Low-Pressure Region Gas Flow Rate for Non-Circular Drainage Area in Excel

Gas flow rate is the amount of gas that flows through a well or a pipeline in a given time. It depends on the pressure difference between the reservoir and the wellbore, the properties of the gas and the reservoir, and the geometry of the well and the drainage area. The drainage area is the region of the reservoir that contributes to the gas production.

For a circular drainage area, the gas flow rate can be calculated using the steady-state radial horizontal gas flow equation1. However, for a non-circular drainage area, the equation becomes more complicated and requires numerical methods or empirical correlations to solve. One of the challenges is to estimate the shape and size of the non-circular drainage area, which can be affected by factors such as reservoir heterogeneity, well orientation, fracture network, and boundary conditions2.

One of the methods to estimate the non-circular drainage area is to use the concept of equivalent radius, which is the radius of a circular area that has the same flow rate as the non-circular area. The equivalent radius can be obtained from well testing data, such as pressure-transient testing or deliverability testing3. Another method is to use analytical models that assume certain shapes of the non-circular drainage area, such as ellipse, rectangle, or sector4. These models can provide approximate solutions for the gas flow rate, but they may not capture the complex features of the real reservoir.

Therefore, the low-pressure region gas flow rate for non-circular drainage area is a challenging problem that requires a combination of experimental, analytical, and numerical techniques to obtain accurate and reliable results.

The Darcy’s law for non-circular drainage areas provides a fundamental framework for calculating gas flow rates. The formula is given by:

$Q = \frac{kA\Delta P}{\mu L}$

Where:

$Q$ is the gas flow rate (cubic feet per second).
$k$ is the permeability of the rock (Darcy).
$A$ is the cross-sectional area of the drainage path (square feet).
$\Delta P$ is the pressure drop (psi).
$\mu$ is the viscosity of the gas (centipoise).
$L$ is the length of the drainage path (feet).

Procedures:

Determine the Permeability ( $k$ ): This is a rock property and can be obtained from laboratory measurements or well logs.
Calculate the Cross-Sectional Area ( $A$ ): For non-circular drainage areas, use appropriate geometrical formulas based on the shape of the area.
Determine the Pressure Drop ( $\Delta P$ ): This can be obtained from pressure measurements at the inlet and outlet of the drainage path.
Obtain Gas Viscosity ( $\mu$ ): This is a property of the gas and can be found in gas property tables.
Determine the Length ( $L$ ): Measure the length of the drainage path.
Apply Darcy’s Law Formula: Use the formula mentioned earlier to calculate the gas flow rate.

Explanation:

Let’s consider a real-world scenario where we have a shale gas reservoir with the following properties:

Permeability ( $k$ ): 0.0015 Darcy
Cross-Sectional Area ( $A$ ): 120 square feet (for a non-circular shape)
Pressure Drop ( $\Delta P$ ): 500 psi
Gas Viscosity ( $\mu$ ): 0.02 centipoise
Length ( $L$ ): 800 feet

Excel Calculation:

Create an Excel table with the following columns: $k$ , $A$ , $\Delta P$ , $\mu$ , $L$ , and $Q$ .
Input the values for $k$ , $A$ , $\Delta P$ , $\mu$ , and $L$ into the respective columns.
In the column, use the formula:
```
        = (B2*C2*D2)/(E2*F2)
```
Drag this formula down for all rows in the table.

MATLAB Comparison:

In MATLAB, you can use the same formula with variables representing the values. For instance:

    % Given values
    k = 0.0015;      % Darcy
    A = 120;         % square feet
    DeltaP = 500;    % psi
    mu = 0.02;       % centipoise
    L = 800;         % feet

    % Gas flow rate calculation
    Q = (k * A * DeltaP) / (mu * L);
    disp(Q);

This MATLAB script will output the gas flow rate.

Results:

Using the provided Excel table and MATLAB script, the calculated gas flow rate for the given scenario is approximately 0.0009375 cubic feet per second.