Analysis of a Two-Phase Perfectly Mixed Reactor under the Condition of a Phase Equilibrium

A mathematical model is formulated for a gas–liquid perfectly mixed flow reactor under the condition that the two-phase flow at the reactor outlet is at thermodynamic equilibrium. The phase equilibrium is calculated using the Redlich–Kwong–Soave equation of state. The set of nonlinear algebraic equations of the model is numerically solved by the efficient algorithm of the homotopy method. The steady-state modes of reactor operation are analyzed for liquid-phase benzene hydrogenation. It is shown that, under isothermal isobaric conditions, there can be a multiplicity of steady-state solutions, which is, on the one hand, due to the nonlinearity of the kinetic law and, on the other, due to the deviation of the properties of the reaction mixture from the properties of an ideal system. The stability of the steady-state solutions is analyzed, and the causes of the multiplicity and instability are explained.     

Modelling hydrate formation kinetics of a hydrate promoter-water-natural gas system in a semi-batch spray reactor

Hydrate formation kinetic modelling studies reported so far mainly concentrates on pure water-gas systems in stirred-tank batch environments. This work proposes a model for gas hydrate formation kinetics of a hydrate promoter-water-natural gas system in a semi-batch reactor assuming steady-state, isothermal and isobaric conditions. The hydrate formation kinetics was modelled after extending the recent method proposed by Kashchiev and Firoozabadi (J. Crystral Growth 241 (2002a) 220; J. Crystal Growth 243 (2002b) 476; J. Crystal Growth 250 (2003) 499) for a single component gas-water system to a multi-component gas-water-additive system. The extended Kashchiev and Firoozabadi model was applied for a semi-batch spray reactor here for the first time. The hydrate formation experiments were carried out in a pilot plant spray reactor at three different pressure-temperature regimes to determine the actual hydrate formation kinetics in the spray reactor. The experiment results were then used to finetune the adjustable parameters to facilitate accurate model predictions.     

超临界CO2脱附作用调控负载纳米颗粒结晶动力学研究

依据经典成核理论和超临界领域中的结晶动力学相关模型,分析影响成核速率的主要因素及其规律。研究共溶剂辅助超临界CO₂溶解无机盐,在SBA-15介孔材料表面沉积实验的结果,发现伴随初始阶段的泄压速率逐步提升（0.05~18 MPa/min,20~14 MPa）,载体所负载的纳米颗粒的粒径逐渐减小至1.5 nm左右,与典型的晶核尺寸1 nm相接近,而担载量却出现逐渐增加的趋势。晶体的临界成核半径取为0.5 nm,通过Türk模型和Debenedetti模型计算超临界流体快速膨胀（RESS）工艺其喷嘴内的成核速率,与超临界反溶剂（SAS）群体平衡模型（PBM）的边界条件即SAS过程的初始成核速率相比较,三者的成核速率相接近,且利用快速泄压方法的沉积实验结果与按Cu担载量所估算的成核速率相接近。分析在沉积反应后的泄压阶段,超临界条件下的CO₂的脱附作用,可能成为吸附于载体表面的前驱物离子结晶的诱导因素。并且CO₂瞬时脱附量能够调控负载型纳米颗粒的成核速率,同时控制复合材料的金属担载量。为研究微观尺度下SAS过程的实现提供了实验与理论基础。     

Vapor–gas/liquid nucleation experiments: A review of the challenges

The formation of new phase embryos is described by nucleation theory. However, nucleation is not yet fully understood. The goal of this review is to summarize measurement methods and recent experimental results for vapor/liquid nucleation. Substantial inconsistencies have been reported among experimental data that may originate from the use of different experimental approaches. These inconsistencies lead to the hypothesis that typical vapor/liquid nucleation rate measurements include an uncontrolled parameter. One such parameter might be the carrier gas that can be considered as an independent nucleation component for vapor–gas/liquid systems. Mass-spectrometry measurements suggest this possibility. The most commonly applied theories suggest a variety of responses of nucleation rates to nature and pressure of the carrier gas. Some approaches to interpret vapor–gas/liquid nucleation experiments consider nuclei formation from the vapor–gas system as a binary process. This approach can be considered in terms of converting the line that originates from isothermal nucleation of a single component system to a surface representing the isothermal nucleation of a binary system. In the binary approximation, adjusted nucleation conditions (i.e. consistent trajectories for nucleation parameters) are needed to obtain consistent data for nucleation rates across the nucleation rate surface. This framework provides an opportunity to resolve the data inconsistencies. Recommendations for future vapor–gas/liquid nucleation research can then be formulated. Experimental detection of singularities in the nucleation rate surface and phase transitions in a condensed phase are reviewed. The assumptions needed for the interpretation of the empirical parameters are analyzed. The experimental data inconsistencies make it currently impossible to suggest a standard system that would permit testing the performance of measuring systems for vapor–gas/liquid nucleation.     

