Well-Reservoir Coupling on the Numerical Simulation of Horizontal Wells in Gas Reservoirs

Abstract

AbstractWellbore flow and its coupling with porous media has been an active field of research, mainly because wellbore hydraulics (especially in complex geometry wells, like horizontal or multilateral) plays an important role in the pressure and production profiles. An inherent difficulty is associated to the multiscale nature of the flow problem: the cell hosting the well is generally much larger than wellbore radius. As a consequence, average pressure in a cell is not a good approximation of the well pressure. Moreover, at the interface between well and reservoir there is a change in flow pattern, from porous media to pipe flow. In this work a well-reservoir coupling technique is developed and applied to the numerical simulation of horizontal wells in gas reservoirs. This model considers wellbore hydraulics and storage.We consider the 3D single-phase isothermal flow of a compressible fluid in porous media and 1D single-phase isothermal flow of a compressible fluid in the wellbore. In both regions, mass conservation, momentum balance and real gas equation of state are the governing equations. Conservative forms are used for continuity and momentum. Flow continuity and pressure equilibrium are considered at the interface between well and reservoir. The nonlinear partial differential equations can be rewritten to allow the coupling of the pressure field between the porous media (reservoir) and the free media (well) by means of an implicit formulation for the finite difference method presented. A hybrid grid technique was applied to improve the description of the flow close to the wellbore. In addition, pressure in reservoir and wellbore are solved simultaneously, while velocities in wellbore are updated at every iterative step. An iterative method to solve numerically the resulting linear system for the primitive variable pressure was developed and it includes the wellbore/reservoir coupling into a finite difference numerical model.This methodology is useful for the analysis of transient pressure and velocity behavior in both reservoir and wellbore including the change in flow pattern from porous media to pipe flow. Effects of permeability, gas specific gravity, formation damage and grid refinement are considered in different sensitivity analysis for several well-reservoir systems. Results for pressure and pressure derivative followed the expected behavior of the reservoir model chosen, both in early and long times. Effects of friction, convection and compressibility in wellbore hydraulics were successfully included in the numerical approach.