Use of the memory concept to investigate the temperature profile during a thermal EOR process

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 profile is governed by the heat transfer between the rock matrix and flowing fluids, which is highly dependent on the thermal and rheological properties of the rock and fluids involved. In this work, the role of temperature-dependent rock and fluid properties in the development of the temperature profile during the thermal process was investigated employing the continuous time function as “memory.” Mathematical models were developed in terms of a group of heat transfer dimensionless numbers that correlate the varying rock and fluid properties. New heat transfer dimensionless numbers are proposed which can be characterized by rock and fluid properties. The model equations were then solved numerically through MATLAB programming to produce temperature profiles for a typical steam flood where the rock and fluid temperatures are assumed unequal throughout the reservoir, i.e. the rock does not attains the fluid temperature instantaneously. Results reveal the development of a temperature profile within the growing condensed water zone that is flowing ahead of the steam zone. The rock and fluid temperature profiles were found sensitive to the rheological properties, time and fluid velocity. The proposed model would be useful for better prediction of reservoir performance.