Viscous Fingering Research Articles

Technology Focus: History Matching and Forecasting (April 2023)

_ This year’s history matching and forecasting selections cover topics that include performance prediction of a polymerflood pilot in a heavy oil reservoir, multivariate characterization and modeling of a paleo zone, and multiwell pressure history matching in an unconventional reservoir. The authors of paper SPE 206247 developed a history-matched reservoir simulation model for a polymerflood pilot to enhance heavy oil recovery on the Alaska North Slope. According to the authors, the viscous fingering effect in the reservoir during waterflooding and the restoration of injection conformance during polymerflooding were effectively represented. Using the history-matched model, studies were conducted to investigate the oil-recovery performance under different development strategies, with consideration for sensitivity to polymer parameter uncertainties. In paper IPTC 22034, the authors present an approach that incorporates characterization of paleo zones, parameterization of paleo-zone conductivity, and application of flow profiles as a guide in the history-matching study of a conceptual reservoir simulation model under reservoir uncertainty. The authors conclude that the modeled paleo zone acts as a baffle inducing a partial confinement of the injectors. Solving a global optimization problem to minimize the mismatch between the instantaneous shut-in pressure and treatment pressures measured in the field and simulated by the model, for all stages and all wells, is the subject of paper SPE 204162. According to the authors, the technique reduces overfitting by minimizing the number of variables used for history matching, by increasing the number of wells and stages that are simultaneously matched, and by reproducing the dominant behavior of all stages instead of capturing the detailed behavior of specific stages. Recommended additional reading SPE 210224 Rate-Transient-Analysis-Assisted Numerical History Matching and Co-Optimization of CO2 Storage and Huff ’n’ Puff Performance for a Near-Critical Gas Condensate Shale Well by Hamidreza Hamdi, University of Calgary, et al. URTeC 3724391 Fractional Dimension Rate-Transient Analysis in Unconventional Wells: Application in Multiphase Analysis, History Matching, Forecasting, and Interference Evaluation by Behnam Zanganeh, Chevron, et al. SPE 200908 Application of an Integrated Ensemble-Based History-Matching Approach—An Offshore Field Case Study by Usman Aslam, Emerson, et al.

Developing methodology and experimental procedure эfor experimental microfluidic study of chemical enhanced oil recovery

The concern of this research was to review the different methodology on microfluidic experiments conducted to study chemical enhanced oil recovery methods on micromodel chips. In general, there are several ways to study EOR methods such core flooding and microfluidics. The disadvantage of first method is that the flow processes inside the core sample cannot be imagined. Hence, the second method helps us to fully visualize how fluid flow behaviour occurs though the porous medium of the rocks. The various chemical EOR processes such as surfactant flooding, polymer flooding and ASP flooding were studied on microfluidic chips. These chemicals were injected into micromodels to drive out crude oil. It helps to understand the interactions between crude oil and chemicals, the advancement of front developed between displacing and displaced fluids and the viscous fingering effect. Visual studies enabled us to understand the effectiveness of polymer, surfactant and alkaline separately and as combined. The different experimental methodologies to study the EOR methods are reviewed. Mainly experiments divided into two main groups: methods of geological characterisations influence to fluid transport while others study oil displacement at different condition, such high temperature, high pressure, low or high salinity, highly viscous oil. We reviewed methodologies applied to study an oil displacement by polymer, surfactant-polymer (SP) and alkaline surfactant polymer (ASP) solutions, their interactions and transport in porous media. Based on reviewed article the experimental procedure was developed. Analyses of published materials have helped to design and direct the methodology of research.

Suppressing Viscous Fingering in Porous Media with Wetting Gradient.

