Showing papers on "Viscous fingering published in 2021"

Wettability and Lenormand's diagram

Abstract: Fluid–fluid displacement in porous media has been viewed through the lens of Lenormand's phase diagram since the late 1980s. This diagram suggests that the character of the flow is controlled by two dimensionless parameters: the capillary number and the viscosity ratio. It is by now well known, however, that the wettability of the system plays a key role in determining the pore-scale displacement mechanisms and macroscopic invasion patterns. Here, we endow Lenormand's diagram with the impact of wettability using dynamic and quasi-static pore-network models. By using the fractal dimension and the ratio of characteristic viscous and capillary pressures we delineate the five principal displacement regimes within the extended phase diagram: stable displacement, viscous fingering, invasion percolation, cooperative pore filling and corner flow. We discuss the results in the context of pattern formation, displacement-front dynamics, pore-scale disorder and displacement efficiency.

The Effect of Surface Roughness on Immiscible Displacement Using Pore Scale Simulation

Abstract: Pore scale immiscible displacement is crucial in oil industry. The surface roughness of throat is an important factor affecting water–oil interface movement. In this paper, the Navier–Stokes (N-S) equation coupled with the phase-field method is adopted to analyze the oil–water flow and interface movement in single channel, considering different surface roughness, diverse wettability and various capillary numbers. The simulation results show that the resistance increases significantly due to the surface roughness. The velocity of interface movement in rough channels is slower than that in smooth channels. The existence of asperities strengthens the interface deformation and promotes the formation of fingering phenomenon. The water flooding process presents different flow patterns in the rough channel with diverse wettability, and the influence of wall roughness on oil–water interface movement is different under various wettability conditions. There is an approximate exponential relationship between the ratio of interface length to channel length and capillary number. When the capillary number exceeds 0.03574, the phenomenon of viscous fingering is obvious, and the influence of capillary number is amplified by roughness.

Pore-scale simulation of miscible viscous fingering with dissolution reaction in porous media

Abstract: Global climate change is happening but may be mitigated by the technology of geological carbon dioxide ( CO 2) sequestration. To gain comprehensive insights into this approach, we perform pore-scale simulations of displacement between two miscible fluids in porous media using a new multiple-relaxation-time lattice Boltzmann model. This study marks the first attempt to investigate viscous fingering dynamics in miscible displacement, considering the coexistence of viscosity contrast and dissolution reaction. Simulation results capture different fingering patterns that depend on dissolution (Damkohler number Da), diffusion (Peclet number Pe), and viscosity contrast (viscosity ratio R). From simulations of unstable viscous flows, dissolution is found to delay fingering onset, slow down fingering propagation, and inhibit or reinforce the late-stage fingering intensity. In simulations with stable viscosity contrasts, the displacement features fingering phenomena when dissolution is fast enough. In addition, we conduct a parametric study to assess the impact of Pe, R, and Da. The results suggest that increasing Pe or R destabilizes fingering, but increasing Da first suppresses and gradually intensifies fingering. Finally, for every fixed Da, we determine the phase boundary between stable and unstable regimes in a Pe–R phase plane. A unified scaling law is developed to approximate boundary lines obtained under different Da values. By comparing reactive and nonreactive cases, we classify four distinct regimes: stable, unstable, reactive stable, and reactive unstable. These pore-scale insights are helpful in understanding and predicting the displacement stability during the geological CO 2 sequestration, which is of importance to the pre-evaluation of the storage efficiency and safety.

An improved multicomponent pseudopotential lattice Boltzmann method for immiscible fluid displacement in porous media

Abstract: In this work, we introduce an improved multicomponent (MC) pseudopotential lattice Boltzmann method (LBM) for the simulation of immiscible fluids displacement in porous media. The model is based on a set of recent developments from the literature in addition to a newly introduced treatments of the pressure boundary conditions at the inlet and outlet. It is shown that the model provides several favorable features such as realistic viscosity ratio and independent tuning of surface tension from the viscosity ratio. Additionally, the model is shown to suppress a non-physical behavior of the original MC pseudopotential model in which changes of entrapped fluids volumes are observed during displacement processes. The model is characterized using the Laplace and contact angle tests. Then we show that the model provides stable and satisfactory results for immiscible fluids displacement. Moreover, primary drainage and imbibition displacement processes were simulated in a heterogeneous porous medium. The simulation results showed that the introduced model was able to correctly capture many physical phenomena of oil-water displacements in porous media. Irreducible water and residual oil saturations resulted from the simulations are comparable to realistic values. The displacement processes were simulated at different wetting conditions and the results were in good agreement with experimental results.

