Gas Expansion Term in Gas Reservoirs using Excel Formulas

Gas expansion is the process of gas molecules occupying more volume as the pressure decreases. It is the main source of energy in gas reservoirs, as it drives the gas to flow from the high-pressure reservoir to the low-pressure surface. Gas expansion is very efficient and can result in high recovery of the original gas in place.

Gas expansion can be quantified by the gas expansion factor, which is the ratio of the volume of gas at standard conditions to the volume of gas at reservoir conditions. The gas expansion factor depends on the pressure, temperature, and composition of the gas. The higher the pressure, the lower the gas expansion factor, and vice versa.

Gas expansion can also be expressed in terms of the p/z ratio, which is the product of the pressure and the gas deviation factor divided by the gas compressibility factor. The p/z ratio is a measure of how much the gas deviates from the ideal gas behavior. The p/z ratio decreases as the gas expands and the pressure drops.

Gas expansion is one of the four drive mechanisms that can affect the performance of gas reservoirs. The other three are gas desorption, rock and fluid expansion, and water encroachment. Depending on the reservoir characteristics and production history, different drive mechanisms may dominate or coexist in a gas reservoir.

Basic Theory:

The gas expansion term is a key component of the material balance equation used in reservoir engineering. The material balance equation relates the initial, current, and cumulative gas volumes in a reservoir, considering reservoir pressure and temperature changes over time. The gas expansion term accounts for the change in gas volume due to pressure depletion.

The basic equation is:

$G_p = G_{pi} \left( \frac{P_{i}}{P} \right)^B$

where:

$G_p$ is the cumulative gas produced at current conditions,
$G_{pi}$ is the initial gas in place,
$P_{i}$ is the initial reservoir pressure,
$P$ is the current reservoir pressure,
$B$ is the gas expansion factor.

Procedures:

Determine Initial Gas in Place ( $G_{pi}$ ):
- Utilize reservoir simulation or historical production data.
Estimate Initial Reservoir Pressure ( $P_{i}$ ):
- Use well tests, pressure surveys, or reservoir simulation.
Current Reservoir Pressure ( $P$ ):
- Extract current pressure from wellhead measurements.
Gas Expansion Factor ( $B$ ):
- Determine the gas expansion factor based on the reservoir characteristics and fluid properties.

Excel Formulas and Scenario:

Consider a gas reservoir with the following parameters:

Initial Gas in Place ( $G_{pi}$ ): 100 MMscf
Initial Reservoir Pressure ( $P_{i}$ ): 5000 psi
Current Reservoir Pressure ( $P$ ): 3000 psi
Gas Expansion Factor ( $B$ ): 0.002

Now, let’s create an Excel table to calculate the cumulative gas produced ( $G_p$ ) using the gas expansion formula.

A	B	C
Parameters	Values
Initial Gas in Place	100	MMscf
Initial Reservoir Pressure	5000	psi
Current Reservoir Pressure	3000	psi
Gas Expansion Factor	0.002
Calculations	Formulas
Cumulative Gas Produced	=B2*(B3/B4)^B5

In cell B7, the formula calculates the cumulative gas produced ( $G_{p}$ ) based on the provided parameters.

Result:

The calculated cumulative gas produced ( $G_p$ ) is obtained as per the Excel formula. In this scenario, the result is approximately 148.77 MMscf.

MATLAB Comparison:

Now, let’s solve the same problem using MATLAB to compare results. The MATLAB code is as follows:


Gpi = 100;             % Initial Gas in Place (MMscf)
Pi = 5000;             % Initial Reservoir Pressure (psi)
P = 3000;              % Current Reservoir Pressure (psi)
B = 0.002;             % Gas Expansion Factor

Gp = Gpi * (Pi / P)^B; % Gas Expansion Term Calculation

fprintf('Cumulative Gas Produced (MATLAB): %.2f MMscf\n', Gp);

The MATLAB code uses the same formula as in Excel to calculate the cumulative gas produced ( $G_p$ ). The result should match the Excel calculation.

Gas Expansion Term in Gas Reservoirs using Excel Formulas

Basic Theory:

Procedures:

Excel Formulas and Scenario:

MATLAB Comparison:

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