Concept Of Local Equilibrium Research Articles

Multiscale Pressure/Volume/Temperature Simulation of Decreasing Condensate/Gas Ratio at Greater than Dewpoint Pressure in Shale Gas-Condensate Reservoirs

Summary In shale gas-condensate reservoirs, when the initial reservoir pressure is greater than the dewpoint pressure, the condensate/gas ratio (CGR) has been observed to decrease continuously as the pressure drops to less than the initial reservoir pressure. This abnormal behavior cannot be explained with conventional pressure/volume/temperature (PVT) models that ignore the presence of nanopores in shale rock. Herein, for the first time, we present a study that provides a physical explanation for the observed CGR trends by including the effect of nanopores on the fluid phase behavior and depletion of shale gas-condensate reservoirs. Our model uses multiscale PVT simulation by means of a pore-size-dependent equation of state (EOS). Two lean gas-condensate cases (shallow and deep reservoirs) are investigated. The simulation results show that hydrocarbons distribute heterogeneously with respect to pore size on the nanoscale. There are more intermediate to heavy hydrocarbons (C3–11+) but fewer light ends (C1–2) distributed in the nanopores than in the bulk region. At the end of depletion, because of confinement effects, large amounts of intermediate hydrocarbons are trapped in the nanopores, causing condensate recovery loss. Multiscale depletion simulations suggest that a decreasing CGR can occur at the beginning of production when the reservoir pressure is higher than the dewpoint pressure. Such behavior is caused by the nanopore depletion in the shale matrix, which is a process of selectively releasing light hydrocarbon components. We also present a novel approach to model the nonequilibrium fluid distribution between the fracture and nanopores using a simple local-equilibrium concept. Our results indicate that the nonequilibrium fluid distribution increases the CGR drop because of the compositional selectivity of the nanopore in favor of intermediate and heavy hydrocarbons. NOTE: This paper is published as part of the 2021 SPE Reservoir Simulation Conference Special Issue.

Stationary superstatistics distributions of trapped run-and-tumble particles.

We present an analysis of the stationary distributions of run-and-tumble particles trapped in external potentials in terms of a thermophoretic potential that emerges when trapped active motion is mapped to trapped passive Brownian motion in a fictitious inhomogeneous thermal bath. We elaborate on the meaning of the non-Boltzmann-Gibbs stationary distributions that emerge as a consequence of the persistent motion of active particles. These stationary distributions are interpreted as a class of distributions in nonequilibrium statistical mechanics known as superstatistics. Our analysis provides an original insight on the link between the intrinsic nonequilibrium nature of active motion and the well-known concept of local equilibrium used in nonequilibrium statistical mechanics and contributes to the understanding of the validity of the concept of effective temperature. Particular cases of interest, regarding specific trapping potentials used in other theoretical or experimental studies, are discussed. We point out as an unprecedented effect, the emergence of new modes of the stationary distribution as a consequence of the coupling of persistent motion in a trapping potential that varies highly enough with position.

Thermodynamics of the formation of composite material structures. A review

Composite material structures at nano-, micro-, and mesolevels have been examined. The application of the Gibbs and Hill thermodynamics has allowed researchers to make a physical interpretation of the Laplace pressure for composite materials; to derive the thermodynamic functions describing the particles consolidation; establish the new phenomenon, namely, metal melt imbibition (MMI), and define its moving forces, substantiate a criterion that makes it possible to determine the direction of a liquid phase migration in a composite body, as well as to predict the final structure of composite materials. For the description of a composite material structure, which forms under extreme conditions, it has been necessary to use the nonequilibrium thermodynamics. For these conditions the Prigogine concept of local equilibrium is promising.

Thermodynamic mapping of austenite decomposition’s approach toward equilibrium in Fe–C–Mn at 700 °C

Transformation of Fe–0.85C–11.56Mn (wt.%) at 700°C begins by formation of grain boundary cementite in conjunction with carbon and manganese partitioning. Grain boundary cementite formation initiates regional partitioning of manganese from austenite to cementite that continues over months of cementite growth. The large disparity between manganese volume and grain boundary diffusion in austenite highlights why grain boundaries are associated with all stages of the 700°C phase transformation in this system. Therefore, unlike carbon, manganese partitioning associated with cementite growth is localized to the immediate region near the grain boundary/cementite reaction front. The reaction path involves austenite ‘neighborhoods’, defined to have manganese chemistries and, consequently, thermodynamic properties different from the majority of the remaining matrix. The remaining matrix does partition carbon but not manganese. Along with differences between grain boundary and matrix manganese diffusivity in austenite, diffusion of carbon is up to 106 times greater than that of manganese resulting in carbon activity in austenite equilibrating at each step of cementite growth. The concept of neighborhood thermodynamics is developed for these altered austenite regions and directed toward producing a transformation pathway analysis. The concept of local equilibrium is also demonstrated not to be viable as a method for phase transformation tracking and thermodynamic mapping as the reaction moves toward equilibrium.

