Viscous Fingering Research Articles

Pore-scale characterization of CO2 front progress through a porous medium using a free energy model based on Phase-Field Lattice Boltzmann Method

Pore-scale simulation of CO2 front progression through a porous medium has been investigated by a free energy model based on phase-field lattice Boltzmann method. Visualization of the fluids distribution in the breakthrough time reveals a strong dependence of front pattern on viscous and capillary forces interaction. Therefore, the dominance of each force imposes a different front pattern on the system. According to the percolation theory, increasing the capillary number reduces the invading fluid saturation and, consequently, the sweep efficiency, because the viscous fingering regime will intensify. However, a uniform pattern is observed when the mobility ratio is high, whereas the front evolution is facilitated in the opposite case. Impressive results have also been obtained regarding the wetting conditions. Since an upward trend in the displacement efficiency from strong drainage to strong imbibition processes is expected, this trend has changed due to the capillary suction effects in the strong imbibition process. According to experimental studies, the viscous fingering phenomenon will be proportional to the capillary suction. Furthermore, new areas have also been introduced to predict the displacement regimes.

Morphology and electrical properties of high-speed flexography-printed graphene.

Printed graphene electrodes have been demonstrated as a versatile platform for electrochemical sensing, with numerous examples of rapid sensor prototyping using laboratory-scale printing techniques such as inkjet and aerosol jet printing. To leverage these materials in a scalable production framework, higher-throughput printing methods are required with complementary advances in ink formulation. Flexography printing couples the attractive benefits of liquid-phase graphene printing with large-scale manufacturing. Here, we investigate graphene flexography for the fabrication of electrodes by analyzing the impacts of ink and process parameters on print quality and electrical properties. Characterization of the printed patterns reveals anisotropic structure due to striations along the print direction, which is related to viscous fingering of the ink. However, high-resolution imaging reveals a dense graphene network even in regions of sparse coverage, contributing to robust electrical properties even for the thinnest films (< 100nm). Moreover, the mechanical and environmental sensitivity of the printed electrodes is characterized, with particular focus on atmospheric response and thermal hysteresis. Overall, this work reveals the conditions under which graphene inks can be employed for high-speed flexographic printing, which will facilitate the development of graphene-based sensors and related devices.

Pore-scale study of drainage processes in porous media with various structural heterogeneity

Multiphase flow in porous media is widely encountered in many scientific and engineering fields. In this work, Voronoi diagram is used to reconstruct porous structures with low permeability and high heterogeneity, and the color-gradient lattice Boltzmann method is employed to simulate two-phase displacement with high viscosity ratio. Three benchmarks are utilized to validate the model, which are the Young-Laplace test, the contact angle test and the relative permeability in a 2D channel. Effects of capillary number, structural heterogeneity and wettability are analyzed. The results show that a higher capillary number leads to viscous fingering with a higher recovery rate. The connectivity rate is used to quantify the continuous wide pores, showing that structure heterogeneity will increase the probability of continuous wide pores, which promotes the formation of gas channeling, thus reducing the recovery rate. However, local structure modifications, providing that the overall homogeneity is retained, would not induce significant differences in recovery rates and displacement patterns. Complex pore structures will also cause capillary snap off, leading to more dead-end fingerings and more complicated two-phase dynamic behaviors. Meantime, a more wetting invading phase would induce a stop-wait-overlap phenomenon, which would increase the recovery rate and render the displacement more compact.

Numerical analysis of the pore-scale mechanisms controlling the efficiency of immiscible displacement of a pollutant phase by a shear-thinning fluid

Knowledge of the pore-scale physics of underground multiphase flows is essential to devise efficient soil remediation methods. However, the immiscible displacement of pollutant through the injection of a shear-thinning fluid remains poorly understood. The current work presents a full set of direct numerical simulations in which a Newtonian contaminant is displaced by a Carreau fluid or, alternatively, by a Newtonian fluid, in three porous media with different degrees of microstructural complexity. Imbibition, drainage and neutral wettability cases are considered, and the sensitivity of residual pollutant saturation to Carreau’s law parameters is also assessed. The present results allow for the quantification of the performance of immiscible displacement using shear-thinning invading fluids. This performance is shown to depend on the value of capillary number and the heterogeneity of the porous microstructure, which determine the relative importance of viscous fingering, capillary forces and pollutant trapping behind the invasion front.

