A mathematical model for thermal flooding with equal rock and fluid temperatures

Accurate prediction of the temperature profile within a reservoir undergoing a thermal recovery process is a key factor in process design, production forecasting, and reservoir management. Such a profile is governed by the rock and fluid properties and heat transfer between them. As a result, the temperature distribution is highly dependent on the thermal and rheological properties of the rock and fluids. The present research investigates the role of temperature-dependent rock and fluid properties in the development of the temperature profile during thermal flooding of an oil reservoir. The concept of "memory" is included to analyze the evolution of rock/fluid properties as continuous time functions. A mathematical model is developed in terms of a group of heat transfer dimensionless numbers that correlate the varying rock and fluid properties. The model equation was solved numerically through MATLAB programming language to produce temperature profiles for a typical thermal flood where the rock attains the fluid temperature instantaneously. The temperature distribution was found to concave down smoothly within the heated region. The proposed heat transfer dimensionless numbers, which characterize the process and encompass many of its variables, provide relationships between the rock and fluid properties within the porous medium. They have significant roles in the temperature profile as related to continuous alteration phenomena in addition to system fluid velocity, time, and other rheological parameters of rock and fluid. The mathematical model and its numerical solution are useful for better prediction of reservoir performance.