Effect Of Viscosity Contrast Research Articles

Effect of viscosity contrast on the dynamics of a sheared lamellar mesophase

Effect of viscosity contrast on the dynamics of a sheared lamellar mesophase

Experimental study on the role of polymer addition in Saffman–Taylor instability in miscible flow displacement

The role of nonlinear rheology of polymeric fluids in finger formation and the ensuing morphology of the patterns in miscible flow displacement is examined experimentally. The poly(ethylene oxide) (PEO) is introduced in either displaced or displacing fluid. The PEO solutions exhibit shear-thinning viscosity as well as normal stresses. As viscous fingering is primarily caused by the viscosity contrast between two miscible fluids, the zero-shear viscosities of the two fluids are controlled mainly by their composition. The contribution of rheological behavior in fingering is studied by varying the molecular weight of the polymer. The development of fingering patterns in PEO solutions is observed to be more complex showing more branches and tip-splitting vis-à-vis Newtonian fluid even for the same value of effective viscosity contrast regardless of polymer addition in either fluids. Particularly, flow displacement with displaced PEO solution exhibits significantly intensified patterns such that a fractal-like growth is observed when PEO solution of either high concentration or high molecular weight is being displaced. The additional nonlinear behavior, sidebranching, tip-splitting, and shielding is attributed to the inhomogeneity in fluid viscosity and normal stresses (or elasticity) due to local flow behavior. While shear-thinning behavior promotes the longitudinal growth of fingers leading to the shielding effect, the presence of normal stresses inhibits longitudinal growth of fingers promoting fingers in the transverse direction that imparts tip-splitting. Overall, the nonlinear rheology of the fluids gives rise to the effects, in addition to the viscosity modifications, and hence, is crucial for determining the morphology of the fingering instability.

New phase diagram of miscible viscous fingering instabilities in porous media with dead-end pores

Classical miscible viscous fingering (VF) instability occurs when a less viscous fluid displaces a more viscous one in porous media with pores that are all well connected. Here, we investigate numerically how non-negligible dead-end pores, together with a limited mass transfer rate Da between the two pore types, affect fingering dynamics. We identify a new stabilizing mechanism induced by a reduction of effective viscosity contrast at an intermediate Da, which leads to a new phase diagram for VF instabilities in a Péclet number—Pe–Da parameter space and an elimination of fingers and tip-splitting at low and large values of Pe, respectively. A scaling analysis, along with an analysis of interfacial lengths, accurately predicts the boundary of the flow regimes and explains the origin of the new stabilizing mechanism.

Lattice Boltzmann Simulation of Multicomponent Porous Media Flows With Chemical Reaction

Flows with chemical reactions in porous media are fundamental phenomena encountered in many natural, industrial, and scientific areas. For such flows, most existing studies use continuum assumptions and focus on volume-averaged properties on macroscopic scales. Considering the complex porous structures and fluid–solid interactions in realistic situations, this study develops a sophisticated lattice Boltzmann (LB) model for simulating reactive flows in porous media on the pore scale. In the present model, separate LB equations are built for multicomponent flows and chemical species evolutions, source terms are derived for heat and mass transfer, boundary schemes are formulated for surface reaction, and correction terms are introduced for temperature-dependent density. Thus, the present LB model offers a capability to capture pore-scale information of compressible/incompressible fluid motions, homogeneous reaction between miscible fluids, and heterogeneous reaction at the fluid–solid interface in porous media. Different scenarios of density fingering with homogeneous reaction are investigated, with effects of viscosity contrast being clarified. Furthermore, by introducing thermal flows, the solid coke combustion is modeled in porous media. During coke combustion, fluid viscosity is affected by heat and mass transfer, which results in unstable combustion fronts.

