CSG Material Balance

Introduction

According to King (1993), Coal-seam and Devonian shales are characterized by a dual-porosity nature.

Primary porosity is characterized by very fine pores with large internal surface area where there is a large amount of adosprtion sites for the storage of significant quantities of gas. The primary porosity generally has very low permeability (essentailly inmobile according to Darcy’s Law). As a result, gas transport is assumed is often assumed to be a diffusion process. Gas stored by adsorption is often modelled with an adsorption isotherm .

The secondary-porosity system of coal seams and Devonian shales consists of the natural-fracture system inherent in these reservoirs. This fracture system acts as a sink to the primary-porosity system and as a conduit to production wells. With respect to coal seams, this secondary porosity is often anistropic in nature.

• Free Ga s: The amount of free gas in the natural cleats or fractures is generally quite small because of:

  1. Small fracture space

  2. High water saturation

• Absorbed Gas: Forms the majority of natural gas production from CSG.

Material Balance

The King material balance is used in the AFA software. It accounts for both free and adsorbed gas as discussed in isotherms , but no solution gas. This solution must be solved numerically for current reservoir pressure as a function of gas produced and water produced (via average water saturation)

It is also important to note that this formulation does not account for undersaturated conditions. In undersaturated conditions, we use a water material balance.

Where:

A = drainage area, acres

B_g = Gas formation volume factor (ft³/Mscf); which is effectively z-factor

Q_g=G_p = Gas produced (Mscf)

S_wbar= average water saturation (dim)

S_wi = initial water saturation (dim)

P_i = Initial Reservoir Pressure (psia)

P_wf = Flowing wellbore pressure (psia)

h = Thickness

ρ_c= Coal Density (g/ccm)

P_L = Langmuir Pressure (psia)

V_L = Langmuir Volume (scf/ton)

The average water saturation is calculated using King approach shown below:

The above solution which is heavily documented in many sources uses the following in the denominator:

This is a limiting form of the following equation (where only the first two terms of e^x expansion series is used):

At higher pressures, the approximate solution can lead to substantial differences in water saturation, and therefore relative perm, and gas/water production rates. In AFA, the full form is used.

Where:

A = area (ft²)

B_w = water formation volume factor (ft³/scf or rbbl/bbl)

c_w = water compressibility (1/psia)

c_f = cleat formation compressibility (1/psia) - often much higher than conventional rock porosity

h = net pay (ft)

p = pressure (psia)

p_i = initial reservoir pressure (psia)

S_wbar= average water saturation (dim)

S_wi = initial water saturation (dim)

W_e = encroached water (bbls)

W_p = produced water (bbls)

φ_i = initial porosity (dim)

Reference

• King, G. R., Material-Balance Techniques for Coal-Seam and Devonian Shale Gas Reservoirs With Limited Water Influx, 1993, SPE Reservoir Engineering

• Clarkson, C. R., Unconventional Reservoir Rate-Transient Analysis: Volume I and II, 2021  Gulf Professional Publishing