| The scope of this research is to extend a proposed new physically based inverse method to uncertainty quantification on a large scale aquifer flow inversion, to significantly improve the computation efficiency on multiple inversions for stochastic ensembles, and to incorporate uncertainty measures in inversion outcomes. The problem considered is to invert two-dimensional steady-state flow in a heterogeneous groundtruth model (500x500 grid) with two hydrofacies. From the true model, an increasing number of wells were sampled to obtain facies types, hydraulic heads, and fluxes. Based on experimental indicator histograms and directional variograms computed from the sampled facies, Sequential Indicator Simulation (SIS) was employed to generate 100 hydrofacies realizations with a 100 x 100 geostatistical grid. Each realization was conditioned to the facies measurements at the wells for which a set of estimated hydrofacies hydraulic conductivities (Ks), flow fields, and boundary conditions (BCs) were estimated using the physically based inverse method.;Because of the parameter quantification, a large number of inverse simulations are needed for which computation efficiency is critical. However, because inverse problems can be ill-posed given insufficient or inaccurate observation data, the inversion systems of equations can exhibit high condition numbers. In such cases, inverse solution time was greatly increased, for which robust, accurate, and efficient solution techniques (i.e., preconditioning and solvers) are needed. First, to improve the condition number of the inversion coefficient matrix, coordinate transform, scaling, and Gaussian Noise Perturbation (GNP) techniques were implemented, which results in a speedup of 200X by calling the same serial iterative solver. Some model reduction studies were also conducted and discussed. Then, to further improve the speed of the iterative solution therefore the inverse problem can be scaled up to much larger grids, a highly scalable parallel solver was developed and implemented. With the developed parallel solver, it takes only 150s (CPU time) to invert a 500 x 500 problem with 100 processors. A parallel scaling study further reveals that ideal speedup was achieved in solving the inversion matrices. Moreover, model reduction was explored to understand the computation-resolution trade-off in inversion.;After computation improvement, uncertainty quantification becomes feasible. The accuracy of inversion was evaluated against: (a) heterogeneity representation and resolution of the inverse problem, (b) observation data quality, and (c) data quantity. The chosen evaluation criteria consist of model precision (MP) and model accuracy (MA). Three inverse grids, an SIS grid, an SA grid with smoothed facies distribution, and a coarsened gird (50 x 50), were first inverted using the same error-free data from 12 wells. Conductivities are estimated with a precision of +/-0.15% (SIS), +/-1.5% (SA), +/-3% (coarsened) of their true values, respectively.;Also, some co-effect analyses were conducted to further quantify model uncertainty and reveal the importance of each factor using such model evaluation criteria as MP and MA. After the quantification study, it is obtained that data quantity always play a prominent role in MP and MA. Data quality is critical to MA but has limited influence on MP. The impact of heterogeneity resolution is always mild, which implies the possibility of upscaling and computation-resolution trade-off. In addition, for BCs, different sections exhibit distinctive model behaviors which were discussed also. In general, exploration regions always yield lower precision and poor accuracy, but good robustness to the change of model conditions is also shown in these areas. The regions with lower hydraulic heads exhibit better inverted outcomes, which implies the importance of the selection of the datum. Milder total head variation also results in more satisfactory model performance. Finally, decent stability of the uncertainty of MA and MP makes it possible to predict model behavior using observed model status information. (Abstract shortened by UMI.). |
