Page 303 - Fundamentals of Reservoir Engineering

CHAPTER 8

REAL GAS FLOW: GAS WELL TESTING

8.1 INTRODUCTION

The first part of this chapter describes how the basic differential equation for radial fluid
flow, equ. (5.1), can be approximately linearized for real gas flow. This is achieved
using the real gas pseudo pressure function

p pdp
m(p) = 2
p µΖ
b
and subsequently, all equations in the chapter are expressed in terms of m(p) functions
rather than real pressures. The constant terminal rate solution of the radial diffusivity
equation is then presented in dimensionless form, equivalent to the p D functions for
liquid flow, and the solution is applied to the analysis of gas well tests. A similar
approach is used for analysing pressure buildup tests in solution gas drive reservoirs,
below bubble point pressure.

8.2 LINEARIZATION AND SOLUTION OF THE BASIC DIFFERENTIAL EQUATION FOR
THE RADIAL FLOW OF A REAL GAS

By assuming mass conservation, Darcy's law and applying the definition of fluid
compressibility, the basic equation for the radial flow of a single phase fluid in a porous
medium was derived in chapter 5 as

1 ∂ kρ ∂ p ∂ p
c
r = φρ (5.1)
rr ∂ µ r ∂ t ∂
This equation was linearized for liquid flow by deletion of terms, assuming that

- µ was independent of pressure

∂ p ∂ p 2
- was small and therefore was negligible
r ∂ r ∂

- c was small and constant so that cp << 1

which resulted in the radial diffusivity equation

1 ∂ ∂ p φµ c p
∂
r = (5.20)
rr r ∂ k t ∂
∂
Because this equation is linear for liquid flow, simple analytical methods could be
applied to describe stabilized inflow (Chapter 6) and the constant terminal rate solution
(Chapter 7). The assumptions made in linearizing equ. (5.1) are inappropriate when
applied to the flow of a real gas. In the first place, gas viscosity is highly pressure
dependent. Secondly, the isothermal compressibility of a real gas is