Correction Factor Hammerlindl in Excel Formula

Correction factor Hammerlindl is a method of estimating the permeability of a reservoir rock based on the porosity and the pore size distribution. It is also known as the Kozeny-Carman equation or the specific surface equation.

The basic idea is that the flow of fluid through a porous medium depends on the size and shape of the pores, as well as the viscosity and pressure of the fluid. The correction factor Hammerlindl accounts for the variation of the pore geometry by using a parameter called the specific surface, which is the ratio of the surface area of the pores to the volume of the pores.

Basic Theory

The Correction Factor Hammerlindl is utilized to correct pressure drawdown and build-up data for finite conductivity effects in a wellbore. This factor is particularly relevant when analyzing well performance in heterogeneous reservoirs, where variations in permeability significantly impact fluid flow.

The formula for the Correction Factor Hammerlindl is given by:

Where:

is the Correction Factor Hammerlindl.
and are the final and initial times, respectively.
and are the final and initial dimensionless pressure drawdown or build-up, respectively.

Procedures for Implementation in Excel

Data Collection:
- Gather pressure drawdown or build-up data.
- Record initial and final times ( $t_0$ and $t_1$ ).
- Note the corresponding dimensionless pressure values ( $h_0$ and $h_1$ ).
Excel Formula:
- In an Excel spreadsheet, create columns for time ( $t$ ) and dimensionless pressure ( $h$ ).
- Use the formula $C_f = \frac{{\ln(t_1/t_0)}}{{\ln(h_1/h_0)}}$ to calculate the Correction Factor Hammerlindl.
Data Visualization:
- Construct a graph of the corrected pressure data using the Correction Factor Hammerlindl.

Application

Let’s consider a practical scenario:

$t_0 = 1$ hour
$t_1 = 10$ hours
$h_0 = 0.8$
$h_1 = 0.4$

Excel Implementation and Calculation

Excel Table:

Time (hours) Pressure

1 0.8

10 0.4
Excel Formula:In an Excel cell, use the formula $C_f = \frac{{\ln(10/1)}}{{\ln(0.4/0.8)}}$ to calculate the Correction Factor Hammerlindl.
Calculation: $C_f \approx -0.601$

Time (hours)	Pressure
1	0.8
10	0.4

MATLAB Comparison

For MATLAB users, the same Correction Factor Hammerlindl can be calculated using the following script:


      % MATLAB Script
      t0 = 1;
      t1 = 10;
      h0 = 0.8;
      h1 = 0.4;

      Cf = log(t1/t0) / log(h1/h0);

      % Display the result
      disp(['Correction Factor Hammerlindl (MATLAB): ', num2str(Cf)]);

Running this script will yield a result similar to the one obtained in Excel.