Rate-controlled constrained equilibrium (RCCE) is a reduction technique used to describe the time evolution of complex chemical reacting systems. This method is based on the assumption that a nonequilibrium system can reach its final equilibrium state by a series of RCCE states determined by maximizing entropy or minimizing relevant free energy. Those constraints are imposed by some small number of slow reactions. Much research has been done on this method and many RCCE models of C 1 − C 4 hydrocarbon fuel combustion have been established by the previous researchers. Those models show good performance compared with the result of detailed kinetic model (DKM). In this study, RCCE method is further developed to model normal pentane ( n - C 5 H 12 ) combustion with least number of constraints. The chemical mechanism for DKM contains 133 species and 922 reactions. Two sets of constraints were found during the study: (1) 16 constraints for the normal pentane and pure oxygen mixture and (2) 14 constraints for the mixture of normal pentane and oxygen with argon as diluent. Results of the first constraint set were compared with result of DKM and results of the second constraint set were compared with those of DKM and experimental data by calculating their ignition delay times. Comparisons showed that the first set of constraints had relatively good accuracy and the second set of constraints agreed very well with the experimental data.

When hydrogen is produced from a biomass or coal gasifier, it is necessary to purify it from syngas streams containing components such as CO, CO 2 , N 2 , CH 4 , and other products. Therefore, a challenge related to hydrogen purification is the development of hydrogen-selective membranes that can operate at elevated temperatures and pressures, provide high fluxes, long operational lifetime, and resistance to poisoning while still maintaining reasonable cost. Palladium-based membranes have been shown to be well suited for these types of high-temperature applications and have been widely utilized for hydrogen separation. Palladium's unique ability to absorb a large quantity of hydrogen can also be applied in various clean energy technologies, like hydrogen fuel cells. In this paper, a fully analytical interatomic embedded atom method (EAM) potential for the Pd-H system has been developed, that is easily extendable to ternary Palladium-based hydride systems, such as Pd-Cu-H and Pd-Ag-H. The new potential has fewer fitting parameters than previously developed EAM Pd-H potentials and is able to accurately predict the cohesive energy, lattice constant, bulk modulus, elastic constants, melting temperature, and the stable Pd-H structures in molecular dynamics (MD) simulations with various hydrogen concentrations. The EAM potential also well predicts the miscibility gap, the segregation of the palladium hydride system into dilute ( α ), and concentrated ( β ) phases.

In our previous study, a series of experiments had been conducted by applying different pressure depletion rates in a 1 m long sand-pack. In this study, numerical simulation models are built to simulate the lab tests, for both gas/oil production data and pressure distribution along the sand-pack in heavy oil/methane system. Two different simulation models are used: (1) equilibrium black oil model with two sets of gas/oil relative permeability curves; (2) a four-component nonequilibrium kinetic model. Good matching results on production data are obtained by applying black oil model. However, this black oil model cannot be used to match pressure distribution along the sand-pack. This result suggests the description of foamy oil behavior by applying equilibrium black oil model is incomplete. For better characterization, a four-component nonequilibrium kinetic model is developed aiming to match production data and pressure distribution simultaneously. Two reactions are applied in the simulation to capture gas bubbles status. Good matching results for production data and pressure distribution are simultaneously obtained by considering low gas relative permeability and kinetic reactions. Simulation studies indicate that higher pressure drop rate would cause stronger foamy oil flow, but the exceed pressure drop rate could shorten lifetime of foamy oil flow. This work is the first study to match production data and pressure distribution and provides a methodology to characterize foamy oil flow behavior in porous media for a heavy oil/methane system.

The rate-controlled constrained-equilibrium (RCCE), a model order reduction method, assumes that the nonequilibrium states of a system can be described by a sequence of constrained-equilibrium kinetically controlled by relatively a small number of constraints within acceptable accuracies. The full chemical composition at each constrained-equilibrium state is obtained by maximizing (or minimizing) the appropriate thermodynamic quantities, e.g., entropy (or Gibbs functions) subject to the instantaneous values of the constraints. Regardless of the nature of the kinetic constraints, RCCE always guarantees correct final equilibrium state. Ignition delay times measured in shock tube experiments with low initial temperatures are significantly shorter than the values obtained by constant volume models. Low initial temperatures and thus longer shock tube test times cause nonideal heat transfer and fluid flow effects such as boundary layer growth and shock wave attenuation to gradually increase the pressure (and simultaneously increase the temperature) before ignition. To account for these effects, in this paper, the RCCE prescribed enthalpy and pressure (prescribed h / p ) model has been further developed and has been applied to methane shock tube ignition delay time simulation using GRI-Mech 3.0. Excellent agreement between RCCE predictions and shock tube experimental data was achieved.

