An aggregation model reduction method for one‐dimensional distributed systems

A method for deriving reduced dynamic models of one‐dimensional distributed systems is presented. It inherits the concepts of the aggregated modeling method of Lévine and Rouchon originally derived for simple staged distillation models and can be applied to both spatially discrete and continuous systems. The method is based on partitioning the system into intervals of steady‐state systems, which are connected by dynamic aggregation elements. By presolving and substituting the steady‐state systems, a discrete low‐order dynamic model is obtained. A characteristic property of the aggregation method is that the original and the reduced model assume identical steady states. For spatially continuous systems, the method is an alternative to discretization methods like finite‐difference and finite‐element methods. Implementation details of the method are discussed, and the principle is illustrated on three example systems, namely a distillation column, a heat exchanger, and a fixed‐bed reactor. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

A DISCRETE RELAXATION METHOD FOR SOLVING MULTI-COMPONENT DISTILLATION PROBLEMS

A computational method for solving multi-component distillation problems is presented, where the steady state composition profiles of a column are determined by solving the vapor-liquid equilibrium problem for each stage sequentially to convergence. The Rachford-Rice equation is solved for each stage and the calculations are continued until the column temperature profile converges to the steady state solution. The computational efficiency of this method is found to be comparable to the relaxation method in which the differential equations describing the transient behaviour of the column are solved. The advantages of the method presented here are its conceptual simplicity and its ease to program.     

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.     

精馏过程的动态模拟

在各类典型精馏过程稳态模型的基础上,建立了6类典型非稳态精馏模型,并对动态精馏过程的开环响应进行了模拟计算.计算结果表明,实际精馏塔内存在的非平衡效应和惯性效应对非稳态精馏的动态响应过程有很大影响,其中惯性效应的影响更为突出.本文建立的三维非平衡混合池动态精馏模型充分地考虑了精馏过程中的非平衡效应和惯性效应,因此相信能够更适合于模拟实际的动态精馏过程.     

Design and Control Comparison of Alternative Separation Methods for n‐Heptane/Isobutanol

The binary mixture of n‐heptane and isobutanol forms an azeotrope at atmospheric pressure, with a composition of 66.9 mol % n‐heptane and a temperature of 364 K. Several methods of separation are possible. This study compares the steady‐state economics and the dynamic controllability of three alternative separation techniques: a two‐column extractive distillation process, a two‐column pressure‐swing distillation process, and a single column with a refrigerated condenser.     

Analysis of the Start‐up Process for Reactive Distillation

The start‐up procedure of a distillation column is a time‐ and energy‐consuming process. Further, the products during the start‐up time are off specification and cannot easily be recycled as for conventional distillation but must costly be disposed of. In this paper, a process model to simulate the barely analyzed start‐up procedure for a reactive distillation from the cold and empty state to steady state is presented. The start‐up of a reactive distillation column has been modeled with gPROMS. The advantage of a cold and empty start‐up is the consistent and reproducible initialization. Commercial simulators do not give the opportunity to start form a cold and empty state, e.g., a column modeled with Hysys must be shut down from a steady state to be able to model the complete start‐up process, which is not possible, for example, for a batch process. Also, a change in the describing equations and discontinuities in process variables is difficult to handle within the simulation. In this paper, the start‐up strategies normally used for distillation without reaction are examined and applied to reactive distillation. It will be shown that the widely used strategy of total reflux is not suitable for reactive distillation. A simplified model to derive a time constant which describes the influence of parameter setting changes, like heating power, reflux ratio and feed composition on the start‐up time, is introduced and validated.     

Bifurcation analysis of index infinity DAE parabolic models describing reactors and reacting flows

We show that most steady‐state models of chemical reactors and reacting flows in which convection effects are dominant and diffusion/conduction is neglected in the flow direction but included in the transverse directions, may change from parabolic type with a unique solution to index infinity differential‐algebraic equation (DAE) type with an infinite number of steady‐state solutions depending on the values of the reaction parameters. When a model is of index infinity, standard numerical methods may find only one of the solutions corresponding to latest possible ignition. We present complete bifurcation analysis of these models, a method for finding all solutions, determine the stability and, for some simpler cases, the domain of initial conditions attracted to these states. We also demonstrate that the various steady‐state solutions of the DAE systems are best found by integrating the transient hyperbolic versions of the models with appropriately selected capacitance terms and initial conditions. © 2016 American Institute of Chemical Engineers AIChE J, 63: 295–305, 2017     

Solving multicolumn equilibrium stage operations by total linearization

An efficient, reliable and easily programmed method for solving systems of equilibrium stage separation devices is described. The method is an extension of an algorithm developed by Ishii and Otto⁽⁹⁾ for single columns. It solves all equations simultaneously, takes advantage of the basic tridiagonal matrix form form of the linearized steady state equations and can handle configurations which include distillation columns, absorbers and reboiled absorbers. The solution for a thermally coupled distillation system is presented.     

