Search

This study demonstrates the efficacy of a short-cut method such as the Global Minimization Algorithm (GMA),(1,2) that uses assumptions of ideal mixtures, constant molar overflow (CMO) and pinched columns, in pruning the search-space of distillation column configurations for zeotropic multicomponent separation, to provide a small subset of attractive configurations with low minimum heat duties. The short-cut method, due to its simplifying assumptions, is computationally efficient, yet reliable in identifying the small subset of useful configurations for further detailed process evaluation. This two-tier approach allows expedient search of the configuration space containing hundreds to thousands of candidate configurations for a given application. [ABSTRACT FROM AUTHOR]

Chemical reactions on the surface or throughout a thermoplastic fiber present an interesting and challenging reaction engineering problem. This paper presents the design and implementation of a modular multiphase continuous stirred tank reactor for the sulfonation of polyethylene fibers. Polyethylene fiber tows, composed of 1000-6000 filaments, are sulfonated in a series of stirred tank reactors. Fundamental reaction engineering principles are applied to address common batch-to-continuous reactor challenges, such as heat and mass transfer, material balances, and reaction kinetics. The introduction of polymer fibers to a continuous process also requires the solution of practical problems associated with fiber processing. Additional considerations are introduced for designing a reactor system for continuous processing of fiber using liquid with a batch reactor or CSTR contacting pattern in each vessel and containing the effluent gaseous reaction byproducts in a controlled vent stream. The overall sulfonation reaction stoichiometry was determined such that ≈1 mol of SO3 reacts per mol of CH2 fed. Additionally, carbon sulfonation selectivity was determined to be 95-99%, depending on the sulfonation conditions. [ABSTRACT FROM AUTHOR]

This work is a continuation and extension of previously published study showing that the perturbed-chain statistical associating fluid theory (PC-SAFT) is an efficient and robust approach for calculating thermodynamic properties of the mixtures containing ionic liquids (ILs) [J. Phys. Chem. B 2012, 116, 5002–5018]. The modeling strategy presented in the original paper was based on application of infinite dilution activity coefficients of molecular solutes in ILs (γ∞) to calculate binary corrections for the PC-SAFT combining rules. In this work, the idea is further investigated, in particular extended to a broader spectrum of pure fluids (the model parametrization is provided for almost 100 ILs), and evaluated based on a large compilation of liquid–liquid equilibrium (LLE) data, including more than 400 distinct and diverse ternary systems and a number of higher systems. Three PC-SAFT modeling strategies are proposed and systematically reviewed in order to elucidate an effect of γ∞ data on the quality of LLE predictions. Experimental versus predicted impact of ILs’ cation and anion on LLE for different kinds of binary subsystems of molecular compounds is also highlighted and discussed. Finally, the results obtained with the PC-SAFT are confronted with the calculations carried out with conductor-like screening model for real solvents (COSMO-RS), often perceived or referred to as the state-of-the-art predictive tool of modern thermodynamics of liquid solutions. [ABSTRACT FROM AUTHOR]

The continuous production of LaCrO3 particles (average edge size 639 nm, cube-shaped) by continuous hydrothermal flow synthesis using supercritical water is reported for the first time. By varying the reaction conditions, it was possible to suggest a reaction mechanism for the formation of this perovskite material. Moreover, dual-phase oxygen transport membranes were manufactured from the as-synthesized LaCrO3 particles and (ZrO2)0.89(Y2O3)0.01(Sc2O3)0.10 (10Sc1YSZ), and oxygen permeation fluxes up to 5 x 10-8 mol cm-2 s-1 were measured on a 1 mm thick membrane. [ABSTRACT FROM AUTHOR]

An algorithm is presented for constructing complete asphaltene PT phase diagrams. The algorithm works with any equation of state capable of providing consistent fugacity coefficients and appropriate derivatives for gas, oil, and asphaltene-rich phases. SRK, PC-SAFT, and CPA were successfully applied. The algorithm has been validated against multiphase PT flash calculations, and the results are further shown to agree with asphaltene simulation results in the open literature. Construction of the asphaltene PT phase diagram is fast and robust even in near-critical regions. Examples are shown illustrating the multitude of possible appearances of an asphaltene PT phase diagram. The algorithm has been modified to take an injection gas amount as specification, which allows for construction of asphaltene Px phase diagrams showing the response of phase boundaries to gas injection. Usage of the algorithm to get a full overview of the behavior of the asphaltene precipitation of the fluid is demonstrated. [ABSTRACT FROM AUTHOR]

Channeling of gas can reduce mass transfer performance in multiphase micropacked-bed reactors. Viscous and capillary forces cause this undesired and often unpredictable phenomenon in systems with catalyst particle sizes of hundreds of micrometers. In this work, we acoustically modify flow in a micropacked-bed reactor to reduce gas channeling by applying high-power sonication at low ultrasonic frequencies (~40 kHz). Experimental residence time distributions reveal two orders of magnitude reduction in dispersion with ultrasound, allowing for nearly plug-flow behavior at high flow rates in the bed. Sonication appears to partially fluidize the packed-bed under pressurized cocurrent two-phase flow, effectively improving dispersion characteristics. [ABSTRACT FROM AUTHOR]

The turbulence characteristics in the presence of bubbles is very important for multiphase processes such as froth flotation. The turbulence characteristics in an aerated Denver flotation cell were investigated using a high speed stereoscopic particle image velocimetry technique at single-phase (water) and two-phase (water and air) systems to provide insight into the change in liquid phase hydrodynamics. The effect of the gas flow rate (0.043-0.125 cms-1) and Reynolds number (107 000-154 000) on the fluid flow properties were investigated. The results showed that the flow pattern at the both systems was the radial-type flow. The presence of air bubbles changed the local turbulence characteristics (mean velocity, the root-mean-square velocity, turbulence kinetic energy dissipation, and turbulence kinetic energy). The results obtained may be useful for deeper investigation about the effect of the turbulence properties on the hydrodynamic characteristics and subprocesses in the mechanical flotation cells. [ABSTRACT FROM AUTHOR]

