Nonlinear formulation based on EoS-free method for compositional flow simulation

Abstract

Compositional simulation is necessary for the modeling of complex EOR processes. For accurate simulation of compositional processes, we need to couple solution of nonlinear conservation laws for multicomponent multiphase flow and transport, with a system of equations describing the phase behavior of the mixture at q thermodynamic equilibrium. The complexity of the problem requires extensive computations and consumes significant CPU time. We present an efficient and robust framework for the computation of the thermodynamic phase behavior associated with multi-component multiphase flow in porous media. The method is based on adaptive interpolation of supporting tie-lines in compositional space. For the parameterization of full solution of a complex compositional problem we need only a limited number of supporting tie-lines in compositional space. We use a special approach for the adaptive construction of these tie-lines, depending on predefined precision. The parameterized tie-lines are triangulated using Delaunay tessellation, and natural-neighbor interpolation technique is used inside the supporting simplex. The computation of phase behavior for the composition simulation then becomes an iteration-free procedure and does not require any EoS computations. Based on this method, we developed a new nonlinear formulation for fully-implicit compositional simulation for both immiscible and miscible displacement. The treatment of nonlinearities, associated with complex thermodynamic behavior of the fluid, is based on the new set of unknowns - tie-line parameters, which allows for efficient representation of the subcritical region. For the supercritical region we use the standard compositional set of variables that based on the overall composition. A new criterion is proposed for the identification of changes between sub- and super-critical regions, and the robust variable substitution is applied during the simulation process. The efficiency and accuracy of the method is demonstrated for several multi-dimensional compositional problems of practical interest. For the tested problems, the proposed method significantly reduces the computational cost of the thermodynamic calculation compared with the standard EoS-based approach. Moreover, the method shows substantially better nonlinear convergence in the case of near-miscible gas injection simulation.