An OpenMP Parallel Implementation for Numerical Simulation of Gas Reservoirs Using Intel Xeon Phi Coprocessor

The objective of this work is to parallelize, using the Application Programming Interface (API) OpenMP (Open Multi-Processing) and Intel Xeon Phi coprocessor based on Intel Many Integrated Core (MIC) architecture, the numerical method used to solve the algebraic system resulting from the discretization of the differential partial equation that describes the single-phase flow in a gas reservoir. The set of governing equations are the continuity equation, the Darcy’s law and an equation of state. The Hydraulic Diffusivity Equation (HDE), for the unknown pressure, is obtained from this set of fundamental equations and it is discretized by means of the Finite Difference Method (FDM) along with a time implicit formulation. Different numerical tests are performed in order to study the computational efficiency of the parallelized versions of Conjugate Gradient (CG), BiConjugate Gradient (BiCG) and BiConjugate Gradient Stabilized (BiCGStab)methods,and different production scenarios were considered for horizontal wells and single-phase gas flow. The influence of different physical parameters as, for example, permeability on the wellbore pressure is also considered. Speed-up results are considered in order to evaluate the performance of the parallel algorithms. Keywords: Numerical reservoir simulation, Finite difference method, Sparse algebraic system, Iterative methods, OpenMP, Parallelization.