Stress-Dependent Permeability of Reservoir Rock and Its Influence on Well Flow Rate: Experiment and Simulation

Abstract

Thermobaric tests are performed on Bazhenov oil-bearing shale containing above 10% of kerogen in view to determine its rheological properties. The test specimen under a statistical axial load is heated stepwise at temperatures $T_{n} = 60$, 100 and 150 ℃ with measurements of height $H\left( t \right)$. The temperature is risen if relative velocity of $H$ gets less than 0.05. Deformation of the specimen is described by Kelvin–Voigt model, within which the inverse problem is stated and solved to determine Young module $E_{n}$ and effective viscosity $\eta_{n}$ of rocks by $H\left( t \right)$. The results of solution are approximated by two-parameter exponential functions, $E = E\left( T \right)$ and $\eta = \eta \left( T \right)$ relationships are established.

The lab-scale test bench is designed and manufactured to study the relationship of granular geomaterials permeability versus stresses. A polyurethane measurement cell of parallelepiped shape is filled with sized sand; controllable vertical stress $\sigma$ is applied to different sections of the top edge. The constant gas pressure $p$ is created on one of vertical edges, while gas flow rate $Q\left( {p,\sigma } \right)$ is recorded on the opposite edge. The mathematical model of experimental is developed. Hypothesizing that permeability depends on effective stress according to the exponential law with coefficient $\beta$ in index, the analytical solution is found to the problem on stationary filtration in a cell under a non-uniform stress state. The researchers propose the process for quantitative estimation of $\beta$ based on minimization of the relative discrepancy functional between $Q$ and the theoretical value of gas flow rate. It is appeared that $\beta$ can be determined without reference to gas viscosity and an initial permeability of geomaterial packing. According to the present test results $\beta$ magnitude used to reduce slightly with stress growth.

The poroelastic model describing evolution of geomechanical and hydrodynamic fields in a near-well zone was employed for comparative analysis of metering characteristics of a well in terms of the routine deformation and poroperm parameters of production oil-bearing beds. It is demonstrated that a disregard of the established empirical relationships of permeability versus effective stresses and temperature can result in an appreciable upward bias of oil production prediction.