RESnet: 3D direct-current resistivity simulation using the equivalent resistor network circuit

Abstract

Thin and highly conductive objects are challenging to model in 3D direct-current (DC) problems because they often require excessive mesh refinement that leads to a significant increase in computational costs. RESistor network (RESnet) is a novel algorithm that converts any 3D geo-electric simulation to solving an equivalent 3D resistor network circuit. Two features of RESnet make it an attractive choice in the DC modeling of thin and conductive objects. First, in addition to the conductivity with units of Siemens per meter (S/m) defined at the cell centers (cell conductivity), RESnet allows conductive properties defined on mesh faces and edges as face conductivity with units of S and edge conductivity with units of S·m, respectively. Face conductivity is the thickness-integrated conductivity, which preserves the electric effect of sheet-like conductors without an explicit statement in the mesh. Similarly, edge conductivity is the product of the cross-sectional area and the intrinsic conductivity of a line-like conductive object. Modeling thin objects using face and edge conductivity can avoid extremely small mesh grids if the DC problem concerns electric field responses at a much larger scale. Second, once the original simulation is transformed into an equivalent resistor network, certain types of infrastructure, similar to above-ground metallic pipes, can be conveniently modeled by directly connecting the circuit nodes, which cannot interact with each other in conventional modeling programs. Bilingually implemented in MATLAB and Python, the algorithm has been made open source to promote wide use in academia and industry. Three examples are provided to validate its numerical accuracy, demonstrate its capability in modeling steel well casings, and indicate how it can be used to simulate the effect of complex metallic infrastructure on DC resistivity data.