3.1 Introduction

This chapter includes steady- and pseudo-steady-state equations for gas flow through a reservoir. For each subsection, flow equations for vertical wells are described first, followed by mathematical equations for horizontal wells. The mathematical determinations of the equations are avoided; this role is filled much better by other publications.1 ^?5 Field examples are included to provide hands-on understanding of various solution techniques and their applications.

3.2 Steady-State Gas Flow

Steady-state equations for gas flow through a reservoir are given below. Gas flow rate is proportional to the pressure-squared terms. This is generally employed when reservoir pressures are less than 2500 psia. In terms of gas pseudopressure, the gas flow rate is directly proportional to pseudopressure. The pseudopressure is defined as

or

Also,

where

• q _g = gas flow rate, mscfd

• p _e = pressure at external radius, r _e, psia

• p _wf = wellbore flowing, psia

• = average viscosity, cP

• z= average gas compressibility, dimensionless

• T = reservoir temperature, R

• r _e = drainage radius, ft

• = effective wellbore radius, ft

• k = permeability, mD

• h = thickness, ft

• P _sc = base pressure, psia

• T _sc = base temperature, R

The correct value of (1 / z) _avg to use in the equation for gas is . It has been found that for most natural gases a value of (1/ z) _avg evaluated at the arithmetic average pressure ( p _e ? p