Development of Proxy Models for Predicting and Optimizing the Time and Recovery Factor at Breakthrough During Water Injection in Oil Reservoirs

Abstract

Numerical reservoir simulation studies can be used to plan water injection projects to delay time and maximize oil recovery at water breakthrough which is time-consuming and computationally expensive. Combining computationally inexpensive proxy models and optimization algorithms is a solution to this problem. In this study, the Box-Behnken design method and response surface methodology were used to develop two proxy models which showed the relationship between time and recovery factor at water breakthrough with six independent variables namely porosity, horizontal permeability, water viscosity, bottom-hole pressure, water injection rate and vertical permeability. A comparison of actual and predicted values for time and oil recovery factor at water breakthrough was found to be in good agreement with each other. An average absolute percentage error of 2.038% and 1.217%, a root mean square error of 0.08 and 0.0000988, and coefficients of determination, R² of 0.9984 and 0.9946 were obtained for time and recovery factor at water breakthrough respectively. These are indications that the developed models are accurate, valid, and reliable. The models were further validated by comparing the actual and predicted water breakthrough time and recovery factor at water breakthrough using input variables that were not used in model development. These were also in close agreement with each other. The MATLAB multi-objective genetic algorithm was used to determine at a specific average porosity and permeability value, the best optimum controllable variables that maximized the objective functions. These were found to be 10.8978 years and 0.786 respectively and agreed with simulation results obtained using similar input parameter values.