Continental Drift with Deep Cratonic Roots

The influence of the continental lithosphere and its root (or keel) on the continental drift of Earth is a key element in the history of plate tectonics. Previous geodynamic studies of mantle flow suggested that the cratonic root is moderately mechanically coupled with the underlying mantle, and stable continental drift on Earth's timescales occurs when the effective viscosity contrast between the continental lithosphere and the underlying mantle is approximately 103. Both geodynamics and seismological studies indicate that mechanically weak mobile belts (i.e., orogenic or suture zones) that surround cratons may play a role in the longevity of the cratonic lithosphere over geologically long timescales (i.e., over 1,000 million years) because they act as a buffer region against the high-viscosity cratons. Low-viscosity asthenosphere, characterized by slow seismic velocities, reduces the basal drag force acting on the cratonic root, which may also contribute to the longevity of the cratonic lithosphere. ▪ The role of the continental lithosphere and its root on the continental drift is reviewed from recent geodynamic and seismological studies. ▪ The cratonic root is moderately mechanically coupled with the underlying mantle and deformed by mantle flow over geological timescales. ▪ Orogenic belts or suture zones that surround cratons act as a buffer to protect cratons and are essential for their longevity. ▪ Low-viscosity asthenosphere may reduce the basal drag acting on the cratonic root and also contribute to its stability and longevity.

How Does Viscosity Contrast Influence Phase Mixing and Strain Localization?

AbstractUltramylonites—intensely deformed rocks with fine grain sizes and well‐mixed mineral phases—are thought to be a key component of Earth‐like plate tectonics, because coupled phase mixing and grain boundary pinning enable rocks to deform by grain‐size‐sensitive, self‐softening creep mechanisms over long geologic timescales. In isoviscous two‐phase composites, “geometric” phase mixing occurs via the sequential formation, attenuation (stretching), and disaggregation of compositional layering. However, the effects of viscosity contrast on the mechanisms and timescales for geometric mixing are poorly understood. Here, we describe a series of high‐strain torsion experiments on nonisoviscous calcite‐fluorite composites (viscosity contrast, ηca/ηfl ≈ 200) at 500°C, 0.75 GPa confining pressure, and 10−6–10−4 s−1 shear strain rate. At low to intermediate shear strains (γ ≤ 10), polycrystalline domains of the individual phases become sheared and form compositional layering. As layering develops, strain localizes into the weaker phase, fluorite. Strain partitioning impedes mixing by reducing the rate at which the stronger (calcite) layers deform, attenuate, and disaggregate. Even at very large shear strains (γ ≥ 50), grain‐scale mixing is limited, and thick compositional layers are preserved. Our experiments (1) demonstrate that viscosity contrasts impede mechanical phase mixing and (2) highlight the relative inefficiency of mechanical mixing. Nevertheless, by employing laboratory flow laws, we show that “ideal” conditions for mechanical phase mixing may be found in the wet middle to lower continental crust and in the dry mantle lithosphere, where quartz‐feldspar and olivine‐pyroxene viscosity contrasts are minimized, respectively.

On the breakup of a permeating oil droplet in crossflow filtration: Effects of viscosity contrast

The critical velocity of dislodgment of a permeating oil droplet in crossflow filtration is an important parameter in the analysis of the filtration of produced water systems using membrane technology. In this work, the effects of the viscosity contrast between the droplet and the surrounding fluid on the critical velocity of dislodgment are investigated. In the limit when the viscosity of the droplet approaches infinity, the gripping of the crossflow field on the droplet is maximum. When the viscosity contrast is finite, the smaller the viscosity contrast is, the smaller the gripping becomes. In order to highlight this effect, a comprehensive computational fluid dynamics study is conducted. A permeating droplet in the crossflow field is considered with the viscosity contrast ranging within two orders of magnitude. For each scenario, the critical velocity of dislodgment is determined by increasing the velocity incrementally until breakup occurs for every viscosity contrast. It is found that an increase in the viscosity contrast results in a decrease in the critical velocity of dislodgment. This represents a direct manifestation of the effect of the gripping of the droplet by the crossflow field, which increases as the viscosity contrast increases. Modification of the critical velocity of dislodgment, therefore, needs to be considered to account for this effect of viscosity contrast. The formula that was developed to estimate the critical velocity of dislodgment has been modified, and comparison with simulation gives a very good match.