Nonlinear wave modeling and dynamic analysis of internal thermally coupled distillation columns

Internal thermally coupled distillation column (ITCDIC) is a frontier in the energy saving distillation research. It is well known for the complex dynamics, which challenge the establishment of an excellent reduced model for further control strategy design greatly. In this article, a physical approach of the ITCDIC process based on nonlinear wave theory is explored, where it is first discovered that traditional wave theory in conventional distillation columns (CDIC) could not be directly applied in ITCDIC, due to: First, the internal thermal coupling results in mole flow rates varying evidently over each stage, which not only makes the wave modeling of the wave phenomenon in ITCDIC more difficult but also makes wave dynamics greatly different between ITCDIC and CDIC; Second, an interesting wave phenomenon of ITCDIC is discovered that waves located in the rectifying section and stripping section travel under opposite tendencies when the steady state is disturbed by the step change of thermal condition q, one sharpens and the other is likely to spread synchronously, it means the movement of wave profiles in ITCDIC could not be simply described by shock wave velocity, which is usually used in wave modeling of CDIC; more seriously, shapes of the self‐sharpening wave profiles in ITCDIC change obviously during the traveling processes, which further reveals that shape influence on wave velocity has to be considered in the wave modeling of ITCDIC. A rigorous wave velocity and a natural wave velocity are derived, respectively, based on which, the detailed analyses of traveling wave characteristics are carried out. A novel wave velocity, based on the profile trial function which has been well developed by Marquardt, is further derived to consider the obvious change of profile shape. And a completed nonlinear wave model of ITCDIC is thereby established by combining the proposed wave velocity with thermal coupling relations and material balance relations. The benzene‐toluene system is illustrated as an example, where component concentration prediction and distinct dynamic characteristics are carried out in detail based on the proposed nonlinear wave models. The research results reveal the accuracy and validity of the proposed nonlinear wave model of ITCDIC. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Simulation of Membrane Distillation for Purifying Water Containing 1,1,1‐Trichloroethane

Vacuum membrane distillation is modeled for the purification of water containing organic matter. The separation medium is a hollow‐fiber membrane contactor that is simplified to a two‐dimensional structure with a single porous membrane wall. The model considers the transport phenomena of a vacuum membrane distillation system in porous media, in which the aqueous volatile organic solution was considered as an incompressible and steady fluid. The numerical simulation of the two‐dimensional model of vacuum membrane distillation for an aqueous solution of 1,1,1‐trichloroethane was established under steady state. The effects of the bulk feed temperature and the feed flow rate on the percentage of 1,1,1‐trichloroethane removal from an aqueous solution are discussed.     

Design and Control of Ionic Liquid‐Catalyzed Reactive Distillation for n‐Butyl Acetate Production

A simulation study of n‐butyl acetate production with the [Hpy][HSO₄] ionic liquid catalyst was performed. Due to the lack of phase equilibrium data, the binary interaction parameters of the NRTL model for ionic liquid and reactive species were calculated by the COSMO‐RS technique. A reactive distillation process with recycled ionic liquid stream was proposed, and the column configuration was optimized by minimization of the total annual capital. The novel process is considerably efficient and economic compared to the traditional reactive distillation process of nonionic liquids. With the steady‐state parameters, a plant‐wide control structure was further developed to evaluate the robustness of the control system by exerting the disturbances of feed flow rate and feed composition. Dynamic simulation results suggest that the control scheme with a composition controller is timely and effective.     

热泵精馏的控制研究

通过对精馏塔的系统特性进行分析,确定了适宜的控制方案,采用稳态模拟技术确定了灵敏板,并进行稳态闭环测试,在此基础上确定了闭式热泵精馏系统的控制方案.文中运用动态模拟技术对确定的热泵精馏控制系统的动态特性进行分析.结果表明,当系统出现扰动时,本文提出的热泵精馏控制方案能够使系统快速达到新的稳态,方案可行,且具有较强的抗扰动能力.     

Relay feedback identification for processes under drift and noisy environments

Relay feedback identification methods are widely used to find the process ultimate information and tune proportional‐integral‐derivative controllers. The conventional relay feedback method has several disadvantages, which include poor estimates of the process ultimate information for low‐order processes, chattering of relay for noisy environments, and asymmetric relay responses for constant biases or slow drifts in the process outputs. Methods to mitigate each of the above disadvantages are available. However, a systematic method to treat all of them has not been studied yet. Here, simple relay feedback methods that resolve these problems by introducing band‐pass filters in the feedback loop are proposed. The high‐pass filter part in band‐pass filter removes a constant bias or low frequency drift, and the low‐pass filter part removes high frequency noise and high‐order harmonic terms in the relay feedback oscillation, resulting better estimates of the process ultimate information. Because filters used for the proposed methods are able to reject constant biases, the process steady state gains can be estimated without disturbing the relay feedback oscillations and first order plus time delay (FOPTD) models can be obtained by combining the process steady state gains with the relay oscillation information. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Use of multipoint algorithms and continuation methods in the solution of distillation problems

The use of multipoint algorithms combined with continuation methods for the solution of difficult steady-state distillation problems is illustrated. The characteristics of the different combinations of methods are presented and compared by solving a variety of distillation problems. The associated problem of multiple solutions is presented and a method for solving problems of this type is proposed and demonstrated.     

