H. Ted Davis

Dispersion in flow through porous media—I. One-phase flow

In this paper we extend our previous study (Sahimi et al., 1986, Chem. Engng Sci.41, 2103–2122) of dispersion processes in porous media occupied by two fluid phases. We report results of Monte Carlo investigations of dispersion in two-phase flow through disordered porous media represented by square and simple cubic networks of pores of random radii. The percolation theory of Heiba et al. (1982, SPE 11015, 57th Annual Fall Meeting of the Soc. Petrol. Engrs) is used to determine the statistical distribution of phases in the porespace. One of the phases is assumed to be strongly wetting on the porewall in the presence of the other phase. A pore size distribution is chosen which yields through the percolation theory of Heiba et al. network relative permeabilities that are in agreement with the available experimental data. As in one-phase flow dispersion is diffusive in the cases simulated, i.e. it can be described by the convective-diffusion equation. Longitudinal dispersivity in a given phase rises greatly as the saturation of that phase approaches residual (i.e. its percolation threshold); transverse dispersivity also increases, but more slowly. As residual saturation of a phase is neared, the backbone of the subnetwork occupied by the phase becomes increasingly tortuous, with local mazes spotted along it that are highly effective dispersers. Dispersivities are found to be phase, saturation and saturation history dependent. Some limited Monte Carlo experiments with a residence time representation of the effects of deadend paths within a phase or reversible adsorption on the pore walls demonstrate that the approach developed can be extended to study the influence of such delay mechanisms on the dispersion process.

HOW LIQUIDS SPREAD ON SOLIDS

A theory of the wetting of solids by liquids is put forward. The theory accounts for capillary pressure gradient, gravitational potential gradient, surface tension gradient, disjoining pressure gradient driving forces of flow in thick thin-films and of surface diffusion in thin thin-films. Disjoining pressure stems from the way intermolecular forces aggregate in submicroscopically thin films. For thick thin-films of slowly varying thickness the lubrication approximation to velocity distributions is appropriate. With this approximation the spontaneous, unsteady, two-dimensional spreading of liquid is shown to be governed by a nonlinear convective-diffusion equation for the evolution of the film thickness profile. The predictions of the theory agree with Marmur and Lelahs (1980, 1981) observations of water drops spreading on glass and with Bascom, Cottington and Singleterrys (1964) and Ludviksson and Lightfoots (1971) observations of oils spreading on high energy surfaces. The theory is used to analyze D...

Pore-scale simulation of dispersion

Tracer dispersion has been simulated in three-dimensional models of regular and random sphere packings for a range of Peclet numbers. A random-walk particle-tracking (PT) method was used to simulate tracer movement within pore-scale flow fields computed with the lattice-Boltzmann (LB) method. The simulation results illustrate the time evolution of dispersion, and they corroborate a number of theoretical and empirical results for the scaling of asymptotic longitudinal and transverse dispersion with Peclet number. Comparisons with nuclear magnetic resonance (NMR) spectroscopy experiments show agreement on transient, as well as asymptotic, dispersion rates. These results support both NMR findings that longitudinal dispersion rates are significantly lower than reported in earlier experimental literature, as well as the fact that asymptotic rates are observed in relatively short times by techniques that employ a uniform initial distribution of tracers, like NMR.

EVIDENCE FOR SINGLE FILE DIFFUSION OF ETHANE IN THE MOLECULAR SIEVE ALPO4-5

Abstract We measure the diffusion of ethane in very large crystals of the molecular sieve AlPO 4 -5 (provided by M. Davis) using pulsed field gradient (PFG) NMR. Thanks to the large crystal size and the long longitudinal relaxation time, the mean square displacement could be monitored over times that arranged over an order of magnitude. The mean square displacement was proportional to the square root of time, providing strong evidence that the ethane molecules are moving in a single file, i.e. they are unable to pass each other. This is the first direct experimental evidence for single-file diffusive motion — a phenomenon that is probably widely prevalent in both industrial catalytic and biological systems.

Microscopic dynamics of fluids confined between smooth and atomically structured solid surfaces

Molecular dynamics and the grand canonical Monte Carlo techniques are employed to simulate the structure and dynamics of a fluid in a slit micropore at equilibrium and under Couette flow. Calculated quantities include the fluid’s density profiles, pair correlation functions, diffusion coefficients, normal pressure, stress tensor, and velocity profiles. Simulation results for fluids in equilibrium with the same bulk fluid, but confined by either atomically smooth or structured face centered cubic pore walls are compared. At the conditions considered, fluid in the contact layer next to structured walls exhibits enhanced fluid order which is not altered by flow for pores capable of accommodating two fully developed fluid layers (i.e., for pores wider than 2.5 molecular diameters across). At narrower pore widths, the equilibrium fluid structure is changed by flow and the fluid is more sensitive to shear‐induced changes in the diffusivity and normal pressure. The layer average density profiles of the confined ...

