Reference Viscosity Research Articles

Thermal and magnetic evolution of Mercury with a layered Fe-Si(-S) core

Elucidating the structure and composition of Mercury is important for understanding its interior dynamics and evolution. The planet is characterised by unusual chemical characteristics and a weak magnetic field generated in a large metallic core, and its early evolution was also marked by the presence of a magnetic field, widespread volcanism and global contraction. Here we develop a parameterised model of coupled core-mantle thermal and magnetic evolution considering a layered Fe-Si(-S) core structure with chemical and physical properties of the mantle and the core based on previous laboratory studies. We seek successful solutions that are consistent with observations of Mercury's long-lived dynamo, total global contraction, present-day crustal thickness, and present-day interior structure. Successful solutions have a mantle reference viscosity >1021 Pa s (corresponding to a present-day bulk mantle viscosity >2×1020 Pa s), a silicon concentration in the core >13 wt%, a present inner core radius of ∼1000−1200 km and a thermally stable layer ∼ 500−800 km thick below the core-mantle boundary. Our results show that if present, a molten FeS layer atop the core has minimal effect on Mercury's long-term thermal and magnetic evolution. Predictions from our models can be tested with upcoming Bepi-Colombo observations.

A two-capillary viscometer for temperatures up to 473 K and pressures up to 100 MPa—operation and verification at low pressure

In this paper, we described the design and construction of a new two-capillary viscometer with several novel technical solutions for viscosity and density measurements. Our design, which is based on the low-pressure principle, featured numerous improvements in hardware and procedure that allowed the greatly extended range of pressure. The new design adopted a (2 × 2) capillary configuration, utilizing different combinations of four capillaries to enable viscosity measurements with a wide range of flow rates, temperatures, and pressures. The design temperature range is 213 K–473 K, and the pressure range is up to 100 MPa. The viscometer was specifically designed for measuring the viscosity of pure CO2 and CO2-rich mixtures, addressing the scarcity of data in conditions relevant to carbon capture, transport, and storage. Our facility is capable of viscosity measurements in different thermodynamic states; gaseous, liquid, supercritical, and critical regions. A commercial densimeter is integrated to measure density under the same temperatures and pressures. We aimed for a total uncertainty target of better than 0.03%. The performance of the viscometer was validated by measurements with pure CO2 at 298.15 K and zero density. We observed a deviation of less than 0.03% between the reference viscosity of CO2 of this work and accurately calculated data using ab initio quantum mechanics with a standard uncertainty of 0.2%. Our primary focus in this paper was to provide a detailed description of the design and construction of the apparatus, emphasizing improvements and introducing new solutions to other research groups in constructing similar instruments suitable for low- and high-pressure viscosity measurements with high accuracy.

Gas viscosities from a semiconductor-manufacturing mass-flow controller

We obtain gas viscosities with a pressure-based mass-flow controller used for semi-conductor manufacturing, a rate-of-change approach, and a physics-based calculation. The novelty of this method is that it is used in an industrial process whose main goal is not to measure viscosities. In this way, for pressures of the order of 10 kPa and 25 ∘C and 35 ∘C, we obtain for seven gases viscosities with mean absolute errors with respect to reference viscosities of less than 1%. Using this method, we report viscosities for two semiconductor-manufacturing gases not available in the open literature: hexafluoroisobutene (CAS # 382-10-5) and 1,1,3,3,3-pentafluoropropene (690-27-7).

On the Relative Importance of Buoyancy and Thickening of Aging Lithosphere in Mantle Upwelling and Crustal Production Beneath Global Mid‐Ocean Ridge System

