Production Rate Decline In Pressure-sensitive Reservoirs
Authors: Samaniego V. Fernando , Cinco L. Heber 
Published: March 2010

Abstract
This paper investigates the influence of pressure-dependent fluid and rock properties on well production decline in constant wellbore pressure tests. The rock properties considered variable are permeability, porosity, pore compressibility and formation thickness, and the fluid properties are density, compressibility and viscosity. Single-phase flow through the porous medium is considered. Various geometries, ratios of initial to wellbore pressure, and data sets of rock and fluid properties are studied. For all practical ratios of initial to wellbore pressure and for transient flow conditions, production rate decline expressed in terms of a dimensionless rate qD is essentially the same as the production rate decline qD1 for constant property liquid flow. The only exceptions occur for bounded reservoirs after the flow is affected by the outer boundary. These deviations are such that in pressure-sensitive systems production rate declines faster than in constant-property systems. It is shown that variable property decline solutions, when/compared to constant property decline solutions, do not follow any of the three common types of production decline curves-exponential, hyperbolic or harmonic. Type curve matching of variable property production rate decline to constant property flow solutions gives the correct size of the reservoir, but, other reservoir parameters can be in error. When variable property type curves are used for matching, all reservoir parameters are correctly estimated. The method of Jacob and Lohman(19) and of van Poollen(21) are properly modified to account for the pressure-dependency of rock and fluid properties.

Introduction
It is well accepted that porous media are not always rigid and non-deformable. This should influence the transient well behaviour. A frequent assumption is to use average values forboth pressure-dependent rock and fluid properties. This helps to reduce the errors involved, but does not totally eliminate them.
When rock and fluid property changes are important over the pressure range of interest, then these changes cannot be neglected and a variable property solution should be obtained.
A flow equation considering the pressure dependency of all rock and fluid properties has been presented in the literature(1). This equation, when expressed as a function of a pseudo-pressure m(p), resembles the diffusivity equation. Samaniegoet al.(2.3) studied this variable property problem for a greater variety of flow conditions. These authors only investigated constant rate cases.
There are two basic radial flow cases in the flow of fluids through porous media:constant well rate; andconstant well pressure.
It is the purpose of this study to investigate the influence of pressure-dependent rock and fluid properties on the constant pressure case. One of the objectives is to find out how production rate decline would vary in these pressure-dependent systems, and if methods of analysis for constant pressure flow testing can be properly modified to account for the variation of rock and fluid properties.

Mathematical Formulation
The mathematical model used in this work is based on the assumptions usually used in well testing theory: horizontal flow, with no gravity effects, a fully penetrating well, an isothermal single-phase fluid, obeying Darcy's, law and an isotropic homogeneous formation.