Viscous Fingering Research Articles

Cavitation dynamics in creeping flow

We investigate the heterogeneous cavitation phenomenon in water when a spherical surface is abruptly separated from a nearby flat substrate, at a distance of approximately 10 nm. By tracking the surface separation using Newton ring positions, and capturing the bubble evolution with a high-speed camera on a microscope, we compare our experimental findings with hydrodynamic predictions at low Reynolds numbers. Upon upward movement of the spherical surface, the resulting bubble develops branched fingers through the Saffman–Taylor instability. Simultaneously, negative liquid pressures in the range $\sim$ 10 atm are observed. These large tension values occasionally lead to secondary nucleation events. The bubble sizes satisfy a predicted Family–Vicsek scaling law where the bubble area is proportional to the inverse bubble lifetime. The fact that creeping flow cavitation bubbles are more short-lived the larger they are separates them from bubbles that are governed by inertial dynamics.

Periodic dynamics in viscous fingering

The displacement of a viscous liquid by air inside a Hele-Shaw channel is an archetype for nonlinear pattern-forming systems. Typically, bubbles or fingers of air propagate steadily at low values of the capillary number Ca = μ U * / σ , where μ is the viscosity of the liquid, U * is the speed of the bubble or finger and σ is the surface tension at the air–liquid interface. However, as the capillary number increases, the advancing interface can exhibit disordered pattern-forming dynamics. We demonstrate experimentally that a sustained, remote perturbation of the bubble tip can drive time-periodic dynamics. We exploit the propensity of a group of bubbles to propagate in steady spatial arrangements inside a Hele-Shaw channel with a centralized depth-reduction to apply a sustained pressure perturbation ahead of the bubble as it propagates. The oscillation cycle is initiated by the splitting of the bubble tip, via the Saffman–Taylor instability, which is promoted by the local flow-field conditions. The restoral of the bubble tip follows naturally because the system is driven by a fixed flow rate and the perturbed bubble is attracted to the weakly unstable, steadily propagating state that is set by the ratio of imposed viscous and capillary forces. The splitting and restoral mechanisms do not rely on the specific perturbation used in this study, suggesting a generic mechanism for periodic dynamics of propagating curved fronts subject to steady flow-field perturbations.

CO2 foam structure and displacement dynamics in a Hele–Shaw cell

The substitution of CO2 gas with CO2 foam for improved mobility control has recently attracted research attentions in enhanced oil recovery (EOR) as well as aquifer and soil remediation. However, the interplay between CO2 foam properties and oil displacement remains less investigated. In this work, using clear visualizations, we systematically investigate the dynamic advection-dominated foam morphology, its corresponding viscosity, and the efficiency and dynamics of oil displacement process by CO2 foam in a Hele–Shaw cell under the effects of gas ratio (Rg), fluid injection rates (Qt), and surfactant type. Clear visualization enables particle image velocimetry to calculate actual, rather than nominal, foam velocity that significantly affects the estimated foam viscosity. Our results demonstrate that at elevated gas ratios under constant total injection rate, larger and more uniform bubbles with less number density and greater interfacial area are obtained. Increasing the injection rates leads to finer foam texture at a constant gas ratio. Different foam structures have an impact on the foam viscosity, with a general increasing trend of viscosity for larger bubbles as Rg increases from 0.5 to 0.85. The higher the foam viscosity, the more stable displacement interfaces with less viscous fingers are observed, leading to improved sweeping rates. The green surfactants (saponin + Cellulose NanoFibers) provide foams with higher viscosity and, thus, more stable displacement interfaces. These findings highlight the important effect of Rg–dependent foam structure on its viscosity, which in turn is crucial for controlling the mobility of CO2 foam to maximize oil recovery rate during EOR processes.

