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On vapour flow in a hot porous layer

Published online by Cambridge University Press:  26 April 2006

Shaun D. Fitzgerald  and
Andrew W. Woods
Shaun D. Fitzgerald
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics and Department of Earth Sciences, University of Cambridge CB3 9EW, UK Present address: Department of Petroleum Engineering, Stanford University, Standford, CA 94305, USA.
Andrew W. Woods
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics and Department of Earth Sciences, University of Cambridge CB3 9EW, UK
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Abstract

The motion of isothermal vapour in a permeable rock is governed by a nonlinear diffusion equation for the vapour pressure. We analyse vapour flow described by this equation in both bounded and unbounded domains. We then apply these solutions to describe the controls on the rate of vaporization of liquid invading a hot permeable rock. In an unbounded domain, we determine asymptotic similarity solutions describing the motion of vapour when it is either supplied to or removed from the reservoir. Owing to the compressibility, these solutions have the property that vapour surfaces migrate towards the isobar on which the vapour has the maximum speed.

In contrast, if vapour is supplied to or removed from a closed bounded system sufficiently slowly then the vapour density and pressure rapidly become approximately uniform. As more vapour is added, the mean pressure gradually increases and vapour surfaces become compressed. If liquid slowly invades a hot bounded porous layer and vaporizes, the vapour pressure becomes nearly uniform. As more liquid is added, the reservoir gradually becomes vapour saturated and the vaporization ceases.

In an open bounded system, with a constant rate of vapour injection, the flux of vapour across the reservoir becomes uniform. If liquid is injected slowly and vaporizes then again the vapour flux becomes spatially uniform. However, the vapour flux now increases slowly as the liquid invades further into the rock, as a result of the decreased resistance to vapour flow from the interface to the far boundary.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 293 , 25 June 1995 , pp. 1 - 23
Copyright
© 1995 Cambridge University Press

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