Non-equilibrium Thermodynamic Model Research Articles

Effects of non-equilibrium phase behavior in nanopores on multi-component transport during CO2 injection into shale oil reservoir

Injecting CO2 into shale oil reservoirs is one of the most effective methods for enhancing oil recovery (EOR) while simultaneously facilitating CO2 capture, utilization, and storage (CCUS). However, it is not always that gas dissolution or condensate evaporation reaches equilibrium instantaneously during the CO2 injection process. In cases where equilibrium is not attained instantaneously, conventional vapor-liquid equilibrium models will have certain limitations in characterizing phase transition hysteresis. These limitations will affect the accuracy of simulating multi-component transport in porous media. In this paper, a robust and generic vapor-liquid non-equilibrium thermodynamic model considering nano-confinement effects (NC) was established by introducing component mass transfer rates proportional to the chemical potential difference. The established model was then used to modify the fully-compositional, projection-based embedded discrete fracture model (pEDFM). Furthermore, C++ hybrid programming and the Graphics Processing Unit (GPU) parallel method were both used to accelerate both the nonlinear and linear solvers. By comparing with results from MATLAB Reservoir Simulation Tools (MRST), Eclipse, and tNavigator, the accuracy and advantages of our solver were demonstrated. The results show that if the underground fluid undergoes a phase transition from a vapor-liquid two-phase state to a single-phase state, non-equilibrium thermodynamic effects need to be considered, and the simulation results show a larger two-phase zone, higher bottom hole pressure, and lower cumulative liquid production. But the nano-confinement effects will weaken the non-equilibrium thermodynamic effects.

Phonon thermophoresis of crystalline nanoparticles in liquids.

Our nonequilibrium thermodynamic model of thermodiffusion in molecular liquid systems is used to examine the role of thermal phonons in the thermophoresis of liquid suspensions of crystalline nanoparticles, which tend to have high thermal conductivity. The Soret coefficient used to characterize stationary thermodiffusion is related to differences in entropy between a particle and the body of liquid that it displaces. Calculated phonon Soret coefficients for graphite and diamond nanoparticles in three polar solvents are used to establish parameters where the phonon mechanism is expected to dominate particle thermophoresis compared to slip-flow caused by forces induced in the surface layer by the temperature gradient. Because the active mode of thermal conductivity in crystals varies with particle size, phonon thermophoresis is expected to dominate within a specific range of particle size, which varies with the properties of the particle and suspending liquid. For graphite and diamond particles in polar solvents the model estimates a size range of around 10-100 nm. Finally, thermophoretic particle accumulation is ultimately limited by the increasing concentration of particles having high thermal conductivity because the zone of particle concentration decreases the local temperature gradient that drives thermophoresis. The respective nonperturbing concentration is evaluated as the function of the size of a given material.

Non-equilibrium thermodynamic modelling of cooling path dependent phase evolution of Li2SiO3 from Li2O-SiO2 melt by considering mixed kinetic phenomena and time-dependent concentration fields

Efficient recovery of Li2SiO3 or other Li compounds from slag streams generating from pyrometallurgical treatment of lithium ion batteries (LIBs) requires fundamental understanding of the kinetics that govern slag solidification. In this work, a non-equilibrium thermodynamic model that incorporates mixed internal kinetics of diffusion and interface mobility, influenced by external cooling paths, is developed to investigate for the first time, the dependence of the phase evolution rate of Li2SiO3 from Li2O-SiO2 melt, on the available driving forces and time-dependent concentration fields. Experiments with different thermal profiles were performed for inverse identification of the kinetic coefficients. It turned out that different cooling rates (1.5Kmin−1, 5Kmin−1 and 10Kmin−1) depict an initial dominance of thermodynamic driving force superseded by kinetic forces in subsequent phase evolution. A certain interface velocity maximum is exhibited during phase formation, where the magnitude decreases progressively from 5.5 × 10−7ms−1 to 3.9 × 10−7ms−1 to 2.1 × 10−7ms−1 with a decrease of the cooling rates.

