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Submitted to: Advances in Water Resources
Publication Type: Peer Reviewed Journal Publication Acceptance Date: 6/26/2011 Publication Date: 7/13/2011 Citation: Skaggs, T.H. 2011. Assessment of critical path analyses of the relationship between permeability and electrical conductivity of pore networks. Advances in Water Resources. 34:1335-1342. Interpretive Summary: The permeability of a porous material is a measure of the rate at which water can flow through the material. Materials with small pores typically transmit water slowly and thus have low permeability, whereas materials with larger pores have a higher permeability. The permeability of soil and rock are critical to a number of important hydrological processes such as infiltration, flooding, erosion, evaporation, groundwater flow, and the movement of pollutants belowground. Scientists have long sought to understand how different arrangements of pores in rock or soil lead to different permeabilities. In this work, we examined a method of calculating the permeability based on statistical information about the arrangement of pores. The research will benefit scientists investigating the permeability of geological materials and their impact on critical hydrological processes. Technical Abstract: Critical path analysis (CPA) is a method for estimating macroscopic transport coefficients of heterogeneous materials that are highly disordered at the micro-scale. Developed originally to model conduction in semiconductors, numerous researchers have noted that CPA might also have relevance to flow and transport processes in porous media. However, the results of several numerical investigations of critical path analysis on pore network models raise questions about the applicability of CPA to porous media. Among other things, these studies found that (i) in well-connected 3D networks, CPA predictions were inaccurate and became worse when heterogeneity was increased; and (ii) CPA could not fully explain the transport properties of 2D networks. To better understand the applicability of CPA to porous media, we made numerical computations of permeability and electrical conductivity on 2D and 3D networks with differing pore-size distributions and geometries. A new CPA model for the relationship between the permeability and electrical conductivity was found to be in good agreement with numerical data, and to be a significant improvement over a classical CPA model. In sufficiently disordered 3D networks, the new CPA prediction was within ±20% of the true value, and was nearly optimal in terms of minimizing the squared prediction errors across differing network configurations. The agreement of CPA predictions with 2D network computations was similarly good, although 2D networks are in general not well-suited for evaluating CPA. Numerical transport coefficients derived for regular 3D networks of slit-shaped pores were found to be in better agreement with experimental data from rock samples than were coefficients derived for networks of cylindrical pores. |