Surface Charge Affecting Fluid–Fluid Displacement at Pore Scale

AbstractEfficiency in fluid–fluid displacement is drastically reduced by viscous fingering, limiting the overall effectiveness in enhanced oil recovery, membrane science, and lateral flow devices used in biomedical applications. Local instabilities at the fluid–fluid interface lead to finger‐like patterns when a less viscous fluid displaces an immiscible fluid of higher viscosity. This widely observed phenomenon in multiphase flow inside porous media is infamously intricate to control, especially for given geometry and viscosity ratio. The presented study uses a highly controlled microfluidic porous network structure with tailored ionic surface strength. The direct correlation of viscous fingering evolution on the porous structure's zeta potential at a pore‐scale level is demonstrated via polyelectrolyte coatings using a layer‐by‐layer technique. Displacement patterns are tuned from vigorous viscous fingering over stable displacement to corner flow events across a broad range of capillary numbers depending on the applied coatings. The experimental data show an increasing trend of oil recovery with increasing surface wettability, consistent with several previous findings. Furthermore, the results reveal that surface zeta potential correlates positively with recovery rate but negatively with the displacement stability quantified by the fractal dimension. These insights enable a more targeted porous media design to obtain optimal multiphase flow control.

Viscous fingering during heavy-oil displacement by chemical solutions: Emulsion instability and partial-miscibility

The viscous fingering morphologies at a particular stage of emulsion displacements are observed to follow similar development patterns as that of the partially-miscible viscous fingering behavior (existent between the commonly studied fully miscible and immiscible systems). Chemically-induced viscous fingering before and after the finger droplet development resembling the partially-miscible fluid behavior is investigated using fractal dimensions and various -classic and modified-dimensionless scaling groups. We demonstrate, through the quantitative analysis using the empirical data collected from our previous experimental study, that the finger droplet formation morphologies observed in partially-miscible injection are indicative of an emulsion hydrodynamic instability behavior. The dominant parameters responsible for such droplet formation and their relationship to fractal dimension and hydrodynamic stability are mapped in a phase diagram with the original experimental images. • Emulsions from the droplet morphologies require an external force to maintain stability. • Emulsion stability is predominantly dependent on the viscosity force. • Low IFT is associated with the droplet generation after the initiation of the finger break. • Two types of “self-similar” behaviors per the categorization based on the saturation profiles. • Fractal dimension is proportional with surface tension and an inversely proportional to viscosity.

Phase-field modeling of wormhole formation and growth in carbonate matrix acidizing

Acidic fluid flow in geologic formations leads to mineral dissolution and, under certain circumstances, to localized dissolution forming a dendritic pattern, known as wormhole. Such patterns of conduits and caves are often observed in karstic aquifer and deliberately engineered in oil and gas well stimulation with acid injection. Two different kinds of instability are thought to cause wormholes. One is heterogeneous property in rocks. The other is a process itself such as reaction infiltration or viscous fingering. To assess each one properly, we need to separate one from the other. While most numerical studies rely on randomly seeded material heterogeneities to induce wormholes, Daccord and Lenormand (1987a) demonstrated that even water injection into a homogeneous plaster can form wormholes. Here, we focus on the process instability driven by reaction-infiltration in homogeneous materials. We apply a phase-field approach, which diffuses a sharp interface in a continuous manner and show that it is capable of simulating wormhole without random seeds by accounting for the energy expenditure in the dissolution topology. We verified the model against the sharp interface counterpart in one-dimensional simulations. We then performed the two-dimensional simulations to qualitatively validate wormhole formation and growth patterns against acid injection experiments on carbonate rocks under radial flow conditions. Our simulation results indicate that the injected acid is rapidly consumed near the acid entry point at low injection rates while the live acid becomes available at the tip of the dissolved cavity under high rates and thus wormhole starts to grow resulting in much faster acid breakthrough.

