Simultaneous heat and mass transfer in binary distillation—I: Theory

Binary distillation in continuous contact equipment is modeled as a simultaneous heat and mass transfer process. In order to account for the interactions between heat and mass transfer between the two phases, the equations developed from enthalpy and material balances are analyzed simultaneously and it is revealed that the individual phase mass transfer coefficients can be evaluated rigorously by measuring liquid phase compositions and temperatures in distillation experiments. Using the theoretical relations, it is proved that the liquid phase in a distillation column will be saturated if and only if there is negligible resistance to mass transfer in the liquid film. For the case of comparable resistances in both phases, the possible amount of superheat in the liquid phase would be considerable and thus convenient to determine experimentally. The liquid phase temperatures are shown to be important in experimental analysis (i.e. in determining the individual phase transfer coefficients) but not in design applications. For the latter case, the model equations reduce to the conventional mass transfer relations which are not as sensitive to temperatures.     

非平衡级速率模型用于催化精馏过程的模拟计算

采用非平衡级速率模型对醋酸甲酯水解的催化精馏中试过程进行了模拟计算,反应精馏段催化剂填料层的气相和液相传质系数用自行测定的经验关联式计算,提馏段的填料层传质系数用Onta的关联式,反应速率根据所测定的宏观反应动力学方程结合催化剂包的效率因子进行计算,得到令人满意的结果．     

Concentration profiles in a packed distillation column

Concentration profiles in a pilot plant-sized packed distillation column were measured by sampling both the liquid and the vapour in ten positions along the column. The results were compared with the profiles obtained by computer simulation from the plug flow and backmixing models. It was found that the stagewise backflow model reproduced the experimental profiles well. The corresponding mass transfer coefficients were greater than those calculated for the plug-flow model and could be better correlated with the vapour velocity. However, the corresponding backmixing coefficients were rather low, the equivalent eddy diffusivity in the liquid phase being of the order of 10^?3m²/s.     

Modeling of batch extractive distillation

New data on the concentration profiles in a packed column during extractive distillation of benzene–heptane mixture in the presence of N-methylpyrrolidone as a separating agent have been obtained. A calculation method for the process based on partial mass transfer coefficients in the vapor and liquid has been proposed. The calculated and experimental data have been compared. It has been shown that both continuous and batch extractive distillation are calculated more precisely using the proposed model compared to the equilibrium model.     

Interpretation of mass transfer measurements in bubble columns considering dispersion of both phases

Mass transfer measurements in two bubble columns with an inner diameter of 100 resp. 140 mm with the systems air/water/carbon dioxide and nitrogen/n-propanol/carbon dioxide have been evaluated with the axial dispersion model. The dispersion coefficients of both phases have been determined in separate investigations. As the results revealed a strong influence of the liquid viscosity, additional dispersion coefficient measurements have been carried out with the system air/glycol. It could be shown that the liquid phase dispersion coefficient decreases with increasing viscosity while the gas phase dispersion coefficient increases with increasing liquid viscosity. Both coefficients are strongly dependent on the gas throughput and the column diameter. Using these coefficients, the mass transfer coefficients have been calculated by fitting the calculated concentration profile to the measured values and by splitting the volumetric mass transfer coefficient with the experimental value of the interfacial are a. The results agree best with a correlation of Calderbank and Moo-Young.     

Transport equations for distillation of ethanol and water from the entropy production rate

We have derived a set of transport equations for heat and mass transfer across a liquid-vapour interface in distillation columns. We have used the entropy production rate on each tray, and integrated through the interface, when the liquid is not in equilibrium with the vapour. The set, that defines overall coefficients of transport, includes contributions from the interface, from the vapour film, and from the liquid film. It is shown, using data for a rectifying column that separates ethanol and water, that the coefficients can be determined by fitting the transport equations to the entropy production rate, with the constant thickness of one of the films as the only adjustable variable. Almost all of the entropy production is due to mass transfer between the phases. Coefficient values were determined for a large and a small value for the film thickness ratio as a function of temperature. The distribution of the entropy production rate between the phases depends largely on the film thickness, but its distribution between mass and heat transfer contribution does not depend on this variable. A contribution from the Soret or Dufour effect is found for large liquid films. The driving force for mass transfer, calculated with coefficients and rates, compared well with average values, which were calculated from the experimental data. The set of equations was compared to the Maxwell-Stefan equation set. Since it contains the interface contribution and coupling, it can be used to asses common approximations.     

