Parameterization of element balance formulation in reactive compositional flow and transport

We present a novel nonlinear formulation for modeling reactive-compositional transport in the presence of complex phase behavior related to dissolution and precipitation in multi-phase systems. This formulation is based on the consistent element balance reduction of the molar (overall composition) formulation. To predict a complex phase behavior in such systems, we include the chemical equilibrium constraints to the multiphase multicomponent negative flash calculations and solve the thermodynamic and chemical phase equilibrium simultaneously. In this solution, the phase equilibrium is represented by the partition coefficients whereas the chemical equilibrium reaction is represented by the activity coefficients model. This provides a generic treatment of chemical and thermodynamic equilibrium within an EOS SSI loop by modification of the multiphase flash to accommodate chemical equilibrium. Using the Equilibrium Rate Annihilation matrix allows us to reduce the governing unknowns to the primary set only while the coupling between chemical and thermodynamic equilibrium is captured by a simultaneous solution of modified multiphase flash equations. An input in this thermodynamic computation is an element composition of the mixture when an output contains fractions of components in each phase, including solids. This element balance molar formulation along with the modified formulation for multiphase flash has been tested in a simple transport model with dissolution and precipitation reactions. The same approach will be later used to model a system involving kinetic reactions. The simulation of more general practical models is performed using the recently developed Operator-Based Linearization (OBL) technique. In the modified version of the OBL, the nonlinear element based governing equations are formulated in terms of space and state-dependent parameters constrained by the solution of the extended multiphase flash based on molar element compositions. This approach helps us to add equilibrium reaction capabilities to the computationally efficient OBL technique.