PARAMETRIC ANALYSIS OF FLOW IN A VERTICAL POROUS CHANNEL WITH MULTIPLE FRACTURES

Resumo

During the drilling stage of oil wells, the flow of drilling fluids through the annular space is influenced by discontinuities and high-permeability regions in the geological formation. This phenomenon, known as lost circulation, reduces operational efficiency and compromises well integrity. One of the preventive control methods for this issue is the selection of a drilling fluid whose formulation is best suited to the drilling phase and well characteristics. This process can be assisted through numerical simulations using CFD (Computational Fluid Dynamics), where the annular space is simplified as a vertical channel, fractures are modeled as transverse channels with constant thickness through which leakage flow occurs, and the high-permeability geological formation is treated as a porous medium. This characterization refers to a partially porous and fractured channel (PPFC), modeled as a bidisperse porous medium, where both the free-flow and porous regions are considered homogeneous. This study aims to analyze lost circulation in a PPFC with multiple discrete fractures. The flow is assumed to be steady, incompressible, and the fluid is modeled as a power-law fluid. The porous medium is considered isotropic. Flow in the free channel and fractures is governed by the Navier-Stokes equations, while flow in the high-permeability region is described by the generalized porous media equation proposed by Vafai and Tien (1981). Numerical simulations are performed using the finite volume method in OpenFOAM version 24.06, employing an adapted version of the porousSimpleFoam solver to represent non-Newtonian fluid flow in porous media. The simulations are set up with a porosity of ε = 0.7 and permeability of 10⁻⁶ m². The drilling fluid is idealized with a consistency index k = 0.205 Pa·sⁿ, a power-law index n = 0.568, a density ρ = 1012.60 kg/m³, and a Reynolds number Re = 1000, calculated based on the annular space.  The results are obtained from combinations of 2 or 3 fractures with thicknesses eₓ = 4, 16, and 40 mm, spaced at distances h = 100, 200, and 400 mm. The analysis focuses on evaluating the velocity, pressure, and viscosity fields, the leakage rate, and the pressure drop along the channel.