A statistical mechanics framework for constructing nonequilibrium thermodynamic models

Abstract Far-from-equilibrium phenomena are critical to all natural and engineered systems, and essential to biological processes responsible for life. For over a century and a half, since Carnot, Clausius, Maxwell, Boltzmann, and Gibbs, among many others, laid the foundation for our understanding of equilibrium processes, scientists and engineers have dreamed of an analogous treatment of nonequilibrium systems. But despite tremendous efforts, a universal theory of nonequilibrium behavior akin to equilibrium statistical mechanics and thermodynamics has evaded description. Several methodologies have proved their ability to accurately describe complex nonequilibrium systems at the macroscopic scale, but their accuracy and predictive capacity is predicated on either phenomenological kinetic equations fit to microscopic data or on running concurrent simulations at the particle level. Instead, we provide a novel framework for deriving stand-alone macroscopic thermodynamic models directly from microscopic physics without fitting in overdamped Langevin systems. The only necessary ingredient is a functional form for a parameterized, approximate density of states, in analogy to the assumption of a uniform density of states in the equilibrium microcanonical ensemble. We highlight this framework’s effectiveness by deriving analytical approximations for evolving mechanical and thermodynamic quantities in a model of coiled-coil proteins and double-stranded DNA, thus producing, to the authors’ knowledge, the first derivation of the governing equations for a phase propagating system under general loading conditions without appeal to phenomenology. The generality of our treatment allows for application to any system described by Langevin dynamics with arbitrary interaction energies and external driving, including colloidal macromolecules, hydrogels, and biopolymers.

Osmotically driven beading instability in axons: Continuum theory, perturbation analysis and finite element implementation

Axonal beading or formation of multiple beads along an axon is characteristic of many brain pathological states like Alzheimer's, Parkinson's and traumatic injuries. Despite the many existing experimental studies, the underlying mechanisms of this shape instability remain still poorly understood. In this paper, we establish a combined theoretical and numerical framework to study the governing key factors of this morphological transformation. We develop a three-dimensional (3D) non-equilibrium large deformation thermodynamic model with two main parts: the central axoplasm which is considered as a polyelectrolyte hydrogel and the encapsulating cortical membrane which is modeled as an incompressible hyperelastic layer with surface energy and growing surface. The model constitutive and evolution equations are then extracted employing thermodynamic balance principles for both bulk and surface material points. It is shown that the second law of thermodynamics indicates that the axolemma growth rate is proportional to the membrane tension which is in perfect agreement with the available experimental findings. While the developed model is general and can be extended to cover other types of axonal beadings, for the sake of simplicity, here, we focus on osmotically driven axisymmetric beadings which are compressible viscoelastic periodic modulations. We solve the corresponding governing equations using the linear perturbation method. This perturbation analysis proves that: 1) the beading instability is a rate dependent phenomenon that is controlled by the axolemma growth, 2) the initially dominant beading waves (the fastest waves) might be replaced only by longer waves which are more stable and 3) the wavelength of the fastest beads should vary roughly linearly with the axonal radius. These main findings are all in good agreement with the existing experimental results. Finally, the finite element implementation of the model is also presented to verify the results of the linear stability analysis for slow waves. The obtained axisymmetric finite element results are in good agreement with the corresponding theoretical findings.

Heat transfer effect on the performance of three-heat-reservoir thermal Brownian refrigerator

Abstract A finite-time thermodynamic (FTT) model of three-heat-reservoir thermal Brownian refrigerator is established in this paper. This model can be equivalent to the coupling of a thermal Brownian engine and a thermal Brownian refrigerator with heat transfer effects. Expressions for cooling load and coefficient of performance (COP) are derived by combining FTT and non-equilibrium thermodynamics (NET). The system performance is studied and compared with those of previous models. For fixed internal parameters, the thermal conductance distributions among three heat exchangers are optimized for maximal cooling load. For fixed inventory allocations, the internal parameters are also optimized for maximal cooling load. Finally, the double-maximum cooling load is obtained by optimizing internal parameters and external thermal conductance distributions simultaneously, and the optimal operating temperatures are also derived. Results show that half of total thermal conductance should be placed in condenser to reject heat to ambient under maximal cooling load regime. The heat transfer determines system performance by controlling the working temperatures and the coupling of two external loads. The system works in reversible state when COP reaches its maximum value. The new performance limits can predict that of three-heat-reservoir thermal Brownian refrigerator more accurately, and also include those of NET model.