The viscous fingering phenomenon often occurs when a low-viscosity fluid displaces a high-viscosity fluid in a homogeneous porous media, which is an undesirable displacement process in many engineering applications. The influence of wetting gradient on this process has been studied over a wide range of capillary numbers (7.5 × 10-6 to 1.8 × 10-4), viscosity ratios (0.0025 to 0.04), and porosities (0.48 to 0.68), employing the lattice Boltzmann method. Our results demonstrate that the flow front stability can be improved by the gradual increase in wettability of the porous media. When the capillary number is less than 3.5 × 10-5, the viscous fingering can be successfully suppressed and the transition from unstable to stable displacement can be achieved by the wetting gradient. Moreover, under the conditions of high viscosity ratio (M > 0.01) and large porosity (Φ > 0.58), wetting gradient improves the stability of the flow front more significantly.

Characterization of Bubble Transport in Porous Media Using a Microfluidic Channel

This study investigates the effect on varying flow rates and bubble sizes on gas–liquid flow through porous media in a horizontal microchannel. A simple bubble generation system was set up to generate bubbles with controllable sizes and frequencies, which directly flowed into microfluidic channels packed with different sizes of glass beads. Bubble flow was visualized using a high-speed camera and analyzed to obtain the change in liquid holdup. Pressure data were measured for estimation of hydraulic conductivity. The bubble displacement pattern in the porous media was viscous fingering based on capillary numbers and visual observation. Larger bubbles resulted in lower normalized frequency of the bubble breakthrough by 20 to 60 percent. Increasing the flow rate increased the change in apparent liquid holdup during bubble breakthrough. Larger bubbles and lower flow rate reduced the relative permeability of each channel by 50 to 57 percent and 30 to 64 percent, respectively.

Lattice Boltzmann modeling of the coupled imbibition-flowback behavior in a 3D shale pore structure under reservoir condition

Imbibition and flowback of fracturing fluid usually occur in the shale matrix after hydraulic fracturing, which significantly impacts shale gas production and environmental protection. The rocks of deep shale gas reservoirs are under high-temperature and high-temperature conditions. There are rich micro-nano pores with various pore structures in deep shale. In addition, the flowback behavior is significantly affected by the imbibition behavior because the flowback begins after the end of the imbibition. Therefore, an accurate pore-scale description of the coupled imbibition-flowback behavior is crucial to understand the flowback mechanism and its impacts. In this paper, a pseudo-potential lattice Boltzmann method is employed to simulate the coupled imbibition-flowback behavior in a digital shale core, where the digital core is reconstructed by Markov Chain-Monte Carlo method based on scanning microscope images of deep shale cores. The microcosmic mechanism of the imbibition and flowback is studied under deep shale conditions. The influence of some factors, such as pore structure, fluid viscosity, wettability, and flowback pressure difference, on the flowback behavior of fracturing fluid is investigated. It is found that the fracturing fluid advances almost uniformly throughout the pore space during the imbibition process. The fracturing fluid is easy to adsorb on the pore wall, and the shale gas is located in the middle of the pore space. The viscous fingering is clearly observed during the flowback process, where shale gas flows through large pores to form a flow channel, and the fracturing fluid stays in tiny pores. The flowback rate increases gradually with the flowback time and eventually tends to be almost constant. The wettability, flowback pressure difference, and pore structure significantly influence the flowback behavior, while the fracturing fluid viscosity has a smaller effect on the flowback process.

Experiments on Marangoni spreading – evidence of a new type of interfacial instability

Marangoni spreading on thin films is widely observed in nature and applied in industry. It has serious implications for airway drug delivery, especially in surfactant displacement therapy. This paper reports the results of experimental investigations of a surfactant-laden droplet spreading on films made of more viscous Newtonian fluids as well as on films made of viscoelastic fluids. The experiments used particle seeding, the transmission-speckle method and particle tracking velocimetry (PTV) to determine the deformation of the film–droplet interface and to measure velocity fields. Radially aligned patterns were observed on Newtonian films. Similar patterns, but with much smaller wavenumber, were observed on viscoelastic films in combination with rapid azimuthal variations of the film thickness. The Saffman–Taylor instability at the film–droplet interface explains the formation of patterns on a more viscous Newtonian film, and their onset requires exceeding the critical capillary number. The pattern formation on viscoelastic films is correlated with an instability at the film–droplet–air contact line when the liquid is expelled radially by the spreading droplet. PTV revealed azimuthal variations of the velocity field in the vicinity of the contact line. The observed contact line instability is different from previously reported fingering instabilities of Newtonian thin films. A simple scaling law accounting for the Marangoni-stress-induced elastic shear deformation is proposed to describe the flow field in the patterns formed in the viscoelastic films.