The rate-controlled constrained-equilibrium (RCCE), a model order reduction method, has been further developed to simulate the combustion of propane/oxygen mixture diluted with nitrogen or argon. The RCCE method assumes that the nonequilibrium states of a system can be described by a sequence of constrained-equilibrium states subject to a small number of constraints. The developed new RCCE approach is applied to the oxidation of propane in a constant volume, constant internal energy system over a wide range of initial temperatures and pressures. The USC-Mech II (109 species and 781 reactions, without nitrogen chemistry) is chosen as chemical kinetic mechanism for propane oxidation for both detailed kinetic model (DKM) and RCCE method. The derivation for constraints of propane/oxygen mixture starts from the eight universal constraints for carbon-fuel oxidation. The universal constraints are the elements (C, H, O), number of moles, free valence, free oxygen, fuel, and fuel radicals. The full set of constraints contains eight universal constraints and seven additional constraints. The results of RCCE method are compared with the results of DKM to verify the effectiveness of constraints and the efficiency of RCCE. The RCCE results show good agreement with DKM results under different initial temperature and pressures, and RCCE also reduces at least 60% CPU time. Further validation is made by comparing the experimental data; RCCE shows good agreement with shock tube experimental data.

Water vapor adsorption and desorption isotherms and kinetics studies on three Sichuan Basin shale samples were performed at 298 K by an accurate gravimetric method. The adsorption equilibrium data were fitted using both Dent model and Modified Dent model to estimate the adsorption characteristic of water on the primary and secondary sites. The primary site adsorption is restricted to a monolayer while the secondary site adsorption is associated with multilayer sorption. A positive correlation was found between clay mineral content and monolayer sorption content. The isosteric heats of sorption of water were determined from the equilibrium data and they decreased with the increase of adsorption amount. The adsorption/desorption hysteresis were studied with the pore structure. The kinetics of water vapor adsorption was studied with the unipore model and linear driving force mass transfer (LDF) model. The effective diffusivity and kinetic rate constant varied with the increase of relative pressure, which suggested diffusion of water vapor on shale corresponding to a combination of adsorption on primary sites, adsorption on secondary sites, formation of water clusters, and capillary condensation.

This study presents an analysis of coupling steam, CO 2 and O 2 reforming of CH 4 using the thermodynamic equilibrium constant method. Effects of molar ratio of O 2 /CH 4 , H 2 O/CH 4 and CO 2 /CH 4 on reforming characteristics in both carbon deposition and carbon-free systems are analyzed. The results indicate that CH 4 conversion rate, H 2, and CO yield increase with increasing O 2 /CH 4 molar ratio in two systems. In addition, the carbon elimination is achieved when O 2 /CH 4 ratio increases to 0.31, and changing the amount of O 2 can be an effective way to alter n(H 2 )/n(CO) ratio in the carbon deposition systems. CH 4 conversion rate increases with increasing H 2 O/CH 4 ratio in the carbon-free system, while it declines in the carbon deposition system. H 2 O plays a role of altering n(H 2 )/n(CO) ratio, and its effects on two systems are opposite. The deposited carbon is totally eliminated when H 2 O/CH 4 ratio increases to 0.645. The increase of CO 2 /CH 4 molar ratio leads to a rapid increase of CO 2 conversion when CO 2 /CH 4 ratio is less than 0.5. A slightly change of CO 2 /CH 4 ratio can result in a huge difference on n(H 2 )/n(CO) ratio in both systems, and carbon elimination is achieved at CO 2 /CH 4 = 0.99. The analyzed results have theoretical significance to efficiently catalyze methane coupling.

A large potential is contributed to the energetic utilization of biomass, whereby thermochemical gasification seems to be especially interesting. In order to contribute to a better understanding of the thermochemical conversion process in the gasifier, mathematical models are used. An intensive effort is made in development of mathematical models describing the gasification process and a large number of models, considerably differing in their degree of simplification, and their applications are reported in literature. In the present article, a brief review of models applied, mainly focused on equilibrium models, is provided and a robust and flexible modified stoichiometric equilibrium model, for modeling a novel gasifier, is presented.

