Restricted Equilibrium Research Articles

Industrial-scale Fixed-bed Coal Gasification: Modeling, Simulation and Thermodynamic Analysis

We have developed a process model to simulate the behavior of an industrial-scale pressurized Lurgi fixed-bed coal gasifier using Aspen Plus and General Algebraic Modeling System (GAMS). Reaction characteristics in the fixed-bed gasifier comprising four sequential reaction zones—drying, pyrolysis, combustion and gasification are respectively modeled. A non-linear programming (NLP) model is developed for the pyrolysis zone to estimate the products composition which includes char, coal gases and distillable liquids. A four-stage model with restricted equilibrium temperature is used to study the thermodynamic equilibrium characteristics and calculate the composition of syngas in the combustion and gasification zones. The thermodynamic analysis shows that the exergetic efficiency of the fixed-bed gasifier is mainly determined by the oxygen/coal ratio. The exergetic efficiency of the process will reach an optimum value of 78.3% when the oxygen/coal and steam/coal mass ratios are 0.14 and 0.80, respectively.

Modelling super-equilibrium in biomass gasification with the constrained Gibbs energy method

The biomass gasification process is modelled by utilising constrained thermodynamic equilibrium. The formation of char, tar, ammonia and light hydrocarbons and related syngas composition were described by extending the conventional chemical system with additional immaterial constraints and by defining process-dependent values for these constraints.Six different model structures were evaluated from global thermodynamic equilibrium to fully constrained local equilibrium. When models were validated against gasification setups, it was not necessary to fully constrain the system, as sufficient results were obtained by implementing constraints for char, tar, ammonia, CH4 formation as well as for the amount of carbon in light hydrocarbons. The method was shown to be versatile when it was validated against other gasification setups: by altering the models defining the constraints a new gasification conditions could be simulated.A clear benefit of the proposed method is that the gasification process can be resolved as a restricted partial equilibrium with a single calculation step. Another benefit is that chemical reactions, gasification enthalpy and the states of the system are estimated concurrently.

Simulation of a pilot‐scale dual‐fluidized‐bed gasifier for biomass

A dual‐fluidized‐bed gasifier was constructed and operated at the Woodland Biomass Research Center in Woodland, CA. The pilot‐scale gasifier had a capacity of 5 tons/day of feedstock and was based on the Pyrox process developed by Kunii et al. In this system, the fluidized‐bed combustion process with air is separated from the biomass gasification process with steam and recycle gas. This decreases the nitrogen content in the producer gas. The heat released in the combustion of the char is transported by a ceramic bed material circulating between the combustor and gasifier. Commercial wood pellets were used as feedstock for the present study. Gas composition, temperatures, and pressures were measured to characterize the operation of the gasifier. A positive feature of the system was the high circulation rate and efficient energy transfer between the combustor and gasifier. Analysis of the system was performed using Aspen Plus™ software to calculate mass and energy‐balances. A restricted equilibrium model for the producer‐gas composition agreed reasonably well with the measured non‐equilibrium gas composition for most gases. The restricted equilibrium model over‐predicted the H2 concentrations. A more complex rate‐based kinetic model would be necessary to fully capture the details of the non‐equilibrium gas composition in this pilot‐scale gasifier. © 2014 American Institute of Chemical Engineers Environ Prog, 33: 732–736, 2014

Simulation of Syngas Production from Municipal Solid Waste Gasification in a Bubbling Fluidized Bed Using Aspen Plus

A comprehensive process model is developed to simulate municipal solid waste (MSW) gasification in a bubbling fluidized bed using an Aspen Plus simulator. The model is based on a combination of modules that the Aspen Plus simulator provides, representing the three stages of gasification (devolatilization, partial oxidation, and steam reforming). The restricted equilibrium method is used to correct the deviation caused by uncompleted equilibrium of gasification system. Effects of operating parameters, including gasification temperature, equivalence ratio (ER), oxygen percentage in the enriched air (OP), MSW moisture content, and steam/MSW ratio (S/M), on the syngas composition and gasifier efficiency are analyzed. Higher temperature favors the production of H2 and CO and leads to higher gasification efficiency. Increasing ER improves the CO yield and the carbon conversion of MSW at lower ERs. The optimal value of ER for air gasification of MSW in this study is found to be 0.35. The use of enriched air elev...

