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Multi-Scale Simulation of Multiphase Multi-Component Flow in Porous View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Spiral - Imperial College Digital Repository Imperial College London Department of Chemical Engineering Multi-scale simulation of multiphase multi-component flow in porous media using the Lattice Boltzmann Method Jianhui Yang Supervised by Dr. Edo Boek Submitted in part fulfilment of the requirements for the degree of Doctor of Philosophy in Chemical Engineering of Imperial College London and the Diploma of Imperial College London 1 Declaration I hereby declare that this thesis titled Multi-scale simulation of multiphase multi-component flow in porous media using the Lattice Boltzmann Method is entirely my own work under the supervision of Dr. Edo Boek otherwise it is appropriately acknowledged. This work has not been previously sub- mitted in its entirety or in part to any other academic institute for a degree. Jianhui Yang Department of Chemical Engineering Imperial College London 2 The copyright of this thesis rests with the author and is made available under a Creative Commons Attribution Non-Commercial No Derivatives licence. Researchers are free to copy, distribute or transmit the thesis on the condition that they attribute it, that they do not use it for commercial purposes and that they do not alter, transform or build upon it. For any reuse or redistribution, researchers must make clear to others the licence terms of this work. 3 Abstract This thesis consists of work mainly performed within the Qatar Carbon- ates and Carbon Storage Research Centre (QCCSRC) project, focusing on the prediction of flow and transport properties in porous media. The di- rect pore scale simulation of complex fluid flow on reservoir rocks is the main topic of this work. A simulation package based on the lattice Boltz- mann method has been developed to study single and multiphase flow as well as thermal and solute dispersion in porous media. The simulator has been extensively validated by comparing simulation results to reference so- lutions. Various numerical experiments have been performed to study the single/multiphase/solute dispersion flow in reservoir rocks. The simulator successfully predicts various transport properties including single phase and relative permeability, capillary pressure, initial-residual saturation, residual cluster size distribution and dispersion coefficient. The prediction has been compared to available experimental data and was generally found to be in good agreement. The simulator is also ready for exploring the two-phase dynamic problem with coupled and nonlinear physical processes including the effect of wettability, surface tension and hysteresis. To improve the efficiency of the lattice Boltzmann simulations, an opti- mised collision model and corresponding parallel operation are proposed and implemented. A sparse storage scheme which significantly reduces the mem- ory requirement has been designed and implemented for complex porous media. Due to the application of these optimisation schemes, it is possible to perform simulations on large scale samples (Size >1024x512x512). The optimised code shows very good and promising performance, and nearly ideal scalability was achieved. 4 The publications as a result of this research are: Yang, J. and Boek E. S. A comparison study of multi-component Lat- tice Boltzmann models for flow in porous media applications, Computers & Mathematics with Applications 65.6 (2013): 882-890. Yang, J. and Boek, E. S. Quantitative determination of molecular propa- gator distributions for solute transport in homogeneous and heterogeneous porous media using lattice Boltzmann simulations, Submitted to Water Re- sources Research (Accepted). Chapman, E. M., Yang, J., Crawshaw, J. P., and Boek, E. S. Pore Scale Models for Imbibition of CO2 Analogue Fluids in Etched Micro-model junc- tions Using Micro-fluidic Experiments and Direct Flow Calculations, Energy Procedia, 37 (2013): 3680-3686. Shah, S. M., Yang, J., Crawshaw, J., Gharbi, O., Boek, E. S. Predicting porosity and permeability of carbonate rocks from core-scale to pore-scale using Medical CT, Confocal Laser Scanning Microscopy and Micro CT, Pro- ceedings of SPE Annual Technical Conference and Exhibition (2013), SPE 166252, New Orleans, Louisiana, USA. Al-Ansi, N., Gharbi, O., Raeini, A. Q., Yang, J. Iglauer, S. Influence of Micro-Computed Tomography Image Resolution on the Predictions of Petrophysical Properties. Proceedings of International Petroleum Technol- ogy Conference (2013), IPTC 16600, Beijing, China. Yang, J., Boek, E. S., Lattice-Boltzmann simulation of single phase flow in reservoir rocks, to be submitted. Yang, J., Boek, E. S., Lattice-Boltzmann simulation of immiscible fluid flow in reservoir rocks and relative permeability calculation, to be submitted. Yang, J., Boek, E. S., Calculation of cluster size distributions for residual oil in sandstones using lattice Boltzmann method, to be submitted. 