A Review of Diffusion and Dispersion in Porous Media

Abstract

Because of the influence of dispersion on miscible-displacement processes, diffusion and dispersion phenomena in porous rocks are of current interest in the oil industry. This paper reviews and summarizes a great deal of pertinent information from the literature.Porous media (both unconsolidated packs and consolidated rocks) can be visualized as a network of flow chambers, having random size and flow conductivity, connected together by openings of smaller size. In such a porous medium, the apparent diffusion coefficient D is less than the molecular diffusion coefficient Do, as measured in the absence of a porous medium. For packs of unconsolidated granular material the ratio D/Do is about 0.6 to 0..7. For all porous rocks, both cemented and unconsolidated, the ratio of diffusion coefficients can also be represented as where F is the formation electrical resistivity factor and is the porosity.If fluids are flowing through the porous medium, dispersion may be greater than that due to diffusion alone. At moderate flow rates the porous medium will create a slightly asymmetrical mix zone (trailing edge stretched out), with the longitudinal dispersion coefficient approximately proportional to the first power of average fluid velocity (if composition is nearly equalized in pore spaces by diffusion). If the velocity in interstices is large enough, there will be insufficient time for diffusion to equalize concentration within pore spaces. In this region, longitudinal dispersion increases more rapidly than fluid velocity.At low velocities in interstices, transverse dispersion is characterized by a region in which transverse diffusion dominates. If the fluid velocity gets high enough, there will be a transition into a region where there is stream splitting with mass transfer but with insufficient residence time to completely damp-out concentration variations within pore spaces.There are several variables that must be controlled to get consistent longitudinal and transverse dispersion results, viz.,edge effect in packed tubes,particle size distribution,particle shape,packing or permeability heterogeneities,viscosity ratios,gravity forces,amount of turbulence, andeffect of an immobile phase. Introduction Diffusion and dispersion in porous rocks are of current interest to the oil industry. This interest arises because of the influence of dispersion on miscible-displacement processes.In a recovery process utilizing a zone of miscible fluid, there is the possibility of losing miscibility by dissipating the miscible fluid or by channeling or ‘fingering" through the miscible zone. Diffusion and dispersion are two of the mechanisms that may lead to mixing and dissipation of the slug. On the other hand, dispersion may tend to damp-out viscous fingers which may be channeling through the miscible slug. Hence, dispersion may be detrimental or beneficial (if it prevents fingering through the miscible zone). Therefore, it is doubly important that we understand these processes.In this paper we review, summarize and interpret a great deal of information from the literature. In particular, we will briefly discuss molecular diffusion in miscible fluids. Then we will discuss what differences to expect for diffusion in a porous rock. If there is movement of the fluid through the rock, then there may be an additional mixing or "dispersion". Furthermore, the dispersion longitudinally (in the direction of gross fluid movement) and transverse to the direction of fluid movement will not be equal. We will discuss both types of dispersion as well as several variables which can affect dispersion (viscosity differences, density differences, turbulence, heterogeneity of media, etc.). This group of variables has sometimes led to difficulty when comparing literature data. DIFFUSION OF MISCIBLE FLUIDS If two miscible fluids are in contact, with an initially sharp interface, they will slowly diffuse into one another. SPEJ P. 70^

Viscous and gravitational contributions to mixing during vertical brine transport in water‐saturated porous media

“…For laboratory experiments in homogeneous, isotropic porous media, Perkins and Johnston [1963] and Fried and Combarnous [1971] agreed that a L is directly proportional to the medium grain size, d g , giving…”

Modelling heat transfer during flow through a random packed bed of spheres

“…5. Experiments yield that there is a gradual transition between the two regions and the turbulence is affected by the packing and particle geometry [35]. Hence there is no definite limit for turbulent flow.…”

Gravity-Enhanced Transfer between Fracture and Matrix in Solvent-Based Enhanced Oil Recovery

“…The effective diffusion coefficient in a porous medium is different from bulk diffusion due to tortuosity and enhanced mixing effects in flowing fluids (see for example Perkins and Johnston (1963) and Bruining et al (2012)). However, we will use the effective diffusion coefficient as a parameter, to obtain an optimal match between the numerical model and the experiment.…”

“…Porous media can be considered as a network of flow chambers, having random size and flow conductivity, connected together by openings of smaller size. In such a system, the apparent diffusion coefficient is less than the molecular diffusion coefficient, as measured in the absence of a porous medium [Perkins and Johnston (1963)]. Consequently, the parameter which is used in the simulation to obtain a history match is an effective diffusion coefficient instead of molecular diffusion coefficient.…”

“…In order to numerically reproduce the experiment with pentane and decalin and obtain the history match, we assign an effective diffusion coefficient of 10 −9 m 2 /s as a starting value, see also Cussler (2007) and Perkins and Johnston (1963). Then we vary the diffusion coefficient to match the recovery profile.…”