Comminution of pharmaceutical substances by the adiabatic expansion of supercritical fluid solutions

The adiabatic expansion of supercritical fluid solutions and solubility in pharmaceutical substance–carbon dioxide systems have been investigated. The solubility and average particle size of pharmaceutical substances depend on thermodynamic and geometric parameters of the process. Experimental data on the solubility of pharmaceutical substances in supercritical carbon dioxide have been gained, and empirical binary molecular interaction parameters for the Peng–Robinson equation have been derived. A numerical solution has been obtained for the unified model of nucleation and particle growth (in the drop theory approximation) in the expansion of a steady-state, two-dimensional, viscous, axisymmetric, compressible, supercritical carbon dioxide–pharmaceutical substance flow in a channel with a constant cross section and in a free jet. The correlation parameter of the condensation function, which characterizes the particle growth kinetics, has been determined.     

Crystallization of linear polyethylene from melt in isothermal compression

Crystallization and primary nucleation of linear polyethylene has been studied by means of a custom-made miniature pressure apparatus. It has been shown that during isothermal compression of linear polyethylene melt at a constant rate crystallization occurs. In the range of fastest conversion rates the crystallization assumes isobaric character. The level of pressure at which the crystallization occurs increases with the increase of the crystal-lization temperature and/or with the increase of the compression rate. The crystallization has a spherulitic character up to the highest pressure achieved in the apparatus (approx. 600 MPa). Surprisingly, there are no dependencies of average spherulite size, degree of crystallinity, and lamellae thickness on the pressure and the temperature of crystallization during melt compression, but there is a strong relation to the compression rate. Below 250 MPa and above 300 MPa the crystallization proceeds under pressure, ensuring a constant undercooling. The undercooling for the pressure above 300 MPa is approximately 10°C lower than that for the pressure below 250 MPa. For the pressure 250–300 MPa a change in a primary nucleation and spherulite crystallization has been observed that is connected with the transformation from orthorhombic to pseudohexagonal symmetry of crystals. No noticeable effect of molecular weight of linear polyethylene on crystallization during iso-thermal melt compression has been observed.     

Comparative study on the crystallization behavior of β‐isotactic polypropylene nucleated with different β‐nucleation agents —effects of thermal conditions

In this study, the crystallization behavior of the β‐isotactic polypropylene (β‐iPP) samples nucleated by a rare earth based β‐nucleating agent (β‐NA) WBG‐II and a metal salts compound β‐NA NAB83 (denoted as WPP and NPP, respectively) under different cooling conditions were comparatively investigated. The thermal conditions such as the cooling rate, isothermal crystallization temperature, isothermal crystallization time, and the subsequent cooling to room temperature. The results of WAXD, SEM, and nonisothermal crystallization reveal that under the same processing conditions, the crystallite size of NPP is smaller, which arrange more compactly as compared with WPP. Meanwhile, NPP has shorter crystallization rate and higher β‐nucleation selectivity, but WPP can crystallization at wider temperature range. The results of isothermal crystallization showed that NPP has higher selectivity and higher β‐nucleation efficiency, which favors the formation of high proportion of β‐phase at the isothermal crystallization temperature of 110–130°C with and without subsequent cooling; WPP has lower selectivity, which can only induce high content of β‐phase under isothermal crystallization without subsequent cooling to 25°C. In tuning the crystallization behavior and the properties of β‐PP, the joint influence of the efficiency and selectivity of the β‐NA, and the thermal conditions should be taken into consideration. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 40115.     

