Rheological Coefficients Research Articles

Experimental research on rheological properties and proppant transport performance of GRF–CO2 fracturing fluid

Abstract In this article, an experimental study on rheological properties and proppant transport performance of the GRF–CO 2 system is performed by using a large-scale high-temperature and high-pressure foam fracturing fluid test system with the correlations for fracturing fluid rheological parameters, critical settling velocity and proppant settling velocity obtained. Research results show that the effective viscosity decreases with increasing temperature and shear rate. The effective viscosity increases with increasing foam quality in foamed cases, and decreases with increasing foam quality in unfoamed cases. The temperature and foam quality effect on parameters of the rheological properties of the fracturing fluid is larger than the pressure in various influencing factors. The critical settling velocity increases with the rise in temperature in foaming cases, and decreases with the rise in foam quality and sand ratio. The reunion phenomenon happens after the sand ratio is more than 25%. The correlations for GRF–CO 2 fracturing fluid rheological index, rheological coefficient, final proppant settling velocity in the solution and the critical settling velocity have been obtained with an average error of calculation less than 14%.

Experimental Research on Rheological Properties of Slick Water Mixed with CO<sub>2</sub> System

Rheological properties of slick water mixed with CO2 system are studied,through the large foam fracturing fluid of high temperature and high pressure experiment system,in detail in this paper, based on the principle of tube type rheometer. The influence laws temperature, foam quality, shear rate and pressure have on the rheological characteristics are studied. The fracturing fluid rheological parameters calculation correlations are also obtained, and the foam quality influence on rheological index and rheological coefficient of the slick water mixed with CO2 system are analyzed.

Flow characteristics of the raw sewage for the design of sewage-source heat pump systems.

The flow characteristics of raw sewage directly affect the technical and economic performance of sewage-source heat pump systems. The purpose of this research is to characterize the flow characteristics of sewage by experimental means. A sophisticated and flexible experimental apparatus was designed and constructed. Then the flow characteristics of the raw sewage were studied through laboratorial testing and theoretical analyses. Results indicated that raw sewage could be characterized as a power-law fluid with the rheological exponent n being 0.891 and the rheological coefficient k being 0.00175. In addition, the frictional loss factor formula in laminar flow for raw sewage was deduced by theoretical analysis of the power-law fluid. Furthermore, an explicit empirical formula for the frictional loss factor in turbulent flow was obtained through curve fitting of the experimental data. Finally, the equivalent viscosity of the raw sewage is defined in order to calculate the Reynolds number in turbulent flow regions; it was found that sewage had two to three times the viscosity of water at the same temperature. These results contributed to appropriate parameters of fluid properties when designing and operating sewage-source heat pump systems.

Selected properties of acetylated adipate of retrograded starch

Native potato starch (NS) and retrograded starch (R – obtained via freezing and defrosting of a starch paste) were used to prepare starch acetates: NS-A and R-A, and then acetylated distarch adipates: NS-ADA and R-ADA. The chemically-modified preparations produced from retrograded starch (R-A; R-ADA) were characterized by a higher degree of esterification compared to the modified preparations produced under the same conditions from native potato starch (NS-A; NS-ADA). Starch resistance to amylolysis was observed to increase (to 30–40g/100g) as a result of starch retrogradation and acetylation. Starch cross-linking had a significant impact on the increased viscosity of the paste in the entire course of pasting characteristics and on the increased values of rheological coefficients determined from the equations describing flow curves. The produced preparation of acetylated retrograded starch cross-linked with adipic acid (R-ADA) may be deemed an RS3/4 preparation to be used as a food thickening agent.

Combining Spatial Models for Shallow Landslides and Debris-Flows Prediction

Mass movements in Brazil are common phenomena, especially during strong rainfall events that occur frequently in the summer season. These phenomena cause losses of lives and serious damage to roads, bridges, and properties. Moreover, the illegal occupation by slums on the slopes around the cities intensifies the effect of the mass movement. This study aimed to develop a methodology that combines models of shallow landslides and debris-flows in order to create a map with landslides initiation and debris-flows volume and runout distance. The study area comprised of two catchments in Rio de Janeiro city: Quitite and Papagaio that drained side by side the west flank of the Maciço da Tijuca, with an area of 5 km2. The method included the following steps: (a) location of the susceptible areas to landslides using SHALSTAB model; (b) determination of rheological parameters of debris-flow from the back-analysis technique; and (c) combination of SHALSTAB and FLO-2D models to delineate the areas more susceptible to mass movements. These scenarios were compared with the landslide and debris-flow event of February 1996. Many FLO-2D simulations were exhaustively made to estimate the rheological parameters from the back-analysis technique. Those rheological coefficients of single simulation were back-calculated by adjusting with area and depth of the debris-flow obtained from field data. The initial material volume in the FLO-2D simulations was estimated from SHALSTAB model. The combination of these two mathematical models, SHALSTAB and FLO-2D, was able to predict both landslides and debris-flow events. Such procedures can reduce the casualties and property damage, delineating hazard areas, to estimate hazard intensities for input into risk studies providing information for public policy and planning.

