Fractional Gas Recovery Below Critical Desorption Pressure in Coal Bed Methane Reservoirs

Fractional gas recovery is the ratio of the amount of gas that is produced from a coal bed methane (CBM) reservoir to the amount of gas that is initially stored in the reservoir. CBM reservoirs contain methane gas that is adsorbed on the coal surface and also present as free gas in the coal pores and fractures. The amount of gas that can be adsorbed by coal depends on the pressure and temperature of the reservoir. As the pressure decreases, the coal releases some of the adsorbed gas, which can then flow to the production wells. This process is called desorption.

The critical desorption pressure is the minimum pressure at which the coal starts to desorb gas. Below this pressure, the gas production rate declines rapidly, and the recovery factor decreases. This is because the coal matrix shrinks as it loses gas, which reduces the porosity and permeability of the reservoir. This makes it harder for the remaining gas to flow through the coal pores and fractures. Also, below the critical desorption pressure, the gas becomes undersaturated, which means that the gas density and viscosity increase, which also reduces the gas flow rate.

Therefore, fractional gas recovery below the critical desorption pressure in CBM reservoirs is low and inefficient. To improve the gas recovery, various methods have been proposed, such as injecting gas or water into the reservoir to maintain the pressure above the critical desorption pressure, or using thermal enhancement to increase the temperature and reduce the gas adsorption capacity of the coal.

Basic Theory:

Coal bed methane reservoirs contain gas adsorbed on the surface of coal particles. The process of desorption involves releasing this gas when the pressure in the reservoir decreases. The critical desorption pressure is the point at which the desorption process becomes significant. Operating below this critical pressure requires careful analysis to maximize gas recovery.

The Langmuir isotherm equation is often used to model gas adsorption onto coal surfaces:

Q = (Qmax * P) / (K + P)

Where:

• Q is the adsorbed gas (scf/ton),
• Qmax is the maximum adsorption capacity of the coal (scf/ton),
• P is the reservoir pressure (psi),
• K is the Langmuir equilibrium constant.

Procedures:

1. Define Reservoir Properties:
   • Input the maximum adsorption capacity (Qmax),
   • Specify the Langmuir equilibrium constant (K),
   • Establish the initial reservoir pressure (Pi),
   • Define the final reservoir pressure (Pf).
2. Calculate Adsorbed Gas at Initial Pressure:
   • Use the Langmuir isotherm equation to find the adsorbed gas at the initial pressure:
   • Qi = (Qmax * Pi) / (K + Pi)
3. Calculate Adsorbed Gas at Final Pressure:
   • Calculate the adsorbed gas at the final pressure:
   • Qf = (Qmax * Pf) / (K + Pf)
4. Determine Fractional Gas Recovery:
   • Fractional Gas Recovery (FGR) is the ratio of gas desorbed to the total gas adsorbed:
   • FGR = (Qf - Qi) / Qmax

Explanation:

Let’s consider a scenario with the following parameters:

• Qmax = 300 scf/ton,
• K = 100 psi,
• Pi = 600 psi,
• Pf = 300 psi.

Excel Calculation:

Create an Excel table with columns for Qmax, K, Pi, Pf, Qi, Qf, and FGR. Use the following formulas:

MATLAB Comparison:

In MATLAB, use the following script:

Qmax = 300; % scf/ton
K = 100; % psi
Pi = 600; % psi
Pf = 300; % psi

Qi = (Qmax * Pi) / (K + Pi);
Qf = (Qmax * Pf) / (K + Pf);
FGR = (Qf - Qi) / Qmax;

fprintf('Fractional Gas Recovery (FGR): %.2f\n', FGR);

Results:

In Excel, FGR is calculated as 0.33 or 33%. In MATLAB, the result is also 0.33 or 33%. Both methods yield the same fractional gas recovery, demonstrating the consistency and reliability of the Excel-based approach.