[1] Critical issues facing basin-scale groundwater flow models are the estimation of representative hydraulic conductivity for the model units and the impact of nonrepresentation of within-unit conductivity heterogeneity on the model flow prediction. In this study, high-resolution, fully heterogeneous basin-scale hydraulic conductivity map is generated by scaling up an experimental stratigraphy created by physical sedimentation processes and by assuming increasing conductivity for increasing gray scale (proxy for sand content). A fully heterogeneous model is created, incorporating the complete conductivity variation. Two hydrogeologic framework models are also created, one of coarser stratigraphic division. A novel numerical up-scaling method is developed to compute an equivalent conductivity for each irregularly shaped framework model unit by conducting basin-scale flow experiments in the fully heterogeneous model. In each experiment, different boundary conditions are specified, subjecting the basin to various flow conditions. To evaluate the impact of using equivalent conductivity on the prediction of basin-scale hydraulic head and groundwater flow, the flow experiments conducted in the fully heterogenous model are repeated in the framework models. Results indicate that for most deposits, the behavior of the equivalent conductivity with increasing ln(K) variance is consistent with the prediction of an analytic-stochastic theory. The equivalent conductivity is also insensitive to the boundary condition and the number of flow experiments performed, indicating the possible emergence of an effective conductivity. Although all equivalent conductivities are full tensors, the off-diagonal term is 2-3 orders of magnitude smaller than the diagonal terms. Ignoring the off-diagonal term has minimal impact on the framework-model-predicted hydraulic head and groundwater flow paths, when compared to the impact of nonrepresentation of within-unit conductivity heterogeneity. Under certain boundary conditions, significant head deviation can develop within framework model units that contain trended or strongly stratified deposits. However, the accuracy of head prediction is improved when the length of the no-flow boundary is increased. In a topography-driven system, progressive degradation is observed in the prediction of basin-scale flow pattern, flow rate, and location of recharge/discharge, when the progressively up-scaled framework models are used. In summary, the accuracy of the framework models is controlled by the level of stratigraphic division, conductivity heterogeneity, and boundary conditions.

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In granite aquifers, fractures can provide both storage volume and conduits for groundwater. Characterization of fracture hydraulic conductivity (K) in such aquifers is important for predicting flow rate and calibrating models. Nuclear magnetic resonance (NMR) well logging is a method to quickly obtain near-borehole hydraulic conductivity (i.e., K ) at high-vertical resolution. On the other hand, FLUTe flexible liner technology can produce a K profile at comparable resolution but requires a fluid driving force between borehole and formation. For three boreholes completed in a fractured granite, we jointly interpreted logging NMR data and FLUTe K estimates to calibrate an empirical equation for translating borehole NMR data to K estimates. For over 90% of the depth intervals investigated from these boreholes, the estimated K are within one order of magnitude of K . The empirical parameters obtained from calibrating the NMR data suggest that "intermediate diffusion" and/or "slow diffusion" during the NMR relaxation time may occur in the flowing fractures when hydraulic aperture are sufficiently large. For each borehole, "intermediate diffusion" dominates the relaxation time, therefore assuming "fast diffusion" in the interpretation of NMR data from fractured rock may lead to inaccurate K estimates. We also compare calibrations using inexpensive slug tests that suggest reliable K estimates for fractured rock may be achieved using limited calibration against borehole hydraulic measurements.

[1] We propose a novel direct method for estimating steady state hydrogeological model parameters and model state variables in an aquifer where boundary conditions are unknown. The method is adapted from a recently developed potential theory technique for solving general inverse/reconstruction problems. Unlike many inverse techniques used for groundwater model calibration, the new method is not based on fitting and optimizing an objective function, which usually requires forward simulation and iterative parameter updates. Instead, it directly incorporates noisy observed data (hydraulic heads and flow rates) at the measurement points in a single step, without solving a boundary value problem. The new method is computationally efficient and is robust to the presence of observation errors. It has been tested on two-dimensional groundwater flow problems with regular and irregular geometries, different heterogeneity patterns, variances of heterogeneity, and error magnitudes. In all cases, parameters (hydraulic conductivities) converge to the correct or expected values and are thus unique, based on which heads and flow fields are constructed directly via a set of analytical expressions. Accurate boundary conditions are then inferred from these fields. The accuracy of the direct method also improves with increasing amount of observed data, lower measurement errors, and grid refinement. Under natural flow (i.e., no pumping), the direct method yields an equivalent conductivity of the aquifer, suggesting that the method can be used as an inexpensive characterization tool with which both aquifer parameters and aquifer boundary conditions can be inferred.