Formation of core–shell structures and viscous fingering in cellulose beads regenerated from [DBNH][OAc]/DMSO

AbstractSuperbase Ionic Liquids (SBILs) are efficient direct-dissolution solvents for cellulose and have found applications such as manufacturing of man-made textile fibers. In this study cellulose beads were prepared from microcrystalline cellulose dissolved in a mixture of SBIL 1,5-diazabicyclo[4.3.0]non-5-enium acetate with dimethyl sulfoxide, [DBNH][OAc]/DMSO, by drop-wise regeneration using water as an antisolvent. This resulted in cellulose regeneration by spinodal decomposition phase separation. The cross-sections of freeze-dried beads were thoroughly investigated using SEM, revealing a complex internal bead structure. Special attention was paid to structures resulting from the inwards moving regeneration front, where the solvent and antisolvent interdiffuse in opposite directions. The phase boundary at the regeneration front showed evidence of Saffman–Taylor instability, i.e., viscous fingering. Altering the diffusion environment surrounding the bead during regeneration resulted in nested layers of cores and shells. The number and placement of the core–shell separations was regulated by the number of transfers between two antisolvent baths and the duration of alternating periods of fast and slow interdiffusion of water and [DBNH][OAc]/DMSO through the bead perimeter. Graphical abstract

Fluorescence visualization dynamics of carbonated water injection processes in homogeneous glass micromodels

Understanding the flow behavior of oil–water phases in porous media is crucial for revealing the kinetic mechanisms underlying oil–water movement. In this study, we designed and constructed a fluorescence visualization experimental platform for carbonated water injection (CWI). We evaluated the effects of nine distinct injection rates on oil production and CO2 sequestration capabilities using three types of homogeneous porous structure micromodels. The microscale oil–water seepage behavior at the pore scale was also explored. The experimental results indicate that optimally increasing the injection rate can improve displacement efficiency, whereas excessively high rates may lead to viscous and capillary fingering. The geometry of the micromodels, particularly the hexagonal matrix, demonstrates potential advantages in enhancing oil displacement due to its uniform flow paths. The capillary number (Ca) significantly influences oil droplet capture behavior within micromodels. For instance, micromodel A captures the largest ganglion area at low Ca values, with a noticeable reduction in average ganglion area as Ca increases. Conversely, micromodels B and C exhibit similar trends in ganglion size variation at high Ca values, suggesting a more uniform impact of pore structure on oil droplet capture behavior. At elevated Ca values, capillary forces exert a more uniform and controlled effect on oil droplet capture and release, minimizing size variability. Additionally, the injection rate plays a critical role in CO2 sequestration, with higher rates promoting convective mixing between CO2 and reservoir fluids, thereby enhancing dissolution and storage efficiency. The complexity of the pore structure, characterized by the presence of micropores and macropores, affects the dissolution kinetics and mobility of CO2, influencing sequestration efficiency. These experimental findings provide valuable insights into the dynamics of oil–water motion and the potential for enhanced oil recovery (EOR) and CO2 storage, offering essential guidance for optimizing CWI strategies in the petroleum industry.

Experimental Study on Oil-Gas Interface Stability Mechanism and Control Method of Gas-Assisted Gravity Drainage

Abstract The stability of oil-gas interface is an important factor affecting the recovery of the gas-assisted gravity drainage (GAGD). In this paper, the interface morphology characteristics of GAGD in porous media under 8 flow rates and 3 displacement dip angles were studied by using a visual physical model. The non-dimensional parameters such as capillary number and bond number were introduced to qualitatively characterize the oil gas interface morphology, and the process of gas invading the pore throat of porous media under different interface morphologies was revealed. The fractal dimension is employed for quantitative characterization of the morphology of the oil gas interface during the GAGD process, and the boundary of stable interface and unstable interface was divided. The study showed that the balance effect of gravity on the competition between capillary force and viscous force was the main reason for the stability of GAGD flooding leading edge. The stability of the oil-gas interface can be ensured by controlling the bond number to be greater than 2.75×10−4 and the capillary number to be less than 2.48×10−3. With a constant bond number, an increase in the capillary number leads to a gradual transition of the oil-gas interface from stable to unstable. Similarly, with a constant capillary number, an increase in the bond number causes the oil-gas interface to shift from stable to unstable. The fractal dimension divides the boundary between stable and non-stable displacement. When Df is greater than 1.87, the oil interface is stable, when Df is less than 1.75, the oil interface is viscous fingering, and when Df is between 1.75 and 1.87, the oil interface is mainly capillary fingering.