Simulate and Analyze of Biomass Gasification in Supercritical Water

On the basis of ASPEN PLUS-based Gibbs free energy minimization, a biomass gasification model was modified by the restricted equilibrium of the RGIBBS reactor and developed and used to simulate glucose. It is showed that the simulation result and experiment result fit well. In the process of pomace gasification in supercritical water, a sensitivity analysis with temperature and pressure is performed and the research of the gas heating value has been done. From the analysis result, without using catalyst, the temperature has influenced on the gas product most and the pressure has little effect on gas product.

Elemental distribution, solute solubility and defect free volume in nanocrystalline restricted-equilibrium Cu–Ag alloys

In this article we study the elemental distribution and solute solubility in nanocrystalline alloys of immiscible components near restricted equilibrium for the case of the binary Cu–Ag system. As predicted from thermodynamic considerations, a grain boundary segregated monophase alloy is observed in the annealed mechanically alloyed state for low Ag content by using atom probe tomography. From the detected Ag solute grain boundary enrichment the segregation free enthalpy is estimated to range between −25 and −49 kJ mol−1 following the McLean equation, in agreement with values reported for coarse-grained Cu–Ag. The extension of the alloying range is described by a two-domain thermodynamic model that considers the excess free volume in the grain boundaries and the strain in the grain interior on the basis of the universal equation of state at negative pressure. To access the grain boundary volumetric strain experimentally, a method based on a combination of density measurements and microscopical quantification of closed pore areas is presented. Moreover, we apply x-ray diffraction line broadening analysis to determine the local strain amplitude, which yields a root-mean-square microstrain of ∼0.3% for a grain size of ∼30 nm. It is shown that the grain boundary free volume represents the major origin for the global solubility enhancement in nanocrystalline Cu–Ag at 503 K.

The multiple-partners assignment game with heterogeneous sales and multi-unit demands: competitive equilibria

A multiple-partners assignment game with heterogeneous sales and multi-unit demands consists of a set of sellers that own a given number of indivisible units of potentially many different goods and a set of buyers who value those units and want to buy at most an exogenously fixed number of units. We define a competitive equilibrium for this generalized assignment game and prove its existence by using only linear programming. In particular, we show how to compute equilibrium price vectors from the solutions of the dual linear program associated to the primal linear program defined to find optimal assignments. Using only linear programming tools, we also show (i) that the set of competitive equilibria (pairs of price vectors and assignments) has a Cartesian product structure: each equilibrium price vector is part of a competitive equilibrium with all optimal assignments, and vice versa; (ii) that the set of (restricted) equilibrium price vectors has a natural lattice structure; and (iii) how this structure is translated into the set of agents’ utilities that are attainable at equilibrium.

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Sensitivity Analysis of Combined Distribution–Assignment Model with Applications

The equilibrium trip distribution–assignment model with variable destination costs (ETDA-VDC) is critical for the modeling of evacuation strategies that consider transportation network capacity. The model is an improvement over the combined distribution–assignment model because it integrates the destination cost function. With mild requirements, a rectified restriction approach was developed to generate a restricted equilibrium problem, in which the applicability of the implicit function theorem was proved. Explicit expressions of the derivatives of model variables for perturbations of input variables and parameters of the ETDA-VDC model were derived. The results of a simple numerical example were used to demonstrate four applications: sensitivity-based algorithm for the bilevel network capacity model, analysis of paradox, identification of critical parameters, and access control. The usefulness and importance of the sensitivity expressions were also demonstrated.

Distance measures between free trade and autarky for the world economy

We develop a methodology to determine numerically how globalized the world economy is. We present a global general equilibrium model capturing major OECD economies and a residual rest of world for which alternative metrics of distance between observed, free trade and autarky equilibria can be developed. We use data for 2000 and report a number of distance measures between the 2000 observed trade restricted equilibrium and both free trade and autarky equilibria noting the absence of prior literature on metrics of distance between equilibria. The measures are used to determine the degree to which the world economy is globalized.

Learnability of Heterogeneous Misspecification Equilibrium

This paper investigates the learnability of the equilibrium under adaptive learning with heterogeneous and misspecified models. Agents have imperfect and mutually different information sets of economic variables, so they form heterogeneous expectations under learning rules that are differently underparameterized. Under heterogeneous learning, the economy converges to a type of restricted perceptions equilibrium, which here is called a Heterogeneous Misspecification Equilibrium (HME). The paper finds that the HME is more learnable than the equilibrium under homogeneous and correctly specified learning rules that corresponds to a rational expectations equilibrium (REE); in other words, the stability conditions of the HME are less stringent than those of the REE. In a basic NK model with a Taylor-type monetary policy rule, for example, the central bank is allowed to choose a wider range of values of policy parameters to ensure the learnability of the HME than that permitted to ensure the learnability of the REE, that is, the Taylor principle. In addition, if the correlation between demand and supply shocks is low, the stability conditions of the HME become further less stringent so that the central bank might not have to address the learnability of the equilibrium.