A Nonlinear Mechanical Model for Predicting the Dynamics Response of Materials under a Constant Loading

The paper is designed to provide a theoretical mechanical model taking into account elastic, viscous and inertial nonlinearities simultaneously, for predicting the time dependent response of some materials under a constant loading. Numerical illustrations are carried out to investigate the effects of rheological coefficients action on the model.

A model of acoustic absorption in fluids based on a continuous distribution of relaxation times

This work extends the quasi-equilibrium relaxation theory of sound absorption in liquids to the case of continuous distribution of relaxation times. Such extension is needed when absorption mechanisms are not confined to the action of viscosity and heat conduction, but are mainly due to the excitation of a large number of internal molecular degrees of freedom. In this case the conventional Navier–Stokes equations are not sufficient to describe the fluid motion, and additional equations are required to model normal relaxation stresses. When relaxation frequencies form a sufficiently dense distribution, as is the case for many biological fluids, it makes sense to consider the limit of continuously distributed relaxation frequencies, in order to obtain the required equation for normal relaxation stresses.In contrast to its discrete counterparts, the proposed method avoids the use of a potentially infinite number of relaxation equations for a given set of distinct relaxation frequencies. Instead, these are replaced by a single evolution equation of Boltzmann type whose right-hand side is a linear combination of the time derivatives of density and entropy. The rheological functions appearing before these derivatives are expressed in terms of the absorption coefficient. Since the dependence of absorption coefficient on sound frequency is measurable experimentally, these rheological coefficients can be recovered from experimental data.The key feature of the present study is that a closed system of equations of motion can be formulated directly from absorption measurement data on the basis of the theory proposed for the very wide range of absorption laws that can occur in practice.As an illustration of the generality of the present method, a number of absorption laws documented in the experimental literature are considered in detail, in order to derive the coefficients of the related systems of equations of motion for these liquids. For example, the methodology based on modelling of acoustic absorption in biologically soft tissue by the employment of fractional derivatives, which has been recently developed in the literature, is shown to be a special case of the proposed theory.

Physical meaning of the rheological coefficients in the generalized Casson model

The coefficients of the previously proposed generalized flow model of structured systems have been interpreted. The cohesive force between particles in disperse systems has been calculated from rheological data. The number of aggregated particles in a disperse system is estimated using the kinetic equation method.

시멘트 페이스트의 유동 특성에 관한 평가방법 비교연구

This study investigates the influence of various blending factors on cement paste fluidity and find out the most effective evaluation method of cement paste flow, comparing flow test apparatuses such as ring flow(R-F), flow cone(F-C) and mini slump(M-S). A viscometer also measures the rheology coefficients to secure faithful numerical data. Firstly, series I examines cement paste, affected by several cement products and mineral admixture types in the range of W/B 40%, ordinary fluidity, and W/B 30%, high fluidity. In this series, the three types of cement product depended on companies, are randomly used and the mineral admixture, such as fly ash, blast furnace slag and silica fume, are incorporated in the cement paste, in response to the ratio of 10, 20, to 30%, respectively. In addition, series II studies various chemical admixture types, affecting the cement paste. This series is carried out with manufacturing companies and component types in the range of W/C 30%, high fluidity. For the manufacturing companies, randomly four products are used and for the component types, polycaboxylate, melamine, naphthalene and lignosulfonate type are chosen. Test results showed that in the fluidity test of cement paste considering various types of blending factors, R-F exhibited similar tendency with F-C and M-S. In the analysis of consistency curves measured by viscometer, the fluidity evaluation method using flow test apparatuses was significantly effective, except for the some of the low fluidity specimens. In conclusion of this study, R-F was the most convenient, faithful and effective fluidity evaluation method of cement paste.

若材齢コンクリートのクリープ及び拘束変形特性

In this paper, the creep behavior and the restrained deformation property for early age concrete were investigated by the rheological analysis method based on the burgers model for a non-linear function and the iterative analysis method based on the creep superposition. According to the analysis, the following results were clarified: 1) The creep behavior in early age could be considered by the rheological coefficient model on a time dependence for early age concrete. 2) The restrained deformation analysis method based on creep solution by the rheological coefficient model was proporsed. 3) The rheological analysis method based on the burgers model for a non-linear function was effective for early age concrete.

