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Influence of Wetting on Viscous Fingering Via 2D Lattice Boltzmann Simulations
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 $$M\in [0.01,100]$$ M ϵ [ 0.01 , 100 ] and wetting angles in the range $$\theta _w\in [180^\circ ,0^\circ ]$$ θ w ϵ [ 180 ° , 0 ° ] 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.
Bidisperse and polydisperse suspension rheology at large solid fraction
At the same solid volume fraction, bidisperse and polydisperse suspensions display lower viscosities, and weaker normal stress response, compared to monodisperse suspensions. The reduction of viscosity associated with size distribution can be explained by an increase of the maximum flowable, or jamming, solid fraction. In this work, concentrated or "dense" suspensions are simulated under strong shearing, where thermal motion and repulsive forces are negligible, but we allow for particle contact with a mild frictional interaction with interparticle friction coefficient of 0.2. Aspects of bidisperse suspension rheology are first revisited to establish that the approach reproduces established trends; the study of bidisperse suspensions at size ratios of large to small particle radii (2 to 4) shows that a minimum in the viscosity occurs for zeta slightly above 0.5, where zeta=phi_{large}/phi is the fraction of the total solid volume occupied by the large particles. The simple shear flows of polydisperse suspensions with truncated normal and log normal size distributions, and bidisperse suspensions which are statistically equivalent with these polydisperse cases up to third moment of the size distribution, are simulated and the rheologies are extracted. Prior work shows that such distributions with equivalent low-order moments have similar phi_{m}, and the rheological behaviors of normal, log normal and bidisperse cases are shown to be in close agreement for a wide range of standard deviation in particle size, with standard correlations which are functionally dependent on phi/phi_{m} providing excellent agreement with the rheology found in simulation. The close agreement of both viscosity and normal stress response between bi- and polydisperse suspensions demonstrates the controlling in influence of the maximum packing fraction in noncolloidal suspensions. Microstructural investigations and the stress distribution according to particle size are also presented.
Impact of Rheology Models on Horizontal Well Polymer Flooding in a Heavy Oil Reservoir on Alaska North Slope: A Simulation Study
Polymer rheology can have either a positive or a negative effect on polymer flooding performance under varied circumstances. Many researchers have studied the effect of polymer rheology in a vertical well, but no field scale studies have been conducted to investigate whether polymer rheology is beneficial to polymer flooding in heavy oil reservoirs developed by horizontal wells. In this paper, we conducted a numerical simulation study to examine the effect of HPAM polymer rheology on a polymer flooding pilot, which is the first-ever project conducted on a heavy oil reservoir from Alaska North Slope (ANS) developed by horizontal wells. Three rheology types were considered in the study including the apparent viscosity measured during coreflooding of using a HPAM polymer, the bulk viscosity measured with a viscometer, and a Newtonian flow model. The results suggest that using the bulk viscosity in simulation underestimates the conformance control and the water-oil-ratio reduction capability of the HPAM polymer solution. When the apparent viscosity is used, the incremental oil and sweep were largely increased, and the optimal recovery period of polymer flooding was extended greatly, especially for the heterogeneous formations. Therefore, the rheology type of polymer plays a significant role in the incremental oil recovery and injection profile of the horizontal well system given the pilot test conditions. This study has provided practical guidance to field operators for the ongoing polymer flooding pilot on ANS and will also provide valuable information for other polymer projects conducted in similar conditions.
Comparison of High-Speed Operating Characteristics of Size 215 Cylindrical-Roller Bearings as Determined in Turbojet Engine and in Laboratory Test Rig
A comparison of the operating characteristics of 75-millimeter-bore (size 215) cylindrical-roller one-piece inner-race-riding cage-type bearings was made using a laboratory test rig and a turbojet engine. Cooling correlation parameters were determined by means of dimensional analysis, and the generalized results for both the inner- and outer-race bearing operating temperatures are compared for the laboratory test rig and the turbojet engine. Inner- and outer-race cooling-correlation curves were obtained for the turbojet-engine turbine-roller bearing with the same inner- and outer-race correlation parameters and exponents as those determined for the laboratory test-rig bearing. The inner- and outer-race turbine roller-bearing temperatures may be predicted from a single curve, regardless of variations in speed, load, oil flow, oil inlet temperature, oil inlet viscosity, oil-jet diameter or any combination of these parameters. The turbojet-engine turbine-roller-bearing inner-race temperatures were 30 to 60 F greater than the outer-race-maximum temperatures, the exact values depending on the operating condition and oil viscosity; these results are in contrast to the laboratory test-rig results where the inner-race temperatures were less than the outer-race-maximum temperatures. The turbojet-engine turbine-roller bearing, maximum outer-race circumferential temperature variation was approximately 30 F for each of the oils used. The effect of oil viscosity on inner- and outer-race turbojet-engine turbine-roller-bearing temperatures was found to be significant. With the lower viscosity oil (6x10(exp -7) reyns (4.9 centistokes) at 100 F; viscosity index, 83), the inner-race temperature was approximately 30 to 35 F less than with the higher viscosity oil (53x10(exp -7) reyns (42.8 centistokes) at 100 F; viscosity index, 150); whereas the outer-race-maximum temperatures were 12 to 28 F lower with the lower viscosity oil over the DN range investigated.