Electrohydrodynamic viscous fingering of leaky dielectric fluids in a channel

Viscous fingering is a commonly observed interfacial instability during fluid displacement, where a fingerlike shape is formed at the fluid interface when a more viscous fluid is displaced by a less viscous fluid. In this study, a hybrid numerical model based on the lattice Boltzmann method and finite difference method is developed for investigating the control of viscous fingering of leaky dielectric fluids confined in a channel using electrohydrodynamics. Extensive simulations are carried out for studying the effects of the strength and direction of the electric field as well as the fluid properties, including the permittivity ratio and conductivity ratio, on viscous fingering. It is shown that a horizontal electric field, i.e., when the direction of the electrical field is perpendicular to the direction of fluid motion, can either promote or suppress the viscous fingering, depending on the permittivity ratio and conductivity ratio. For a vertical electric field, the extent of promotion of viscous fingering first decreases and then increases with the increase in conductivity ratio at a constant permittivity ratio. Also, various interfacial morphologies, such as broad fingers and thin jets, are observed under different fluid properties. A phase diagram for both the horizontal and vertical electric field is established based on the simulations with different permittivity and conductivity ratios to characterize the interfacial morphologies. This study offers insight into the electrohydrodynamic effects on the viscous fingering of leaky dielectric fluids, which could facilitate the control of multiphase flow in various applications, such as enhanced oil recovery and coupled chromatographic systems for separation.

Numerical simulations of miscible displacement in an inclined channel by lattice Boltzmann method

The interfacial instability between miscible fluids in a channel is determined by many factors, such as viscosity contrast and the inclination angle. Considering the effect of the gravity field, we investigate the displacement phenomenon between two miscible fluids with different viscosities in an inclined channel. The results show that when the concentration Rayleigh number RaC<105, the inclination angle θ ranges from 0° to 90°, and the natural logarithm of the viscosity ratio R > 0; there are three fluid–fluid interfacial instability regions, namely, viscous fingering, “Kelvin–Helmholtz” (K–H) instability, and “Rayleigh–Taylor” (R–T) instability. A scaling analysis is developed to describe the time evolution of the displacement as described by the displacement efficiency at a fixed viscous ratio. Our analysis indicates that in the viscous fingering region, the time evolution of the displacement efficiency gradually increases with t scaling due to fingering formations; in the K–H and R–T regions, the displacement efficiency rapidly increases with t1+RaC/106. When considering the effect of the viscosity ratio in the K–H instability region, the displacement efficiency scales as η∼t1+RaC/106R0.1. In addition, when the inclination angle is negative or R < 0, the instability phenomenon is not obvious, and the displacement efficiency decreases as the inclination angle or R decreases.

The Development of Outbreaks of Forest Insects on Different Spatial Scale

The work is dedicated to the discussion of the possibilities of describing the dynamics of the forest insect outbreaks development on different spatial scales. The properties of outbreaks were considered on a microspatial scale, where the distribution patterns of individuals across different food sources within the boundaries of a local territory or a stand were analysed, and on a macrospatial scale, where the focus of the analysis were the indicators of the photosynthetic apparatus (leaves or needles) removal over the entire territory of the locus, including primary, secondary and migratory loci. When analysing the microspatial distribution of caterpillars on trees within loci on different stages of gradation, the model of the individuals’ distribution on fodder trees was used as a second order stage transition. The macrospatial processes that occur during the outbreak development include, firstly, the growth of an existing outbreak and the emergence of new connected damaged areas of the forest, and secondly, the emergence of new unconnected secondary foci. To characterise the outbreaks, their fractal dimension D and the characteristics of the “viscous fingers” on the border of the outbreaks were used. Remote sensing data were used to calculate these characteristics. The proposed approaches can be used to predict the development of forest insects outbreak. When constructing and verifying the models, we used data from the Siberian silkworm census and the trees colonisation rate in the outbreak zone, as well as the remote sensing data on the areas and shapes of the foci in the regions of the Krasnoyarsk Territory during an outbreak of the Siberian silk moth Dendrolimus sibiricus Tschetv. in 2015–2019.