Tectonic inheritance controls nappe detachment, transport and stacking in the Helvetic nappe system, Switzerland: insights from thermomechanical simulations

Abstract. Tectonic nappes have been investigated for more than a hundred years. Although geological studies often refer to a “nappe theory”, the physical mechanisms of nappe formation are still disputed. We apply two-dimensional numerical simulations of shortening of a passive margin to investigate the thermomechanical processes of detachment (or shearing off), transport and stacking of nappes. We use a visco-elasto-plastic model with standard creep flow laws, Drucker–Prager and von Mises yield criteria. We consider tectonic inheritance with two initial mechanical heterogeneities: (1) lateral heterogeneity of the basement–cover interface due to half-grabens and horsts and (2) vertical heterogeneities due to layering of mechanically strong and weak sedimentary units. The model shows detachment and horizontal transport of a thrust nappe that gets stacked on a fold nappe. The detachment of the thrust sheet is triggered by stress concentrations around the sediment–basement contact and the resulting brittle–plastic shear band that shears off the sedimentary units from the sediment–basement contact. Horizontal transport is facilitated by a basal shear zone just above the basement–cover contact, composed of thin, weak sediments that act as a décollement. Fold nappe formation occurs by a dominantly ductile closure of a half-graben and the associated extrusion of the half-graben fill. We apply our model to the Helvetic nappe system in western Switzerland, which is characterized by stacking of the Wildhorn thrust nappe above the Morcles fold nappe. The modeled structures, the deformation rates and the temperature field agree with data from the Helvetic nappe system. Mechanical heterogeneities must locally generate effective viscosity (i.e., ratio of stress to viscoplastic strain rate) contrast of about 3 orders of magnitude to model nappe structures similar to the ones of the Helvetic nappe system. Our results indicate that the structural evolution of the Helvetic nappe system was controlled by tectonic inheritance and that material softening mechanisms are not essential to reproduce the first-order nappe structures.

An efficient numerical algorithm for solving viscosity contrast Cahn–Hilliard–Navier–Stokes system in porous media

Two-phase flow with viscosity contrast at the pore scale is modeled by a time-dependent Cahn–Hilliard–Navier–Stokes model and belongs to the class of diffuse interface method. The model allows for moving contact line and varying wettability. The numerical scheme utilizes an efficient pressure-correction projection algorithm, in conjunction with interior penalty discontinuous Galerkin schemes for space discretization developed within the framework of a distributed parallel pore-scale flow simulation system. The effect of viscosity contrast on the phase distribution is studied in relation with capillary forces and wettability. The algorithm is numerically robust and lends itself naturally to large-scale 3D numerical simulations.

Solvent diffusion and dispersion in partially saturated porous media: An experimental and numerical pore-level study

Recent research on unlocking the solvent dispersion as a physical blending process in porous media has been mainly focused on core-scale observations. Pore-level studies of multiphase displacements can help to develop models that correlate rock macro-scale characteristics with its small-scale features, particularly for unsaturated rocks where the intricate fluid arrangements cause dynamic events to be localized in preferential pathways. In this work, to draw new insights into the physics of pore-level interfaces and crystallize the role of small-scale phenomena on the efficiency of solvent-aided bitumen recovery processes, numerical simulations coupled with experiments are conducted in pore-level domains. We simulate fluid flow and transport phenomena through millimeter-sized three-dimensional slabs of consolidated and unconsolidated packings of grains representing the geological rock types of the McMurray formation. We propose a robust numerical workflow for simulation of miscible-floods in unsaturated porous media and investigate the impact of matrix heterogeneity, connate water, cementation, and injection velocity on the longitudinal dispersion coefficient. In particular, primary drainage is simulated at low capillary numbers resulting in two-phase fluid occupancies through pore space domains. Finite element simulations are then carried out in order to solve the mixing advection-diffusion equations within the water-free pore space, and lastly, the effluent history is analyzed to predict the dispersion coefficient in both fully- and partially-saturated conditions and evaluate the efficiency of miscible displacements in the presence of microheterogeneities. A new analytical model for calculation of dispersivity, together with the numerical simulation results, is utilized to adjust a general model for the prediction of longitudinal dispersion coefficient in unsaturated sandy porous media of either uniform or non-uniform grains. Moreover, miscible-flood experiments at low to high injection velocities are conducted in a transparent glass micromodel. According to the results, rock micro-heterogeneities and immobile water both increase the longitudinal dispersion coefficient, and two-phase equilibria control the velocity field by creating connected regions of brine and low resistance oil-filled channels and consequently influence the solute transport and mixing processes. The effect of viscosity contrast on the longitudinal dispersion coefficient is also noteworthy, as the viscous fingering at unfavorable viscosity ratios widens the mixing zone.