Tuning capillary flow in porous media with hierarchical structures

Abstract: Immiscible fluid-fluid displacement in porous media is of great importance in many engineering applications, such as enhanced oil recovery, agricultural irrigation, and geologic CO2 storage. Fingering phenomena, induced by the interface instability, are commonly encountered during displacement processes and somehow detrimental since such hydrodynamic instabilities can significantly reduce displacement efficiency. In this study, we report a possible adjustment in pore geometry which aims to suppress the capillary fingering in porous media with hierarchical structures. Through pore-scale simulations and theoretical analysis, we demonstrate and quantify combined effects of wettability and hierarchical geometry on displacement patterns, showing a transition from fingering to compact mode. Our results suggest that with a higher porosity of the 2nd-order porous structure, the displacement can keep compact across a wider range of wettability conditions. Combined with our previous work on viscous fingering in such media, we can provide a complete insight into the fluid-fluid displacement control in hierarchical porous media, across a wide range of flow conditions from capillary- to viscous-dominated modes. The conclusions of this work can benefit the design of microfluidic devices, as well as tailoring porous media for better fluid displacement efficiency at the field scale.

Optimal Wetting Angles in Lattice Boltzmann Simulations of Viscous Fingering

Abstract: We conduct pore-scale simulations of two-phase flow using the 2D Rothman–Keller colour gradient lattice Boltzmann method to study the effect of wettability on saturation at breakthrough (sweep) when the injected fluid first passes through the right boundary of the model. We performed a suite of 189 simulations in which a “red” fluid is injected at the left side of a 2D porous model that is initially saturated with a “blue” fluid spanning viscosity ratios $$M = u _\mathrm{r}/ u _\mathrm{b} \in [0.001,100]$$ and wetting angles $$\theta _\mathrm{w} \in [ 0^\circ ,180^\circ ]$$ . As expected, at low-viscosity ratios $$M= u _\mathrm{r}/ u _\mathrm{b} \ll 1$$ we observe viscous fingering in which narrow tendrils of the red fluid span the model, and for high-viscosity ratios $$M \gg 1$$ , we observe stable displacement. The viscous finger morphology is affected by the wetting angle with a tendency for more rounded fingers when the injected fluid is wetting. However, rather than the expected result of increased saturation with increasing wettability, we observe a complex saturation landscape at breakthrough as a function of viscosity ratio and wetting angle that contains hills and valleys with specific wetting angles at given viscosity ratios that maximize sweep. This unexpected result that sweep does not necessarily increase with wettability has major implications to enhanced oil recovery and suggests that the dynamics of multiphase flow in porous media has a complex relationship with the geometry of the medium and the hydrodynamical parameters.

Fluid Meniscus Algorithms for Dynamic Pore-Network Modeling of Immiscible Two-Phase Flow in Porous Media

Abstract: We present in detail a set of algorithms for a dynamic pore-network model of immiscible two-phase flow in porous media to carry out fluid displacements in pores. The algorithms are universal for regular and irregular pore networks in two or three dimensions and can simulate both drainage displacements and steady-state flow. They execute the mixing of incoming fluids at network nodes, distribution of fluids to outgoing links and coalescence of bubbles. Implementing these algorithms in a dynamic pore-network model we reproduce some of the fundamental results of transient and steady-state two-phase flow in porous media. For drainage displacements we reproduce the different flow patterns corresponding to viscous fingering, capillary fingering and stable displacement by altering capillary number and viscosity ratio. In steady-state flow we verify non-linear rheological properties and transition to linear Darcy behavior while increasing the flow rate. Finally we verify relations between the seepage velocities of two-phase flow in porous media considering both disordered regular networks and irregular networks reconstructed from real samples.