Micro and meso fabrication emerged from Saffman-Taylor instability developed in Hele-Shaw cell

Micro and meso fabrication emerged from Saffman-Taylor instability developed in Hele-Shaw cell

Hoop compression driven instabilities in spontaneously formed multilayer graphene blisters over a polymeric substrate

The blistering of elastic membranes is prone to elastic-solid as well as substrate-based mechanical instabilities. The solid-based instabilities have been well-explored in the mechanically indented blisters of elastic membranes over the rigid/solid substrates, but an integrated study illustrating the underlying mechanism for the onset of solid as well as substrate-based instabilities in the spontaneous blistering of a 2D material is still lacking in the literature. In this article, an extensive experimental as well as analytical analysis of the spontaneous blister-formation in the multilayer graphene (MLG) flakes over a polymeric substrate is reported, which elucidates the involved mechanism and the governing parameters behind the development of elastic-solid as well as viscoelastic-substrate based instabilities. Herein, a ‘blister-collapse model’ is proposed, which infers that the suppression of the hoop compression, resulting from the phase-transition of the confined matter, plays a crucial role in the development of the instabilities. The ratio of blister-height to flake-thickness is a direct consequence of the taper-angle of the MLG blister and the thickness-dependent elasticity of the upper-bounding MLG flake, which shows a significant impact on the growth-dynamics of the viscous fingering pattern (viscoelastic-substrate based instability) under the MLG blister.

Simulation of Nonlinear Viscous Fingering in a Reactive Flow Displacement: A Multifractal Approach

fractal analysis of viscous fingering of a reactive miscible flow displacement in homogeneous porous media is investigated and multifractal spectrum, and fractal dimension are introduced as two essential features to characterize the irregularity of finger patterns. The Reaction of the two reactant fluids generates a miscible chemical product C in the contact zone. Considering the similarity between chemical products and coastline, monofractal and multifractal analyzes are performed. In monofractal analysis, the box-counting method is implemented on binary images and in multifractal analysis, due to the image processing; the fractal characteristics of viscous fingering instability are analyzed by means of fractal quantities such as Holder exponent, multifractal spectrum, f (α)-image and fractal dimension dynamics. Fractal analysis shows that the fractal dimension increases with time. Also, by considering five different nonlinear simulations, the results show that in the case both sides of the chemical product C are unstable, the multifractal spectrum curve has the highest peak, which means the more complex finger patterns lead to more values of fractal dimension. In addition, a comparison between different values of Ar is conducted and the results show similar behavior. However, small value of aspect ratio leads to a broader width of the multifractal spectrum curve. Furthermore, f (α)-images of concentration contour were investigated for different precisions and some undetectable finger patterns were observed in these images. It can be concluded that the use of f (α)-image represents more detailed image than concentration contours.

Experimental study of viscous fingering in sand-pack model for heavy oil reservoir