Uncovering the impact of morphology of porous media and capillary number on immiscible oil recovery using computational fluid dynamics

Pore-scale simulation and analysis of oil displacement in digital rocks has shown great promise in tracking oil recovery in porous media. This paper examines three digital rocks with varying pore and throat radii but the same porosities, studying their behavior under immiscible oil recovery through waterflooding. Computational fluid dynamics was used to conduct numerical simulations to observe the impact of rock morphology on breakthrough times, residual oil saturations, and oil displacement patterns. The validity of the simulation mechanism is confirmed in both imbibition and drainage conditions through the pore doublet Chatzis' experiment. This study consisted of 33 separate simulations which varied in mobility ratios, interfacial tensions, and injection velocities. The findings suggest that smaller pore and throat radii result in higher oil recovery and water percolation and faster breakthrough times that facilitates the effects of viscous fingering. An increase in capillary number was found to have a significant impact on oil recovery in larger pores and throats.

Capsule polymer flooding for enhanced oil recovery

To solve the problems of shear degradation and injection difficulties in conventional polymer flooding, the capsule polymer flooding for enhanced oil recovery (EOR) was proposed. The flow and oil displacement mechanisms of this technique were analyzed using multi-scale flow experiments and simulation technology. It is found that the capsule polymer flooding has the advantages of easy injection, shear resistance, controllable release in reservoir, and low adsorption retention, and it is highly capable of long-distance migration to enable viscosity increase in deep reservoirs. The higher degree of viscosity increase by capsule polymer, the stronger the ability to suppress viscous fingering, resulting in a more uniform polymer front and a larger swept range. The release performance of capsule polymer is mainly sensitive to temperature. Higher temperatures result in faster viscosity increase by capsule polymer solution. The salinity has little impact on the rate of viscosity increase. The capsule polymer flooding is suitable for high-water-cut reservoirs for which conventional polymer flooding techniques are less effective, offshore reservoirs by polymer flooding in largely spaced wells, and medium to low permeability reservoirs where conventional polymers cannot be injected efficiently. Capsule polymer flooding should be customized specifically, with the capsule particle size and release time to be determined depending on target reservoir conditions to achieve the best displacement effect.

A numerical investigation to assess changes to displacement front and by-passed zones employing kinetic interface-sensitive tracer

An important aspect in groundwater remediation is to understand changes of multiphase fluid front morphology and stagnant regions on macro scale. However, the prediction of those changes during two-phase flow remains a challenging task due to the interplay of various physical factors. Recent laboratory experiments have demonstrated tracers' ability to predict deformation in the front of a two-phase flow system by utilizing a new reactive tracer known as, the kinetic interface sensitive tracer (KIS). This research employs a reactive transport model coupled with a macro-scale two-phase flow model to numerically analyse how viscosity ratio, capillary number, and heterogeneities on the tracer's signal and its impact the frontal deformation. One homogeneous and two heterogeneous types of porous media are considered. The background porous medium is a fine-grained, low-permeability medium, with a coarser, high-permeability lenses, generating heterogeneous material properties. The high-permeability lenses account for 25 % of the total model area and are arranged in either periodic or random patterns. The findings are evaluated using four parameters (effective front length, swept area, front roughness, and transition zone length). The flow patterns dominating the shape of the front are characterized by the viscous and capillary forces i.e. capillary number and the viscosity ratio between the two fluids. The results show that changes in flow regimes can be quantified using effective front length, thus employing the effective front length the viscous fingering regions can be quantified. Furthermore, front roughness and transition zone length are extracted and their relevance to the by-passed zones is presented. The slope of the reactive KIS tracer breakthrough curve, plotted on a phase diagram, can also be used to predict the existence of the by-passed zones for a low viscosity ratio. Finally, changes in front roughness and transition zone length induced by the inclusions are correlated to the slope of the KIS tracer BTC. The findings of this study can contribute to a better understanding of the impact of different flow regimes on the KIS tracer breakthrough signals and the linkages between the tracer signals and the front sizes.

Chemical-Assisted CO2 Water-Alternating-Gas Injection for Enhanced Sweep Efficiency in CO2-EOR.

