Showing papers on "Herschel–Bulkley fluid published in 1985"
TL;DR: In this article, the simple Cross model is shown to be a useful empiricism for many non-Newtonian fluids, including those which have hitherto been thought to possess a yield stress.
Abstract: New experimental data obtained from constant stress rheometers are used to show that the yield stress concept is an idealization, and that, given accurate measurements, no yield stress exists. The simple Cross model is shown to be a useful empiricism for many non-Newtonian fluids, including those which have hitherto been thought to possess a yield stress.
582 citations
TL;DR: In this paper, the Coulomb yield criterion is applied to predict the immersed weight of grains undergoing bed load transport in a steady granular fluid shear flow, and the ratio of the shear stress to the normal stress is nearly constant at the depth of no motion.
Abstract: Data obtained in an annular shear cell are interpreted to evaluate a dynamic Coulomb yield criterion at the boundary separating flowing and stationary grains in a steady granular fluid shear flow. The ratio of the shear stress to the normal stress is nearly constant at the depth of no motion, suggesting a dynamic balance between the mobilizing effect of the applied shear stress and the stabilizing effect of the normal stress which results from the immersed weight of the moving grains. We suggest that the yield criterion can be applied to predict the immersed weight of grains undergoing bed load transport.
71 citations
TL;DR: In this article, it was shown that the creeping cone-and-plate flow of an Oldroyd-B fluid is unstable with respect to an infinitesimal disturbance.
Abstract: It is shown that the creeping cone-and-plate flow of an Oldroyd-B fluid is unstable with respect to an infinitesimal disturbance. The critical Weissenberg number for the case of the Maxwell fluid is about 2.
69 citations
Patent•
02 May 1985
TL;DR: In this article, an in-line, noninvasive device and method for calculation of consistency of non-Newtonian fluid flowing in a laminar manner through a non-rotating conduit where the consistency is calculated directly from a power-law model equation employing as independent variables pressure head loss over a specific distance and the bulk velocity of the fluid.
Abstract: Provided herein is an in-line, non-invasive device and method for calculation of consistency of a non-Newtonian fluid flowing in a laminar manner through a non-rotating conduit where the consistency is calculated directly from a power-law model equation employing as independent variables pressure head loss over a specific distance and the bulk velocity of the fluid.
45 citations
TL;DR: In this article, a computational procedure is developed for solving the problem of a circular hydraulic fracture propagating under the action of frac-0fluid being pumped in at a central wellbore.
Abstract: A computational procedure is developed for solving the problem of a circular hydraulic fracture propagating under the action of frac-0fluid being pumped in at a central wellbore. The crack is modelled as continuous distributions of ring dislocations and the resulting elasticity singular integral equation is solved numerically. The fluid flow equations are approximated by local and global interpolation finite difference schemes. The coupling between elasticity and fluid flow is handled numerically, by, two different algorithms: one iterates on crack tip velocity whereas the other varies the time step size until it agrees with the chosen increment in crack length. Sample results are given; it is found that the velocity algorithm is computationally more, efficient and more stable. The model allows detailed tracing of pressure distribution and fluid flow in the fracture, even under complex conditions of cyclic injection and fluid rheology. It may serve as a stand-alone model of (horizontal) hydrafracs–especially at shallow depths–or it may be used as a reference frame to test the various numerical formulation/algorithms required for the ongoing development of a fully 3-D hydrafrac simulator.
38 citations
TL;DR: In this paper, a dynamic, filter-cake controlled, leak-off coefficient which is dependent on the shear rate and shear stress at the fracture face is introduced, and a test apparatus is described in which the fluid leakoff is measured under conditions of temperature, rate of shear, duration of shears and fluid flow pattern encountered under fracturing conditions.
Abstract: When filter-cake building additives are used in fracturing fluids, the commonly applied static, API filtration test of 30 minutes duration is unsatisfactory, since in a dynamic situation (such as exists while fracturing) the formation of thick filter-cake will be inhibited by the shearing forces of the fracturing fluid. A dynamic, filter-cake controlled, leak-off coefficient which is dependent on the shear rate and shear stress at the fracture face is therefore introduced, and a test apparatus is described in which the fluid leak-off is measured under conditions of temperature, rate of shear, duration of shear and fluid flow pattern encountered under fracturing conditions. The effect of rock permeability, shear rate and differential pressure on the dynamic leak-off coefficient is presented for various, commonly used fracturing fluid/fluid-loss additive combinations.