The effect of air preheating in a biomass CFB gasifier using ASPEN Plus simulation

Abstract In the context of climate change, efficiency and energy security, biomass gasification is likely to play an important role. Circulating fluidised bed (CFB) technology was selected for the current study. The objective of this research is to develop a computer model of a CFB biomass gasifier that can predict gasifier performance under various operating conditions. An original model was developed using ASPEN Plus. The model is based on Gibbs free energy minimisation. The restricted equilibrium method was used to calibrate it against experimental data. This was achieved by specifying the temperature approach for the gasification reactions. The model predicts syn-gas composition, conversion efficiency and heating values in good agreement with experimental data. Operating parameters were varied over a wide range. Parameters such as equivalence ratio (ER), temperature, air preheating, biomass moisture and steam injection were found to influence syn-gas composition, heating value, and conversion efficiency. The results indicate an ER and temperature range over which hydrogen (H 2 ) and carbon monoxide (CO) are maximised, which in turn ensures a high heating value and cold gas efficiency (CGE). Gas heating value was found to decrease with ER. Air preheating increases H 2 and CO production, which increases gas heating value and CGE. Air preheating is more effective at low ERs. A critical air temperature exists after which additional preheating has little influence. Steam has better reactivity than fuel bound moisture. Increasing moisture degrades performance therefore the input fuel should be pre-dried. Steam injection should be employed if a H 2 rich syn-gas is desired.

Investigation of interfacial adhesion in nylon-6 fibre/NBR composites through restricted equilibrium swelling technique

Short nylon-6 fibre reinforced acrylonitrile butadiene rubber (NBR) composites were prepared and the interfacial adhesion was evaluated by the restricted solvent swelling technique. The solvents used were N,N-dimethyl formamide (DMF), dimethyl sulphoxide (DMSO) and acetonitrile. As the fibre content increased, the solvent uptake decreased, which has been attributed to the increased hindrance to solvent penetration due to better fibre–rubber interaction. It was observed that the ratio of change in volume fraction of rubber before and after swelling to the volume fraction of rubber before swelling (V 0 – V r/V 0) was lower for a bonding agent added composite, compared to the unbonded one. Anisotropic swelling studies were carried out to analyze the extent of fibre alignment and fibre–matrix interaction. It was seen that in strongly bonded composites, the swelling mainly took place in the thickness direction. The rubber–fibre interaction has also been examined by the Lorenz–Parks and Kraus equations.

Surface Forces at Restricted Equilibrium, in Solutions Containing Finite or Infinite Semiflexible Polymers

We use density functional theory to investigate how the presence of polymers influence the interactions between adsorbing or nonadsorbing flat surfaces, forming a slit geometry. The study is primarily made under “restricted equilibrium” conditions, i.e., below a threshold separation, the chains are allowed to equilibrate conformationally between the surfaces, but they are unable to diffuse into or out from the slit. This is believed to be a reasonable model for commonly encountered experimental situations, when the surfaces are large and adsorbing and the polymers are long. Using a recently presented density functional theory, we are able to compare predictions for chains of finite and infinite length. A major advantage of the infinite chain formulation is that it is a high resolution theory, and predictions from the finite length version will exactly approach the ones for infinite chains, when the degree of polymerization becomes large enough. Our study spans across a relatively large number of relevant system parameters, such as bulk concentration, surface adsorption strength, polymer length, and chain flexibility. The response in terms of the net surface interaction, to a change of a system parameter, is often nonmonotonic. We also make comparisons with predictions at full equilibrium, where the diffusion constraint has been relaxed. We give a specific example of how a diffusion-limited process can lead to hysteresis effects, similar to those observed in many surface force measurements. Finally, in a separate section of this work, we have included some direct experimental comparisons, demonstrating the relevance and applicability of restricted equilibrium conditions to “real world” scenarios. The computational power of the density functional approach is here highlighted, with calculations including semiflexible 20000-mers.

