Gas Solubility in Coalbed Methane Reservoirs in Excel

Gas solubility in coalbed methane reservoirs is the amount of gas that can dissolve in the water and coal matrix under certain pressure and temperature conditions. Gas solubility depends on several factors, such as the type and rank of coal, the composition and salinity of water, the pressure and temperature of the reservoir, and the composition of the gas. Gas solubility affects the gas storage and production mechanisms of coalbed methane reservoirs, as well as the estimation of gas reserves and recovery.

Basic Theory:

Gas solubility in CBM reservoirs is governed by Henry’s Law, which states that the amount of gas dissolved in a liquid is directly proportional to the partial pressure of that gas above the liquid. The solubility equation is given by:

$C = H \cdot P$

Where:

$C$ is the gas concentration in solution (mole/volume),
$H$ is Henry’s constant (mol/(L·atm)),
$P$ is the partial pressure of the gas in the reservoir (atm).

Procedures:

Determine Reservoir Conditions:
- Collect reservoir data including temperature ( $T$ ) and pressure ( $P_{reservoir}$ ).
Calculate Henry’s Constant:
- Utilize empirical correlations or laboratory data to determine $H$ based on the coal composition and temperature.
Define Partial Pressure of Gas:
- Estimate the partial pressure ( $P_{gas}$ ) using reservoir pressure and gas composition data.
Excel Formulas:
- In Excel, set up a table with columns for temperature, reservoir pressure, gas composition, and calculated solubility.
- Use the formula $C = H \cdot P_{gas}$ for each row to calculate gas solubility.

Explanation:

Let’s consider a scenario where the CBM reservoir has a temperature of 50°C, a reservoir pressure of 800 atm, and a gas composition of 90% methane and 10% nitrogen.

Scenario:

Temperature ( $T$ ): 50°C
Reservoir Pressure ( $P_{reservoir}$ ): 800 atm
Gas Composition: Methane (90%), Nitrogen (10%)

Calculation:

Determine Henry’s Constant ( $H$ ):
- Assume $H$ is 0.015 mol/(L·atm) based on empirical correlations.
Calculate Partial Pressure ( $P_{gas}$ ):
- $P_{gas} = P_{reservoir} \times \text{Gas Composition}$
- $P_{gas} = 800 \, \text{atm} \times 0.90$ (for methane)
- $P_{gas} = 720 \, \text{atm}$
Excel Calculation:
- In Excel, use the formula $C = H \times P_{gas}$ for each gas component.
- $C_{methane} = 0.015 \, \text{mol/(L·atm)} \times 720 \, \text{atm} = 10.8 \, \text{mol/L}$
- $C_{nitrogen} = 0.015 \, \text{mol/(L·atm)} \times 80 \, \text{atm} = 1.2 \, \text{mol/L}$