A power-law mixing rule has been developed to determine apparent diffusion coefficient of a binary gas mixture on the basis of molecular diffusion coefficients for pure gases in heavy oil. Diffusion coefficient of a pure gas under different pressures and different temperatures is predicted on the basis of the Hayduk and Cheng's equation incorporating the principle of corresponding states for one-dimensional gas diffusion in heavy oil such as the diffusion in a pressure–volume–temperature (PVT) cell. Meanwhile, a specific surface area term is added to the generated equation for three-dimensional gas diffusion in heavy oil such as the diffusion in a pendant drop. In this study, the newly developed correlations are used to reproduce the measured diffusion coefficients for pure gases diffusing in three different heavy oils, i.e., two Lloydminster heavy oils and a Cactus Lake heavy oil. Then, such predicted pure gas diffusion coefficients are adjusted based on reduced pressure, reduced temperature, and equilibrium ratio to determine apparent diffusion coefficient for a gas mixture in heavy oil, where the equilibrium ratios for hydrocarbon gases and CO 2 are determined by using the equilibrium ratio charts and Standing's equations, respectively. It has been found for various gas mixtures in two different Lloydminster heavy oils that the newly developed empirical mixing rule is able to reproduce the apparent diffusion coefficient for binary gas mixtures in heavy oil with a good accuracy. For the pure gas diffusion in heavy oil, the absolute average relative deviations (AARDs) for diffusion systems with two different Lloydminster heavy oils and a Cactus Lake heavy oil are calculated to be 2.54%, 14.79%, and 6.36%, respectively. Meanwhile, for the binary gas mixture diffusion in heavy oil, the AARDs for diffusion systems with two different Lloydminster heavy oils are found to be 3.56% and 6.86%, respectively.

The rate-controlled constrained-equilibrium (RCCE) model reduction scheme for chemical kinetics provides acceptable accuracies in predicting hydrocarbon ignition delays by solving a smaller number of differential equations than the number of species in the underlying detailed kinetic model (DKM). To yield good approximations, the method requires accurate identification of the rate controlling constraints. Until recently, a drawback of the RCCE scheme has been the absence of a systematic procedure capable of identifying optimal constraints for a given range of thermodynamic conditions and a required level of approximation. A recent methodology has proposed for such identification an algorithm based on a simple algebraic analysis of the results of a preliminary simulation of the underlying DKM, focused on the degrees of disequilibrium (DoD) of the individual chemical reactions. It is based on computing an approximate singular value decomposition of the actual degrees of disequilibrium (ASVDADD) obtained from the DKM simulation. The effectiveness and robustness of the method have been demonstrated for methane/oxygen ignition by considering a C1/H/O (29 species/133 reactions) submechanism of the GRI-Mech 3.0 scheme and comparing the results of a DKM simulation with those of RCCE simulations based on increasing numbers of ASVDADD constraints. Here, we demonstrate the new method for shock-tube ignition of a natural gas/air mixture, with higher hydrocarbons approximately represented by propane according to the full (53 species/325 reactions) GRI-Mech 3.0 scheme including NO x formation.

Chemical composition and thermodynamics properties of different thermal plasmas are calculated in a wide range of temperatures (300–100,000 K) and pressures (10 −6 –100 atm). The calculation is performed in dissociation and ionization temperature ranges using statistical thermodynamic modeling. The thermodynamic properties considered in this study are enthalpy, entropy, Gibbs free energy, specific heat at constant pressure, specific heat ratio, speed of sound, mean molar mass, and degree of ionization. The calculations have been done for seven pure plasmas such as hydrogen, helium, carbon, nitrogen, oxygen, neon, and argon. In this study, the Debye–Huckel cutoff criterion in conjunction with the Griem’s self-consistent model is applied for terminating the electronic partition function series and to calculate the reduction of the ionization potential. The Rydberg and Ritz extrapolation laws have been used for energy levels which are not observed in tabulated data. Two different methods called complete chemical equilibrium and progressive methods are presented to find the composition of available species. The calculated pure plasma properties are then presented as functions of temperature and pressure, in terms of a new set of thermodynamically self-consistent correlations for efficient use in computational fluid dynamic (CFD) simulations. The results have been shown excellent agreement with literature. The results from pure plasmas as a reliable reference source in conjunction with an alternative method are then used to calculate the thermodynamic properties of any arbitrary plasma mixtures (mixed plasmas) having elemental atoms of H, He, C, N, O, Ne, and Ar in their chemical structure.

