Formulation of a Transient Multi-Phase Thermal Compositional Wellbore Model and its Coupling with a Thermal Compositional Reservoir Simulator

Abstract

Abstract In this paper, we develop the detailed formulation of a transient multi-phase thermal compositional wellbore model and couple it with a thermal compositional reservoir simulator. We consider the presence of at most three phases which are an aqueous phase (water with dissolved CO2), a hydrocarbon liquid phase and a hydrocarbon vapor phase. The volume of wellbore is divided into a set of 1-D control volume grids. The mass balance equations for all components and the total energy balance equation are discretized over the wellbore control volumes. The transient total momentum balance equation (along the wellbore) and the drift-flux model equations for gas-liquid and oil-water systems are discretized over a set of backward staggered grids with respect to the wellbore grids. Following the assumption that the hydrocarbon phases inside a wellbore control volume are in equilibrium, a set of constraint equations are introduced to enforce the equality of the fugacity of each component in both hydrocarbon phases. The solution algorithm for the wellbore model is similar to the one for a compositional reservoir simulator, where, the sets of simulation equations and unknowns are divided into the sets of primary and secondary equations and unknowns which are solved sequentially. The appearance and disappearance of the hydrocarbon phases follow the phase stability and two-phase flash calculations. The wellbore model is fully coupled with a reservoir simulator at the bottom of the well. The interaction of wellbore with reservoir is handled with definition of source terms in the mass and energy balance equations and is obtained from continuity of force, energy and mass fluxes across the reservoir/wellbore interface. The boundary conditions for the wellbore model depend on the well control which includes the specified pressure or production rate at wellhead. Within the computational results section, the validation of the wellbore model against the analytical solution for the shock tube problem is presented. Moreover, the coupled wellbore/reservoir simulator is used to model the drawdown and buildup tests of a well in a single-layer reservoir, and a relatively long period of production from a multi-layer volatile oil reservoir.