A multiphase flow profile inside a helically coiled tubular device (HCTD) was observed by using a high-speed camera. Gas-liquid slug flow observations revealed that the Taylor vortices are influenced by secondary flow due to the centrifugal force acting perpendicular to the flow direction. Hence, mixing inside the liquid slug is enhanced by the combination of Dean and Taylor vortices in HCTD. The modular design of a specific type of HCTD, that is, the coiled flow inverter (CFI) is elucidated by the representation of a new design space diagram. Continuous precipitation of calcium carbonate (CaCO3) was investigated for modular CFI made of polyvinyl chloride (PVC) tubes (di = 3.2 mm) with slug flow patterns. CaCO3 was continuously precipitated along CFI with a conversion of ca. 90%. CFI provided a narrower particle size distribution with median particle diameters around 28 µm and more uniform morphology in comparison to a batch reactor. [ABSTRACT FROM AUTHOR]

Separation and purification of gas mixtures using selective adsorbents is widely used in different industries such as gas drying, air separation, and H2 purification. Equilibrium analysis involving adsorption of binary gas mixtures provides important information related to the adsorbent performance in the separation of gases. In this study, a novel technique termed "differential column technique" was developed for binary isotherm measurement employing streams containing carbon dioxide, carbon monoxide, and ethylene at different compositions. This technique is based on measuring the gas desorption by changing equilibrium pressure conditions. The isotherm curve was generated by summing desorption amounts desorbed at each pressure step. Through the application of this technique, the single-component isotherms of CO2, CO, and ethylene on zeolite NaY were measured, and the isotherms were compared to the results obtained by a standard gravimetric technique. (The average relative deviation is less than 6%.) The main advantage of the technique is the significant time savings, e.g., one experimental run is required to generate an isotherm compared to multirun experiments using a standard breakthrough technique, in addition to using a simpler experimental setup and generally smaller amount of sample (agglomerated or in a powder form). Another important feature of this technique is the relatively simple extension that allows measurements of gas mixture equilibria. As such, the proposed technique has the potential to be used as a fast screening technique for adsorbent selection based on single-component or mixture analysis. To investigate the consistency of the proposed technique, the binary isotherms of competitive, CO2-C2H4, and noncompetitive, CO2-CO, mixtures were investigated at different gas compositions. In addition, the effects of sorbate concentrations in the gas phase and interactions with the NaY zeolite active surface were investigated in relation to the adsorption selectivity and capacity, i.e., strong interaction of both CO2 and ethylene with NaY site resulted in close adsorption selectivity 0.8 ≤ SCO2/C2H4 ≤ 1.7, while CO2 adsorbed more selectively compared to CO, 14 ≤ SCO2/CO ≤ 30, as a result of weak CO interaction with the adsorbent sites. Finally, the binary adsorption isotherms and selectivity were predicted by the multisite Langmuir model using the single component's isotherm parameters. Modest agreements (error ≤ 28%) were obtained between the predicted and experimental results. [ABSTRACT FROM AUTHOR]

Dew point specifications are of high interest in the natural gas industry. The CPA equation of state (EoS) was previously validated against both water content and phase equilibrium data. Moreover, solid model parameters were estimated for four natural gas main components (methane, ethane, propane, and carbon dioxide). In this study we have extended the use of CPA EoS to perform equilibrium temperature calculations for natural gas main components with (mono-)ethylene glycol (MEG) as an inhibitor. The ternary systems with aqueous MEG solution include methane, ethane, propane, carbon dioxide, and hydrogen sulfide. The quaternary systems with aqueous MEG solution include methane + ethane, methane + propane, methane + n-heptane, and methane + n-octane. Three multicomponent systems (>4 components) were also studied. The temperature range of the literature data is between 241.25-333.15 K, and the pressure range is between 0.1-24.8 MPa. The results in all cases are compared against experimental data, and very good agreement with experimental data is obtained. [ABSTRACT FROM AUTHOR]

The accurate prediction of the conditions of a pressurized jet upon its expansion to atmospheric pressure is of fundamental importance in assessing the consequences associated with accidental releases of hazardous fluids from pressurized containments. An integral multiphase compressible jet expansion model which for the first time accounts for turbulence generation is presented. Real fluid behavior is accounted for applying a suitable equation of state. By use of the accidental release of two-phase CO2 from a pressurized system as an example, the proposed model is shown to provide far better predictions of the fully expanded jet momentum and hence its downstream flow characteristics as compared to existing integral models where the impact of turbulence generation is ignored. [ABSTRACT FROM AUTHOR]

Three-phase processes in which particle suspension has to be achieved in conjunction with gas dispersion are traditionally carried out in sparged, baffled stirred tanks. The operation of such tanks can suffer, however, from particles tending to block the sparger holes. A viable alternative might be provided by uncovered unbaffled stirred tanks (UUSTs), where gas self-injection can occur when the free-surface vortex reaches the impeller blades and gas bubbles begin to be ingested by the liquid. In this work, the particle suspension and liquid aeration performances in three-phase UUSTs were experimentally investigated and compared with relevant literature correlations concerning baffled systems. The results show that, at least at the investigated scale, UUSTs are more efficient for suspending particles than relevant baffled systems. Impeller clearance scarcely affects power requirements. Finally, a down-pumping PBT with D/T = 1/3 was found to be the best choice for attaining complete suspension under self-aeration conditions. [ABSTRACT FROM AUTHOR]

Confined fluids such as oil and gas mixtures inside tight reservoirs are systems that can experience high capillary pressure difference between the liquid and gas phases. This capillary pressure difference has an effect on the phase equilibrium and in some cases is considerably high. We presented an algorithm which can reliably compute the whole phase envelope for multicomponent mixtures when there is a capillary pressure difference. It uses an equation of state for the phase equilibrium and the Young-Laplace equation for the capillary pressure model. The algorithm proves to be robust and efficient for test mixtures with wide ranges of compositions at different capillary radii and vapor fractions. The calculation results show that the phase envelope changes everywhere except at the critical point. The bubble point and the lower branch of the dew point show a decrease in the saturation pressure, whereas the upper branch of the dew point shows an increase. The cricondentherm is shifted to a higher temperature. We also presented a mathematical analysis of the phase envelope shift due to capillary pressure based on linear approximations. The resulting linear approximation equations can predict the correct direction of the phase envelope shift. Combined with the multicomponent Clapeyron equation, the equations reveal why the shift changes direction for the saturation pressure at the cricondentherm and for the saturation temperature at the cricondenbar. The equations can be used to estimate the magnitude of shift, and the approximation is close for the change in the bubble point pressure. [ABSTRACT FROM AUTHOR]