CO2-enhanced oil recovery (CO2-EOR) is a crucial method for CO2 utilization and sequestration, representing an important zero-carbon or even negative-carbon emission reduction technology. However, the low viscosity of CO2 and reservoir heterogeneity often result in early gas breakthrough, significantly reducing CO2 utilization and sequestration efficiency. A water-alternating-gas (WAG) injection is a technique for mitigating gas breakthrough and viscous fingering in CO2-EOR. However, it encounters challenges related to insufficient mobility control in highly heterogeneous and fractured reservoirs, resulting in gas channeling and low sweep efficiency. Despite the extensive application and research of a WAG injection in oil and gas reservoirs, the most recent comprehensive review dates back to 2018, which focuses on the mechanisms of EOR using conventional WAG. Herein, we give an updated and comprehensive review to incorporate the latest advancements in CO2-WAG flooding techniques for enhanced sweep efficiency, which includes the theory, applications, fluid displacement mechanisms, and control strategies of a CO2-WAG injection. It addresses common challenges, operational issues, and remedial measures in WAG projects by covering studies from experiments, simulations, and pore-scale modeling. This review aims to provide guidance and serve as a reference for the application and research advancement of CO2-EOR techniques in heterogeneous and fractured reservoirs.

Oscillation-free implicit pressure explicit concentration discontinuous Galerkin methods for compressible miscible displacements with applications in viscous fingering

The system of compressible miscible displacements is widely adopted to model surfactant flooding in enhanced oil recovery techniques, where a low-viscosity fluid is injected underground to replace the high-viscosity oil. When the mobility ratio of the injected fluid to oil is high, the waterflood front tends to be unstable and exhibits a finger-like growth pattern, known as viscous fingering. Due to its unstable nature, the viscous fingering phenomenon is sensitive to mesh orientation and numerical discretization. Therefore, high-order numerical methods are preferable to reduce numerical artifacts and mesh dependence. In this paper, we propose a high-order discontinuous Galerkin method for the coupled nonlinear system of compressible miscible displacements to simulate the viscous fingering fluid instability in porous media. We adopt the IMplicit Pressure Explicit Concentration time marching approach based on implicit-explicit Runge-Kutta methods to achieve high-order temporal accuracy. Additionally, we introduce an oscillation-free damping term to control the spurious oscillations encountered in the waterflood front due to the large gradient of saturation. We have conducted ample numerical tests in two space dimensions to demonstrate the effectiveness and robustness of the proposed schemes in recovering viscous fingering.

Radial displacement patterns of shear-thinning fluids considering the effect of deformation

Radial injection of shear-thinning fluids into rock fractures is ubiquitous in subsurface engineering practices, including drilling, hydraulic fracturing, and rock grouting. Yet, the effect of injection-induced fracture deformation on radial displacement behavior of shear-thinning fluids remains unclear. Through radial injection experiments of shear-thinning fluids displacing an immiscible Newtonian fluid in a Hele–Shaw cell, we investigate the fracture deformation behavior during injection and the fluid–fluid displacement patterns under this impact. A mixed displacement pattern is observed where the invasion front gradually evolves from unstable (viscous fingering) to stable (compact displacement) as the injection proceeds. We demonstrate that the combined effect of shear-thinning property and radial flow geometry plays a controlling role in the evolution of the patterns. At high flow rates, the fracture dilation induced by high injection pressure tends to reduce the displacement efficiency in stages. Based on linear stability analysis, we propose a theoretical criterion for the transition of interfacial stability considering the viscosity of injected fluids and fracture deformation, which agrees well with the experimental observations. This research underscores the importance of rock deformation on two-phase flow dynamics in fractured media.

Enhanced Removal of Brine From Porous Structures by Supercritical CO2.

Supercritical CO2 (sCO2) removes water from brine held in pumice stone at levels well above the solubility of water in sCO2. The higher water removal results from a combination of passive emulsification of water in sCO2 and viscous fingering of sCO2 through the saturated pumice. This leads to higher levels of salt deposition than that expected from solubility considerations alone. These deposits could impact the injectivity of sCO2 as well as its movement in the subsurface. The finding that the water concentration in sCO2 is not necessarily capped at the solubility limit should influence the parametrization of injection models.

