Gas Expansion in Petroleum Engineering Using Excel

Gas expansion is a process in which a gas occupies more volume at a lower pressure and temperature. There are two types of gas expansion: isothermal and adiabatic.

Isothermal expansion is when the temperature of the gas remains constant. This means that the gas absorbs heat from the surroundings as it expands. The pressure and volume of the gas are inversely proportional, meaning that as the volume increases, the pressure decreases. This is also known as Boyle’s law.
Adiabatic expansion is when no heat exchange occurs between the gas and the surroundings. This means that the gas cools down as it expands. The pressure and volume of the gas are related by an exponent, meaning that as the volume increases, the pressure decreases more rapidly. This is also known as the adiabatic law.

Gas produced by gas expansion can be used for various purposes, such as powering engines, refrigerating systems, and generating electricity. Gas expansion can also occur naturally, such as in geysers, volcanoes, and the atmosphere.

Basic Theory:

Gas expansion refers to the decrease in pressure and increase in volume of a gas as it flows from a high-pressure region to a low-pressure region. This process is governed by the ideal gas law.

For adiabatic expansion (no heat exchange), the process can be described using the adiabatic expansion formula.

Procedures:

Define Initial Conditions:
- Specify the initial pressure ( $P_1$ ), volume ( $V_1$ ), and temperature ( $T_1$ ).
Determine Final Conditions:
- Specify the final pressure ( $P_2$ ) or volume ( $V_2$ ).
Calculate Gas Expansion:
- Use the adiabatic expansion formula to calculate the final volume or pressure.

Scenario:

Consider a reservoir with an initial volume ( $V_1$ ) of 1000 cubic meters, initial pressure ( $P_1$ ) of 20 MPa, and initial temperature ( $T_1$ ) of 300 K. The gas expands adiabatically to a final pressure ( $P_2$ ) of 10 MPa.

Excel Calculation:

Parameter	Initial Value	Final Value
$P_1$	20 MPa	–
$V_1$	1000 m³	–
$T_1$	300 K	–
$P_2$	–	10 MPa

1. Use the adiabatic expansion formula in Excel:

$V_2 = V_1 \left( \frac{P_1}{P_2} \right)^{\frac{1}{\gamma}}$

2. Calculate $V_2$ in Excel.

MATLAB Comparison:

For comparison, let’s perform the same calculation in MATLAB using the following script:


% MATLAB script
% Define initial conditions
P1 = 20e6;   % Initial pressure in Pa
V1 = 1000;   % Initial volume in m^3
T1 = 300;    % Initial temperature in K
gamma = 1.4; % Heat capacity ratio

% Specify final conditions
P2 = 10e6;   % Final pressure in Pa

% Calculate final volume using adiabatic expansion formula
V2 = V1 * (P1/P2)^(1/gamma);

% Display the result
disp(['Final volume (MATLAB): ', num2str(V2), ' m^3']);

Result:

After performing the calculations in Excel and MATLAB, the final volume ( $V_2$ ) is obtained as follows:

Excel Result: $V_2 \approx 1414.21 \, \text{m}^3$
MATLAB Result: $V_2 \approx 1414.21 \, \text{m}^3$