Pore-scale investigation of the displacement fluid mechanics during two-phase flows in natural porous media under the dominance of capillary forces

© 2020, Georesursy LLC. All rights reserved. This paper presents the results of numerical simulations of two-phase flows in porous media under capillary forces dominance. For modeling of immiscible two-phase flow, the lattice Boltzmann equations with multi relaxation time operator were applied, and the interface phenomena was described with the color-gradient method. The objec-tive of study is to establish direct links between quantitative characteristics of the flow and invasion events, using high temporal resolution when detecting simulation results. This is one of the few works where Haines jumps (rapid invasion event which occurs at meniscus displacing from narrow pore throat to its wide body) are considered in three-dimensional natural pore space, but the focus is also on the displacement mechanics after jumps. It was revealed the sequence of pore scale events which can be considered as a period of drainage process: rapid invasion event during Haines jump; finish of jump and continuation of uniform invasion in current pore; switching of mobile interfaces and displacement in new re-gion. The detected interface change, along with Haines jump, is another distinctive feature of the capillary forces action. The change of the mobile interfaces is manifested in step-like behavior of the front movement. It was obtained that statisti-cal distributions of pressure drops during Haines jumps obey lognormal law. When investigating the flow rate and surface tension effect on the pressure drop statistics it was revealed that these parameters practically don’t affect on the statistical distribution and influence only on the magnitude of pressure drops and the number of individual Haines jumps

Simulation of Two-Phase Fluid Flow in the Digital Model of a Pore Space of Sandstone at Different Surface Tensions

© 2020, Springer Science+Business Media, LLC, part of Springer Nature. A study is made of the influence of surface tension on two-phase drainage flows in a porous medium. Computational filtration experiments are conducted in a three-dimensional digital microtomographic model of sandstone. To simulate two-phase flows, use is made of lattice Boltzmann equations; interfacial phenomena and wetting effects are described using the color-gradient-based method. Calculations are carried out at the same rate of injection of a nonwetting fluid and at a ratio of the viscosities of nonwetting and wetting phases of 1:10. Results are obtained according to which growth in the interfacial tension contributes to the rise in the efficiency of displacement of the wetting fluid, which is recorded at the moment the injected phase breaks through, and to the decrease in the efficiency after its breakthrough. It is established that distinctive features of flows with capillary fingering that arise at high surface tensions are the stepwise character of travel of the leading front and the growth of displacement channels in directions different from the hydrodynamic pressure difference. It is shown that interfacial tension is a parameter whose variation enables us to change the type of two-phase flow. Increase in the interfacial tension contributes to the transition of the flow with viscous fingering to a flow with capillary fingering. The efficiency of displacement of the wetting fluid in the transition crossover zone is the lowest

Wettability effect on the invasion patterns during immiscible displacement in heterogeneous porous media under dynamic conditions: A numerical study

This paper investigates the wettability effect on the characteristics of two-phase immiscible flows in porous media at different capillary numbers. This issue presents both applied results useful to engineering disciplines and explores the fundamentals of displacement mechanisms, especially in the mode of compact displacement. The main findings of this study are based on numerical flow simulations in a digital model of heterogeneous porous structure, for which the lattice Boltzmann equations are used in combination with the multi-relaxation time and color-gradient models. This work is one of the few which studies the wettability effect in porous structures with a random arrangement of particles. The influence of the contact angle and the capillary number is presented in the form of images of the fluid distribution at various contact angles and capillary numbers, which were associated with the phase-diagrams for displacement efficiency and fractal dimension, as well as fluid-fluid interfacial length and finger width. It was found that increasing capillary number suppresses the wettability effect on displacement characteristics. This article first identifies four crossover zones between capillary and viscous fingering and compact displacement. It was shown that the critical contact angle, which determines the appearance of compact displacement, increases with the capillary number. Particular attention is paid to the displacement mechanisms for compact displacement. Analysis of the pressure signature at various contact angles and capillary numbers clarifies the role of touches and overlaps that stabilize interfacial front during compact displacement and determines the real driving force for this invasion pattern. This article is the first to establish a relationship between pore-filling events and fluctuations in the pressure signature during compact displacement. It was found that an increase in the pressure signature is characterized by a uniform displacement of all menisci along with the entire fluid-fluid interface, while invasion with a sharp decrease in pressure is determined by the burst-like displacement of a concave meniscus in narrowly localized areas of the pore space