As a novel research issue, the operating performance assessment for industrial processes has received growing interest in recent years. In this study, a multiple hypotheses testing-based operating optimality assessment and nonoptimal cause identification method is proposed to handle the online assessment of the batch processes with multiphase and uneven-length characteristics. A new Gaussian mixture model (GMM)-based offline phase division procedure is proposed. Compared to the existing methods, it can not only ensure that each phase contains the consecutive sampling instants but can also retain the characteristics of phase-uneven-length for retaining more-accurate phase information. The extra post-processing is not needed in phase division, and the assessment models of each phase are set up along with it. In online application, both the local and global online assessments are performed for a new batch based on the multiple hypotheses testing technology by controlling the false discovery rate. For the nonoptimal batch, the cause variables can be determined based on the variable contributions to the assessment index. Finally, the effectiveness of the proposed method is verified through a fed-batch penicillin fermentation process. [ABSTRACT FROM AUTHOR]

The multicomponent (binary and ternary) adsorption equilibria of three volatile organic compounds (VOCs) (acetone, toluene, and n-hexane) on activated carbon were studied under supercritical carbon dioxide (scCO2) conditions. The multicomponent adsorption equilibrium data were obtained at 313-353 K and 4.2-10.0 MPa and depended on the affinities of the adsorbates for the adsorbent. The amounts of adsorbed VOCs decreased with increases in the pressure and decreases in the temperature, owing to the effects of the CO2 density. The measured adsorption equilibria were correlated within 5.5% of the average relative deviation to the Dubinin-Astakhov equation using two parameters. These parameters, which were determined based on these correlations, provided information on the multicomponent adsorption equilibria of the VOCs under scCO2 conditions while considering the interactions between the VOCs and the adsorbent, the bulk phase CO2 density, and the competitive adsorption of the VOCs and CO2 in the adsorbed phase. [ABSTRACT FROM AUTHOR]

Cuckoo Search (CS), which is a nature-inspired stochastic optimization method, has been successfully applied for estimating binary interaction parameters of universal quasichemical (UNIQUAC) and nonrandom two-liquid (NRTL) activity coefficient models for liquid-liquid ternary systems involving 12 imidazolium and phosphonium ionic liquids (ILs). Thirty-nine ternary systems, comprising 371 experimental tie-lines, were correlated by the UNIQUAC and NRTL models. The results, expressed by deviations between experimental and calculated mole fractions, are very satisfactory, with global deviation values of 0.0053 (UNIQUAC) and 0.0072 (NRTL), which are 63% and 45% better than literature reported values. Three quaternary systems and one quinary system were taken from literature to compare the capability of CS algorithm with genetic algorithm (GA) and particle swarm optimization (PSO) algorithm. The global % root-mean-square deviation (RMSD) value obtained with CS algorithm was ~0.14-0.85% as compared to ~1.0-2.0% with GA and PSO algorithms. This shows a higher efficiency for the CS algorithm in solving global optimization problems involved in the thermodynamic modeling of multicomponent systems. [ABSTRACT FROM AUTHOR]

The Group Contribution with Association Equation of State (GCA-EoS) has been successfully applied to represent the global phase behavior of carbon dioxide mixtures with alkanes. Using a single set of parameters, the model is able to predict vapor-liquid and liquid-liquid equilibria of binary mixtures not included in the parametrization procedure. Special emphasis was set on describing the transformation between types of fluid phase behavior to reduce the jeopardy of predicting incorrect liquid split. This family of binary systems has been investigated in previous works; however, this is the first time that GCA-EoS was shown to be able to represent the transformation between types of phase behavior as the length of the alkyl chain increases. The model was tested against an experimental database covering C3-C36 alkanes, temperatures from 210 to 660 K, and pressures up to 400 bar. The wide range of conditions and the parametrization strategy are keys to develop a robust thermodynamic tool for predicting multiphase behavior. [ABSTRACT FROM AUTHOR]

This work introduces a multiobjective optimization approach to integrate the design and control of multicomponent distillation sequences. The evaluation of the control properties and the design of the distillation systems were evaluated through the calculation of the condition number and the total annual cost of each design, respectively. Three distillation systems, including the direct sequence, the indirect sequence, and the dividing wall column along with three mixtures with representative ease of separation index (ESI) values and three different feed compositions, were studied. In addition, in a posterior stage to the optimization process, the Eco-indicator 99 for each design was estimated to quantify the environmental impact of the distillation systems. The results offer the trade-offs between the control properties and the design, which is shown through Pareto optimal solutions that enable selection of the solutions that establish the proper balances between both objectives. [ABSTRACT FROM AUTHOR]

This paper deals with the phenomenologicalcharacteristics of themultiphase flow in a 3D urea prilling tower under conditions closeto those of the industrial-scale process, considering the simultaneousheat and momentum transfer and the droplet solidification, using thecomputational fluid dynamics technique. The Euler–Lagrangeapproach is used to represent the multiphase flow. Solidificationof the droplets was considered by means of an unsolidified core model,which predicts the thickness of the solid phase formed from the surfaceto the center of the droplets during the evolution of their trajectoriesin the continuous phase. The global operational performance of theprocess was evaluated on the basis of the solidification and breakingindexes defined from local variables obtained from numerical simulations.Solidification index values in the range of 0.83–1.00 wereobtained from simulations, and the internal resistance to heat transferwas found to strongly affect the solidification phenomenon. A nonsymmetricalflow was used to evaluate the breaking index of droplets broken becauseof impact with the walls. The global thermal properties associatedwith the droplets, i.e., the surface and core temperatures and theoverall heat-transfer coefficient, had values of 34.37 °C, 115.79°C, and 19.29 W/m2K, respectively, for droplets witha diameter of 1.2 mm. The air temperature at the top of the towerwas 74.26 °C for droplets of this diameter. [ABSTRACT FROM AUTHOR]

Emulsionsare multiphasic fluid systems in which liquid dropletsare dispersed in another immiscible liquid. The main components ofan emulsion are the two liquid phases, typically oil and water, andthe emulsifier, which stabilizes the interface between the two liquidphases. Emulsifiers can be a variety of molecules, such as polymers,amphiphilic surfactants, and proteins, and they can also be colloidalparticles. Emulsion phase inversion is the process of interconversionbetween two types of simple emulsions: water-in-oil and oil-in-wateremulsions. Phase inversion can be induced by shifting the emulsifieraffinity from one phase to the other, which is called transitionalphase inversion. It can also be triggered by a change in the water-to-oilratio of the emulsion, which leads to a process known as catastrophicphase inversion. With recent advances in the stabilization of emulsionsusing colloidal particles and stimuli-responsive surfactants, numerousnovel emulsion systems that undergo emulsion phase inversion by meansof various mechanisms have been developed. In this review, we highlightthe most recent developments in the field of emulsion phase inversion,focusing on transitional phase inversion, inversion of particle-stabilizedemulsions, and flow- and shear-induced phase inversion. We also discussand compare state-of-the-art analytical methods that have been usedto detect and understand the emulsion phase inversion process. Ourcoverage spans from the early concepts of Bancroft’s rule throughthe concept of semiquantitative hydrophilic–lipophilic balanceto the more recent theoretical models used to predict and controlphase inversion phenomena. We conclude this review by presenting anoutlook on the future directions and outstanding problems that warrantfuture investigations to fully understand the mechanism of emulsionphase inversion at the single-droplet level. [ABSTRACT FROM AUTHOR]

