title: Lattice-Boltzmann studies on the effect of the morphological properties of porous medium in immiscible displacements
Creators: name: Zhang, Han
Publisher: name: University of Liverpool Repository
Year: 2023

description: Immiscible two-phase flow in the porous medium is unquestionably of great significance in numerous natural and industrial processes. It has been well established and accepted that in addition to the fluid properties, the morphology of the porous medium also plays a significant role in the final volumetric throughput of a particular fluid. Especially topological features of the pore structures have been found to exert a strong influence on the hydrodynamic behaviour of two-phase flows as they express a measure of pore space and consequently flow path connectivity and availability. The current study investigates the effect of the pore space connectivity, expressed through the Euler characteristic, on the hydrodynamic behaviour of a water-wet, oil-water two-phase system under three different states: transient state, steady-state, and low driving forces. Two-dimensional simulations are conducted in an artificially generated porous medium with the same grain size and grain density using a multi-relaxation time multi-component multiphase lattice-Boltzmann model. The transient study showed that the wetting phase saturation and the degree of pore network homogeneity have a significant impact on the dynamic evolution of wetting and non-wetting phase topology, which is governed by a series of coalescence and snap-off events. It is also observed that the macroscopic steady-state of the velocity field does not imply topological steadiness, \textcolor{black}{which can be a significant element in designing artificial filters to reach certain requests}. The impact of the pore space morphology on the transient dynamics of the two-phase flow is monitored and quantified through a series of hydrodynamic and topological parameters that signify the underlying flow transport processes. After the immiscible two-phase flow is relaxed to steady-state, the topological features of the porous medium are shown to significantly affect the macroscale capillary pressure and relative permeability curves for drainage and imbibition but in different ways. It is also demonstrated that pore space connectivity has a strong influence on the fluid phase distribution and fragmentation patterns in the porous structure depending on the displacement process. Understanding the fluid phase connectivity transformation is important in the petroleum extraction process to optimise operations. In the case of immiscible displacements under low driving force in the porous medium, it is shown that as the driving force decrease, the flow processes enter the low capillary region. \textcolor{black}{The low capillary region commonly appears in gravity-driven flows such as groundwater permeation and storage of oil and gas under the surface.} Pore structures with different Euler characteristics behave differently in the low capillary region which can be observed through the non-linear region of relative permeability and capillary number. In addition, the pore network homogeneity is also crucial in phase connectivity development under low driving forces. The current study is focused on the effect of pore space connectivity on immiscible two-phase flows in two-dimension. However, a complete description of the morphological properties of the porous medium effect in immiscible displacements can not be accomplished. For future work, the effect of higher viscosity ratios and other geometrical properties of the porous medium can be considered. Moreover, this study can be expanded to three-dimensional to investigate the impact of curvature. Immiscible two-phase flow in the porous medium is unquestionably of great significance in numerous natural and industrial processes. It has been well established and accepted that in addition to the fluid properties, the morphology of the porous medium also plays a significant role in the final volumetric throughput of a particular fluid. Especially topological features of the pore structures have been found to exert a strong influence on the hydrodynamic behaviour of two-phase flows as they express a measure of pore space and consequently flow path connectivity and availability. The current study investigates the effect of the pore space connectivity, expressed through the Euler characteristic, on the hydrodynamic behaviour of a water-wet, oil-water two-phase system under three different states: transient state, steady-state, and low driving forces. Two-dimensional simulations are conducted in an artificially generated porous medium with the same grain size and grain density using a multi-relaxation time multi-component multiphase lattice-Boltzmann model. The transient study showed that the wetting phase saturation and the degree of pore network homogeneity have a significant impact on the dynamic evolution of wetting and non-wetting phase topology, which is governed by a series of coalescence and snap-off events. It is also observed that the macroscopic steady-state of the velocity field does not imply topological steadiness, \textcolor{black}{which can be a significant element in designing artificial filters to reach certain requests}. The impact of the pore space morphology on the transient dynamics of the two-phase flow is monitored and quantified through a series of hydrodynamic and topological parameters that signify the underlying flow transport processes. After the immiscible two-phase flow is relaxed to steady-state, the topological features of the porous medium are shown to significantly affect the macroscale capillary pressure and relative permeability curves for drainage and imbibition but in different ways. It is also demonstrated that pore space connectivity has a strong influence on the fluid phase distribution and fragmentation patterns in the porous structure depending on the displacement process. Understanding the fluid phase connectivity transformation is important in the petroleum extraction process to optimise operations. In the case of immiscible displacements under low driving force in the porous medium, it is shown that as the driving force decrease, the flow processes enter the low capillary region. \textcolor{black}{The low capillary region commonly appears in gravity-driven flows such as groundwater permeation and storage of oil and gas under the surface.} Pore structures with different Euler characteristics behave differently in the low capillary region which can be observed through the non-linear region of relative permeability and capillary number. In addition, the pore network homogeneity is also crucial in phase connectivity development under low driving forces.The current study is focused on the effect of pore space connectivity on immiscible two-phase flows in two-dimension. However, a complete description of the morphological properties of the porous medium effect in immiscible displacements can not be accomplished. For future work, the effect of higher viscosity ratios and other geometrical properties of the porous medium can be considered. Moreover, this study can be expanded to three-dimensional to investigate the impact of curvature.