A well simulator for homogeneous reservoirs based on formulations of the isogeometric boundary element method

Abstract

The development of a simulator for homogeneous reservoirs with application in producer wells (represented by a sink) and the aquifer analysis is obtained by combining the Boundary Element Method (BEM), the Isogeometric Formulation using NURBS (Non Uniform Rational B-Spline) as shape functions, and also the Axisymmetric Formulation. The Isogeometric Formulation makes the discretization of geometric model (mesh generation), which is the step of numerical analysis that is more time consuming for the engineer, be no longer necessary, since the same functions that describe the geometry also approximate the field variables in the BEM. In other words, the same discretization used in the geometric model, generated in CAD (Computer Aided Design) modeling programs, also is used by the BEM. The oil and water reservoirs, as simplified models for validation of the new mathematical methodology, can be fully represented by the analysis of a plane passing through the axis of rotational (axial) symmetry. The dimension of the problem is reduced from three to two dimensions: radial and axial directions only, and all variables in the circumferential direction are assumed to be constant. When the geometry and the problem variables are both axisymmetric, then the problem is considered fully axisymmetric. The isogeometric and axisymmetric formulations are coupled to obtain the well simulator for the single and double phase case, i.e. one or two incompressible fluids inside the reservoir. The determination of boundary conditions for the model, including the analysis of fluids interface movement, is also presented. The final code is a new tool for the analysis of gas/water coning phenomenon and quick drawdown problem in homogeneous reservoirs, as validation models. Validation of the results is carried out by comparing with others numerical methods and analytical results.