Rheological Law Research Articles

The Evaluation and Application Effect of a Completion Fluid System in Daqing Oilfield

In order to better protect the Daqing Oilfield Sanan oil field development, make experimental analysis and field applications of Sanan's core.Through the relationship between rheology and fluid loss ,achieve JGN best dosage of the entire completion fluid system, completion rheological law and evaluated regular patten.The effect of field application is obvious, improve strength of the oil production , the skin factor and injection pressure is reduced, and made better protect the reservoir effect.

A Computational Model of Oxygen Transport in the Cerebrocapillary Levels for Normal and Pathologic Brain Function

The oxygen exchange and correlation between the cerebral blood flow (CBF) and cerebral metabolic rate of oxygen consumption (CMRO2) in the cortical capillary levels for normal and pathologic brain functions remain the subject of debate. A 3D realistic mesoscale model of the cortical capillary network (non-tree like) is constructed using a random Voronoi tessellation in which each edge represents a capillary segment. The hemodynamics and oxygen transport are numerically simulated in the model, which involves rheological laws in the capillaries, oxygen diffusion, and non-linear binding of oxygen to hemoglobin, respectively. The findings show that the cerebral hypoxia due to a significant decreased perfusion (as can occur in stroke) can be avoided by a moderate reduction in oxygen demand. Oxygen extraction fraction (OEF) can be an important indicator for the brain oxygen metabolism under normal perfusion and misery-perfusion syndrome (leading to ischemia). The results demonstrated that a disproportionately large increase in blood supply is required for a small increase in the oxygen demand, which, in turn, is strongly dependent on the resting OEF. The predicted flow-metabolism coupling in the model supports the experimental studies of spatiotemporal stimulations in humans by positron emission tomography and functional magnetic resonance imaging.

Continuum description for the characteristic resistance sensed by a cylinder colliding against granular medium

In this paper, we experimentally and theoretically study the resistance force that develops when a cylinder with a flat face colliding against dry quartzite sand. Observations from experimental data clearly show that the acceleration curves are characterized by a double-peak structure. The first agitated peak can be attributed to a shock process where sand responds elastically, and the valley bottom in the double-peak structure is related to a limited plastic load when a fully plastic region is formed in the sand, while the second agitated peak corresponds to a the occurrence of the maximum of viscous force in a homogeneous developed bulk flow. We use slip line theory (SL) developed in plastic mechanics to capture the value at the valley bottom, adopt the double shearing theory (DS), together with a Local Rheological Constitutive Law (LRCL) suggested in this paper, to capture the drag force generated in a homogeneous bulk flow. Good agreements in the comparisons between numerical and experimental results support the characteristic resistance by the cylinder to predict granular states.

Depth and minimal slope for surface flows of cohesive granular materials on inclined channels

AbstractWe present analytical predictions of the depth and onset slope of the steady surface flow of a cohesive granular material in an inclined channel. The rheology of Jop, Forterre & Pouliquen (Nature, vol. 441, 2006, pp. 727–730) is used, assuming co-axiality between the stress and strain-rate tensors, and a coefficient of friction dependent on the strain rate through the dimensionless inertial number $I$. This rheological law is augmented by a constant stress representing cohesion. Our analysis does not rely on a precise $\mu (I)$ functional, but only on its asymptotic power law in the limit of vanishing strain rates. Assuming a unidirectional flow, the Navier–Stokes equations can be solved explicitly to yield parametric equations of the iso-velocity lines in the plane perpendicular to the flow. Two types of channel walls are considered: rough and smooth, depicting walls whose friction coefficient is respectively larger or smaller than that of the flowing material. The steady flow starts above a critical onset angle and consists of a sheared zone confined between a surface plug flow and a deep dead zone. The details of the flow are discussed, depending on dimensionless parameters relating the static friction coefficient, cohesion strength of the material, incline angle, wall friction, and channel width. The depths of the flow at the centre of the channel and at the walls are calculated by a force balance on the flowing material. The critical angle for the onset of the flow is also calculated, and is found to be strongly dependent on the channel width, in agreement with experimental results on heap stability and in rotating drums. Our results predict the important conclusion that a cohesive material always starts to flow for an incline angle lower than 90° between smooth walls, whereas in a narrow enough channel with rough walls, it may not flow, even if the channel is inclined vertically.

