Generalized Form of Gas Material Balance

Introduction

For non-conventional reservoir several phenomena can happen in the reservoir. These phenomena can completely change the shape of …

Model

The produced gas can be calculate as:

where the remaining gas can be written as the gas absorbed in the reservoir matrix plus the the free gas present in the pore space at the current reservoir pressure. For the particular case, we use the Langmuir adsorption Isotherm, therefore the remaining gas is:

where:

is drainage area - [acres];

is reservoir thickness - [ft];

is dry, ash-free Langmuir volume constant - [scf/ton];

is average ash fraction - [-];

is average equilibrium moisture - [-];

is current reservoir pressure - [psia];

is Langmuir pressure constant - [psia];

is current average water saturation - [-];

is average bulk reservoir density - [g/cm³].

The initial gas in place is the sum of initial adsorbed gas in the reservoir matrix and and the free gas present in the pore space at the initial reservoir pressure:

Depending of the type of reservoir, the rock porosity can vary. Usually, the porosity changing is modelled as:

where:

is the rock volume compressibility - [psia^-1];

is the initial reservoir pressure - [psia];

is the initial porosity - [-];

Most of the authors simplify the model above of porosity changing using Taylor expansion, as show below:

however, this approximation can just be used if the pressure difference is in order of 100 to 200 psia, as it can be seen in the figure below:

For this reason, in the generic form of the material balance, the original model will be used.

The generic material balance also needs to account for water influx, water production and in some of type of reservoir, also needs to account for the volume of water present in the reservoir. Therefore, the remaining water volume in the reservoir can be written as:

Replacing the for initial reservoir water and analogous to remaining water, yields:

Therefore, the water saturation can be written as:

Considering a real gas las, the gas factor volume formation can be written as:

Replacing the above definition in the material balance for gas, we can define a general factor that accounts for compressibility factor , adsorption, and changing in saturation due to water influx, water production and original water present in the reservoir:

and for initial reservoir condition we can write :

in this case, the general equation for gas material balance assumes the same form of the conventional one:

Reference

John, S., 2011. Fundamentals of Coalbed Methane Reservoir Engineering. Penn Well Corporation, Tulsa.