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Muzemder, ATMSH., M.S. December 2020 Geology PORE-SCALE GEOMETRY and INTRA-PORE TORTUOSITY CONTROLS on FLOW ENHANCEMENT

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Muzemder, ATMSH., M.S. December 2020 Geology PORE-SCALE GEOMETRY and INTRA-PORE TORTUOSITY CONTROLS on FLOW ENHANCEMENT Muzemder, ATMSH., M.S. December 2020 Geology PORE-SCALE GEOMETRY AND INTRA-PORE TORTUOSITY CONTROLS ON FLOW ENHANCEMENT DUE TO BOUNDARY SLIP (72 pp.) Thesis Advisor: Kuldeep Singh ABSTRACT At the solid-liquid interface in porous media, fluid velocity profiles can be significantly modified in the existence of a slip boundary condition. The boundary slip, in contrast to conventional no-slip boundary condition exists due to the hydrophobic nature of media grains and can significantly control the flow behavior in media with small pore-throat, e.g. siltstones and shale. The degree of slip is represented by slip-length which is the distance from the wall- fluid interface to where the linearly extrapolated fluid velocity profile reaches the velocity of wall or u = 0. Most pore-scale studies to date, presume a no-slip boundary condition, and a few who have investigated aspects of slip-boundary presume a simplified straight tube or a non- tortuous pore domain, such as in pore-network modeling. Therefore, how the degree of tortuosity and pore-geometry control flow enhancement in porous media during slip flows remains unexplored. In this computational study, we design two distinct types of pore geometries; 1) Diverging-converging pores (DCST) which consists of variable amount of tortuosity resulting from a staggered packing of sediment grains, 2) capillary tubes which take form of; a) sinusoidal and b) helical shapes with variable amount of tortuosity. To represent size variations in pore-throats (d), domains are isotropically scaled in log-space for all DCST and capillary pore channels with d between 0.1 µm to 100 µm, which are obtained from fine siltstones to sandstone reservoirs. By using Comsol Multiphysics FEM simulator, Navier-Stokes (N-S) equation accounting for no-slip and slip boundary conditions are solved numerically for examining the modifications in flow behavior. To quantify flow behavior modifications and its causes, we examine variations in velocity, permeability, and energy dissipation form the of pore domains. Results demonstrate that pore geometry has a great contribution to modifying the emergent Darcy flow behavior and flow enhancement factor (E) with differences over several order of magnitude as systematically increase in boundary slip from no-slip condition. In DSCT pores, flow enhancement factor shows limited flow enhancement of ‘S’-shaped characteristics curve in log-log space with high or low boundary slips. In comparison, in capillary sine and helix pores, E increases linearly in an unlimited manner in log-log space with an increase of boundary slip. Furthermore, pore-throat sizes have a great control on how a given slip length enhances effective flow. Larger pore-throats have a marginal impact on flow enhancement whereas smaller pore- throats (i.e., < 10 µm) have substantial influence on the flow enhancement. In DCST pores, the diverging-converging nature of pores offers an increase in energy dissipation, resulting resistance to flow and therefore, contribute to the asymptote in the flow enhancement factor in low to high boundary slips. The energy dissipation rate (ɛ) of capillary straight tube pores (both in distribution and magnitude) remains stable when no-slip or slip boundary conditions are employed. However, as tortuosity increases, i.e., uncompacted sine and helix pores, there is a marginal amount of flow resistance offers, which leads to an infinite rise in the flow enhancement. Outcomes of this study may relevant to the applications of contaminant transport in aquifers, storage of chemical wastes, hydrocarbon recovery and many other engineering applications. PORE-SCALE GEOMETRY AND INTRA-PORE TORTUOSITY CONTROLS ON FLOW ENHANCEMENT DUE TO BOUNDARY SLIP A thesis submitted to Kent State University in partial fulfillment of the requirements for the Degree of Master of Science By A T M Shahidul Huqe Muzemder December 2020 © Copyright All rights reserved Except for previously published materials Thesis written by A T M Shahidul Huqe Muzemder B.S., Shahjalal University of Science and Technology, 2012 M.S., Kent State University, 2020 Approved by Kuldeep Singh , Advisor Daniel Holm , Chair, Department of Geology Mandy Munro-Stasiuk , Interim Dean, College of Arts and Sciences TABLE OF CONTENTS TABLE OF CONTENTS…………………………………………………………………... v LIST OF FIGURES………………………………………………………………………... vii ACKNOWLEDGEMENTS………………………………………………………………... ix CHAPTER 1: INTRODUCTION………………………………………………………….. 01 1.1 MOTIVATION AND PROBLEM STATEMENT…………………………………. 01 1.2 THESIS GOAL AND RESEARCH OBJECTIVES……………………………....... 06 1.3 SIGNIFICANCE OF RESEARCH…………………………………………………. 