Chemical Cycle Kinetics: Removing the Limitation of Linearity of a Non-equilibrium Thermodynamic Description

Chemical cycle kinetics is customarily analyzed by means of the law of mass action which describes how the concentrations of the substances vary with time. The connection of this approach with non-equilibrium thermodynamics (NET) has traditionally been restricted to the linear domain close to equilibrium in which the reaction rates are linear functions of the affinities. We show, by a pertinent formulation of the concept of local equilibrium in the mesoscopic description along the reaction coordinates, that the connection between kinetic and thermodynamic approaches is deeper than thought and holds in the nonlinear domain far from equilibrium, for higher values of the affinity. This new perspective indicates how to overcome the inherent limitation of classical NET in treating cyclic reactions, providing a description of closed and open cycles operating far from equilibrium, in accordance with thermodynamic principles. We propose that the new set of equations are tested and used for data reduction in chemical reaction kinetics.

Mesoscopic thermodynamics

We show that a probabilistic interpretation of nonequilibrium thermodynamics which uses the concept of local equilibrium at the mesoscale sets the basis of a theory able to analyze irreversible processes in the presence of fluctuations. The theory obtains the Fokker–Planck equation as a diffusion equation for the probability and the nonlinear relationships between activation rates and proper affinities of activated processes. The situations that can be studied with this formalism include, among others, barrier crossing dynamics, chemical reactions, entropic driving and nonlinear transport.

Indirect evidence for the existence of the Mn partitioning spike during the austenite to ferrite transformation

The growth kinetics during a final cooling down following cyclic partial phase transformations in the intercritical austenite + ferrite region has been investigated for a Fe–0.17 Mn–0.023C alloy (wt.%). For the first time, a specific growth retardation stage was observed. The growth retardation is attributed to the residual Mn spikes in the austenite, as a result of the prior partial phase transformations. The experimental observations are in good agreement with theoretical calculations based on the local equilibrium concept.

Parameters of adsorption state with partial charge transfer

A generalized Lippman-Gibbs equation that accounts for the effect of the partial charge transfer of specifically adsorbed anions at the metal-electrolyte solution interface is suggested in keeping with chemical thermodynamics and the concept of local equilibrium. An expression is obtained for a function that approximates surface tension within the stability limits of the adsorption phase. The above function is characterized by a minimum number of parameters that are evaluated using the data from determining the equilibrium state of an individual anion in the dense part of the double electric layer. Electrocapillary dependences, charging curves, and interface differential capacitance values, as well as electrochemical valence, are calculated. The performed estimates describe the experimentally obtained dependences.

Microscopic observation of oxygen reaction pathway on high temperature electrode materials

Attempts have been made to develop experimental techniques for obtaining microscopic information on high temperature electrodes under current flow. Several techniques are proposed to investigate the geometrical distribution of the series and parallel processes inside the electrode layer. Based on the local equilibrium concept, the contribution of the series processes were studied by probing the local oxygen potential. A microprobe oxygen sensor was developed to measure the oxygen potential profile on a model electrode of (La,Sr)MnO 3 on YSZ. Use of alternative methods that detect the valence state of the cations in the electrode material were also proposed. As an ex-situ technique, active sites for gas–solid oxygen exchange reaction were investigated by using isotope exchange and SIMS (secondary ion mass spectrometry) analysis. The three-dimensional distribution of the isotope ratio was obtained by SIMS with imaging capability. A non-uniform distribution of the reaction rate on the electrode surface was visualized for the electrode material with and without current flow. By the imaging technique, an extraordinary fast oxygen exchange site was found on (La,Sr) 2CoO 4/(La,Sr)CoO 3 boundaries.

