Constant Relative Volatilities Research Articles

Analytical expression and its application of Rayleigh fractionation for ternary mixtures

The Rayleigh equation is an important fundamental equation in distillation, isotope separation, hydrology and many other fields. However, it is only applicable to binary systems. In this work, analytical expressions are derived describing the composition of the residual liquid in Rayleigh fractionation for ternary systems with constant relative volatilities. The expressions are in the form of parameter equations, and the range of the parameter is analyzed from a mathematical perspective. Two methods for calculating the compositions of the residual liquid and the distillate are presented. The analytical equations are verified by calculating the liquid compositions for multi-stage flash cascades. The compositions of the streams involved in Rayleigh fractionation are investigated with the analytical equations and the results are compared with those in an equilibrium flash process. It indicates that Rayleigh fractionation achieves a better degree of separation than equilibrium flash. The physical significance of the parameter in the equations is interpreted based on the residue curve. Finally, an example is given to show that the analytical expressions produce results with better precision compared to applying numerical methods directly on the system of differential equations. The analytical equations for ternary mixtures are expected to cast some new light on other fields involving Rayleigh fractionation and to promote the development of many disciplines.

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.

A generalized approach for the conceptual design of distillation columns with complex configurations

A generalized approach for the conceptual design of complex distillation columns including multiple-feed/side stream columns and columns with side sections is presented. The new design approach assumes constant relative volatility mixtures and constant molar flow rates within each column section. Furthermore, it is based on the identification of all possible constant composition zones in a column including those around the feed sections and those around the side stream sections. Each set of constant composition zones is characterized by the relevant mass transfer sections along with the respective Eigenfunctions and split. Accordingly, new design algorithms are proposed for rapid and accurate calculation of all relevant design parameters at pinch conditions for all studied complex column configurations separating ideal behaving multicomponent mixtures. For mixtures with up to four components, separation geometries of complex distillation columns are established; allowing thereby the analysis of the geometric properties of such complex columns. Finally, it is shown that the developed algorithms can be successfully applied to providing good estimates of design parameters for complex distillation columns separating highly non-ideal azeotropic mixtures, after approximating the latter by appropriate constant relative volatility pseudo-ideal mixtures.

Control of Quaternary Reactive Distillation Columns: Effects of Number and Location of Temperature Loops

The most frequently studied ideal system for reactive distillation columns is the quaternary system with two reactants and two products. The vast majority of reactive distillation literature on control uses two-point inferential control structures with conventional tray selection techniques such as singular value decomposition (SVD) and relative gain array (RGA) analysis. Another common practice for the ideal systems is the assumption of constant relative volatilities. This paper compares two control structures with different number of temperature loops and two alternative sets of tray locations, in terms of the controllability of systems with temperature-dependent relative volatilities. It is observed that a three-point inferential control structure with a new set of tray locations based on a semisystematic method improves the control performance for all three systems studied. This improvement is particularly significant in the purity of the distillate stream as the temperature dependency increases.

A simple, reliable and fast algorithm for the simulation of multicomponent distillation columns

This work has developed a simple, reliable and fast algorithm for the simulation of multicomponent distillation columns, where any equilibrium stage can accept a feed-stream and/or a vapor-side-stream and/or liquid-side-stream. The new scheme considers internal molar overflows and constant relative volatilities to avoid the need of heat balances and vapor–liquid equilibrium calculations. The solution scheme is founded on a Newton-based formulation in block algebra, which relies in a simple, reliable and fast algorithm. Although the proposed calculation scheme can be classified as an approximate method, it is very useful when accurate phase equilibrium and enthalpy data are lacking. Numerical experimentations show good agreement with the results obtained with well-known rigorous simulation approaches.

Pinch Point Calculations and Its Implications on Robust Distillation Design

Rising energy costs and growing environmental awareness motivate a critical revision of the design of distillation units. Systematic design techniques, such as the rectification body, column profile map, and temperature collocation methods, require exact knowledge of all pinch points in a particular system, because these stationary points delineate the possible composition trajectories realizable in separation columns. This paper demonstrates novel methods for rigorously determining all pinch points for the constant relative volatility, ideal and non-ideal systems. Constant relative volatility and ideal solution systems are transformed into one-dimensional polynomial and nonlinear functions, regardless of the number of the components. A deflation method is proposed to locate all zeros in ideal and non-ideal zeotropic problems. For more challenging non-ideal problems, a novel hybrid sequential niche algorithm is used to solve hard azeotropic problems successfully. Finally, the design implications of these pinch point locations are investigated to show how new separation configurations can be devised. Methodically the paper points out the use of rigorous pinch point computations in conjunction with continuous composition profiles for robust distillation design.

