Optimization based Upscaling of Hydrogeological Properties for Saturated Flow and Transport Simulation

Navin K C. Twarakavi , Debasmita Misra, and Sukumar Bandopadhyay

Heterogeneity is one of the main characteristics associated with many variables in nature. One of the questions that commonly arise in fluid flow and transport problems is the treatment of heterogeneity in large-scale models. During the model development stage of large-scale scale models, the necessity to upscale (coarsen) the spatial data of variables arises. For that purpose, it is important to find equivalent parameters that reproduce the effective behavior of the system discretized at a certain scale. In case of saturated flow and transport problems, one of the key variables is the hydraulic conductivity. Upscaling of spatial data for variables leads to errors in the final model due to (a) loss of information about the system, (b) displacement of key features in the model such as sources, sinks as a result of the coarseness. Therefore, it is desirable to reduce the errors incurred due to coarser spatial discretization by creating optimal upscaled estimates of hydrogeological properties such as permeability. In this research, we have introduced a novel concept of upscaling that uses a support-vector machine inspired approach to optimize upscaling of hydrogeological properties for flow and transport simulations. The optimization based approach embraces certain acceptable error intrinsically in the model structure to optimize the upscaling of hydrogeological properties necessary for flow and transport simulations. The developed optimization based approach for upscaling is compared with other methods (wavelets and geometric mean) for their effectiveness in different saturated flow and transport scenarios. It has been observed that the optimization based upscaling performs better than the other methods. It was also observed that incorporating an acceptable error within the model structure vastly improves the model results.