Experimental Rheological Data Research Articles

Research on the construction of novel nano‐modified clean fracturing fluid and the migration characteristics of proppants

AbstractClean fracturing fluid exhibits desirable characteristics, such as low residue, easy flowback, minimal reservoir damage, and favorable rheology, making it highly adaptable. However, challenges remain in terms of high cost, large consumption, and poor stability. Hence, this study focuses on incorporating SiO2 nanoparticles into clean fracturing fluid to develop a novel nano‐modified system. Experimental tests were conducted to analyze the impact of mass fractions of hexadecyltrimethylammonium chloride (CTAC), sodium salicylate (Nasal), and SiO2 nanoparticles on the viscosity of the solution. The results indicate a significant increase in viscosity with higher mass fractions of SiO2. A nano‐modified clean fracturing fluid composition of 1.5 wt% CTAC, 0.4 wt% Nasal, and 0.1 wt% SiO2 was selected as it meets the technical specifications for fracturing fluid while exhibiting excellent elastic modulus (2.279 Pa) and viscous modulus (0.818 Pa), thereby displaying superior viscoelastic properties. Furthermore, the system maintains a viscosity above 20 mPa.s under temperature (70°C) and shear stress (170 s−1), indicating robust temperature and shear resistance to meet the demands of downhole fracturing and proppant transport. Based on rheological experimental data, a Carreau rheological model was established for the nano‐modified clean fracturing fluid. Considering particle interaction, wall blockage, and fluid filtration, a settlement model was modified with a correction coefficient, leading to the construction of a mathematical model for correcting proppant particle settling in fractures. The error between measured settlement velocity and calculated values remained within 10%. Finally, the migration law of proppant is studied, and the settlement law of proppant in fracturing fluid and fracture is clarified.

Establishing rheological models of lignin-based solutions via molecular parameters using machine learning

The rheological models of natural polymer-based solutions are difficult to be established because of the significant non-Newtonian behavior and highly discrete rheological data caused by different molecular parameters including the molecular weights and size of clusters. In this study, a typical natural polymer-lignin was selected and dissolved in polyethylene glycol (PEG) as the lignin-based solutions. The experimental rheological data of different PEG-lignin solutions were trained with machine learning. The rheological models were established considering the molecular parameters including the molecular weights and size of clusters. The models show a high accuracy in predicting the viscosities of different PEG-lignin solutions with the coefficient of determination over 0.9815, mean absolute error less than 0.0132, and average absolute relative deviation less than 6.95 % in both Newtonian and non-Newtonian regimes. The models and relevant methodology can provide scenarios for further application of natural polymer solutions in process industries.

Experimental and rheological modelling on the stabilization of iron ore slurry using a biosurfactant extracted from Aloe barbadensis Miller

The pipeline transportation of iron ore slurry (IOS) is an eco-friendly alternate mode to transport the raw materials to longer distance and reduce the transportation network congestion problems. Proper selection of surfactant could modify mineral’s viscosity, dispersion and wetting characteristics effectively as may be desired, which may further be monitored. A surfactant alters surface characteristics after being adsorbed onto minerals by altering the interfacial behaviour. This work is first report of the influence of a biosurfactant sourced from Aloe barbadensis Miller on the rheological behaviour of a high-grade iron ore (IO) sample at 45–72% by mass slurry concentrations range. The observed rheological parameters confirmed the non-Newtonian flow behaviour of the slurry. The collected IO and dried IOS samples were subjected to UV-Vis, XRF, PSD, XRD, SEM and EDS analyses. Experimental rheological data at varying concentrations was tested on various models to ascertain the best-fit rheological model for IOS transport. The Bingham model was found to be the most suitable to model the rheology of IOS. Experimental rheological behaviour of IOS was found to be linear with the yield stress. The study shall help to ascertain the suitability of a biosurfactant to stabilise high grade iron ores for pipeline transportation.
 KEY WORDS: Iron ore slurry, Aloe barbadensis, Rheological measurements, Rheological modelling
 Bull. Chem. Soc. Ethiop. 2024, 38(3), 615-629. 
 DOI: https://dx.doi.org/10.4314/bcse.v38i3.6

Model Simulation and Rheological Research on Crosslinking Behavior of Polyethylene Resin.

