GPU-accelerated Lattice Boltzmann Method (LBM) for Studying Fluid Flow and Solute Transport in Porous Media — Applications in Geoenvironment and Geoenergy

Introduction:

The constitutive relationships for fluid flow and solute transport in porous media, such as capillary pressure-saturation curves, relative permeability-saturation curves, dispersivity-saturation, and mass transfer rates, form the cornerstones of continuum-scale Darcy-scale flow and transport. These relationships link the porous medium characteristics to the macroscopic proxies and parameters.

The complex nature of geological samples representing heterogeneous complex layered porous media in pore-scale controls the macroscopic two-phase flow and solute transport. One ubiquitous heterogeneity in natural rocks is the pore size spatial distribution and correlation that can be inferred and characterized using pore-scale imaging techniques such as x-ray computed tomography.

Figure 1. Solving advection-diffusion-reaction equations on real porous media geometry of geological media after acquiring high-resolution x-ray tomography and digital image analysis for segmenting tomograms. Click here for a bigger version.

The Lattice Boltzmann Method (LBM) is widely used for diverse geoenvironmental and geo-energy applications to simulate fluid flow and solute transport in porous media. Numerical modeling of advection-diffusion-reaction (ADR) processes pose a formidable computational challenge due to the complex geometry of the porous media and the multiscale multicomponent nature of the flow, transport, and reactions.

Computational fluid dynamics (CFD) based on the Navier-Stokes equations is now widely used in industry, often run on high-performance computer clusters of CPU nodes. Direct Numerical Simulation of pore-scale processes can delineate moments of interest (in space and time) and elucidate underlying mechanisms and governing factors in ADR studies.

The LBM is based on the Boltzmann equation and kinetic theory as opposed to the conventional CFD that directly solves the NS equations. A promising advantage of LBM over NS solvers is the inherent capabilities for parallelism owing to the local data access pattern. In LBM, the computation on each node is independent, and the data transmission only happens between two adjacent nodes. This localized data communication mode and inherent additivity of its numerical implementation make LBM ideal for GPU parallel computation.

GPU parallel computation becomes increasingly more desired because of the high performance and efficiency of traditional computation on CPUs. The computation capacity of GPUs is order(s) of magnitude greater than the mainstream CPUs in terms of memory bandwidth and peak performance. Therefore, CUDA-enabled GPU parallel computation will shape the future of demanding computational tasks such as those in porous media research.

Research Objectives:

This thesis aims to achieve a numerical framework for regions of interest in mesoscale at a significantly reduced computational cost. To do so, we propose to couple a lattice Boltzmann Method (LBM) solver running on graphics processing units (GPUs) using CUDA (Compute Unified Device Architecture) with or without a Navier-Stokes (NS) solver running on computation on central processing units (CPUs).

Research Scope:

Solving advection-diffusion-reaction (ADR) equations for pore-scale porous media flows flow based on real geometry (static/dynamic) of x-ray tomography imaging data became a paramount direction in Computational Geosciences due to the variety and versatility of applications. It requires multidisciplinary tasks of image processing, computational fluid modeling, and high-performance computing. We suggest implementing volumetric LBM (VLBM) for velocity field simulation as an improved technique for precisely tracking solid to fluid ratio on the smooth solid boundary lattices, coupling the direct flow simulator with the multicomponent solute transport and, if necessary, with a geochemical module such as Phreeqc or Reaktoro for voxel-based local equilibrium and kinetic reactions.

For each part, candidates will have training and responsibilities to develop the necessary tools for carrying out the research, conducting the research to answer open questions, following the overall objectives, and compiling a report/manuscript to present the results and discuss findings.

With active participation and supervisors' directions, the candidates will have an opportunity to be involved in state-of-the-art research, receive training in experimental and modeling techniques, familiarize themselves with reactive transport studies, and be part of a lively curiosity-driven research group.

In collaboration with supervisors, the candidates will disseminate the project outcome in conference proceedings, if possible, peer-reviewed articles. The project will be an opportunity to start learning and working with techniques for studying the fluid flow and reactive transport processes relevant not only for CO2 storage but also for hydrogen storage, geothermal energy, waste disposal, and environmental studies. In addition, this project will be an opportunity to master programming skills (CUDA, C++, and Python), a big plus for any future career.

Published Sep. 5, 2022 12:52 PM - Last modified Sep. 5, 2022 12:52 PM

Scope (credits)

60