Unsteady Stefan problem with kinetic interface conditions for rarefied gas deposition

The Stefan problem is a phase transition problem with a moving interface between two phases, originally established for solid and liquid. The influence of kinetic theory-based non-equilibrium thermodynamic models on the classical Stefan problem for deposition or sublimation processes is investigated. The gas phase is assumed to be in the rarefied slip regime, so default continuum and equilibrium models struggle. The results are dependent on the well-studied Knudsen and Mach numbers, defined at the phase transition interface. The differences from the classical model become significant as the Knudsen number, and correspondingly the level of rarefaction, increases. We observe influences on the temperature, pressure, phase transition speed and deviation from the saturation conditions.

Selective permeation up a chemical potential gradient to enable an unusual solvent purification modality

The need for energy-efficient recovery of organic solutes from aqueous streams is becoming more urgent as chemical manufacturing transitions toward nonconventional and bio-based feedstocks and processes. In addition to this, many aqueous waste streams contain recalcitrant organic contaminants, such as pharmaceuticals, industrial solvents, and personal care products, that must be removed prior to reuse. We observe that rigid carbon membrane materials can remove and concentrate organic contaminants via an unusual liquid-phase membrane permeation modality. Surprisingly, detailed thermodynamic calculations on the chemical potential of the organic contaminant reveal that the organic species has a higher chemical potential on the permeate side of the membrane than on the feed side of the membrane. This unusual observation challenges conventional membrane transport theory that posits that all permeating species move from high chemical potential states to lower chemical potential states. Based on experimental measurements, we hypothesize that the organic is concentrated in the membrane relative to water via favorable binding interactions between the organic and the carbon membrane. The concentrated organic is then swept through the membrane via the bulk flow of water in a modality known as "sorp-vection." We highlight via simplified nonequilibrium thermodynamic models that this "uphill" chemical potential permeation of the organic does not result in second-law violations and can be deduced via measurements of the organic and water sorption and diffusion rates into the carbon membrane. Moreover, this work identifies the need to consider such nonidealities when incorporating unique, rigid materials for the separations of aqueous waste streams.

Effect of heat transfer on the performance of thermal Brownian heat pump

<p indent="0mm">A finite-time thermodynamic model of the thermal Brownian heat pump is established in this paper. The heat transfer between a reservoir and viscous medium is assumed to obey Newton’s law. The expressions for the heating load and coefficient of performance (COP) are derived. The effects of heat transfer on thermal Brownian heat pump performance are analyzed, and the valid working region of a thermal Brownian heat pump is obtained. The performance characteristics of the Brownian heat pump are compared with those of the macro endoreversible Carnot heat pump. For a fixed total heat-exchanger inventory, the distribution of heat-exchanger inventory is optimized for maximizing the heating load. The results indicate that the new model with thermal resistance delivers less heating load than the nonequilibrium thermodynamic model, and the new performance characteristics are closer to reality. The system performance can be improved by enhancing the heat transfer between the reservoir and the heat pump. An optimal heat-exchanger inventory ratio exists for maximizing the heating load, and the COP is irrelevant to the heat-exchanger inventory. When the total heat-exchanger inventory is infinite, the model becomes a nonequilibrium thermodynamic one. The heating load can be improved by reducing the reservoir temperature difference, and the COP is not affected by the reservoir temperatures.

Nonequilibrium thermodynamic model of thermoelectricity and thermodiffusion in semiconductors.

