Injectivity Index in Petroleum Engineering Using Excel

The Injectivity Index is a measure of how easily a fluid can be injected into a reservoir. It is calculated by dividing the injection rate by the pressure drop across the injection interval. A higher Injectivity Index means that the injection process is more efficient and requires less pressure to inject the same amount of fluid. The Injectivity Index depends on the properties of the reservoir, such as permeability, thickness, and size, as well as the properties of the injected fluid, such as viscosity and density.

The Injectivity Index can be used to characterize the performance of different injection methods, such as water flooding, gas injection, or CO2 injection. It can also be used to monitor the changes in reservoir quality over time, such as the formation of fractures, the reduction of permeability, or the increase of pressure. The Injectivity Index can help optimize the injection strategy and maximize the oil recovery.

The injectivity index (II) is expressed mathematically as:

Where:

• is the injectivity index,
• is the injected fluid volume (measured in barrels per day, bbl/day), and
• is the pressure drop across the wellbore (measured in pounds per square inch, psi).

Procedures to Calculate Injectivity Index in Excel:

1. Collect Data: Gather data on the injected fluid volume () and the pressure drop across the wellbore ().
2. Create an Excel Table: Open Microsoft Excel and organize your data in a table with appropriate column headers, such as “Day,” “Injected Volume (bbl/day),” and “Pressure Drop (psi).”
3. Insert Formulas: In a new column, insert the formula for injectivity index ():

      

4. Calculate Results: Apply the formula to each row of data to obtain the injectivity index for each corresponding day.

Explanation:

Let’s consider a scenario with the following data for a water injection well:

• Day 1:
  • Injected Volume (): 500 bbl/day
  • Pressure Drop (): 150 psi
• Day 2:
  • Injected Volume (): 600 bbl/day
  • Pressure Drop (): 180 psi

Excel Calculation:

Now, let’s perform the calculations:

• Day 1:
• Day 2:

Result: The injectivity index remains constant at 3.33 bbl/day/psi for both days in our scenario.

MATLAB Comparison:

In MATLAB, the injectivity index can be calculated using similar formulas. Here’s a sample MATLAB code snippet for our scenario:

% Data
Q = [500; 600]; % Injected Volume (bbl/day)
DeltaP = [150; 180]; % Pressure Drop (psi)

% Calculating Injectivity Index
II = Q ./ DeltaP;

% Displaying Results
disp('Injectivity Index for Each Day:');
disp(II);