The handling of multiphase systems applied in mixer-settler processes, in which phase separation characteristics are exploited, is to date still a challenge for the chemical industry. Approaches for analyzing the influencing parameters on these systems can be of use, especially regarding equipment design and technical applicability. In this contribution, a guideline is presented and applied in a case study for a surfactant-containing multiphase system implemented in a hydroformylation mini-plant. Herein, the most relevant investigated parameters such as temperature, concentrations of reactants, system pressure, and stirrer characteristics are analyzed. This is followed by an analysis of various internal fittings including their influence on the temperature profile within the settler. The results of the systematic analysis are used to design a highly flexible, modular, and efficient settler for the separation of up to three liquid phases. [ABSTRACT FROM AUTHOR]

The multicomponent potential adsorption theory (MPTA) is revisited in this work for polar and associating systems. MPTA is used in combination with the CPA equation of state. Previous studies have shown that both MPTA and other theories present difficulties for complex systems. Some of these problems could be due to the fact that the original MPTA assumes that a given adsorbent has the same adsorption capacity (for example, porous volume) for all the adsorbed substances and is adjusted simultaneously to many data. This is a simplified picture, as experimental data indicate that the adsorption capacities of the various components may also differ. In this paper we develop a scheme for the distribution of the potential, which accounts for the presence of the porous space occupied either by just one component or by both components. These capacities are determined by adjustment of the potentials to experimental data on single-component adsorption. We show that MPTA involving the different adsorption capacities for the different components is capable of predicting binary adsorption data for most of the mixtures considered. In our application of MPTA, we used both the well-known Dubinin-Radushkevich-Astakhov potentials and the potentials directly restored from experimental data by solving the inverse problem. Application of the latter potentials clearly demonstrates the importance of the difference in adsorption capacities. However, the quality of prediction of binary adsorption is similar for both potentials. Thus, we feel that there is no need to use more complex potentials provided that the difference in the individual adsorption capacities is accounted for. [ABSTRACT FROM AUTHOR]

Hydraulicfracturing is a technique for enhancing the extractionof oil and gas from deep underground sources. Two important goalsduring this process are to achieve a final fracture with a predefinedgeometry and to have a proper distribution of proppant material withinthe fracture to keep the fracture walls open and allow oil and gasto flow to the surface. The hydraulic fracturing system contains limitedreal-time measurements of the actual fracture conditions largely dueto the remote subterranean location where the fracture propagates.The fracturing process is characterized by multiphase transport, proppantsettling, and coupling of fluid and fracture growth mechanics, alloccurring within a time-varying spatial domain. These features presenta challenge for the implementation of online feedback control of thefracture growth and proppant placement, and there are very few accountsof attempting this goal in the open literature. To address these issues,the current work proposes a control strategy that allows for closed-loopmodel-based control of the hydraulic fracturing process. Previouswork introduced a dynamic fracture model capable of describing thefracture propagation, fluid and particle transport, proppant bankformation, and fracture closure processes necessary to determine thefracture state evolution and predict the fracture’s final performance.The QDMC (quadratic-dynamic matrix control) form of model-based controlis studied. A particle filter provides a means for effective stateestimation due to limited real-time measurements. Controlling thefracture geometry and proppant distribution within a hydraulic fractureis a novel application for real-time model-based control. Resultsof a numerical study are provided to demonstrate the performance ofthe closed-loop system. [ABSTRACT FROM AUTHOR]

Thispaper proposes a new method combining the multivariate trajectoryanalysis and the principal component analysis (PCA) for multiphasebatch process monitoring. To handle the uneven length problem, thetrajectories of process variables are calculated instead of the originalsamples. For online monitoring, similar trajectories are extractedby just-in-time learning (JITL) with historical trajectories and thePCA model is constructed, which can deal with the missing data problemas well. Furthermore, to acquire a more reliable monitoring performance,a new distance-based measurement is proposed to show the locationof samples. For performance evaluation, case studies of a numericalexample and a simulated penicillin fermentation process are provided,with detailed comparisons to traditional methods. [ABSTRACT FROM AUTHOR]

Emulsificationof crude oil and water may significantly affectthe flow characteristics of the multiphase flow in gathering lines.Obviously, emulsification of a crude oil–water system is greatlyaffected by conditions such as shear intensity, water fraction, andtemperature. However, there has been a lack of quantitative studyof the emulsified water fraction of crude oil–water systemsunder various conditions of water fraction, temperature, and shearintensity. In this work, experiments were conducted by using a stirredvessel calibrated for the determination of mean shear rate, and theemulsified water fractions under flowing conditions were determinedby extrapolation of the separated water volume to the moment whenstirring was just terminated. Full emulsification of water was observedin a specific range of shear rates and below a critical water fraction,and only partial emulsification might occur above this critical waterfraction. The range of shear rates in which full emulsification mightoccur became larger with a decrease in the water fraction, but itdid not change with temperature in the studied range from 40 to 90°C. For partial emulsification, the emulsified water fractionunder flowing conditions was found to correlate well with the entropyproduction rate of viscous flow or energy dissipation rate regardlessof the differences in water fraction, temperature, and shear rate,and a power law equation might well fit the data. [ABSTRACT FROM AUTHOR]

Deoxidation and refining of liquidsteel is the site of many complexphenomena, such as liquid–gas–solid multiphase flow,turbulence, precipitation, agglomeration, and extraction of multicomponentinclusions. The steel industry is very interested in developing aframework to integrate these different mechanisms. This is based onthree pillars: chemical thermodynamics, population balance, and transportphenomena. Accordingly, a homebrewed thermo-kinetics code is interfacedwith a commercial Computer Fluid Dynamic code through a populationbalance module. The population balance module resorts to the classicQuadrature Method of Moments extended to multicomponent inclusions.This paper is focused on a comparison between three-dimensional numericalresults obtained with or without taking into account precipitationkinetics. This distinction is important since under an assumptionof local equilibrium, harmful inclusions are completely dissolvedbefore the continuous casting occurs, whereas when using precipitationkinetics, harmful inclusions can be present in the final product.This is consistent with industrial samples. [ABSTRACT FROM AUTHOR]