AbstractBeneath mid‐ocean ridges, mantle upwelling and decompression melting are fundamental processes contributing to the formation of oceanic crust. Previous geodynamic models have suggested that mantle upwelling driven by separating plates can be intensified by thermochemical buoyancy and the thickening of aging lithosphere, resulting in thicker crust. However, the relative contributions of these factors to crustal accretion remain uncertain. We conducted numerical modeling in three scenarios to investigate this: (a) buoyant flow models incorporating age‐dependent lithospheric thickening as a reference; (b) passive flow models incorporating age‐dependent lithospheric thickening to isolate the effect of buoyancy; and (c) passive flow models that neglect age‐dependent lithospheric thickening to isolate its effect. Models are performed under varying potential mantle temperatures (Tp), viscosity structures, and spreading rates. The model‐predicted crustal thickness suggests that both buoyancy and thickening of aging lithosphere increasingly contribute to crustal production as spreading rate decreases. However, given the range of reference mantle viscosities examined here (1019–1020 Pa s), except in ultraslow spreading rates with lower reference viscosity and warmer Tp, the impact of the thickening of aging lithosphere predominates over buoyancy. Furthermore, the relative importance of buoyancy‐induced crustal production increases as spreading rates decrease. Variations in Tp further amplify the variability in crustal thickness compared to that at fast‐spreading ridges where passive upwelling dominates, when combined with 3‐D effects of buoyant flow on altering axial crustal production at ultraslow‐spreading ridge segments. This 4‐D effects of buoyant flow on melt production may explain the observed more variable crustal thickness at ultraslow‐spreading ridges.

Viscosity of imidazolium ionic liquids and mixtures of ILs from entropy scaling using the PC-SAFT and ePC-SAFT equations of state

Entropy scaling is a promising method for the development of engineering models for transport properties of ionic liquids (ILs). Here we present two entropy scaling models for the viscosity of ionic liquids and their mixtures at various temperatures and pressures: 1) a molecular-based approach treating each IL as one pure species and using the PC-SAFT equation of state (EoS); and 2) treating each ion as a separate species and using the ePC-SAFT EoS. Both approaches were correlated to viscosity data of 12 ionic liquids from the imidazolium cation class and three different anions comprising 4233 data points with overall average absolute deviations (%AARDs) of less than 8 % over a wide range of temperature and pressures. The ion-based approach was better able to correlate IL viscosity at low temperatures and/or high pressure (to 4011 bar) than the molecular approach. The functional entropy-scaling coefficients for both models were regressed as linear functions of molecular weight, which allowed good prediction of another nine ionic liquids not in the training set. Interestingly, both approaches well predict the viscosity of binary mixtures of imidazolium ionic liquids. In addition, the effect of various reference viscosities and comparison with the Peng-Robinson EoS was performed.

Europa’s structural conditions for the existence of subsurface ocean and the absence of metallic core-driven magnetic field

During the Galileo spacecraft’s flyby of Europa, magnetic field measurements detected an inductive signal due to the response of Europa’s interior conductors to temporal fluctuations in the Jovian magnetic field. In contrast, no signatures of intrinsic magnetic field originating from the dynamo motion in the metallic core were acquired. These measurements suggest that a global sub-surface ocean containing electrolytes exists beneath the solid ice shell and that the metallic core lacks convection. Europa’s interior is expected to be divided into the metallic core, rocky mantle and hydrosphere based on the moment of inertia factor estimated from gravity field measurements. Specifically, the thickness of the outermost water layer is 120–170 km, and the radius of the metallic core is 0.12–0.43 times the surface radius. No systematic investigation of Europa’s internal evolution has been conducted to estimate the current state of the subsurface ocean and to explain the absence of a core dynamo field within such uncertainty for internal structure and material properties (especially ice properties). Herein, I performed a numerical simulation of the long-term thermal evolution of Europa’s interior and investigated the temporal changes in the ocean thickness as well as the temperature and heat flow of the metallic core. If the ice reference viscosity is greater than 5 × 1014 Pas, the sub-surface ocean can persist even in the absence of tidal heating. In the case of a tidal heating of 10 mW/m2 and 20 mW/m2, the ice shell thickness is ≤90 km if the ice reference viscosity is ≥1 × 1015 and 1 × 1014 Pas, respectively. Regardless of the ice reference viscosity, if the tidal heating is ≥50 mW/m2, the shell thickness will be ≤40 km. The thermal history of the metallic core is determined by the hydrosphere thickness and the metallic core density, and is unaffected by variations in the ice shell (ocean) thickness. Preferred conditions for the absence of the core dynamo include CI chondritic abundance for the long-lived radioactive isotopes, lower initial core–mantle boundary (CMB) temperature and thicker hydrosphere. The core may be molten without convection if the composition is near the eutectic in a Fe–FeS alloy, or not molten (without convection) if the composition is near the Fe or FeS endmember. Specifically, if the rocky mantle has a CI chondritic radioisotope abundance, any core composition and hydrosphere thickness allow the absence of the core dynamo if the initial temperature at the CMB is lower than 1,250 K. If the rocky mantle has the ordinary chondritic radioisotope abundance, or a higher initial temperature (∼1,500 K) at the CMB, the core density lower than 6,000 kg/m3 is preferred for the absence of the core dynamo. In the case of the core composition near the eutectic one, a hydrosphere thicker than 150 km is required for the lacking core dynamo. The lower pressure of Europa’s rocky mantle due to its thinner hydrosphere compared with that of Ganymede may facilitate heat transfer in the mantle, lowering its temperature and making dynamo motion more challenging.

