Fluid Mass Density Research Articles

Calculation Modeling of Adsorbed and Bulk-Phase Oil Resources Based on Molecular Dynamics Simulations

Summary Nanopores prevalent in shale reservoirs significantly impact shale oil occurrence characteristics due to the strong intermolecular forces between crude oil molecules and the pore walls. Unlike bulk-phase oil, which is more readily recoverable with current technologies, the behavior of oil within these small-scale environments presents unique challenges. This study utilizes molecular dynamics simulations (MDSs) to investigate the characteristics of shale oil in slit nanopores, with the goal of refining a model that estimates the quantities of both bulk and adsorbed oil in shale reservoirs. We constructed models for three types of nanopores—organic graphene, illite, and quartz—using n-hexane (n-C6H14) as a proxy for shale oil. Our analysis reveals that mineral composition significantly influences fluid adsorption capacity, ranked as graphene > illite > quartz. Unlike prior research, we found that the critical flow pore diameter, which dictates the transition from adsorbed to free-flowing oil, cannot be simplistically equated to the combined thickness of adsorption layers. Specifically, in graphene pores with a diameter of 3.8 nm, the fluid mass density at the pore center still exhibits adsorption layer characteristics, forming up to nine layers. Building on these insights, we revised the shale reservoir resource estimation model to account for adsorption variances across different pore types. Our findings highlight the significant role of adsorbed oil in nanopores within shale reservoirs. Data from the Gulong shale oil block in the Daqing oil field indicate that adsorbed oil constitutes 37.15% of geological reserves, while bulk-phase oil accounts for the remaining 62.85%. This research provides essential data for accurately calculating shale oil reserves in nanopores, which are crucial for the effective exploitation of shale oil reservoirs.

Thermal Conductivity of a Fluid-Filled Nanoporous Material: Underlying Molecular Mechanisms and the Rattle Effect.

Nanoporous materials are central to the energy and environmental crisis, with key applications in adsorption, separation, and catalysis. While confinement and surface effects on fluids severely confined in their porosity are well documented, the thermal behavior of nanoporous solids subjected to fluid adsorption remains puzzling in many aspects. With striking phenomena such as the so-called rattle effect, through which fluid/solid collisions decrease the overall thermal conductivity, the solid thermal conductivity and, more generally, heat transfer and dispersion in these complex systems challenge classical approaches (e.g., mixing rules including effective medium approaches fail to capture such effects as shown here). In particular, a robust molecular framework to describe the crossover between the decrease in thermal conductivity through the rattle effect in very narrow pores and the increase in thermal conductivity when replacing vacuum with a fluid phase in larger pores is still missing. Here, using a prototypical model of fluid-filled nanoporous materials (a Lennard-Jones phase confined in an all-silica zeolite), we perform a molecular simulation study to shed light on the parameters that govern the rattle effect in nanoporous solids. First, by varying the fluid/fluid, fluid/solid, and solid/solid interaction strengths as well as the fluid number density and mass density, we unravel the ingredients that lead to the essential coupling between fluid adsorption and phonon transport. Second, despite this complex interplay, inspired by pioneering molecular approaches on the rattle effect, we show that all data obey a simple statistical physics model that relies on the change in the speed of sound due to the fluid adsorbed density and the decrease in phonon lifetime due to scattering by fluid molecules. This framework, which provides a simple formalism to rationalize the thermal behavior of this class of solid/fluid composites, points to a decrease in thermal conductivity upon fluid confinement (up to 30% in some cases). Such an effect paves the way for the design of novel applications involving fluids in interaction with nanoporous materials.