We present a self-consistent model rooted in nonequilibrium thermodynamics for defining concentration gradients in the electron/hole pairs and electric-field gradients in an intrinsic semiconductor created upon exposure to a temperature gradient. The model relies on the equation for entropy production expressed through phenomenological equations for the electron/hole flux, with the imposed condition that the resulting concentration profiles of the electrons and holes are identical. The chemical potentials of electrons, holes, and parent atoms of the lattice, which are contained in the flux equations, are calculated on the basis of the temperature-dependent equilibrium dissociation reaction: lattice atom ↔ electron + hole. Electron/hole concentration profiles resulting from the temperature gradient, along with the associated gradient in the electric field, are expressed through equilibrium microscopic parameters of the semiconductor, which include the effective masses of electrons and holes, the energy gap width, and the Debye temperature. The resulting expressions contain neither kinetic nor fitting parameters, and predict values in reasonable (order-of-magnitude) agreement with empirical data. Finally, the model predicts a measurable additional thermodiffusion-based Seebeck effect when the temperature difference is on the order of several tens of degrees across a nonisothermal semiconductor working as a power supply under conditions of optimal power transport.

Defect substructure energy landscape in polycrystalline Al under large deformation: insights from molecular dynamics

Tens-nanometer sized defect substructures such as dislocation network, nanotwin and new grain or phase may form during solid phase processing (SPP), which affect the energy landscape, hence, the stability and evolution of phase and structure. Developing non-equilibrium thermodynamic models needs the correlation among the energy, defect substructure and deformation. In the current work, we use molecular dynamics (MD) method to simulate defect substructure evolutions in polycrystalline Al under compress and shear stresses. The effect of local stresses on the formation and transformation of typical defect substructures were analyzed. It was found that transitions from FCC, nanotwin, HCP, BCC, HCP to FCC lead to the formation of subgrains facilitated with large grain rotation. Our results demonstrate that point defect concentrations (e.g., HCP, dislocation core atoms) can be used as internal variables to describe defect substructures, such as dislocations, nanotwins and sub-grain boundaries. An energy landscape of defect substructures in polycrystalline Al under compress and shear stresses was established which shows unstable and metastable defect substructures. Approaches to developing more accurate energy landscapes for understanding and predicting microstructure evolution under SPP was discussed.

CO2/CH4 Separation via Carbon-Based Membrane: The Dynamic Role of Gas-Membrane Interface.

Membrane separation is considered one of the most promising CO2/CH4 separation technologies currently available because it is a safe, environment-friendly, and economical method. However, the inability of membrane materials to reconcile the trade-off between permeability and permeation selectivity limits their further applications; moreover, the mechanism underlying this process is unclear, which is mainly determined by the performance of gas adsorption and diffusion. Therefore, this paper describes the effect of gas adsorption and diffusion on membrane separation by assessing the fundamental gas-membrane and gas-gas interactions. Combining molecular simulation methods (Monte Carlo and molecular dynamics simulation) and a thermodynamic model called "linearized nonequilibrium thermodynamic transfer model", we investigate the permeability and permeation selectivity for CO2/CH4 in five carbon-based membranes and propose a general method for screening membrane materials. The interaction-dominated mechanism derived in this work provides new insights into membrane separation and facilitates the screening of high-performance membrane materials.

Heat to Hydrogen by Reverse Electrodialysis—Using a Non-Equilibrium Thermodynamics Model to Evaluate Hydrogen Production Concepts Utilising Waste Heat

The reverse electrodialysis heat engine (REDHE) is a promising salinity gradient energy technology, capable of producing hydrogen with an input of waste heat at temperatures below 100 °C. A salinity gradient drives water electrolysis in the reverse electrodialysis (RED) cell, and spent solutions are regenerated using waste heat in a precipitation or evaporation unit. This work presents a non-equilibrium thermodynamics model for the RED cell, and the hydrogen production is investigated for KCl/water solutions. The results show that the evaporation concept requires 40 times less waste heat and produces three times more hydrogen than the precipitation concept. With commercial evaporation technology, a system efficiency of 2% is obtained, with a hydrogen production rate of 0.38 gH2 m−2h−1 and a waste heat requirement of 1.7 kWh gH2−1. The water transference coefficient and the salt diffusion coefficient are identified as membrane properties with a large negative impact on hydrogen production and system efficiency. Each unit of the water transference coefficient in the range tw=[0–10] causes a −7 mV decrease in unit cell electric potential, and a −0.3% decrease in system efficiency. Increasing the membrane salt diffusion coefficient from 10−12 to 10−11 leads to the system efficiency decreasing from 2% to 0.6%.

