Leverett J-Function in Petroleum Engineering using Excel Formulas

The Leverett J-function is a way of describing how fluids behave in porous rocks, such as those found in oil and gas reservoirs. It relates the pressure difference between two fluids, such as water and oil, to the properties of the rock and the fluids. The pressure difference is important because it affects how the fluids move and distribute in the rock.

The Leverett J-function is based on the idea that the rock can be modeled as a bundle of tiny tubes, called capillaries, that have different sizes and shapes. The fluids in the capillaries are affected by the surface tension, which is the force that makes the fluid surface act like a stretched elastic membrane. The surface tension causes the fluid to curve at the contact with the rock, forming an angle called the contact angle. The contact angle depends on how wettable the rock is, meaning how much the rock prefers one fluid over another.

The Leverett J-function combines the pressure difference, the surface tension, the contact angle, the permeability, and the porosity of the rock into a single dimensionless number. This number is constant for a given fluid saturation, which is the fraction of the rock space occupied by a fluid. The Leverett J-function can be used to compare the capillary behavior of different rocks with similar pore types and wettability, but with different permeability and porosity.

The Leverett J-function is useful for estimating the fluid distribution and recovery in a reservoir. It can also be used to convert the capillary pressure data obtained from laboratory experiments, such as mercury injection, to the reservoir conditions, such as oil/water or gas/oil systems. However, the Leverett J-function has some limitations and assumptions, such as ignoring the effects of gravity, temperature, and fluid composition. Therefore, it should be applied with caution and verified with field data.

The Leverett J-function, denoted as J, characterizes the efficiency of water displacement in an oil reservoir during water flooding. It is defined as the ratio of the fractional flow of water to the saturation of water in the porous medium. Mathematically, it is expressed as:

$J = \frac{{q_w}}{{S_w - S_{wi}}}$

Where:

$J$ is the Leverett J-function,
$q_w$ is the Darcy flow rate of water,
$S_w$ is the water saturation,
$S_{wi}$ is the initial water saturation.

Procedures:

Calculate Darcy flow rate ( $q_w$ ) using relevant reservoir parameters.
Determine the water saturation ( $S_w$ ) at a specific point in the reservoir.
Input the initial water saturation ( $S_{wi}$ ).
Use the Leverett J-function formula to calculate $J$ .

Consider an oil reservoir with the following parameters:

Darcy flow rate ( $q_w$ ): 5000 bbl/day
Water saturation ( $S_w$ ): 0.3
Initial water saturation ( $S_{wi}$ ): 0.1

Excel Calculation:

Create an Excel table with the following columns:
- Darcy Flow Rate ( $q_w$ )
- Water Saturation ( $S_w$ )
- Initial Water Saturation ( $S_{wi}$ )
- Leverett J-Function ( $J$ )
Input the values for $q_w$ , $S_w$ , and $S_{wi}$ .
In the “Leverett J-Function” column, use the formula:
```
=A2/(B2-C2)
```
Drag this formula down for each row.

MATLAB Comparison:

In MATLAB, use the following script:

    % Input parameters
    qw = 5000;     % Darcy flow rate (bbl/day)
    Sw = 0.3;      % Water saturation
    Swi = 0.1;     % Initial water saturation

    % Calculate Leverett J-Function
    J = qw / (Sw - Swi);

    % Display the result
    disp(['Leverett J-Function (MATLAB): ', num2str(J)]);

Results:

Excel Calculation: $J \approx 25,000$
MATLAB Calculation: $J \approx 25,000$

Leverett J-Function in Petroleum Engineering using Excel Formulas

Procedures:

Excel Calculation:

MATLAB Comparison:

Results:

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