A Study of Plane, Radial Miscible Displacement in a Consolidated Porous Medium
- R.G. Bentsen Jr. (The Pennsylvania State U.) | R.F. Nielsen (The Pennsylvania State U.)
- Document ID
- Society of Petroleum Engineers
- Society of Petroleum Engineers Journal
- Publication Date
- March 1965
- Document Type
- Journal Paper
- 1 - 5
- 1965. Society of Petroleum Engineers
- 5.3.1 Flow in porous media
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This paper reports an experimental study of the transition zone in plane, radial, miscible, liquid displacement in a homogeneous porous medium. The viscosity of the displacing liquid is greater than that of the displaced liquid in most of the runs, to avoid viscous fingers. A consolidated natural medium was chosen so dispersion would be high enough for measurement. Porosity was 19.5 per cent and permeability was 310 md. The material was Berea sandstone in a circular sector 1.9 cm thick and 91.4 cm in radius. Compositions of produced fluids were determined with a chemical oscillometer in a manner similar to that described by Peffer. Fluid distribution in the plane, radial miscible displacements agreed with the mathematical theory of Raimondi, et al for favorable mobility ratios.
Numerous papers have been published on theory and experiments relating to miscible fluid displacement in porous media. Some excellent reviews have appeared in the petroleum production literature, and it is not necessary to repeat the references listed in these reviews. Most previous experimental work has involved unidirectional flow, although the theory has been extended to radial and multi-directional flow. The experimental work involving multi-directional flow generally has been related to problems other than the extent of the transition zone and the fluid distribution therein, except for some cases where viscous fingering or heterogeneity of the porous media were predominant factors. This paper reports an experimental study of the transition zone in plane, radial, miscible, liquid displacement in a homogeneous porous medium. The viscosity of the displacing liquid is greater than that of the displaced liquid in most of the runs, to avoid viscous fingers. A consolidated natural medium was chosen so that the dispersion would be high enough for measurement.
A solution of the plane, radial dispersion equation for the injection of a finite slug of a second fluid is
If injection of the second fluid is continued indefinitely (infinite slug) the second error function becomes unity, and the equation can be written
In the experiments to be described, the molecular diffusion constant D can be neglected in the theory. Then differentiation of Eq. 2 gives, for C= 0.5,
If it is assumed that, in a finite slug, the maximum concentration of slug material occurs at a time half way between the times at which the head and tail pass a given point, then Eq. l gives
where R is the radius of the undiluted slug just after injection.
All runs were carried out on a slab of Berea sandstone in the shape of a circular sector, 1.9 cm thick and 91.4 cm in radius.
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