Dynamics of a Highly Viscous Circular Blob in Homogeneous Porous Media

Viscous fingering is ubiquitous in miscible displacements in porous media, in particular, oil recovery, contaminant transport in aquifers, chromatography separation, and geological CO2 sequestration. The viscosity contrasts between heavy oil and water is several orders of magnitude larger than typical viscosity contrasts considered in the majority of the literature. We use the finite element method (FEM)-based COMSOL Multiphysics simulator to simulate miscible displacements in homogeneous porous media with very large viscosity contrasts. Our numerical model is suitable for a wide range of viscosity contrasts covering chromatographic separation as well as heavy oil recovery. We have successfully captured some interesting and previously unexplored dynamics of miscible blobs with very large viscosity contrasts in homogeneous porous media. We study the effect of viscosity contrast on the spreading and the degree of mixing of the blob. Spreading (variance of transversely averaged concentration) follows the power law t 3 . 34 for the blobs with viscosity ∼ O ( 10 2 ) and higher, while degree of mixing is found to vary non-monotonically with log-mobility ratio. Moreover, in the limit of very large viscosity contrast, the circular blob behaves like an erodible solid body and the degree of mixing approaches the viscosity-matched case.

Experimental study on droplet generation in flow focusing devices considering a stratified flow with viscosity contrast

High throughput analysis is highly demanded in a variety of chemical reactions. Droplet microfluidics offers unique advantages over traditional multi-well plate systems for high throughput analysis such as providing a confined and more controllable environment for single particle or cell analysis. Driven by the need to improve the efficiency of encapsulating one particle or cell into one individual droplet without complicating geometric and operating conditions, this study experimentally investigated the effects of viscosity contrast between two miscible fluids that together serve the dispersed fluid on the ordering of particles before they are encapsulated into droplets by another immiscible fluid. Five scenarios with different viscosity contrast were systematically considered and a physical model of droplet size for each scenario was developed based on experimental results and scaling laws. The five different scenarios include two with pure 10% glycerol and pure 80% glycerol as the dispersed phase, respectively, and three others where these two fluids are either side by side or one is accompanied by the other. Droplet size and formation period for these scenarios were compared and analyzed considering the same geometric and flow conditions. It is found that the stratified flow structures formed in the first junction by the two miscible fluids (10% and 80% glycerol solutions) strongly influence droplet formation dynamics such as droplet size and formation frequency. Each scenario finds its own applications. The scenario with 80% glycerol surrounded by 10% glycerol provides the optimized means for particle encapsulation. However, the scenario with two fluids side by side in the first junction generates droplets with high monodispersity for the largest range of flow ratios, which is useful for high throughput reactions involving different reagents.

Stability of gravitationally unstable double diffusive transient boundary layers with variable viscosity in porous media

We study the double diffusive convection (DDC) in porous media through linear stability analysis (LSA) and direct numerical simulations (DNS). Unlike the previous studies that assume static solutal or thermal fields, the developed model is able to capture the transient behavior of both fields. We show that under the assumption of static field, the role of Lewis number cannot be distinguished. Under transient fields, we conclude that higher Lewis numbers result in earlier instability of the boundary layers. Moreover, the effect of viscosity contrast is explained in terms of the mobility of the boundary layer. The DNS results confirm the validity of LSA predictions. We also obtain the critical Rayleigh number and show that in the presence of viscosity contrast, it can be much smaller than the conventional limit of 4π2. This study provides a better understanding of the transient nature of DDC in the presence of viscosity variations. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2471–2482, 2017

Effect of viscosity contrast on plume formation in density stratified fluids

We perform two and three dimensional numerical simulations of plume formation in density and viscosity stratified fluid systems. We show that the ambient to plume fluid viscosity ratio strongly affects the near wall plume structures (line or sheet plumes) such as plume spacing and shape of plumes. We observe that where mushroom-like plumes are observed for lower viscosity ratios, taller plumes with bulbous heads form for high viscosity ratios. Plume structure and spacing are in good agreement with experimental results. By studying the geometry of the line plumes and the flow in the circulation cells, we discuss the mechanisms of their formation and the dynamics of merging. We show that an increase in the viscosity ratio decreases the total length of line plumes in the planform which indicates a decreased mixing at higher viscosity ratios.

