A Permeability Evolution Model of Double-Porosity Media with Consideration of Temperature and Pressure Variations

Abstract

Reservoir heat treatment (RHT) can improve rock seepage capacity. Recently, it has been considered as a potential technology to enhance unconventional oil and gas recovery. This work presents a permeability evolution model to describe the thermal cracking effects of double-porosity media under temperature change and certain formation pressure. Moreover, to verify the accuracy of the model, a typical double-porosity media (tight sandstone) is selected as the sample, and the permeability of the sample is tested using a simulated formation heating device. Firstly, according to the observation results under SEM, 400°C is regarded as the transition temperature of porous and fractured media. The two-parameter exponential function and the improved "cubic law" are used to characterize the permeability of the pore part and the fracture part respectively. Secondly, rock is comprised of matrix grains and pore space. In the model hypothesis, the volume of the matrix grains is just a function of temperature, and the pore space is compressed or released under the action of effective stress, considering the difference of deformation between the matrix grains and the pore space, the Hooke's law based on engineering strain and natural strain is adopted for them respectively. Thirdly, the influence of temperature on crack spacing and opening is analyzed based on the energy principle and Weibull distribution. Finally, a permeability evolution model is established for the whole process of thermal expansion and cracking. The model describes two phases. In the first phase, the matrix grains expand under confining pressure, and at the same time accumulate thermal stress. In the second phase, after the thermal stress overcomes the confining pressure, the porosity recovers and cracks are gradually damaged and formed. The interaction between thermal stress and confining pressure is controlled by introducing a modulation factor. Due to the difference of component properties, the rock has obvious non-uniform thermal fracture phenomenon. Therefore, in this model, three parameters are introduced to ensure the robustness of the model: the contribution of deformation behavior of the matrix grains and pore space to crack opening, the influence of effective stress on crack opening, and the crack proportion of effective seepage. The results indicate that the model can describe the permeability evolution behavior of double-porosity media under certain confining pressure and temperature changes, it provides theoretical guidance for RHT to enhance oil and gas recovery.