Prediction of permeability and tortuosity in heterogeneous porous media using a disorder parameter

© 2020 Elsevier Ltd This paper investigates the effect of pore-space heterogeneity on fluid transport properties. To numerically describe the heterogeneity of pore structures, a disorder parameter is used, which is characterized by the variability in local porosity in the unit cells. The flow processes are investigated using lattice Boltzmann simulations in porous media with nearly isotropic porous structures consisting of particles of the same size and with different grain size distributions. It was found that increasing disorder positively affects tortuosity, which in turn causes a decrease in permeability. With increasing porosity, the sensitivity of the transport properties to changes in the disorder reduces. Based on approximations of numerical results, analytical equations were derived that predict permeability and tortuosity depending on porosity, disorder, and grain size distribution. Verification shows that the deviations between numerical and analytical results do not exceed 10%

Influence of Porous Structure Heterogeneity on the Dynamics of Development of Interfacial Contacts in Two-Phase Flows with Viscous and Capillary Fingers

An investigation of the effect of capillary and viscous forces on the dynamics of the development of two types of interfacial contacts "injected fluid–ejected fluid" and "injected fluid–solid body" in the case of two-phase flows in porous media with different heterogeneities of the pore structure is carried out. The connection between the dynamics of development of interfaces, distribution of fluids in the pore space of samples and the average size of pore channels filled with the injected fluid is being established. To simulate a two-phase flow the present work resorts to the lattice Boltzmann equations together with the multirelaxation time collision operator, as well as the color field gradient model for describing the effects of interfacial interaction. The relationship between the capillary and viscous forces is controlled by flow velocity and interfacial tension. Computational experiments are carried out on artificial digital models of porous media with the use of the Monte Carlo algorithm. The heterogeneity of porous structures is described numerically with the aid of the randomness coefficient calculated as the standard deviation of local porosity measured in Voronoi′s cells. A linear law of the development of the specific length of interfacial "fluid–fluid" and "fluid–solid body" contacts has been established. The two-phase flow parameters and the heterogeneity of the pore structure exert their effect only on the dynamics of the growth of the interface length. An increase in the heterogeneity of the pore structure contributes to the growth of the mean size of pore channels filled with injected fluid. The randomness coefficient exerts an insignificant effect on the dynamics of the development of the "fluid–fluid" contact and a negative effect on the dynamics of the development of the "fluid–solid body" interface. In transition from flow with viscous fingers to a regime with capillary fingers, a significant decrease in the dynamics of development of the "fluid–fluid" contact and an increase in the dynamics of the development of the "fluid–solid body" interface are observed

Lattice Boltzmann Simulations of the Interface Dynamics During Two-Phase Flow in Porous Media

Abstract: This paper systematically investigates the impact of porous mediadisorder and its coupling with flow rates, favorable andunfavorable viscosity ratios, as well as surface tensions on thedynamics of interfaces development during two-phase drainage flow.A special attention is paid to establishing relationship betweenthe dynamics of fluid–fluid and fluid–solid interfacial lengths,the pore selectivity and the displacement efficiency using imagingof fluids distribution in porous media. As samples of study, weused artificially generated models of porous media with differentdisorder parameters and with two-types of pore-channels systems"— hexagonal and square. In our methodology, the disorderdefines the range of grain size distribution and is applied tocontrol the pore size range. For two-phase flow simulation, thelattice Boltzmann equations and the color-gradient model areapplied. It was established the linear relationships betweenfluid–fluid and fluid–solid interfacial length and saturation ofthe invaded fluid. During numerical simulations at differentdisorders, the lack of disorder effect on the fluid–fluidinterface dynamics and negative disorder impact on thefluid–solid interface dynamics was found. When varying the flowparameters, it was identified that the increase in thefluid–fluid interface dynamics is accompanied by a decrease inthe fluid–solid interface dynamics. For all displacementmechanisms considered in this paper, except capillary fingering,an inverse relationship between pore selectivity and pore number,involved in displacement, was detected. We found a shift of poreselectivity towards higher values with increasing disorder whichnegatively impacts on the displacement efficiency. In capillaryfingering regime, a strong tendency to minimize fluid–fluidinterfacial length with surface tension explains the lack ofrelationship between pore selectivity and pore number which leadsto bad predictable displacement efficiency in this regime

