Model Of Separation Process Research Articles

Modelling for control analysis and design in complex industrial separation and liquefaction processes

Dynamic simulation of complex industrial systems is discussed, and a summary is presented of over a decade of work in the modelling, simulation and control of cryogenic separation and liquefaction processes. The work includes not only successful applications but also the development of tools to facilitate the construction of the simulation flowsheets and their effective use in control system analysis and design. The use of these tools and of two commercial dynamic simulation packages is reviewed. The question of what is a required level of modelling detail in dynamic simulation applications is addressed.

Modelling and simulation of nonlinear chromatographic separation processes: a comparison of different modelling approaches

Chromatographic processes provide a powerful tool for the separation of multicomponent mixtures in which the components have different adsorption affinities. As an alternative to conventional batch chromatography as a discontinuous process, the simulated moving bed (SMB) process as a continuous chromatographic separation process gained more and more impact recently. Mathematical modelling and simulation of batch chromatographic processes is widely documented in the literature. For the modelling of SMB chromatographic processes two different strategies exist. The first one considers the corresponding true moving bed process neglecting the cyclic switching and thus the dominating dynmics of the process. The second alternative which is considered within this framework is to connect dynamic models of single chromatographic columns while considering the cyclic port switching in order to represent the dynamics of the real process correctly. We here describe three different approaches for the modelling and simulation of chromatographic separation processes with nonlinear adsorption thermodynamics described by the Langmuir isotherm. The first one is a rigorous modelling and numerical simulation approach, the second one is based on the equilibrium theory and proceeds from the analytical solution for binary separation processes based on nonlinear wave propagation. The third approach only includes nonidealities caused by the limited mass transfer rates. All approaches are analyzed and compared with respect to complexity, accuracy and computational time.

Modellierung und effektive numerische Simulation von chromatographischen Trennprozessen im SMB‐Betrieb

AbstractModeling and Efficient Computational Simulation of Simulated Moving Bed Chromatographic Separation Processes.Chromatographic separation processes provide a powerful tool for the separation of mixtures in which the components have different adsorption affinities, especially when high purities are required. In this area, simulated moving bed (SMB) technology is becoming an important technique for large‐scale continuous chromatographic separation processes since it provides the advantages of a continuous countercurrent operation while avoiding the technical problem of a true moving bed. Because of the complex dynamics of the process, the choice of the optimal operation parameters and the control of the process in order to keep the product specifications at any time is not straightforward. For this challenging task, a reliable dynamic model of the process is necessary which is accurate enough as well as efficient enough in order to permit its online use for model based control. The purpose of this contribution is to review the state of the art in dynamic modeling of SMB chromatographic separation processes, highlighting new trends and results in the design of computationally effective simulation models suitable for online applications.

Modeling of homogeneous reactive separation processes in packed columns

The coupling of physical separation and chemical reactions in one unit operation, the so-called reactive separation processes (RSPs), are of increasing interest for scientific investigation and industrial application. RSPs tend to be very complex due to strong physico-chemical interactions, and a number of the model assumptions that are adequate for traditional unit operations may not be suitable in this new context. Models used to simulate RSPs should therefore be highly accurate in order to reflect this complexity. On the other hand, it is not always economical nor feasible to use the most sophisticated models for a range of different applications, such as process and equipment design, the determination of optimal operating policies, model-based control, etc., and the model complexity has to be adapted to the purpose. In many cases however, it is not evident which simplifications are appropriate, so that the uncertainty concerning adequate ways to model RSPs is still significant. Kreul et al. (1996a, b) have published a very detailed rate-based model and first simulation results for RSPs including reaction kinetic terms in the bulk and the film areas. In this paper, a detailed model investigation is presented, as well as a systematic deduction of possible model simplifications. The completely kinetic model and the corresponding equilibrium stage model are applied to various homogeneously catalyzed reactive distillation and reactive absorption processes. A number of simulation results are presented for four very different test systems. It is concluded that equilibrium and rate-based approaches can lead to significantly larger differences in calculated concentrations profiles for RSPs than for non-reactive operations, so that the additional effort of more complex modeling may be justified. In addition, it is demonstrated that if the kinetics of the mass and energy transfer between the phases are calculated explicitly, in most cases the consideration of interaction phenomena such as diffusional and direct reaction-transfer interaction is not necessary.

Modeling for Control Analysis and Design in Complex Industrial Separation and Liquefaction Processes

Dynamic simulation of complex industrial systems is discussed, and a summary is presented of over a decade of work in the modeling, simulation and control of cryogenic separation and liquefaction processes. The work includes not only successful applications but also the development of tools to facilitate the construction of the simulation flowsheets and their effective use in control system analysis and design. The use of these tools and of two commercial dynamic simulation packages is reviewed. The question of what is a required level of modeling detail in dynamic simulation applications is addressed.