Short-cut methods for the optimal design of simple and complex distillation columns

New short-cut methods providing optimal design parameters for distillation columns with simple and complex configurations including two-feed and one-feed-one-side-stream columns are presented. The methods assume constant relative volatilities and constant molar flow rates within each distillation section. The design equations are based on the Underwood equations for the calculation of minimum reflux (reboil) ratio, the analytical formulations of the distillation line, the Eigenfunction and the number of theoretical stages for each mass transfer section of the column. Furthermore, the geometrical properties of a given separation are considered. Optimization algorithms based on the minimization of the total number of theoretical stages of the column with taking into account the mass balance at each feed section have been elaborated. In comparison to the boundary value method the new short-cut methods require a minimum number of specifications; they do not need any graphical support, and provide a lower total number of theoretical stages particularly for complex configurations. The new short-cut methods have been extended to the design of columns separating azeotropic mixtures by approximating the latter by appropriate pseudo-ideal mixtures. Several separation examples for azeotropic mixtures, including different types of splits as well as columns with simple and complex configurations were tested and show a very good agreement with the simulation results obtained with Radfrac (Aspenplus).

A Shortcut Method for Binary Distillation Column Design

AbstractBased on Smoker (1938) analytical solution for binary distillation with constant relative volatility, Jafarey et al. (1979) derived a simple approximate design equation for the number of theoretical stages. This equation is modified to improve its predictions. This modified equation is particularly useful in computer process control applications because it gives an expression for the separation factor which is independent of the output parameters.

Extension of a Method for the Design of Divided Wall Columns

AbstractFor most separations, a fully thermally coupled distillation column or divided wall columns are thermodynamically more efficient than conventional columns. This paper develops a method for the design of divided wall columns consisting of multi‐component mixtures (more than three components) with constant relative volatilities and a relatively sharp separation between the key components.

Overall plate efficiency of a binary distillation column: new approach

New formulae for the determination of both tray and overall plate efficiencies of a binary distillation column are presented. They only require the liquid and vapour phases concentrations of the more volatile component on each tray and assumption of constant relative volatility for their use. The new formulae gave very close predictions of the tray efficiency compared to those predicted using the traditional Murphree formula. The overall plate efficiency is obtained analytically without the usual Henry's law and Straight equilibrium curve assumptions. Keywords : binary, efficiency, distillation, partial, plate Journal of Applied Science, Engineering and Technology Vol. 5(1&2) 2005: 49-55

On the multiple solutions of the flash equations

Input multiplicity is an important feature of industrial processes. In this paper, we extend the work by Tiscareño et al. [1998. Multiplicity of the solutions of the flash equations. Chemical Engineering Science 53, 671–677] to analyze multiple solutions of the flash equations when a product mole fraction of one component is specified and the vapor fraction or the temperature is calculated. For this type of multiplicity to arise, at least one stationary point for the mole fractions with respect to vapor fraction or temperature must exist. By using a constant relative volatility model, we demonstrate the uniqueness of the stationary point, and show the necessary and sufficient conditions for the existence of such a stationary point. From these results one can state that systems with a constant relative volatility assumption can only present second-order input-multiplicities.

Integrating product and process design with optimal control: A case study of solvent recycling

This paper proposes the simultaneous integration of environmentally benign solvent selection (product design), solvent recycling (process design) and optimal control for the separation of azeotropic systems using batch distillation. The previous work performed by Kim et al. (2004. Entrainer selection and solvent recycling in complex batch distillation. Chemical Engineering Communications 191(12), 1606–1633) combines the chemical synthesis and process synthesis under uncertainty. For batch distillation, optimal operation is also important due to the unsteady state nature of the process and high operating costs. Optimal control allows us to optimize the column operating policy by selecting a trajectory for the reflux ratio. However, there are time-dependent uncertainties in thermodynamic models of batch distillation due to the assumption of constant relative volatility. In this paper, the uncertainties in relative volatility were modeled using Ito processes and the stochastic optimal control problem was solved by combined maximum principle and non-linear programming (NLP) techniques. Then the previous work of optimal solvent selection and recycling was coupled with optimal control. As a real world example for this integrated approach, a waste stream containing acetonitrile–water was studied. The optimal design parameters obtained by Kim et al. (2004. Entrainer selection and solvent recycling in complex batch distillation. Chemical Engineering Communications 191(12), 1606–1633), for this separation were used and the optimal control policy is computed first without considering uncertainties by variable transformation technique. The deterministic optimal control policy improves the product yield by 4.0% as compared to the base case, verified using a rigorous simulator for batch distillation. When the stochastic optimal control policy was computed representing the relative volatility as an Ito process, a similar recovery rate was obtained from simulations, but the batch time was reduced significantly, producing the most profitable operation.