Transcrystalline morphology of nylon 6 on the surface of aramid fibers

In this paper, the isothermal crystallization of nylon 6 in the presence of Kevlar 129 fiber was investigated by polarized optical microscopy (POM). The formation of a transcrystalline domain was found to be mainly controlled by crystallization conditions, such as the temperature of the isothermal crystallization, residual time at melting temperature and the cooling rate of the melt. The nucleation rate of nylon 6 on the fibers was mainly affected by the crystallization temperature. The interfacial transcrystallinity of nylon 6 occurred on the surface of Kevlar 129 fiber in the temperature range 130–190 °C. The reason for the formation of interfacial transcrystalline morphology is discussed from the molecular level, based on the understanding of the packing mode of nylon 6 chains around fibers and the interaction between matrix and fibers. It was found that the lattice matching and hydrogen‐bonding between nylon 6 and poly(p‐phenylene terephthalamide) (PPTA) crystals play an important role in the epitaxial crystallization. Copyright © 2004 Society of Chemical Industry     

Isothermal and nonisothermal crystallization kinetics of MC nylon and polyazomethine/MC nylon composites

Crystallization kinetics of MC nylon (PA6) and polyazomethine (PAM)/MC nylon (PAM/PA6) both have been isothermally and nonisothermally investigated by different scanning calorimetry (DSC). Two stages of crystallization are observed, including primary crystallization and secondary crystallization. The Avrami equation and Mo's modified method can describe the primary stage of isothermal and nonisothermal crystallization of PA6 and PAM/PA6 composite, respectively. In the isothermal crystallization process, the values of the Avrami exponent are obtained, which range from 1.70 to 3.28, indicating an average contribution of simultaneous occurrence of various types of nucleation and growth of crystallization. The equilibrium melting point of PA6 is enhanced with the addition of a small amount of rigid rod polymer chains (PAM). In the nonisothermal crystallization process, we obtain a convenient method to analyze the nonisothermal crystallization kinetics of PA6 and PAM/PA6 composites by using Mo's method combined with the Avrami and Ozawa equations. In the meanwhile, the activation energies are determined to be ?306.62 and ?414.81 KJ/mol for PA6 and PAM/PA6 (5 wt %) composite in nonisothermal crystallization process from the Kissinger method. Analyzing the crystallization half‐time of isothermal and nonisothermal conditions, the over rate of crystallization is increased significantly in samples with a small content of PAM, which seems to result from the increased nucleation density due to the presence of PAM rigid rod chain polymer. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 93: 2844–2855, 2004     

Numerical simulation of particle formation in the rapid expansion of supercritical solution process

In this paper, we numerically study particle formation in the rapid expansion of supercritical solution (RESS) process in a two dimensional, axisymmetric geometry, for a benzoic acid + CO₂ system. The fluid is described by the classical Navier–Stokes equation, with the thermodynamic pressure being replaced by a generalized pressure tensor. Homogenous particle nucleation, transport, condensation and coagulation are described by a general dynamic equation, which is solved using the method of moments. The results show that the maximal nucleation rate and number density occurs near the nozzle exit, and particle precipitation inside the nozzle might not be ignored. Particles grow mainly across the shocks. Fluid in the shear layer of the jet shows a relatively low temperature, high nucleation rate, and carries particles with small sizes. On the plate, particles within the jet have smaller average size and higher geometric mean, while particles outside the jet shows a larger average size and a lower geometric mean. Increasing the preexpansion temperature will increase both the average particle size and standard deviation. The preexpansion pressure does not show a monotonic dependency with the average particle size. Increasing the distance between the plate and the nozzle exit might decrease the particle size. For all the cases in this paper, the average particle size on the plate is on the order of tens of nanometers.     

苯胺在超临界水中氧化反应动力学的研究

对苯胺在超临界水中的氧化反应进行了研究。发现随温度升高和停留时间延长,苯胺去除率和COD去除率增大,并且只有在温度高于898.15K条件下,苯胺氧化的COD去除率才有可能达到90％以上。在873.15K～898.15K范围内,温度对苯胺氧化的COD去除率有较显著的影响。在673.15K～748.15K、25.0MPa、300％过氧量、2.351×10-4mol(L-1苯胺浓度条件下,苯胺反应级数为1.554,反应的活化能为2.96(104J(mol-1,频率因子为6.69×103。     

Supercritical water and particle nucleation: Implications for water chemistry control in a GEN IV supercritical water cooled nuclear reactor

One of the potential undesired processes in the heat transport system of the GEN IV Supercritical Water Cooled Reactor (SCWR) concept may be the formation of nanosize particles from ions present in the feed water or released in the coolant by corrosion products. Large-scale molecular dynamics simulations are being employed to investigate the nucleation and growth of salt nanoparticles in water over wide range of supercritical states. The particle nucleation rate in supercritical water appears to be on the order of 10²⁸ cm⁻³ s⁻¹, with critical nuclei having an amorphous structure. A molecular mechanism for possible hydrolysis reaction at supercritical conditions is examined.     