Microscopic dynamics of flow in molecularly narrow pores

Flow of fluids confined in molecularly narrow pores is studied by molecular dynamics. Strong density variations across the pore render the usual dependence of the local viscosity on local density inappropriate. At separations greater than four molecular diameters flow can be described by a simple redefinition of local viscosity. In narrower pores a dramatic increase of effective viscosities is observed and is due to the inability of fluid layers to undergo the gliding motion of planar flow. This effect is partially responsible for the strong viscosity increases observed experimentally in thin films that still maintain their fluidity.

Toward understanding microemulsion microstructure: A small‐angle x‐ray scattering study

The microemulsion phases formed in solutions of octane, commercial surfactant, and alcohol with various brines are examined with small‐angle x‐ray scattering (SAXS), electrical conductivity, and viscosity techniques. Models based on monodisperse populations of swollen micelles or microemulsion ‘‘droplets’’ adequately represent the SAXS data at low volume fractions of brine. Introduction of hard‐sphere interactions with the Percus–Yevick approximation allows us to model the composition dependence of the radius of gyration and isothermal compressibility up to volume fractions of brine near a percolation threshold for electrical conductivity. For brine volume fractions above the percolation threshold, a mean field attractive interaction term is needed to model the variation of isothermal compressibility; however, the same theory fails to model the composition dependence of the apparent radius of gyration. But predictions from a model for a bicontinuous microemulsion structure that is geometrically irregular yet topologically ordered and that evolves continuously into swollen (inverted) micellar solutions at low volume fraction of water (oil) are in good agreement with the SAXS and electrical conductivity data over a wide range of brine volume fractions.

Toward understanding microemulsion microstructure. II

Many equilibrium microemulsion phases can solubilize hydrocarbon and water in all proportions in a continuous progression of states without any visibly abrupt transition. At the extremes are solutions of swollen micelles and swollen inverted micelles. Contending pictures of the midprogression microstructures are (1) crowded swollen micelles and crowded swollen inverted micelles, which cannot coexist alone, and (2) bicontinuous structures, parts of which can be micellar. Which is correct? The most extensive published evidence is electrical conductivity, small‐angle x‐ray scattering (SAXS), and viscosity data on microemulsions made in our laboratory with an alkylaryl sulfonate mixture that is a commercial type of surfactant. We report here complementary data with a comparable pure surfactant and analyze at length the SAXS evidence. We note that the pure surfactant appears to narrow the ranges over which swollen disjoint interacting micelles exist. We conclude that the continuous progression through buildup ...

Hydrodynamic dispersion in confined packed beds

Pore-scale simulations of monodisperse sphere packing and fluid flow in cylinders have reproduced heterogeneities in packing density and velocity previously observed in experiment. Simulations of tracer dispersion demonstrate that these heterogeneities enhance hydrodynamic dispersion, and that the degree of enhancement is related to the cylinder radius, R. The time scale for asymptotic dispersion in a packed cylinder is proportional to R2/DT, where DT represents an average rate of spreading transverse to the direction of flow. A generalization of the Taylor–Aris model of dispersion in a tube provides qualitative predictions of the long-time dispersion behavior in packed cylinders.

Gradient theory of wetting transitions

Abstract The physics of fluids near solids is studied with the gradient theory of inhomogeneous fluids. The theory defines fluid structure in terms of the equation of state of homogeneous fluid, the fluid-solid interaction potential, and the influence parameters of inhomogeneous fluid, the latter being moments of intermolecular distributions. Density profiles predicted by the theory reveal a first-order transition from zero to nonzero contact angle, the apparent angle of intersection of a fluid interface with the solid surface. When the states of two fluid phases lie near a critical point, one of the near-critical fluids is prevented from contacting any third phase by a wetting film of the other near-critical fluid. Far enough from critical points, however, the apparent contact angle is nonzero. The surface phase transition persists to temperatures and compositions where wetting film can no longer exist as bulk phase. The surface transition terminates at a critical temperature T es , below the bulk critical temperature T c . The variation of contact angle with fluid-fluid interfacial tension, a Zisman plot, is investigated. Two simple limiting relationships are found: one valid when the wetting transition is very near critical, where Cahns critical point scaling law holds, the other valid when the wetting transition is far from critical, where the Good-Girifalco correlation holds. Gradient theory predictions of fluid structure near solids are compared with Monte Carlo simulations of fluids near solids, and with the predictions of theories based on the approximate density functional integral equation.