Thermal Brownian heat engine with external and internal irreversibilities

A finite time thermodynamic model of irreversible thermal Brownian heat engines with various irreversibilities is built. The analytical expressions of power and efficiency are derived. The working temperatures are solved by combining equations, the essential performance characteristics of heat engine are further analyzed. The relationships among optimal performance indicators and design parameters are also studied. The optimal performance characteristics are obtained by optimizing the internal parameters and thermal conductance ratio of heat exchangers. The optimal working regions and optimal working temperatures are also given. Finally, the new model performance is compared with that of the non-equilibrium thermodynamic one, and the significance of the new model is illustrated. The results show that the new model can be simplified to the existing models, and the optimal performances of those existing models with different irreversible factors can also be derived through the optimization relation in this paper. The power and efficiency have extreme values about barrier height, thermal conductance ratio and external load, respectively. When those parameters are optimized simultaneously, the corresponding values of the working temperature are optimal for the heat engine. The kinetic energy will reduce power and efficiency, which is different from the result of the non-equilibrium thermodynamic models.

Nonequilibrium thermodynamic model of diffusion processes in the steel - carbon thin film tribological system

A nonequilibrium thermodynamic model of dissipative processes in the tribological system steel – carbon thin film was developed. Cross coefficients and driving forces in the Onsager equation for the diffusion of carbon onto the friction surface of hypereutectoid steel are calculated. The thermodynamic conditions for the implementation of the selective transfer process in the tribological system under consideration are determined. Simple differential equations are obtained for the tribological system of carbon steel - graphite, which describe the effect of stresses on the diffusion of carbon, production based on nonequilibrium thermodynamics. It is shown, that the implementation of selective transfer requires the development of diffusion processes without the formation of excess phases. Therefore, carbon steel should be alloyed mainly with elements of the first group that increase the thermodynamic activity of carbon in steel - silicon, nickel, copper, cobalt and phosphorus. Recommendations are formulated on metallic materials choosing for minimal contact wear in contacted pairs of machines parts.

Mass transfer behavior of methane in porous carbon materials

AbstractThe low mass transfer rate in porous materials hinders the use of adsorbed natural gas as vehicle fuel. Fundamentally, the mass transfer rate depends on the structures of the adsorbents and the operating conditions. Therefore, in this study, the effects of adsorbent (activated carbons) structure and operating conditions on the mass transfer rate of methane (main component of natural gas) were investigated quantitatively, providing a theoretical basis for the synthesis of efficient adsorbent materials. By performing Monte Carlo and molecular dynamics simulations and utilizing a nonequilibrium thermodynamic linearization transfer model, the mass transfer behavior of methane in porous carbon materials was quantitatively evaluated, specifically focusing on the material structure, operating conditions, and feasibility of using natural gas as vehicle fuel. The proposed linear nonequilibrium thermodynamic mass transfer model is applicable to interfacial gas species and provides a valuable tool for gas separation.

When theories and experiments meet: Rarefied gases as a benchmark of non-equilibrium thermodynamic models

The role of thermodynamics in deriving constitutive equations is unique, and various approaches have been developed in the last decades. In the present paper, the frameworks of Extended Irreversible Thermodynamics (EIT) and Non-Equilibrium Thermodynamics with Internal Variables (NET-IV) are discussed and compared to each other on the basis of a particular problem of rarefied gases. In this comparison, both theoretical and experimental aspects are taken into account. Eventually, an experiment by Meyer and Sessler covering a wide range of pressures and frequencies is investigated. Here, concentrating on the scaling properties and the density dependence of parameters, the change of speed of sound in terms of frequency and pressure is recovered using NET-IV, and this fitting is compared to the results of Lebon and Cloot using EIT. NET-IV and EIT are seen to be more flexible than Rational Extended Thermodynamics (RET) concerning the functional form of the transport coefficients, which gives them some advantages over RET in some ranges of values of gas density.