08 1.4 THESIS OUTLINE…………………………………………………………………. 08 CHAPTER 2: METHODOLOGY…………………………………………………………. 09 2.1 PORE GEOMETRY DESIGN……………………………………………………… 09 2.1.1 DIVERGING-CONVERGING PORES…………………………………... 10 2.1.2 CAPILLARY TUBES…………………………………………………….. 11 2.1.2.1 SINUSOIDAL CAPILLARY……………………………… 11 2.1.2.2 HELICAL CAPILLARY………………………………....... 12 2.2 COMPUTATIONAL FLUID DYNAMICS (CFD)………………………………… 12 2.3 DARCY’S LAW……………………………………………………………………. 13 2.4 DIMENSIONLESS PARAMETERS……………………………………………….. 14 2.4.1 GEOMETRIC TORTUOSITY……………………………………………. 14 2.4.2 REYNOLDS NUMBER…………………………………………………… 15 2.4.3 HYDRAULIC SHAPE FACTOR…………………………………………. 15 2.4.4 FLOW ENHANCEMENT FACTOR…………………………………....... 16 2.4.5 ENERGY DISSIPATION FACTOR……………………………………… 16 CHAPTER 3: RESULTS AND DISCUSSIONS……………………………….................. 17 3.1 RESULTS…………………………………………………………………………… 17 3.2 COMPUTED FLOW FIELDS……………………………………………………… 18 3.2.1 DCST……………………………………………………………………… 18 3.2.2 SINUSOIDAL AND HELICAL PORES…………………………………. 20 3.3 FLOW ENHANCEMENT………………………………………………………….. 23 3.3.1 DCST……………………………………………………………………… 23 v 3.3.2 SINUSOIDAL AND HELICAL PORES…………………………………. 27 3.4 THEORETICAL MODEL FOR FLOW ENHANCEMENT……………………….. 29 3.4.1 STRAIGHT CAPILLARY PORE………………………………………… 30 3.4.2 DCST……………………………………………………………………… 31 3.4.3 APPLICABILITY OF THE THEORETICAL MODELS……………........ 31 3.5 THE COEFFICIENT, C WITH INTRA-PORE TORTUOSITY AND PORE GOMETRY……………………………………………………………………………. 35 3.6 THE LIMITS ON FLOW ENHANCEMENT IN DCST PORES…………………... 37 3.7 PHYSICAL MECHANISM FOR VARIATIONS IN FLOW ENHANCEMENT .... 38 3.7.1 ENERGY DISSIPATION………………………………………………… 39 3.7.1. 1 SPATIAL DISTRIBUTION OF ENERGY DISSIPATION IN DCST PORES…………………………………………………………………………… 39 3.7.1. 2 SPATIAL DISTRIBUTION OF ENERGY DISSIPATION IN CAPILLARY PORES....................................................................................................... 40 3.8 ENERGY DISSIPATION FACTOR ……………………………………………….. 43 3.8.1 DCST PORES……………………………………………………………... 43 3.8.2 SINUSOIDAL AND HELICAL PORES…………………………………. 45 3.9 THE LIMIT OF ENERGY DISSIPATION VS. THE LIMIT OF FLOW ENHANCEMENT………………………………………………………………………. 47 3.10 DISCUSSIONS……………………………………………………………………. 49 CHAPTER 4: SUMMARY………………………………………………………………… 52 REFERENCES ……………………………………………………………………………. 55 vi LIST OF FIGURES Figure 1: Representation of different pore geometries. (a) An axis symmetric diverging converging staggered tortuous pore and 2D section of an axis symmetric tortuous pore channel (b) Different tortuous diverging converging staggered tortuous pores, (c) Sinusoidal capillary tube pores, (d) Helical capillary tube pores.…………………………………………….. 10 Figure 2: (a-l) representation of changes in velocity field in 2D axis-symmetric DCST pore geometries as a result of no-slip (b = 0) to slip boundary conditions. (l) Maximum velocity obtained when intra-pore tortuosity (τG = 1.02) is minimum, i.e., when pore geometry is close to straight tube and slip length is maximum (b = 10-4 [m]) and with the increases of intra- pore tortuosity, velocity also decreases…………………………………….. 18 Figure 3: Flow-fields showing spatial velocity distribution from no-slip (b = 0) to various slip boundary conditions. (a-h) spatial velocity distribution in 3D sine tube tortuous capillary pores; (i-l) changes in velocity field in 3D straight tube, i.e., (τG = 1) and (m-t) changes in spatial velocity distribution in 3D helix capillary pores. In five different tortuous geometries, velocity is maximum in straight tube (l) when maximum slip length is applied (b =10-4 [m]). As tortuosity increases in both the sine and helix tubes, the average velocity decreases as well..………………………………………… 20 Figure 4: (a-c) represents flow enhancement behavior with respect to different slip lengths (b) for different pore throats diameter ranges from 0.1µm to 100 µm in DCST pores, (e-g) in sine tube capillary pores and (i-k) in helix tube capillary pores. Legends for subfigures (a-k) are show in subfigures (i & g). (d, h, and l) show how all computed flow enhancement for various pore-throats collapse into a single curve as function of non-dimensional slip length (b/d)..……………......................................................................... 25 Figure 5: (a) shows how computed flow enhancement factor (E) for various pore- throats (d) (0.1µm to 100 µm) in different tortuous pores show good fit to the equation (19) for DCST pores,(b) for sine tube capillary pores, (c) for helix capillary pores as a function of dimensionless slip length (b/d)……… 33 vii Figure 6: Relationship between geometric tortuosity (τG) with theoretical constant C (equation 19). a) in DCST pore, b) in sine pore, c) in helix pore…………... 35 Figure 7: Maximum change in in flow enhancement (∆E) and the coefficient C from the theoretical model (equation 19) show exponential relationship with the hydraulic shape factor (β) in different pore throats (d) (0.1µm to 100 µm) for various DCST pore geometries………………………………………….
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