Horizontal miscible displacements through porous media: the interplay between viscous fingering and gravity segregation

We consider miscible displacements in two-dimensional homogeneous porous media where the displacing fluid is less viscous and has a different density than the displaced fluid. We find that the dynamics evolve through nine possible regimes depending on the viscosity ratio, strength of density variations and the strength of the background flow, as characterized by the Péclet number. At early times the interface is dominated by longitudinal diffusion before undergoing a transition to a slumping regime where vertical flow is important. At intermediate times, vertical flow and diffusion can be neglected and there are three different limiting solutions: a fingering limit; an injection-driven gravity-current limit; and a density-driven gravity-current limit. Finally at late times, transverse diffusion becomes important and there is a transition from an apparent shutdown regime to a viscously enhanced Taylor-slumping regime. In each of the regimes, the dominant scalings are identified and reduced-order models for the evolution of the concentration field are developed. Lastly, three case studies are considered to illustrate the dominant physical balances in the geophysically relevant setting of geological $\textrm {CO}_2$ storage.

A Review of High‐Temperature Foam for Improving Steam Flooding Effect: Mechanism and Application of Foam

With the exploitation of light oil approaching saturation, the exploitation of heavy oil is of particular importance. Thermal recovery technology is typically used in heavy oil recovery, such as steam flooding (SF), steam‐assisted gravity drainage, and cyclic steam stimulation. However, SF technology brings problems such as gravity overlap, viscous fingering, and channeling, reducing the sweep efficiency and oil recovery efficiency. Some studies have proposed that foam and steam should be injected into the reservoir together to plug, turn, and reduce viscosity. Heavy oil production occurs mostly under high‐temperature conditions, which require that the foaming agents have good foaming ability in this environment. The generated foam should have good stability. Meanwhile, the mechanism of steam foam enhancing oil recovery (EOR) also changes. Therefore, the research on the mechanism and application of steam foam technology is discussed. First, the basic theory of foam is introduced, and the research on the mechanism of steam foam EOR is discussed. Second, the application of steam foam in the laboratory and the field is summarized. Finally, the full text is summarized and some prospects are made, to provide some help for future research.

Transition from viscous fingers to compact displacement during unstable drainage in porous media

The immiscible displacement of a viscous fluid by a less viscous one in a porous medium is known to be unstable and often results in dendritic fingering patterns, where the pressure gradient is screened internally and only advanced invading parts grow. We present experiments in porous media, systematically varying the imposed injection pressure ($P$) and viscosity ratio ($M$) of the invading to defending fluid. A crossover to more stable and compact invasion structures is found for higher $P$ and $M$. This compact invasion regime onset is observed even for $M&lt;{10}^{\ensuremath{-}3}$. We show that the pressure gradient is not screened in this regime and invasion patterns exhibit rich internal flow dynamics.

Effect of nonlinear drag on the onset and the growth of the miscible viscous fingering in a porous medium

Effect of nonlinear drag on the onset and the growth of the miscible viscous fingering in a porous medium

Pore-scale study of the anisotropic effect on immiscible displacement in porous media under different wetting conditions and capillary numbers

This article investigates the effect of anisotropy on two-phase flows in porous media (both drainage and imbibition) under various wetting angles and capillary numbers. The focus is on the applied results useful to petroleum engineering. Mathematical modeling based on lattice Boltzmann equations in combination with multi-relaxation time and color-gradient model is used as a research tool. This paper proposes a new method for creating digital models of porous media, based on a combination of a quartet structure generation set and Monte-Carlo algorithms. The advantage is the ability to control both heterogeneity and anisotropy. This paper presents visual phase diagrams of the invasion patterns in anisotropic samples as a function of wetting angle and capillary number. The results show that the ratio between capillary and viscous forces is highest for the sample with favorable anisotropy, which has the biggest permeability, and decreases on going to unfavorable anisotropy (lowest permeability). This effect leads to the finding that boundary capillary numbers, which determine the transition between crossover mode and invasion patterns (viscous and capillary fingering, and compact displacement), are shifted towards lower values as anisotropy increases. The images of fluid distributions are numerically described using fractal dimension and displacement efficiency. It was found that the anisotropic effect is most pronounced at capillary fingering and does not significantly affect the invasion characteristics in the imbibition mode. The sensitivity of the fractal dimension and displacement efficiency to a change in the wetting angle is maximal at favorable anisotropy and decreases on going to unfavorable anisotropy. During drainage, the fractal dimensions, estimated for favorable and unfavorable anisotropy, show opposite trends depending on the capillary number. In the imbibition mode, there is an increase in the fractal dimension with an increase in the capillary number for all porous structures. In addition, this paper investigates the anisotropy effect on the «injected fluid - skeleton » interfacial length under different wetting and dynamic conditions. It was shown that the anisotropy has no significant effect on this parameter, and the best interaction efficiency was found with a compact displacement, and the least with a viscous fingering. Also, the influence of the no-flow and periodic boundary conditions on the invasion characteristics is examined. The results show that boundary conditions do not significantly affect the invasion in the sample with favorable anisotropy for any wetting angles. Periodic boundary conditions negatively influence the displacement efficiency for samples with isotropic and unfavorable structures at drainage, but no noticeable effect was found during imbibition. • The anisotropic effect is most pronounced with capillary fingering. • Anisotropy does not significantly affect invasion during imbibition. • Anisotropy has no significant effect on the «injected fluid - skeleton » interface. • Boundary conditions do not affect invasion with favorable anisotropy for any wettability.