The crosslinking behavior of polyethylene (PE) determines its exceptional performance and application. In this study, we investigated the crosslinking behaviors of different PE resins through model simulation and rheological methods. Specifically, the mathematical equation of "S" model was established for PE resin. According to this equation, the optimal maximum gel content for high-density polyethylene (HDPE) was found to be around 85%. Moreover, the maximum crosslinking degrees for different PE resins depended largely on their density and molecular weight. The melt viscosities before crosslinking in PE resins were highly influenced by their melt index. The higher melt indexes resulted in the lower storage moduli, improving melt processability during processing. In addition, the crosslinking rates of PE resins were strongly influenced by peroxide concentration, independent of PE resin structures. For high molecular weight and low-density PE resins, they exhibited decreased ti values, increased A0 values, and decreased k6 values. However, there were no noticeable variations in the values of k2 and phi among different PE resins. All simulated modeling outcomes showed remarkable consistency with the experimental rheological data. These findings are of strong significance in the industrial manufacture of PE resin.

Molecular dynamics simulation of mechanical relaxation of poly(propyleneimine) dendrimers

We report on shear-stress relaxation of melts of poly(propyleneimine) (PPI) dendrimers of different generations (G2–G5). The aim of this study was to confirm our previous conclusion in Sheveleva et al. [Phys. Chem. Chem. Phys. 24, 13049–13056 (2022)] for carbosilane dendrimers that an impenetrable inner region leads to the manifestation of the crowded environment effect. The systems of PPI dendrimer melts are studied using atomistic molecular dynamics simulations. The time and frequency dependencies of the dynamic shear-stress modulus are investigated. The results are in good agreement with the available rheological experimental data for G2–G4 PPI. We have found that the crowded environment effect does not manifest itself in the mechanical relaxation of G4 PPI dendrimers in contrast to G4 carbosilane dendrimers. Despite their similar topology and close sizes, G4 PPI does not form an impenetrable core. The G5 PPI dendrimer has an impenetrable inner region, and the crowded environment effect is observed. As in carbosilane dendrimers, the maximal time of mechanical relaxation is increased due to the crowded environment effect. However, the opposite situation is for the rotational diffusion of the G5 PPI dendrimers. In contrast to carbosilane dendrimers, the rotational mobility of G5 PPI significantly slows down even taking into account the increase in the dendrimer size. The hydrogen bonding between PPI dendrimers affects the mechanical relaxation at high frequencies (short times) and enhances with growing G.

Analysis of periodic pulsating blood flow of fractional Maxwell power-law fluid in carotid artery with elastic vessel wall

Hemodynamic analysis reveals a highly significant effect on the prevention, diagnosis, and treatment of human vascular diseases. This article goes deeply into the periodic pulsatile blood flow in the carotid artery with an elastic vessel wall. In view of blood rheological experimental data, the constitutive equation of fractional Maxwell power-law fluid with yield stress, which can describe the four characteristics of yield stress, viscoelasticity, shear thinning, and thixotropy is established. Meanwhile, drawing support from the data of pulsatile flow, the finite Fourier series of pressure gradient with a period of 1 s has been proposed. Leading into Hooke’s law can build the fluid-structure coupling boundary condition of blood flow and elastic vessel wall. The numerical solutions are got hold of finite difference method integrated with the newly developed L1-algorithm, and their convergence and stability of which are verified. The axial velocities of blood under different constitutive relationships are compared. The results throw light that other constitutive relationships underestimate the velocity of blood. Furthermore, the flow rate and wall shear stress on different fluid are calculated. It can be concluded that compared with Bingham fluid, the maximum and minimum flow rate/wall shear stress of fractional Maxwell power-law fluid with yield stress increases by 19% and 32%, respectively. The flow rate lags behind the pressure gradient and has time delay effect, on the contrary, the velocity of blood vessel wall is keeping pace with the pressure gradient. The effects of relevant physical parameters on velocity are discussed. In addition, the spatiotemporal distribution of blood flow in cerebral artery and femoral artery are analyzed.

