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This dissertation is concerned with the mathematical modelling of oil recovery by steam injection using analytical techniques.
An integral method for generating approximate solutions to the one and two- (three-) dimensional steam injection processes is presented. Due to the qualitatively different character of the problem the one- and two- (three-) dimensional cases are examined separately.
The applicability of the method for the determination of the rate of growth of the steam zone volume in one-dimensional systems is considered. An extensive study of the heat transfer in the surroundings and the hot liquid zone is carried out to complement the one-dimensional implementation of the technique. The resulting class of moving boundary problems and their methods of solution are discussed in detail. The results obtained are then combined with the integral technique to derive upper and lower bounds, asymptotic solutions and approximate solutions to the rate of growth of the steam zone. The important physical parameters are identified and their significance in the design of the process is outlined. In particular, the very important effect of heat transport in the surroundings and the hot liquid zone is fully accounted.
For two- (three-) dimensional systems, a more detailed version of the integral method is developed to account for the effect of gravity segregation in the determination of the steam front shape. A non-linear partial differential equation that describes the evolution of the steam front shape in gravity dominated systems is derived. The significance of the various physical parameters in the performance of a three-dimensional steam injection process is discussed by providing a solution to the equation derived, in the limit of predominantly viscous flows.
A critical evaluation of the existing analytical models is presented and the regions of their validity established. The potential of the techniques developed, particularly in the heat transfer area, to treat a class of in-situ thermal methods is also clearly indicated