Elucidating the roles of electrolytes and hydrogen bonding in the dewetting dynamics of the tear film

This study explores the impact of electrostatic interactions and hydrogen bonding on tear film stability, a crucial factor for ocular surface health. While mucosal and meibomian layers have been extensively studied, the role of electrolytes in the aqueous phase remains unclear. Dry eye syndrome, characterized by insufficient tear quantity or quality, is associated with hyperosmolality, making electrolyte composition an important factor that might impact tear stability. Using a model buffer solution on a silica glass dome, we simulated physiologically relevant tear film conditions. Sodium chloride alone induced premature dewetting through salt crystal nucleation. In contrast, trace amounts of solutes with hydroxyl groups (sodium phosphate dibasic, potassium phosphate monobasic, and glucose) exhibited intriguing phenomena: quasi-stable films, solutal Marangoni-driven fluid influx increasing film thickness, and viscous fingering due to Saffman-Taylor instability. These observations are rationalized by the association of salt solutions with increased surface tension and the propensity of hydroxyl-group-containing solutes to engage in significant hydrogen bonding, altering local viscosity. This creates a viscosity contrast between the bulk buffer solution and the film region. Moreover, these solutes shield the glass dome, counteracting sodium chloride crystallization. These insights not only advance our understanding of tear film mechanics but also pave the way for predictive diagnostics in dry eye syndrome, offering a robust platform for personalized medical interventions based on individual tear film composition.

Microfluidic system for generating a three-dimensional (3D) vascularized islet-on-a-chip model

Diabetes is a disease associated with the insufficiency of pancreatic endocrine part, consisting mainly of pancreatic islets. Currently, diabetes is considered the fastest growing civilization disease. Globally, over 440 million people suffer from diabetes, and it is estimated that this number will increase to 700 million by 2045. Pancreatic islets are complex, highly vascularized mini-organs, and only the development of a fully functional vascularized pancreatic islet model could lead to the progress of knowledge about diabetes evolution, new therapeutic strategies, and the islet generation for applications in regenerative medicine. Therefore, the main goal of our study was to develop a microfluidic system for the simultaneous culture of two three-dimensional (3D) research models. The device presented in this article was used to simultaneously culture a model of a blood vessel composed of endothelial cells (HUVEC) developed using the Viscous Finger Patterning (VFP) technique and a model of the pancreatic islet, which was developed using a co-culture of α and β cells. During the research, device production method was optimized, and for this purpose, the most precise micro-milling technique was compared with the rapid prototyping technique - 3D printing. The spatial arrangement of cells in the developed models, their morphology, and viability were visualized using fluorescence staining and confocal microscopy analysis. This article presents preliminary research to develop a long-term culture of a complex model imitating the connection between the microvessel and the pancreatic islet, which in the future will be used to develop new therapeutic strategies or generate fully functional islets.

Time‐varying Extremum Graphs

AbstractWe introduce time‐varying extremum graph (tveg), a topological structure to support visualization and analysis of a time‐varying scalar field. The extremum graph is a sub‐structure of the Morse–Smale complex. It captures the adjacency relationship between cells in the Morse decomposition of a scalar field. We define the tveg as a time‐varying extension of the extremum graph and demonstrate how it captures salient feature tracks within a dynamic scalar field. We formulate the construction of the tveg as an optimization problem and describe an algorithm for computing the graph. We also demonstrate the capabilities of tveg towards identification and exploration of topological events such as deletion, generation, split and merge within a dynamic scalar field via comprehensive case studies including a viscous fingers and a 3D von Kármán vortex street dataset.

IMMISCIBLE VISCOUS FINGERING MODELING OF TERTIARY POLYMER FLOODING BASED ON REAL CASE OF HEAVY OIL RESERVOIR MODEL

In immiscible displacements, lower viscosity injected fluids with higher mobility than crude oil can create viscous fingers, affecting displacement efficiency. The Buckley–Leverett approach for relative permeabilities (kr) may not represent accurately 2D features like increased water saturation in viscous fingering. Based on the physics issue, this work applies Sorbie's 4-Steps methodology to a 3D simulation of an offshore heavy oil reservoir focusing on waterflooding and tertiary polymer flooding, assessing their impact on oil production forecasts. It also explores the application of this methodology to coarse grid simulation models, employing pseudo kr functions by data assimilation. During tertiary polymer injection, two processes were identified in oil displacement: viscous crossflow mechanism and oil bank mobilization by a second finger. This combination resulted in earlier and increased oil production. For both strategies, refining the grid increased simulation runtime from minutes to days compared to coarse grids, making it impractical for intensive processes. From data assimilation, the best solution with matched field indicators reduced runtime from days to minutes. This study expanded the 4-Steps methodology for 3D reservoir simulation, proposing kr as uncertainties. Data assimilation enhances the methodology, generating pseudo kr for coarser grid simulations, reducing computational costs, and capturing small-scale phenomena.

