Pore-scale characterization and fluid-flow simulation: application of the Lattice Boltzmann method to conventional and unconventional rocks

2014-11-25Flow and transport in porous rocks is controlled by the pore structures and surface chemistry that, in part, defines a porous material. Pores are commonly in the micron range for conventional oil and gas formations while often in the nano-meter range for unconventional resources. Traditionally, core experiments are performed for characterization of reservoir rocks. Recently, with advances in imaging and computational power, we are able to image the pores in most relevant rocks and to construct a digital rendering of the rock that can subsequently be used for modeling of flow and transport processes. ❧ In this manuscript, we introduce a workflow that takes the rock images as input. In the first stage of the workflow, a 3D image is analyzed to find effective and total porosities. Single-phase flow simulation, using the Lattice Boltzmann Method (LBM), is then performed to evaluate directional (e.g. x, y and z) permeability of the rock sample. Finally, two-phase flow simulations are performed on the pore geometries dictated by the sample image to determine multiphase characteristics, including relative permeability of the rock sample. ❧ To place imaging technology in context, we compare and discuss the insight and understanding about the pore structure characteristics of rocks, specifically for Monterey shale samples that can be obtained from various characterization techniques. The characterization techniques considered here include: (i) Mercury injection capillary pressure experiments (MICP), (ii) Brunauer, Emmett and Teller (BET) – Nitrogen adsorption experiments, (iii) High-Resolution X-ray CT (HRXCT), and (iv) Focused Ion Beam – Scanning Electron Microscopy (FIB-SEM). The HRXCT and FIB-SEM characterization data are utilized to reconstruct (visualize) the 3D structures of the rocks; which are then used to calculate the permeabilities of these shale samples via LBM flow simulations. ❧ The LBM approach for flow simulation is a specific discretized form of the Boltzmann equation. The Boltzmann equation, the cornerstone of Kinetic theory, is discussed and the derivation of different 2D and 3D LBM schemes is presented. The 3D single-phase LBM approach is then used for calculating the flow field at the pore scale and allows us to calculate directional permeabilities. We demonstrate the application of LBM in this context for sandstone as well as shale images. ❧ Shan and Chen multiphase LBM is used for two-phase flow modeling in this work. Benchmark studies for two-phase systems, including surface area minimization and Laplace law, are presented. Wetting phenomena in 2D and 3D is subsequently discussed. With all components of LBM validated and in place, we then proceed to calculate the relative permeability curves for 2D examples of porous rocks. The effect of viscous coupling on relative permeability curve is then discussed. ❧ In the last section, we study the dynamics of capillary-driven fluid invasion in three different settings including: a) a single capillary tube, b) a porous column and c) a fractured porous media. A Lambert W functional form is proposed to describe the invasion dynamics in a single capillary tube, that predicts both early time Washburn-type behavior (√t) and late time exponential decay behavior. We extend the formulation to describe homogenous porous media and to include viscosity, pressure and gravity effects in both advancing and defending fluids. Solutions for closed systems, where the advancing fluid compresses the defending fluid, are then developed. Finally, we extend the theory to describe fractured systems, and propose a convolution integral formulation and a new explicit solution