An Investigation of Transient Flow of Reservoir Fluids Considering Pressure-Dependent Rock and Fluid Properties
Authors: Samaniego V. F. , Brigham W.E. , Miller F.G. 
Published: December 2007

Abstract
In this study we investigate the influences of pressure-dependent fluid properties and pressure-dependent fluid properties and stress-sensitive rock properties on pressure transient analysis. Single-phase flow through the porous medium is considered. These pressure-dependent terms are accounted for by use of a dimensionless pseudopressure mD(1, tD); a large variety of rates, pseudopressure mD(1, tD); a large variety of rates, geometries, and inner and outer boundary conditions are studied. For all practical production rates and most boundary conditions the pseudopressure solutions, in terms of mD(1, tD) are essentially the same as the conventional solutions using pD(1, tD) that have been documented for constant-property liquid flow. The only exceptions occur when the system studied has a closed outer boundary, and the pressure transient bas occurred for a long enough time to be affected by this boundary. in these cases, a simple adjustment can be made to the mD(1, tD) solutions to bring them in line with the pD(1, tD) solutions.

Introduction
As early as 1928, it was recognized that porous media are not always rigid and nondeformable. porous media are not always rigid and nondeformable. This problem is usually handled by means of properly chosen "average" properties. This method properly chosen "average" properties. This method only reduces the errors involved and generally does not eliminate these errors.
Classical treatments solve the diffusivity equation, which assumes that the diffusivity is a constant independent of pressure. When both pressure and property changes are small, the constant-property property changes are small, the constant-property assumption is justified. If, instead, rock and fluid property changes are important over the pressure property changes are important over the pressure range of interest, these changes cannot be neglected and a variable-property solution should be obtained.
Raghavan et al. derived a flow equation considering that rock and fluid properties vary with pressure. This equation, when expressed as a pressure. This equation, when expressed as a function of a pseudopressure, m(p), resembles the diffusivity equation. They studied pressure drawdown tests in radial bounded reservoirs produced at a constant mass rate. These test results were obtained for only a specific set of rock and fluid properties. Because this work included only a few cases, there was a need to study the use of the m(p) method for a greater variety of flow conditions.
This paper presents the results of an investigation of the application of the m(p) method to drawdown, buildup, injection, and falloff testing. Results were obtained for five different sets of rock and fluid properties. The investigation also includes the effects of wellbore damage and wellbore storage.

MATHEMATICAL FORMULATION
To formulate the mathematical model, the assumptions usually used in well-testing theory are applied. We assume horizontal flow with no gravity effects, a fully penetrating well, isothermal single-phase fluid obeying Darcy's law, an isotropic and homogeneous formation, and purely elastic rock properties. That is, physical property changes with properties. That is, physical property changes with stress changes are reversible. In the radial systems, allowance is made for a region of reduced or improved permeability near the wellbore.
The assumption of horizontal flow is not quite valid because of changes in porosity and height with pressure. However, it is easily shown that the vertical component of flow is negligible for practical rock properties and can properly be practical rock properties and can properly be neglected. Gavalas and Seinfeld also made this assumption.
The rock properties needed in the flow equation porosity, permeability, and pore compressibility as porosity, permeability, and pore compressibility as functions of pressure - are found in the literature only for sandstones. It has been concluded that, in consolidated sandstones, the deformations are usually purely elastic. Therefore, only these are considered in this study. Other rocks may not behave as elastic materials.
SPEJ
P. 140