EVOLUTION OF THE BALANCE-EQUATIONS IN SATURATED THERMOELASTIC POROUS-MEDIA FOLLOWING ABRUPT SIMULTANEOUS CHANGES IN PRESSURE AND TEMPERATURE

A mathematical model is developed for saturated flow of a Newtonian fl uid in a thermoelastic, homogeneous, isotropic porous medium domain un der nonisothermal conditions. The model contains mass, momentum and en ergy balance equations. Both the momentum and energy balance equations have been developed to include a Forchheimer term which represents th e interaction at the solid-fluid interface at high Reynolds numbers. T he evolution of these equations, following an abrupt change in both fl uid pressure and temperature, is presented. Using a dimensional analys is, four evolution periods are distinguished. At the very first instan t, pressure, effective stress, and matrix temperature are found to be disturbed with no attenuation. During this stage, the temporal rate of pressure change is linearly proportional to that of the fluid tempera ture. In the second time period, nonlinear waves are formed in terms o f solid deformation, fluid density, and velocities of phases. The equa tion describing heat transfer becomes parabolic. During the third evol ution stage, the inertial and the dissipative terms are of equal order of magnitude. However, during the fourth time period, the fluid's ine rtial terms subside, reducing the fluid's momentum balance equation to the form of Darcy's law. During this period, we note that the body an d surface forces on the solid phase are balanced, while mechanical wor k and heat conduction of the phases are reduced.