Thermoelastic response of fluid‐saturated porous rock

Abstract

A linear theory for fluid‐saturated, porous, thermoelastic media is developed. The theory allows for compressibility and thermal expansion of both the fluid and solid constituents. A general solution scheme is presented, in which a diffusion equation with a temperature‐dependent source term governs a combination of the mean total stress and the fluid pore pressure. In certain special cases, this reduces to a diffusion equation for the pressure alone. In addition, when convective heat transfer and thermoelastic coupling can be neglected, the temperature field can be determined independently, and the source term in the pressure equation is known. Drained and undrained limits are identified, in which fluid flow plays no role in the deformation. In the drained case, the medium behaves as a simple thermoelastic body with the properties of the porous skeleton with no fluid present. In the undrained limit, the fluid is trapped in the pores, and the material responds as a thermoelastic body with effective compressibility and thermal expansivity determined in part by the fluid properties. The theory is further specialized to one‐dimensional deformation, and several illustrative problems are solved. In particular, the heating of a half space is explored for constant temperature and constant flux boundary conditions on the thermal field, and for drained (zero pressure) and impermeable (zero flux) conditions on the fluid pressure field. The behavior of these solutions depends critically upon the ratio of the fluid and thermal diffusivities, with very large and very small values of this parameter corresponding to drained and undrained responses, respectively.

Dike‐induced earthquakes: Theoretical considerations

“…Pore pressure increases due to heating by the magma are not considered here. Because this increase is nearly inversel) proportional to the square root of the hydraulic diffusivity to [Delaney, 1982;McTigue, 1986], rocks in which pore pressure increases are significant tend to be rocks in which pore pressures cannot diffuse over distances of tens of meters on the timescale of the passage of the stress concentration at the dike tip (<103 s for a dike velocity >10 -• m/s and a potential earthquake source dimension of about 100 m). For example, for a 500øC temperature increase Delaney [1982] computes a pore pressure increase of about 1 MPa in low-porosity rock with to < 10 -2 m2/s; in 103 s this pressure increase would diffuse a distance of only (tot) 1/2 ---3 m. Such pressure changes could be important in the days following intrusion (> 105 s).…”

Mesure de la perméabilité in situ du sel

“…Faute d'expériences spécifiques sur le sel étu dié, on prendra pour ce coefficient la valeur vraisem blable de 0,1 proposée par McTigue (1986) Ghoreychi, 1996) et sur des échantillons de sel du même site, mis en contact avec un fluide (Cosenza ;1996). L'application numérique a été effectuée avec les valeurs suivantes : la pression de pores initiale Po = 1 MPa; la contrainte initiale σo = 10MPa; l'exposant de la loi de fluage n = 3 ; le coefficient de Poisson drainé v0 = 0,3 ; le coefficient de Biot b = 0,1.…”

Fracturing processes due to temperature and pressure nonlinear waves propagating in fluid‐saturated porous rocks

“…The complete expression of the energy balance for the fluidrock mixture (in which a local thermal equilibrium between fluid and rock is assumed and rock velocity, dissipative diffusion term due to fluid-rock friction, thermoelastic coupling terms representing sources of adiabatic deformation, and the fluid thermal expansivity term are all neglected) can be written as [Bejan, 1984;McTigue, 1986 …”

“…Since the classic solutions by McTigue [1986] and Rice and Cleary [1976] as well as the solitary T-P waves discussed by Natale and Salusti [1996] and Garcia and Natale [1999] and the nonlinear waves of both Merlani et al [1997] and Natale et al [1998] are all invariant for scale transformations, we limit ourselves to analyzing here the set of solutions f = f(z/X/•), which are invariant for such transformations, as this set of functions entails most of the physically interesting cases: indeed, novel nonlinear solutions are discussed here. Following up recent models discussed by Merlani et al [1997], a mechanical analogy of such processes, such as the motion of a material point under the effect of a time-dependent external force, is also presented and investigated both analytically and numerically.…”

“…To analyze hydrothermal systems perturbed from their steady state into transient conditions characterized by rock deformation-fracturing, modern thermoporoelasticity theory [Rice and Cleary, 1976;McTigue, 1986] and their specific effects on the migration of fluid fronts was made by Natale et al [1998]. They considered parameter variability, assuming that rock deformation may lead to rock failure as pore fluid pressure approaches the breakdown pressure of the overburden rock.…”