Modeling A Natural Permeability Field With Multifractals: A Simulation Approach

Multifractal models are helpful in characterizing complex natural phenomena like spatial variations in subsurface permeability which in turn, is crucial for predicting fluid flow and mass transfer in the subsurface. This study investigates the applicability of multifractal models in capturing the complex spatial variability of such natural permeability fields. A set of previously studied two-dimensional multifractal models with the same spectrum of dimensions but different visual appearances were considered. These were evaluated for their connectivity and were compared using time-varying response curves by employing a streamline simulator, TRACE3D. Next, to test if multifractals can realistically model subsurface heterogeneity, a soil section representing a natural permeability field and previously identified as a multifractal was considered. This permeability field was modeled using a second set of multifractal models. Three different strategies were considered, each of which included a deterministic model and a suite of random realizations that were compared with the natural data in terms of their respective recovery curves. It was found that the optimal modeling strategy is the one where the multifractal generator is extracted directly from the soil section image. As opposed to previous multifractal modeling approaches, this study considers time-varying flow response curves for evaluating the efficiency of a modeling strategy and offers a range of possible solutions for understanding subsurface heterogeneity rather than using a single deterministic model. The work therefore demonstrates the potential of multifractal models in capturing the heterogeneity of natural permeability fields and offers an alternative geomodeling approach.