DEVELOPING A MATHEMATICAL MODEL TO HISTORY MATCH AND FORECAST RESERVOIR’S PRODUCTION

ABSTRACT This study presents the development of a mathematical model that will history match and predict the production of the reservoir using multiple quadratic regression analysis. The study was driven by the weaknesses of conventional physics-based simulators, which are both data and computation-intensive and thus less available to academic and small-scale users. Synthetic datasets that were representative of reservoir performance were created, and they included the independent variables of reservoir pressure and water cut and dependent variables of cumulative oil, gas and water production. This model was done in Microsoft Excel by the matrix operations and regression analysis functions to derive a multivariate quadratic regression equation describing the non-linear relationship between declining pressure, increasing water cut and cumulative production. The model was particularly accurate statistically, and coefficients of determination (R2) of 0.9999 for oil and gas, and 1.0 for water, showing that the model fits the observed and predicted data almost perfectly. The results of the forecasting were realistic depletion trends that are in line with the reservoir engineering theory, i.e., cumulative production increases with pressure decline, and the increase in water production is a slow increase towards the later depletion stages. The model offers a physically consistent, cost-effective and easily repeatable means of reservoir performance prediction, especially where there is limited data. To add to the robustness and generalization, future studies need to consider time-varying variables and combine hybrid machine learning approaches.