Open AccessA theory of slow fluid flow through a porous thermoelastic matrix
Author(s) -
Morland L. W.
Publication year - 1978
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1978.tb04279.x
Subject(s) - thermoelastic damping , compressibility , dilatant , mechanics , constitutive equation , fluid dynamics , herschel–bulkley fluid , matrix (chemical analysis) , darcy's law , isotropy , thermodynamics , porous medium , porosity , classical mechanics , materials science , physics , geotechnical engineering , geology , finite element method , thermal , composite material , quantum mechanics
Summary. Slow flow of linearly viscous fluid through a linear isotropic thermoelastic matrix is described. The interaction body force is Darcy's law, and the constitutive laws for the partial stresses assume that porosity changes of strain order occur and that porosity is a linear function of the partial pressures in matrix and fluid. A further dependence on deviatoric matrix stress allows a description of dilatancy. The laws are expressed in terms of four distinct compressibilities and a mixture shear modulus, and various strong inequalities between the compressibilities are examined. A consolidation theory for an incompressible fluid is derived, and the restrictions required to recover an uncoupled diffusion equation for the matrix compression are determined. Convection equations for large temperature differences across a horizontal layer are derived, allowing finite fluid expansion, and it is shown that the fluid flow equations uncouple from the matrix equilibrium equation in the case of steady flow, but not in the case of unsteady flow.