Structural and rheological properties of microheterogeneous systems ‘solid hydrocarbons–liquid hydrocarbons’

Due to the aggregation of paraffin crystallites, the paraffin-containing disperse system in a nonpolar dispersion medium exhibits non-Newtonian and thixotropic rheological behavior. Experimental flow curves for the highly paraffinaceous crude oil as well as the model systems ‘paraffin–vaseline oil’ were described by the Casson equation. The Casson model was used to connect rheological coefficients and colloidal characteristics of the dispersion. For this purpose, the evaluation of the radius of the primary particle was made, based on the Casson model and those concerned with the interactions between the paraffin particles in nonpolar medium.

STUDY ON A METHOD OF OBTAINING RHEOLOGICAL COEFFICIENTS OF HIGH-FLOW CONCRETE WITH NUMERICAL ANALYSIS

STUDY ON A METHOD OF OBTAINING RHEOLOGICAL COEFFICIENTS OF HIGH-FLOW CONCRETE WITH NUMERICAL ANALYSIS

Thermo-viscoplastic parameter identification formulated as an inverse finite element analysis of the hot torsion test

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Hydrodynamic interactions in colloidal crystals: (II). Application to dense cubic and tetragonal arrays

Wavevector dependent friction factors, which together with the elastic properties determine the hydrodynamic damping of harmonic lattice waves in colloidal crystals, are calculated for cubic arrays of rigid spheres at low, intermediate and high sphere volume fractions, including simple cubic (SC), body-centred cubic (BCC) and face-centred cubic (FCC) lattices. Exact numerical data are presented for the rheological coefficient appropriate to pure vortex motion of particles, the so-called spin viscosity. These results for the spin viscosity are obtained for all three cubic lattices and for the whole range of volume fractions. An expression suitable for low volume fractions is derived that approximates the converged numerical data within an error of only 3%, for volume fractions up to 75% of the close packing concentration for all of the three cubic packing types. Spin viscosities of extremely dense cubic arrays are calculated on basis of lubrication theory which yields new expressions for BCC and FCC lattices, while reproducing a known result for the SC case. Constant contributions of many-particle hydrodynamic interactions are determined that yield a first correction to the lubrication expressions, appropriate for the three cubic lattices. Two types of body-centred tetragonal (BCT) arrays are considered. The first type (BCT1) consists of aligned rows of close-touching spheres, where variations of the volume fraction can be accomplished by changing the distance between these rows. The second type (BCT3) has a constant structure, such that the concentration can be varied by changing the size of the spheres. The two characteristic drag coefficients are calculated numerically for steadily sedimenting BCT arrays of both types and at all concentrations. Likewise two characteristic spin viscosities are computed for these structures. Analytical results suitable to dilute BCT3 arrays are presented for drag coefficients and spin viscosities. The expressions for the spin viscosities represent an approximation within 3%, for volume fractions up to 60% of the close packing concentration.

Identification du comportement rhéologique par analyse inverse

.The use of the inverse method principle for analysing rheological tests is presented. It is based on the finite element simulation, capable of taking into account the whole complexity of the test, especially in terms of self-heating and strain localisation phenomena. The identification of rheological parameters is then ensured by solving an inverse problem. The principle is to find the rheological coefficients which permit one to obtain the optimal comparison between the experimental measurements and the numerical resolution.

Connection of microstructure to rheology in a microemulsion model.

The rheological properties of self-assembling fluids are studied within the framework of a simple time-dependent Landau-Ginzburg model. In addition to the Langevin relaxation dynamics, the order parameter field is subject to a kinematic deformation process due to a shear velocity field. The Hamiltonian contains a Gaussian part which has proven to be important in the study of self-assembly, as well as ${\mathrm{\ensuremath{\varphi}}}^{4}$ and ${\mathrm{\ensuremath{\varphi}}}^{2}$(\ensuremath{\nabla}\ensuremath{\varphi}${)}^{2}$ contributions. In the disordered phase and for low shear rate, the relevant rheological coefficients (excess viscosity, first and second normal stress coefficient) can be calculated perturbatively. The essential ingredient is the one-loop, self-consistent solution of the evolution equation for the quasistatic structure factor. In the case of steady shear, we find shear thinning behavior, a positive first, and a negative second normal stress difference for all values of the shear rate. For oscillatory shear, it turns out that the self-assembling structures give rise to viscoelastic behavior. Analytic results are derived for the limiting cases of low and high frequency. For low steady shear, all results can be expressed in scaling form using the correlation lengths d and \ensuremath{\xi} originally defined for microemulsion under equilibrium conditions and scaling functions already known from the pure Gaussian treatment. This suggests a class of experiments where neutron scattering data can be compared to viscosity results. For low to high shear rates, the one-loop equations have also been solved numerically, and we display the nonequilibrium structure factors arising from this approach. \textcopyright{} 1996 The American Physical Society.