Dynamic Viscosity Measurement Method Based on the Stokes Drag of Prolate Ellipsoidal Mass

Viscometer plays an important role in the field of tribology. One way to measure viscosity is to use the Stokes drag principle in the underdamped harmonic oscillation phenomenon. This paper proposes a dynamic viscosity measurement method based on the related physical laws. Our experimental model involves a prolate ellipsoidal mass that experiences underdamped harmonic oscillation within viscous liquid samples. We observed the oscillations of the prolate ellipsoid to obtain the viscous damping coefficient of each sample and substituted it to the theoretical formula of dynamic viscosity. Experimental data suggest that the mathematical model has failed to predict the viscosity values of the samples. In addition, the regression curve of the reference viscosity and the measured viscous damping coefficient shows that the two quantities have an exponential relation instead of linear relation as explained in the theoretical model. We considered the regression formula as the empirical measurement transfer function and used it to measure the viscosity of an ISO VG 150 industrial oil sample. This measurement resulted in a 2.40 % of relative error percentage. Lastly, this measurement method is only valid for measuring samples with viscosities ranging from 0.0400 Pa s to 0.256 Pa s.

Holistic Evaluation of Reservoir Oil Viscosity in Breidablikk Field – Including Mud Gas Logging Approach

Breidablikk is a green field on the Norwegian Continental Shelf that just started the preproduction drilling of 23 wells in two structures. We have two reservoir fluid samples from exploration wells in each structure with relatively high viscosity of 4 and 8 cP, respectively. Our dynamic reservoir simulations on the Breidablikk Field indicate that any change in the viscosity in each direction can lead to a 20 to 30% difference in oil recovery. Therefore, updating our reservoir models with the viscosity distribution in the field along with the drilling activities is important. Currently, our models assume homogeneous reservoir oil viscosities across each structure. In this study, our primary aim is to conduct a holistic evaluation of the reservoir oil viscosity, using multiple methods to determine the most effective approach for qualitatively mapping the oil viscosity across the field, distinguishing between the low- and high-viscosity regions. The technologies chosen for this assessment are standard mud gas data, advanced mud gas data, and analysis of oil extracts from cuttings, given they have previously demonstrated their capability to estimate fluid properties while drilling or within a limited time frame, as evidenced by the work of Cutler et al. (2022). The methods were compared using pressure/volume/temperature (PVT) measurements as a benchmark. As of today, this method is considered the most reliable to obtain reservoir fluid properties, and in consequence, these measurements serve as the reference viscosity values in the study. The results of our analysis in Breidablikk show that an approach based on advanced mud gas data provide an oil quality classification that distinguishes between high- and low-viscosity reservoir oils, using the ethane/n-pentane ratio as the best parameter correlated to reservoir oil viscosity in Breidablikk. The threshold for the two viscosity regions is identified from a reservoir fluid database from the Breidablikk-Grane area, and the oil viscosity region estimated from advanced mud gas data agrees well with the PVT measurements. The viscosity estimation using a standard mud gas approach based on methane to propane compositions indicates that this technology cannot correctly differentiate between low- and high-viscosity region wells in the Breidablikk Field. Hence, it is not recommended. Further findings from our analysis indicate that the utilization of oil-based mud, combined with a high drilling speed, significantly affects the quality of the cuttings in Breidablikk. Consequently, the application of traditional geochemical analysis methods on cutting extracts is challenging. Therefore, this method is not recommended for the qualitative identification of the viscosity region of a given well. Benchmarking all available technologies allows us to select a real-time, reliable, and cost-efficient method to qualitatively estimate reservoir oil viscosity in Breidablikk. The selected method is field-specific and not general for other heavy oil fields. In summary, providing an accurate reservoir oil viscosity mapping at an early stage in field development plays a crucial role in the further optimization of drilling targets and ultimately leads to improved oil recovery (Halvorsen et al., 2016; Maraj et al., 2021).