Reactivekinetics coupled with population balance model (PBM) andcomputational fluid dynamics (CFD) was implemented to simulate silvernanoparticles (AgNPs) formation in a microtubular reactor. The quadraturemethod of moments, multiphase model theory, and kinetic theory ofgranular flow were employed to solve the model, and the particle sizedistributions (PSD) were calculated. The simulation results were validatedby synthesizing AgNPs experimentally in an actual microtubular reactorfor comparison with the PSD. The results confirmed the effectivenessof the model and its applicability in predicting AgNPs formation andits PSD evolution in the microtubular system. Finally, benefitingfrom its superiority, in that the influence of reactive kinetics andfluid dynamics on particle evolution could be considered separately,the model was employed to verify predictions and inferred conclusionsin our previous works, which were difficult to verify through experiment. [ABSTRACT FROM AUTHOR]

A multiphase reactive fluid dynamicmodel has been applied to simulatea complete chemical looping reforming (CLR) system, including an airreactor (AR), a fuel reactor (FR), a cyclone, and a loop seal. A two-fluidmodel with consideration of frictional stress between particles athigh solid concentrations is used. A bubble-structure-dependent dragcoefficient model is proposed and incorporated into the computationalfluid dynamics (CFD) code to account for the effect of multiscalestructures in the bubbling fluidized reactor. The predictions by themodel are in good agreement with the experimental results. Flow pattern,profiles of bubbles, and distributions of gas compositions and temperaturesare obtained. In addition, the influence of reaction temperature,operating velocity, and H2O/CH4molar ratioon the gas concentration is also investigated. [ABSTRACT FROM AUTHOR]

Today development, design, and optimization of the various processes is carried out with the help of process simulators.The reliability of the results mainly depends on the quality of thethermodynamic model and the model parameters used. While gEmodels can be applied for calculation of the phaseequilibrium behavior of multicomponent systems using only binary experimentaldata, group contribution methods like UNIFAC or modified UNIFAC Dortmundallow prediction of the required thermophysical properties usingonly a limited number of group interaction parameters. For systemscontaining supercritical components equations of state like Soave–Redlich–Kwongor Peng–Robinson or group contribution equations of state (GCEOS)like the predictive Soave–Redlich–Kwong (PSRK) or thevolume-translated Peng–Robinson group contribution equationsof state (VTPR) can be applied. In different papers it was alreadyshown that VTPR is a very powerful thermodynamic model. In this papernew group interaction parameters for 192 group combinations are presented,so that the actual matrix now contains group interaction parametersfor 252 group combinations. In this paper predicted results of theVTPR group contribution equation of state are compared with the resultsobtained using modified UNIFAC Dortmund or the PSRK method. [ABSTRACT FROM AUTHOR]

The effects of SO2flowrate, SO2mole fraction,iodine content and water content on the Bunsen reaction were experimentallystudied for the thermochemical iodine–sulfur cycle for hydrogenproduction. One multistage reaction mechanism on the Bunsen reactionhas been hypothesized, considering the kinetic characteristics. Theappearance of a liquid–liquid equilibrium (LLE) phase separationwas in the range of 20–40 min in the apparatus we chose. Anincrease in iodine content and a decrease in water content improvedLLE separation characteristics to the H2SO4phaseand HIx phase. The H2S formation side reaction easily occurredwith the increase in water content and decrease in iodine content.The optimal operating condition that the inlet SO2molefraction exceeds 0.12 coupled with initial I2/H2O molar ratio exceeding 0.284 has been proposed based on the experimentalresults, for the criteria of improving the separation characteristicsand preventing side reactions. [ABSTRACT FROM AUTHOR]

Thisarticle deals with the phase stability analysis of multicomponentsystems via the determination of all the stationary points of theso-called tangent plane distance function, which is known as an importantbut difficult problem of the thermodynamics of phase equilibrium,where high nonlinearities are inherent aspects of the different thermodynamicmodels commonly used in the description of this distance function.To analyze phase stability described from different models, we combinethree basic procedures here that were selected in order to attackpoints that we deem of relevant difficulty. To this end, we encapsulatein a single iterative algorithm the following steps: (i) polarizationof a merit function associated with first-order stationary conditionsof the phase stability problem, in order to avoid (or at least minimize)the repetition of stationary points previously calculated; (ii) astochastic optimization method, which (at each iteration of the encapsulationalgorithm) minimizes mtimes the same merit functionpolarized with the predetermined stationary points, using mdifferent seeds for a reliable random number generator(where mis a given integer), in order to calculatenew stationary points; (iii) a change of variables designed to allowthe numerical method to work in the unconstrained optimization framework,providing the location of stationary points near the boundary of theoriginal feasible set. Using the NRTL and UNIQUAC models for liquid–liquidequilibria at low pressures and the Soave–Redlich–Kwongand Peng–Robinson cubic equations of state for vapor–liquidequilibria at high pressures, we analyze 9 multicomponent systemsstudied in the literature, equipped with different feed compositions,totaling 32 tested mixtures, whose component numbers ranged between3 and 12. We show 14 new stationary points obtained here that werenot detected by methods previously used by other authors. [ABSTRACT FROM AUTHOR]

A comprehensive, real-time PAT processmonitoring scheme of usingnear-infrared (NIR) spectroscopy, focused beam reflectance measurement(FBRM), and particle vision microscopy (PVM) was established for processcharacterization and process understanding of a model dynamic multicomponentpharmaceutical antisolvent crystallization system. The NIR spectrawere subjected to principal component analysis (PCA) to constructthe process trajectory; and the final products were characterizedby X-ray powder diffraction (XRPD), raman spectrometry, and microscopy.Regardless of the PAT technique (i.e., the NIR–PCA method,the FBRM method, and the PVM method) used, this study shows that thenucleation induction time (tind) increaseswith temperature. In addition, correlations were observed with R2of 0.70–0.98 between PVM method andFBRM method and of 0.58–0.84 between NIR–PCA methodand FBRM method. Accounting for the dynamic nature of the experimentsand changes in the liquid volume (V) as a functionof time, a simplified classical nucleation theory model was derivedto reveal the relationship between ln(tindV) and (ln S)−2(Sis the supersaturation ratio). Regions of verystrong and very weak dependence on (ln S)−2were identified. Final product characterization and in-process observationsof particle morphology at t= tindcollectively support that heterogeneous- and homogeneous-nucleationmechanisms are responsible for low Sand high Sregions, respectively. Therefore, the utility of an integrated-PATapproach for understanding a dynamic multicomponent antisolvent crystallizationprocess and elucidating the nucleation mechanism was demonstrated. [ABSTRACT FROM AUTHOR]