Viscous fingering phenomenon in porous media has a great impact on industrial processes, such as enhanced oil recovery processes. The previous experimental works mainly used Hele-Shaw models and micromodels to investigate viscous fingering mechanisms. However, Hele-Shaw models simulate porous media flow in a narrow gap with no pore structure. Micromodels’ pore structures are simplified, and the material used to make micromodel generally has different wettability compared with real rocks. Therefore, a large-dimensions of 40 cm × 20 cm× 0.5 cm sand-pack model with a vertical well in the center is used in this study to mimic real reservoir in terms of pore structure, wettability conditions and real radial flow. To the best of our knowledge, there is no reported literature on viscous fingering experimental study for radial flow in real sand-pack models. Immiscible flooding processes with high viscosity ratios ranging from 853.9 to 32080 and different injection rates ranging from 0.01 to 0.5 ml·min−1 were conducted. The viscous fingering phenomena were captured and analyzed qualitatively and quantitatively. As capillary number increases, more unstable interfaces and complicated finger structures were visually observed and validated through fractal dimension analysis. These experimental results are in well agreement with previously reported results obtained from Hele-Shaw models and micromodels. The dimensionless number (Ca*µr2) analysis suggests viscosity has a greater effect on viscous fingering compared with injection rate, which was consistent with the conclusion of micromodel studies. Besides critical injection rate (0.01–0.05 ml∙min−1), increasing the viscosity ratio to a critical viscosity ratio (2946) leads to a significant decrease of breakthrough time, which was not reported in the literature. And different from linear displacement in which the viscous fingering followings two stages, additional pseudo-stable displacement could be generated after the rapid finger generation stage and combination stage for the radial displacement.

Interfacial Dynamics of Miscible Displacement of Shear-Thinning Fluid in a Vertical Channel

The displacement of a shear-thinning fluid by a denser and less viscous Newtonian fluid in a vertical duct is investigated using experiments and numerical simulations. We study how shear-thinning and increased viscosity contrast between the fluids affect the displacement. Our results show that the degree of shear-thinning significantly influences the development of interfacial patterns and the growth of perturbations. In the weakly shear-thinning regime, the displacement progresses as a stable displacement with no visible instabilities. Increasing the viscosity of the displaced fluids result in a Saffman–Taylor type instability with several finger-shaped channels carved across the width of the duct. In the strongly shear-thinning regime, a unique viscous finger with an uneven interface is formed in the middle of the displaced fluid. This finger eventually breaks through at the outlet, leaving behind considerably stagnant wall layers at the duct side walls. We link the onset of viscous fingering instability to the viscosity contrast between the fluids, and the stabilizing density difference, as expressed through a modified, unperturbed pressure gradient for the two fluids. Numerical simulations are performed with both an initial flat interface, and with a perturbed interface, and we find good qualitative agreement between experimental observations and computations.

Impact of interfacial rheology on finger tip splitting.

Fluid-fluid interfaces, laden with polymers, surfactants, lipid bilayers, proteins, solid particles, or other surface-active agents, often exhibit a rheologically complex response to deformations. Despite its academic and practical relevance to fluid dynamics and various other fields of research, the role of interfacial rheology in viscous fingering remains fairly underexplored. A noteworthy exception is the work by Li and Manikantan [Phys. Rev. Fluids 6, 074001 (2021)2469-990X10.1103/PhysRevFluids.6.074001], who used linear stability analysis to show that surface rheological stresses act to stabilize the development of radial viscous fingering at the linear regime. In this paper, we perform a perturbative, second-order mode-coupling analysis of the system and investigate the influence of interfacial rheology on the morphology of the fingering structures at early nonlinear stages of the dynamics. In particular, we focus on understanding how interfacial rheology impacts the emblematic finger tip-widening and finger tip-splitting phenomena that take place in radial viscous fingering in Hele-Shaw cells. We describe the viscous Newtonian fluid-fluid interface by using a Boussinesq-Scriven model, and derive a generalized Young-Laplace pressure jump condition at the fluid-fluid interface. In this framing, we go beyond the purely linear description and use Darcy's law to obtain a perturbative mode-coupling differential equationwhich describes the time evolution of the perturbation amplitudes, accurate to second order. Our early nonlinear mode-coupling results indicate that regardless of their stabilizing action at the linear regime, interfacial rheology effects favor finger tip widening, leading to the occurrence of enhanced finger tip-splitting events.

Miscible viscous fingering in a packed cylindrical column: Theory and numerics

Linear and nonlinear analyses on miscible viscous fingering (VF) in a cylindrical packed column is conducted. The effects of boundary conditions on the onset conditions of instability are suggested as a function of log-viscosity ratio and P\'eclet number. Through two- and three-dimensional (2D and 3D) simulations based on the finite element method, we clearly visualize the effect of the lateral boundary on the onset and the growth of VF. Our 3D simulations explain the experimental results available in the literature by suitably choosing the parameters.