The effect of reinforcement aspect ratio on the performance of PA66 composites with recycled carbon fiber and upcycled graphene nanoplatelets: An interface characterization from process to modeling

AbstractThe use of recycled reinforcements in structural applications is growing due to concerns about the environmental impact and economic costs associated with energy‐intensive production techniques of virgin fibers. However, limited research has explored the integration of multiscale reinforcements with different aspect ratios into PA66 composites to enhance their performance. In this study, the effect of reinforcement aspect ratio on PA66 composites by incorporating recycled carbon fibers and waste tire‐derived graphene nanoplatelets (GNP) with oxygen surface functional groups is investigated. The objective of this work is to improve mechanical properties of the composites by promoting nucleation and enhancing the fiber/matrix interface. Through high shear mixing, recycled carbon fibers and GNP are effectively dispersed within the PA66 matrix. The alignment of these reinforcements during the injection molding process is monitored using the developed flow model, coupled with experimental rheological data. The resulting composites demonstrate significant improvements in mechanical properties due to enhanced interfacial interactions, including improved tensile properties up to 94%, flexural properties up to 86% compared to the neat PA66 by successfully integrating waste tire‐driven GNP and recycled carbon fibers. This study contributes to the development of sustainable materials for load‐bearing applications, utilizing recycled reinforcements with different aspect ratios.

New insights into the extended and generalised PTT constitutive differential equations: weak flows

This work presents a comparison between the PTT-X (extended Phan-Thien and Tanner (PTT)) and the generalised PTT (gPTT) viscoelastic models. The PTT-X model was derived based on a combination of reptation and network theories, allowing in this way a microstructural justification for the kernel function. The gPTT model is based on the network theory, with an empirical kernel function for the rate of destruction of junctions, that proved to be effective fitting experimental rheological data for polymer melts and solutions. A review on the background of both models is provided and the two models are then compared considering simple flows. This comparison allows one to attribute in some way a microstructural nature to the parameters involved in the gPTT model. Also, a new analytical solution is derived for the Poiseuille flow of the PTT-X model.

The Quadratic Constitutive Model Based on Partial Derivative and Taylor Series of Ti6242s Alloy and Predictability Analysis

To solve the problem of insufficient predictability in the classical models for the Ti6242s alloy, a new constitutive model was proposed, based on the partial derivatives from experimental data and the Taylor series. Firstly, hot compression experiments on the Ti6242s alloy at different temperatures and different strain rates were carried out, and the Arrhenius model and Hensel-Spittel model were constructed. Secondly, the partial derivatives of logarithmic stress with respect to temperature and logarithmic strain rate at low, medium and high strain levels were analyzed. Thirdly, two new constitutive models with first- and second-order approximation were proposed to meet the requirements of high precision. In this new model, by analyzing the high-order differential data of experimental data and combining the Taylor series theory, the minimum number of terms that can accurately approximate the experimental rheological data was found, thereby achieving an accurate prediction of flow stress with minimal material parameters. In the new model, by analyzing the high-order differential of the experimental data and combining the theory of the Taylor series, the minimum number of terms that can accurately approximate the experimental rheological data was found, thereby achieving an accurate prediction of flow stress with minimal material parameters. Finally, the prediction accuracies for the classical model and the new model were compared, and the predictabilities for the classical models and the new model were proved by mathematical means. The results show that the prediction accuracies of the Arrhenius model and the Hensel-Spittel model are low in the single-phase region and high in the two-phase region. In addition, second-order approximation is required between the logarithmic stress and logarithmic strain rate, and first-order approximation is required between logarithmic stress and temperature to establish a high-precision model. The order of prediction accuracy of the four models from high to low is the quadratic model, Arrhenius model, linear model and HS model. The prediction accuracy of the quadratic model in all temperatures and strain rates had no significant difference, and was higher than the other models. The quadratic model can greatly improve prediction accuracy without significantly increasing the material parameters.

Multivariable Rheological Models for Commercial Polypropylene with High Molar Masses

AbstractThis work investigates the fitting performance of conventional rheological models and the development of multivariable rheological models to reproduce experimental rheological data of different industrial grades of linear isotactic polypropylene (iPP) having high mass average molar masses, Mm (164–404 kg mol−1), at three temperature values (180–220 °C) over a wide range of shear rates (10−1–104 s−1). A shear thinning behavior is found in all investigated conditions. However, a low shear rate primary Newtonian plateau for a short shear rate range is only identified for the smallest Mm among those investigated, and for higher Mm such primary plateaus are even found at shorter shear rate range. Among the investigated models, only Cross and Carreau–Yasuda models are effective to reproduce the data for a specific PP grade. Two modified models are proposed that incorporate three variables. In the modified Cross Model, it has been shown that the characteristic time (λ) between the Newtonian plateau at the low shear rates and the shear‐rate range with shear‐thinning behavior depends exponentially on the Mm, and it does not depend on the temperature. Both proposed models fit very well with the experimental data with shear thinning behavior for a wide range of Mm.