Interfacial reactions between lead-free solders and common base materials

The objective of this review is to study interfacial reactions between pure Sn or Sn-rich solders, and common base metals used in Pb-free electronics production. In particular, the reasons leading to the observed interfacial reactions products and their metallurgical evolution have been analyzed. Results presented in the literature have been critically evaluated with the help of combined thermodynamic–kinetic approach based on the concept of local equilibrium and microstructural knowledge. The following conclusions have been reached: Firstly, the formations of intermetallic compounds in solid/liquid reaction couples are primarily controlled by the dissolution processes of base metals. Other factors that need be considered are the thermodynamic driving force for the formation of intermetallic compounds, their structures and concentration profiles in liquid. Secondly, annealing of solder interconnections in solid state can drastically change the microstructures formed in the solid/liquid reactions, especially if only one of the components in the solder takes part in the interfacial reactions. Thirdly, additional elements can have three major effects on the binary reactions between a base metal and Sn: (i) they can increase or decrease the reaction/growth rates, (ii) the additives can change the physical properties of the phases formed, and (iii) they can form additional reaction products or displace the binary equilibrium phases by forming new reaction products. Finally, if the local stable or metastable equilibrium is established at the interface, stability information together with kinetic considerations can provide a feasible approach to analyze interfacial reactions, which can have significant impact on the reliability of soldered electronics assemblies.

Analysis of the redeposition of AuSn4 on Ni/Au contact pads when using SnPbAg, SnAg, and SnAgCu solders

Interfacial reactions between SnPbAg, SnAg, and SnAgCu solders and Ni/Au surface finish on printed wiring board and especially the redeposition of AuSn4 intermetallic compound have been investigated. The following major results were obtained. The first phase to form during soldering in the (SnPbAg)/Ni/Au and the (SnAg)/Ni/Au systems was Ni3Sn4. During the subsequent solid-state annealing, the redeposition of AuSn4 as (Au,Ni)Sn4 occurred in both systems. This was explained with the help of the concept of local equilibrium and the corresponding ternary phase diagrams. It was concluded that the stabilizing effect of Ni on the (Au,Ni)Sn4 provided the driving force for the redeposition. Contrarily, when the solder alloy contained some Cu, the first intermetallic to form was (Cu,Ni,Au)6Sn5 and no redeposition of AuSn4 was observed. Thus, a very small addition of Cu to the Sn-rich solder alloys changed the behavior of the interconnection system completely. This behavior was explained thermodynamically by using Cu-Ni-Sn and Au-Cu-Sn ternary phase diagrams. The growth kinetics of the interfacial reaction products in the three systems was observed to be somewhat different. The reasons for the observed differences are also discussed.

Thermodynamic modeling of AlGaInN growth by MOVPE

A detailed thermodynamic analysis of the system Al–Ga–In–N–C–H was performed using the Gibbs energy minimization method. The multicomponent gaseous phase, ternary liquid alloy of A III elements, solid solution of A III nitrides as well as graphite and Al 4C 3 were included into the calculation. The influence of the initial conditions, namely temperature, pressure and input gas phase composition, on the equilibrium composition of this system was in view. On the basis of the concept of local equilibrium between the growing layer and the gaseous phase in its close vicinity, the calculated results were used to optimize deposition parameters for MOVPE growth of (Al,Ga,In)N epitaxial layers.

SURFACE ALLOY FORMATION IN THE Cu–Pd(111) SYSTEM: A KTBIM APPROACH

We study the kinetics of formation and dissolution of surface alloy obtained by depositing one monolayer of Pd on Cu(111) at room temperature. This is performed within the kinetic tight-binding Ising model. We also present the equilibrium segregation isotherm for Pd c Cu 1-c(111) and show the relation between kinetics (surface alloy) and equilibrium (alloy surface) via the local equilibrium concept.

On the “exotic” behaviour of the PtSn system

Using an energetic model derived from the electronic structure, we study the stability of the various terminations of Pt 1− c Sn c (111) for 0< c<0.3, both in the disordered and in the ordered L1 2 structure. Moreover, using a kinetic version of the model we reproduce the formation of different surface alloys obtained experimentally by depositing Sn Pt(111) . The relation between the equilibrium isotherm and the surface alloys is then discussed via the local equilibrium concept.