Transport of Water in a Biconstituent Elastic Medium

A phenomenological equation is established for water transport in a biconstituent, isotropic, isothermal elastic medium. The equation includes a term related to the water content gradient and a term related to the deformation gradient. It is shown that in the case of an infinite plate, the transport law can be similar to Fick’s law in which water flux is proportional to the water content gradient alone. The apparent transport coefficient then depends on the hygroscopic and rheological coefficients of the medium. Experimental analysis of the evolution of water content profiles of agar gel plates validates this transport law and makes it possible to deduce the variation in apparent transport coefficient according to water content. Transport coefficients associated with water content and deformation gradients and applicable to any geometrical features are deduced.

Mixing of a Generalized Newtonian Fluid in a Cavity

Mixing of a generalized Newtonian fluid in a corotating discontinuous cavity flow is studied. The flow period and the rheological coefficients are used as parameters. Using geometrical construction of periodic orbits and bifurcation analysis we find mixing windows in the parameter space. A system within a mixing window is capable of producing uniform mixtures. Some bifurcation values have also been determined. A system whose parameters are in the neighborhood of these values will mostly not produce a uniform mixture. The main conclusion is that shear thinning degrades mixing in the cavity flow.

Surface Properties of Protein Alcoholic Solutions

Abstract Dynamic surface dilational properties of alcoholic solutions of proteins (Bovine Serum Albumine (BSA) and β-casein) were studied by the damped longitudinal waves (0.1-1 Hz) method as a function of the ethanol content. At low ethanol contents (0-5%, v/v) the BSA solutions and the β-casein at 12%, v/v, exhibited viscoelastic behavior. At high ethanol content, the BSA solution surface displayed an elastic behavior. Absolute surface rheological coefficients (high-frequency elasticity E T o , low-frequency elasticity E (0), the constant rate of relaxation k r , and the intrinsic surface viscosity η s ) of the surface at its quasiequilibrium were obtained from the frequency spectra of the waves' characteristics. We have introduced two models: one based on the adsorption-desorption of protein aggregates and another based on a conformational change surface reaction, which could fit our results. The decrease of E T o , k r , and η s when ethanol content increases has been related to the decrease of surface coverage by protein.

The rheology of solutions of associating polymers: Comparison of experimental behavior with transient network theory

The properties of aqueous solutions of model HEUR associative thickeners under dynamic and steady shear have been studied as a function of concentration, molecular weight, temperature, and hydrophobic end‐cap length. It is shown that solutions of AT behave as near perfect Maxwell fluids inasmuch that Cole–Cole plots of the dynamic moduli are almost exactly semi‐circular. An Arrhenius law temperature dependence of the static viscosity and relaxation time is also observed, providing confirmation of a single relaxation process. In certain other respects, AT solutions show more complex behavior, e.g., the Cox–Merz rule is not obeyed, with the steady shear viscosity showing a weaker dependence on shear rate than does the complex viscosity upon frequency. Furthermore, weak shear thickening is seen to precede shear thinning in steady shear. The above results are consistent with the predictions of a transient network theory presented recently by Tanaka and Edwards and Jenkins (generalized Green–Tobolsky theory). This does not however explain the strong effect of concentration on the various rheological coefficients. For example, the theory predicts a linear dependence of high‐frequency modulus and static viscosity on concentration, whereas in practice they are found to be more like quadratic and cubic, respectively, at low concentrations.In previous publications this strong dependence has been taken to mean that the network chains are entangled to the point where reptation dynamics determines the time scale of relaxation. This supposition has been tested by mixing solutions of AT with different relaxation times (achieved by means of different end‐cap lengths), on the basis that the mixed solutions should show an intermediate relaxation time if reptation is important. In practice, mixtures of two and three AT were found to show two or three sharp relaxation times, implying that the chains relax independently. It is shown that the true explanation of the strong concentration dependencies is connected with a different kind of change of network topology with concentration. An elementary statistical‐mechanical model, supported by Monte Carlo simulation, is used to argue for a gradual transition from, at low concentrations, micelles built predominantly from looped chains to, at high concentrations, a fully developed network comprising micelles linked by bridging chains. When the transient network theory is modified so as to take the presence of loops into account, it produces results in semiquantitative agreement with experiment.