24 citations
TL;DR: In this paper, the equivalence between a scalar field and a viscous fluid is investigated, showing that under certain circumstances, both can generate, from Einstein's equations, the same space-time geometry.
Abstract: An example of the equivalence between a perfect fluid and a viscous fluid is presented, showing that the Schwarzschild interior solution obtained from a perfect fluid can also be derived from a viscous fluid with heat conduction. The equivalence between a scalar field and a viscous fluid is investigated, showing that under certain circumstances, both can generate, from Einstein’s equations, the same space‐time geometry. Some examples are presented and, in particular, it is shown that every plane‐symmetric solution deduced from a scalar field can also be derived from a viscous fluid.
15 citations
TL;DR: In this article, the authors examined the effective medium properties of a dilute suspension of spheres in a second-order fluid under linear shear and showed that the term linear in volume fraction increases the corresponding rheological coefficient, just as in the Newtonian case.
Abstract: We examine the effective medium properties of a dilute suspension of spheres in a second-order fluid under linear shear. Since the second-order fluid is the first step toward the general viscoelastic fluid, the results obtained may provide a qualitative feel for the problem in which the suspending fluid obeys a more complicated (and realistic) constitutive relation. The dissipation in the medium is calculated by determining the rate of working by surface forces; this is compared to the dissipation in a homogeneous fluid to give the effective properties. The results show that the term linear in volume fraction increases the corresponding rheological coefficient, just as in the Newtonian case. It is to be noted that the second-order dissipation is zero for simple shear and other weak flows, whereas for strong flows the small correction may increase or decrease the overall dissipation.
13 citations
TL;DR: In this paper, the exact solution of the torsional flow of a class of Oldroyd-type fluids is kinematically similar to that for a Newtonian fluid, and it is shown by a linearized stability analysis and by numerical integration that the basic flow is unstable at high Weissenberg numbers.
Abstract: It is shown that the exact solution of the torsional flow of a class of Oldroyd-type fluids is kinematically similar to that for a Newtonian fluid. Furthermore, it is shown by a linearized stability analysis and by numerical integration, that the basic flow is unstable at high Weissenberg numbers. An Oldroyd fluid which has a negative second-normal stress coefficient is found to be more stable than one with zero (or positive) second-normal stress coefficient in this flow.
10 citations
TL;DR: In this article, an experimental program was carried out to determine the laminar regime kinematics and normal stress differences of a viscoelastic fluid in wiggle flow employing noncontact measurement techniques.
Abstract: An experimental program was carried out to determine the laminar regime kinematics and normal stress differences of a viscoelastic fluid in wiggle flow employing non-contact measurement techniques. The viscoelastic fluid was a 5% by weight solution of polyisobutylene dissolved in Primol 355, a high purity mineral oil. The kinematics were determined by Laser-Doppler Anemometry and compared with the data obtained for a Newtonian fluid, Primol 355, under identical flow conditions. It was found that the normalized axial velocity versus axial position curves along the centerline for both fluids superimposed at very low flow rates, an experimental verification that a viscoelastic fluid behaves like a Newtonian fluid under very low shear rates. However, at higher flow rates the behaviour of the viscoelastic fluid curves changed appreciably whereas the Newtonian fluid curves did not change at all. Thus, the effect of flow rate on viscoelastic fluid behaviour was also experimentally established. The normal stress differences were determined using a stress-birefringence apparatus. Data obtained along the centerline clearly exhibited a delayed growth of stress which should be attributed to the expected memory effects in viscoelastic fluid flow.
5 citations
TL;DR: In this article, a numerical simulation of entry flow in a slit die has been undertaken for a fluid that is Newtonian in shear but exhibits normal stresses (Boger fluid).
