Graduate Thesis Or Dissertation
 

Solutions to some linear evolutionary systems of equations : study of the double porosity model of fluid flow in fractured rock and its applications.

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  • The present work is a study of three degenerate, linear parabolic systems of equations, each of which represents a version of the so-called double porosity model for underground fluid flows in natural fractured rock. These systems of equations together with initial and boundary conditions describe single-phase flows in fluids, slightly compressible, in large confined homogeneous reservoirs under general conditions including those of typical well tests. Analytic solutions are given as convolutions of initial and source data with fundamental solutions for each system. We establish that the problems are well-posed for all initial conditions likely to arise in practice. We obtain, using the theory of generalized functions, classes of all functions in which solutions exist, are unique and depend continuously on the initial data for appropriate restrictions. We consider two of the models to be the main versions relevant for flows in natural fractured rock, including typical basalt formations. They apply to short-time flows on order of the duration of typical pressure transient tests, and they are potentially useful for obtaining accurate values of formation parameters from well test data. We also show that the inverse problems of estimating parameters from well data are well-posed, i.e., that parameter values obtained are unique and depend continuously on the data.
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  • File scanned at 300 ppi (Monochrome) using Capture Perfect 3.0.82 on a Canon DR-9080C in PDF format. CVista PdfCompressor 4.0 was used for pdf compression and textual OCR.
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file details BodvarssonGudrunM1991.pdf 2017-08-01 公开 下载