On the multiple solutions of the reactive distillation column for production of fuel ethers

A systematic study of the operating conditions and parameter sensibility of multiple steady states in a reactive distillation column for production of fuel ethers is presented. The multiplicity analysis is performed using bifurcation diagrams for several scenarios using the process simulator Aspen One Aspen Plus. Our results indicate that the main variables that affect both the presence and behavior of multiple solutions in the reactive distillation column are the reflux ratio, the reboiler duty and the thermal condition in the feed stream. In particular, we have determined that the vapor–liquid stream in the feed has a major influence on the occurrence of this phenomenon and this parameter especially establishes the type of multiplicity that can occur in the reactive distillation column for production of fuel ethers.     

Optimal operation of a batch packed distillation column

Optimal policies for a batch packed distillation unit are examined for the cases of variable reflux ratio and variable boilup rates. This work was to act as a follow-up to Converse's work⁽¹⁾ for a batch plate distillation column with variable reflux policy. For the cases studied, it would seem that the boilup rate optimal policy yields better performance for the still than the reflux ratio optimal policy. The results of the present analysis and those of other authors seem to indicate that more effort should in the future be devoted to new modes of operation rather than to various refinements of the model used in the present and past studies. The present exploratory work seems to support the need for further studies using a packed rectifying section with variable boilup policy along with a novel mode of operation such as that considered by Mayur et al,⁽⁶⁾.     

Mathematical simulation of the performance of the solid liquid extractors—I: Diffusion batteries

The extraction in purely countercurrent solid liquid extractors is extensively discussed in literature. In practice, the local mode of phase-contact often deviates from the overall counter-currence as is the case in e.g. belt type extractors and diffusion batteries. In the diffusion battery the local phase contact in each of the columns is, in essence, an instationary column process. However, from an overall point of view the extraction approaches a purely contercurrent process, dependent on the choice of the number of columns in the system and the cycle time. The differential equations describing mass transfer in this extractor were solved by numerical methods. The exit concentrations in cyclic steady state are averaged over one time cycle to obtain the extraction efficiency. Results of the calculations are presented as a correlation between the number of “plug flow” and “true” transfer units. It is shown that deviations from pure countercurrent are small when 4 or more columns are used under normal operating conditions.     

A flexible solution method for generalized equilibrium stage columns

This paper presents a flexible solution method for the process design and simulation of generalized equilibrium stage absorption or distillation columns for solving a wide range of multistage, multicomponent separation problems in the petroleum or petrochemical industries. Although the model was developed to increase the control flexibility of product components in a solution, it was found that it also increases the efficiency of convergence at the expense of greater core usage. The mathematical model includes overall material balances, component material balances, energy balances, summation equations and specification equations. These nonlinear equations are solved simultaneously via the matrix partitioning technique together with the popular Newton-Raphson iterative algorithm. The method is applicable for both absorption and distillation columns with multiple feeds and sidedraws. This model will offer more flexible choices of the column specifications such as tray temperature, overhead product rate, reflux ratio, boilup ratio, tray vapor/liquid flow and product purity/recovery. The composition dependent equilibrium and enthalpy correlations such as Chao-Seader, Grayson-Streed, and Soave-Redlich-Kwong are incorporated into the mathematical model. Most problems can be easily converged with less than ten iterations.     

Foam fractionation of solutions containing two surfactants in stripping and reflux columns

An experimental and theoretical investigation was undertaken in order to examine the effect of concentration, foam flow rate and feed flow rate on the separation of sodium dodecylbenzene sulfonate and sodium lauryl sulphate from solutions containing the two surfactants, in stripping and reflux columns. The experimental results indicated the conditions under which a stripping foam fractionation column behaves according to the model of an infinite column. Within the present experimental range reflux columns behaved always according to the model of an infinite column. Using this model it is possible to predict relative separation of surfactants in stripping and reflux columns from experimental data obtained in simple columns. Experiments with modified total reflux columns indicate great potential for batch foam fractionation.     

Monotone iteration methods with adaptive collocation for solving coupled systems of nonlinear boundary value problems

Monotone iteration procedures are developed for the solution of a class of coupled and highly nonlinear boundary value problems. These procedures are of guaranteed convergence and can be used for a numerical investigation of the multiplicity structure of steady-state solutions. The monotone iterations provide also a basis for an automatic scheme for adapting and refining the collocation point grid between iterations. The local error of approximation is controlled very accurately and problems exhibiting extremely steep multiple concentration profiles of significantly different scales can be treated.     

