ON THE THEORY OF PRESSURE AND TEMPERATURE NONLINEAR-WAVES IN COMPRESSIBLE FLUID-SATURATED POROUS ROCKS

Thermo-pore-elastic equations describing fluid migration through fluid -saturated porous media at depth in the crust are analyzed theoretical ly following recent formulations of Rice and Cleary (1976), McTigue (1 986) and Bonafede (1991). In this study these ideas are applied to a r ather general model, namely to a deep hot and pressurized reservoir of fluid, which suddenly enters into contact with an overlaying large co lder fluid-saturated layer. In a one-dimensional idealization this sys tem can be described by two nonlinear differential heat-like equations on the matrix-fluid temperature and on the fluid overpressure over th e hydrostatic value. The nonlinear couplings are due to Darcy thermal advection and to the mechanical work rate. Here we first sketch nonlin ear solutions corresponding to Burgers' ''solitary shock waves'', whic h have recently been found valid for rocks with very low fluid diffusi vity. Subsequently other nonlinear transient waves are discussed, such as ''thermal'' and ''compensated'' waves, which are found to exist fo r every value of the parameters present in the equations involved. One interesting aspect of these mechanisms is that the resulting time-sca les are particularly small. Moreover, in order to figure out the syste m time-evolution and the role played by the fluid diffusivity/thermal diffusivity ratio, a mechanical similitude is proposed, which we treat both analytically and numerically. Although for realistic systems the se solutions are somewhat idealized, they allow one to gain fundamenta l insight into fluid migration mechanisms in volcanic areas and in fau lt regions under strong frictional heating. As already discussed by Mc Tigue, the theory is also of interest in studying areas of nuclear was te disposal. Furthermore such a theoretical study allows one to invest igate the site at depth at which such nonlinear waves are generated.