Variable Viscosity Fluid Research Articles

Pressure build-up during CO2 storage in partially confined aquifers

Abstract Geologic CO 2 sequestration in saline aquifers is an attractive option for GHG mitigation, but an associated risk is pressure buildup in the aquifer, which could increase the probability of fracturing the seal or activating a fault. We report on a series of simulations to quantify this risk factor. This work also evaluates injectivity limitations from the “backpressure” at sealing faults, a potentially important factor in assessing the number of wells (and hence the cost) needed for storage. We simulate injection of CO 2 at rates and durations appropriate for capture from coal-fired power plants. The target formations are deep saline aquifers partially confined by faults. We inject at fixed rate, subject to an upper bound on the injection pressure; none of the simulations shown here reach this threshold. Compositional (Peng–Robinson equation of state) simulations are carried out with CMG’s GEM reservoir simulator with different locations and geometries of sealing faults in aquifers, with several values of rock compressibility. We evaluate two parameters: CO 2 injectivity vs. time, and pressure profile in the aquifer. From the latter we obtain a risk parameter defined as the location of a contour of 50 psi above hydrostatic. Such a parameter is suitable for inclusion in a Certification Framework for geologic storage ([C.M. Oldenburg, S.L. Bryant, J.-P. Nicot, N. Kumar, Z. Yingqi, Certification framework based on effective trapping for geologic carbon sequestration (abs.), in: Seventh Annual Conference on Carbon Capture & Sequestration: Addressing the knowledge, policy, regulatory and technology gaps to expedite CCS deployment, Pittsburgh, Pennsylvania, May 5–8, Abstract #817, 2008.)]. A single sealing fault has little influence on injectivity as long as it is beyond the radial extent of the CO 2 plume. Rock compressibility has negligible influence on injectivity and pressure contours. As the number or proximity of faults increases, the injectivity decreases slightly. In contrast to injectivity, contours of elevated pressures are sensitive to faults. They extend farther as the number or proximity of faults increases, increasing the area of influence and thus the risk of failure (seal fracture, fault activation) significantly. Thus well placement relative to known faults is an important design consideration. The effect of aquifer depth on pressure build-up due to injection is also investigated. The variation of fluid viscosity with pressure and temperature (brine viscosity is much more sensitive than CO 2 viscosity) is the dominant effect on injectivity and pressure build-up. An important overall message is that contours of elevated pressure extend much farther into the aquifer than the CO 2 plume itself. Thus risk assessment that focuses exclusively on CO 2 may underestimate actual project risk.

Waves in an elastic tube filled with a heterogeneous fluid of variable viscosity

By treating the artery as a prestressed thin elastic tube and the blood as an incompressible heterogeneous fluid with variable viscosity, we studied the propagation of weakly non-linear waves in such a composite medium through the use of reductive perturbation method. By assuming a variable density and a variable viscosity for blood in the radial direction we obtained the perturbed Korteweg–deVries equation as the evolution equation when the viscosity is of order of ε 3 / 2 . We observed that the perturbed character is the combined result of the viscosity and the heterogeneity of the blood. A progressive wave type of solution is presented for the evolution equation and the result is discussed. The numerical results indicate that for a certain value of the density parameter sigma , the wave equation loses its dispersive character and the evolution equation degenerates. It is further shown that, for the perturbed KdV equation both the amplitude and the wave speed decay in the time parameter τ .

Effects of Low Water Temperature on Longshore Sediment Transport on a Subarctic Beach, Hudson Bay, Canada

Measurements of longshore sand transport, wave breaker height, longshore current velocity, and water temperature and salinity were carred out on a subarctic beach under varying water temperature conditions during summer and fall. Water temperature during summer varied from 9°C to 17°C, while temperature ranged from −1.75°C to 1.25°C during the fall experiments. During periods with low water temperatures, considerably higher rates in both bedload and suspended sediment transport were observed compared with the results obtained during summer with similar wave heights and current velocities. The increase in suspended sediment transport associated with low water temperatures is likely due to lower sediment fall velocities resulting from significant increases in fluid kinematic viscosity, which ranged from 1.1 to 1.37 × 10−6 m2 s−1 in summer and from 1.74 to 1.92 × 10−6 m2 s−1 in the fall. Less but still significant increase in bedload sediment transport in cold water is interpreted to be the result of temperature-induced variations in fluid viscosity that affect turbulence and boundary layer dynamics as well as bed configuration. Frazil ice occurred on some occasions during the fall experiments, but with the small number of samples collected when frazil ice crystals were present in the water column, it was not possible to establish a relationship between sediment transport rates and the presence or absence of ice. Our results nevertheless indicate that in cold climate regions extremely low water temperatures may cause a substantial increase of coastal sediment transport.