Modeling of Chromatographic Separation Processes Using Nonlinear Wave Theory

This paper presents a simplified approach for the dynamic modeling of chromatographic separation processes based on the model of the ideal chromatogaphic column, the thermodynamic equilibrium being described by the Langmuir isotherm, and nonlinear wave propagation. The approach has been applied to batch chromatography and to the SMB-(Simulated Moving Bed) process. Simulation examples for both cases are given and the limitations of the model are shown. The approach has proved to be computational efficient and to allow additional insight into the process dynamics.

Parabolic intraparticle concentration profile assumption in modeling and simulation of nonlinear simulated moving-bed separation processes

This communication will focus on the application of the LDF (Linear Driving Force) mass transfer model in the mathematical simulation moving-bed separation processes with nonlinear adsorption isotherms to compare with the linear pore diffusion model, in order to determine its validity as well as to establish the equivalence between the two models.

GLOPEQ: A new computational tool for the phase and chemical equilibrium problem

Calculation of phase and chemical equilibrium represents a crucial phase in the modeling of many separation processes. For conditions of constant temperature and pressure, a necessary and sufficient condition for the true equilibrium solution is that (i) the total Gibbs free energy of the system be at its global minimum, or (ii) the minimum of the tangent plane distance function be nonnegative for all phase models used to represent the system. In this work, the goal is to obtain equilibrium solutions corresponding to a global minimum of the Gibbs free energy as efficiently as possible, for cases where the liquid phase or phases can be modeled by the NRTL, UNIQUAC, UNIFAC, Wilson, modified Wilson and ASOG equations. Vapor phases whose behavior can be described as ideal can also be handled. In achieving this goal, there are two distinct problems of relevance: (i) the minimization of the Gibbs free energy, denoted (G), and (ii) the minimization of the tangent plane distance function, or the tangent plane stability criterion, denoted (S). For all these activity coefficient models, GLOPEQ (GLobal OPtimization for the Phase and chemical EQuilibrium problem) can guarantee global solutions for problems (G) and (S), but a combined algorithm employs them in tandem, using (G) to generate candidate equilibrium solutions which can then be verified for thermodynamic stability by solving (S). Two key features of the combined algorithm are that (i) as much information as is possible is obtained from local searches, and (ii) it is preferable to verify a globally stable equilibrium solution using the tangent plane criterion, as this problem contains fewer variables than the minimization of the Gibbs free energy. Results for several examples are presented, and all but one of them are for the case of phase equilibrium, due to the paucity of examples for reacting systems that employ excess Gibbs free energy models.

Estimating return period wave heights and wind speeds using a seasonal point process model

A method of extreme value analysis is described which incorporates a model reflecting the seasonality of the environment. A point process model is employed with the arrival of storms described as a Poisson process and a generalised Pareto distribution to model the magnitude of the storm. Separate point process models are constructed for each season and then aggregated to provide a basis for estimating the return values. The construction of separate models, including the use of seasonal thresholds, ensures that more appropriate models are fitted to each season's data. The method also reflects the completeness of the environmental record, avoiding the bias that can result from missing data. The potential benefits of the approach include greater accuracy, robustness to missing data and the provision of seasonal return values for mobile systems deployed on a temporary basis. The method is demonstrated in estimating the N year significant wave heights and wind speeds in the northern North Sea.

Risk, Conflict, Mothers' Parenting, and Children's Adjustment in Low-Income, Mexican Immigrant, and Mexican American Families

