The Coupled Mathematical Model of Reservoir Temperature Field, Stress Field and Fluid Seepage Field

Abstract

In the process of exploitation for oil and gas fields, especially with the high pressure water injected, or the course of steam-injected thermodynamic oil exploitation, reservoir pressure and temperature are constantly changing, which can lead to the reservoir porous medium deformation, and reservoir deformation will affect the reservoir pressure and temperature in turn. Fluid seepage, temperature change and rock deformation of reservoir are influenced by the other two, which just be called as the seepage-stress (strain)-temperature fields coupling. According to theories about rock mechanics, heat transfer, seepage mechanics and petroleum engineering, in this article the coupled mathematical model of reservoir temperature field, stress field and fluid seepage field was established, and all the coupled equations were solved at the same time by applying the fully coupling algorithm, as well as the process and method to establish the model of three field coupling law were studied with the application of the finite element analysis software ADINA. Here we just set the block Wa38 of Xiaowa oil filed as a case to study the coupling model of three fields. Consequences show that if the seepage field and the stress field are coupled at first as well as the seepage field and the temperature field, then followed by the third field, results of these two ways are close to each other, but the result will be really different if the stress field and the temperature field are firstly coupled. Usually the former two coupled ways are more suitable for the oil field, and their results are more in line with the real reservoir development dynamic. As we can see, the closer the distance from the wellbore, the more obviously the total displacement, temperature field, stress field and seepage field will change; on the contrary, the farther the distance from the wellbore, the more unobvious the changes will be. It is worthy to point out that the establishment of the model also can provide a theoretical basis for the study of numerical simulation of thermal recovery, the stability of borehole wall for thermal wells and ground subsidence caused by discovery.