Constant Molar Overflow Research Articles

Relaxing the constant molar overflow assumption in distillation optimization

AbstractThe constant molar overflow (CMO) framework, while useful for shortcut distillation models, assumes that all components have the same latent heats of vaporization. A simple transformation, from molar flows to latent‐heat flows, allows shortcut models to retain the mathematical simplicity of the CMO framework while accounting for different latent heats, resulting in the constant heat transport (CHT) framework for adiabatic distillation columns. Although several past works have already proposed this transformation in the literature, it has not been well utilized in recent times. In this article, we show the utility of this transformation in upgrading various applications such as identifying energy‐efficient multicomponent distillation configurations based on heat duty rather than surrogate vapor flow. The method transforms the diagram to a diagram. Furthermore, we derive new and insightful analytical results in distillation, such as cumulative latent‐heat stage fractions having monotonic profiles within a distillation column under the CHT framework.

Shortcut Distillation Model for Heat Integration

Distillation is a common process unit that requires substantial energy input. The energy input can be reduced by applying heat integration methods to the distillation system. A shortcut distillation model that does not require rigorous stage-by-stage calculation is proposed here to reduce computational difficulty. As traditional shortcut models utilizing the constant molar overflow (CMO) assumption are not sufficiently accurate for the study, the shortcut model used in this study utilizes a non-CMO assumption. A relation is derived from approximate material and energy balances to predict the change in liquid and vapour flows throughout the column. Coupled with material and energy balances over sub-sections and the entire column, the model can fully specify a distillation column. The model can be used for energy targeting in conjunction with heat integration models to simultaneously optimize the process. A case study was carried out on an air separation unit (ASU). Results of the case study showed that the energy required is 197 Wh per kg of pure O2 produced. The results obtained are encouraging with close agreement when compared to an ASPEN simulation as the differences are below 2 %. However, the heat integration results of the MHEX from both the model and the ASPEN simulation showed a minimum temperature approach (DTmin) of almost 0. This is probably due to the usage of the ideal method where enthalpy calculation depends only on temperature.

Simulation and performance improvement of cryogenic distillation column, using enhanced predictive Peng–Robinson equation of state

In this study, a cryogenic distillation column has been designed and simulated via a computer code based on the theta method of convergence. The required thermodynamic properties are determined from the enhanced predictive Peng-Robinson (E-PPR 78) equation of state which has a good accuracy in predicting the corresponding thermodynamic properties of natural gas components. The combined code of distillation column/equation of state has been verified with that of another study. In the present study, the results are achieved by the constant molar over-flow and inclusion of energy equations assumptions. In order to have more accuracy in the results, the energy equations were considered in the column calculations. For improvement of column operational conditions, a parametric study is carried out. The results show that by the proper selection of reflux ratio, column operating pressure, feed plate location and considering energy constraints, the molar concentration of methane is decreased from 66.14% in the initial state to 13.75% in the improved state.

Continuous Cyclic Distillation for Binary Solvent Exchange: The Batch Stack

As the pharmaceutical industry adopts continuous processes, batch distillation for solvent exchange will need to be replaced with a continuous distillation process. Cyclic distillation is adapted to solvent exchange, and a simplified calculation method that does not assume constant molar overflow is developed for binary systems. A three-stage cyclic distillation for exchange of methanol with water designed for a bottoms product that is 90% water produces a 99.3% methanol distillate, uses 25.4% less solvent than constant volume batch distillation, and is roughly equivalent to a five-stage continuous distillation. When water is the feed solvent and is exchanged with methanol, a three-stage cyclic distillation uses 54.4% and 40.0% less solvent than constant volume batch distillation and a three-stage continuous distillation, respectively.