Abstract: A numerical simulation of entry flow in a slit die has been undertaken for a fluid that is Newtonian in shear but exhibits normal stresses (Boger fluid). Experimentally measured normal stress and viscosity data are included in a simple rheological model. Flow patterns reveal the existence of vortices in the reservoir corners. Vortex size and intensity increase rapidly with elasticity level.
TL;DR: In this article, a linearized approximation for both the convective inertia terms and the nonlinear terms involved in the fluid constitutive law is used, which is transformed to a coordinate system in such a way as to result in a linear diffusion-type equation for the vorticity in the Newtonian case, and for the viscoelastic case.
TL;DR: In this paper, the exact kinematics for the squeezing flow from a cone of a general viscoelastic fluid were reported, and a network model that allows stress overshoot and shear-thinning in the start-up of a shear flow was adopted to obtain numerical values for the stresses.
Abstract: The paper reports an exact kinematics for the squeezing flow from a cone of a general viscoelastic fluid. To obtain numerical values for the stresses, a network model that allows stress overshoot and shear-thinning in the start-up of a shear flow is adopted. Both these features are important in this flow. For the special case of an Oldroyd-B fluid it is shown that there is a limiting Weissenberg number above which at least one component of the stresses increases unboundedly with time.
TL;DR: In this article, a mathematical development is presented to calculate the fracturing fluid coefficient obtained from laboratory studies assuming this to be a combination of fracturing fluid coefficients and filter cake coefficient and experimental results indicate that fluid loss values can be a function of temperature, pressure differential, rate of shear, and degree of non-Newtonian behavior of the fracture fluid.
Abstract: A test apparatus is designed to carry out dynamic as well as static fluid loss tests of fracturing fluids. This test apparatus simulates the pressure difference, temperature, rate of shear, duration of shear, and fluid flow pattern expected under fracture conditions. For a typical crosslinked fracturing fluid, experimental results indicate that fluid loss values can be a function of temperature, pressure differential, rate of shear, and degree of non-Newtonian behavior of the fracturing fluid. A mathematical development is presented to calculate the fracturing fluid coefficient obtained from laboratory studies assuming this to be a combination of fracturing fluid coefficient and filter cake coefficient.
TL;DR: In this article, the equivalence between a perfect fluid with electromagnetic field and a viscous fluid with heat flux is considered, where heat flux, shear tensor, and other fluid parameters are readily calculated out of the magnetohydrodynamic fluid parameters.
Abstract: In this paper the equivalence between a perfect fluid with electromagnetic field and a viscous fluid with heat flux is considered. Heat flux, shear tensor, and other fluid parameters are readily calculated out of the magnetohydrodynamic fluid parameters.
TL;DR: In this paper, the laminar flow of an electrically conducting non-Newtonian fluid (Rivlin-Encksen type) past an infinite porous flat plate was studied.
Abstract: This article studies the laminar flow of an electrically conducting non-Newtonian fluid (Rivlin-Encksen type) past an infinite porous flat plate to a step function change in suction velocity in the presence of a transverse magnetic field. The Laplace transform technique has been employed to solve the basic differential equations. The solutions of the velocity profile and skin-friction are obtained and the effects of the visco-elastic parameter, the magnetic field and the time parameter on the fluid flow have been studied in several tables.
Journal Article•
TL;DR: In this paper, a generalized viscoplastic fluid model that has both parts as well as two major rheological properties (i.e., the normal stress effect and soil yield criteria) is shown to be sufficiently accurate, yet practical, for general use in debris flow modeling.
Abstract: A viable rheological model should consist of both a time-independent part and a time-dependent part. A generalized viscoplastic fluid model that has both parts as well as two major rheological properties (i. e. , the normal stress effect and soil yield criteria) is shown to be sufficiently accurate, yet practical, for general use in debris flow modeling. Other rheological models, such as the Bingham plastic fluid model and the so-called Coulomb-viscous model, are compared in terms of the generalized viscoplastic fluid model.
TL;DR: In this article, it was shown that in the region adjacent to a solid wall, a Newtonian fluid in turbulent flow can be regarded as an oriented Ericsson-Leslie fluid whose defining constants are subject to certain conditions.