Synergistic enhancing effect of xanthan gum, carboxymethyl cellulose and citric acid on the stability of betacyanins in fermented red dragon fruit (Hylocereus polyrhizus) drink during storage

Nowadays, the demand for using healthy natural pigments (betacyanins) in the food industry is increasing. The present study aimed to overcome the circumstances that render the betacyanins instability in the red dragon fruit drink using mild approaches. These included optimised fermentation, incorporation of anionic polysaccharide mixture solution [xanthan gum (XG, 0.30–0.40 %, w/v) and carboxymethyl cellulose (CMC, 0.50–0.90 %, w/v)] and also addition of citric acid (CA, 0.05–0.20 %, w/v). The results of this study showed that the hydrocolloid mixture solution of XG and CMC significantly increased the samples' viscosity, pH and °Brix but reduced the aw, while betacyanins concentration had no significant change. The incorporation of CA at increasing concentration only reduced the samples’ pH significantly without affecting the viscosity, aw and °Brix. Among all fermented samples, Formulation 3E (0.40 % XG + 0.50 % CMC + 0.20 % CA) had achieved the desired commercial reference viscosity while also successfully minimised betacyanins degradation from 60.18 % to 14.72 %, had the best pH stability and no significant change in viscosity, aw and °Brix values after 4-week storage at 25 °C. The fermented red dragon fruit drink with betacyanins stabilised by Formulation 3E can be produced and served as an independent functional drink product and as a stable, functional ingredient (natural colourant) for the food industry.

Rapid determination of viscosity and viscosity index of lube base oil based on near-infrared spectroscopy and new transformation formula

Viscosity and viscosity index are the key product properties in lubricating oil production process. Rapid and even online analysis of viscosity and viscosity index through near-infrared (NIR) spectroscopy combined with chemometrics is helpful to optimize the production process. However, due to the nonlinear effect, the commonly used linear multivariate correction method is not effective. In this work, the feasibility of four existing viscosity linear transformation formulas for establishing NIR models was studied, and a new viscosity linear transformation formula was developed based on the viscosity-gravity constant. The experimental results showed that three of the four existing viscosity linear transformation formulas made some improvement on the viscosity prediction of base oil, but not as good as the newly established viscosity linear transformation formula. For viscosity index, the accuracy of modeling with reference viscosity index directly was much better than calculating by prediction viscosity value. Both of the viscosity and viscosity index prediction results of NIR analysis were in good agreement with the results of reference method, indicating that the determination can meet the needs of rapid and on-line analysis in industrial field.