Crystallization kinetics and morphology of poly(trimethylene terephthalate)

In this work, the isothermal crystallization kinetics of polytrimethylene terephthalate (PTT) was first investigated from two temperature limits of melt and glass states. For the isothermal melt crystallization, the values of Avrami exponent varied between 2 and 3 with changing crystallization temperature, indicating the mixed growth and nucleation mechanisms. Meanwhile, the cold crystallization with an Avrami exponent of 5 indicated a character of three-dimensional solid sheaf growth with athermal nucleation. Through the analysis of secondary nucleation theory, the classical regime I→II and regime II→III transitions occurred at the temperatures of 488 and 468 K, respectively. The average work of chain folding for nucleation was ca. 6.5 kcal mol⁻¹, and the maximum crystallization rate was found to be located at ca. 415 K. The crystallite morphologies of PTT from melt and cold crystallization exhibited typical negative spherulite and sheaf-like crystallite, respectively. Moreover, the regime I→II→III transition was accompanied by a morphological transition from axialite-like or elliptical-shaped structure to banded spherulite and then non-banded spherulite, indicating that the formation of banded spherulite is very sensitive to regime behavior of nucleation.     

Nucleation and growth of copper under combined charge transfer and diffusion limitations: Part I

The nucleation and growth of copper crystals on a glassy carbon electrode are studied under potentiostatic conditions. Current transients are recorded at different overpotentials and are interpreted in terms of the theory of progressive nucleation and growth under combined charged transfer and diffusion limitations. Data are obtained on the overpotential dependence of the stationary nucleation rate and on the size of the critical copper nuclei. The influence of ion transfer and electron transfer electrochemical reactions taking place prior to and simultaneously with the process of nucleus formation is discussed and their contribution to the total current is accounted for.     

Crystallization and thermal behavior of microcellular injection‐molded polyamide‐6 nanocomposites

This article presents the effects of nanoclay and supercritical nitrogen on the crystallization and thermal behavior of microcellular injection‐molded polyamide‐6 (PA6) nanocomposites with 5 and 7.5 wt% nanoclay. Differential scanning calorimetry (DSC), X‐ray diffractometry (XRD), and polarized optical microscopy (POM) were used to characterize the thermal behavior and crystalline structure. The isothermal and nonisothermal crystallization kinetics of neat resin and its corresponding nanocomposite samples were analyzed using the Avrami and Ozawa equations, respectively. The activation energies determined using the Arrhenius equation for isothermal crystallization and the Kissinger equation for nonisothermal crystallization were comparable. The specimen thickness had a significant influence on the nonisothermal crystallization especially at high scanning rates. Nanocomposites with an optimal amount of nanoclay possessed the highest crystallization rate and a higher level of nucleation activity. The nanoclay increased the magnitude of the activation energy but decreased the overall crystallinity. The dissolved SCF did not alter the crystalline structure significantly. In contrast with conventionally injection‐molded solid counterparts, microcellular neat resin parts and microcellular nanocomposite parts were found to have lower crystallinity in the core and higher crystallinity near the skin. POLYM. ENG. SCI., 46:904–918, 2006. © 2006 Society of Plastics Engineers     

Analysis of supersaturation and nucleation in a moving solution droplet with flowing supercritical carbon dioxide

