Summary It is known that dispersion in porous media results from an interaction between convective spreading and diffusion. However, the nature and implications of these interactions are not well understood. Dispersion coefficients obtained from averaged cup-mixing concentration histories have contributions of convective spreading and diffusion lumped together. We decouple the contributions of convective spreading and diffusion in core-scale dispersion and systematically investigate interaction between the two in detail. We explain phenomena giving rise to important experimental observations such as Fickian behavior of core-scale dispersion and power-law dependence of dispersion coefficient on Péclet number. We track movement of a swarm of solute particles through a physically representative network model. A physically representative network model preserves the geometry and topology of the pore space and spatial correlation in flow properties. We developed deterministic rules to trace paths of solute particles through the network. These rules yield flow streamlines through the network comparable to those obtained from a full solution of Stokes’ equation. Paths of all solute particles are deterministically known in the absence of diffusion. Thus, we can explicitly investigate purely convective spreading by tracking the movement of solute particles on these streamlines. Then, we superimpose diffusion and study dispersion in terms of interaction between convective spreading and diffusion for a wide range of Péclet numbers. This approach invokes no arbitrary parameters, enabling a rigorous validation of the physical origin of core-scale dispersion. In this way, we obtain an unequivocal, quantitative assessment of the roles of convective spreading and diffusion in hydrodynamic dispersion in flow through porous media. Convective spreading has two components: stream splitting and velocity gradient in pore throats in the direction transverse to flow. We show that, if plug flow occurs in the pore throats (accounting only for stream splitting), all solute particles can encounter a wide range of independent velocities because of velocity differences between pore throats and randomness of pore structure. Consequently, plug flow leads to a purely convective spreading that is asymptotically Fickian. Diffusion superimposed on plug flow acts independently of convective spreading (in this case, only stream splitting), and, consequently, dispersion is simply the sum of convective spreading and diffusion. In plug flow, hydrodynamic dispersion varies linearly with the pore-scale Péclet number when diffusion is small in magnitude compared to convective spreading. For a more realistic parabolic velocity profile in pore throats, particles near the solid surface of the medium do not have independent velocities. Now, purely convective spreading (caused by a combination of stream splitting and variation in flow velocity in the transverse direction) is non-Fickian. When diffusion is nonzero, solute particles in the low-velocity region near the solid surface can move into the main flow stream. They subsequently undergo a wide range of independent velocities because of stream splitting, and, consequently, dispersion becomes asymptotically Fickian. In this case, dispersion is a result of an interaction between convection and diffusion. This interaction results in a weak nonlinear dependence of dispersion on Péclet number. The dispersion coefficients predicted by particle tracking through the network are in excellent agreement with the literature experimental data for a broad range of Péclet numbers. Thus, the essential phenomena giving rise to hydrodynamic dispersion observed in porous media are (1) stream splitting of the solute front at every pore, causing independence of particle velocities purely by convection; (2) velocity gradient in pore throats in the direction transverse to flow; and (3) diffusion. Taylor's dispersion in a capillary tube accounts only for the second and third of these phenomena, yielding a quadratic dependence of dispersion on Péclet number. Plug flow in the bonds of a physically representative network accounts only for the first and third phenomena, resulting in a linear dependence of dispersion on Péclet number. When all the three phenomena are accounted for, we can explain effectively the weak nonlinear dependence of dispersion on Péclet number.

We present results of a detailed investigation of the steam/ solvent-coinjection-process mechanism by use of a numerical model with homogeneous reservoir properties and various solvents. We describe condensation of steam/solvent mixture near the chamber boundary. We present a composite picture of the important phenomena occurring in the different regions of the reservoir and their implications for oil recovery. We compare performances of various solvents and explain the reasons for the observed differences. An improved understanding of the process mechanism will help with selecting the best solvent and developing the best operating strategy for a given reservoir. Results indicate that as the temperature drops near the chamber boundary, steam starts condensing first because its mole fraction in the injected steam/solvent mixture (and hence its partial pressure and the corresponding saturation temperature) is much higher than the solvent's. As temperature declines toward the chamber boundary and steam continues to condense, the vapor phase becomes increasingly richer in solvent. At the chamber boundary where the temperature becomes equal to the condensation temperature of both steam and solvent at their respective partial pressures, both condense simultaneously. Thus, contrary to steam-only injection, where condensation occurs at the injected steam temperature, condensation of steam/solvent mixture is accompanied by a reduction in temperature in the condensation zone and the farther regions. However, there is little change in temperature in the central region of the steam chamber. The condensed steam/solvent mixture drains outside the chamber, leading to the formation of a mobile liquid stream (drainage region) where heated oil, condensed solvent, and water flow together to the production well. The condensed solvent mixes with the heated oil and further reduces its viscosity. The additional reduction in viscosity by solvent more than offsets the effect of reduced temperature near the chamber boundary. As the steam chamber expands laterally because of continued injection and as temperature in the hitherto drainage region increases, a part of the condensed solvent mixed with oil evaporates. This lowers the residual oil saturation (ROS) in the steam chamber. Therefore, ultimate oil recovery with the steam/solvent-coinjection process is higher than that in steam-only injection. The higher the solvent concentration in oil at a location, the greater is the reduction in the ROS there. Our explanation is corroborated by the experimental results reported in the literature, which show smaller ROS in the steam chamber after a steam/solvent-coinjection process. A lighter solvent has a lower viscosity, a higher volatility, and a higher molar concentration of solvent in the drainage region. Thus, a lighter solvent causes a greater reduction in the viscosity of the heated oil and also leads to a lower ROS. Therefore, the lightest condensable solvent (butane, under the conditions investigated) provides the most favorable results i...

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A simple and transparent coordinate space derivation of the eigenvalue condition for the Ðnite-temperature Schro dinger equation for a system of electrons and protons is given, which contrasts with and establishes the correctness of the earlier derivation of the same equation based on somewhat specialized techniques such as the Funke-Hecke theorem. We recall that solutions of this equation were shown to provide an unconventional explanation of unidentiÐed solar emission lines.

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractLocal displacement efficiency in miscible floods is significantly affected by mixing taking place in the medium. Despite decades of research on mixing and dispersion, there remain questions about the amount of mixing occurring at pore-scale (hereinafter local). This study has investigated the local mixing experimentally as well as computationally.We developed a thin electrical-conductivity probe to measure local solute concentration to quantify local mixing. Miscible tracer displacement experiments were carried out in a homogeneous sand pack. Local solute concentrations measured at several radial and axial positions using the probe indicate non-zero local mixing. The core scale mixing is the same as the local mixing for the homogeneous pack.Local mixing is also investigated by solving the Navier-Stokes and convection-diffusion equations in two dimensional packing of circular disks. The computational studies qualitatively support the experimental observations for the homogeneous sand pack and explain the mixing mechanism inside the pore body. Mixing results from velocity variations in pore throats and bodies and molecular diffusion. The converging-diverging flow around sand grains causes the solute front to stretch, split and rejoin. In this process, the area available for diffusion increases by an order of magnitude. Diffusion tends to reduce local variation in solute concentration inside the pore body. If the fluid velocity is small, diffusion is able to homogenize solute concentration inside each pore. Increasing the fluid velocity has the same effect on local mixing as decreasing diffusion coefficient by the same factor. In limit of very large fluid velocity (or no diffusion) local mixing tends to zero and core-scale mixing is entirely caused by variations in velocity.