Structural equation modeling was used to test mothers' supportive parenting and inconsistent discipline practices as mediators of the effects of multiple risk factors and family conflict on children's conduct disorder and depression. Data were collected from 121 predominantly Spanishspeaking, low-income, Mexican immigrant and Mexican American families. Separate process models were tested for children's and mothers' reports. For children's reports, mothers' supportive parenting partially mediated the effects of family conflict on children's depression. For mothers' reports, inconsistent discipline practices fully mediated the influence of multiple risk factors on children's depression and partially mediated the influence of multiple risk factors on children's conduct disorder. Only children's reports showed direct effects between family conflict and children's conduct disorder and depression. Higher levels of maternal acculturation were related to lower levels of inconsistent discipline practices and less depression in children. Key Words: acculturation, child adjustment, family conflict, Mexican Americans, parenting, reporter agreement. Mexican Americans are the most rapidly growing ethnic group in the United States, particularly in the Southwest, and are overrepresented in lowincome categories (U.S. Bureau of the Census, 1993). Yet there have been few studies of influences on parenting practices and children's adjustment in this population. As a result, there is little empirical basis for the development of preventive and therapeutic interventions for families of this ethnic group who are at risk or who have children with adjustment problems. Low-income, predominantly Spanish-speaking, Mexican immigrant and Mexican American families represent a particular developmental niche or context for children in the U.S. Developmental niche, conceptualized by Super and Harkness (1986), refers to children's immediate, culturally structured environments and the effects these environments have on children's development. Three components of developmental niches are physical and social settings, culturally influenced customs and interactions (e.g., childrearing practices), and individual characteristics of children and their caretakers (e.g., psychological characteristics). These components interact dynamically, can be in accord or discord, and are regulated by homeostatic mechanisms to maintain stability (Harkness & Super, 1995). The family, as a developmental niche, is also an open system that interacts across its boundary with its surrounding contexts. The family is influenced by these contexts and, at the same time, exerts an impact on them (Bronfenbrenner, 1989; Lerner, Castellino, Terry, Villarruel, & McKinney, 1995). This study delineates some of the processes operating in the developmental niches of children in low-income, predominantly Spanish-speaking, Mexican immigrant and Mexican American families. More specifically, we wanted to determine whether mothers' parenting practices mediated the effects of the risk factors that these families experience and family conflict on children's adjustment. Research conducted mostly with groups other than Mexican Americans has identified various risk factors in children's and adolescents' contexts that increase the likelihood of adjustment problems (Hawkins, Catalano, & Miller, 1992). Certainly, one of the most salient of these risk factors is poverty and the accompanying financial strain on all family members (Anderson, Williams, McGee, & Silva, 1989; Costello, 1989; Farrington et al., 1990). However, it is the number of risk factors that a family experiences rather than any single risk factor like poverty that best predicts children's developmental outcomes (Rutter, 1990; Sameroff, Seifer, Zax, & Barocas, 1987). Families experiencing multiple risk factors (e.g., financial hardship, low maternal education, maternal depression) or numerous negative life events (e. …

Optimization of Magnetizing Reduction and Magnetic Separation of Iron Ores by Experimental Design.

An experimental design of magnetizing reduction and magnetic separation of Egyptian low grade iron ore has been conducted using a data developed from applying the conventional single-factor experimentation in order to get the real optimum conditions of the processing. A model has been developed for magnetizing reduction to describe the relationship between the extent of reduction and the reduction temperature, time and reducing gas flow rate, whereas another model for magnetic separation process was deduced correlating the ore size and reduction time to the iron recovery in the magnetic concentrate.

Computer-aided process design: The design of an affinity-based continuous separation process

The exploration and design of novel processes and modified process configurations can be improved by process simulation. The development of an adequate process model, however, is the crucial step. When the development of a rigorous model is hindered by the lack of fundamental data a different approach has to be taken. Such an approach is described for a continuous biospecific adsorption process. A method for the analysis of fixed bed breakthrough data was developed and tested. Models for batch and continuous separation processes were built, based on the variation of the analysis parameters. The deduced models could be verified against fixed bed and continuous adsorption experiments. Simulation studies were conducted to assess the optimal process configuration with regard to the product purity and the controllability of the process. Furthermore comparisons of batch and continuous adsorption processes with respect to adsorbent and utility consumption were carried out.

Aspects of modeling, design and operation of membrane-based separation processes for gaseous mixtures

This paper presents a computer aided system, which can be used for simulation, design and operation of membrane-based gas separation processes. The computer aided system consists of a general model for the membrane-based gas separation process and a robust, reliable and flexible method of solution. The mathematical model consists of equations for the conservation of mass and momentum, which allows the consideration of effects such as pressure drops and various flow patterns within the permeator. The method of solution for the set of differential equations employs orthogonal collocation and decouples the set of equations by linearization in order to facilitate the calculation of sensitivities. In the current implementation, membrane modules with cocurrent or countercurrent flows and permeate pressure drops can be handled. Numerical results covering examples of simulation of gas separation units and effects of different variables on the design and operation of these processes are presented.

Mathematical modelling and calculation of membrane separation processes

In order to develop a methodology for mathematical modelling of membrane separation processes in continuous systems of the complete mixing and complete displacement type, theoretical and experimental studies were undertaken. The problem of determining a limiting concentration in the processed medium and the conditions for its achievement are described. New correlation results for current concentration and concentrate and permeate flow rates with membrane surface area are presented. The non-steady (dynamic) states of a membrane separation process, i.e. the start-up period from initial conditions to steady state, and transient responses because of modification of inlet conditions are presented as analytical expressions and formulae. The theoretical results and empirical formulae are tested using experimental data obtained during membrane concentration of biotechnology products.