Effect of surface structure on fluid flow and heat transfer in cold and hot wall nanochannels

Nanochannels consisting of hot and cold walls with periodic rectangular and triangular nanostructures were simulated by molecular dynamics in this paper, the periodic size dimensionless parameters φ was defined to describe the dimension of nanostructures on the wall. The results show that the addition of nanostructures leads to the variation of mass density distribution of fluid near the wall. A hot wall with nanostructures can promote the appearance of a fluid high-potential area near it. The discrepant attraction for fluid from the wall caused by the different wall conditions leads to different flow characteristics in nanochannels. Fluid velocity growth rate near the hot wall is 10.5% higher than that near the cold wall. Average velocity of the fluid near the hot wall is 5.1% higher than that of fluid near the cold wall. A wall with rectangular nanostructures at φ = 0.28 shows minimum flow resistance among rough hot walls, while a wall with triangular nanostructures at φ = 0.14 has minimum flow resistance among rough cold walls. Heat is transferred from the hot wall to the cold wall through fluid flow. Wall conditions impact the heat transfer situation of fluid in flow boundary by changing the fluid mass density contribution. The addition of nanostructures and decrease of nanostructures size is beneficial for heat transfer while unfavorable for fluid flow, convective heat transfer was influenced by their combination. For a wall with 300 K, the addition of rectangular nanostructures at φ = 0.07 has the best convective heat transfer performance. For a wall with 200 K temperature, increasing triangular nanostructures at φ = 0.14 on the wall can reach the best convective heat transfer capacity. This paper can provide a theoretical foundation for the optimization of nanochannels to achieve best convective heat transfer ability.

Lift force in odd compressible fluids.

When a body moves through a fluid, it can experience a force orthogonal to its movement called lift force. Odd viscous fluids break parity and time-reversal symmetry, suggesting the existence of an odd lift force on tracer particles, even at vanishing Reynolds numbers and for symmetric geometries. It was previously found that an incompressible odd fluid cannot induce lift force on a tracer particle with no-slip boundary conditions, making signatures of odd viscosity in the two-dimensional bulk elusive. By computing the response matrix for a tracer particle, we show that an odd compressible fluid can produce an odd lift force. Using shell localization, we provide analytic expressions for the drag and odd lift forces acting on the tracer particle in a steady state and also at finite frequency. Importantly, we find that the existence of an odd lift force in a steady state requires taking into account the nonconservation of the fluid mass density due to the coupling between the two-dimensional surface and the three-dimensional bulk fluid.

Accurate mass flow and density of bubbly liquids using speed of sound augmented Coriolis technology

Speed of sound augmented Coriolis technology utilizes a process fluid sound speed measurement to improve the accuracy of Coriolis meters operating on bubbly liquids. This paper presents a theoretical development and experimental validation of speed of sound augmented Coriolis meters. The approach utilizes a process fluid sound speed measurement, based on a beam-forming interpretation of a pair of acoustic pressure transducers installed on either side of a Coriolis meter, to quantify, and mitigate, errors in the mass flow, density, and volumetric flow reported by two modern, dual bent-tube Coriolis meters operating on bubbly mixtures of air and water with gas void fractions ranging from 0% to 5%. By improving accuracy of Coriolis meters operating on bubbly liquids, speed of sound augmented Coriolis meters offer the potential to improve the utility of Coriolis meters on many existing applications and expand the application space of Coriolis meters to address additional multiphase measurement challenges.The sources of measurement errors in Coriolis meters operating on bubbly liquids have been well-characterized in the literature. In general, conventional Coriolis meters interpret the mass flow and density of the process fluid using calibrations developed for single-phase process fluids which are essentially incompressible and homogeneous. While these calibrations typically provide sufficient accuracy for single-phase flow applications, their use on bubbly liquids often results in significant errors in both the reported mass flow, density and volumetric flow. Utilizing a process fluid sound speed measurement and an empirically-informed aeroelastic model of bubbly flows in Coriolis meters, the methodology developed herein compensates the output of conventional Coriolis meters for the effects of entrained gas to provide accurate mass flow, density, volumetric flow, and gas void fraction of bubbly liquids.Data presented are limited to air and water mixtures. However, by influencing the effective bubble size through mixture flow velocity, the bubbly liquids tested exhibit decoupling characteristics which spanned theoretical limits from nearly fully-coupled to nearly fully-decoupled flows. Thus, from a non-dimensional parameter perspective, the data presented is representative of a broad range of bubbly liquids likely to be encountered in practice.