A study of mass transfer behaviour in a catalytic distillation column

Catalytic distillation (CD) is a process where reaction and separation take place simultaneously in a distillation column. Recently, a new CD process for the aldol condensation of acetone to diacetone alcohol and mesityl oxide was developed in our laboratory. Owing to the unique structure used to support catalysts in the CD column, mass transfer data are needed to model the CD process. The mass transfer behaviour in the CD column has been studied both for the reactive and non-reactive sections of the column in our laboratory. Based on the experimental results, general correlations for the mass transfer coefficients have been established and the 95% confidence intervals for the associated parameters were obtained. The experimental results indicated that the catalyst bags did not play a significant role for the separation between the vapour and liquid phases. The mass transfer correlations developed in this study have been used successfully to model the CD process for the aldol condensation of acetone carried out in our laboratory.     

Simultaneous heat and mass transfer for multicomponent distillation in a wetted-wall column

A simultaneous heat and mass transfer model was applied to multicomponent distillation in a wetted-wall column. Experiments were carried out, using the benzene-toluene-ethylbenzene ternary system, in a wetted-wall column of 2.2 cm i.d. and 100 cm long equipped with special probes designed for simultaneous liquid sampling and temperature measurements. The experimental results show that the bulk liquid phase was saturated, indicating no resistance to mass transfer in the liquid film. Confirmation of the liquid phase saturation was made through a comparison of the experimentally measured liquid temperature with the calculated bubble point temperature. The average deviation between the measured and calculated temperatures was found to be 0.26°C.Individual mass transfer rates were evaluated locally by measuring compositions and temperatures as functions of column height and were compared to theoretical predictions using the exact film model solution of the Maxwell-Stefan multicomponent equations developed by Krishna and Standart. The comparison shows good agreement with average deviations of 15.76% for benzene, 23.09% for toluene and 23.23% for ethylbenzene.     

A new approach to fluid separation modelling in the columns equipped with structured packings

An analogy between the flow patterns in real separation columns equipped with structured packing and film flow is used to develop a new modelling approach. The packing is represented as a bundle of channels with identical triangular cross section. The dimensions of the channels as well as their number are derived from the packing geometry. The channel inner surface is wetted by a liquid flowing downwards, whereas the rest of the volume is occupied by a countercurrent vapour flow. Both phases are assumed to be totally mixed at regular intervals, determined by the corrugation geometry of the packing. The mathematical model is based on a set of partial differential equations describing hydrodynamics and mass and heat transport phenomena. These equations are complemented by the conjugate boundary conditions at the phase interface. A numerical solution of the model yields velocity profiles as well as concentration and temperature fields throughout the column. The model is verified using experimental data for a binary distillation in a column equipped with Montz-Pak A3-500.     

Simultaneous heat and mass transfer in binary distillation—II: Experimental

A theoretical study of simultaneous heat and mass transfer in binary distillation has shown that heat and mass transfer coefficients can be appropriately evaluated if liquid phase temperatures and compositions are measured as functions of height in a column. In this study, the experiments were carried out in a wetted-wall column using a methanol-water binary system at one atmosphere.Special probes were designed to determine the state of the liquid phase. Temperatures were measured with microthermocouples and liquid samples were analyzed with a high precision refractometer. The liquid phase was found to be saturated which indicated, in accordance with the conclusions from a theoretical study, that all the resistance to mass transfer was in the vapor phase. Local transfer coefficients were calculated using the composition data as a function of column height. The results were correlated by an equation showing close agreement with the Chilton-Colburn equation. $\text{k}{}_{\mathrm{y}}\text{a}{}_{\mathrm{m}}\text{V}\text{= 0.039}\text{Sc}{}_{\mathrm{y}}$^{?$\text{2}\text{3}$}Re_y^?0.20 cm^?1.It is concluded that mass transfer in the vapor phase is the controlling resistance in distillation and that there is no additional evaporation within the liquid phase caused by heat transferred from the vapor phase as proposed by some previous investigators.     