A New System to Analyze Pulsatile Flow Characteristics in Elastic Tubes for Hemodynamic Applications

In this research, we present a new designed experimental setup for study of characteristics of pulsatile flow in elastic tubes, aiming to simulate arterial blood flow. This system includes four major components: (1) a pulsatile pump producing original arterial flow, (2) an elastic element to simulate coupling of the heart with the arterial system, (3) an elastic tube with mechanical characteristics of the arterial wall and assembly of pressure transducers to monitor inlet and outlet pulsatile pressures and the resultant pulsatile pressure gradient and (4) a resistant element to simulate peripheral resistant distal the artery. The system is capable of performing under different mechanical conditions, including tubes with different elastic moduli and fluids with different viscosities. Experimental results showed a precise ability of producing original blood flow waves and recording pressure pulses and pressure gradient waves under different mechanical conditions. The resultant pressure pulses were compatible with the diastolic-systolic pressure pulses of typical arteries. The system showed an accurate sensitivity to variations of fluid viscosity and elasticity of tube wall. Experimental results showed that stiffening of the wall resulted in decrease of mean pressure gradient pulse. Results also showed that an elevated fluid viscosity led to a higher mean value of pressure gradient and less fluctuation of pressure gradient pulse. Results are in good agreement with theoretical considerations of higher energy dissipation and consequent pressure drop by increased fluid viscosity. The designed experimental setup might be used in evaluation of hemodynamic parameters in patho- physiological situations such as stenotic arteries and age related stiffening.

Head-on-collision of nonlinear waves in a fluid of variable viscosity contained in an elastic tube

In this work, treating the arteries as a thin walled, prestressed elastic tube and the blood as an incompressible viscous fluid of variable viscosity, we have studied the interactions of two nonlinear waves, in the long wave approximation, through the use of extended PLK perturbation method, and the evolution equations are shown to be the Korteweg-deVries–Burgers equation. The results show that, up to O( ϵ 3/2), the head-on-collision of two nonlinear progressive waves is elastic and the nonlinear progressive waves preserve their original properties after the collision. The phase functions for each wave are derived explicitly and it is shown that they are not straight lines anymore, they are rather some curves.

Galerkin Least-Squares Multifield Approximations for Flows of Inelastic Non-Newtonian Fluids

The aim of this work is to investigate a Galerkin least-squares (GLS) multifield formulation for inelastic non-Newtonian fluid flows. We present the mechanical modeling of isochoric flows combining mass and momentum balance laws in continuum mechanics with an inelastic constitutive equation for the stress tensor. For the latter, we use the generalized Newtonian liquid model, which may predict either shear-thinning or shear-thickening. We employ a finite element formulation stabilized via a GLS scheme in three primal variables: extra stress, velocity, and pressure. This formulation keeps the inertial terms and has the capability of predicting viscosity dependency on the strain rate. The GLS method circumvents the compatibility conditions that arise in mixed formulations between the approximation functions of pressure and velocity and, in the multifield case, of extra stress and velocity. The GLS terms are added elementwise, as functions of the grid Reynolds number, so as to add artificial diffusivity selectively to diffusion and advection dominant flow regions—an important feature in the case of variable viscosity fluids. We present numerical results for the lid-driven cavity flow of shear-thinning and shear-thickening fluids, using the power-law viscosity function for Reynolds numbers between 50 and 500 and power-law exponents from 0.25 to 1.5. We also present results concerning flows of shear-thinning Carreau fluids through abrupt planar and axisymmetric contractions. We study ranges of Carreau numbers from 1 to 100, Reynolds numbers from 1 to 100, and power-law exponents equal to 0.1 and 0.5. Besides accounting for inertia effects in the flow, the GLS method captures some interesting features of shear-thinning flows, such as the reduction of the fluid stresses, the flattening of the velocity profile in the contraction plane, and the separation of the boundary layer downstream the contraction.