Особенности экспериментального изучения устойчивого и неустойчивого вытеснения в ячейке Хеле-Шоу, заполненной стеклянными шариками

The paper presents the results of an experimental study of immiscible displacements: displacement of water by oil (stable) and displacement of oil by air or water (unstable) at constant pressure drop in the Hele-Shaw cell filled with glass balls, which is a physical model of a porous fracture in an oil reservoir. The presented data allows one to draw a logical conclusion: the higher the inlet pressure, the higher the displacement efficiency. With the same oil displacement time in the Hele-Shaw cell, the passed volume of the gas significantly exceeds that of the water. The displacement by water is more complete, though. Displacements are highly dependent on inhomogeneity of the model skeleton, most significantly for the flow at low pressure drop. At the edges of the model, where the volume of the dispersed medium is greater, the motion is faster. When displacement in the model with balls is stable, the flow spreads out towards the outlet and takes a "funnel" shape that gradually expands; the motion is directed through the channel passed. For unstable displacement at low pressure drop, the motion occurs along the edges of the cell; with an increase in the pressure drop, the motion becomes more uniform, and the " viscous fingers" begin to "branch" and grow even at a distance from the outlet.

Particle Behaviours in Free Surface Flow of Particle Suspensions

In this study, the suspension flows in a Hele-Shaw cell were experimentally examined. We focused on the free surface of suspension in a Hele-Shaw radial flow and discussed the effect of particle behaviors on the change in surface shape. The test fluids used were two kinds of suspension with a different particle size. The volumetric fraction of each fluid was 40 vol.%. In the observation of free surface in the Hele-Shaw flow, it was found that concave and convex parts appeared on the free surface with a time. Furthermore, at the inside region of surface undulation, the occurrence of the particle-induced viscous fingering was confirmed. Measuring velocity profiles inside the viscous fingering using the particle imaging velocimeter (PIV), we found that the velocity in the fingering region became higher than those of entire suspension. The difference between the particle velocity inside fingering and that of entire suspension suggested that the shear flow in the Hele-Shaw cell affected the particle behaviors. Furthermore, since the temporal changes in the fingering shape was different between both fluids, the particle behaviors inside the viscous fingering might relate to the particle migration in the perpendicular direction to flow direction due to the local change in the shear deformation.

Green materials for carbon storage in depleted oilfields: An experimental study

The incessant rise in global temperature due to the large increase in anthropogenic carbon emissions over the past century threaten to undo gains made by human civilization and it has become essential that techniques to reduce atmospheric carbon be explored. For this, carbon-negative technologies like carbon geo-storage hold high vitality for industrial applications. In carbon geo-storage, captured CO2 is injected into the subsurface formations like depleted oilfields. However, the injected CO2 tends to undergo viscous fingering, bypassing small pore throats and consequently, the volumetric storage efficiency is reduced. Thus, there is a need for new mobility control agents which not only improve the volumetric storage efficiency of CO2 but also help alter rock surface for longer CO2 retention. Thus, in this study, the use of a novel green surfactant (S) has been explored in conjunction with natural polymers (P), guar gum and xanthan gum for CO2 mobility control. The composition of the SP solution was finalized via contact angle studies in presence of CO2. Following this, CO2 injection at varying flow rates (30–90 ml/h) was investigated in sand-packs of porosity 27–31% and permeability ≈682–812 mD which was saturated with a residual reservoir brine of 4 wt% NaCl. The role of the green SP solution was validated by injecting a slug of 0.3 pore volume (PV) before CO2 injection and the time to breakthrough for gas, the liquid return before breakthrough and the pressure drop profiles were carefully analyzed. It was found that the inclusion of green surfactant improved carbon retention by a factor of 3–4.5 (in the presence of other polymers) which was also demonstrated by an increase in areal coverage inside the sand-pack (as established from the pressure drop studies). Thus, the use of a green SP solution is proposed as a mobility control agent for carbon storage in depleted oilfields.

