Klinkenberg Gas Effect in Excel

The Klinkenberg gas effect is a phenomenon that occurs when measuring the permeability of porous media to gases, especially in low-permeability rocks. It is caused by the slippage of gas molecules along the pore walls, which reduces the resistance to flow and increases the apparent permeability. The effect depends on the pressure, the molecular weight of the gas, and the size of the pores.

To correct for the Klinkenberg effect, one can either perform the permeability test at several pressures and extrapolate to infinite pressure, or use an empirical correlation to estimate the correction factor. The corrected permeability represents the permeability to a gas at infinite pressure or to a liquid that does not react with the rock. The Klinkenberg effect is important for petrophysical properties of gas reservoirs, as it affects the flow of gas in the subsurface.

The Klinkenberg effect arises due to the slip flow of gas molecules in the near-wellbore region. In traditional permeability calculations, Darcy’s law is applied, assuming that the flow is viscous and follows a linear relationship between pressure and flow rate. However, in low-permeability reservoirs, the Klinkenberg effect becomes significant, introducing a correction factor to account for the slippage of gas molecules.

The Klinkenberg correction factor (Ck) is defined as follows:

$Ck = 1 + \frac{b}{p}$

Where:

$Ck$ is the Klinkenberg correction factor.
$b$ is the Klinkenberg slip factor.
$p$ is the mean gas pressure.

Procedures in Excel:

Input Parameters:
- Create an Excel table with the following columns: Depth (ft), Permeability (md), Porosity, Temperature (°F), Gas Pressure (psia), and Klinkenberg Slip Factor ( $b$ ).
Calculate Klinkenberg Correction Factor:
- In a new column, use the formula $Ck = 1 + \frac{b}{p}$ to calculate the Klinkenberg correction factor.
Incorporate Correction in Permeability:
- Create a new column for corrected permeability using the formula $\text{Permeability}_{\text{corrected}} = \frac{\text{Permeability}}{Ck}$ .

Example Scenario:

Let’s consider a well with the following parameters:

Depth	Permeability	Porosity	Temperature	Gas Pressure	$b$	$Ck$	Permeability_corrected
5000	5	0.15	150	1000	0.0002	=1+B2/C2	=B2/D2

Now, let’s calculate the corrected permeability for the given scenario:

$Ck = 1 + \frac{0.0002}{1000} \approx 1.0000002$

$\text{Permeability}_{\text{corrected}} = \frac{5}{1.0000002} \approx 4.9999975 \, \text{md}$

MATLAB Comparison:

For comparison, you can use MATLAB to perform the same calculations using the Klinkenberg equation and check if the results match those obtained in Excel.

In MATLAB:


% Input parameters
b = 0.0002;
p = 1000;

% Calculate Klinkenberg correction factor
Ck = 1 + b/p;

% Calculate corrected permeability
Permeability_corrected = 5 / Ck;

disp(['Klinkenberg Correction Factor (Ck): ' num2str(Ck)]);
disp(['Permeability_corrected: ' num2str(Permeability_corrected) ' md']);

By comparing the MATLAB results with the Excel calculations, you can ensure the accuracy and reliability of your computations.

Result:

The corrected permeability for the given scenario is approximately $4.9999975$ md after considering the Klinkenberg gas effect. This example illustrates the importance of accounting for slip flow in low-permeability reservoirs for more accurate reservoir engineering calculations.

Procedures in Excel:

Example Scenario:

MATLAB Comparison:

Result:

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