Odd surface waves in two-dimensional incompressible fluids
We consider free surface dynamics of a two-dimensional incompressible fluid with odd viscosity. The odd viscosity is a peculiar part of the viscosity tensor which does not result in dissipation and is allowed when parity symmetry is broken. For the case of incompressible fluids, the odd viscosity manifests itself through the free surface (no stress) boundary conditions. We first find the free surface wave solutions of hydrodynamics in the linear approximation and study the dispersion of such waves. As expected, the surface waves are chiral and even exist in the absence of gravity and vanishing shear viscosity. In this limit, we derive effective nonlinear Hamiltonian equations for the surface dynamics, generalizing the linear solutions to the weakly nonlinear case. Within the small surface angle approximation, the equation of motion leads to a new class of non-linear chiral dynamics governed by what we dub the chiral Burgers equation. The chiral Burgers equation is identical to the complex Burgers equation with imaginary viscosity and an additional analyticity requirement that enforces chirality. We present several exact solutions of the chiral Burgers equation. For generic multiple pole initial conditions, the system evolves to the formation of singularities in a finite time similar to the case of an ideal fluid without odd viscosity. We also obtain a periodic solution to the chiral Burgers corresponding to the non-linear generalization of small amplitude linear waves.
Micro- and nano-scale hollow TiO{sub 2} fibers by coaxial electrospinning: Preparation and gas sensing
We report the preparation of micro- and nano-scale hollow TiO{sub 2} fibers using a coaxial electrospinning technique and their gas sensing properties in terms of CO. The diameter of hollow TiO{sub 2} fibers can be controlled from 200 nm to several micrometers by changing the viscosity of electrospinning solutions. Lower viscosities produce slim hollow nanofibers. In contrast, fat hollow microfibers are obtained in the case of higher viscosities. A simple mathematical expression is presented to predict the change in diameter of hollow TiO{sub 2} fibers as a function of viscosity. The successful control over the diameter of hollow TiO{sub 2} fibers is expected to bring extensive applications. To test a potential use of hollow TiO{sub 2} fibers in chemical gas sensors, their sensing properties to CO are investigated at room temperature. - Graphical abstract: Microstructures of as-prepared and calcined hollow TiO{sub 2} fibers prepared by the electrospinning technique with a coaxial needle. Dynamic response at various CO concentrations for the sensor fabricated with the hollow TiO{sub 2} fibers. Highlights: > Hollow TiO{sub 2} fibers were synthesized using a coaxial electrospinning technique. > Their diameter can be controlled by changing the viscosity of electrospinning solutions. > Lower viscosities produce slim hollow nanofibers. > In contrast, fat hollow microfibers are obtained in the case of higher viscosities. > Successful control over the diameter of hollow TiO{sub 2} fibers will bring extensive applications.
Fragility correlates thermodynamic and kinetic properties of glass forming liquids
Graphical abstract: The suggested new fragility parameter correlates viscosity and configurational entropy. - Highlights: • A new fragility function, F=ΔT/ΔC{sub p}×C{sub p}{sup l}/T{sub g} has been proposed. • A three parameter viscosity function using the new F reproduces Angell fragility plot. • A new ΔC{sub p} function is derived which directly relates Adam–Gibbs function with the fragility based viscosity function. - Abstract: In our earlier communication we proposed a simple fragility determining function, ([NBO]/V{sub m}{sup 3}T{sub g}), which we have now used to analyze several glass systems using available thermal data. A comparison with similar fragility determining function, ΔC{sub p}/C{sub p}{sup l}, introduced by Chryssikos et al. in their investigation of lithium borate glasses has also been performed and found to be more convenient quantity for discussing fragilities. We now propose a new function which uses both ΔC{sub p} and ΔT and which gives a numerical fragility parameter, F whose value lies between 0 and 1 for glass forming liquids. F can be calculated through the use of measured thermal parameters ΔC{sub p}, C{sub p}{sup l}, T{sub g} and T{sub m}. Use of the new fragility values in reduced viscosity equation reproduces the whole range of viscosity curves of the Angell plot. The reduced viscosity equation can be directly compared with the Adam–Gibbs viscosity equation and a heat capacity function can be formulated which reproduces satisfactorily the ΔC{sub p} versus ln(T{sub r}) curves and hence the configurational entropy.