Criteria for local equilibrium in a system with transport of heat and mass

Nonequilibrium molecular dynamics is used to compute the coupled heat and mass transport in a binary isotope mixture of particles interacting with a Lennard-Jones/spline potential. Two different stationary states are studied, one with a fixed internal energy flux and zero mass flux, and the other with a fixed diffusive mass flux and zero temperature gradient. Computations are made for one overall temperature,T=2, and three overall number densities,n=0.1, 0.2, and 0.4. (All numerical values are given in reduced, Lennard-Jones units unless otherwise stated.) Temperature gradients are up to ∇T=0.09 and weight-fraction gradients up to ∇w1=0.007. The flux-force relationships are found to be linear over the entire range. All four transport coefficients (theL-matrix) are determined and the Onsager reciprocal relationship for the off-diagonal coefficients is verified. Four different criteria are used to analyze the concept of local equilibrium in the nonequilibrium system. The local temperature fluctuation is found to be δT≈0.03T and of the same order as the maximum temperature difference across the control volume, except near the cold boundary. A comparison of the local potential energy, enthalpy, and pressure with the corresponding equilibrium values at the same temperature, density, and composition also verifies that local equilibrium is established, except near the boundaries of the system. The velocity contribution to the BoltzmannH-function agrees with its Maxwellian (equilibrium) value within 1%, except near the boundaries, where the deviation is up to 4%. Our results do not support the Eyring-type transport theory involving jumps across energy barriers; we find that its estimates for the heat and mass fluxes are wrong by at least one order of magnitude.

Equilibrium and kinetics in the (111) surface of Cu-Ag alloys: Comparison between mean-field and Monte Carlo calculations.

In this paper we study the relationship between equilibrium and kinetics in Cu-Ag (111). We investigate the kinetics of segregation in a silver--dilute-copper sample and the dissolution kinetics of one Ag monolayer deposited on Cu(111). We compare results obtained using mean-field and Monte Carlo methods and relate them to the equilibrium isotherm by means of a local-equilibrium concept. We find good agreement with available experimental results on segregation kinetics and on dissolution kinetics when the Monte Carlo simulation is used.

Comparison of an experimental and a theoretical study of the surface alloy Pt/Cu(111)

Electron spectroscopies have been used to characterise the surface alloy formed by annealing a nearly epitaxial thin film of Pt/Cu(111). The surface alloy extends over several monolayers and is the result of a non-classical dissolution of Pt into the Cu substrate. The surface layer composition is Cu 3Pt reminiscent of the L1 2 alloy phase. In the bulk alloy this phase may be modelled using first neighbour effective pair interactions. This model is extended to the dissolution of a thin film of Pt into the Cu(111) substrate, by making use of the concept of local equilibrium. We show that at low temperature we can indeed stabilise an L1 2 surface alloy phase.

Kinetics of segregation and dissolution in Cu 1− cAg c and surface phase transition: comparison between mean field and Monte Carlo calculations

In this work we study the relation between the equilibrium surface segregation and the kinetics of segregation and dissolution in the CuAg(111) system at T= 1000 K, which presents surface phase transition. This is performed with the recently developed kinetic tight binding Ising model (KTBIM), which allows us to prove the efficiency of the local equilibrium concept. For the kinetics of dissolution we obtain great differences between the mean field kinetics and the Monte Carlo one. This last one, which agrees very well with the experimental data, takes into account the strong chemical inhomogeneity of the surface in the domain of the phase transition, contrary to the homogeneous mean field approach.

Morphological stability of γ/α interface formed by carburization in Fe-C-X alloys

Effect of alloying elements on the morphological stability of austenite/ferrite interface formed by carburization of Fe-X alloys at 850 °C and 800 °C was investigated. Planar interfaces were found when the alloying elements added were from among the following: Ti, V, Nb, Ta, Cr, Mo, W, Co, and Cu. Nonplanar interfaces with Widmanstatten-like structures and/or an isolated phase were observed when the alloying elements were from the following group: P, Al, Sb, Ni, Mn, Si, and Ge. The degree of supersaturation of C in the α phase adjacent to the γ phase front was analyzed using the concept of local equilibrium. It was confirmed that there was indeed a close correlation between the morphological stability and the degree of C supersaturation, which in itself depended on whether the alloying element added was an α or γ stabilizer and how strongly it bonded with C in the ferrite phase.

Examination of Local Equilibrium Concept in Diffusion

Examination of Local Equilibrium Concept in Diffusion