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 since they often require excessive mesh refinement that leads to a significant increase in computational costs. 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 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, like 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 show how it can be used to simulate the effect of complex metallic infrastructure on dc resistivity data.

A Feasibility Study of Land CSEM Surveys With a Near-Casing Source for Hydraulic Fracturing Monitoring

“…Other scholars have achieved rapid computation of the direct current responses of the steel casing within the grid by improving the conductivity parameters of the nodes, thereby eliminating the need for grid refinement [27]. Certain scholars have employed edge conductivity to model steel casings [28], [29], [30]. This approach does not require additional degrees of freedom to represent the intricate geometry of the casing, thereby notably improving the efficiency of 3D simulations in steel casing fracturing models.…”

“…This study was based on the FVM, employing the edge conductivity equivalent method [28] for 3D forward modeling of the land CSEM method with steel casing wells and a near-casing source. First, we derived a finitevolume 3D forward modeling algorithm and introduced the edge conductivity equivalent method.…”