Impact of viscous fingering and permeability heterogeneity on fluid mixing in porous media

AbstractFluid mixing plays a fundamental role in many natural and engineered processes, including groundwater flows in porous media, enhanced oil recovery, and microfluidic lab‐on‐a‐chip systems. Recent developments have explored the effect of viscosity contrast on mixing, suggesting that the unstable displacement of fluids with different viscosities, or viscous fingering, provides a powerful mechanism to increase fluid‐fluid interfacial area and enhance mixing. However, existing studies have not incorporated the effect of medium heterogeneity on the mixing rate. Here, we characterize the evolution of mixing between two fluids of different viscosity in heterogeneous porous media. We focus on a practical scenario of divergent‐convergent flow in a quarter five spot geometry prototypical of well‐driven groundwater flows. We study by means of numerical simulations the impact of permeability heterogeneity and viscosity contrast on the breakthrough curves and mixing efficiency, and we rationalize the nontrivial mixing behavior that emerges from the competition between the creation of fluid‐fluid interfacial area and channeling.

Experimental study of the growth of mixing zone in miscible viscous fingering

An experimental study is performed to quantify the growth of the mixing zone in miscible viscous fingering. Rectilinear flow displacement experiments are performed in a Hele-Shaw cell over a wide range of viscosity ratios (1–1225) by injecting water into glycerol solutions at different flow rates. All the experiments are performed at high Peclet numbers and linear growth in mixing zone is observed. The mixing zone velocity increases with the viscosity ratio up to viscosity ratios of 340 and the trend is consistent with Koval’s model. However, at higher viscosity ratios, the mixing velocity plateaus signifying no further effect of viscosity contrast on the growth of mixing zone. The front (fingertip) velocities also increase up to viscosity ratios of 340 above which the velocities plateau.

Effect of viscosity contrast on gravitationally unstable diffusive layers in porous media

We investigate the effect of viscosity contrast on the stability of gravitationally unstable, diffusive layers in porous media. Our analysis helps evaluate experimental observations of various diffusive (boundary) layer models that are commonly used to study the sequestration of CO2 in brine aquifers. We evaluate the effect of viscosity contrast for two basic models that are characterized with respect to whether or not the interface between CO2 and brine is allowed to move. We find that diffusive layers are in general more unstable when viscosity decreases with depth within the layer compared to when viscosity increases with depth. This behavior is in contrast to the one associated with the classical displacement problem of gravitationally unstable diffusive layers that are subject to mean flow. For the classical problem, a greater instability is associated with the displacement of a more viscous, lighter fluid along the direction of gravity by a less viscous, heavier fluid. We show that the contrasting behavior highlighted in this study is a special case of the classical displacement problem that depends on the relative strength of the displacement and buoyancy velocities. We demonstrate the existence of a critical viscosity ratio that determines whether the flow is buoyancy dominated or displacement dominated. We explain the new behaviors in terms of the interaction of vorticity components related to gravitational and viscous effects.