Handling hazardous multiphase reactionsin flow brings not onlysafety advantages but also significantly improved performance, dueto better mass transfer characteristics. In this paper, we presenta continuous microreactor setup, capable of performing olefin autoxidationswith O2, under solvent-free and catalyst-free conditions.Owing to the transparent reactor design, consumption of O2can be visually followed and exhaustion of the gas bubbles marksa clear end point along the channel length coordinate. Tracking theposition of this end point enables measuring effective rate constants.The developed system was calibrated using the well-studied β-pinenesubstrate, and was subsequently applied to the synthetically interestingtransformation of (+)-valencene to (+)-nootkatone. For the latter,a space-time yield was obtained that is at least 3 orders of magnitudelarger than that realized with established biotechnology approaches. [ABSTRACT FROM AUTHOR]

An optical fiber reflectance probeis developed for fast, in situdetection of phase transitions between heterogeneous and homogeneousstates in multiphase systems. Experiments with two binary systems,methanol–cyclohexane and carbon dioxide–methanol, areconducted to demonstrate the capability of the reflectance probe tocapture the phase transitions in both liquid–liquid mixturesand gas expanded liquids (GXLs). The instantaneous revelation of transitionin the latter from the gas–liquid two-phase state to a singlephase at sufficiently high pressures provides important informationfor use and further investigation of this fully expanded regime. Thecurrent probe can withstand high pressures up to 100 bar and temperatures100 °C, which suggests its applicability in many practical processes. [ABSTRACT FROM AUTHOR]

Wereport on the control of three types of dividing wall columns:columns with the dividing wall in the lower (DWCL), middle (DWCM),and upper (DWCU) portions of the column. The relative gain array (RGA)and condition number (CN) for these three column types are calculatedfor two different multicomponent systems. Based on these results,promising control structures are identified and tested in Aspen Dynamics.The results indicate that DWCU has the worst control performance ofthe three column types. DWCL outperforms DWCM in most cases, but thedifference in controllability is not likely to justify the choiceof a column configuration with higher costs. [ABSTRACT FROM AUTHOR]

Anexperimental and numerical study of the individual and competitiveadsorption of BTX compounds (benzene, toluene, and o-xylene) in aqueous solution was carried out in a fixed-bed columnfilled with activated carbon. The equations of transport were discretizedusing the finite volumes method and an algorithm was implemented inthe Fortran programming language. The results obtained in all casesshowed that o-xylene is the contaminant which is most competitivefor the active site of the adsorbent, and over time it is able todesorb the compounds which have a lower affinity and adsorb to thefree active sites. The result is that the local concentration of theweakly adsorbed component in the fluid phase is higher and surpassesthe dimensionless concentration. This finding appeared to be relatedto the Biot number. As the Biot number increased the rate of competitiveadsorption decreased, and the form of the breakthrough curves is flatwith a lower breakpoint. This is due to the low intraparticle resistanceand also the reduced contact time required to reach saturation. [ABSTRACT FROM AUTHOR]

Theidea of applying the gas–liquid–solid (GLS) three-phasecirculating fluidized bed to CO2capture by aqueous ammoniais proposed in this work. A three-phase circulating fluidized bedtest rig was built, and a series of experiments were carried out tostudy the multiphase flow and gas–liquid mass transfer behavior.Compared with the conventional reactors, the solids in the three-phasecirculating fluidized bed can break up bubbles into much smaller onesand distribute them more uniformly. The experimental results showa three-phase circulating fluidized bed can provide larger interfacearea, longer residence time, and higher mass transfer efficiency.Based on these results, the process for CO2capture byaqueous ammonia using a three-phase circulating fluidized bed wasdesigned conceptually and its feasibility was studied preliminarilyby Apsen Plusa simulation software. When the mole fractionof aqueous ammonia is about 5.16% in the three-phase circulating fluidizedbed, more than 90% of the CO2can be absorbed and the ammoniaescaping ratio is very small. The three-phase circulating fluidizedbed presents great potential in CO2separation by aqueousammonia. [ABSTRACT FROM AUTHOR]

This paper presents a numerical studyof multiphase flow in hydrocycloneswith different configurations of cyclone size and spigot diameter.This is done by a recently developed mixture multiphase flow model.In the model, the strong swirling flow of the cyclone is modeled usingthe Reynolds stress model. The interface between liquid and air coreand the particle flow are both modeled using the so-called mixturemodel. The solid properties are described by the kinetic theory. Theapplicability of the proposed model has been verified by the goodagreement between the measured and predicted results in a previousstudy. It is here used to study the effects of cyclone size and spigotdiameter when feed solids concentration is up to 30% (by volume),which is well beyond the range reported before. The flow featurespredicted are examined in terms of the flow field, pressure drop,and amount of water split to underflow, separation efficiency andunderflow discharge type. The simulation results show that the multiphaseflow in a hydrocyclone varies with cyclone size or spigot diameter,leading to a different performance. A smaller cyclone results in anincreased cut size, a decreased pressure drop and a sharper separation,and, at the same time, an increased water split (thus worse bypasseffect) and a more possibly unstable operation associated with ropedischarge, particularly at relatively high feed solids concentrations.Both large and small spigot diameters may lead to poor separationperformance. Accordingly, an optimum spigot diameter can be identifieddepending on feed solids concentration. It is also shown that forall the considered hydrocyclones, a better separation performanceand a smoother running state can be achieved by the operation at alower feed solid concentration. [ABSTRACT FROM AUTHOR]

A review of multiphase catalyticprocesses in biomass conversion is presented, with an emphasis onthe underlying kinetics, mechanism, and reaction engineering aspects.The distinguishing features and current state of development of catalystsand processes for a few selected examples of biomass conversion arepresented, including hydrogenolysis and tandem reforming/hydrogenolysisof polyols to glycols and linear alcohols, hydrodeoxygenation of bio-oils,and polyols conversion to lactic acid along with possible reactionpathways. The complexities of multistep and multiphase catalytic reactionsand kinetics modeling associated with hydrogenolysis and hydrodeoxygenationare discussed with a brief overview of reaction engineering aspects. [ABSTRACT FROM AUTHOR]