Development and demonstration of a rolling ball viscometer for molten salts with near-minimum liquidus NaCl–KCl
The thermophysical characterization of molten chloride and fluoride salts is a key interest for the development of advanced molten salt nuclear reactors. Viscosity is one thermophysical property of interest; a high-accuracy understanding of this property is necessary for modeling the thermal energy transfer and mass flow rate for a given molten salt system. Only a few methods have consistently been used to measure the viscosity of molten chloride and fluoride salt systems, and large discrepancies have been observed in the literature between independent studies of nearly identical salt systems. As such, exploration of novel measurement methods or implementations may allow for further validation, improved measurement accuracy, and overall improved understanding about optimal approaches for measuring molten salt viscosity. Here, in this study, a novel implementation of the rolling ball viscometry method was used to measure the viscosity of a 44/56 mol % mixture of NaCl–KCl within a temperature range of 714–838 °C, with the intent to demonstrate the feasibility of this technique for molten salt viscosity measurement cross-validation. The purity of this salt was confirmed through laser-induced breakdown spectroscopy. Measured viscosities were approximately 1.3–1.0 cP within this temperature range, and the overall uncertainty was 10.8%, which was determined through Gaussian error propagation. The results agree reasonably well with measured viscosities of similar NaCl–KCl mixtures in the literature (within 2%–20% depending on the temperature and study), although the experimental error in some of these comparative studies may be significant.
Stripped elliptical galaxies as probes of ICM physics. II. Stirred, but mixed? Viscous and inviscid gas stripping of the Virgo elliptical M89
Elliptical galaxies moving through the intracluster medium (ICM) are progressively stripped of their gaseous atmospheres. X-ray observations reveal the structure of galactic tails, wakes, and the interface between the galactic gas and the ICM. This fine-structure depends on dynamic conditions (galaxy potential, initial gas contents, orbit in the host cluster), orbital stage (early infall, pre-/post-pericenter passage), as well as on the still ill-constrained ICM plasma properties (thermal conductivity, viscosity, magnetic field structure). Paper I describes flow patterns and stages of inviscid gas stripping. Here we study the effect of a Spitzer-like temperature dependent viscosity corresponding to Reynolds numbers, Re, of 50–5000 with respect to the ICM flow around the remnant atmosphere. Global flow patterns are independent of viscosity in this Reynolds number range. Viscosity influences two aspects. In inviscid stripping, Kelvin–Helmholtz instabilities (KHIs) at the sides of the remnant atmosphere lead to observable horns or wings. Increasing viscosity suppresses KHIs of increasing length scale and thus observable horns and wings. Furthermore, in inviscid stripping, stripped galactic gas can mix with the ambient ICM in the galaxy’s wake. This mixing is suppressed increasingly with increasing viscosity, such that viscously stripped galaxies have long X-ray bright, cool wakes. We provide mock X-ray images for different stripping stages and conditions. While these qualitative results are generic, we tailor our simulations to the Virgo galaxy M89 (NGC 4552), where Re≈50 corresponds to a viscosity of 10% of the Spitzer level. Paper III compares new deep Chandra and archival XMM-Newton data to our simulations.
Rheological Behavior of Xanthan Gum Solution Related to Shear Thinning Fluid Delivery for Subsurface Remediation
Xanthan gum, a biopolymer, forms shear thinning fluids which can be used as delivery media to improve the distribution of remedial amendments injected into heterogeneous subsurface environments. The rheological behavior of the shear thinning solution needs to be known to develop an appropriate design for field injection. In this study, the rheological properties of xanthan gum solutions were obtained under various chemical and environmental conditions relevant to delivery of remedial amendments to groundwater. Higher xanthan concentration raised the absolute solution viscosity and increased the degree of shear thinning. Addition of remedial amendments (e.g., phosphate, sodium lactate, ethyl lactate) caused the dynamic viscosity of xanthan gum to decrease, but the solutions maintained shear-thinning properties. Use of simple salt (e.g. Na+, Ca2+) to increase the solution ionic strength also decreased the dynamic viscosity of xanthan and the degree of shear thinning, although the effect is a function of xanthan gum concentration and diminished as the xanthan gum concentration was increased. At high xanthan concentration, addition of salt to the solution increased dynamic viscosity. In the absence of sediments, xanthan gum solutions maintain their viscosity properties for months. However, xanthan gum solutions were shown to lose dynamic viscosity over a period of days to weeks when contacted with saturated site sediment. Loss of viscosity is attributed to physical and biodegradation processes.