Dendritic patterns from shear-enhanced anisotropy in nematic liquid crystals.

Controlling the growth morphology of fluid instabilities is challenging because of their self-amplified and nonlinear growth. The viscous fingering instability, which arises when a less viscous fluid displaces a more viscous one, transitions from exhibiting dense-branching growth characterized by repeated tip splitting of the growing fingers to dendritic growth characterized by stable tips in the presence of anisotropy. We controllably induce such a morphology transition by shear-enhancing the anisotropy of nematic liquid crystal solutions. For fast enough flow induced by the finger growth, the intrinsic tumbling behavior of lyotropic chromonic liquid crystals can be suppressed, which results in a flow alignment of the material. This microscopic change in the director field occurs as the viscous torque from the shear flow becomes dominant over the elastic torque from the nematic potential and macroscopically enhances the liquid crystal anisotropy to induce the transition to dendritic growth.

Viscous fingering patterns for Hele-Shaw flow in a doubly connected geometry driven by a pressure differential or rotation

Viscous fingering patterns that occur at the interface between two immiscible fluids of differing viscosities in a Hele-Shaw cell are normally studied mathematically via a nonlinear moving boundary problem with a single interface. Here we study a more realistic model which involves a doubly connected region of the more viscous fluid bounded by two interfaces. We simulate this model numerically using a level set method, supported by linear stability analysis and some experiments. Various results are presented for configurations in which the flow is driven by either a pressure difference or by rotating the entire Hele-Shaw cell.

Viscous fingering instabilities in spontaneously formed blisters of MoS2 multilayers.

The viscous fingering in the Hele-Shaw cell can be suppressed by replacing the upper-bounding rigid plate with an elastic membrane. Recently, graphene multilayers while polymer-curing-induced blistering showed the dynamical evolution of viscous fingering patterns on a viscoelastic substrate due to their thickness-dependent elasticity. Under certain conditions, the elastic solid-based instability couples with the viscoelastic substrate-based instability. The mechanisms underlying such a coupling in the blisters of 2D materials and the dynamical evolution of the viscous fingering patterns underneath the blisters are yet to be addressed. Herein, we investigate the viscous fingering instabilities in spontaneously formed blisters of MoS2 multilayers, and provide thorough analytical and experimental insights for the elucidation of the dynamical evolution of the viscous fingering patterns and the coupled instabilities in the blisters. We also estimate the interfacial adhesion energy of the MoS2 flakes over a (poly)vinyl alcohol (PVA) substrate and the confinement pressure inside the MoS2 blisters using a conventional blister-test model. It is observed that the presence of instability gives rise to anomalies in the modeling of the blister test. The adhesion mechanical insights would be beneficial for fundamental research as well as practical applications of 2D material blisters in flexible optoelectronics.

NUMERICAL SIMULATION OF MULTIPHASE FLOW IN A POROUS MEDIUM IN THE PRESENCE OF HEAT AND MASS TRANSFER BETWEEN PHASES

The work is focused on unstable displacement of a viscous liquid from a porous medium in the presence of chemical interactions between phases. When a viscous liquid is displaced by a less viscous liquid or gas, the Saffman−Taylor instability develops at the displacement front: the less viscous liquid breaks through the layer of the more viscous liquid being displaced, forming "viscous finger" channels in it. With the development of instability, the initially flat interface is perturbed, and the area of contact between the phases increases. This phenomenon must be taken into account when modeling the displacement process with chemical reactions between phases, since the extension of the contact line between the reacting phases leads to an increase in the rate of the chemical reaction. The article provides a mathematical model for describing the process of oil displacement by the thermogas method: when oil is displaced by a mixture of heated water vapor and gas, which enters into an exothermic chemical reaction with oil, resulting in a decrease in oil viscosity and formation CO2, which leads to better displacement. Also, the mathematical model implies the possibility of accounting for subgrid instability by including additional flow terms into the equations. The results of computational experiments based on the described mathematical model are presented.