Understanding Gas Expansion Factor and Its Calculation in Excel

Gas expansion factor is a measure of how much a gas expands when it is released from a high-pressure reservoir to a low-pressure surface condition. It is also called gas formation volume factor or gas deviation factor. It tells us how many units of reservoir volume are occupied by one unit of gas at standard conditions.

For example, if the gas expansion factor is 1000 RB/scf, it means that one standard cubic foot (scf) of gas at the surface occupies 1000 reservoir barrels (RB) of volume in the reservoir. This is because the gas molecules are more tightly packed in the reservoir due to the high pressure, and they spread out more when the pressure is reduced at the surface.

The gas expansion factor depends on the pressure, temperature, and composition of the gas. It can be calculated using the real gas equation, which relates these variables to the gas compressibility factor. The gas compressibility factor is a correction factor that accounts for the deviation of real gases from ideal gas behavior. It can be determined experimentally or estimated from empirical correlations.

The gas expansion factor is important for estimating the gas reserves and production rates in a reservoir. It also affects the density and viscosity of the gas, which influence the flow behavior and pressure drop in the pipes and wells.

Basic Theory

The gas expansion factor is derived from the ideal gas law, which states:

$PV = nRT$

Where:

$P$ is the pressure,
$V$ is the volume,
$n$ is the number of moles,
$R$ is the ideal gas constant, and
$T$ is the temperature.

The gas expansion factor ( $GEF$ ) can be expressed as:

$GEF = \frac{V_{\text{actual}}}{V_{\text{standard}}}$

This factor allows us to convert gas volumes measured under different conditions to a standardized set of conditions,
typically defined as 60°F (15.6°C) and 14.696 psia (1 atm).

Procedures for Gas Expansion Factor Calculation in Excel

Step 1: Input Parameters

Create an Excel table and input the following parameters:

Column A: Gas volume at actual conditions ( $V_{\text{actual}}$ ) in cubic feet.
Column B: Actual pressure ( $P_{\text{actual}}$ ) in psia.
Column C: Actual temperature ( $T_{\text{actual}}$ ) in Rankine.

Step 2: Standard Conditions

Define standard conditions in your Excel sheet:

Standard Pressure ( $P_{\text{std}}$ ): 14.696 psia.
Standard Temperature ( $T_{\text{std}}$ ): 520.67 Rankine (60°F).

Step 3: Gas Expansion Factor Calculation

In a new column, use the following Excel formula for gas expansion factor:

$\text{GEF} = \frac{P_{\text{std}} \times T_{\text{actual}}}{P_{\text{actual}} \times T_{\text{std}}}$

Example

Let’s consider the following scenario:

$V_{\text{actual}} = 500$ cubic feet
$P_{\text{actual}} = 100$ psia
$T_{\text{actual}} = 600$ Rankine

Calculation and Results

Apply the gas expansion factor formula to calculate $GEF$ :

$GEF = \frac{14.696 \times 600}{100 \times 520.67}$

$GEF \approx 1.788$

This means that the gas volume at standard conditions would be approximately 1.788 times the volume at the actual
conditions.

MATLAB Comparison

To solve the same problem in MATLAB, you can use the following code:


% Input parameters
V_actual = 500; % cubic feet
P_actual = 100; % psia
T_actual = 600; % Rankine

% Standard conditions
P_std = 14.696; % psia
T_std = 520.67; % Rankine

% Gas expansion factor calculation
GEF = (P_std * T_actual) / (P_actual * T_std);

disp(['Gas Expansion Factor (MATLAB): ', num2str(GEF)]);

Compare the MATLAB result with the Excel result to ensure accuracy.