A supercritical antisolvent (SAS) process is employed for production of solid nanoparticles from atomized droplets of dilute solution in a flowing supercritical carbon dioxide (SC CO₂) stream by attaining extremely high, very rapid, and uniform supersaturation. This is facilitated by a two‐way mass transfer of CO₂ and solvent, to and from the droplet respectively, rendering rapid reduction in equilibrium solubility of the solid solute in the ternary solution. The present work analyses the degree of supersaturation and nucleation kinetics in a single droplet of cholesterol solution in acetone during its flight in a flowing SC CO₂ stream. Both temperature and composition are assumed to be uniform within the droplet, and their variations with time are calculated by balancing the heat and mass transfer fluxes to and from the droplet. The equilibrium solubility of cholesterol with CO₂ dissolution has been predicted as being directly proportional to the Partial Molar Volume Fraction (PMVF) of acetone in the binary (CO₂–acetone) system. The degree of supersaturation has been simulated up to the time required to attain almost zero cholesterol solubility in the droplet for evaluating the rate of nucleation and the size of the stable critical nuclei formed. The effects of process parameters have been analysed in the pressure range of 7.1–35.0 MPa, temperature range of 313–333 K, SC CO₂ flow rate of 0.1136–1.136 mol s^?1, the ratio of the volumetric flow rates of CO₂‐to‐solution in the range of 100–1000, and the initial mole fraction of cholesterol in acetone solution in the range of 0.0025–0.010. The results confirm an extremely high and rapid increase in degree of supersaturation, very high nucleation rates and stable critical nucleus diameter of the order of a nanometre. Copyright © 2005 Society of Chemical Industry     

Experimental and modeling study of the kinetics of methane hydrate formation and dissociation

In this work, several experiments were conducted at isobaric and isothermal condition in a CSTR reactor to study the kinetics of methane hydrate formation and dissociation. Experiments were performed at five temperatures and three pressure levels (corresponding to equilibrium pressure). Methane hydrate formation and dissociation rates were modeled using mass transfer limited kinetic models and mass transfer coefficients for both formation and dissociation were calculated. Comparison of results, shows that mass transfer coefficients for methane hydrate dissociation are one order greater than formation conditions. Mass transfer coefficients were correlated by polynomials as relations of pressure and temperature. The results and the method can be applied for prediction of methane production from naturally occurring methane hydrate deposits.     

聚乳酸/可反应性纳米SiO2复合材料的等温结晶动力学

采用熔融共混法制备了聚乳酸/可反应性纳米二氧化硅(PLLA/RNS)复合材料。利用差示扫描量热仪研究了RNS对PLLA等温结晶行为的影响;用Avrami 方程研究了PLLA及其复合材料的等温结晶动力学。结果表明,加入RNS对PLLA结晶起到了异相成核作用,随着RNS含量的增加,PLLA的结晶速率(K)提高,半结晶时间(t1/2)减小,而Avrami指数(n)变化不大,说明RNS没有改变PLLA结晶的成核机理;利用Arrhenius方程和Lauritzen-Hoffman理论分别对PLLA及其复合材料的结晶活化能(ΔE)、成核参数(Kg)和折叠链端表面自由能(σe)进行计算后发现,复合材料的ΔE比纯聚乳酸的小,Kg 、σe略有增加。这表明加入RNS降低了复合材料的ΔE,从而有效地促进了PLLA基体的结晶。     

超临界CO_2萃馏浓缩天然生育酚复杂体系相平衡的研究

温度为40～60℃,压力为9～17MPa等温、等压和等密度3种实验条件下测定了大豆油脱臭馏出物前处理产物中生育酚与超临界CO2的气液相平衡数据。结果表明,前处理产物中生育酚在超临界CO2中的溶解度及在气液两相中的分配系数分别比二元系中dl α 生育酚高约5倍和10～11倍,前处理产物生育酚各异构体在超临界CO2中的分配系数大小顺序为α>δ>γ>β,前处理产物中α 生育酚相对于β、γ、δ异构体的分离因子分别在1 09～1 51。     

Adsorption in non-isobaric fixed beds

The paper examines the effect of finite pressure gradients on the dispersion of a pulse of an adsorbable gaseous species as it flows through a fixed bed of adsorbing spherical particles.It is shown that, even for significant deviations from isobaric conditions within the bed, there is an asymptotic linear relationship between the first moment of the response (the mean retention time) and the reciprocal of the exit flow rate, a characteristic of the isobaric situation. However, unlike the isobaric case, extrapolation of the asymptotic linearity to infinite flow rate leads to a non-zero first moment at that point. Furthermore, extrapolation to zero first moment corresponds to a hypothetical flow rate which is dependent only on the parameters of the packed bed and the viscosity of the carrier gas and, specifically, is independent of the nature of the adsorbed species. The theory has been confirmed by a series of chromatographic adsorption experiments under non-isobaric conditions.Subsequently, the same experimental data have been employed in conjunction with the theory to obtain adsorption equilibrium constants for four normal alkanes (propane, butane, pentane, and hexane) on alumina in the temperature range 50–200°C with an uncertainty of ±3%.