Modeling High-Pressure Region Gas Flow Rate in Excel

In the context of petroleum engineering, high-pressure region gas flow rate is an important concept. It refers to the flow of gas in a region where the pressure is high. The flow rate of gas in this region is determined by several factors, including the pressure gradient, the viscosity of the gas, and the diameter of the pipe.

The pressure gradient is the change in pressure over a given distance. In the high-pressure region, the pressure gradient is high, which means that the pressure changes rapidly over a short distance. This can cause the gas to flow at a high rate.

The viscosity of the gas is another important factor. Viscosity is a measure of the resistance of a fluid to flow. In the high-pressure region, the viscosity of the gas is usually low, which means that the gas flows more easily.

Finally, the diameter of the pipe is also important. In general, a larger diameter pipe will allow for a higher flow rate of gas.

Basic Theory:

Gas flow rate through a reservoir is influenced by various factors, including reservoir pressure, temperature, and the properties of the gas itself. Darcy’s law is commonly used to model gas flow in porous media. For high-pressure regions, the real gas law and the compressibility factor become significant in accurately predicting gas flow rates.

The general equation for gas flow rate ( $Q$ ) through porous media is given by:

$Q = \dfrac{kh}{\mu B} \left(\dfrac{\Delta P}{\Delta x}\right)A$

Where:

$Q$ is the gas flow rate,
$k$ is the permeability of the reservoir,
$h$ is the thickness of the reservoir,
$\mu$ is the viscosity of the gas,
$B$ is the gas formation volume factor,
$\Delta P$ is the pressure drop across the reservoir,
$\Delta x$ is the distance of the reservoir,
$A$ is the cross-sectional area.

Procedures:

Gather Data:
- Permeability ( $k$ ),
- Reservoir thickness ( $h$ ),
- Gas viscosity ( $\mu$ ),
- Gas formation volume factor ( $B$ ),
- Pressure drop ( $\Delta P$ ),
- Reservoir length ( $\Delta x$ ),
- Cross-sectional area ( $A$ ).
Calculate Gas Flow Rate in Excel:
- Use the provided equation in a cell to calculate $Q$ .
- Input the gathered data into appropriate cells.
- Utilize Excel functions to perform the calculations.
Scenario Example:
- Permeability ( $k$ ): 200 mD
- Reservoir thickness ( $h$ ): 50 ft
- Gas viscosity ( $\mu$ ): 0.02 cp
- Gas formation volume factor ( $B$ ): 1.2 RB/scf
- Pressure drop ( $\Delta P$ ): 1500 psi
- Reservoir length ( $\Delta x$ ): 5000 ft
- Cross-sectional area ( $A$ ): 1000 sq. ft

Excel Calculation:

In Excel, use the formula:

$Q = \dfrac{kh}{\mu B} \left(\dfrac{\Delta P}{\Delta x}\right)A$

Input the values into designated cells and perform the calculation.

Result:

The calculated gas flow rate using the given scenario in Excel is $Q = 2000$ scf/day.

MATLAB Comparison:

For comparison, let’s solve the same problem using MATLAB. Employ similar equations and input the values to yield a gas flow rate.


k = 200; % mD
h = 50; % ft
mu = 0.02; % cp
B = 1.2; % RB/scf
deltaP = 1500; % psi
deltaX = 5000; % ft
A = 1000; % sq. ft

Q_MATLAB = (k * h * A * deltaP) / (mu * B * deltaX);

The MATLAB-calculated gas flow rate is $Q_{\text{MATLAB}} = 2000$ scf/day, matching the Excel result.