Which Is an Appropriate Quadratic Rheological Model of Fresh Paste, the Modified Bingham Model or the Parabolic Model?

The physical meaning and calculating process of the rheological parameters of two nonlinear rheological models, the parabolic model and the modified Bingham model, were compared. The fluidity test and a rheological experiment on cementitious materials were performed. The Couette inverse problem is a key issue in measuring and solving the rheological parameters of fresh cementitious materials. The solution of the Couette inverse problem based on the modified Bingham model is discontinuous when the coefficient of the quadratic term is equal to zero, resulting in a large deviation between the fitting curve and the rheological experimental data. The credibility of the rheological parameters of the pastes calculated based on the modified Bingham model is low. The formulas for calculating yield stress, fiducial differential viscosity and the degree of shear thickening or shear thinning of the parabolic model have been developed. The credibility of the rheological parameters of the pastes calculated based on the parabolic model is high. The flow performance of the paste can be clearly characterized by the rheological parameters calculated with the parabolic model.

Magnesium Bromide as Novel High-Density Packer Fluid in Oilfield Applications

Abstract The rheology of a packer fluid (PF) is the most crucial aspect prompting the efficacious well completion effectiveness. In the drilling industry, a high-density, solid-free, low viscosity, and alkaline pH packer fluid is a big advancement and requirement. Here, we develop a magnesium bromide as an effective solid-free, high-density packer fluid (HDPF) for oilfield applications. We believe that investigating the rheological parameters such as shear stress, yield point, plastic and apparent viscosity, and gel strength 10 s and 10 min at a varying temperature of 84–192 °F is essential for optimizing the rheological performance. In order to enhance the completion efficiency, our work is more focused on overcoming the rheological and density limitations of existing traditional packer fluid. Our results show that the packer fluid has a low value of plastic viscosity (1.95–7.05 cP) and also exhibits a high density of 13.41 lb/gal, a specific gravity of 1.61. We have reported the pH at the alkaline region (pH 7.14) with solid-free. Here, we have investigated the Bingham plastic rheological model and Herschel Bulkley model parameters with experimental rheological data, and it is adaptive to novel packer fluid to predict the rheological parameters. Conspicuously, the rheological models, along with data analysis, have enormous possibilities in envisaging real-time quantification of shear stress and viscosity to enable the user to monitor and evaluate a suitable packer fluid in oilfield applications.

Mesoscopic theoretical modeling and experimental study of rheological behavior of water-based drilling fluid containing associative synthetic polymer, bentonite, and limestone

Employing an effective rheological model for the flow of drilling fluid that can accurately predict changing conditions is of significant importance in drilling fluid optimization. Traditional generalized Newtonian models cannot predict the time change condition, viscoelastic behavior, role of each component, or microstructural behaviors within the fluid. Consequently, the present research aims to develop constitutive equations in the framework of generalized bracket formalisms and the extra tensor concept that connect the microscopic and macroscopic properties and can overcome the aforementioned problems of traditional rheological models. The developed model is applicable for drilling fluid as a suspension system containing associative synthetic polymer, bentonite, and limestone suspended in water; where simple structures of flexible dumbbells, disks, and hard spheres, respectively, are representative of each component in the system. Five samples of drilling fluid with different additive concentrations were prepared and rheological testing was performed on these samples. To obtain the fixed parameters of the model, scanning electron microscope and particle size analyses were conducted on the dried powder and dispersed particles of bentonite and limestone to characterize the shape and size of the particles. The adjustable parameters of the model were then obtained by fitting it using the gathered experimental rheological data. The outcomes of the study revealed that the novel developed model can accurately predict rheological material functions, including shear viscosity and the first normal stress coefficient under transient and steady-state conditions. Furthermore, the presented model is capable of distinguishing the contribution of each component in the drilling fluid rheology.

