Numerical Simulation of non-Darcy Oil Flow in Naturally Fractured Reservoirs: Horizontal Well

Grazione de Souza¹; Mayksoel Medeiros de Freitas¹; Helio Pedro Amaral Souto¹

¹ Instituto Politécnico-UERJ

doi:10.20906/CPS/COB-2015-0212

Resumo

Numerical simulation of oil flow is applied to obtain estimates for the pressure drop in hydrocarbon reservoirs under different production strategies. Due to differences in properties such as porosity and permeability between the porous medium and fractures in a heterogeneous reservoir, there is a growing interest to study flow regimes in fractured reservoirs. In Naturally Fractured Reservoirs (NFRs), for example, permeability and porosity different values are due to geological factors. In this work, a numerical simulator has been developed in order to study the non-Darcy oil flow (inertial) in Naturally Fractured Reservoirs for a horizontal well. The physical and mathematical models consider a three-dimensional and isothermal single-phase flow. Non-Darcy effects are incorporated using the Barree and Conway's model, taking into account the inertial effects of the flow. The nonlinear partial differential equations are discretized using the finite difference method and a time implicit formulation. The numerical code also allows the use of mesh refinement, in order to represent fractures, providing a better capture of the physical phenomena in regions close to the fractures. A factorization preconditioning technique has been chosen for the numerical solution of the system of algebraic equations, due to their ability to solve matrix equations for problems where the heterogeneity is an important feature. Several production scenarios for hydrocarbons primary recovery have been considered. As expected, it has been concluded that the spatial variation of the properties of the porous medium, due to the heterogeneity of the reservoir, and the flow regime have significant influence in determining the pressure and velocity fields, with a consequent impact on the changes of pressure for the production well.

Palavras-chave: Barree and Conway's model; finite-difference method; oil flow; naturally fractured reservoir; non-Darcy flow