Nonlinear waves in an elastic tube with variable prestretch filled with a fluid of variable viscosity

In the present work, by employing the reductive perturbation method to the nonlinear equations of an incompressible, prestressed, homogeneous and isotropic thin elastic tube and to the exact equations of an incompressible Newtonian fluid of variable viscosity, we have studied weakly nonlinear waves in such a medium and obtained the variable coefficient Korteweg-deVries–Burgers (KdV–B) equation as the evolution equation. For this purpose, we treated the artery as an incompressible, homogeneous and isotropic elastic material subjected to variable stretches both in the axial and circumferential directions initially, and the blood as an incompressible Newtonian fluid whose viscosity changes with the radial coordinate. By seeking a travelling wave solution to this evolution equation, we observed that the wave front is not a plane anymore, it is rather a curved surface. This is the result of the variable radius of the tube. The numerical calculations indicate that the wave speed is variable in the axial coordinate and it decreases for increasing circumferential stretch (or radius). Such a result seems to be plausible from physical considerations, like Bernoulli’s law. We further observed that, the amplitude of the Burgers shock gets smaller and smaller with increasing time parameter along the tube axis. This is again due to the variable radius, but the effect of it is quite small.

Onset of Marangoni convection in variable-viscosity fluid layer subject to uniform heat flux from below

The onset of stationary Marangoni instabilities in a horizontal fluid layer with free surface deformation and heated from below with a uniform heat flux is considered theoretically using linear stability theory. The explicit solution is obtained and the influences of temperature-dependent viscosity, surface deformability, gravity waves and heat transfer mechanism at the free surface on the stability thresholds are investigated. Small stabilizing effect is observed in fluids with a small viscosity variation while large viscosity variation strongly destabilizes the fluid layer. The stability thresholds are critically dependent on viscosity variation, surface deformation and heat transfer mechanism.

Irreversibility analysis of variable viscosity channel flow with convective cooling at the walls

This study investigates the inherent irreversibility in the flow of a variable (temperature-dependent) viscosity fluid through a channel with parallel plates. The channel is narrow so that the lubrication approximation may be applied, and the temperature-dependent nature of viscosity is assumed to follow an exponential model. The system is assumed to exchange heat with the ambient surroundings following Newton’s cooling law. Using a perturbation method coupled with a special type of Hermite–Padé approximation technique, the simplified governing nonlinear equations are solved and the important properties of overall flow structure, including velocity field, temperature field, and thermal criticality conditions are derived, which essentially expedite obtaining expressions for volumetric entropy generation numbers, irreversibility distribution ratio, and the Bejan number in the flow field. PACS Nos.: 44.10.+a, 47.11.–j, 47.15.gm

Effects of thermal radiation and variable fluid viscosity on free convective flow and heat transfer past a porous stretching surface

Free convective boundary layer flow and heat transfer of a fluid with variable viscosity over a porous stretching vertical surface in presence of thermal radiation is considered. Fluid viscosity is assumed to vary as a linear function of temperature. The symmetry groups admitted by the corresponding boundary value problem are obtained by using a special form of Lie group transformations viz. scaling group of transformations. A third-order and a second-order coupled ordinary differential equations corresponding to the momentum and the energy equations are obtained. These equations are then solved numerically. It is found that the skin-friction decreases and heat transfer rate increases due to the suction parameter. Opposite nature is noticed in case of blowing. With the increase of temperature-dependent fluid viscosity parameter (i.e. with decreasing viscosity), the fluid velocity increases but the temperature decreases at a particular point of the sheet. Due to suction (injection) fluid velocity decreases (increases) at a particular point of the surface. Effects of increasing Prandtl number as well as radiation parameter on the velocity boundary layer is to suppress the velocity field and the temperature decreases with increasing value of Prandtl number. Due to increase in thermal radiation parameter, temperature at a point of the surface is found to decrease.

Boundary Effect on Marangoni Convection in a Variable Viscosity Fluid Layer

The onset of Marangoni convection in a horizontal fluid layer with a free surface overlying a solid layer heated from below is studied. Problem is focused on the effect of the solid layer depth or its conductivity. The viscosity group, Rv, Biot number, Bi, depth ratio, dr and conductivity ratio, kr, are significant on determining the critical Marangoni number Mc with the corresponding critical wavenumber αc. The characteristics problem is solved numerically. Results show that the temperature-dependent viscosity destabilizes the fluid system but it behaves oppositely when a higher relative thermal conductivity ratio or higher depth ratio is taken.