This manuscript presents experimental results on the reduction of sulfur oxide emissions from combustion of a high-sulfur content pulverized bituminous coal (Illinois #6 Macoupin) using a dry sorbent injection method. The coal particles were in the size range of 90–125 μ m and were blended with calcium-, sodium-, potassium-, and magnesium-containing powdered sorbents at different proportions. The alkali/sulfur molar ratios were chosen to correspond to stoichiometric proportions (Ca/S = 1, Mg/S = 1, Na 2 /S = 1, and K 2 /S = 1) and the effectiveness of each alkali or alkali earth based sorbent was evaluated separately. Combustion of coal took place in a drop-tube furnace, electrically heated to 1400 K under fuel-lean conditions. The evolution of combustion effluent gases, such as NO x , SO 2 , and CO 2 was monitored and compared among the different sorbent cases. The use of these sorbents helps to resolve the potential of different alkali metals for effective in-furnace sulfur oxide capture and possible NO x reduction. It also assesses the effectiveness of various chemical compounds of the alkalis, such as oxides, carbonates, peroxides, and acetates. Reductions in SO 2 emissions were in the range of 5–72%, with sodium being the most effective metal followed by potassium, calcium, and then magnesium. Acetates were effective as dual SO 2 and NO x reduction agents.

Intermittency of sustainable energy or waste heat availability calls for energy storage systems such as thermal batteries. Thermochemical batteries based on a reversible solid–gas (MgCl 2 –NH 3 ) reactions and NH 3 liquid–gas phase change are of specific interest since the kinetics of absorption are fast and the heat transfer rates for liquid–vapor phase change are high. Thus, a thermochemical battery based on reversible reaction between magnesium chloride and ammonia was studied. Two-dimensional experimental studies were conducted on a reactor in which temperature profiles within the solid matrix and pressure and flow rates of gas were obtained during discharging processes. A numerical model based on heat and mass transfer within the salt and salt–gas reactions was developed to simulate the NH 3 absorption processes within the solid matrix, and the results were compared with experimental data to determine dominant heat and mass transfer processes within the salt. It is shown that for high permeability salt beds, the reactor uniformly adsorbs gaseous ammonia until the bed reaches the equilibrium temperature, then adsorbs gas near the cooled boundaries as the reaction front moves inward. In that mode, the heat transfer is the dominant factor in determining reaction rates.

Waste heat driven ammonia/water Kalina cycles have shown promise for improving the efficiency of electricity production from low-temperature reservoirs (T < 150 °C). However, there has been limited application of these systems to utilize widely available, disperse, waste heat streams for smaller scale power production (1–10 kWe). Factors limiting increased deployment of these systems include large, costly heat exchangers, and concerns over safety of the working fluid. The use of mini- and microchannel (D < 1 mm) heat exchangers has the potential to decrease system size and material cost, while also reducing the working fluid inventory, enabling penetration of Kalina cycles into these new markets. However, accurate methods of predicting the heat and mass transfer in microscale geometries must be available for designing and optimizing these compact heat exchangers. In the present study, the effect of different heat and mass transfer models on the calculated Kalina cycle condenser size is investigated at representative system conditions. A detailed heat exchanger model for a liquid-coupled microchannel ammonia/water condenser is developed. The heat exchanger is sized using different predictive methods to provide the required heat transfer area for a 1 kWe Kalina system with a source and sink temperature of 150 °C and 20 °C, respectively. The results show that for the models considered, predicted heat exchanger size can vary by up to 58%. Based on prior experimental results, a nonequilibrium approach is recommended to provide the most accurate, economically sized ammonia/water condenser.

A 2D model and heat transfer mechanism are proposed to analyze and study oxidative steam reforming of methane (OSRM) in a membrane reactor. The model describes mass and thermal dispersions for gas and solid phases. It also accounts for transport through the membrane. The effects of operating parameters on methane conversion and H 2 yield are analyzed. The parameters considered are the bed temperature (800–1100 K), molar oxygen-to-carbon ratio (0.0–0.5), and steam-to-carbon ratio (1–4). The results show that our model prevents overestimation and provides valuable additional information about temperature and concentration gradients in membrane reactor which is not available in a simple one-dimensional approach. Simulation results show that large temperature and concentration gradients cannot be avoided. The particle properties and the bed diameter have a considerable effect on the extent of gas mixing. Effective gas mixing coefficient also increases with increasing gas and solid velocity. In membrane reactor, simulation results show that mixing which depends on operational and design parameters has a strong effect on the hydrogen conversion. Also, the removal of hydrogen with membranes breaks equilibrium barrier leading to efficient production of hydrogen, reduced reactor size, and tube lengths. The model can be used in real-time simulation of industrial reactors for control and optimization purposes.

