A Biot model describing wave propagation in a porous solid saturated by a three-phase fluid Juan E. Santos 1,2 and Gabriela B. Savioli 1 1 - Instituto del Gas y del Petróleo, Facultad de Ingeniería, Universidad de Buenos Aires 2 - Department of Mathematics, Purdue University Universidad Nacional de La Plata, CONICET SUMMARY We present a model for the propagation of waves in a poroelastic medium saturated by a three-phase viscous, compressible fluid: oil, water and gas. The kinetic and dissipative energy density functions in the equations of motions are determined in terms of the mass densities of the solid and fluid phases. It is assumed that the flow is laminar, obeys Darcy’s law for the three phases and is described in terms of the absolute permeability and three- phase relative permeability functions. The pressure differences between the oil and water phases and the oil and gas phases are included in the model using two capillary pressure functions. The elastic constants in the stress-strain relations are determined employing gedanken experiments that generalize those of Biot’s theory for single-phase fluids. The presence of capillary forces imply the existence of four compressional waves, one fast and three slow, denoted Type I, II, III and IV waves, and one shear wave. Numerical examples show the phase velocities and attenuation coefficients of all waves for a sample of Nivelsteiner sandstone saturated by oil, gas and water. THE MODEL S o , S w , S g : oil, water and gas saturations, S o + S w + S g = 1  solid and θ -fluid displacements averaged over the bulk material, θ = o, w, g : strain tensor, , : total stress of the bulk material : θ -fluid pressure,   s u u u      ~  u u s ~ , ij ij ij       : stress tensor in the solid ij ij ij         s ij u     u ~       p p p      , w o o ow p p S Pc     o g g go p p S Pc   Capillary pressures:  p : reference pressure