脉冲筛板萃取柱中传质过程的研究

在内径40mm实验脉冲筛板柱中,用30%磷酸三丁酯-硝酸-水体系测定了各种操作条件下两相稳态传质浓度剖面、液滴直径分布和分散相体积分数.根据多级返流模型拟合实际浓度剖面推算得到真实的体积传质系数K_(oDa)和两相返混参数,并进而计算出相际传质系数K_(oD).对标准板和分散-聚合型板两种柱结构内的传质过程进行了分析和讨论.研究结果表明,在本实验范围内,脉冲筛板柱内相际传质系数可按单液滴湍流内循环传质模型来预测.     

塔板上流型变化对板效率影响的计算传质学

利用能够描述塔板上气液两相错流过程的流体力学模型,建立了同时模拟气液两相流动与传质过程的数学模型;通过对气液两相传质方程和流体力学模型方程的联立求解,计算得到了塔板上液相速度分布和气液两相浓度分布的数值解,考察了气相完全混合和气相部分混合两种条件下塔板上的气液两相浓度分布,同时考察了气相完全混合时流型变化对塔板效率的影响.     

蒸馏塔板上汽液传质系数的确定——非平衡池法(Ⅰ)模型的建立及求解

本文提出一种确定蒸馏塔板上汽液传质系数的新方法——非平衡池法.该法将塔板沿液流方向分为适当数目的串联非平衡池,通过联立求解每一池各相的物料衡算、能量衡算、相平衡和传质传热速率方程,可从塔板入口组成得到出口组成.调整汽液传质系数使计算的出口组成与实测值相等,从而可确定出两相传质系数.方程组用混合牛顿法求解.     

A MATHEMATICAL MODEL AND SIMULATION FOR NON ISOTHERMAL GAS ABSORPTION WITH CHEMICAL REACTION

In this paper, the principles of mass and heat transfer for a non-isothermal gas absorption with chemical reaction have been described. The examples of carbon monoxide complexing with aluminum cuprous tetrachloride solution and carbon dioxide absorbed by monoethanolamine aqueous solution in packed column have been simulated and computed with a mathematical model which considered of both mass and heat transfer, gas and liquid resistance. The fundamental differential equations of the process are treated with forth order Runge-Kutta method. Through simulating and computing, the temperature profiles and concentration profiles of both gas and liquid phase along the packed height have been visualized. The results are reasonably accurate and conform with pilot plant experimental data.     

Extraction of rare earth metals with a multistage mixer-settler extraction column

Extraction behavior of rare earth metals within a mixer-settler extraction column has been analyzed with the stage efficiency calculated from mass transfer coefficients and interfacial area. The mass transfer coefficient within the dispersed drops is determined from a rigid sphere model by taking into account the residence time distribution of drops, and the coefficient around the drops is calculated by Ranz-Marshall's correlation with the terminal settling velocity of a rigid sphere. The interfacial area of dispersed drops is calculated by the use of correlations for the drop diameter and the holdup of dispersed phase in the mixer-settler extraction column. The calculated results for the separation of samarium and gadolinium with a five-stage mixer-settler extraction column are compared with the experimental results at various agitation speeds and flow ratios between two phases. The extraction behavior in the multistage column is explained by a model based on the hydrodynamics and the mass transfer within the mixer. Effects of the pH value in aqueous phase, the extractant concentration in organic phase and the number of stages on the extraction behavior in the mixer-settler column are also shown.     

Modelling reactive absorption of CO2 in packed columns for post-combustion carbon capture applications

A rate-based process model for the reactive absorption of carbon dioxide (CO₂) from a gas mixture into an aqueous monoethanolamine (MEA) solution in a packed column is developed. The model is based on the fast second-order kinetics for the CO₂-MEA reactions and takes into account the mass transfer resistances. The heat effects associated with the absorption and chemical reaction are included through energy balances in the gas and liquid phases. Appropriate correlations for the key thermodynamic and transport properties and for the gas-liquid mass transfer are incorporated into the model to ensure reliable predictions. The model predictions are validated by simulating a series of experiments conducted in pilot and industrial scale absorption columns with random and structured packings reported in the literature. Comparisons between the simulation results and the experimental data reveal good quality predictions of the gas phase CO₂ and MEA concentrations and the liquid temperature along the column height. The sensitivity studies reveal that the correlations for the gas- and liquid-film mass transfer coefficients given by Onda et al. (1968) provide better predictions than the penetration theory of Higbie (1935) and the correlation of Bravo et al. (1985).     