Saffman-Taylor instability in a radial Hele-Shaw cell for a shear-dependent rheological fluid

Abstract: We present the study of viscous fingering in the radial hele shaw cell, using the shear-dependent rheological fluid which transitions from the Newtonian to shear thinning behaviour, at low shear rates. The experimental observations show that the characteristic features of the fingering phenomena in the case of shear-thinning flow (such as side branching, growth of second generation fingers, inhibition of tip splitting), is observed at late times, from an initial Newtonian regime. On account of the asymmetry of the fingering structure, the local shear rate is non-uniform. This leads to different rheological behaviour in different sections of the network locally, revealing contrasting local fingering patterns, specific to the respective fluid rheological state based on the local shear rate. This is also explained using the numerical simulations for such rheological fluid, in the two-phase porous media flow. The fingering features, such as the length, width are quantified as a function of the flowrate. We have also observed detachment of the fingers beyond a certain critical size of the fingering network. Finally, the stability of the fingering is also investigated at ultra low flow rates, which suggests that the duration of stability exists much beyond what is predicted using the linear stability analysis for classical Newtonian flows.

Influence of Wetting on Viscous Fingering Via 2D Lattice Boltzmann Simulations

Abstract: We present simulations of two-phase flow using the Rothman and Keller colour gradient Lattice Boltzmann method to study viscous fingering when a “red fluid” invades a porous model initially filled with a “blue” fluid with different viscosity. We conducted eleven suites of 81 numerical experiments totalling 891 simulations, where each suite had a different random realization of the porous model and spanned viscosity ratios in the range $$M\in [0.01,100]$$ and wetting angles in the range $$\theta _w\in [180^\circ ,0^\circ ]$$ to allow us to study the effect of these parameters on the fluid-displacement morphology and saturation at breakthrough (sweep). Although sweep often increased with wettability, this was not always so and the sweep phase space landscape, defined as the difference in saturation at a given wetting angle relative to saturation for the non-wetting case, had hills, ridges and valleys. At low viscosity ratios, flow at breakthrough is localized through narrow fingers that span the model. After breakthrough, the flow field continues to evolve and the saturation continues to increase albeit at a reduced rate, and eventually exceeds 90% for both non-wetting and wetting cases. The existence of a complicated sweep phase space at breakthrough, and continued post-breakthrough evolution suggests the hydrodynamics and sweep is a complicated function of wetting angle, viscosity ratio and time, which has major potential implications to Enhanced Oil Recovery by water flooding, and hence, on estimates of global oil reserves. Validation of these results via experiments is required to ensure they translate to field studies.

Viscous fingering of miscible annular ring

Abstract: Miscible viscous fingering (VF) of the annulus of a more viscous fluid radially displaced by a less viscous fluid is investigated through both numerical computations and experimental study We aim to understand how VF with finiteness in a radial displacement different from the classical radial VF and the instability of a slice displaced rectilinearly with a uniform velocity It is observed that the VF of a miscible annular ring is a persistent phenomenon in contrast to the transient nature of VF of a miscible slice Although new fingers cease to appear after some time but due to the radial spreading of the area available for VF, a finite number of fingers always remain at a later time when diffusion is the ultimate dominating force A statistical analysis is performed for the numerical data and it is found that the second moment of the averaged profile, variance, is a non-monotonic function of time, contrary to variance in classical radial VF and rectilinear VF with one fluid sandwiched between layers of another The minimum in the variance indicates the interaction of two fronts which is visible in terms of pressure fingers, but not the concentration fingers indicating a faster growth of pressure than the concentration growth In addition, for existence of critical parameters for instability in terms of viscosity contrast and amount of sample, the variation of the finger length with flow rate is found to be dependent on the amount of the more viscous fluid confined in the annulus

Influence of interfacial rheology on viscous fingering

Abstract: Complex surfactant-laden interfaces exhibit surface rheological stresses when deforming against themselves, which in turn affects the flow and stability of the adjacent bulk fluids. We investigate, for the first time, the impact of interfacial rheology on the Saffman-Taylor or viscous fingering problem and demonstrate the stabilizing role of surface viscosity. We show that surface viscosity slows the growth of unstable protrusions, resulting in thicker fingers. We use these insights to highlight the quantitative changes that occur when a typical surface-viscous surfactant is present in a multiphase fluid displacement problem.