甲基氯硅烷精馏流程的模拟与优化

采用Aspen plus软件对工业七塔精馏过程进行全流程建模与模拟,优化工艺参数,研究了新的精馏节能工艺。对一甲塔等7个精馏塔采用双因素水平的灵敏度分析,考察了塔釜采出率、回流比、进料位置和塔顶压力对产品浓度和热负荷的影响,确定一甲塔最优的工艺参数：塔釜摩尔采出率为0.92,摩尔回流比为130,塔顶压力为0.18 MPa,总理论板数为400,在210块理论板位置进料。在此基础上,针对高能耗的脱高塔/脱低塔,模拟研究了双效精馏新工艺,新工艺可节省39.70%的年总成本;针对一甲塔模拟研究了热泵精馏新工艺,新工艺可降低41.42%的年总成本。     

联合精馏分离四氢呋喃-水共沸物的实验及优化模拟

由于四氢呋喃与水会生成沸点64 ℃的最低共沸物,采用三塔联合精馏的方法对其进行分离。根据文献资料选择乙二醇作为萃取精馏过程的萃取剂,并在脱水塔中对萃取精馏塔产物进行脱水。选择Aspen Plus软件对工艺流程进行模拟。选择Wilson模型及RadFrac模块对单塔工艺参数进行模拟及优化,确定了各塔进料板与回流比等最适宜参数。经实验考察的项目结果均与模拟结论一致。脱水塔产物四氢呋喃含水量可低至170 μg/g。根据优化后的参数在Aspen Plus中进行全工艺流程的闭合与模拟,终产物四氢呋喃的质量分数可达0.9995,收率为0.9988。其质量分数优于常见双塔萃取精馏流程。     

Calculation of multistage countercurrent separation processes-I. Multicomponent multistage rectification by differentiation with respect to an actual parameter

The method proposed generates without trial-and-error a family of solutions depending on a sequence of values of a parameter under consideration, e.g. reflux ratio, side-stream flows, condenser duty etc. The technique may be successfully used for a parametric study of a particular column. The method requires the knowledge of the solution of the distillation problem for the initial value of the parameter considered. The procedure is effective for cases where solution for a great number of parameter values is required.     

DESIGN OF A COMPOSITION ESTIMATOR FOR INFERENTIAL CONTROL OF DISTILLATION COLUMNS

In distillation column control, secondary measurements such as temperatures and flows are widely used in order to infer product composition. This paper addresses the design of the linear static estimators using the secondary measurements for estimating product compositions of distillation columns. Based on the unified framework for the estimator design, the relationships among various static estimators are discussed in terms of the estimator structure. Il is shown that the projection estimator is equivalent to the regression estimators in the special cases. Since the projection estimator heavily depends on the measured inputs such as reflux flow and heat input to the reboiler due to its structural characteristic, the estimation performance is far more sensitive to measurement noise and nonlinearity of them, compared wiih the regression estimators based on the PCR or PLS method. It is also found that the use of the measured inputs leads to performance deterioration of both the projection and regression estimators because of their nonlinear effects on the product compositions especially in high-purity columns. Design guidelines for the PCR and PLS estimators are presented by analyzing the results of the simulation studies on a high-purity column example. The estimator based on the guidelines is robust to sensor noise and has a good predictive power     

简化外部热耦合双精馏塔的控制与优化

针对具有3个换热器结构的外部热耦合双精馏塔(S-EHIDDiC),提出了一种新型的控制与优化策略。顶部与底部换热器的热负荷能够改变高压精馏塔的回流量和低压精馏塔的上升汽量,因而可以用来控制高压精馏塔塔顶和低压精馏塔塔底的产品质量。这种控制方法与常规精馏塔的LV控制结构相似。S-EHIDDiC还有多余的决策变量(如进料分流比,高压精馏塔塔压和中间换热器的热负荷),可以对稳态操作进行优化。闭环仿真证明了这种控制结构的可行性,稳态优化也提高了系统的热力学效率。     

Modeling and in-depth analysis of the start-up of dividing-wall columns

Saving potentials of up to 30% in capital and operating costs are the driving forces behind the increase in the application of dividing-wall columns in industry. However, a lack of knowledge still exists when dealing with the start-up of dividing-wall columns, which is inherently a strongly nonlinear process. Here, for the first time the start-up of dividing-wall columns is explored, where the starting point is an empty column at ambient conditions. A model is presented which is capable of predicting the dynamic discrete-continuous changes which are characteristic of dividing-wall columns. The proposed process model takes into account the heat transfer across the dividing wall as well as the vapor distribution below the dividing wall. The degree of accuracy of the model is clearly determined by comparing different simplifications, e.g. a constant vapor distribution ratio equal to the steady-state value. The detailed studies were carried out with strict product specifications so that the influence of process parameters could be quantified. The rigorous process model and the obtained simulation results presented in this study provide a promising basis for developing and applying optimal start-up policies for dividing-wall columns.     

On the dynamics of distillation processes—IV Uniqueness and stability of the steady state in homogeneous continuous distillations

Recent numerical studies by Magnussen et al.[1] have shown that multiple steady state solutions can be exhibited by the constant molar overflow (CMO) model for ternary azeotropic distillation in a multistaged column. This has such important consequences for distillation control, design and startup that further experimental and analytical work is desirable.This paper addresses the problem of uniqueness and stability of the steady state in the continuous distillation of homogeneous mixtures. It is shown that multiple steady state solutions are not exhibited by either binary homogeneous distillations in a multistage CMO column or multicomponent homogeneous distillations in a single stage CMO column (flash distillation). Therefore, the multiplicity is a consequence of multicomponents and multiple stages.     