Proppant Placement Using Alternate-Slug Fracturing

Summary New fracturing techniques, such as hybrid fracturing (Sharma et al. 2004), reverse-hybrid fracturing (Liu et al. 2007), and channel (HiWAY) fracturing (Gillard et al. 2010), have been deployed over the past few years to effectively place proppant in fractures. The goal of these methods is to increase the conductivity in the proppant pack, providing highly conductive paths for hydrocarbons to flow from the reservoir to the wellbore. This paper presents an experimental study on proppant placement by use of a new method of fracturing, referred to as alternate-slug fracturing. The method involves an alternate injection of low-viscosity and high-viscosity fluids, with proppant carried by the low-viscosity fluid. Alternate-slug fracturing ensures a deeper placement of proppant through two primary mechanisms: (i) proppant transport in viscous fingers, formed by the low-viscosity fluid, and (ii) an increase in drag force in the polymer slug, leading to better entrainment and displacement of any proppant banks that may have formed. Both these effects lead to longer propped-fracture length and better vertical placement of proppant in the fracture. In addition, the method offers lower polymer costs, lower pumping horsepower, smaller fracture widths, better control of fluid leakoff, less risk of tip screenouts, and less gel damage compared with conventional gel fracture treatments. Experiments are conducted in simulated fractures (slot cells) with fluids of different viscosity, with proppant being carried by the low-viscosity fluid. It is shown that viscous fingers of low-viscosity fluid and viscous sweeps by the high-viscosity fluid lead to a deeper placement of proppant. Experiments are also conducted to demonstrate slickwater fracturing, hybrid fracturing, and reverse-hybrid fracturing. Comparison shows that alternate-slug fracturing leads to the deepest and most-uniform placement of proppant inside the fracture. Experiments are also conducted to study the mixing of fluids over a wide range of viscosity ratios. Data are presented to show that the finger velocities and mixing-zone velocities increase with viscosity ratio up to viscosity ratios of approximately 350. However, at higher viscosity ratios, the velocities plateau, signifying no further effect of viscosity contrast on the growth of fingers and mixing zone. The data are an integral part of design calculations for alternate-slug-fracturing treatments.

Single layer folding in simple shear

Despite the common occurrence of simple shear deformation, laboratory and numerical simulations of folding have so far been almost exclusively in pure shear. Here we present a series of finite-element simulations of single layer folding in simple shear up to high shear strains (γ ≤ 4, and up to 75% shortening of the folding layer). In the simulations we vary the viscosity contrast between layer and its surroundings (25–100), the stress exponent (1 or 3) and the kinematics of deformation (pure- versus simple shear). In simple shear fold trains do not show a clear asymmetry, axial planes form perpendicular to the developing fold train and rotate along with the fold train. Differences in geometries between folds formed in simple and pure shear folds are thus difficult to distinguish visually, with simple shear folds slightly more irregular and with more variable axial plane orientation than in pure shear. Asymmetric refraction of an axial planar cleavage is a clearer indication of folding in simple shear. The main effect of an increase in stress exponent is an increase in effective viscosity contrast, with only a secondary effect on fold geometry. Naturally folded aplite dykes in a granodiorite are found in a shear zone in Roses, NE Spain. Comparison of the folded dykes with our numerical simulations indicates a viscosity contrast of around 25 and a stress exponent of 3. The natural folds confirm that at this moderate viscosity contrast, a significant amount of shortening (20–30%) is achieved by layer thickening instead of folding.

Strain analysis and rheology contrasts in polymictic conglomerates: An example from the Seine metaconglomerates, Superior Province, Canada

Deformed conglomerates typically display contrasting strains between different lithological clast populations and matrix, which can be exploited to provide information about effective viscosity contrasts. We analyzed three different clast populations (granitoid, mafic volcanic, and felsic volcanic) across a strain gradient in the Seine metaconglomerates of Ontario, Canada. We calculated finite strain using the R f/ φ method and bootstrap statistics. Granitoid clasts exhibited the least amount of strain, while the mafic and felsic clasts had similar, greater strains. We assumed that the bulk finite strain was recorded by the mafic clasts, given their large proportion of the rock and their similar composition to the matrix. We calculated effective viscosity contrasts using the finite strain information, assuming Newtonian viscous rheology. The two volcanic clast populations have similar effective viscosities, regardless of strain magnitude, with ratios of felsic/mafic ranging from 0.27 to 2.12 and average ratio of 1.19. The granitoid clasts are significantly more competent than the mafic clasts with effective viscosity ratios ranging from 2.35 to 12.39 and average ratio of 5.61. The results are consistent with a qualitative competence hierarchy of granitoid > felsic ≥ mafic, although the quantitative effective viscosity ratios change with strain magnitude. Consequently, the effective viscosity contrast between clast types is strain dependent and possibly deformation path dependent.