Thixotropic gravity currents

AbstractWe present a model for thixotropic gravity currents flowing down an inclined plane that combines lubrication theory for shallow flow with a rheological constitutive law describing the degree of microscopic structure. The model is solved numerically for a finite volume of fluid in both two and three dimensions. The results illustrate the importance of the degree of initial ageing and the spatio-temporal variations of the microstructure during flow. The fluid does not flow unless the plane is inclined beyond a critical angle that depends on the ageing time. Above that critical angle and for relatively long ageing times, the fluid dramatically avalanches downslope, with the current becoming characterized by a structured horseshoe-shaped remnant of fluid at the back and a raised nose at the advancing front. The flow is prone to a weak interfacial instability that occurs along the border between structured and de-structured fluid. Experiments with bentonite clay show broadly similar phenomenological behaviour to that predicted by the model. Differences between the experiments and the model are discussed.

Effect of Moisture on the Behaviour of an Extruded Clay Paste

In the industrial process, the moisture of the clay sheet obtained by extrusion and pressed to form a tile varies in time. It depends on the nature and the mixing of the raw materials during the production. In order to model and undersand the influence of the moisture on the pressing step, it is necessary to determine the parameters of the rheological and tribological laws. A study of the rheological behaviour, based on free compression tests on cylinder samples, allowed to use an elasto-visco-plastic behaviour for the extruded clay paste. The different constitutive parameters were estimated by an inverse analysis based on the experimental force/displacement curves. The identification was performed with the optimisation algorithm implemented in the commercial software Forge® 2009. The influence of the water content in the paste on the rheological parameters was identified and fitted using linear models. The friction factor was measured from tests on a rectilign tribometer. To understand the influence of the moisture, we simulated a compression test, using Forge® involving the shaping of a tile lug. This geometry is representative of the state of stress during the pressing of the tile, in an area currently sujected to defects. The numerical model show that an increase of eighteen percent of the moisture allows to decrease by half the pressing force.

Study on the Flow Behavior of Underbalanced Circulative Micro-Foam Drilling Fluid

Underbalanced drilling is a new method for the exploratory development of low pressure and permeability reservoirs; circulative micro-foam drilling fluid is a new technology which is developed for realizing near-balanced drilling and underbalanced drilling. The flow behavior of circulative micro-foam drilling fluid in wellbore was researched by applying HPHT experiment apparatus. It is concluded that the flow behavior parameters of circulative micro-foam drilling fluid is only related to temperature but not to pressure; the constitutive equation accords with the rheological law of power-law fluid, the expressions of consistency coefficient and liquidity index were obtained through analyzing the flow behavior experiment data under the condition of HTHP. The density of circulative micro-foam drilling fluid increases as the increase of pressure and decreases as the increase of temperature, but in wellbore the rate of increase as pressure is greater than that of decrease as temperature, so the density of drilling fluid in wellbore is greater than that under ground condition. The fluid drag force of micro-foam drilling fluid in annulus were analyzed theoretically and the pressure distribution formulas of micro-foam drilling fluid in wellbore were given.

Lateral spreading processes in mountain ranges: Insights from an analogue modelling experiment