Prediction of petroleum viscosity from molecular weight and density

165 crude oils with viscosity, density, and molecular weight variation in the range 0.54 – 24135cP; 0.746 – 1.016 g/cm3; 117–579 g/mol respectively were examined for viscosity prediction using eight available in the literature models and three more, developed in this work models. The best empirical model was that of Sinha et al., 2020 with % AAD (absolute average deviation) = 18.2 %, The ANN (artificial neural network) model for the data set of the 165 crude oils outperformed the empirical correlations with % AAD = 17.7 %. 93 crude oils with viscosity, density, molecular weight, and SARA composition data variation in the range 2.3 – 23 000cP; 0.819 – 0.992 g/cm3; 179–579 g/mol; Sat.: 26.0–79.3 %; Aro:11.9–52.8 %; Res.: 2.5–30.9; Asp.:0.1–19.6 % respectively were also examined for viscosity prediction by the available in the literature empirical correlations and another new developed empirical correlation that includes besides molecular weight and density, the crude oil saturate content. The best empirical model was that developed in this work with saturate content inclusion, that showed % AAD = 23.8 %. The ANN model for the data set of 93 crude oils again outperformed the empirical correlations with % AAD = 18.8 %. The most accurate model predicting viscosity was found the new developed in this work model on the base of a reference viscosity at a particular temperature and molecular weight with %AAD = 2.5 %.

Shear-Wave Elastography and Viscosity PLUS for the Assessment of Peripheric Muscles in Healthy Subjects: A Pre- and Post-Contraction Study.

Viscosity is a novel parameter, recently introduced in the use of elastographic techniques, correlating to shear-wave dispersion. The purpose of this study was to provide normal reference viscosity values for the peripheral muscles in healthy volunteers. This prospective study included 38 subjects who underwent US examinations between November 2021 and January 2022. Measurements were taken on the calf and the deltoid muscles in both pre- and post-contraction states. The age range was 21–29 years, with a median of 26 years. The SWE and ViPLUS values in the deltoid muscles were significantly higher than in the soleus muscles in both pre- and post-contraction sets (p = 0.002). There were statistically significant differences between the pre- and post-contraction values for both the SWE and ViPLUS values in the subgroup analysis. The ICC estimates and the 95% confidence intervals were based on a mean rating (k = 2), an absolute agreement, and a two-way random-effects model, demonstrating excellent agreement between the measurements taken by the two examiners.

Physics Augmented Correlations and Machine Learning Methods to Accurately Calculate Dead Oil Viscosity Based on the Available Inputs

Summary Viscosity is one of the key parameters that is necessary to describe the fluid flow and pressure propagation in porous media as well as flow in pipes and various types of conduits. In this study, we have developed two different approaches to be able to estimate the viscosity seamlessly from a fraction to a million centipoise range. Our first approach was based on a trainable explicit expression that uses a reference viscosity measured at any temperature. This is a very common situation as the viscosity may have already been measured at reservoir temperature. Using the reference viscosity concept for many data sets, we also demonstrated the validity and tuneability of the proposed approach to predict the viscosities for the entire temperature range of interest. Our second method is developed for the cases that we did not have any viscosity measurements or no valid viscosity measurements. For such circumstances, we have utilized the extreme gradient boost (XGB) method algorithm (XGB Method) (Friedman 2001; Chen et al. 2015) using leave-one-out cross-validation (LOOCV) (Shao 1993), to be able to estimate the viscosity for the entire range of viscosities that are encountered for crudes. Some of the details of hybrid methods and other regression/machine learning methods and the role of the asphaltenes are already discussed by Sinha et al. (2019, 2020). The current approach uses a richer data set than any of the published papers with very limited input parameters: reservoir temperature, API gravity, and molecular weight, and the tuneability of the models is constrained with the molecular weight of the crudes.

Influence of Thermal Stratification on the Structure and Evolution of the Martian Core

AbstractThe apparent end of the internally generated Martian magnetic field at 3.6–4.1 Ga is a key event in Martian history and has been linked to insufficient core cooling. We investigate the thermal and magnetic evolution of the Martian core and mantle using parameterized models and considered three improvements on previous studies. First, our models account for thermal stratification in the core. Second, the models are constrained by estimates for the present‐day areotherm. Third, we consider core thermal conductivity, , values in the range 5–40 W as suggested by recent experiments on iron alloys at Mars core conditions. The majority of our models indicate that the core of Mars is fully conductive at present with core temperatures greater than 1940 K. All of our models are consistent with the range of W . Models with an activation volume of 6 (0) require a mantle reference viscosity of Pa s.

