Graduate Thesis Or Dissertation
 

Indirect parameter identification algorithm in radial coordinates for a porous medium

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  • The decision to bury high level nuclear wastes in deep geological formations led to the study of the Hanford Nuclear Reservation as one of three possible sites for the first nuclear waste repository in the United States. To adequately evaluate the environmental impact of siting nuclear waste repositories in basalt aquicludes, it is essential to know the effects on parameter identification algorithms of thermal gradients that exist in these basaltic aquicludes. Temperatures of approximately 60° C and pressures of approximately 150 atms can be expected at potential repository sites located at depths of approximately 1000m. The phenomenon of over-recovery has been observed in some pumping tests conducted at the Hanford Nuclear Reservation. This over-recovery phenomenon may possibly be due to variations in the fluid density caused by thermal gradients. To asses the potential effects of these thermal gradients on indirect parameter identification algorithms, a systematic scaling of the governing field equations is required in order to obtain dimensionless equations based on the principle of similarity. The constitutive relationships for the specific weight of the fluid and for the porosity of the aquiclude are assumed to be exponentially dependent on the pressure gradient. The dynamic pressure is converted to the piezometric head and the flow equation for the piezometric head is then scaled in radial coordinates. Order-ofmagnitude estimates are made for all variables in unsteady flow for a typical well test in a basaltic aquiclude. Retaining all nonlinear terms, the parametric dependency of the flow equation on the classical dimensionless thermal and hydraulic parameters is demonstrated. These classical parameters include the Batchelor, Fourier, Froude , Grashof, and Reynolds Numbers associated with thermal flows. The flow equation is linearized from order-of-magnitude estimates based on these classical parameters for application in the parameter identification algorithm. Two numerical solutions are presented which predict hydraulic head given a continuous set of flow parameters. The first solution uses a totally numerical finite difference scheme while the second combines an analytical solution with a numerical solution. A radial coordinate system is utilized for describing an anisotropic confined aquifer. The classical inverse parameter identification problem is solved using an indirect method. This method is based on the minimization of a objective function or error criterion consisting of three parts: 1) least-squares error of head residuals; 2) prior information of flow parameters; and 3) regularization. An adjoint equation is incorporated into the method to eliminate the need to differentiate the heads with respect to the parameters being identified, increasing the stability of the algorithm. Verification of the parameter identification algorithm utilizes both "synthetic", computed generated input data and field data from a well test for a confined aquifer within the Columbia Plateau near Stanfield, Oregon. The method used is found to give parameter estimates which are both stable and unique.
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