Thedownflow slurry bubble column reactor is gaining importanceas a simple and inexpensive means of achieving efficient multiphasecontact and mass-transfer operations. Knowledge about the effectsof solids on gas–liquid–solid systems is minimal inthe literature. In the present work, the effect of the presence ofsolids on the mass-transfer characteristics for gas–liquid–solidsystem is experimentally investigated in a downflow slurry bubblecolumn with an internal diameter of 0.05 m. The mass-transfer coefficientwas evaluated using the electroreduction of ferricyanide ions as themodel reaction. The effects of superficial slurry velocity, gas velocity,slurry viscosity, and gas holdup on the mass-transfer coefficientwere analyzed. The experimental results showed that the mass-transfercoefficient in the column is influenced more by the superficial slurryvelocity than the superficial gas velocity. In this work, the mass-transferefficiency in the gas–liquid–solid downflow bubble columnreactor was analyzed for different concentrations of the slurry (0.1–1.0wt %) and different sizes of the particles (2.21–96.0 μm).Empirical correlations were developed for the downflow slurry systemwith the different variables to interpret the mass-transfer phenomena.The developed correlation for mass-transfer efficiency as a functionof quality of mixedness was also interpreted by the information entropytheory. The present analysis on mass-transfer characteristics andmodels for predicting the mass-transfer coefficient can provide insightinto a further understanding of multiphase reactors in industrialapplications. [ABSTRACT FROM AUTHOR]

A combined particle image velocimetry(PIV) and particle imagethermometry (PIT) method was applied to visualize and measure simultaneouslythe 2-D velocity and temperature fields in a crystallizer. The 2-Dsupersaturation field can be also determined before nucleation orseeding takes place. The hydrodynamic behavior in an internal loopairlift crystallizer was studied for different air flow rates, spargertypes, and crystal holdups to get insight in the optimal process conditionsfor this crystallizer, i.e. uniform temperatures and particle concentration.The 2-D velocity and temperature gradients showed that in a 2 L crystallizerthe mixing is sufficient to ensure uniform supersaturation profilesat an overall superficial air velocity higher than 2.3 mm/s. Suspensiontests showed that a superficial air velocity of 7 mm/s was sufficientto avoid settling of the crystals. This air flow rate assured thelifting of the solids from the bottom of the crystallizer for crystalswith a mean size of 1.5 mm and holdups up to 10 wt %. Both the circulationvelocity and the crystal holdup which could be totally suspended increasedwith the air flow rate. For the ammonium sulfate–water system,the crystal growth behavior, which is also influenced by the mixing,was theoretically studied. The growth of the crystals in an airliftcrystallizer behaves comparable to that in a suspension stirred crystallizer,and no evidence for mass transfer limitation of the crystal growthwas found. [ABSTRACT FROM AUTHOR]

Multicomponentadsorption of gas mixtures on diverse solid surfacesis important in many applications. However, there are still many questionson the practical applicability of the available theories, especiallyfor polar systems. In this work, we consider three well-known theoriessuitable for the prediction of multicomponent adsorption with parametersobtained solely from correlating single gas/solid data. We have testedthem over an extensive database with emphasis on polar systems (bothgases and solids). The three theories are the multicomponent Langmuir,the ideal adsorbed solution theory (IAST), and the multicomponentpotential adsorption theory (MPTA). We have not attempted to improve/modifythe methods in any way but have used them in their original form,as the purpose of our work is to illustrate the capabilities and inherentlimitations of the models for predicting multicomponent adsorption.We have ensured that the description of single gas/solid systems isas accurate as possible, but besides this, the calculations for multicomponentsystems are straight predictions. The work revealed on one side thatall three theories yield for some systems similar predictions, withIAST and MPTA performing overall better than the multicomponent Langmuir.On the other hand, it is also shown that all the three theories, despitethe good results in some cases, have serious limitations particularlyfor water and to some extent also for certain polar solids. Both strengthsand weaknesses of the three models are discussed. [ABSTRACT FROM AUTHOR]

Wedescribe the application of a validation and uncertainty quantificationmethodology to multiphase computational fluid dynamics modeling, demonstratingthe methodology with simulations of a pilot-scale circulating fluidizedbed. The overall pressure drop is used as the quantity of interest(QoI); the solids circulation rate and the superficial gas velocityare chosen as the uncertain input quantities. The uncertainty in theQoI, caused by uncertainties in input parameters, surrogate model,spatial discretization, and time averaging, is calculated, and themodel form uncertainty is estimated by comparing simulation resultswith experimental data. The spatial discretization error was determinedto be the most dominant source of uncertainty, but the applicabilityof the method used to calculate that uncertainty needs to be furtherinvestigated. The results of the analysis are expressed as a probabilitybox (p-box) plot. A p-box similarly constructed for predictive simulationswill give the design engineer information about the confidence inthe predicted values. [ABSTRACT FROM AUTHOR]

ThisResearch Note proposes an innovative modeling and computationalscheme for investigating industrial three-phase flows with aggregation.The scheme is applied on an industrially relevant application: dissolvedair flotation. Aggregate formation is modeled locally using a sophisticatedsubgrid model, and a concept involving massless tracer particles isinvoked to transport the aggregate properties, along with the flow.The model is able to account for the formation and consumption ofall entities involved and to track their respective properties, onlyat a moderate computational cost. [ABSTRACT FROM AUTHOR]

Threedifferent gas–liquid–solid reactor configurationshave been used to investigate the performance of a P-doped NiMo/Al2O3catalyst in the hydrodesulfurization of dibenzothiophene.The commonly used millipacked bed reactor with 250–500 μmcatalyst particles diluted with 125 μm inert particles, a micropackedbed reactor with 55–90 μm catalyst particles, and a slurryreactor with 150–250 μm catalyst particles were usedin the catalyst performance testing program. It appeared that theinherently small particle size in the packed beds causes the hydrodynamicsto be dramatically different compared to the industrially appliedtrickle-bed reactors. For particles smaller than typically 2 mm thecapillary forces predominate over the viscous and gravitational forces,in sharp contrast to large-scale industrial reactors. Since the gasflow follows preferential pathways through beds consisting of smallparticles, the poor radial dispersion of the gaseous components cancause mass-transport limitations, even for a rather slow reactionsuch as the hydrodesulfurization (HDS) of dibenzothiophene, as a resultof the strong inhibition by the reaction product H2S. Anadapted criterion is proposed for estimation of the contribution ofpoor radial dispersion in catalyst performance testing. [ABSTRACT FROM AUTHOR]