Stability Analysis of Miscible Viscous Fingering in Bingham and Carreau Fluids

Stability Analysis of Miscible Viscous Fingering in Bingham and Carreau Fluids

Effect of anisotropies in formation of viscous fingering in lifting plate Hele-Shaw cell

ABSTRACT This study presents an experimental investigation of viscous fingering formation under anisotropies in Hele-Shaw cell. The lifting plate Hele-Shaw cell employed in this study comprises of two parallel plates firmly positioned one over another with a minuscule gap filled with high viscous fluid, and a low viscous fluid flows through this gap. Two fluids of different viscosity interact in this cell and instabilities are generated due to the viscosity difference. These instabilities need to be suppressed to get controlled and stabilised patterns. Literatures presented these instabilities and explored the various techniques to stabilise them. In this study, a novel strategy consists of use of anisotropy and protrusion on the lower plate of the cell to suppress instabilities is presented. The holes and protrusions explicitly generate the least resistance to the flow of low viscous fluid (air). This results in control flow and guided path for low viscous fluid (air) penetrating into a high viscous fluid. These methods have given excellent control over the instabilities, and beautifully controlled naturally inspired patterns are obtained. Microfractals present in nature, such as leaf venation, honeycomb pattern, are examined and imitated by the proposed method. Experimental results confirm the acceptability of this control strategy.

Multi-scale flow patterns during immiscible displacement of oil by water in a layer-inhomogeneous porous media

This paper presents the results of numerical study of the relationship between micro-and macroscale flows during immiscible displacement in a two-layer porous medium. A feature of the proposed approach is the allowance for large-scale capillarity induced flow due to curvature of the displacement front in macro-inhomogeneous porous medium. The physical mechanisms determining the development of viscous instability in a layer-inhomogeneous porous medium are considered, the methods for suppressing viscous fingers formation based on the stabilization of the displacement front due the action of capillary forces are proposed.

The Influence of Bimodal Heterogeneity on Viscous Fingering of a Miscible Interface in Porous Media

The flow regimes and the dynamics of the front in miscible displacements are controlled by the interactions between the mechanisms of instability involved in such processes. The instabilities may be driven by unfavorable gravity or mobility ratios or by the heterogeneity of the medium providing favorable paths for the more mobile fluid. In this work, the effect of porous medium heterogeneity with two scales of permeability variations on the frontal instability and fluid mixing have been investigated. The base mode of permeability variations has a smaller wavelength and higher frequency while the imposed mode has a larger wavelength. The effect of such a bimodal heterogeneity on the growth of mixing zone length (MZL) has been studied and the development of the previously recognized flow regimes in layered porous media have been examined. Compared to the unimodal medium comprising the base wave, in the bimodal cases with large contrast between the wavelengths of the two periodic profiles the dominance of each wave length at a different time scale predictably enhances the growth of fingers in the early and late stages. Interestingly and less intuitively, even in cases with close wave numbers between the combined modes faster growth of the mixing zone length is observed. In such cases, the coherence of equal layers in a unimodal layered medium is disturbed by the second wave number resulting in fading of the lateral diffusion regime. However, bimodal heterogeneity may attenuate the instability compared to the unimodal system with the imposed wave’s frequency.

A bottom-up approach to construct or deconstruct a fluid instability

Fluid instabilities have been the subject of study for a long time. Despite all the extensive knowledge, they still constitute a serious challenge for many industrial applications. Here, we experimentally consider an interface between two fluids with different viscosities and analyze their relative displacement. We designed the contents of each fluid in such a way that a chemical reaction takes place at the interface and use this reaction to suppress or induce a fingering instability at will. This process describes a road map to control viscous fingering instabilities in more complex systems via interfacial chemical reactions.