Identification of spatially varying parameters in distributed parameter systems
The problem of identifying spatially-varying parameters in distributed parameter systems arises in the description of petroleum reservoirs and subsurface aquifers. The major difficulty in developing successful solution techniques lies in the ill-posedness in the sense that small errors in the data may cause large deviations of the solutions. The goal of this thesis is to develop numerically stable identification algorithms on the basis of the regularization approach for classes of parabolic systems. In Chapter Two, the regularization identification theory is rigorously developed for quasilinear parabolic systems. This serves as a theoretical basis of an automatic history-matching algorithm for dry gas reservoirs developed in Chapter Four. A systematic procedure is presented for constructing the algorithm in three steps: formulation, discretization and optimization. In Chapter Three, a novel piecewise regularization approach is rigorously developed for the identification of spatially discontinuous parameters in second-order parabolic systems. The results are applied to history-matching of one-dimensional fractured reservoirs. In Chapter Five, a novel regularization history-matching algorithm is developed which is capable of incorporating a priori point estimates of unknown parameters. A multi-objective index is formulated and optimized in a stepwise estimation process; simple rules-of-thumb are presented for determining the optimal weights. Extensive numerical experiments are performed in each phase of the work. The results clearly show that the regularization is an effective method for obtaining a well-behaved approximate estimate for an ill-posed identification problem and that incorporation of available a priori information can enhance the accuracy of the estimate.
- Research Organization:
- Michigan Univ., Ann Arbor, MI (USA)
- OSTI ID:
- 5498075
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
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03 NATURAL GAS
NATURAL GAS DEPOSITS
RESOURCE ASSESSMENT
PETROLEUM DEPOSITS
ALGORITHMS
AQUIFERS
CALCULATION METHODS
FORECASTING
FRACTURED RESERVOIRS
ONE-DIMENSIONAL CALCULATIONS
SPACE DEPENDENCE
SPATIAL DISTRIBUTION
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GEOLOGIC DEPOSITS
MATHEMATICAL LOGIC
MINERAL RESOURCES
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030200 - Natural Gas- Reserves
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