived to simulate the CDI process in heterogeneous porous media comprising two different pore sizes. It is based on a theory for capacitive charging by ideally polarizable porous electrodes without Faradaic reactions or specific adsorption of ions. A two steps volume averaging technique is used to derive the averaged transport equations in the limit of thin electrical double layers. The two-equation model is compared to a one-equation model based on the principle of local equilibrium previously derived. The effective transport parameters for isotropic porous media are calculated by solving the corresponding closure problems. An approximate analytical procedure is proposed to solve the closure problems. Numerical and theoretical calculations show that the approximate analytical procedure yields adequate solutions. The constraints that determined whether to use the two-equation or a one-equation model are discussed. A numerical analysis shows that the value of an interphase pseudo-transport coefficient determines which model to use. The source terms that appear in the porous solid phase make more difficult to achieve local equilibrium.