Abstract The results of a study on gravitational induced lateral spreading phenomena are here reported. The lateral spreading processes are widely represented in the Italian Apennines due to the widespread overlapping of stiff rock masses on more ductile ones. The stress–strain evolution of these processes was investigated by combining an analogical and a numerical modelling approach. The analogue modelling reproduced the evolution of a carbonate ridge thrust over a clayey flysch with reference to the case-study of Mt. Roccatagliata–Mt. Sant'Angelo ridge. The rock mass juxtaposition was reproduced in a laboratory experiment by overlapping a brittle concrete on a viscous ductile material; these materials were selected with rheological properties, physically scaled with respect to the natural rock mass prototypes. The spreading phenomenon was modelled by opening horizontal panels in sequential stages and monitoring the resulting stresses within the ductile material during the experiment. A stress–strain modelling was also performed by an FDM numerical solution; this modelling replied the laboratory experiment by testing the use of different rheological constitutive laws. The resulting stresses and morphological evolutions are comparable with the analogical laboratory experiment only if a time-dependent rheological behaviour is assumed for the ductile material. The results show that lateral spreading processes can be properly investigated by combining analogue and numerical modelling techniques which take into account the viscous-plastic behaviour of the used materials.

Valorization of Asphalt Rubber Fine Powder in Road Field

In the framework of valorization of the worn tires and environment preservation, several techniques exist in many fields. In Algeria, and since 2005, about 19 facilities are carried out using the so-called `Pneusol' technique. Currently, researches are interested in the use of rubber fine powder (RFP) that results from worn tires crushing. The letters constitute a cumbersome waste.[1,2] The present work presents, beginning from an experimental investigation, the possible using of tire scrap in road coating. The main purpose of such mixture is to improve certain mechanical properties, and also to reduce waste materials in the urban or agricultural zones leading to environmental and human damage. The mean study approach refers to the behavior of asphaltic concrete containing fine powders. The latter is produced by crushing of rubbery products and worn-out tires through dry and wet processes. Changes in rheological laws and in mechanical properties of the bituminous powder mixture are checked by means of experiments. The present study highlights the influence of fine powder content, size distribution and mixing conditions on some product properties such as deformation modulus, compactness and creep. The experimental results of the whole survey lead to interesting correlations. In addition, the rubber fine powder (RFP) is recognized taking into account road and environment interests. This appears to be, economically, interesting.

Strong lateral strength contrasts in the mantle lithosphere of continents: A case study from the hot SW Canadian Cordillera

Abstract This study aims at quantifying the 3-D variability in lithosphere strength of the south-eastern Canadian Cordillera and adjacent craton to the east. Strength is calculated in a forward manner, starting from rheological laws of brittle and ductile deformation. The work flow calculates a temperature model based on a multi-layer compositional model and subsequently estimates the strength distribution from both the compositional and temperature models. The temperature modeling involves numerical inversion and cubic spline algorithms which enable to impose boundary conditions that account better for strong lateral variations in lithosphere thickness and lateral heat flow. This addresses the lithosphere structure between the Canadian Cordillera and craton. The Canadian Cordillera is marked by a hot and thin lithosphere of ~ 60 km thickness that stands in contrast to a cold and thick craton of ~ 170 km thickness to the east, which consequently results in pronounced changes in bulk lithosphere strength. The high surface heat flow of the Cordillera interior and its contrast with the Foreland Basin can be reproduced by temperature models that combine elevated mantle heat flow due to the thin lithosphere and higher crustal heat production from magmatic intrusions. A series of rheological models, which examines the role of different temperature input models, composition and strain rate, shows that the first-order strength pattern is persistent. For the hot Canadian Cordillera, strength resides for > 80% in the upper crust and with integrated lithosphere strength of 2.0–3.5⋅106 MPa⋅m. For the cold craton, the upper mantle provides > 75% of the integrated strength with values of 4.0–8.0⋅106 MPa⋅m for the crust and 20–65⋅106 MPa⋅m for the lithosphere. Effective elastic thickness is estimated between 5 and 15 km for the Cordillera and 40–80 km for the craton. This illustrates the Cordillera to craton transition as a prominent rheological feature for upper mantle flow dynamics and spatial seismicity trends.

