Parameterization of Element Balance Formulation in Reactive Compositional Flow and Transport

Abstract

A novel formulation for modeling nonlinear reactive-compositional transport comprising of complex phase behaviors with chemical and thermodynamic interactions is presented. The precipitation/dissolution of minerals during reactive flow in subsurface reservoirs is modeled in the newly designed simulation framework. This framework uses molar formulation with a consistent reduction of governing mass balance equations from component to element mole fractions. The thermodynamic phase behaviour is extended by including the chemical equilibrium reactions in the multiphase thermodynamic flash. This allows for a general treatment of chemical and thermodynamic equilibrium in a fully couple and implicit manner. The governing component conservation equations are reduced to element conservation equations using the Equilibrium Rate Annihilation matrix. The element composition of the mixture serves as an input for these computations whereas the output is fractions of components in each phase, including solids. To solve the resulting nonlinear element based governing equations, we use the Adaptive Operator-Based Linearization (OBL) approach where the governing equations are formulated in terms of space and state-dependent parameters. The proposed framework is utilized for modeling of several challenging flow and transport problems with dissolution and precipitation reactions. This is the first time when a multiphase multicomponent flash using element fractions as an input is coupled with an element balance compositional formulation and validated for multidimensional problems of practical interest. In addition, an efficient parametrization using adaptive OBL approach improves both robustness and performance of complex reactive-compositional flow and transport.

Reactive transport in porous media: a review of recent mathematical efforts in modeling geochemical reactions in petroleum subsurface reservoirs

“…The molar variable formulation was first introduced by [97] and fully tested for compositional reservoir simulations by [62]. First, we define a new porosity term, ̂ , that refers to the reactive porosity defined as the volume occupied by the solids that do not participate in chemical reactions and related to by: Reactions coupled Mass conservation equations [28] Phase equilibrium and local constraints [44,45,46] Reaction relations [29,30] Local reactions decoupled Mass conservation equations [28] Equilibrium reaction relations (localized) [30] Phase equilibrium and local constraints [44,45,46] Kinetic reaction relations [29] Kinetic reaction relations [29] Vol:.…”

“…It is also possible to integrate an adaptive OBL scheme within the process of the simulation adding to the efficiency of the reservoir simulator. This technique is quite useful in reducing the complications of the phase behavior calculations and has been rigorously tested for complex geothermal and multicomponent flow and transport problems with buoyancy [65], and for reactive flow of species in reservoirs [62]. The working flow of the OBL approach is shown in Fig.…”

“…The work of [62] presented a 1-D case of calcite dissolution using element formulation and molar variables. The dissolution and precipitation reactions were given by, The test was implemented using the OBL approach, and the equilibrium constants for the equilibrium reactions were scaled up to show the effects of the reactions on the overall system.…”

Integrated Framework for Modelling of Thermal-Compositional Multiphase Flow in Porous Media

“…It allows extracting complex physics-related computations from the main simulation loop, leaving only an algebraic multilinear interpolation kernel instead. It has been shown that the approach is applicable to various challenging physics, including thermal-compositional problems Khait and Voskov (2017b), buoyancy-dominated flow Khait and Voskov (2018a) and chemical multiphase flow and transport Kala and Voskov (2018).…”