Onset and growth of viscous fingering in miscible annular ring

We investigate the onset and growth of viscous fingering (VF) of miscible annulus in a radial Hele-Shaw cell. Systematic numerical study on a finite annulus domain is performed by employing finite element method solver in COMSOL Multiphysics software. We justify that concentration field analysis is not a good choice for dynamic study in radial flows. Instead, velocity magnitude is a better tool to understand the dynamics. Therefore, we propose velocity field analysis to better differentiate the stable and unstable states and present a new stability criterion using the velocity field method. Most interestingly, using the velocity field analysis and the new stability criterion, we show a restabilization of the VF at a critical time when the system becomes diffusion dominant and able to provide both the onset time, τon (time at which instability develops), and the time at which the interface returns to the stable state, τd. Furthermore, the study successfully suggests the critical values for several dimensionless parameters, the Péclet number (Pe), log-viscosity ratio (R), and volumetric ratio (ra) and time (τ), to induce instability. When Pe is higher than 103, the evolution of VF instability is no longer enhanced by Pe, and Rc converges to a certain value. In particular, for the transiently unstable system of low Pe, the restabilization of VF instability is identified even though R is higher than Rc. The unstable system (τ>τon) returns to the stable state as injection time increases further. Moreover, we obtained a critical value of the volumetric ratio (rc,a).

Velocity of viscous fingers in miscible displacement: Intermediate concentration

We investigate one-phase flow in porous medium corresponding to a miscible displacement process in which the viscosity of the injected fluid is smaller than the viscosity in the reservoir fluid, which frequently leads to the formation of a mixing zone characterized by thin fingers. The mixing zone grows in time due to the difference in speed between its leading and trailing edges. The transverse flow equilibrium (TFE) model provides estimates of these speeds. We propose an enhancement for the TFE estimates, and provide its theoretical justification. It is based on the assumption that an intermediate concentration exists near the tip of the finger, which allows to reduce the integration interval in the speed estimate. Numerical simulations were conducted that corroborate the new estimates within the computational fluid dynamics model. The refined estimates offer greater accuracy than those provided by the original TFE model.

Influence of binder content on gas-water two-phase flow and displacement phase diagram in the gas diffusion layer of PEMFC: A pore network view

Understanding the gas-water flow dynamics in the gas diffusion layer (GDL) is one of the keys to improving the proton exchange membrane fuel cell's (PEMFC) overall performance and avoiding water flooding. Yet, the relationship between the two-phase flow and micro-scale GDL structures (including binder, PTFE, and fiber skeleton) is not well understood. In this study, three-dimensional GDL structures with different fractions of binder contents (φb=0%∼50%) and a fixed porosity of 75.6 % are confidently reconstructed based on high-resolution images from the confocal microscope, implying that the addition of binder will increase the number of large pores and cause a bimodal throat size distribution through morphology analysis. Thereafter, drainage simulations are performed under a wide range of capillary number (−9 < log Ca <0) and viscosity ratio (−3 < log M < 2) by the pore network model (PNM), which robustly predicts the displacement phase diagram of viscous fingering, capillary fingering, stable displacement, and transitional regime. In the viscous fingering and stable displacement regime, the nonwetting phase saturation (Snw) is nearly the same for different φb, implying the fluid invading pathway does not change much with the addition of binder. However, in the capillary fingering regime (refer to the actual operating conditions), Snw increases rapidly with φbat the breakthrough time and its transient value continues to increase until the steady state, which may be attributed to the increased fractions of pores above the capillary threshold attributed by the bimodal throat size distribution. In addition, the effective water permeability increases sharply with φb, whereas the gas permeability remains almost constant, which means such pore structure alteration by adding the binder is beneficial to water disposal in PEMFC. This research provides insights into delineating the effect of pore and throat size distribution alteration by adding binder on two-phase dynamics in GDL.