Local Thermodynamic Description of Isothermal Single-Phase Flow in Simple Porous Media

Darcy’s law for porous media transport is given a new local thermodynamic basis in terms of the grand potential of confined fluids. The local effective pressure gradient is determined using non-equilibrium molecular dynamics, and the hydraulic conductivity and permeability are investigated. The transport coefficients are determined for single-phase flow in face-centered cubic lattices of solid spheres. The porosity changed from that in the closest packing of spheres to near unity in a pure fluid, while the fluid mass density varied from that of a dilute gas to a dense liquid. The permeability varied between 5.7 times {10^{-20}} hbox {m}^2 and 5.5 times {10^{-17}} hbox {m}^2, showing a porosity-dependent Klinkenberg effect. Both transport coefficients depended on the average fluid mass density and porosity but in different ways. These results set the stage for a non-equilibrium thermodynamic investigation of coupled transport of multi-phase fluids in complex media.

Automatic Measurement of the Dependence on Pressure and Temperature of the Mass Density of Drilling Fluids

Summary Drilling fluids are subject to substantial variations in pressure and temperature while they are circulated in a well. These changes are so great that the mass density of the drilling fluid varies significantly during circulation. Accurate estimation of the hydrostatic and hydrodynamic pressures therefore requires a reliable model of the pressure and temperature dependence of the mass density of the drilling fluid. Usually, the mass density of a drilling fluid is measured manually with a mud balance. The pressure and temperature dependence of the mass density of the fluid [i.e., its pressure, volume, and temperature (PVT) behavior] is then calculated from a PVT model of its components and their relative proportions. However, variations in the composition of the fluid mix and uncertainties in the PVT behavior of each component may lead to inaccuracies. To overcome these limitations, an apparatus has been designed to measure the PVT behavior of the drilling fluid directly and automatically. The setup measures both the mass density and the speed of sound of the fluid at specific conditions of pressure and temperature. It is possible to estimate the adiabatic compressibility from the speed of sound in the liquid mix. The device utilizes a heat exchanger from which the specific heat capacity of the drilling fluid can be derived. The isothermal compressibility can be calculated by combining the specific heat capacity and the adiabatic compressibility. While estimating the specific heat capacity using the heat exchanger, the thermal conductivity of the fluid is also estimated as a byproduct. A PVT model of the drilling fluid is obtained by combining measurements made at different conditions of pressure and temperature. The automatic and continuous provision of drilling fluid PVT behavior enhances the precision of model predictive drilling control systems and, at the same time, can simplify their configuration, therefore making them more accessible to any drilling operation.

Wave Propagation for Axisymmetric Wave Motion in Buried Pipes Conveying Viscous Flowing Fluid

This work investigated the wave propagation characteristics of buried pipes conveying viscous flowing fluid under axisymmetric wave motion, where the coupling pipe–soil and pipe–fluid effects are both taken into account. The fluid was assumed to be viscous, isotropic, and irrotational. The coupled equations of wave motion were obtained based on Love’s thin shell theory. The analytical fluid-dominated (s=1) wave dispersion relations of buried fluid-conveying pipes are given. In addition, studies were carried out to scrutinize the effects of the soil, flow velocity, fluid viscosity, fluid mass density, and pipe geometry on wave propagation of buried fluid-conveying pipes. Results show that the higher fluid velocity can lead to larger phase velocity and smaller wave attenuation in buried pipes. In addition, viscous fluid leads to larger wave attenuation compared with ideal fluid.

