Numerical Reservoir Simulation of Shale Gas in the Slip Flow Regime
Camila Lima Chung1; Mayksoel Medeiros de Freitas1; Grazione de Souza1; Helio Pedro Amaral Souto1
1 Instituto Politécnico/UERJ
doi:10.20906/CPS/CILAMCE2015-0191
Resumo
In the last decade a number of engineers and scientists worked on the optimized recovery in unconventional hydrocarbons reserves. Shale gas reservoirs are increasingly becoming important players in the world energy matrix. It is worth noting that for gas flow in porous media there are situations in which the conventional Darcy's law cannot adequately describe the flow. An example is the slip phenomenon, named Klinkenberg's effect, in which rock permeability is a pressure function. Several recent works have been dedicated to incorporate slip phenomena using Knudsen's number, a dimensionless number that relates the mean-free-path of molecules (function of fluid properties) and a characteristic hydraulic radius (dependent of rock properties). Data from some formations appointed that permeability corrections from Klinkenberg's effect can be relevant for low permeability reservoirs. In this work, in order to study slip flow in porous media, a non-linear partial differential equation for pressure unknown is considered. A numerical reservoir simulation code was developed for studying porous media flow in field scale, considering very low permeability gas reservoirs (shale gas) and production through horizontal wells. The physical-mathematical modeling considers three-dimensional, single-phase and isothermal gas flow in porous media. The so-called Klinkenberg gas slippage effect is incorporated using a function of the Knudsen's number in order to determine the apparent gas permeability, considering intrinsic properties such as permeability, porosity, tortuosity, rarefaction coefficient and Klinkenberg's factor. The nonlinear partial differential equations are discretized by means of the finite-difference method along with a implicit approach. A system of algebraic equations is obtained for the unknown pressure after a linearization. A preconditioned approximate factorization technique was chosen for the numerical solution. Different production scenarios are studied, as well as the combined effects of heterogeneities and
Palavras-chave: Finite-Difference Method; Gas flow; Horizontal Well; Klinkenberg's effect; Shale gas