Boundary conditions effect on linearized mud-flow shallow model

The occurrence of roll-waves in mud-flows is investigated based on the formulation of the marginal stability threshold of a linearized onedimensional viscoplastic (shear-thinning) flow model. Since for this kind of non-Newtonian rheological models this threshold may occur in a hypocritical flow, the downstream boundary condition may have a nonnegligible effect on the spatial growth/decay of the perturbation. The paper presents the solution of the 1D linearized flow of a Herschel and Bulkley fluid in a channel of finite length, in the neighbourhood of a hypocritical base uniform flow. Both linearly stable and unstable conditions are considered. The analytical solution is found applying the Laplace transform method and obtaining the first-order analytical expressions of the upstream and downstream channel response functions in the time domain. The effects of both the yield stress and the rheological law exponent are discussed, recovering as particular cases both power-law and Bingham fluids. The theoretical achievements may be used to extend semi-empirical criteria commonly employed for predicting roll waves occurrence in clear water even to mud-flows.

Influence of "Historical Effects" on the Rheological Properties of a Polyacrylonitrile Copolymer Solution

Polyacrylonitrile (PAN) copolymers of different molecular weights were synthesized by a suspension polymerization and precipitation polymerization method. The rheology behaviors of the synthesized PAN copolymers were investigated in relation to their molecular weight, solid content and melting temperature. The influence of "historical effects" on the spinning solution of PAN was studied by analyzing the laws of viscosity considering the diversification time and temperature. The viscosity disciplines of each spinning solution conformed well to the rheological universal laws in a comparison of the suspension polymerization product with that of precipitation polymerization. Viscosity changes in the swelling process of dissolution were gentler in the suspension polymerization product; a small amount of water will quickly debase the solution viscosity, and high-speed mixing can greatly shorten the time required by the spinning solution to reach the final viscosity.

Nonequilibrium thermodynamics and glassy rheology

Mechanically driven glassy systems and complex fluids exhibit a wealth of rheological behaviors that call for theoretical understanding and predictive modeling. A distinct feature of these nonequilibrium systems is their dynamically evolving state of structural disorder, which determines their rheological responses. Here we highlight a recently developed nonequilibrium thermodynamic framework in which the structural state is characterized by an evolving effective disorder temperature that may differ from the ordinary thermal temperature. The specific properties of each physical system of interest are described by a small set of coarse-grained internal state variables and their associated energies and entropies. The dynamics of the internal variables, together with the flow of energy and entropy between the different parts of the driven system, determine continuum-level rheological constitutive laws. We conclude with brief descriptions of several successful applications of this framework.

Hydrolytic weakening of olivine at mantle pressure: Evidence of [1 0 0](0 1 0) slip system softening from single-crystal deformation experiments

To date, most of the experiments performed to quantify the hydrolytic weakening of olivine single crystals have been performed at low confining pressure (and low water fugacities). In order to determine if the degree of hydrolytic weakening changes at higher water fugacities (higher water contents), we have performed a series of high pressure (P) and high temperature (T) deformation experiments in hydrous condition on San Carlos olivine (Fo92) and forsterite (Fo100) single crystals, in a Deformation-DIA apparatus (D-DIA). Deformation was carried out in axial compression along the [110]c crystallographic reference frame direction in order to activate [100](010) dislocation slip system alone, at P ranging from 4 to 7GPa and T=1200°C. Water was supplied during the experiments through dehydration of a talc sleeve (talc→enstatite+coesite+H2O) around the sample, while the differential stress and strain rate of the specimen were calculated from in situ X-ray diffraction and time-resolved imaging, respectively. Run products were investigated using Fourier transform infrared (FTIR) spectroscopy, and optical/electron microscopy (SEM and TEM). Structurally bound hydroxyl content (COH) derived from absorbance in FTIR spectra, based on the Paterson (1982) relation, were typically between 290 and 720ppm H/Si in the run products and the majority of these hydroxyls were observed as distinct peaks in the range of wavenumber from 3620 to 3500cm−1. TEM reveals that the [100](010) slip system was effectively activated and responsible for crystal deformation, and that dislocation glide was significantly assisted by recovering processes such as dislocation climb and dipole annihilation. Combining the experimental data from this study and Mackwell et al. (1985), we estimate the activation volume V∗[110]c for San Carlos olivine in order to produce a reasonable water-fugacity exponent r in the flow law, and obtain V∗[110]c=12.1cm3/mol for r=0 and V∗[110]c=17.3cm3/mol for r=1.2. Comparisons of the strengths of the wet single crystals to the strengths of dry single crystals calculated from the rheological laws (Bai et al., 1991, Darot and Gueguen, 1981, Raterron et al., 2009) indicate that the wet single crystal cylinders were between 1.3 and 1.6 times weaker than their dry counterpart at same conditions, which is consistent with previous studies of [100](010) olivine rheology performed at low confining pressure (300MPa).

