Stochastic modelling of karstic networks of Potiguar Basin, Brazil

Abstract

In this work, the formation of karstic networks is modeled through the phenomenological stochastic differential Langevin equation. The solution of this equation follows through the application of the lattice-gas cellular automata formalism in terms of spatial and temporal discretization. The flow velocity vector is computed using a stochastic dimensionless equation where permeability, porosity, facies, and fracture persistence are the input parameters. Fluid flow is assumed to follow minimum effort paths in a heterogeneous medium from sinkholes or dolines towards springs. The shortest path search is performed using a fast marching algorithm in which fracture persistence is used as a proxy for a velocity field. Additionally, the Langevin equation's memory effect allows the coupling of the widening of the conduits with the amount of flowing water, taking into account dissolution phenomena. As conduits widen, more particles tend to run through them. This work presents a workflow for the modeling of karst generation in carbonate reservoirs. The workflow is applied to the study of an outcrop from Jandaíra Formation, Potiguar Basin, Brazil. High-resolution aerial images of the area, scanlines, and karst facies stacking pattern of an outcrop near this area are the primary data to define the three-dimensional model. Three feasible scenarios of karstification were generated: epigenic, hypogenic, and hybrid karst. As a result, 3D karstic networks form, considering the regional geology, flow conditions, and local heterogeneities.