V. De La Cruz

Seismic wave propagation in a porous medium

A complete set of equations to describe low‐frequency seismic wave phenomena in fluid‐filled porous media is presented. The approach is based on the mathematics of volume‐averaging, aided by order‐of‐magnitude and physical arguments. The results are immediately utilizable by practicing seismologists. Our equations and those of Biot (1956a) are found to be largely consistent in form, and we suggest how Biot’s parameters may be defined in terms of basic physical parameters. The theory predicts two dilatational waves and two rotational waves. Under certain conditions these behave differently than would be expected on the basis of Biot’s theory.

Thermodynamics of Porous Media

Equilibrium thermodynamics for porous media is considered with special emphasis on its basis in pore-scale thermodynamics. It is shown that porosity, the new purely macroscopic variable, enters the relations on the same footing as mass densities and the strain tensors. Biot’s use of elastic energy potential, which lies at the foundation of his theory of poroelasticity, is examined in light of the results obtained here.

Reflection and transmission of seismic waves at the boundaries of porous media

Abstract The mode conversions which occur during the reflection and transmission of seismic waves at the boundaries of porous media are analysed. It is shown how the energy partitioned to the various modes depends on the incident angle and on the physical properties of the fluid and solid components on each side of the boundary. The boundary conditions used here predict the occurrence of bright and dark spots as are currently observed in seismic studies of heavy oil reservoirs. They also give rise to a class of pseudo interface waves which propagate in a direction almost parallel to the surface and which become true interface waves in the limiting case where the porous media degenerate to elastic solids. When thermomechanical coupling is an important attenaution mechanism in one of the media it is also observed to have a substantial effect on the mode conversions which occur at the boundary.

Macroscopic capillary pressure

The macroscopic pressure difference between two immiscible, incompressible fluid phases flowing through homogeneous porous media is considered. Starting with the quasi-static motions of two compressible fluids, with zero surface tension, it is possible to construct a complete system of equations in which all parameters are clearly defined by physical experiments. The effect of surface tension is then formally included in the definition of the specific process under consideration. Incorporating these effects into the pressure equations and taking the limit as compressibilities go to zero, the independent pressure equations are shown to yield indeterminate forms. However, the difference of the two pressure equations is found to yield a new process-dependent dynamical equation.

An analysis of the viability of polymer flooding as an enhanced oil recovery technology

The concept of improving oil recovery through polymer flooding is analysed. It is shown that while the injection of a polymer solution improves reservoir conformance, this beneficial effect ceases as soon as one attempts to push the polymer solution with water. Once water injection begins, the water quickly passes through the polymer creating a path along which all future injected water flows. Thus, the volume of the polymer slug is important to the process and an efficient recovery would require that the vast majority of the reservoir be flooded by polymer. It is also shown that the concept of grading a polymer slug to match the mobilities of the fluids at the leading and trailing edges of a polymer slug does not work in a petroleum reservoir. While this process can supply some additional stability to the slug, it is shown that for the purposes of enhanced oil recovery this additional stability is not great enough to be of any practical use. It is found that in this case the instability has simply been hidden in the interior of the slug and causes the same sort of instability to occur as was the case for the uniform slug.

Null coordinates for spherically symmetric gravitational collapse

Abstract The interior and exterior line-elements for a collapsing spherical cloud of dust are expressed in terms of null coordinates of Kruskals type. This gives a singularity-free description of the complete manifold right down to the singular event of maximum implosion.