5 Acknowledgement I wish to express my deepest gratitude to my supervisor Dr.Edo Boek for his professional guidance, encouragement and providing academic freedom during my study. Without his outstanding supervision, this work would not have been possible. I would like to thank Dr.John Crawshaw for his constructive and practical comments which were crucial to my research. I also thank Nayef Al-Ansi, Oussama Gharbi and Ali Qaseminejad Raeini for offering me the opportu- nity to collaborate with them. A special thanks to Emily Chapman and Shah Saurabh, without their excellent support of experiment work, my re- search could not have been done. I also would like to thank my office mate Farrel Gray, we had countless valuable discussions together. I thank him also for having lunch together every day and for his patience with my slow eating. I would like to thank my wonderful fellow colleagues Emily Chapman, Shah Saurabh, Farrel Gray, Daniel Ross, Christine Seifriedfor and Rudolf Umla for their kindly help, encouragement, valuable comments and I feel honored to work with them. Furthermore, I would like to thank Professor Geoff Maitland and Pro- fessor Omar Matar for serving on my transfer examination committee, and providing constructive comments. My gratitude is also expressed to every member in the Qatar Carbon- ates and Carbon Storage Research Centre (QCCSRC) for their support and wonderful environment for my research and social activity. Last but not least, I deeply thank my parents and my girlfriend for their unconditional support and love, especially my girlfriend, for her understand- ing of my absence and her endless patience. Without their love and encour- agement, it would not be possible for me to finish the study. I gratefully acknowledge funding from the Qatar Carbonates and Carbon Storage Research Centre (QCCSRC), provided jointly by Qatar Petroleum, Shell, and Qatar Science & Technology Park. 6 Contents 1. Introduction 20 2. Background and Literature Review 24 3. Methodology 30 3.1.KinetictheoryandtheBoltzmannequation.......... 30 3.2.H-theorem............................. 31 3.3.Maxwelldistribution....................... 32 3.4.Boltzmann-BGKequation.................... 32 3.5.Single-phaselatticeBoltzmannmethod............. 33 3.6. Bounce-back Boundary Conditions . ............ 36 3.7. Periodic Boundary Condition . ................ 37 3.8. Fixed Pressure or Velocity Boundary . ............ 38 3.9. Multi-Relaxation-Time (MRT) scheme for the lattice Boltz- mannmethod........................... 39 3.10.Multi-componentlatticeBoltzmannmodels.......... 41 3.10.1.TheShan-Chenpseudopotentialmodel........ 41 3.10.2.TheFreeEnergyModel................. 43 3.10.3.TheColourGradientlatticeBoltzmannModel.... 44 3.10.4. Optimised Colour Gradient lattice Boltzmann Model . 46 3.11.LBmethodforSolute/Heattransfer.............. 48 3.12.Macroscopicgoverningequation................. 49 4. Single phase flow in porous media 53 4.1.Introduction............................ 53 4.2. Verifications for the single-phase lattice Boltzmann method . 54 4.2.1. Poiseuille flow simulation and flux calculation in a narrowchannel...................... 54 4.2.2.FlowthroughAPipe................... 57 7 4.2.3.Simulationofflowinfibrousporousmedia....... 60 4.3. Boundary conditions at the solid nodes: a note of warning . 62 4.3.1. A brief review of some second order boundary conditions 63 4.4.Materialsandmethods...................... 65 4.4.1.Bentheimersandstone.................. 65 4.4.2.Conversionfromlatticeunitstophysicalunits.... 67 4.4.3. Calculation of rock permeability ............ 68 4.4.4. Computational details . ................ 68 4.5.Results............................... 70 4.5.1.ValidationofDarcy’slaw................ 70 4.5.2.Effectofsystemsize................... 72 4.5.3. Effect of inlet and outlet boundary conditions . .... 74 4.5.4. Influence of boundary conditions as a function of sys- temsize.......................... 78 5. Comparison study of Multi-Component Lattice Boltzmann models 1 81 5.1. Poiseuille flow simulation for a binary immiscible fluid system withviscositycontrast...................... 81 5.2. Capillary fingering simulation . ................ 84 5.3. Summary . ............................ 88 6. Multi-Component flow in porous media 90 6.1.Introduction............................ 90 6.2. Verifications for the multi-component lattice Boltzmann method 90 6.2.1. Capillary Pressure .................... 90 6.2.2. Relative Permeability . ................ 94 6.3. Experimental and LBM study of multi-phase flow in micro- models............................... 99 6.3.1.Methodology.......................100
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