Gas Cap Shrinkage Analysis in Petroleum Engineering using Microsoft Excel

Gas cap shrinkage is the reduction in volume of the gas cap in a reservoir as the pressure drops below the bubble point. The bubble point is the pressure at which gas bubbles start to form in the oil. When this happens, some of the gas that was dissolved in the oil escapes and joins the gas cap. This causes the oil to shrink and the gas cap to expand. However, the expansion of the gas cap is not enough to compensate for the loss of gas in the oil, so the total volume of the gas cap decreases. This is called gas cap shrinkage.

Gas cap shrinkage affects the recovery of oil from the reservoir, because it reduces the pressure and the drive energy of the gas cap. The gas cap is one of the natural forces that can push the oil towards the wellbore. If the gas cap shrinks too much, the oil production will decline. To prevent this, some methods are used to maintain the pressure and the size of the gas cap, such as gas reinjection or water injection.

Basic Theory

Gas cap shrinkage occurs when the gas in the reservoir undergoes pressure depletion, leading to a reduction in its volume. This phenomenon is often associated with the production of oil from the reservoir. As oil is extracted, the pressure in the reservoir decreases, causing the gas in the gas cap to expand and displace some of the oil. This expansion can result in a decrease in gas volume, known as gas cap shrinkage.

Procedures

Step 1: Gather Reservoir Data

Start by collecting essential reservoir data, including initial gas and oil volumes, reservoir pressure, and other relevant parameters.

Step 2: Apply Gas Cap Shrinkage Formula

The basic formula for gas cap shrinkage is:

$V_{\text{final}} = V_{\text{initial}} \times \left( \frac{P_{\text{final}}}{P_{\text{initial}}} \right)$

where:

$V_{\text{final}}$ is the final gas volume,
$V_{\text{initial}}$ is the initial gas volume,
$P_{\text{final}}$ is the final reservoir pressure,
$P_{\text{initial}}$ is the initial reservoir pressure.

Step 3: Create Excel Spreadsheet

Build an Excel spreadsheet with columns for initial gas volume, initial pressure, final pressure, and the calculated final gas volume using the formula.

Step 4: Enter Reservoir Data

Input the gathered reservoir data into the Excel spreadsheet.

Step 5: Apply Gas Cap Shrinkage Formula in Excel

In the final gas volume column, use the Excel formula to calculate the final gas volume based on the applied gas cap shrinkage formula.

Step 6: Scenario Example

Let’s consider a scenario:

Initial gas volume ( $V_{\text{initial}}$ ): 10,000 cubic meters
Initial reservoir pressure ( $P_{\text{initial}}$ ): 2,000 psi
Final reservoir pressure ( $P_{\text{final}}$ ): 1,500 psi

Step 7: Excel Calculation

Apply the gas cap shrinkage formula in Excel:

$V_{\text{final}} = 10,000 \times \left( \frac{1,500}{2,000} \right) = 7,500 \text{ cubic meters}$

Results

The Excel calculation yields a final gas volume of 7,500 cubic meters for the given scenario.

MATLAB Comparison

To compare results, let’s solve the same problem in MATLAB using similar calculations. Here’s a simple MATLAB script:


        % MATLAB Gas Cap Shrinkage Calculation

        V_initial = 10000;          % Initial gas volume (cubic meters)
        P_initial = 2000;           % Initial reservoir pressure (psi)
        P_final = 1500;             % Final reservoir pressure (psi)

        V_final = V_initial * (P_final / P_initial);
        disp(['MATLAB Result - Final Gas Volume: ' num2str(V_final) ' cubic meters']);

Run this script in MATLAB, and it should display the MATLAB result for the final gas volume.