AA5083 Aluminium Alloy Constants Identification through Inverse Analysis of the Erichsen Test

In this paper, considering an isotropic rheological law of the sheet material and the power law relationship between the stress and the plastic strain, the Erichsen test is used to identify the material constants of AA5083 aluminium alloy coupling experimental tests results with numerical ones obtained by using the finite element method. The function which is minimized by inverse analysis includes simultaneously the load-displacement curve of the punch, the normalized thickness measured at the bulge apex and the distance measured between the thinnest area of the metal sheet and the inner surface of the blankholder.

Numerical solutions for the fluid flow and the heat transfer of viscoplastic-type non-Newtonian fluids

The aim of this work is to provide numerical solutions for the fluid flow and the heat transfer generated in closed systems containing viscoplastic-type non-Newtonian fluids. A lid driven cavity (LDC) and a differentially heated cavity (DHC) are used as test cases. These numerical solutions can be an appropriate tool for verifying CFD codes which have been developed or adapted to deal with this kind of non-Newtonian fluids. In order to achieve this objective, an in-house CFD code has been implemented and correctly verified by the method of manufactured solutions and by some numerical solutions too. Furthermore, a high-performance CFD code (Termo Fluids S.L.) has been adapted and properly verified, by the corresponding numerical solutions, to deal with this kind of non-Newtonian fluids.The viscoplastic behaviour of certain non-Newtonian fluids will be generated from a viscous stress which has been defined by a potential-type rheological law. The pseudoplastic and dilatant behaviours will be studied. On this matter, the influence of different physical aspects on the numerical simulations will be analysed, e.g. different exponent values in the potential-type rheological law and different values of the non-dimensional numbers. Moreover, the influence of different numerical aspects on the numerical simulations will also be analysed, e.g. unstructured meshes, conservative numerical schemes and more efficient and parallel algorithms and solvers.

Influence of the Metal Sheet Parameters on the Results of the Erichsen Test

Considering an isotropic rheological law of the sheet material and the power law relationship between the stress and the plastic strain, the present paper by using the finite element method analyzes the influence of the material parameters on the results of the Erichsen test in terms of force-displacement curve of the punch and the normalized thickness measured at the specimen apex also varying the coefficient of the Coulomb friction law. Moreover for an AA5083 aluminum alloy the results of the numerical simulation of the Erichsen test will be compared to those obtained experimentally.

