Abstract
Simplified models, consisting of single, circular channels and channels of different length and diameter in series and parallel combinations, are used in conjunction with the equations of Poiseuille and Hartmann to demonstrate the dependence of the rate of flow of mercury in the models on channel dimensions when the models are subjected to transverse magnetic fields.
Experimental tests conducted on mercury-saturated, glass-bead packs and a natural rock sample show that a magnetic field applied transversely to the direction of flow retards flow rate. The magnitude of the magnetic effect increased with increasing bead size and field intensity.
Results of this work suggest that magnetic fields have potential in the study of the internal geometry of flow channels in porous media.
Introduction
The purpose of this work is to determine qualitatively by theoretical and experimental considerations whether or not a magnetic method has potential in the study of the basic properties of rock. The nature of the solid surface and the geometry of the pore network in petroleum-bearing rock plays an important role in the flow behavior of fluids in a petroleum reservoir. Hence, any technique of study that would provide new and additional information on the rock matrix would contribute to a better understanding of petroleum reservoir performance. One such technique appearing to offer performance. One such technique appearing to offer promise is in the area of magnetohydrodynamics. promise is in the area of magnetohydrodynamics. While much research, both theoretical and experimental, has been devoted to the problems concerned with the flow of conducting fluids in transverse magnetic fields in single channels, very little information has been published regarding the behavior of conducting liquids in porous media under the influence of a transverse magnetic field. Perhaps this dearth of information can be attributed Perhaps this dearth of information can be attributed to two main causes:the pores and pore connections are generally so small that intense magnetic fields are required to produce Hartmann numbers of sufficient magnitude to exert appreciable influence on flow rate, andthe extreme complexity of the channel systems in porous media render them intractable to theoretical analysis unless numerous assumptions are made to simplify network geometry.
When a conducting fluid moves in a channel in a transverse magnetic field, a force is exerted on the fluid which retards its flow. The magnitude of flow-rate retardation increases with increasing field intensity, channel dimensions and channel-wall conductivity. These magnetohydrodynamic phenomena and theory have been described and developed by various investigators.
Since a petroleum reservoir rock is an interconnected network of pores and channels within a rock framework, one would anticipate that the geometry of the network would exert some influence on the magnitude of the effect of a transverse magnetic field on the rate of flow of a conducting fluid therein.
The purpose of this work is to demonstrate through the use of simple models and experimental data that the magnetic field effect on flow rate has potential for use in determining size and size potential for use in determining size and size distribution of pores in porous materials.
THEORY
Electromagnetic induction in liquids is not completely defined, and the complexities involved in many cases appear to defy true analytical expression. However, by applying some simplifying assumptions, these cases may be made tractable to solution to provide qualitative indication of system behavior. The following analysis was conducted in conjunction with laboratory tests to determine if magnet ohydrodynamics has possible potential as a tool for studying the internal geometry of porous systems.
When a conducting liquid moves in a channel in a transverse magnetic field, an emf is developed in the channel normal to both the channel axis and the magnetic field. This emf causes circulating currents to flow in the liquid as shown in Fig. 1.
SPEJ
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Spectral method solutions of a variable aspect ratio duct flow in a uniform transverse magnetic field with two different thermal boundary conditions