A scale-invariant model of statistical mechanics is applied to describe modified forms of zeroth, first, second, and third laws of classical thermodynamics. Following Helmholtz, the total thermal energy of the thermodynamic system is decomposed into free heat U and latent heat pV suggesting the modified form of the first law of thermodynamics Q = H = U + pV. Following Boltzmann, entropy of ideal gas is expressed in terms of the number of Heisenberg–Kramers virtual oscillators as S = 4 Nk. Through introduction of stochastic definition of Planck and Boltzmann constants, Kelvin absolute temperature scale T (degree K) is identified as a length scale T (m) that is related to de Broglie wavelength of particle thermal oscillations. It is argued that rather than relating to the surface area of its horizon suggested by Bekenstein (1973, “Black Holes and Entropy,” Phys. Rev. D, 7 (8), pp. 2333–2346), entropy of black hole should be related to its total thermal energy, namely, its enthalpy leading to S = 4Nk in exact agreement with the prediction of Major and Setter (2001, “Gravitational Statistical Mechanics: A Model,” Classical Quantum Gravity, 18 , pp. 5125–5142).

In this study, a nonstoichiometric single-phase chemical equilibrium model was developed to simulate atmospheric circulating fluidized bed (CFB) coal gasifiers in reference to the available experimental and simulation data. In the literature, since the single-phase model assumes complete conversion of the solid particles to gas phase, the predictions for the resulting products of the gasifiers considerably deviate from the measured product concentrations. Two different model modifications for carbon conversion and temperature to improve the model results were tested. Particularly, carbon conversion modification has been found to improve the predictive ability significantly. The main reasons of the inaccuracy in the tested cases as well as the performance of some other modifications (quasi-equilibrium approach, empirical correlation for carbon conversion, etc.) were also discussed in comparison with the literature data. An alternative mathematical procedure that simplifies the formulation and numerical implementation was suggested as well.

The rate-controlled constrained-equilibrium method (RCCE) has been further developed to model the combustion process of ethanol air mixtures. The RCCE is a reduction technique based on local maximization of entropy or minimization of a relevant free energy at any time during the nonequilibrium evolution of the system subject to a set of kinetic constraints. An important part of RCCE calculation is determination of a set of constraints that can guide the nonequilibrium mixture to the final stable equilibrium state. In this study, 16 constraints have been developed to model the nonequilibrium ethanol combustion process. The method requires solution of 16 differential equations for the corresponding constraint potentials. Ignition delay calculations of ethanol oxidizer mixtures using RCCE have been compared to those of detailed chemical kinetics using 37 species and 235 reactions. Agreement between the two models is very good. In addition, ignition delay of C 2 H 5 OH/O 2 /Ar mixtures using RCCE has been compared with the experimental measurements in the shock tube and excellent agreement has been reached validating the RCCE calculation.

A comparative assessment is made of two implementations of the rate-controlled constrained-equilibrium (RCCE) method. These are the constraint and constraint potential formulations in which rate equations are solved for the RCCE constraints and constraint potentials, respectively. The two forms are equivalent mathematically; however, they involve different numerical procedures and thus show different computational performance. The main objective of this study is to compare the accuracy and numerical efficiency of the two formulations to attain the most effective implementation of the RCCE in turbulent combustion simulations. The RCCE method is applied to study methane oxygen combustion in an adiabatic, isobaric well stirred reactor. Simulations are carried out over a wide range of initial temperatures and equivalence ratios. Performance studies are conducted and RCCE results are compared with those obtained by direct integration of detailed chemical kinetics. The results show that both methods provide very accurate representation of the kinetics. It is also demonstrated that while the constraint form involves less numerical stiffness, the constraint potential implementation results in more saving in computation time.

We present the foundations of thermodynamics in a novel sequence in which all basic concepts are defined in terms of well known mechanical ideas. Many definitions are new. The order of introduction of concepts is: system (constituents and parameters); properties; state; energy (without heat and work) and energy balance; classification of states in terms of time evolution; existence of stable equilibrium states; available energy; entropy (without heat and temperature) of any state (equilibrium or not) and entropy balance; properties of stable equilibrium states; temperature in terms of energy and entropy; chemical potentials; pressure; work; heat; applications of balances. This novel sequence not only generalizes the subject of thermodynamics to all systems (large or small) and all states (equilibrium and not equilibrium) but also avoids both the conceptual and definitional difficulties that have been recognized by so many teachers, and the confusion experienced by so many students.