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 processes in chemical engineering. We present a general method to account robustly for instantaneous chemical equilibriums in reactive transport. This method is adapted to all kinds 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 (DAEs). 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.

► Reactive transport models require accounting for instantaneous chemical equilibriums.
► A general method is proposed.
► This method can be applied to any kind of hydraulic transport description.
► This method yields the definition of Differential Algebraic Systems with bound constraints.
► An adapted solver is proposed.