Experimental Evidence on the Persistence of Output and Inflation

This article presents experimental evidence from a monetary sticky price economy in which output and inflation depend on expected future inflation. Rational inflation expectations do not allow for persistent deviations of output and inflation following a monetary shock. In the experimental sessions, however, output and inflation display considerable persistence and regular cyclical patterns. This emerges because subjects’ inflation expectations fail to be captured by rational expectations functions. Instead, a Restricted Perceptions Equilibrium (RPE), which assumes that agents use optimal but ‘simple’ forecast functions, describes subjects’ inflation expectations surprisingly well and explains the observed behaviour of output and inflation.

Modelling coal gasification with CFD and discrete phase method

In the present paper the authors describe a computational fluid dynamics model of a two-stage, oxygen blown, entrained flow, coal slurry gasifier for use in advanced power plant simulations. The discrete phase method is used to simulate the coal slurry flow. The physical and chemical processing of coal slurry gasification is implemented by calculating the discrete phase trajectory using a Lagrangian formulation. The particle tracking is coupled with specific physical processes, in which the coal particles sequentially undergo moisture release, vaporisation, devolatilisation, char oxidation and char gasification. Using specified plant boundary conditions, the gasification model predicts a synthesis gas composition that is very close to the values calculated by a restricted equilibrium reactor model tuned to represent typical experimental data. The char conversions are 100 and 86% for the first stage and second stage respectively.

The value of central bank transparency when agents are learning

We examine the role of central bank transparency when the private sector is modeled as adaptive learners. In our model, transparent policies enable the private sector to adopt correctly specified models of inflation and output while intransparent policies do not. In the former case, the private sector learns the rational expectations equilibrium while in the latter case it learns a restricted perceptions equilibrium. These possibilities arise regardless of whether the central bank operates under commitment or discretion. We provide conditions under which the policy loss from transparency is lower (higher) than under intransparency, allowing us to assess the value of transparency when agents are learning.

Surface forces in a confined polymer melt: Self-consistent field analysis of full and restricted equilibrium cases

In full equilibrium the self-consistent field theory for a homopolymer melt confined between two surfaces predicts pronounced oscillatory interaction forces on the monomer length scale. However, when not all the polymer molecules can reversibly equilibrate with the bulk, the trapped molecules may be squeezed, adding a repulsive contribution to the interaction energy. The classical constrained or restricted equilibrium approach by Scheutjens and Fleer two decades ago to deal with this for polymers adsorbed from dilute solutions, breaks down in semidilute and concentrated polymer solutions. We present a generalized restricted equilibrium ansatz applicable also for concentrated polymer solutions. The key idea is that only the adsorbed polymer molecules, i.e., molecules that touch the surface at least once, are forced to remain inside the gap, whereas the nonadsorbing chains are free to move out of the gap when the surfaces approach each other. As in dilute solutions, the forces found in confined melt with trapped adsorbed chains become repulsive. We analyse the dependence of the interaction forces both in full as well as in restricted equilibrium cases as a function of the chain length and the interactions with the surface for a compressible polymer melt.

A simple approach to electromagnetic actuator control based on asymptotically exact linearization

This paper deals with system identification and robust control of a nonlinear electromagnetic actuator and proposes a simple, robust, and easy-to-implement compensation law for linearization, known as asymptotically exact linearization. There are many practical applications where this type of electromagnetic actuator is used: electromagnetic valve actuators of combustion engines, artificial heart actuators, electromagnetic brakes, etc. The investigated system is open-loop unstable and nonlinear and has a restricted equilibrium region. System identification experiments are presented with an emphasis on the design procedure of an Open image in new window controller. The experimental results demonstrate that the controller design problem can be successfully handled within the framework of robust control. This paper reflects a rather pragmatic control approach and, although it does not introduce novel control strategies, might be valuable reading for practicing engineers.

OBTAIN ALGORITHM FOR THE SUPPLY CHAIN NETWORK EQUILIBRIUM PROBLEM

An origin-based solution algorithm, named OBTAIN (origin-based traffic assignment for infrastructure networks), was recently developed for solving the traffic assignment problems (Bar-Gera and Boyce, 2003). This algorithm defines the solution variables in an intermediate way between links and routes, and has been proven to be superior to the link-based Frank-Wolfe method in both computational time for and accurate level of the solution for a large network. To address its usefulness, the OBTAIN algorithm is elaborated in a tutorial manner, especially in its two major steps for updating the restricting subnetworks and origin-based approach proportions, and then applied to a small supply chain network equilibrium problem. The obtained results comply with the sufficient conditions for restricted user equilibrium. Future research includes a real application of large networks and a comparison of the OBTAIN algorithm with the route-based gradient projection (GP) algorithm in terms of computational efficiency.