Investigating lava flow rheology using video analysis and numerical flow models

Lava rheology is a major control on lava flow behavior and a critical parameter in flow simulations, but is very difficult to measure at field conditions or correctly extrapolate from the lab scale. We present a new methodology for investigating lava rheology through a combination of controlled experiments, image analysis and numerical forward modeling. Our experimental setup, part of the Syracuse University Lava Project (http://lavaproject.syr.edu) includes a large furnace capable of melting up to 450kg of basalt, at temperatures well above the basalt liquidus. The lava is poured onto either a tilted bed of sand or a steel channel to produce meter-long flows. This experimental setup is probably the only facility that allows such large scale controlled lava flows made of natural basaltic material.We document the motion of the lava using a high-resolution video camera placed directly above the flows, and the temperature using infrared probes and cameras. After collecting the footage, we analyze the images for lava deformation and compare with numerical forward-models to constrain the rheological parameters and laws which best describe the flowing lava. For the video analysis, we employ the technique of Differential Optical Flow, which uses the time-variations of the spatial gradients of the image intensity to estimate velocity between consecutive frames. An important benefit for using optical flow, compared with other velocimetry methods, is that it outputs a spatially coherent flow field rather than point measurements. We demonstrate that the optical flow results agree with other measures of the flow velocity, and estimate the error due to noise and time-variability to be under 30% of the measured velocity.Our forward-models are calculated by solving the Stokes flow equations on an unstructured finite-element mesh defined using the geometry of the observed flow itself. We explore a range of rheological parameters, including the lava's apparent viscosity, the power-law exponent m and the thermal activation energy. Our measurements of apparent viscosity agree well with predictions of the composition-based Shaw (1972) and GRD model (Giordano, Russell and Dingwell, 2008). We find that for the high-temperature portion of the flow a weakly shear-thinning or Newtonian rheology (m>0.7) with an effective activation energy of B=5500J gives the best fit to the data.Our methodology is the first time that high-resolution optical flow analysis of flowing lava is combined with numerical flow models to constrain rheology. The methodology we present here can be used in field conditions to obtain in-situ information on lava rheology, without physical interaction with the flow and without being limited to point-wise, low strain-rate, local measurements currently available through the use of rotational viscometers in the field.

Brittle–ductile transition zone case study (Zagros–Iran)

A three-dimensional lithosphere model with horizontal dimensions of 1500km×600km and a depth extent of 70km is constructed from available geophysical data to find out strength (as the maximum deviatoric stress the lithosphere supports at a given depth) in Arabia–Eurasia plate boundary zone. The constructed model is first used in the calculation of thermal initial condition and then strength envelopes were calculated using the obtained geotherm and rheological flow laws. Numerical models are run for initial temperature distributions representing cold and hot lithosphere with two different rheology (wet and dry). The obtained mechanical structures were analyzed and compared with other geophysical data; e.g., seismicity-depth and isotherm-depth distributions. Model results for wet and dry rheology indicate that the depth of the brittle–ductile transition is about 8km and 11km for hot geotherm and 10.5km to14km and 21–28 for cold geotherm.The results are in good agreement with focal depth in the Zagros that most earthquakes occur in 8–15km depth i.e. the long-term strength of the continental lithosphere resided only in its upper part, which was contained wholly within the crust. The ILSs (integrated lithospheric strengths) values for a wet crustal rheology have high range of 1.4–10×1012Nm−1, which is mainly the result of a low heat-flow (cold geotherm) and 0.1×1012Nm−1 for wet rheology and hot geotherm.

A comprehensive frictional-kinetic model for gas–particle flows: Analysis of fluidized and moving bed regimes

A comprehensive frictional-kinetic model for collisional and frictional gas–particle flows is presented. The model treats gas and particles as a continuum. The kinetic-collisional stresses are closed using kinetic theory of granular flows (KTGF). The frictional stresses are based on inertial number dependent rheology and dilation laws. From these laws the frictional normal and shear stresses are derived. These individual contributions to the solids stress tensor are treated additively, which requires a modification of the radial distribution function in the frictional regime. The presented model is validated for both, i.e. frictional and collisional dominated, flow regimes: (1) the collisional-frictional gas–particle flow in multiple-spout fluidized beds is studied and (2) the friction dominated discharge of particles from a rectangular bin is considered. In case of the multiple-spout fluidized beds the numerical simulations show excellent agreement with the experimental data of van Buijtenen et al. (2011). The numerical results demonstrate that the presented model is a substantial improvement compared to the coupled CFD-DEM simulations of van Buijtenen et al. (2011) and to the Princeton model (Srivastava and Sundaresan, 2003). In case of the discharge of particles the model predicts height-independent mass flow rates and stagnant shoulders in the corners of the bin. For the computed discharge rates excellent correlation with measurements (relative error e<2.5%) for three different particle diameters is obtained. In contrast, the Princeton model yields relative errors up to e=41.5%. Finally, the computed solids velocities near the exit orifice show good agreement with experimental particle tracking (PT) results as well.