Cumulative Effective Compressibility (Fetkovich) in Excel

Cumulative effective compressibility Fetkovich is a term that describes how much the volume of a gas reservoir changes due to pressure changes and water influx. It depends on four factors: the compressibility of the rock, the compressibility of the water, the solubility of the gas, and the total amount of water associated with the gas reservoir. The more compressible the rock and water are, the more the reservoir volume will shrink when the pressure drops. The more soluble the gas is, the more the reservoir volume will expand when the pressure drops. The more water is associated with the gas reservoir, the more the reservoir volume will decrease due to water influx. Cumulative effective compressibility Fetkovich is used to calculate the original gas in place and the remaining recoverable reserves from pressure and production data. It helps to linearize the plot of pressure divided by gas compressibility factor versus cumulative gas production, which is often curved for high pressure gas reservoirs.

Basic Theory:

The Fetkovich equation for cumulative effective compressibility (Ceff) is given by:

$C_{eff} = \frac{1}{\ln \left( \frac{r_e}{r_w} \right) + S_{wi}}$

Where:

$C_{eff}$ is the cumulative effective compressibility,
$r_e$ is the drainage radius,
$r_w$ is the wellbore radius,
$S_{wi}$ is the initial water saturation.

Procedures:

Determine the reservoir parameters: $r_e$ , $r_w$ , and $S_{wi}$ .
Substitute these values into the Fetkovich equation to calculate $C_{eff}$ .
Use the calculated $C_{eff}$ for reservoir performance predictions and optimization.

Explanation:

The cumulative effective compressibility reflects the overall compressibility of the reservoir. It is particularly useful in understanding the changes in reservoir pressure over time and optimizing production strategies…

Scenario:

Let’s consider a reservoir with the following parameters:

$r_e = 500$ ft,
$r_w = 0.25$ ft,
$S_{wi} = 0.25$ .

Calculation in Excel:

Parameter	Value
$r_e$	500
$r_w$	0.25
$S_{wi}$	0.25

In Excel, use the following formula to calculate $C_{eff}$ :

$C_{eff} = \frac{1}{\ln \left( \frac{500}{0.25} \right) + 0.25}$

…

MATLAB Comparison:

In MATLAB, the calculation can be performed using the same formula for comparison purposes.


    re = 500;
    rw = 0.25;
    Swi = 0.25;

    Ceff = 1 / (log(re / rw) + Swi);

    disp(['Cumulative Effective Compressibility (Fetkovich) in MATLAB: ' num2str(Ceff)]);

Result:

The calculated cumulative effective compressibility ( $C_{eff}$ ) for the given scenario is approximately 0.1275.