T. J. T. Spanos

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.

Pressure Pulsing at the Reservoir Scale: A New IOR Approach

Laboratory tests initiated in January 1997 demonstrated clearly that periodic, large-amplitude, low-frequency stran excitation of porous media leads to large flow enhancements. Based on these results, a new liquid flow enhancement technology for reservoirs was formulated, and a successful full-scale field experiment was executed in early 1999. Other field projects in 1999 through 2001 waterfloods in heavy oil cold production wells with sand influx confirmed the expectation that pressure pulsing, properly executed, increases oil production rate at low cost. The first trial showed that period application of large amplitude, liquid-phase pressure pulses increased oil production rates, decreased water-oil ratio, and increased the percentage of sand produced, even without large-scale injection. Though experience to date is in heavy oil, the process is general and will work in all porous media that have interconnected pore space. Furthermore, the method works in single-phase and two-phase liquid saturated cases, although the presence of large amounts of free gas is detrimental. Based on the field and laboratory work, and considering the nature of the physical processes, it appears likely that pressure pulsing will also help reduce coning and viscous fingering instabilities, help overcome capillary blockages, and result in more total oil recovery over time.

Steady-state countercurrent flow in one dimension

Two phase countercurrent steady-state flow through permeable media in one dimension is discussed. For steady-state countercurrent flow in water wet porous media, a saturation profile is predicted with the water saturation decreasing in the direction that the water phase is flowing. The de la Cruz and Spanos equations predict that the Muskat relative permeability curves for countercurrent flow will be less than the Muskat relative permeability curves for steady-state cocurrent flow. This result has immediate implications regarding the use of external drive techniques to determine relative permeabilities based on the Buckley-Leverett theory and Muskats equations. These equations and current experimental evidence involving countercurrent flow indicate that Muskats equations do not adequately describe the multiphase flow of immiscible fluids.

Pressure Pulsing: The Ups And Downs of Starting a New Technology

W hen technology based on new science is started, there can be a lot of skeptici<,m, which is a healthy reaction. The ~kepticism encountered by PE-TECII as pressure pul!.ing is gradually introduced ha\ been partly overcome, but only in the Canadian heavy oil industry. Here arc some typical remarks we have encountered over the last three year:., accompanied by our responses. u se seismic excitation have, to our knowledge, met with failure in China, Canada, and the United States. Senior engineers from western oil companies have examined claims that mechanical vibrations are being used successfully, they appear unconvinced, even after site visits. Also, the numerous artic les in the Rus~ian

The equations of miscible flow with negligible molecular diffusion

A set of equations with ‘generalized permeability’ functions has been proposed by de la Cruz and Spanos, Whitaker, and Kalaydjian to describe three-dimensional immiscible two-phase flow. We have employed the zero interfacial tension limit of these equations to model two phase miscible flow with negligible molecular diffusion. A solution to these equations is found; we find the generalized permeabilities to depend upon two empirically determined functions of saturation which we denote asA andB. This solution is also used to analyze how dispersion arises in miscible flow; in particular we show that the dispersion evolves at a constant rate. In turn this permits us to predict and understand the asymmetry and long tailing in breakthrough curves, and the scale and fluid velocity dependence of the longitudinal dispersion coefficient. Finally, we illustrate how an experimental breakthrough curve can be used to infer the saturation dependence of the underlying functionsA andB.

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.

Stability of a stationary steam-water front in a porous medium

The instability of a plane front between two phases of the same fluid (steam and water) in a porous medium is considered. The configuration is taken to be initially stationary with the more dense phase overlying the less dense phase. The frontal region is assumed sharp, so that macroscopic boundary conditions can be utilized. This assumption precludes the existence of dispersion instabilities. The stabilizing influence of phrase transition as well as the implication of different macroscopic pressure boundary conditions on the stability of the front are discussed and illustrated.

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.

Automaton Simulations of Dispersion in Porous Media

A thermodynamic lattice gas (automaton) model is used to simulate dispersion in porous media. Simulations are constructed at two distinctly different scales, the pore scale at which capillary models are constructed and large scale or Darcy scale at which probabilistic collision rules are introduced. Both models allow for macroscopic (pore scale) phase separation. The pore scale models clearly show the effect of pore structure on dispersion. The large scale (mega scale) simulations indicate that when the pressure difference between the displacing phase and displaced phase is properly chosen (representing the average pressure gradient between the phases). The simulation results are consistent with both theoretical predictions and experimental observations.