甲醇-苯共沸体系变压精馏分离工艺的动态控制

基于甲醇和苯共沸体系的压敏性,利用Aspen Plus和Aspen Dynamics软件对变压精馏分离该体系的稳态工艺进行了模拟和优化,研究了该工艺的动态特性,提出了控制产品纯度的3种控制结构：基础控制结构、比例控制结构和双比例与温度?组分联合控制结构,通过对控制结构添加±20%的组分和流量干扰测试控制结构的稳定性. 结果表明,基础控制结构基本能实现稳健控制,但不能解决组分干扰引起的产品纯度偏差过大等问题;比例控制结构可实现相对稳健的控制,但改进效果不显著;双比例与温度?组分联合控制结构在受到20%进料和组分干扰后,产品纯度能较快恢复至设定值的99.90%,实现稳健控制.     

Enzymatic catalyzed reactive dividing wall column: Experiments and model validation

A novel process for the integration of chemical reaction and product separation is proposed: the enzymatic catalyzed reactive dividing wall column (eRDWC). The eRDWC combines the highly integrated and complex reactive dividing wall column (RDWC) with the use of a very selective enzymatic catalyst. This apparatus enables the simultaneous production and separation of up to 4 pure product streams. Comprehensive experiments with the reference system of a hexanol and butyl acetate transesterification in a DN 65 pilot scale column show the feasibility of stable steady state operations for this process. A rigorous model for the plant design of an eRDWC wall column is developed. The reaction kinetics and vapor‐liquid‐equilibria for the reference system are measured and implemented in the model. The model is successfully validated using the acquired experimental data. The application of enzymes in continuous reactive distillation processes has the potential to increase the selectivity at milder process conditions. © 2016 American Institute of Chemical Engineers AIChE J, 63: 2198–2211, 2017     

Synthesis of ternary distillation process structures featuring minimum utility cost using the IDEAS approach

A synthesis method for ternary distillation process structures is proposed on the basis of the infinite‐dimensional state‐space (IDEAS) approach. The proposed synthesis procedure consists of two steps. At the first step, the utility cost is minimized. The result of the first step contains many tiny flows among the modules because the number of flows is not included in the objective function. Then, at the second step, an evolutionary procedure for process simplification is executed. In this step, the weighted sum of flow rates is minimized recursively while updating the weights at each iteration. The practical process structure is finally determined from the result of the second simplification step. The developed synthesis procedure was applied to the separation problem of a ternary mixture consisting of benzene, toluene, and o‐xylene. It demonstrated that the proposed procedure provides a process whose liquid composition profile is quite similar to that of a Petlyuk column. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1285–1294, 2018     

Feasible separation regions for distillation II: A generalized distillation limit

The boundary of the feasible separation region consists of several curves that are related to specific types of operating modes of the column. Some of these curves create a well‐known product composition multitude, whereas other curves form a generalized distillation limit. The generalized distillation limit demarcates the sloppy splits (i.e., separations in which the composition of at least one product lies inside the composition space) from regions not accessible by distillation and depends on the thermodynamic state of the feed (a mixture of vapor and liquid in equilibrium or saturated vapor/liquid) and column equipment (total/partial condenser and total/partial reboiler). The mathematical equations describing the generalized distillation limit are obtained based on the relationships between the curves (which form the generalized distillation limit) and specific types of operating modes of the column as well as the material balances for the enriching and stripping columns. Furthermore, the vapor and liquid pinch‐point curves, which go through the feed composition point, are not dependent on the thermodynamic state of the feed and column equipment. In addition, an algorithm for determining the generalized distillation limit is obtained. © 2017 American Institute of Chemical Engineers AIChE J, 2017     

Modeling and analysis of conventional and heat‐integrated distillation columns

A generic model that can cover diabatic and adiabatic distillation column configurations is presented, with the aim of providing a consistent basis for comparison of alternative distillation column technologies. Both a static and a dynamic formulation of the model, together with a model catalogue consisting of the conventional, the heat‐integrated and the mechanical vapor recompression distillation columns are presented. The solution procedure of the model is outlined and illustrated in three case studies. One case study being a benchmark study demonstrating the size of the model and the static properties of two different heat‐integrated distillation column (HIDiC) schemes and the mechanical vapor recompression column. The second case study exemplifies the difference between a HIDiC and a conventional distillation column in the composition profiles within a multicomponent separation, whereas the last case study demonstrates the difference in available dynamic models for the HIDiC and the proposed model. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4251–4263, 2015