Short-Cut Methods versus Rigorous Methods for Performance-Evaluation of Distillation Configurations

This study demonstrates the efficacy of a short-cut method such as the Global Minimization Algorithm (GMA),(1,2) that uses assumptions of ideal mixtures, constant molar overflow (CMO) and pinched columns, in pruning the search-space of distillation column configurations for zeotropic multicomponent separation, to provide a small subset of attractive configurations with low minimum heat duties. The short-cut method, due to its simplifying assumptions, is computationally efficient, yet reliable in identifying the small subset of useful configurations for further detailed process evaluation. This two-tier approach allows expedient search of the configuration space containing hundreds to thousands of candidate configurations for a given application.

Shortcut-based optimization of distillation-based processes by a novel reformulation of the feed angle method

The conceptual design of distillation-based separation processes is a well known and thoroughly investigated research subject in chemical engineering science. Nevertheless, there are only few shortcut methods available that are derived without simplifying assumptions, such as constant relative volatilities or constant molar overflow, allowing for a thermodynamically sound evaluation of the minimum energy demand for the separation of non-ideal mixtures. The current article presents a novel reformulation of the previously introduced feed angle method, which represents a geometrical shortcut method that is based on a direct calculation of characteristic pinch points. The reformulation retains the beneficial properties of the original formulation, providing high accuracy and an equation-based formulation that can be embedded in an optimization problem, while being numerically simpler and requiring significantly less case-specific modifications. The benefit of the so-called FAM+ formulation and the applicability to complex design problems are illustrated on several case studies, including the optimization of a closed-loop flowsheet and a superstructure with two reactors and several distillation columns.

Stage-to-stage calculations of distillation columns by fixed-point iteration and application of the Banach fixed-point theorem

This work presents a novel approach for stage-to-stage calculations of distillation columns based on the MESH equations. No simplifying assumptions such as constant molar overflow are used. The transition from one stage to the next is formulated as a fixed-point problem, which can be solved by fixed-point iteration. Applying the Banach fixed-point theorem, bounds on the minimum energy requirement are derived. Within these bounds a solution to the fixed-point problem is proven to exist and convergence of the fixed-point iteration is guaranteed. Additionally, energy bounds are derived below which it can be guaranteed that no fixed-point exists. The stage-to-stage calculations are combined with an outer optimization loop in order to conduct process simulation and optimization. The approach is illustrated by examples.

Note on flash and distillation systems

Flash and distillation systems evolving on the equilibrium manifold possess stable steady states when the molar flows and the boundary conditions are fixed and a vapor and liquid phase is present at all times. The results extend the range of validity of a local stability theorem for linear, constant molar overflow systems due to Acrivos and Amundson. The approach to stability analysis is motivated by the tangent plane method developed by Gibbs to open systems as it takes advantage of the negative curvature of the entropy surface to construct a Lyapunov function. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3322–3332, 2013

An Efficient Method of Constructing Pinch Point Curves and Locating Azeotropes in Nonideal Distillation Systems

An efficient, robust, ODE-based formulation of the continuation problem is presented for the automatic construction of all branches of the pinch point curves in any homogeneous distillation system (even highly nonideal ones) that can be represented using an activity coefficient model, with any number of components and for any adiabatic, nonreactive column configuration. Constant molar overflow is assumed. The curve is parametrized by reflux ratio, making it particularly applicable to distillation design and synthesis. Naturally, it can be used to find pinch point locations at a given finite reflux, as this is simply a subset of the pinch point curve. The method can also automatically locate all N-component azeotropes very efficiently (orders of magnitude faster than commercial process simulators). It has the additional advantage of being solvable using tools already available in typical mathematical software packages. A computer implementation of the proposed method is available.

