Equivalent hydraulic conductivity of an experimental stratigraphy: Implications for basin-scale flow simulations



[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.