Thermal stratification and rollover phenomena in liquefied natural gas tanks

A non-equilibrium multilayer thermodynamic model is developed to predict the thermal stratification and rollover phenomena in liquefied natural gas (LNG) storage tanks. This model considers the boundary layer formation along the tank walls and uses an adaptive mesh to accommodate the changes in the LNG level in the tank over time. The accuracy of the model is verified against experiment data available in the literature to predict the thermal stratification and rollover in cryogenic storage tanks. A parametric study is conducted to investigate the key factors affecting the rollover start time. The results indicate that in an LNG storage tank at atmospheric pressure, the ratio between the amount of fresh LNG loaded to the tank (cargo) and the amount of LNG left in the tank (heel) prior to the loading of cargo, and the methane concentration in the cargo layer have direct effects on the rollover start time. The amount of heat transfer to the tank, the tank aspect ratio, and the nitrogen concentration in the heel or cargo layers affect the LNG evaporation rate. Our results indicate that the cargo to heel ratio should be determined with caution to prevent the rollover in LNG storage tanks.

An analysis of the ballast voyage of an LNG Carrier. The significance of the loading and discharging cycle

• Introduction of the Loading and Discharging Cycle in the analysis of laden and ballast voyages of LNG carriers. • Conjugate heat transfer analysis of the insulation- cargo system. • Projection of the Loading and Discharging Cycle on to the boiling curve. • Explanation of the pressure fluctuations observed during the laden voyage. • Ballast voyage being controlled by thermodynamic equilibrium. • Laden voyage being controlled by the boiling curve. A conjugate heat transfer analysis combined with a non-equilibrium thermodynamic model for LNG ageing during ship transportation has been developed based on experimental data. The laden and the ballast voyages are being considered as a continuous and inseparable process interconnected through the loading and discharging cycle with the thermal dynamics of the insulation of the cargo containment system. The loading and discharging cycle is instrumental not only in the understanding of the ballast voyage behavior but it is also the key for the explanation of the pressure fluctuations during the laden voyage as soon as the insulation temperatures during the cycle are projected on to the boiling curve. Thus, the pressure fluctuations may be attributed to the complex and turbulent vapor release mechanism associated with the various boiling modes imposed by the temperature non-uniformity over the insulation surface of the tanks. The secondary barrier temperature measurements of the insulation show that significant temperature variations exist across the tank walls, suggesting, that different heat fluxes cross the primary insulation barrier and consequently different boiling modes (regimes) simultaneously exist on the tank wall surface which is in contact with the liquid cargo. Moreover, the on-board pressure and temperature measurements in the tank reveal that the gas and the liquid phases during the ballast voyage are almost in local thermodynamic equilibrium, since the tank walls are interacting primarily with the gas phase and the multi-boiling regimes envisaged by the boiling curve are no longer the defining characteristic of the physical process. This is an important finding, resulting in a drastic reduction of the required computational effort, compared with the laden voyage, enabling the use of simpler equations of state and even Raoult’s ideal mixture law.

Nonlinear thermodynamics of biological signal transduction for predicting conservation of entropy production rate

Cell signal transduction is an example of a nonequilibrium phenomenon. In this study, a nonequilibrium nonlinear thermodynamic model was formulated. First, we obtained a condition in which the Onsager’s reciprocity theorem holds in the signal transduction. Second, it was found that the entropy production rate per signal molecule is conserved through signal transduction. Finally, it was determined that when Onsager’s reciprocity theorem does not hold, fluctuation circulation is given by the phosphorylation rate of signal molecules. The simple relation implies that the fluctuation circulation can be an essential quantity of the signal transduction amount. These results expand the limit of nonequilibrium thermodynamics and can be used to provide ideas for signal transduction quantification.