Effect of the Elastic Constants on the Pressure Behavior of Vertical Wells

Escobar, Freddy Humberto (Surcolombiana U.) | Munoz, Oscar Armando (U. of Stavanger) | Brinez, Diego Fernando (Ecopetrol SA) | Guzman, Julio Cesar (Halliburton Latin America S.A.) | Cantillo, Jose Humberto


Everyday, it is more frequent and common to adequately know the dynamical behavior of stress and strain sensitive formations and to improve their geomechanical characterization, as well. For this purpose, a coupled simulator of fluid flow and rock deformation was used in this study to investigate the impact of the elastic constants of the rocks during a well pressure test. The results were compared with those obtained for a reservoir with average properties in which the geomechanical effects were neglected.

The numerical experiments were focused on simulating drawdown tests for four different scenarios as follows: a standard case without geomechanical effects, two cases with isotropic initial state of stress and two cases with anisotropic stress. For interpretation and comparison purposes, we utilized the TDS technique to determine the reservoir parameters of the simulated pressure data. The results allow us to visualize that Young's modulus causes a pronounced effect on the pressure test during pseudosteady-state flow which leads to a wrong estimation of reservoir drainage area; a range of values were established above which its variation does not cause important effects. On the other hand, it was found that variations of Poisson's ratio are not significant since they fit in a small range of the values customary reported in the literature.

1. Introduction
Since conventional reservoir engineering has overlooked geomechanics effects, research on reservoir geomechanics has lately increased. Recent investigations2-5 have concluded that an adequate characterization of stress-dependent reservoirs can help to achieve a more realistic reservoir forecast and, then, appropriate decisions regarding production optimization can be made. For these goals, coupled models to simulate both fluid flow and rock deformation behavior have been developed.

In this paper, a study for evaluation the effect of the rock's elastic constant on pressure transient tests using a coupled simulator is presented. The results permitted to establish a range of high influence of the elastic constant values during well pressure tests. The study also allowed us to discard critical values for the elastic constants which generate high numerical instability and possess low practical application.

2. Simulation Background
In this study a numerical coupled simulator developed by Alcalde and Wills1 was used. The numerical model consists of a fully implicit 3D finite difference solution in cylindrical coordinates with irregular grid using lattice grid points. The model considers the following assumptions: (i) the rock is deformable under an elastic, nonlinear behavior, (ii) monophasic and isothermal flow, (iii) Because of the stress dependence, the fluid and geomechanical properties are subject to temporal and spatial variations. The numerical solution is achieved by a Picard-Gauss-Seidel iteration type2.

The governing equations for the fluid flow in porous media coupled with geomechanical deformation are determined by four expressions which are developed detailly in Ref. 1.