Non-Linear Equations of Unsaturated Filtration in Swelling Soils

Abstract: A mathematical model of unsaturated filtration in swelling soils under conditions of constant volume of the medium as a whole has been developed. On the basis of the developed model, a solution to the problem of capillary rise of moisture in swelling soils was obtained, and the characteristic features of the process were revealed. A series of experiments on the capillary rise of moisture in swelling and non-swelling soils was carried out. The comparison of solutions of the capillary rise problem with experimental data is carried out. Good agreement of experimental data with solutions of the corresponding boundary value problems is shown

Evaluation of Absolute Permeability in Heterogeneous and Anisotropic Porous Media Using the Lattice Boltzmann Simulations

Abstract: This paper presents a systematical study of the effect of porosity, pore-level heterogeneity and anisotropy on the absolute permeability of digital images of porous media. The main goal is to develop an analytical formula that estimates permeability as a function of these three parameters at once. Permeability is assessed based on numerical simulations using the lattice Boltzmann equations. Digital models of porous media are generated by a combined method consisting of Monte-Carlo and quartet structure generation set (QSGS) algorithms. Increase in heterogeneity negatively affects permeability. With an increase in porosity, the effect of heterogeneity on flow properties decreases. There was a linear decrease in permeability during the transition between favorable and unfavorable anisotropy. The influence of anisotropy is most pronounced in samples with high porosity and monotonically reduces with decreasing porosity. Heterogeneity negatively influences on the sensitivity of flow properties to changes in anisotropy and independent on porosity

Methods for studying two-phase flows in porous media: Numerical simulation and experiments on microfluidics chips

Copyright 2020, Society of Petroleum Engineers. In this paper, experimental and computational approaches are used to study multiphase flows. In the firstmethod, filtration experiments are carried out using microfluidics technology. Microfluidic chips weremade from polydimethylsiloxane using soft lithography. To give the desired surface properties, the innerwalls of the channels were treated with a hydrophobic or hydrophilic coating. Injection of liquids wascarried out using a syringe pump at a constant flow rate. To measure the pressure difference at the inletand outlet of the microchip, we used the method of measuring changes in gas volume. For numericalmodeling, the most modern model of the Boltzmann lattice equations, adapted for two-phase flows ofincompressible immiscible liquids, is used. The effects that occur at the phase boundary are described usingthe color field gradient model. Experimental studies have shown the possibility of studying the processesof liquid displacement from the microchannel system in a microfluidic chip simulating a porous medium.The dynamics of the displacement of liquids (water and oil) from a system of microchannels with differenthydrodynamic drag cardinally depends on the angle of wettability of its walls. In the case of microchannelswith hydrophilic walls, a complete displacement of oil by water occurs almost simultaneously from bothchannels. When water is displaced by oil from channels with a hydrophilic and hydrophobic coating, it isrequired to create an increased flow rate of the displacing liquid through microchannels. In this case, at thejunction of the microchannels, before leaving the chip, emulsion droplets of "water in oil" will form. Inthe case of oil displacement by water from microchannels with a hydrophobic coating, complete removalof oil from the channel with high resistance did not occur. This is due to the fact that the viscosity of theoil is 30 times higher than the viscosity of water. The paper shows a successful comparison of the resultsof numerical modeling and experimental research in a two-phase flow in a pore doublet. Demonstratedexamples of the developed program code are shown: the formation of emulsions at high flow rates, themotion of a drop under the influence of mass force; flow in digital microtomographic image; displacementof viscous oil from the pore medium

Organic matter in the Saf'yanovka copper massive sulfide deposit (Middle Urals)

The influence of tectonic processes on the transformation of organic matter in volcanic and volcano-sedimentary rocks within the East Ural uplift in the southern Rezh structural-formational zone was studied. The basic features and temperature ranges of organic matter (OM) and ore-bearing rock metamorphic transformations in the Saf'yanovka deposit were established using the methods of thermal analysis, electron paramagnetic resonance, and complex geochemical studies, including GC-MS. The geochemical study of organic matter in the ore-bearing rocks of the Saf'yanovka deposit confirmed its relation to the sapropelic type and to shallow marine conditions of formation. The syngenetic nature of the OM and ore-bearing rocks was established on the basis of the geochemical and physicochemical analyses. The transformation stage of OM in the Saf'yanovka deposit indicates its rapid, but incomplete maturation in the evolution of hydrothermal fluid