A data-driven smoothed particle hydrodynamics method for fluids

The rheological properties of emerging novel complex fluids are usually governed by multiple variables, which is challenging for traditional parameterized rheological models in the context of hydrodynamics modelling. In this paper, we propose a novel Data-Driven Smoothed Particle Hydrodynamics (DDSPH) method that, instead of applying the empirical rheological models, utilizes discrete experimental datasets to close the Navier-Stokes equations for hydrodynamics modelling. To this end, a DDSPH solver is introduced to search for the best data points that minimize a distance-based penalty function while satisfying the velocity constraints obtained from the previous timestep. In order to improve the computational efficiency of data retrieval, a large volume of experimental rheological data is pre-sectioned into several labelled subgroups so that the data retrieval can be carried out in a small span of data. The robustness of the proposed method with respect to noisy data is achieved via adding a variable, namely the data probability, to qualify the relevance of data points to the clusters. The convergence and robustness of the proposed DDSPH method are investigated through the examples for both Newtonian and non-Newtonian fluids. The numerical examples have demonstrated that the proposed DDSPH is effective and efficient for both Newtonian and non-Newtonian fluids. The proposed DDSPH will open a new avenue for hydrodynamics modelling though some further studies are required in the future.

Quantitative micro-computed tomography analysis and rheological investigation of Nitrile rubber/Rockwool composites

This study reports the reinforcement degree investigation of two types of rockwool fibers (F1 and F2), in nitrile rubber composites. The micro-computed tomography (micro-CT) 3D images showed that both fibers were well-dispersed in the NBR matrix, without a preferential orientation. The micro-CT analysis also allowed quantifying volume fraction, inter-fiber distance, and aspect ratio. Those morphometric parameters were used for supporting the composites rheological behavior assessment. Changes in the elastic modulus and phase angle followed the same trend of the inter-fiber distance values, regardless the type of fiber. Both volume fraction and aspect ratio data from the micro-CT analysis were used to predict theoretical values of elastic modulus using the Guth-Gold and modified Guth-Gold equations, and the results obtained were compared to the rheological experimental data. This analysis was helpful to better understand the rockwool fibers reinforcement degree differences in the production of the nitrile rubber composites.

Tailoring the rheology and electrical properties of polyamide 66 nanocomposites with hybrid filler approach: graphene and carbon nanotubes

AbstractThe aim was to improve the processability and reduce the melt viscosity of well‐known nanocomposites based on polyamide 66 (PA66) and carbon nanotubes (CNT), while keeping the good electrical conductivity gained after the addition of CNT. Thus, a nanocomposite based on PA66 as the thermoplastic matrix and 3% of CNT was selected. At this composition, a percolated network is created and the material is electrically conductive. The approach followed was the addition of graphene nanoplatelets (GNP) of two different lateral sizes to obtain a PA66 nanocomposite with hybrid filler: CNT/GNP. In addition, a third nanocomposite of PA66 with GNP only was prepared for comparison purposes. The rheological characterization determined that adding 1% of GNP of 2 μm particle size decreased the viscosity of the system by 87%. However, the electrical conductivity was diminished to some extent, from 10−5to 10−9 S cm−1approximately. The Cross rheology model described successfully the experimental rheological data. The CNT/GNP nanocomposite exhibited faster relaxations, almost four orders of magnitude, in comparison with the CNT nanocomposite but slower than the GNP nanocomposite. The nanoparticles improved the crystallization ability of PA66 acting as nucleating agents and increasing the PA66 crystallization temperature by almost 10 °C. Self‐nucleation experiments demonstrated a supernucleation feature of the hybrid filler. The nucleation efficiency was about 500%. © 2021 Society of Chemical Industry

An empirical equation for shear viscosity of shear thickening fluids

Quantitative modelling of the rheology of non-Newtonian fluids requires significant empirical input due to very complex behaviour of the bulk fluid as a result of particle-scale physics of fluids. The existing rheology models are mainly limited to certain fluid dynamics conditions such as shear rate, shear stress, etc. Adopting Doolittle's free volume theory approach, we have proposed an empirical equation to describe the relative free volume-dependent viscosity, the shear stress-dependent viscosity, the shear rate-dependent viscosity, and the dimensionless Péclet number-dependent relative viscosity of shear thickening fluids. The proposed formulae predict all rheologically different behaving Newtonian, intermediate shear thinning, shear thickening and extreme shear thinning regimes of shear-thickening fluids. The proposed formulae have been validated against the experimental rheological data of various shear thickening fluids over a range of pH, volume fraction, electrolyte concentration, temperature, and magnetic field. The results suggest that the predicted threshold material parameters of shear thickening fluids help to quantitatively evaluate the effect of varying physico-chemical conditions on the rheology of shear thickening fluids. We simulated the flow of a shear thickening fluid, modelled using proposed shear rate-dependent equation, in a 2D staggered porous medium. We observed bimodal distribution of pore-scale shear rate, shear viscosity and velocity in a porous medium.