Control of fingering instability by vibrations

Abstract: In applications involving the injection of a fluid in a porous medium to displace another fluid, a main objective is the maximization of the displacement efficiency. Displacement fronts moving in porous media are subjected to hydrodynamic instability when a liquid of low viscosity displaces a high-viscosity liquid and consequently finger-like structure forms along the interface. This finger instability is usually undesirable in technical applications and natural filtration processes. We discuss the external periodic forcing as one of the promising ways to control the instability and perform numerical simulation of an initially spherical drop in a porous media under vertical vibrations. The drop is a favorable object to study since in this case one can observe the effect of vibrations on fluid interface domains inclined by different angles with respect to vibration axis. It is shown that under vibrations small-scale perturbations of interface are suppressed and in the case of vibrations of large enough intensity the drop becomes stable. The stability criterion is derived.

A review of one-phase hele-shaw flows and a level-set method for nonstandard configurations

Abstract: The classical model for studying one-phase Hele-Shaw flows is based on a highly nonlinear moving boundary problem with the fluid velocity related to pressure gradients via a Darcy-type law. In a standard configuration with the Hele-Shaw cell made up of two flat stationary plates, the pressure is harmonic. Therefore, conformal mapping techniques and boundary integral methods can be readily applied to study the key interfacial dynamics, including the Saffman–Taylor instability and viscous fingering patterns. As well as providing a brief review of these key issues, we present a flexible numerical scheme for studying both the standard and nonstandard Hele-Shaw flows. Our method consists of using a modified finite-difference stencil in conjunction with the level-set method to solve the governing equation for pressure on complicated domains and track the location of the moving boundary. Simulations show that our method is capable of reproducing the distinctive morphological features of the Saffman–Taylor instability on a uniform computational grid. By making straightforward adjustments, we show how our scheme can easily be adapted to solve for a wide variety of nonstandard configurations, including cases where the gap between the plates is linearly tapered, the plates are separated in time, and the entire Hele-Shaw cell is rotated at a given angular velocity. doi:10.1017/S144618112100033X

Effect of gas generation by chemical reaction on viscous fingering in a Hele–Shaw cell

Abstract: Herein, the effect of gas-bubble generation by a chemical reaction on viscous fingering (VF) is investigated using a Hele–Shaw cell in a miscible two-phase liquid. Sodium bicarbonate (NaHCO3) and citric acid (C6H8O7) solutions were used as displacing and displaced fluids, respectively. As factors affecting the displacement pattern with gas bubbles, four characteristic times of displacement, chemical reaction, bubble nucleation, and bubble coalescence, as well as the viscosity ratio, were discussed. In the experiments conducted herein, the characteristic time of the chemical reaction was shorter than those of other characteristic factors. Bubble coalescence occurred quickly, and the coalescence time was almost the same as the nucleation time. Therefore, if the displacement time changes with the injection flow rate, then the flow pattern changes depending on the competition between the displacement and nucleation times. When the displacement time was shorter than the nucleation time, the bubble generation did not follow the onset of VF. First, a VF pattern was formed, and small gas bubbles were then generated in the mixture inside the fingers. On the backbone of the fingers, small gas bubbles lined up and grew bigger with time. Moreover, when the nucleation time was lower than the displacement time, the bubbles coalesced more rapidly, thereby inducing outward flow with gas nucleation in addition to fluid injection. These gas bubbles prevented the mixing of the displacing and displaced fluids. Furthermore, the effects of C6H8O7 concentration and the viscosity ratio were discussed from the viewpoint of the characteristic time.