Fluid Flow Analysis in Anisotropic Porous Media by Lattice Boltzmann Method

The lattice Boltzmann method (LBM) is applied to simulation of natural convection in anisotropic porous media using Brinkman equation. The Brinkman equation is recovered from a kinetic equation for the density distribution function with a forcing term. The temperature equation is calculated by a kinetic equation for thermal energy distribution function. The velocity profiles of the LBM shows good agreement with those of the analytical solutions for the Poiseuille flow and for the Couette flow filled with anisotropic porous media. For various values of Darcy and Rayleigh numbers, the solutions of the LBM are compared with those of earlier studies in natural convection. This paper leads to the conclusion that the LBM can simulate natural convection in anisotropic porous media for the non-Darcy model

Numerical Modeling of Inertial Flows in Proppant-Reservoir Rock Interfaces

Predicting accurate pressure drops in the reservoirs is essential for estimating the ultimate hydrocarbons recoveries and production rates. In hydraulically fractured wells, inertial flows can cause excessive pressure drops, beyond the predicted values form the Darcy equation. Therefore, predicting these excessive pressure drops through defining non-Darcy factors is of particular significance.;Excessive pressure drops in inertial flows are caused by acceleration/deceleration of fluids, which usually occur when fluids are moving from constricted areas to larger pores and vice versa. In the interface between the propped fracture and the reservoir rock, the pores in the latter are in connection with the former that can generate eddies and thus fluid acceleration/deceleration.;In this work, two-dimensional geometries are generated by combining coarse and tight porous media and their hydraulic properties, i.e., absolute permeability and non-Darcy factors, are calculated using lattice Boltzmann simulations. Based on the simulation results, calculated absolute permeability of generated porous media follows the harmonic averaging theory for flow through series of constituting porous media. However, the non-Darcy factor for the generated geometries are higher than the constituting geometries, which does not conform to any averaging approach. This affirms the common knowledge that non-Darcy factor is a property that cannot be upscaled. The results in this study broadens our knowledge of fluid flow in hydraulic fractures

Fractal model and Lattice Boltzmann Method for Characterization of Non-Darcy Flow in Rough Fractures.

The irregular morphology of single rock fracture significantly influences subsurface fluid flow and gives rise to a complex and unsteady flow state that typically cannot be appropriately described using simple laws. Yet the fluid flow in rough fractures of underground rock is poorly understood. Here we present a numerical method and experimental measurements to probe the effect of fracture roughness on the properties of fluid flow in fractured rock. We develop a series of fracture models with various degrees of roughness characterized by fractal dimensions that are based on the Weierstrass-Mandelbrot fractal function. The Lattice Boltzmann Method (LBM), a discrete numerical algorithm, is employed for characterizing the complex unsteady non-Darcy flow through the single rough fractures and validated by experimental observations under the same conditions. Comparison indicates that the LBM effectively characterizes the unsteady non-Darcy flow in single rough fractures. Our LBM model predicts experimental measurements of unsteady fluid flow through single rough fractures with great satisfactory, but significant deviation is obtained from the conventional cubic law, showing the superiority of LBM models of single rough fractures

Simulation of Flow of Mixtures Through Anisotropic Porous Media using a Lattice Boltzmann Model

We propose a description for transient penetration simulations of miscible and immiscible fluid mixtures into anisotropic porous media, using the lattice Boltzmann (LB) method. Our model incorporates hydrodynamic flow, diffusion, surface tension, and the possibility for global and local viscosity variations to consider various types of hardening fluids. The miscible mixture consists of two fluids, one governed by the hydrodynamic equations and one by diffusion equations. We validate our model on standard problems like Poiseuille flow, the collision of a drop with an impermeable, hydrophobic interface and the deformation of the fluid due to surface tension forces. To demonstrate the applicability to complex geometries, we simulate the invasion process of mixtures into wood spruce samples.Comment: Submitted to EPJ