Optimization of Heterogeneous Batch Extractive Distillation

Heterogeneous extractive batch distillation of the chloroform−methanol minimum-boiling-temperature azeotropic mixture is studied with water as a heterogeneous entrainer. The continuous feeding of water allows recovery of 99 mol % chloroform after condensation of the saddle binary heteroazeotrope water−chloroform. Unlike a homogeneous process, the reflux composition is different from the heteroazeotrope water−chloroform in the vapor overhead. Besides, the distillate recovery is improved by refluxing a portion α of the chloroform-rich distillate phase along with the water-rich entrainer phase. A genetic algorithm is coupled to a constant molar overflow model to study seven operation policies. Optimization parameters are the entrainer flow rate FE/V, the portion αT3 of the distillate-rich phase refluxed to the column during chloroform distillation, and the reflux policy RT5 during methanol distillation. The optimization maximizes a profit function, penalized with recovery yield constraints, whereas purity targets are used as task ending events. All optimized solutions achieve higher than 90 mol % recovery yields and 99 mol % purity for both products chloroform and methanol. The results are confirmed by rigorous simulation showing the good performance of coupling a simplified model and a genetic algorithm as a first approach. The two-piece-wise parameter value operation policies for all three parameters increase profit by 41.8% and reduce total time by 43.8% compared to the single value parameter policy. The parameter influence study ranks RT5 first, αT3 second, and FE/V last. Keeping FE/V constant and using the two-piece-wise αT3 and RT5 value operation is recommended to increase profit.

A RIGOROUS ANALYSIS OF McCABE-THIELE ASSUMPTIONS AND THEIR CONSEQUENCES: CRITICAL ROLE OF PARALLEL ENTHALPY LINES

ABSTRACT The assumptions and results associated with the McCabe-Thiele method of distillation column analysis are brought together within a rigorous analytical framework. Within this framework, the assumption that the saturated liquid and vapor enthalpy curves are parallel lines, apart from adiabatic and isobaric operation of the distillation column, is shown to be sufficient to derive all the major results of the McCabe-Thiele method including the constant molar overflow condition. Then, using a rigorous thermodynamic analysis, a comprehensive set of conditions sufficient for the enthalpy curves to be parallel lines are obtained. Some common systems for which these assumptions hold are discussed. Finally, the conditions under which McCabe-Thiele-like methods occur in other separation processes are outlined, with pointers to a unified picture of separation processes.

‘Costing’ distillation systems from residue curve based designs

At present, when carrying out initial scoping of a project, one of the best ways to do preliminary designs for complicated separation systems is to use residue curve maps. However, in order to compare the different possibilities one needs to do some preliminary costing. As one does not require very accurate costing at this stage, only wishing to eliminate expensive alternatives, one would like to be able to do this directly from the sketches on the residue curve maps. This paper presents methods by which this can be done. In this paper we have limited ourselves to systems with constant relative volatilities, constant molar overflow and the differential equation description of the distillation column. It is shown that, for the rectifying section, by using binary approximations based on the least volatile component, one can obtain reasonable estimates (within a factor of two) for the number of stages. This is done by noting that the changes in the least volatile component are the simplest in nature and using the sum of two binary approximations as the final approximation.

Simulation of a Multicomponent Batch Distillation Column with Total Reflux through the Distillate Receiver

A shortcut procedure applicable to a multicomponent distillation in a batch column with a distillate receiver under total reflux condition was developed. It is based on the assumptions of constant molar overflow, constant vapor boilup rate, and constant relative volatilities. The effect of liquid holdup in each stage and condenser is taken into consideration in modeling the dynamic behavior of the batch column. Estimates of the volume of the distillate receiver, changes in compositions in the receiver and still, concentration profiles of the column, and total distillation time required to complete the separation can be made in the proposed model. Illustrative calculations were performed for the separation of a quaternary system for two cases: an initially empty distillate receiver and an initially filled-up distillate receiver.

Multicomponent Distillation Design through Equilibrium Theory

A new tool for the design of multicomponent distillation columns is presented, which is based on analytical solutions of a suitable mathematical model. The assumptions on which it is built are (i) a large number of stages, which makes it possible to apply a continuous description of the column instead of the usual stage-by-stage equations; (ii) constant molar overflow; (iii) constant relative volatility; and (iv) attainment of vapor−liquid equilibrium everywhere along the column. The resulting model equations are solved in the frame of Equilibrium Theory, which was originally developed to describe chromatographic processes. Through this approach explicit results may be obtained and both the steady state and the dynamic behavior of high-purity columns can be analyzed. In particular, this work focuses on the former, thus obtaining the following results: (i) a complete picture of the different separation regions in the operating parameter plane spanned by the flow-rate ratios in the rectifying and stripping...