Impact of mass transfer coefficient correlations on prediction of reactive distillation column behaviour

A significant part of the safety analysis of a reactive distillation column is the identification of multiple steady states and their stability. A reliable prediction of multiple steady states in a reactive distillation column is influenced by the selection of an adequate mathematical model.For modelling reactive distillation columns, equilibrium (EQ) and nonequilibrium (NEQ) models are available in the literature. The accuracy of the nonequilibrium stage model seems to be limited mainly by the accuracy of the correlations used to estimate the mass transfer coefficient and interfacial area.The binary mass transfer coefficients obtained from empirical correlations are functions of the tray design and layout, or of the packing type and size, as well as of the operational conditions and physical properties of the vapour and liquid mixtures.In this contribution, the nonequilibrium model was used for the simulation of a reactive distillation column. For prediction of the binary mass transfer coefficient for a sieve tray, four correlations were chosen to show their impact on the prediction of the reactive distillation column behaviour. As a model reactive distillation system, the synthesis of methyl tertiary-butyl ether (MTBE) was chosen. The steady-state analysis and the dynamic simulation of the model system were done. Qualitative differences between the steady states were predicted using the chosen correlations.     

Simultaneous heat and mass transfer in a packed binary distillation column

A simultaneous heat and mass transfer model was applied to a binary system in a 3-in. distillation column packed with $\text{1}\text{4}$in. Raschig Rings. MaThe experiments carried out with the toluene-trichloroethylene system show that the liquid phase is saturated, indicating no resistance to mass transfe     

Modelling the coupled transfer of mass and thermal energy in the vapour–liquid region of a nitrogen–oxygen mixture

Current non-equilibrium distillation models do not explicitly include the coupling between thermal and mass fluxes. We present a calculation model for the coupled transfer of mass and thermal energy in the vapour–liquid region of a binary mixture. The region is modelled as a vapour–liquid interface in between two homogeneous films. The entropy production in the vapour–liquid region can be calculated using both irreversible thermodynamics and the entropy balance. The film thickness ratio is found by requiring the entropy production calculated with the two methods to be equal, while keeping the vapour film thickness fixed. Using a nitrogen–oxygen mixture as example, we show that neglecting the coupling between thermal and mass fluxes can have a large impact on the magnitude and direction of the theoretical (net) fluxes. The size of the impact depends on the vapour film thickness, but it is significant for all thicknesses. By increasing the number of control volumes that is used to represent the liquid and vapour films, we also show that the fluxes depend highly on the resistivity profiles in the films. They depend slightly on the interface resistance. A sensitivity analysis of the transport properties shows that accurate values of the Maxwell–Stefan diffusion coefficients in both homogeneous phases and of the liquid phase heat of transfer are most important. Especially the measurable heat flux at the liquid boundary of the system is sensitive to neglect of coupling, to neglect of the interface resistance and to uncertainties in the transfer properties.     

Some aspects of rate-based modelling and simulation of three-phase distillation columns

The application of the bate-based approach to the dynamic and stationary modelling of three-phase distillation columns is presented. The main problem can be seen in finding adequate models for the mass and heat transfer over phase interfaces to be utilised in the Maxwell-Stefan equations. While for the vapour–(continuous) liquid interface, there are a number of methods and data available, the interface between continuous and dispersed liquid phases has not been studied for the case of distillation processes. A reasonable alternative approach to modelling of a three-phase distillation column can be found where the liquid–liquid interface is treated as equilibrium. The adequacy of this modification is supported by phenomena observed on distillation trays, e.g. strong agitation of liquid phases. The resulting combined non-equilibrium and equilibrium model is compared to the classical equilibrium model and also to experimental data for ethanol–water–cyclohexane separation in a number of examples.