Optomechanical Density Sensor for Sample Consumption of Dozens of Nano-Liters Based on Microbubble Microcavity

Benefiting from the bridgework between cavity optomechanics and optofluidics, microbubble resonators (MBRs) have attracted wide attention both in optomechanics sensing and fundamental research. In this work, we present a novel approach for achieving a fluid mass density sensor based on optomechanics in MBRs. The density responsivity can range from -1.27~-1.54 MHz/(g/ml) for 4 types of mechanical modes. The validation of responsivity is analyzed theoretically, and the calculations indicate that a shorter average radius of the shell can achieve higher responsivity. The density responsivity in a smaller sized and thicker MBR can reach -2.147 MHz/(g/ml). Due to the small volume of the MBRs, the sample consumption can be controlled to dozens of nano-liters, which can greatly reduce the cost of sensing expensive biological samples.

Coarse-graining, compressibility, and thermal fluctuation scaling in dissipative particle dynamics employed with pre-determined input parameters

In this study, a Dissipative Particle Dynamics (DPD) method is employed with its input parameters directly determined from the fluid properties, such as the fluid mass density, water compressibility, and viscosity. The investigation of thermal fluctuation scaling requires constant fluid properties, and this proposed DPD version meets this requirement. Its numerical verifications in simple or complex fluids under viscometric or non-viscometric flows indicate that (i) the level of thermal fluctuations in the DPD model for both types of fluids is consistently reduced with an increase in the coarse-graining level and (ii) viscometric or non-viscometric flows of a model fluid at different coarse-graining levels have a similar behavior. Furthermore, to reduce the compressibility effect of the DPD fluid in simulating incompressible flows, a new simple treatment is presented and shown to be very effective.

Wave dispersion in viscoelastic lipid nanotubes conveying viscous protein solution

This work investigates the wave dispersion characteristics in viscoelastic lipid nanotubes conveying protein solution. The protein solution is assumed to be viscous, incompressible, and irrotational. The theoretical formulation is within the framework of the Rayleigh beam theory and the nonlocal strain gradient theory (NSGT). The analytical wave dispersion relations of protein-conveying lipid nanotubes are obtained. Results show that the nonlocal parameter, the material length-scale parameter, the fluid mass density, and the damping coefficient have important effect on wave dispersion characteristics of viscoelastic lipid nanotubes conveying protein solution. These findings are helpful to understand the wave dispersion characteristics of protein-conveying lipid nanotubes.

Computational method for simultaneous inertial measuring of fluid mass flow rate and density

This work represents the decision of the problem of nonstationary one-dimensioned flow of fluid in a straight pipeline. It shows the method to generate non-stationary flow regime based on utilizing additional pipeline in which mechanical oscillations of fluid are being excited. Pressure difference along the length of oscillating fluid appears to be a measure for the density of the fluid and for its mass flow rate. The possibility of creating a new instrument for measuring the density and mass flow rate of a fluid based on results obtained is shown.

Viscous Liquid Threads with Inner Fluid Flow Inside Microchannels

Forming droplets are often accompanied by an interconnecting liquid thread. It is postulated that this phenomenon can only exist as long as a pressure gradient exists within the thread, for instance, when a viscous liquid is conveyed via the liquid thread to the forming droplet. We have built a microfluidic setup to form and sustain a liquid thread, which after a length L ends in a droplet. To prevent the droplet from moving up too fast due to buoyancy, we force the droplet to shift along a tilted ceiling, which can be positioned at three different angles. This enables us to keep the gradual lengthening of the liquid thread under control. Based on the Navier-Stokes equation, we are able to predict the axial shape of such a liquid thread as a function of fluid mass density, initial thread radius, initial fluid velocity at the nozzle, fluid viscosity, and surface tension. Although an explicit solution of the governing differential equations is not known, we managed to find an explicit approximating expression for the shape function, which shows excellent agreement with both the measured and the numerically calculated shape functions. An intriguing phenomenon observed in the experiments is the breakup of the thread. This breakup always occurs close to the droplet. Using our approximating solution, we derive a relation that connects, for any time in the development of the thread, its length and the pressure gradient stemming from, among other effects, the shear at the interface of the liquid thread due to motion of the inner liquid. For relatively short thread lengths, this relation is linear on a log-log scale, due to the fact that in this regime, viscosity effects are dominant. However, if the thread length increases, this relation starts to deviate from linear behavior, due to surface tension effects. We show from the experimental results that the thread starts to show unstable behavior as soon as these capillary effects come into play. We show how to predict the thread length at which the capillary instability sets in for any liquid thread system. It is found that the predicted maximum dimensionless thread length is given by Lmax,pred ≈ 12Ca with Ca the capillary number.

