2.1 Introduction

The aim of this chapter is to develop and present the fundamental equations for flow of gases through porous media, along with solutions of interest for various boundary conditions and reservoir geometries. These solutions are required in the design and interpretation of flow and pressure tests.

To simplify the solutions and application of the solutions, dimensionless terms are used. Assumptions and approximations necessary for defining the system and solving the differential equations are clearly stated. The principle of superposition is applied to solve problems involving interference between wells, variables flow rates, and wells located in noncircular reservoirs. The use of analytical and numerical solutions of the flow equations is also discussed. Formation damage or stimulation, turbulence, and wellbore storage or unloading are given due consideration. This chapter applies in general to laminar, single, and multiphase flow, but deviations due to inertial and turbulent effects are considered. For well testing purposes two-phase flow in the reservoir is treated analytically by the use of an equivalent single-phase mobility.

The equations of continuity, Darcy s law, and the gas equation of state are presented and combined to develop a differential equation for flow of gases through porous media. This equation, in generalized coordinate notation, can be expressed in rectangular, cylindrical, or spherical coordinates and is solved by suitable techniques. The next subsections describe steady-state, pseudo-steady-state, and unsteady-state flow equations including the gas radial diffusivity equation, basic gas flow equations, solutions, and one-, two-, and three-dimensional coordinate systems.

2.2 Steady-State Laminar Flow

Darcy s...