Accounting robustly for instantaneous chemical equilibriums in reactive transport: A numerical method and its application to liquid-liquid extraction modeling

Reactive transport equations are used in numerous application fields: CO2 or nuclear waste storage monitoring, separation process in chemical engineering. We present a general method to account robustly for instantaneous equilibriums in reactive transport. This method is adapted to all kind of hydraulic transport models including 1D to 3D convection-diffusion equations. This leads to the resolution of a bound constrained system of Differential Algebraic Equations (DAE). The algebraic constraints come from the adjunction of mass action laws related to the equilibriums, whereas the bounds account for the positivity of the computed quantities. In order to solve the numerical system associated with our method, we use an adaptation of the DASSL solver, CDASSL, that can handle the resolution of bound constrained DAE systems. We present an application of this method to liquid-liquid extraction modeling. Numerical experiments demonstrate the interest of using the CDASSL solver to ensure the bound constraints are satisfied.