Scaling laws for stagnant-lid convection with a buoyant crust

SUMMARY Stagnant-lid convection, where subduction and surface plate motion is absent, is common among the rocky planets and moons in our solar system, and likely among rocky exoplanets as well. How stagnant-lid planets thermally evolve is an important issue, dictating not just their interior evolution but also the evolution of their atmospheres via volcanic degassing. On stagnant-lid planets, the crust is not recycled by subduction and can potentially grow thick enough to significantly impact convection beneath the stagnant lid. We perform numerical models of stagnant-lid convection to determine new scaling laws for convective heat flux that specifically account for the presence of a buoyant crustal layer. We systematically vary the crustal layer thickness, crustal layer density, Rayleigh number and Frank–Kamenetskii parameter for viscosity to map out system behaviour and determine the new scaling laws. We find two end-member regimes of behaviour: a ‘thin crust limit’, where convection is largely unaffected by the presence of the crust, and the thickness of the lithosphere is approximately the same as it would be if the crust were absent; and a ‘thick crust limit’, where the crustal thickness itself determines the lithospheric thickness and heat flux. Scaling laws for both limits are developed and fit the numerical model results well. Applying these scaling laws to rocky stagnant-lid planets, we find that the crustal thickness needed for convection to enter the thick crust limit decreases with increasing mantle temperature and decreasing mantle reference viscosity. Moreover, if crustal thickness is limited by the formation of dense eclogite, and foundering of this dense lower crust, then smaller planets are more likely to enter the thick crust limit because their crusts can grow thicker before reaching the pressure where eclogite forms. When convection is in the thick crust limit, mantle heat flux is suppressed. As a result, mantle temperatures can be elevated by 100 s of degrees K for up to a few Gyr in comparison to a planet with a thin crust. Whether convection enters the thick crust limit during a planet’s thermal evolution also depends on the initial mantle temperature, so a thick, buoyant crust additionally acts to preserve the influence of initial conditions on stagnant-lid planets for far longer than previous thermal evolution models, which ignore the effects of a thick crust, have found.

Melting Process and Viscosity of Bohemian Historical Glasses Studied on Model Glasses

Analyzing the chemical composition of archaeological glasses can provide an insight into their provenance and raw materials used in their making. However, to the authors’ knowledge, the historical production process itself and melting characteristics of the glasses have not yet been extensively investigated. The main focus of this paper is to describe the melting process of three main types of Bohemian historical glasses: Gothic (14th–1st half of 16th c.); Renaissance (16th–17th c.); and Baroque (end of 17th–18th c.). The model glasses were prepared from natural raw materials and processes that take place during melting were investigated using optical microscopy, SEM-EDS, XRD, and DTA-TG methods. Furthermore, the viscosity of model glasses and thermal dilatation was measured and used to calculate the reference viscosity points. The results illustrate the complexity of historical glass melting, as well as the technological progress between different periods.

Toward Constraining Mars' Thermal Evolution Using Machine Learning

AbstractThe thermal and convective evolution of terrestrial planets like Mars is governed by a number of initial conditions and parameters, which are poorly constrained. We use Mixture Density Networks (MDN) to invert various sets of synthetic present‐day observables and infer five parameters: reference viscosity, activation energy and activation volume of the diffusion creep rheology, an enrichment factor for radiogenic elements in the crust, and initial mantle temperature. The data set comes from 6,130 two‐dimensional simulations of the thermal evolution of Mars' interior. We quantify the possibility of constraining a parameter using the log‐likelihood value from the MDN. Reference viscosity can be constrained to within 32% of its entire range (1019 − 1022 Pa s), when all the observables are available: core‐mantle‐boundary heat flux, surface heat flux, radial contraction, melt produced, and duration of volcanism. Furthermore, crustal enrichment factor (1–50) can be constrained, at best, to within 15%, and the activation energy (105 − 5 × 105 J mol−1) to within 80%. Initial mantle temperature can be constrained to within 39% of its range (1,600–1,800 K). Using the full present‐day temperature profile or parts of it as an observable tightens the constraints further. The activation volume (4 × 10−6 − 10 × 10−6 m3 mol−1) cannot be constrained. We also tested different levels of uncertainty in the observables and found that constraints on different parameters loosen differently, with initial temperature being the most sensitive. Finally, we present how a joint probability model for all parameters can be obtained from the MDN.