Optimal design of azeotropic batch distillation

AbstractThis study explores integrating models with different degrees of detail for optimizing azeotropic batch distillation systems. A detailed dynamic model is used from outside the optimization program both to verify feasibility of the design and to update the parameters needed by the optimization model. The updated parameters are the constant relative volatilities between pseudo‐components, used in a binary Fenske–Underwood–Gilliland‐type model. The approach was used to optimize the design of a batch process for the recovery of spent isopropyl alcohol, which works cyclically to separate the excess water, satisfying an environmentally acceptable specification, and using cyclohexane as entrainer, which in turn is recovered in the same process and recycled. The approach permitted optimizing the batch sizes, number of separation stages, the reflux ratios of a piecewise constant multilevel reflux policy, the extent of each separation, and the size of the intermediate cuts to be recycled, with affordable computation and problem setup times. © 2005 American Institute of Chemical Engineers AIChE J, 2006

SIMPLIFIED OPTIMAL DESIGN OF A BINARY DISTILLATION COLUMN-1 (THEORETICAL NUMBER OF PLATES)

Two novel methods of designing distillation column for binary mixtures are presented with the assumption of a constant relative volatility. The analytical method presents a simple expression from which the actual number of theoretical plates can be calculated. These methods that incorporate the murphree efficiency eliminate the assumption of linearity of the operating curve equations, thus providing us the actual number of theoretical plates as against the ideal number of theoretical plates obtained from some traditional methods. JMDMES Vol.2(1) 2003: 89-97

Effect of Relative Volatility on the Quantitative Comparison of Reactive Distillation and Conventional Multi-unit Systems

A previous paper presented a quantitative economic comparison of reactive distillation with a conventional multi-unit system for a wide range of chemical equilibrium constants. Assuming constant relative volatilities (α = 2), reactive distillation was shown to be less expensive than the conventional process. This paper extends this work to explore how the relative volatilities affect the design of these flowsheets in two ways: (1) relative volatilities between adjacent products and reactants are reduced, and (2) relative volatilities are temperature dependent. A fundamental difference between the two flowsheets is the ability in the conventional process to adjust the reactor temperature and distillation column temperatures completely independently, which is not possible in the reactive distillation process. Results show that when relative volatilities are temperature dependent and decrease significantly as temperatures approach those required for reasonable reaction rates, the reactive distillation colum...

Minimum Energy Consumption in Multicomponent Distillation. 3. More Than Three Products and Generalized Petlyuk Arrangements

We consider separation of ideal multicomponent mixtures with constant relative volatilities and constant molar flows and at constant pressure. The exact analytical solution of minimum energy in a generalized Petlyuk arrangement for separation of N-component feed into M products has been derived. Interestingly, the minimum-energy solution in a complex integrated Petlyuk arrangement is equal to the most difficult split between any pair of the products, as if each single split was to be carried out in an ordinary two-product column. This extends the results for the three-product Petlyuk arrangement from part 2 of the series to a generalized arrangement with any number of products and feed components. The solution is very simple to visualize in the Vmin diagram (part 1 of the series), simply as the highest peak. In addition, we obtain detailed flow rates and component distribution inside the arrangement. We also conjecture that the minimum energy requirement for the generalized extended Petlyuk arrangement is...

Minimum Energy Consumption in Multicomponent Distillation. 1. Vmin Diagram for a Two-Product Column

The Vmin diagram is introduced to effectively visualize how the minimum energy consumption is related to the feed-component distribution for all possible operating points in a two-product distillation column with a multicomponent feed. The classical Underwood equations are used to derive analytical expressions for the ideal case with constant relative volatility and constant molar flows. However, the diagram can also be used for nonideal mixtures. The Vmin diagram is very insightful for assessing multicomponent separation in a single column and is even more powerful for complex column arrangements, such as Petlyuk columns (parts 2 and 3 of this series of papers).

Minimum Energy Consumption in Multicomponent Distillation. 2. Three-Product Petlyuk Arrangements

We show that the minimum energy requirement for separation of a multicomponent mixture in a three-product Petlyuk arrangement is equal to the minimum energy for the most difficult of the two separations (top/middle or middle/bottom product) in a conventional single column. In the Vmin diagram (part 1 of this series), this is simply the highest peak. These results are based on an analytical solution for columns with an infinite number of stages, assuming constant relative volatilities and constant molar flows. The previous analytical results for the Petlyuk column are extended to include nonsharp separations, multicomponent feeds, and any feed quality.

On the Relation between Ideal and Real Mixtures in Multicomponent Distillation

A complete mathematical solution exists for the distillation of ideal multicomponent mixtures, i.e., mixtures with constant relative volatilities, allowing to answer all questions arising in the distillation of such mixtures by relatively simple algebraic equations. As shown in this paper, the distillation of a real mixture of any complexity may – at least qualitatively – be reduced to the distillation of an ideal mixture. The understanding of the distillation behavior of complex real mixtures is thus greatly simplified and useful both in the design as well as the operation of multicomponent distillation columns.

Multicomponent thermally coupled systems of distillation columns at minimum reflux

AbstractA method for calculating the minimum vapor flow in a ternary fully thermally coupled system of distillation columns was developed earlier by Fidkowski and Krolikowski. This method was developed further for fully thermally coupled systems separating four or more components. For multicomponent mixtures having constant relative volatilities and equal latent heats, the method leads to the identification of all of the minimum vapor flow rates in each distillation column that provide the same overall minimum heat duty in the reboiler. The quaternary fully coupled system of columns requires less heat energy than conventional configurations. These savings are often on the order of 20–50%.