Nonlinear ELM simulations based on a nonideal peeling–ballooning model using the BOUT++ code
A minimum set of equations based on the peeling–ballooning (P–B) model with nonideal physics effects (diamagnetic drift, E × B drift, resistivity and anomalous electron viscosity) is found to simulate pedestal collapse when using the BOUT++ simulation code, developed in part from the original fluid edge code BOUT. Linear simulations of P–B modes find good agreement in growth rate and mode structure with ELITE calculations. The influence of the E × B drift, diamagnetic drift, resistivity, anomalous electron viscosity, ion viscosity and parallel thermal diffusivity on P–B modes is being studied; we find that (1) the diamagnetic drift and E × B drift stabilize the P–B mode in a manner consistent with theoretical expectations; (2) resistivity destabilizes the P–B mode, leading to resistive P–B mode; (3) anomalous electron and parallel ion viscosities destabilize the P–B mode, leading to a viscous P–B mode; (4) perpendicular ion viscosity and parallel thermal diffusivity stabilize the P–B mode. With addition of the anomalous electron viscosity under the assumption that the anomalous kinematic electron viscosity is comparable to the anomalous electron perpendicular thermal diffusivity, or the Prandtl number is close to unity, it is found from nonlinear simulations using a realistic high Lundquist number that the pedestal collapse is limited to the edge region and the ELM size is about 5–10% of the pedestal stored energy. Furthermore, this is consistent with many observations of large ELMs. The estimated island size is consistent with the size of fast pedestal pressure collapse. In the stable α-zones of ideal P–B modes, nonlinear simulations of viscous ballooning modes or current-diffusive ballooning mode (CDBM) for ITER H-mode scenarios are presented.
Pressure Modification or Barrier Issues during Polymer Flooding Enhanced Oil Recovery
Effective oil displacement from a reservoir requires adequate and properly directed pressure gradients in areas of high oil saturation. If the polymer bank is too large or too viscous during a polymer flood, the pressure drops from the injection well to the polymer front may act as a pressure modification or barrier by usurping most of the downstream driving force for oil displacement. Polymer injection pressures must be limited. The maximum allowable injection pressure is commonly constrained by caprock integrity, injection equipment, and/or regulations, even though fractures can be beneficial to polymer injectivity. This paper examines when the pressure-barrier concept limits the size and viscosity of the polymer bank during a polymer flood. Analytical and numerical methods are used to address this issue. We examine the relevance of the pressure modification concept for a wide variety of circumstances, including oil viscosities ranging from 10 cp to 1650 cp, vertical wells versus horizontal wells, single versus multiple layered reservoirs, permeability contrast, and crossflow between layers. We also examine the relation between the pressure-barrier concept and fractures and fracture extension during polymer injection. We demonstrate that in reservoirs with single layers, the pressure-barrier concept only limits the optimum viscosity of the injected polymer if the mobility of the polymer bank is less than the mobility of the displaced oil bank. The same is true for multizoned reservoirs with no crossflow between layers. Thus, for these cases, the optimum polymer viscosity is likely to be dictated by the mobility of the oil bank, unless other factors intervene. For multizoned reservoirs with free crossflow between layers, the situation is different. A compromise must be reached between injected polymer viscosity and the efficiency of oil recovery. This work is particularly relevant to viscous oil reservoirs where polymer viscosities are substantially lower than the oil viscosity.
