Incremental cumulative oil production is the amount of oil that is added to the total production by a certain action, such as infill drilling or enhanced oil recovery1. In undersaturated reservoirs, the reservoir pressure is higher than the bubble point pressure, which means that the oil does not contain any free gas. Therefore, the oil production is mainly driven by the expansion of the oil and the dissolved gas, as well as the water influx from the aquifer.
One way to estimate the incremental cumulative oil production in undersaturated reservoirs is to use the material balance equation, which relates the change in reservoir pressure to the change in oil-in-place and the production of oil, gas, and water. Another way is to use numerical simulation models, which can account for the complex flow behavior and interactions of the fluids and the rock in the reservoir. Both methods require accurate data and assumptions about the reservoir properties and the production operations.
In undersaturated reservoirs, the primary recovery mechanism involves the natural energy of the reservoir pushing oil towards the wellbore. Incremental cumulative oil production refers to the additional oil produced over time as a result of various recovery methods, such as water injection or gas injection.
The basic formula for calculating incremental cumulative oil production ( 
) at a given time ( 
) is:
![\[ Np_i = Np_{i-1} + \Delta Np_i \]](https://excelcalculations.refrigeratordiagrams.com/wp-content/ql-cache/quicklatex.com-10226b172b048155ce7ddff211e74f5d_l3.svg "Rendered by QuickLaTeX.com")
Where:
is the cumulative oil production at the previous time period.
is the incremental oil production during the current time period.
Procedures:
- Data Collection:
- Gather historical production data, including cumulative oil production (
) at different time intervals. - Identify the time period for which you want to calculate incremental cumulative oil production.
- Gather historical production data, including cumulative oil production (
- Excel Formulas:
- Create an Excel table with columns for time (
), cumulative oil production (), and incremental cumulative oil production (
). - Use the formula
to calculate incremental cumulative oil production for each time period.
- Create an Excel table with columns for time (
- Scenario Example:
- Let’s consider a scenario with the following data:
(initial cumulative oil production)
barrels at 
year
barrels at 
years
- Let’s consider a scenario with the following data:
- Excel Calculation:
- Use the formula to calculate incremental cumulative oil production for each time period.
- Use the formula
Excel Table:
| Time (Years) | Cumulative Oil Production () |
Incremental Cumulative Oil Production () |
|---|---|---|
| 0 | 0 | – |
| 1 | 1000 | 1000 |
| 2 | 2500 | 1500 |
MATLAB Comparison:
While Excel is a powerful tool, MATLAB offers additional capabilities for complex simulations. In MATLAB, the same calculation can be performed using a script or function with array operations.
% MATLAB Script
t = [0, 1, 2]; % Time array
Np = [0, 1000, 2500]; % Cumulative oil production array
% Calculate incremental cumulative oil production
DeltaNp = diff(Np);
% Display results
disp('Time (Years) Cumulative Oil Production Incremental Cumulative Oil Production');
disp([t', Np', [0; DeltaNp]]);
Result:
Both Excel and MATLAB will yield the same incremental cumulative oil production values. In this scenario, the incremental cumulative oil production at 
is 1000 barrels, and at 
is an additional 1500 barrels.