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.     

Multiplicity of VLLE equations: Case studies

Phase equilibrium calculation involving VLLE is often encountered in design, simulation and optimisation of many chemical processes. Practically, VLLE is numerically solved by a set of equations of chemical potential equilibrium and mass balances, which in theory may lead to multiple solutions due to the high nonlinearity of equations. Here, the multiplicity of VLLE is analysed by continuation method with pressure and composition as parameters. The detailed features of the output multiplicity of VLLE, e.g. the multiple liquid compositions and relative holdups, multiple liquid-liquid boundaries as well as the mixture composition region resulting in multiplicity, are presented. The influence of VLLE on process multiplicity is illustrated through the flash process. Moreover, the effect of the activity model is investigated, which shows that multiplicity of VLLE may change significantly and even disappear using different activity models. The multiplicity study of the VLLE problem is very helpful for evaluating the activity models and parameters and for providing proper initial values for simulation of system with VLLE multiplicity.     

Bifurcation analysis for MTBE synthesis in a suspension catalytic distillation column

A rigorous bifurcation study is presented of methyl tert-butyl ether synthesis by suspension catalytic distillation (SCD). SCD is a new development of catalytic distillation (CD) in which fine catalyst particles are suspended in liquid, not only inherits advantages of CD but overcomes transfer limitations in catalyst bed. A complete equilibrium stage model is developed. Analysis results show that this system is sensitive to the operating parameters: the reflux ratio, the bottom flowrate, the methanol feed, the n-butane feed and the operation pressure, and the characteristic parameter for SCD: the solid/liquid separator ratio. The bifurcation diagram displays very intricate and highly nonlinear steady-state behavior, which can results in as many as seven steady-state solutions for identical column specifications. Especially, the results reveal that the superior column performance can be reached under practical operating conditions because the upper bound of the multiplicity range for the solid/liquid separation ratio is very small.     

Model validation for low and high superficial gas velocity bubble column flows

In the present work, gas-liquid flow dynamics in a bubble column are simulated with CFDLib using an Eulerian-Eulerian ensemble-averaging method in a two-dimensional Cartesian system. The two-phase flow simulations are compared to experimental measurements of a rectangular bubble column performed by Mudde et al. [1997. Role of coherent structures on Reynolds stresses in a 2-D bubble column. A.I.Ch.E. Journal 43, 913-926] and a cylindrical bubble column performed by Rampure et al. [2003. Modeling of gas-liquid/gas-liquid-solid flows in bubble columns: experiments and CFD simulations. The Canadian Journal of Chemical Engineering 81, 692-706] for low and high superficial gas velocities, respectively. The objectives are to obtain grid-independent numerical solutions using CFDLib to reconcile unphysical results observed using FLUENT with increasing grid resolutions [Law, D., Battaglia, F., Heindel, T.J., 2006. Numerical simulations of gas-liquid flow dynamics in bubble columns. In: Proceedings of the ASME Fluids Engineering Division, IMECE2006-13544, Chicago, IL], and to validate computational fluid dynamics (CFD) simulations with experimental data to demonstrate the use of numerical simulations as a viable design tool for gas-liquid bubble column flows. Numerical predictions are presented for the local time-averaged liquid velocity and gas fraction at various axial heights as a function of horizontal or radial position. The effects of grid resolution, bubble pressure (BP) model, and drag coefficient models on the numerical predictions are examined. The BP model is hypothesized to account for bubble stability, thus providing physical solutions.     

OPERATING PROBLEMS OF DISTILLATION COLUMNS: A DISCUSSION

A qualitative knowledge of how a continuous distillation column is expected to react to a physical parameter variation is often required, both in simulation and in practical operation. The topic is discussed in this paper with the aim to indicate some simple predictive rules concerning the steady-state variations, both under open- and closed-loop control. The binary distillation in conventional and non-conventional columns is examined in detail; some indications are also given for the multicomponent distillation in conventional columns. Geometrical constraints and asymptotic solutions are the basis for the adopted approach.     

Transfer Units and Nonkey Component Distributions in Packed Columns at Total Reflux

Abstract

Analytical equations for the number of transfer units (NTU) for multicomponent packed column systems at total reflux have been derived. These expressions are the packed column equivalents of Fenske's equation for staged columns. Two cases are considered in this paper: 1) all mass transfer resistance is assumed to occur in the vapor phase and 2) all mass transfer resistance is assumed to occur in the liquid phase. Using a characterizing parameter (C), it is seen that the distribution ratios of the nonkey components in a given system differ for both packed column cases, which in turn differ from the staged column case. Finally, it is shown that some nonvolatile component may be overheaded in the case where all mass transfer resistance is in the vapor phase, while some component of infinite volatility may be bottomed in the case where all mass transfer resistance is in the liquid phase.