Pressure Barrier Applicability to Polymer Flood Design
Effective oil displacement from a reservoir requires adequate and properly directed pressure gradients in areas of high oil saturation. If the polymer bank is too large or too viscous during a polymer flood, the pressure drop from the injection well to the polymer front may act as a pressure barrier by usurping most of the downstream driving force for oil displacement. Polymer injection pressures must be limited. The maximum allowable injection pressure is commonly constrained by caprock integrity, injection equipment, and/or regulations, even though fractures can be beneficial to polymer injectivity (and even sweep efficiency in some cases). This paper examines when the pressure-barrier concept limits the size and viscosity of the polymer bank during a polymer flood. Both analytical and numerical methods are used to address this issue. We examine the relevance of the pressure barrier concept for a wide variety of circumstances, including oil viscosities ranging from 10-cp (like at Daqing, China) to 1650-cp (like at Pelican Lake, Alberta), vertical wells (like at Tambaredjo, Suriname) versus horizontal wells (like at Milne Point, Alaska), single versus multiple layered reservoirs, permeability contrast, and with versus with crossflow between layers. We also examine the relation between the pressure-barrier concept and fractures and fracture extension during polymer injection. We demonstrate that in reservoirs with single layers, the pressure-barrier concept only limits the optimum viscosity of the injected polymer if the mobility of the polymer bank is less than the mobility of the displaced oil bank. The same is true for multi-zoned reservoirs with no crossflow between layers. Thus, for these cases, the optimum polymer viscosity is likely to be dictated by the mobility of the oil bank, unless other factors (like fracture extension) intervene. For multi-zoned reservoirs with free crossflow between layers, the situation is different. A compromise must be reached between injected polymer viscosity and the efficiency of oil recovery. The relevance of our findings is applied to operations for several existing polymer floods. This work is particularly relevant to viscous-oil reservoirs (like Pelican Lake and others) where the injected polymer viscosities are substantially lower than the oil viscosity
Improving the accuracy of central difference schemes
General difference approximations to the fluid dynamic equations require an artificial viscosity in order to converge to a steady state. This artificial viscosity serves two purposes. One is to suppress high frequency noise which is not damped by the central differences. The second purpose is to introduce an entropy-like condition so that shocks can be captured. These viscosities need a coefficient to measure the amount of viscosity to be added. In the standard scheme, a scalar coefficient is used based on the spectral radius of the Jacobian of the convective flux. However, this can add too much viscosity to the slower waves. Hence, it is suggested that a matrix viscosity be used. This gives an appropriate viscosity for each wave component. With this matrix valued coefficient, the central difference scheme becomes closer to upwind biased methods.
Volatiles, rheology, and mantle convection: Comparing Earth, Venus, and Mars
Silicate rheology is controlled in part by volatile content. The variation of viscosity with position in the mantle will influence the nature of mantle convection; hence, modeling mantle convection and its effect on surface observables such as the geoid places constraints on the viscosity structure of a planet's mantle and may indirectly constrain the volatile distribution. Models of viscous mantle flow and the Earth's geoid indicate that there is roughly a two order of magnitude variation in viscosity between the upper and lower mantles, although there is some disagreement over the depth of the viscosity minimum in the upper mantle. Some studies of post-glacial rebound also support such a viscosity contrast between the upper and lower mantles. On Venus, several highland regions appear to be supported by mantle plumes. Modeling of the geoid and topography of these regions indicates that if these features are plume-related, then the mantle of Venus can not have an Earth-like low viscosity zone in its upper mantle. On Mars, the Tharsis volcanic province has alternatively been explained as supported either by mantle convection or by flexure of a thick lithosphere. If the convective model is correct, then the large geoid anomaly requires that Mars can not have a low viscosity zone in its upper mantle.
A singularity free approach to post glacial rebound calculations
Calculating the post glacial response of a viscoelastic Earth model using the exponential decay normal mode technique leads to intrinsic singularities if viscosity varies continuously as a function of radius. We develop a numerical implementation of the Complex Real Fourier transform (CRFT) method as an accurate and stable procedure to avoid these singularities. Using CRFT, we investigate the response of a set of Maxwell Earth models to surface loading. We find that the effect of expanding a layered viscosity structure into a continuously varying structure is to destroy the modes associated with the boundary between layers. Horizontal motion is more sensitive than vertical motion to the viscosity structure just below the lithosphere. Horizontal motion is less sensitive to the viscosity of the lower mantle than the vertical motion is. When the viscosity increases at 670 km depth by a factor of about 60, the response of the lower mantle is close to its elastic limit. Any further increase of the viscosity contrast at 670 km depth or further increase of viscosity as a continuous function of depth starting from 670 km depth is unlikely to be resolved.
Self-lubricated mantle convection: Two-dimensional models
We present results from convection models allowing for self-lubrication of downflows. Models impose a line source of chemically light, low viscosity material at the top of a convecting layer of temperature-dependent viscosity material. Low viscosity surface material serves as an analog to hydrated sediment/crust and the high viscosity upper portion of the convecting layer as an analog to mantle lithosphere. Slow near surface motion in the convecting layer entrains low viscosity material into zones of downflow, which has a lubricating effect. Once entrained lubricant is deeper than the cold high viscosity portion of the convecting layer, rapid upper boundary layer overturn occurs and system properties change (e.g., heat flux doubles). This marks transition to a lubricated state. Before and after transition, transport properties are dominantly determined by, respectively, the viscosity of mantle lithosphere and that of interior mantle. Lubricated and nonlubricated states appear as distinct regions in system output space suggesting that exchange between them is akin to a phase transition. That such exchange depends on a near surface lubricant implies that the geodynamics of planets lacking such lubricants may fundamentally differ from that of planets possessing them.