Interporosity Flow Coefficient in Petroleum Engineering Using Excel

Interporosity flow coefficient is a parameter that describes how easily fluid flows from the matrix to the fractures in a dual-porosity reservoir. A dual-porosity reservoir is composed of two types of porous media: matrix and fracture. The matrix has low permeability but large storage capacity, while the fractures have high permeability but low storage capacity. Fluid production from the reservoir comes from the matrix, to the fracture, and then to the wellbore.

The interporosity flow coefficient depends on the permeability of the matrix and the fractures, as well as the geometry of the system. It is usually in the range of 10^-4 to 10^-8 and is always used in conjunction with the storativity ratio, which is the ratio of fluid stored in the matrix to the fluid stored in the fractures. Lower values of the interporosity flow coefficient indicate lower fluid transfer between the matrix and the fracture, which means the matrix is more isolated from the fracture network. Higher values of the interporosity flow coefficient imply higher fluid transfer between the matrix and the fracture, which means the matrix is more connected to the fracture network.

The interporosity flow coefficient affects the pressure behavior and the productivity of the well in a dual-porosity reservoir. It determines the shape and the duration of the transition period between the early-time linear flow and the late-time pseudosteady-state flow. It also influences the slope and the intercept of the semilog plot of pressure and pressure derivative data. The interporosity flow coefficient can be estimated from well test analysis using analytical or numerical models that account for the dual-porosity nature of the reservoir.

The interporosity flow coefficient represents the connectivity between the matrix and fracture porosities in a reservoir. In a dual-porosity system, the matrix represents the rock where fluid is stored, and fractures act as conduits for fluid flow. The interporosity flow coefficient helps quantify the ease with which fluid moves between these two types of pores.

The basic formula for calculating the interporosity flow coefficient (α) is:

$\alpha = \frac{K_f}{K_m}$

where:

$\alpha$ is the interporosity flow coefficient,
$K_f$ is the fracture permeability, and
$K_m$ is the matrix permeability.

Procedures

Gather Data: Collect relevant data, including fracture permeability ( $K_f$ ) and matrix permeability ( $K_m$ ).
Calculate Interporosity Flow Coefficient: Use the formula $\alpha = \frac{K_f}{K_m}$ to find the interporosity flow coefficient.
Scenario Example: For a comprehensive understanding, let’s consider a scenario with real numbers.

Example

Consider a reservoir with the following properties:

Fracture Permeability ( $K_f$ ): 100 mD (millidarcies)
Matrix Permeability ( $K_m$ ): 10 mD

Using the formula $\alpha = \frac{K_f}{K_m}$ , we can calculate the interporosity flow coefficient.

Excel Calculation

Let’s set up an Excel table to perform the calculation.

Parameters	Values
Fracture Permeability	100
Matrix Permeability	10
Interporosity Coefficient	=B2/B3

In Excel, the formula for the interporosity coefficient cell (C3) is simply =B2/B3, where B2 is the fracture permeability and B3 is the matrix permeability.

Excel Table

Parameters	Values
Fracture Permeability	100
Matrix Permeability	10
Interporosity Coefficient	10

MATLAB Comparison

For comparison, let’s solve the problem in MATLAB as well.


            % MATLAB Code
            Kf = 100; % Fracture permeability in mD
            Km = 10;  % Matrix permeability in mD

            alpha = Kf / Km; % Interporosity flow coefficient

            % Display the result
            fprintf('Interporosity Flow Coefficient (alpha): %.2f\n', alpha);

The MATLAB code calculates the interporosity flow coefficient using the same formula.

Result

The interporosity flow coefficient (alpha) for the given scenario is 10. This value indicates the relative ease with which fluid can flow between the fractures and the matrix in the reservoir.