Cumulative Oil Production in Undersaturated Oil Reservoirs

An undersaturated oil reservoir is a reservoir in which the initial pressure is greater than the bubble-point pressure of the crude oil. This means that there is no free gas in the reservoir, only liquid oil and some water.

Cumulative oil production is the total amount of oil that has been produced from the reservoir over time. It can be calculated using the material balance method, which states that the change in oil-in-place (STB) in the reservoir is equal to the mass of the oil produced from the wells.

Basic Theory:

Cumulative oil production in an undersaturated oil reservoir can be calculated using the following formula:

$N(t) = \int_{0}^{t} Q(t) \,dt$

where:

$N(t)$ is the cumulative oil production at time $t$ ,
$Q(t)$ is the oil production rate at time $t$ .

Procedures in Excel:

Data Input: Create an Excel table with columns for time ( $t$ ) and oil production rate ( $Q(t)$ ). Ensure that the data is organized chronologically.
Cumulative Oil Production Formula: In a new column, use the cumulative oil production formula to calculate $N(t)$ at each time step. You can use the Excel formula =SUMPRODUCT(Q2:Qn, (B2:Bn-B1:Bn-1)) assuming time is in column B and production rate is in column Q.
Visualization: Create a line chart to visualize the cumulative oil production over time.

Explanation:

Consider a scenario where the oil production rate ( $Q$ ) in an undersaturated oil reservoir varies with time ( $t$ ). The data is tabulated below:

Time (months)	Oil Production Rate (bbl/month)
0	500
1	480
2	450
3	430
4	400

Scenario Calculation in Excel:

Input the provided data into an Excel table.
Use the cumulative oil production formula in a new column.
Create a line chart to visualize the cumulative oil production.

Scenario Calculation in MATLAB:


% MATLAB code for cumulative oil production
time = [0, 1, 2, 3, 4]; % Time in months
production_rate = [500, 480, 450, 430, 400]; % Production rate in bbl/month

cumulative_production = trapz(time, production_rate);

disp(['Cumulative Oil Production in MATLAB: ' num2str(cumulative_production) ' bbl']);

Comparison:

Compare the cumulative oil production results obtained from Excel and MATLAB. The values should be close, validating the accuracy of the calculations in both platforms.