Entropy-generation analysis for variable-viscosity channel flow with non-uniform wall temperature

This paper is an analytical study of inherent irreversibility in the flow of a variable-viscosity fluid through a channel with a non-uniform wall temperature. It is assumed that the channel is narrow and the fluid viscosity varies linearly with temperature. Analytical expressions for fluid velocity and temperature are derived and employed to obtain expressions for volumetric entropy-generation numbers, irreversibility distribution ratio and the Bejan number in the flow field.

Effects of temperature-dependent viscosity on Bénard convection in a porous medium using a non-Darcy model

Temperature-dependent viscosity variation effect on Bénard convection, of a gas or a liquid, in an enclosure filled with a porous medium is studied numerically, based on the general model of momentum transfer in a porous medium. The exponential form of viscosity–temperature relation is applied to examine three cases of viscosity–temperature relation: constant ( μ = μ C ) , decreasing (down to 0.13 μ C ) and increasing (up to 7.39 μ C ). Effects of fluid viscosity variation on isotherms, streamlines, and the Nusselt number are studied. Application of the effective and average Rayleigh number is examined. Defining a reference temperature, which does not change with the Rayleigh number but increases with the Darcy number, is found to be a viable option to account for temperature-dependent viscosity variation.

Effects of current–bed form induced fluid flow on the thermal regime of sediments

Heat transport associated with current–bed form fluid exchange affects biogeochemical and ecological process in a variety of aquatic settings. We simulate turbulent flow over dunes, induced Darcy flow in sediments, and sediment heat transport forced by a diel variation of water column temperature. Heat conduction dominates when the water column current cannot induce rapid fluid exchange. Heat advection becomes important with increasing sediment permeability and/or current velocity, resulting in a complicated space‐time temperature pattern. Weak temperature variations are found beneath dune crests, where water upwells out of the sediments; strong variations are located below dune stoss faces, where water downwells. The relative dominance of heat conduction versus advection is captured by a global Peclet number that depends on dune geometry, and hydrodynamic and thermal properties, including the period of thermal forcing. Thermally induced fluid viscosity variations cause periodic but nonsymmetric changes in fluid flux through the sediments, but do not significantly influence temperature patterns.

Mixed convection with variable viscosity in a vertical annulus with uniform wall temperatures

The steady and laminar mixed convection with a temperature-dependent viscosity in a vertical annular duct with uniform wall temperatures is studied analytically. The flow is considered as purely axial and the fluid density is assumed to be a linear function of temperature. Analytical expressions of the dimensionless velocity distribution, of the dimensionless pressure drop and of the Fanning friction factors are determined. The importance of choosing the mean fluid temperature as the reference temperature in the definition of the difference between the pressure and the hydrostatic pressure is pointed out. The results show that the combined effects of buoyancy forces and of a variable fluid viscosity on the cross-section-averaged Fanning friction factor may be important, and that negative values of this quantity may occur.

The effects of Ohmic heating and viscous dissipation on unsteady MHD and slip flow over a porous rotating disk with variable properties in the presence of Hall and ion-slip currents

The effects of Ohmic heating and viscous dissipation on unsteady laminar magneto-hydrodynamics (MHD) flow of a viscous Newtonian and electrically conducting fluid over a rotating disk taken into account the variable fluid properties (density, (ρ), viscosity, (μ) and thermal conductivity, (κ)) in the presence of Hall and ion-slip currents effects have been examined. These fluid properties are taken to be dependent on temperature. The unsteady Navier–Stokes equations along with the energy equation are reduced to a system of ordinary differential equations by using similarity transformations and the resulting equation system is solved numerically by using a shooting method. Results for the details of the velocity as well as temperature are shown graphically and the numerical values of the skin friction and the rate of heat transfer are entered in tables.

Forced Korteweg-de Vries–Burgers equation in an elastic tube filled with a variable viscosity fluid

In the present work, treating the arteries as a prestressed thin walled elastic tube with a stenosis and the blood as a Newtonian fluid with variable viscosity, we have studied the propagation of weakly nonlinear waves in such a composite medium, in the long wave approximation, by use of the reductive perturbation method [Jeffrey A, Kawahara T. Asymptotic methods in nonlinear wave theory. Boston: Pitman; 1981]. We obtained the forced Korteweg-de Vries–Burgers (FKdVB) equation with variable coefficients as the evolution equation. By use of the coordinate transformation, it is shown that this type of evolution equation admits a progressive wave solution with variable wave speed. As might be expected from physical consideration, the wave speed reaches its maximum value at the center of stenosis and gets smaller and smaller as we go away from the center of the stenosis. The variations of radial displacement and the fluid pressure with the distance parameter are also examined numerically. The results seem to be consistent with physical intuition.