A numericaland experimental study of the monocomponent and multicomponentadsorption and desorption of BTX compounds (benzene, toluene, and o-xylene) in a batch reactor and fixed-bed column was carriedout in aqueous solution at 23 °C, using coconut shell activatedcarbon as the adsorbent. The monocomponent Langmuir isotherm modelbest represented the experimental results (average R2= 0.9952) and the multicomponent Langmuir model, usingthe multicomponent parameters, represented the multicomponent dataobtained in a fixed-bed column better than the monocomponent model.The equations which describe the phenomenology were discretized usingthe Finite Volumes Method with the WUDS and CDS formulations. Theresults for the monocomponent breakthrough curves obtained throughsimulation showed good agreement when compared with the experimentaldata (maximum error of 11.52%). For the monocomponent breakthroughcurves the greatest deviation was observed for the compound whichhad the least affinity for the solid phase (benzene). The best resultsfor the desorption of the BTX compounds from the adsorbent were obtainedusing ethanol as the desorbent solvent, and the average removal percentagesin three cycles of regeneration in the column were 90% for benzene,82% for toluene, and 78% for o-xylene. [ABSTRACT FROM AUTHOR]

Within the framework of the Collaborative Research CentreSFB/TR63 InPROMPT, “Integrated chemical processes in liquid multiphasesystems”, a novel process concept for the hydroformylationof long chain alkenes to aldehydes in microemulsions is investigatedand developed at the Berlin Institute of Technology (Technische UniversitätBerlin), Germany. To start the hydroformylation reaction, a hydrophilicrhodium-ligand-complex is required. By applying a nonionic surfactant,a microemulsion system is formed and thus the hydrophilic catalystis transported into the hydrophobic alkene phase. Next to achievea high conversion rate in the continuously stirred tank reactor, theseparation of the valuable rhodium catalyst from the product phaseposes a challenge. This separation is the crucial step for the technicaland economic feasibility of the overall process concept and plantdesign. Owing to the lack of thermodynamic data for microemulsionmixtures, the design of the phase separation unit strongly dependson experimental results. Consequently, a systematic experimental approachhas been developed to identify potential operating conditions andrelevant design parameters. To classify and find these, a set of experimentalset-ups have been investigated to characterize impact factors on thephase separation such as type of surfactant, different concentrationsof surfactant, olefin, product, and water. With the information gainedthrough the observations the relevant composition of the investigatedmixture and the separation temperature are determined for the operatingconditions. Finally, necessities with regards to plant and processdesign are revealed. [ABSTRACT FROM AUTHOR]

Wood may contain several harmfulchemicals which can be removed by high-temperature treatment. Thisis essentially a drying process under linearly increased gas temperatureup to final gas temperature of 220–230 °C which is a challengingprocess to model. The effective model is useful in process design,evaluation of equipment performance, and troubleshooting. In thisstudy, the REA (reaction engineering approach) is implemented to describethe local evaporation/condensation rate and combined with a systemof equations of conservation to yield a spatial model, called thespatial reaction engineering approach (S-REA), in order to model theheat treatment of wood under constant heating rate. A good agreementbetween the predicted and experimental data is observed. The REA isaccurate to model the local evaporation rate of the heat treatmentof wood. The S-REA is an effective nonequilibrium multiphase approachto model the heat treatment of wood, a simultaneous heat and masstransfer process involving water transformation under linearly increasedgas temperature. [ABSTRACT FROM AUTHOR]

Multiphase flows and in particular dispersed flows are frequently encountered in a variety of important process facilities in the chemical industry; herein, the fluidized bed reactors. Whereas the internal and external solid fluxes in the fluidized bed reactors are generally determined by empirical correlations or prescribed in the Kunii–Levenspiel type of models, the two-fluid models serve as highly relevant in the progress of commercial reactors for processes such as the novel sorption-enhanced steam methane reforming (SE-SMR) technology because the solid flux incorporated in the two-fluid model allows for dynamic modeling of interconnected fluidized bed reactors. Nevertheless, the two- and three-dimensional two-fluid models are yet too computationally demanding for chemical process evaluation studies due to the complexity of the gas–solid flow in the bed. Hence, these models are not efficient for studies of the processes such as the SE-SMR technology where the solid particles are transported between reactor units for utilization and recovery of the characteristic solid property, i.e. CO2-capture and CO2-release. Thus, the aim of the present study is to derive a model that allows for a more complex description of the fluidized bed reactors relative to the frequently used Kunii–Levenspiel type of models. On the other hand, the model should not predict details in the flow, as the two- and three-dimensional two-fluid models, in order to ensure reasonable simulation costs. Hence, in this study, the classical SIMPLE algorithm is extended to compressible two-phase reactive flows. The governing equations are cross-sectional averaged to smooth out the details in the flow. The suggested dynamic one-dimensional Eulerian–Eulerian two-fluid model is applied to investigate the reactive gas–solid flows of the SMR and SE-SMR processes; and moreover, the simulation results are compared with the results of the more complex two-dimensional model with a solid stress closure based on kinetic theory of granular flow. The one-dimensional model predictions of the chemical process performance are in good agreement with the corresponding profiles predicted with the two-dimensional model. The deviations are larger comparing the internal flow details but these do not owe significant impact on the chemical process which to a large extent is determined by the imposed temperature in the reactor. [ABSTRACT FROM AUTHOR]

Theetherification of biodiesel based glycerol with isobutene catalyzedby an ion-exchange resin (NKC-9) was studied in a stirred batch reactor.The effects of temperature, catalyst loading, and feed compositionon the product distribution were investigated. A kinetic model basedon Eley–Rideal mechanism was developed according to the experimentalresults. In this model, three consecutive etherifications and a dimerizationof isobutene were taken into account; isomers in the product werelumped as monoethers (ME), diethers (DE), and dimers of isobutene(DIB); glycerol and isobutene were thought to be adsorbed on the activesites of catalyst and the surface reactions were treated as the ratedetermine step; the acceleration function of ME to the reactions wasalso considered. The activities of components were employed in rateequations with the activity coefficients calculated by UNIFAC. Modelparameters including reaction and adsorption equilibrium constantsas well as rate constants were estimated. The model reliability wasvalidated through the prediction of glycerol conversion and etheryields under different conditions. [ABSTRACT FROM AUTHOR]