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Multiphase Inverse Modeling

Review and iTOUGH2 Applications

Earth Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA

View larger version (75K): [in a new window]   Fig. 1. Contours of the objective function in the three parameter planes (a) log(kabs)–log(pe), (b) log(kabs)–, and (c) –log(pe) (from Finsterle and Faybishenko, 1999). The first row shows the objective function when only cumulative outflow data are used, the second row includes only pressure data, and the third row comprises both the cumulative outflow and pressure data. The planes intersect the parameter space at the global minimum; that is, they contain the best estimate parameter set.

View larger version (101K): [in a new window]   Fig. 2. Fractal permeability field, created from iterated function system (IFS)–generated attractor points (open circles).

View larger version (54K): [in a new window]   Fig. 3. Spatially correlated permeability field created by (a) kriging, and (b,c) sequential Gaussian simulation. The fields are conditioned on permeability data along two vertical boreholes (black dots). Open circles indicate pilot points. Changing the permeability at the center pilot point affects the field in its immediate vicinity; compare panels b and c.

View larger version (61K): [in a new window]   Fig. 4. (a) Discrete fracture network model for TOUGH2; (b) flow paths inducing seepage into underground opening (after Liu et al., 2002).

View larger version (55K): [in a new window]   Fig. 5. (a) Discrete-feature model for TOUGH2 and flow through discrete fracture network and seepage into underground opening (after Finsterle, 2000).

View larger version (49K): [in a new window]   Fig. 6. Seepage prediction with calibrated fracture continuum model (solid line) including results from Monte Carlo simulations (dots) and comparison with synthetic seepage data provided by the discrete-feature model (dash-dotted line). Crosses indicate the simulations with the calibrated parameter set and the permeability realization used during the inversion (after Finsterle, 2000).

View larger version (48K): [in a new window]   Fig. 7. (a) One realization of the heterogeneous permeability field for the fracture continuum; the matrix is homogeneous. (b) Saturation changes induced by release of a water pulse at the top of the model at |X| < 3 for 1 d. The model is symmetric about the line X = 0. While both the fracture and matrix continua occupy the entire model domain, the fracture continuum is shown on the left and the matrix on the right of the symmetry axis.