Transient two-phase flow in granular porous media: Multiscale experimental and numerical investigations of scale and dynamic effects in soil water retention behaviour

What is it about?

Transient two-phase flow in granular porous media

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Photo by Lewis Keegan on Unsplash

Photo by Lewis Keegan on Unsplash

Why is it important?

The two-phase flow seepage is a process in geotechnical and petroleum engineering. Beyond the theory that describes the two-phase flow seepage with various hydraulic boundaries, the core of quantifying multiphase interfacial physics and multiphase flow transportation rests upon the capillary pressure-saturation relationship (Pc-S) in a general two-phase system and the soil water retention curve (SWRC) for the air-water system, and their corresponding relative permeability–saturation relationship (Kr-S). Since the advent of estimating both constitutive relationships using the pore size distribution of a representative elementary volume (REV) of porous media, the two have been synthesized into a singular relationship. Thus, determining Pc-S or SWRC is paramount. Traditional tests employed the axis translation technique (ATT), a two-phase displacement process within a REV spanning a few centimetres. This standard approach measures the static Pc-S or SWRC, overlooking important effects, namely the scale and dynamic effects inherent in Pc-S or SWRC. A limited understanding of multiphase physics in porous media results in discrepancies between laboratory and in-situ SWRC measurements, leading to inadequate modelling predictions. Therefore, the research objectives encompass: (1) macroscale experimental investigations using full-scale column tests to analyze both effects in SWRC, and (2) microscale numerical studies utilizing the Shan-Chen lattice Boltzmann method (SC-LBM) to explore dynamic Pc-S under one-step and multistep transient in/outflow conditions, evaluating its relationship against specific interfacial area (anw) and different flow regimes characterized by Reynolds and Capillary numbers (Re and Ca), given the constraints of geotechnical tests in identifying pore-scale multiphase phenomena and parameters. The experimental research findings are summarized as follows: (1) The full-scale column test, integrating spatial TDR and high-precision tensiometers, is an adept platform for studying scale and dynamic effects in SWRC under static and transient flow conditions. This is due to its capability to continuously measure soil moisture and suction profiles across a full-scale soil profile, encompassing the complete suction and moisture ranges of sandy soil. (2) Establishing such a multifaceted experimental platform posed numerous technical challenges, such as sensor technology application, sensor installation, sensor calibration, soil profile preparation, and hydraulic boundary condition establishment. These challenges were accurately addressed to ensure experimental accuracy and reliability. (3) The analysis of scale effects in SWRC, using both hanging column and full-scale column tests, revealed significant disparities in SWRC for coarse soils concerning air entry value (AEV) and SWRC slope. However, minor variances were observed between these methods for finer and well-graded soils, attributed to inconsistent suction gradients around a REV and pore-scale local heterogeneity. (4) Investigating dynamic effects in SWRC using full-scale column tests demonstrated the reliability of this platform in measuring dynamic SWRC, achieved by substituting the semi-permeable membrane or high AEV ceramic disk with a saturated zone and controlled boundary conditions in this zone. (5) Dynamic coefficients exhibited a log-linear rise with decreasing soil moisture, accurately predicted by the static SWRC slope and soil moisture equilibrium time. (6) A detailed analysis of dynamic coefficients for three samples, ranging from high to low permeability, confirmed Stauffer's model, which describes an uptick in dynamic coefficients with decreasing permeability and increasing AEV. (7) Further analysis highlighted that dynamic SWRC is influenced by dynamic coefficients and groundwater dynamics in the saturated zone—a factor previously overlooked in transient flow tests due to using a semi-permeable membrane instead of a saturated zone. (8) The interplay between dynamic coefficients and groundwater dynamics elucidates the simultaneous presence of significant dynamic effects in SWRC for high-permeable soils and ultra-low permeable reservoirs, harmonizing studies in soil hydrology and petroleum engineering on this subject. The numerical explorations include the following findings: (1) SC-LBM is an efficient numerical tool capable of modelling multiphase interfacial dynamics and transient two-phase seepage by reconstructing immiscible fluid-fluid interfaces using its three pseudo-forces in a density domain. (2) SC-LBM effectively simulated dynamic Pc-S curves for a two-dimensional REV of medium sand under transient one-step and multistep in/outflow, with the ability to simultaneously track interfaces—a pioneering study using this method. (3) The exclusive nature of Pc-S-anw, which encompasses all Pc-S variants (drainage, imbibition, and hysteresis), falls short in dynamic scenarios under transient flow conditions. (4) The analysis of interfaces and flow regimes illustrated that dynamic Pc-S is more pronounced when high seepage flux produces larger anw, Re, and Ca values. (5) Elevated Re values and seepage flux during one-step or multistep transient flow showed a transition from acceleration to deceleration, posing a challenge to the conventional neglect of advective and accelerating inertias in the conventional two-phase seepage equation. (6) Varying pressure boundary conditions yielded different dynamic Pc-S curves and preferential flow paths in the 2-D REV of medium sand, indicating their dependency not just on seepage flux but also on pressure boundaries. This thesis offers innovative macroscale experimental and microscale numerical solutions to investigate dynamic SWRC under transient two-phase flow conditions, infusing more multiphase physical perspectives into the theoretical advancement of transient two-phase seepage from a hydrodynamic rather than thermodynamic standpoint.

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