On MHD and slip flow over a rotating porous disk with variable properties

The steady laminar magnetohydrodynamics (MHD) flow of a viscous Newtonian and electrically conducting fluid over a rotating disk with slip boundary condition is investigated taken into account the variable fluid properties (density, ( ρ), viscosity, ( μ) and thermal conductivity, ( κ)). These fluid properties are taken to be dependent on temperature. The governing equations, which are partial and coupled, are transformed to ordinary ones by utilizing the similarity variables introduced by von Karman and the resulting equation system is solved numerically by using a shooting method. The resulting velocity and temperature distributions are shown graphically for different value of parameters entering into the problem. The numerical values of the radial and tangential skin-friction coefficients and the rate of heat transfer coefficient are shown in tabular form.

On steady flow of a reactive variable viscosity fluid in a cylindrical pipe with an isothermal wall

PurposeThis paper aims to demonstrate an application of a novel approximation technique, for a function whose partial series is known, to a problem in thermal ignition in a combustible variable viscosity fluid.Design/methodology/approachAnalytical solutions are constructed for the governing non‐linear boundary‐value problem using regular perturbation technique (RPT) coupled with computer‐extended series solution (CESS) and a special type of Hermite‐Padé approximant.FindingsThe steady state thermal ignition criticality conditions and their dependent on both Frank‐Kamenetskii and viscous heating parameters are accurately obtained. The results also revealed the rapid convergence of the approximation procedure with gradual increase in the number of series coefficients utilized in the approximants.Originality/valueThe analytical and computational procedures utilized in this paper are advocated as an effective tool for investigating several other parameter dependent nonlinear boundary‐value problems.

Transient mantle convection on Venus: The paradoxical coexistence of highlands and coronae in the BAT region

The coexistence of Venusian highlands, attributed to long-lived axisymmetric mantle plumes, and uncompensated coronae, attributed to transient discrete mantle ‘thermals’, is difficult to reconcile with models of mantle convection under thermally steady-state conditions. However, cratering and geological studies indicate a uniformly young surface age (∼ 700 Myr) as well as a comparable timescale for resurfacing (∼ 100 to 400 Myr), possibly consistent with a recent lithospheric overturn and a transient mantle thermal regime. We use laboratory experiments on free and forced thermal convection at high Rayleigh number ( Ra ∼ 10 7) in a variable viscosity fluid to investigate the steady-state and transient thermal regimes preceding and following such an overturn. From analyses of shadowgraph images and time series of global and local variations in temperature, basal heat flux and viscosity, we establish steady-state stagnant- and active-lid states and characterize two intermediate transient regimes. Flow in steady-state stagnant lid is in the form of intermittent thermals, consistent with published work. During the transition to active-lid convection the stagnant lid is stirred into the interior using a conveyor belt. Spreading of this cold fluid along the hot boundary leads to a transition to a “mixed mode” of flow from the hot boundary: approximately isoviscous thermals rise from the thermal boundary layer ahead of the advancing cold front and low viscosity plumes rise from behind the front, as a result of an enhanced temperature contrast. The longevity of this regime and the timescale for the transient depends on the rate of overturn (Pe) and the aspect ratio of the system (A). The magnitude of local temperature, viscosity and heat flux variations increases with Pe and can exceed steady-state values for active-lid convection. Additional numerical simulations show that the mixed mode regime will occur in the presence of internal heating, and for no- and free-slip boundaries. In contrast, the transition from active-lid to stagnant-lid convection is marked by a change from a flow composed of plumes and large-scale overturning motions to a regime dominated by rising and sinking thermals on a timescale of thermal diffusion. Applied to Venus, our results support a hypothesis that the contemporaneous coexistence of the Atla and Beta highlands regions with interspersed uncompensated coronae is consistent with a transient thermal regime following a lithospheric overturn. It is also expected that such coronae formed > 250 Myr after the uplift of the highlands. Implications of the thermal origin of coronae for Venusian mantle structure are also explored.