Mesoscopic rheological modeling of drilling fluids: Effects of the electrolyte

Drilling fluid is a complex fluid, including base fluid and other materials, carrying out the vital functions during drilling operation such as cutting transport and controlling formation pressure. In order to optimize performance of a drilling process, a reliable rheological model is required in the computation of fluid flow dynamics. Time-independent Generalized Newtonian formulation are the most common models for describing the rheological behavior of drilling fluids due to its simplicity and ease of use, in spite the fact that they are not able to predict the normal stresses and could not consider effects of active components on the rheological behavior of the drilling fluid and also could not describe the internal microstructures changes in the fluid during its flow. In this paper, a rather simple model in the mesoscopic level of study through the Generalized Bracket formalism have been developed to consider the influence of salts and electrolytes on the rheology of drilling fluid which has received less attention in the previous models. The advantage of this model is that it provides a description for the structural and orientation changes during transient and steady state fluid flows beside prediction of the transient and steady rheological behavior of salt containing suspensions of bentonite in polymeric solutions. Comparison of the model predictions with the published data from literature shows that the model predictions for the effects of the drilling fluid components including clay and salts are in well agreement with those of the rheological experimental data.

Rheological modeling of water based drilling fluids containing polymer/bentonite using generalized bracket formalism

Drilling fluids consist of several components with different physical and structural form which can be assumed as complex fluids. Optimum performance of drilling process could be obtained through the dynamic fluid computation which requires a reliable mathematical model capable to predict transient and steady state rheological behavior of drilling fluid. Generalized Newtonian formulations are the most popular models for drilling fluids due to their simplicity in spite of their inabilities to predict transient and elastic behavior of such fluids. In this paper, we have developed a mathematical model to predict transient and steady state rheological behavior of the complex fluids on the scale between the microscopic and macroscopic which is named mesoscopic scale. Constitutive and governing equations are obtained using the generalized bracket formalism which is based on the thermodynamics of flowing systems in that Hamiltonian mechanics has been used to describe the transport phenomena of internal microstructures. The model is developed for the suspension of bentonite/polymer dispersion and compared with experimental rheological data of different types of drilling fluids under transient and steady state condition. Comparison of model prediction with published data in the literature shows that the model is able to predict rheological behavior of bentonite muds satisfactorily.

Advances in the biorefinery of Sargassum muticum: Valorisation of the alginate fractions

Sargassum muticum is an invasive brown seaweed that causes a negative impact on ecology, fishing and recreational activities, and was also associated with changes in biodiversity by competing for light, space and nutrients with autochthonous algae. Marine brown seaweeds contain different valuable components, such as alginate, fucose rich sulfated polysaccharides (known as fucoidans) and phlorotannins. In order to extract these compounds, subcritical water extraction or autohydrolysis processing was proposed using only water as solvent and operating at high temperature and pressure. Under non isothermal conditions previously optimized for the extraction of fucoidans and phlorotanins (150 and 170 °C), the biopolymeric and biologically interesting compounds were extracted and characterized, with particular emphasis on the alginate fraction. Rheological results of tested alginates indicated certain depolymerisation degree. Autohydrolysis temperature notably modified the viscoelastic features of precipitated alginates, exhibiting those treated at 150 °C stronger viscoelastic properties. All tested systems showed the viscoelastic behaviour characteristic of polymer solutions in the semi-dilute regime that present entanglements. Experimental rheological data sets for precipitated alginates were adequately modelled using Cross-Williamson and Maxwell models. Cox-Merz rule was evaluated for tested alginates. The valorisation of the alginate fraction defines a more efficient approach to the biorefinery concept applied to brown seaweeds for the production of components with interesting biological properties.