Evolutionary thermodynamic synthesis of zeotropic distillation sequences

Abstract The objective of this paper is to present a new evolutionary strategy for the synthesis of simple and complex distillation sequences. The initial flowsheet is the reversible multicomponent distillation scheme, which includes as the thermodynamically optimum superstructure many of the possible separation configurations. Assumptions with respect to ideal boiling behaviour or constant molar overflow are not required, but azeotropic systems are excluded. The computation time requirement is extremely low, because only flash-type calculations and no rigorous column simulations are involved. In this approach columns and heat exchangers are successively removed from the initial flowsheet by using thermodynamic information on splits. In this way not only simple sequences, but also sidestream withdrawals, sidestream strippers and sidestream enrichers can be created. The evolutionary strategy and the underlying modification criteria will be illustrated by several examples. Some comments on common heuristic rules and heat-integration possibilities are made in conclusion.

The constant heat transport model and design of distillation columns with one single distributing component

The model approximation of constant molar overflow (CMO) is relaxed to constant heat transport (CHT) along distillation column sections assuming ideal mixtures with constant relative volatilities and constant molar latent heats. A formal analogy can be perfectly derived between CMO and CHT models in the sense that all the formulas and numerical and graphical procedures adequate for use with the CMO model remain valid under the CHT model after simple transformation of the variables. A model of only one distributing component or nondistributing key components is developed. Analytical formulas are derived to calculate the limiting flow rates of such columns. The limiting flow rates of Petlyuk systems are also determined in this way

Analysis and algorithms for multistage separation processes

Multistage equilibrium separation processes involving binary homogeneous mixtures are analyzed. For several sets of specifications, it is shown that these process models admit a unique steady-state solution without the need for a constant molar overflow assumption or other energy balance or phase equilibria simplifications. The steady-state model equations are analyzed directly. Consequently, the analysis is constructive and gives insight into the behavior and development of algorithms for solving multistage separation process model equations in both the binary and multicomponent cases. To illustrate this, a new generalized Broyden acceleration technique is developed and used in the context of a sum-rates algorithm to solve several example problems. Numerical results show that the proposed acceleration method is comparable to Newton acceleration and clearly outperforms traditional Broyden acceleration. Other properties predicted by the analysis are also illustrated. 21 refs., 4 figs.

Minimum reflux behavior of complex distillation columns

AbstractA continuum model for multicomponent distillation in the minimum reflux limit, first proposed by Nandakumar and Andres, is refined for the special case of constant relative volatility (CRV) and constant molar overflow (CMO) and is extended to columns with multiple feeds and multiple products. A relaxation algorithm for calculating steady‐state conditins in any minimum reflux CRV, CMO column is established. This generalization of Underwood's classic treatment of single‐feed columns is used to explore the characteristics of several single‐feed and multiple‐feed distillation systems. Critical operating points at which the steady‐state composition profile in a minimum reflux column is indeterminate are identified and analytical expressions predicting the location of these points are established.

Independent Single-input-single Output Control Schemes for Dual Composition Control of Binary Distillation Columns

The steady-state interaction measure of dual composition control schemes for binary distillation columns is examined under the assumptions of constant relative volatility and constant molar overflow. An exhaustive enumeration is made of the control schemes that use column flows or their ratios as manipulated variables and product compositions as the controlled variables. Using a redundancy criterion, it is shown that 34 classes of dual composition control schemes have independent values for the interaction measure. This number reduces to 17 when the feed is a saturated liquid or gas. For high purity columns, the interaction measure of the above 34 control schemes approaches the values for the (L, V), (D, V), and (L3) control schemes. In this case none of the control schemes has a desirable interaction measure.

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.