A Coupled Transient Wellbore/Reservoir-Temperature Analytical Model

Summary This work presents a new coupled transient wellbore/reservoir thermal analytical model, consisting of a combined reservoir/casing/tubing system. The analytical model considers flow of a slightly compressible, single–phase fluid in a homogeneous infinite–acting reservoir system and provides temperature–transient data for drawdown and buildup tests at any gauge location along the wellbore. The model accounts for Joule–Thomson (J–T), adiabatic–fluid–expansion, conduction, and convection effects. The wellbore–fluid mass density is modeled as a function of temperature, and the analytical solution makes use of the Laplace transformation to solve the transient heat–flow differential equation, accounting for a transient wellbore–temperature gradient ∂T/∂z. The solutions presented assume moderate– to high–permeability reservoirs and do not consider skin effects in the formation. Results of the analytical model are compared with those of a commercial thermal simulator and with those of available models in the literature. Our model provides more accurate transient–temperature–flow profiles along the wellbore in comparison with previous analytical models in the literature. Furthermore, a generalization of a well–known parameter–estimation method from transient–temperature data is provided.

A new empirical correlating equation for calculating effective viscosity of nanofluids

AbstractIn this paper, an empirical correlation for the nanofluid viscosity is proposed. The new equation for the nanofluid effective dynamic viscosity, normalized by the dynamic viscosity of the base liquid, is derived from a wide selection of experimental data available in the literature. This correlation presented the viscosity of the nanofluid as a function of the base fluid viscosity, nanoparticle volume fraction, nanoparticle diameter, nanoparticle temperature, and mass density of the base fluid. The new correlation was evaluated against 898 experimental data for the viscosities of nanofluid collected from the literature. The experimental data included different working nanofluids, such as alumina, Iron, and silica, where the diameter of nanoparticles was ranging between 10 and 350 nm, suspended in water, propylene glycol, and kerosene. The predicted results were then compared with many other published experimental results for different nanofluids and very good concordance between these results was observed. In general, this correlation has higher accuracy and precision.

Nonlinear dynamic characteristics of functionally graded sandwich thin nanoshells conveying fluid incorporating surface stress influence

In the present work, nonlinear dynamics of fluid-conveying functionally graded material (FGM) sandwich nanoshells is investigated. In order to describe the large-amplitude motion, the von Kármán nonlinear geometrical relations are taken into account. Compressibility and viscidity of the fluid are neglected, and the velocity potential and Bernoulli's equation are used to describe the fluid pressure acting on the nanoshells. Based on the classical shell theory and incorporating the surface stress effect, the governing equations are derived by using Hamilton's principle. After that, the Galerkin method is used to discretize the equation of motion, resulting in a set of ordinary differential equations with respect to time. The ordinary differential equations are solved analytically by utilizing the method of multiple scales. Results show that the surface stress plays important roles on the nonlinear vibration characteristics of fluid-conveying FGM sandwich thin-walled nanoshells. Furthermore, the fluid speed, the power-law index, the fluid mass density, the core thickness and the initial surface tension can also influence the vibration characteristics of fluid-conveying FGM sandwich nanoshells.