A nonlinear and time‐dependent visco‐elasto‐plastic rheology model for studying shock‐physics phenomena

AbstractWe present a simple and efficient implementation of a viscous creep rheology based on diffusion creep, dislocation creep, and the Peierls mechanism in conjunction with an elasto‐plastic rheology model into a shock‐physics code, the iSALE impact code. Our approach is based on the calculation of an “effective viscosity” which is then used as a reference viscosity for any underlying viscoelastic (or even visco‐elasto‐plastic) model. Here we use a Maxwell‐model which best describes stress relaxation and is therefore likely most important for the formation of large meteorite impact basins. While common viscoelastic behavior during mantle convection or other slow geodynamic or geological processes is mostly controlled by diffusion and dislocation creep, we show that the Peierls mechanism dominates at the large strain rates that typically occur during meteorite impacts. Thus, the resulting visco‐elasto‐plastic rheology allows implementation of a more realistic mantle behavior in computer simulations, especially for those dealing with large meteorite impacts. The approach shown here opens the way to more faithful simulations of large impact basin formation, especially in elucidating the physics behind the formation of the external fault rings characteristic of large lunar basins.

Entropy-scaling based pseudo-component viscosity and thermal conductivity models for hydrocarbon mixtures and fuels containing iso-alkanes and two-ring saturates

Recently, Rokni et al. [1,2] developed entropy-scaling based pseudo-component techniques to predict the viscosity and thermal conductivity of hydrocarbon mixtures and fuels up to high temperature and pressure conditions using only two calculated or measured mixture properties (number average molecular weight and hydrogen-to-carbon ratio). The models are accurate for many hydrocarbon mixtures that do not contain branched compounds (7 and 2% mean absolute percent deviation (MAPD) for viscosity and thermal conductivity, respectively, on average). However, predictions for some hydrocarbon mixtures and fuels containing iso-alkanes are often less accurate (16 and 19% MAPD for viscosity and thermal conductivity, respectively, on average). To improve predictions, it was proposed by Rokni et al. [1,2] to fit one model parameter using an experimental reference viscosity or thermal conductivity data point, which may not be ideal if experimental reference data are not available. In order to make these models more practical, this study fits empirical correlations for the model parameters, so that accurate predictions can be made without fitting model parameters. The correlations enable viscosity and thermal conductivity predictions for a wide range of hydrocarbon mixtures and fuels, including those containing branched alkanes, and no longer require input of any experimental reference viscosity or thermal conductivity data. The correlations are temperature (fit to data from 288 to 550 K) and pressure (fit to data from 1 to 4,400 bar) dependent and are functions of average molecular weight, hydrogen-to-carbon ratio, iso-alkane and two-ring saturate concentrations. Viscosity and thermal conductivity predictions were found to improve to within 5 and 2% average MAPD, respectively, relative to experimental data for the hydrocarbon mixtures and fuels considered in this study.

Higher-Order Models for Resonant Viscosity and Mass-Density Sensors.

Advanced fluid models relating viscosity and density to resonance frequency and quality factor of vibrating structures immersed in fluids are presented. The numerous established models which are ultimately all based on the same approximation are refined, such that the measurement range for viscosity can be extended. Based on the simple case of a vibrating cylinder and dimensional analysis, general models for arbitrary order of approximation are derived. Furthermore, methods for model parameter calibration and the inversion of the models to determine viscosity and/or density from measured resonance parameters are shown. One of the two presented fluid models is a viscosity-only model, where the parameters of it can be calibrated without knowledge of the fluid density. The models are demonstrated for a tuning fork-based commercial instrument, where maximum deviations between measured and reference viscosities of approximately ±0.5% in the viscosity range from 1.3 to 243 mPas could be achieved. It is demonstrated that these results show a clear improvement over the existing models.