This element composition of the mixture serves as an input to the modified multiphase flash computations, whereas the output is fractions of components in each phase, including solids. Therefore, the primary set of governing equations are the element balance equations and the kinetic equations. The element balance equation written in terms of overall component mole fractions is modified and defined in terms of element mole fractions. Equilibrium Rate Annihilation matrix allows us to reduce the governing component conservation equations to element conservation equations, while the coupling between chemical and thermodynamic equilibrium is captured by a simultaneous solution of modified multiphase flash equations. This provides a generic treatment of chemical and thermodynamic equilibrium within the successive substitution loop of mulmultiphase flash to accommodate chemical equilibrium reactions (precipitation and dissolution reactions). In this solution, the phase equilibrium is represented by the partition coefficients, whereas the chemical equilibrium reaction is represented by the activity coefficients model.

To predict the complex phase behavior in such systems, we include the chemical equilibrium constraints to the multiphase multicomponent negative flash calculations and solve the thermodynamic phase and chemical phase equilibria simultaneously. The proposed formulation is based on the consistent element balance reduction of the molar (overall composition) formulation. We apply this formulation to model precipitation/dissolution of minerals in reactive multiphase flow in subsurface reservoirs. We present a novel nonlinear formulation for modeling reactive-compositional flow and transport in the presence of complex phase behavior due to a combination of thermodynamic and chemical equilibria in multi-phase systems.

Non reactivity balance