A nonlinear surface-stress-dependent model for vibration analysis of cylindrical nanoscale shells conveying fluid

• A nonlinear surface-stress-dependent nanoshell model is developed. • Flowing fluid is taken into account in the cylindrical nanoshells. • Nonlinear free vibration of fluid-conveying cylindrical nanoshells is studied. • Surface stress influences nonlinear vibration characteristics of fluid-conveying nanoshells. • Shell theory is used to model the present fluid-conveying nanostructures. A nonlinear surface-stress-dependent nanoscale shell model is developed on the base of the classical shell theory incorporating the surface stress elasticity. Nonlinear free vibrations of circular cylindrical nanoshells conveying fluid are studied in the framework of the proposed model. In order to describe the large-amplitude motion, the von Kármán nonlinear geometrical relations are taken into account. The governing equations are derived by using Hamilton's principle. Then, the method of multiple scales is adopted to perform an approximately analytical analysis on the present problem. Results show that the surface stress can influence the vibration characteristics of fluid-conveying thin-walled nanoshells. This influence becomes more and more considerable with the decrease of the wall thickness of the nanoshells. Furthermore, the fluid speed, the fluid mass density, the initial surface tension and the nanoshell geometry play important roles on the nonlinear vibration characteristics of fluid-conveying nanoshells.

PATCHWORK: A Multipatch Infrastructure for Multiphysics/Multiscale/Multiframe Fluid Simulations

We present a "multipatch" infrastructure for numerical simulation of fluid problems in which sub-regions require different gridscales, different grid geometries, different physical equations, or different reference frames. Its key element is a sophisticated client-router-server framework for efficiently linking processors supporting different regions ("patches") that must exchange boundary data. This infrastructure may be used with a wide variety of fluid dynamics codes; the only requirement is that their primary dependent variables be the same in all patches, e.g., fluid mass density, internal energy density, and velocity. Its structure can accommodate either Newtonian or relativistic dynamics. The overhead imposed by this system is both problem- and computer cluster architecture-dependent. Compared to a conventional simulation using the same number of cells and processors, the increase in runtime can be anywhere from negligible to a factor of a few; however, one of the infrastructure's advantages is that it can lead to a very large reduction in the total number of zone-updates.

Density distribution function of a self-gravitating isothermal compressible turbulent fluid in the context of molecular clouds ensembles

We have set ourselves the task of obtaining the probability distribution function of the mass density of a self-gravitating isothermal compressible turbulent fluid from its physics. We have done this in the context of a new notion: the molecular clouds ensemble. We have applied a new approach that takes into account the fractal nature of the fluid. Using the medium equations, under the assumption of steady state, we show that the total energy per unit mass is an invariant with respect to the fractal scales. As a next step we obtain a nonlinear integral equation for the dimensionless scale Q which is the third root of the integral of the probability distribution function. It is solved approximately up to the leading-order term in the series expansion. We obtain two solutions. They are power-law distributions with different slopes: the first one is -1.5 at low densities, corresponding to a equilibrium between all energies at a given scale, and the second one is -2 at high densities, corresponding to a free fall at small scales.

2-D CFD time-dependent thermal-hydraulic simulations of CANDU-6 moderator flows

The distribution of the fluid temperature and mass density of the moderator flow in CANDU-6 nuclear power reactors may affect the reactivity coefficient. For this reason, any possible moderator flow configuration and consequently the corresponding temperature distributions must be studied. In particular, the variations of the reactivity may result in major safety issues. For instance, excessive temperature excursions in the vicinity of the calandria tubes nearby local flow stagnation zones, may bring about partial boiling. Moreover, steady-state simulations have shown that for operating condition, intense buoyancy forces may be dominant, which can trigger a thermal stratification. Therefore, the numerical study of the time-dependent flow transition to such a condition, is of fundamental safety concern. Within this framework, this paper presents detailed time-dependent numerical simulations of CANDU-6 moderator flow for a wide range of flow conditions. To get a better insight of the thermal-hydraulic phenomena, the simulations were performed by covering long physical-time periods using an open-source code (Code_Saturne V3) developed by Électricité de France. The results show not only a region where the flow is characterized by coherent structures of flow fluctuations but also the existence of two limit cases where fluid oscillations disappear almost completely.