Multiplicity in numerical solution of non-linear models: Separation processes

This paper analyzes the solutions from equilibrium based simulation models for separation processes with respect to multiplicity of solutions. The causes of multiplicity are investigated and it is shown for distillation columns, when and how multiplicity can be obtained and how it is conncted to design and operation of the separation process. Some of the causes of multiplicity are traced to over-design of staged separation processes and to values of specified variables. It is shown that the number of multiple solutions may be related to the number of stages while the number of acceptable solutions depend on the set of specified variables. Numerical examples covering simple distillation column models and heterogeneous azeotropic distillation operations are presented.

Modelling of separation processes on the basis of the general model for mechanical macroprocesses

In process industries, input fluctuations of essential raw material characteristics, e.g. particle size distribution, chemical and mineralogical composition, moisture, ash content, calorific value, etc., can greatly influence the efficiency of separation and other processes in particle technology. Furthermore, the efficiency of separation processes can decrease in the course of the starting-up period due to instationary states and transient phenomina. On the basis of the general model for mechanical macro-processes, the following examples are treated and compared with practical results and experience. (1) The transfer of stochastic fluctuations through a process unit; in this case, the dynamic behaviour is described by (a) the dispersion model and (b) the model of a cascade of ideally mixed vessels. As a result, the reduction of fluctuations (characterized, for example, by means of the standard deviation) can be calculated. (2) Applying the general model for mechanical macroprocesses to a special separation process (turbulent cross-flow classifier, pulp division model) it is possible to show that instationary states impair the separation efficiency, for example, to the separation sharpness derived from the grade efficiency curve (Tromp distribution curve).

A steady state equation-oriented simulator for separation processes of solutions with weak electrolytes

An equation-based simulator for modelling and design of countercurrent diffusion separation processes with equilibrium chemical reactions is described. The general mathematical model of the separation process for mixtures containing weak electrolytes is developed. The extended UNIQUAC-Debye-Hbckel equation originally proposed by Sander et al. is used to predict activity coefficients in such mixtures. Both phase and chemical equilibria are taken into account. Calculation of the model parameters for the H 2O-NH 3-CO 2 system is discussed. Computational experiences are illustrated with a laboratory separation column simulation for the industrially important system H 2O-NH 3-CO 2.

The modelling and computer simulation of mineral treatment processes — current status and future trends

This paper reviews the status of mineral processing models, and the simulator structures in which they are used. The modelling process is briefly considered in the context of model classification, data adjustment and parameter estimation. The features of a good simulator are enumerated, and recent progress in simulator development and application is discussed.Models currently available are reviewed, with particular reference to those incorporated in the JKMRC Simulator, JKSimMet. and its derivatives. These include crushers, SAG mills, ball mills, screens, hydrocyclones and other classifiers. The status of flotation and mineral liberation models is considered, and recently developed models of dense medium separation and gravity concentration processes are described.It is concluded that simulation for process design and optimisation is now an established technique, as evidenced by its increasing use by practising engineers through commercially available simulator software. Emphasis is placed on the importance of seeking the most effective process models as a basis for the successful use of simulation in practical applications.The challenges for the future include modelling mineral liberation, flotation and other concentration processes, and the further development and application of dynamic simulators.

Thermodynamic tuning in separation process simulation and design

A strategy for the thermodynamic modelling of separation processes is described. On the basis of a sensitivity analysis, the most sensitive model parameters for each critical separation task are tuned in accordance with the experimental information and the separation requirements. A realistic description of the process conditions is obtained by choosing for parameter estimation the regions of maximum sensitivity. The procedure is illustrated by tuning an equation of state to the fractionation problem of ethylene production. A single parameter matrix is obtained valid for all the critical separation problems of low- and high-pressure ethylene plant distillation processes.

Statistical analysis of mass-transfer parameters for sorption processes and models

The determination of mass-transfer parameters for sorption processes involving microporous solids such as activated carbon, ion-exchange resins, and soil particles and aggregates is an important element in the modeling and design of separation and purification processes and in the description of sorption phenomena in natural and environmental systems. Such determinations are typically carried out by fitting appropriate mathematical models to sets of rate data obtained in laboratory or field-scale experiments. An aspect of such determinations that has been largely neglected is the evaluation of statistical confidence. Determination of confidence for sorption parameters is made difficult by the use of nonlinear mathematical models and the existence of multiple, jointly determined parameters. This paper presents a method for determining preliminary estimates of confidence intervals for two jointly determined mass-transfer parameters describing sorption by microporous solids in fixed-bed reactors. An application of the method to examine the statistical significance of dissolved background organic substances on rates of adsorption of a specifically targeted compound, p-dichlorobenzene, from different complex aqueous solutions is presented.