Pinch-point Curves Research Articles

Conceptual analysis of single-feed heterogeneous distillation columns

<p class="Abstractandkeywordscontent">Separation in heterogeneous distillation columns is attained by interaction of two liquid and one vapor phases, interaction of three phases involves complexities due to the determination of vapor-liquid-liquid equilibrium and hence, in the design of separation units. Nevertheless, the liquid-liquid equilibrium allows developing separations that may be unfeasible by vapor-liquid equilibrium. In this way, heterogeneous azeotropic distillation is a useful operation for the separation of azeotropic and close-boiling mixtures. In this work, a new methodology for evaluating the feasibility of this process is developed. This methodology is an extension of that proposed by Castillo <em>et al</em>. (1998) for homogeneous systems. Operation leaves for heterogeneous systems are calculated using the concept of pinch point curves in order to establish the process feasibility. Heterogeneous columns with external decanter are considered as the only heterogeneous stage (OHED: only heterogeneous external decanter). The initialization process for the column calculation requires the selection of the distillate composition using thermodynamic criteria in order to guarantee homogeneous phases within the column. A system with industrial and academic relevance was considered as case study: water-acetic acid-amyl acetate. Results show that the developed shortcut method allows evaluating process feasibility and estimating design parameters, without the use of trial and error procedures implemented, with the aid of simulation tools.</p><div> </div>

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.

Energy Requirements of Distillation: Exergy, Pinch Points, and the Reversible Column

This paper considers the problem of finding minimum energy requirements of a single-feed adiabatic distillation column for a given separation task. Over the years, many attempts to understand this problem have been made. This paper presents an approach which is at the intersection of the thermodynamic and geometric points of view. In it, an analysis of multicomponent distillation is carried out via the notion of power of separation, which is akin to compositional exergy. It is shown mathematically that this concept, although taking its roots in thermodynamics, has a strong link with the geometry of liquid composition trajectories in multicomponent distillation and is also related to the traditional McCabe−Thiele diagram for binary distillation. By considering pinch-point curves for adiabatic column sections and their link with reversible column profiles, a characterization of minimal energy requirements of the single-feed adiabatic distillation process is proposed. As a consequence, a shortcut method to determine minimal energy requirements of multicomponent distillation is introduced. Examples validating this approach for multicomponent distillation of ideal, nonideal, zeotropic, and azeotropic mixtures with up to six components are presented. These examples indicate that the new method can, in principle, treat any number of mixture components. All types of pinch behavior are covered, that is, the method can find minimal energy designs associated to feed, saddle, or tangent pinch points. Case studies where pinched minimum energy solutions exist, where pinched solutions can be reduced to nonpinched solutions, and where no pinched solutions exist are presented. In all these cases, the new method can find, if they exist, pinched and nonpinched solutions.

Difference points in reactive and extractive cascades, V: Determining reaction distribution from separatrix manifolds

The effect of reaction distribution policy on a reactive column profiles is analyzed. We find that the extent reaction on a single reactive stage can greatly influence the feasibility and termination of subsequent non-reactive stages. We develop a method to quantitatively predict when perturbing the amount of reaction on a single stage will subsequently force the column profile to become infeasible or otherwise fail to meet global design targets. To predict such behavior we rely on the map of stable invariant manifolds over the saddle branch of an isoreflux pinch point curve. We show how this method can be used to select reactive stages and distribute reaction over a column section profile to meet certain design criteria. We also show how this method can be used to find limits on overall extent reaction within a column or extent reaction on a single stage.

Non-pinched, minimum energy distillation designs

Non-pinched, minimum energy solutions are important class of distillation designs that offer the potential advantage of a better trade-off between capital investment and operating costs. In this paper, two important tasks associated with non-pinched distillation designs are studied. Thus the novel contributions of this work to the literature are (1) A comprehensive methodology for finding non-pinched minimum energy designs. (2) Understanding of the reasons for the existence of non-pinched distillation designs. It is shown that the recent shortest stripping line distance approach of Lucia et al. [Lucia, A., Amale, A. and Taylor, R., 2007, Distillation pinch points and more. Comput Chem Eng, available on-line] is capable of systematically and reliably finding non-pinched, minimum energy distillation designs. In addition, we provide an understanding of the reasons behind the existence of non-pinched designs, which include trajectories that follow unstable branches of a pinch point curve in azeotropic systems, the inherent looping structure of trajectories in hydrocarbon separations, and the presence of ancillary constraints in multi-unit processes like extraction/distillation. Several distillation examples are studied and many numerical results and geometric illustrations are presented that show the shortest stripping line distance methodology is indeed a powerful and systematic tool for computing non-pinched, minimum energy designs and that support the underlying reason we provide for the existence of non-pinched designs.

Can the Operating Leaves of a Distillation Column Really Be Expanded?

Residue curves and pinch point curves are used to determine the operation leaves and hence the feasible region for distillation columns operating at a specific distillate and bottoms composition for all possible constant reflux and reboil ratios. In this paper we will experimentally show that we can expand the operating leaves of the rectifying section beyond the pinch point curve by varying the reflux ratio within the distillation column, and we will also show theoretically that this method can be used to cross the simple distillation boundaries.

Sectional and overall reachability for systems with S-shaped distillation lines

Total and minimum reflux bounds serve as limiting case scenarios for determining feasibility in azeotropic distillation columns. Specifically, all reachable feed compositions in a staged rectifying or stripping section have been reported as the union of points enclosed by the distillation and pinch-point curves through a desired product. By eigenvalue considerations of pinch bifurcations and geometric analysis of fundamental region structures, the region of all reachable compositions has seemingly been identified. Additional insights are needed to fully characterize the feasible compositions in a subset of azeotropic mixtures. This article describes how sectional profiles can actually cross pinch-point curves and generate a region of additional feasibility outside the one previously reported. It also demonstrates how a substantially larger region between the distillation line and pinch-point curve after the intersection is only accessible by composition profiles going through the extended region. This extended reachable region is explained by evaluating the conditions for a fixed point in composition space. The effect on sectional profiles is illustrated for both an artificially parametric VLE manifold and a nonideal azeotropic system with more than one simple distillation region. Sectional profiles extended beyond the traditional bounds affect coupled sections in a distillation cascade.

Influence of multicomponent mass transfer on homogeneous azeotropic distillation

Residue-curve and distillation-line maps are useful tools for the design of azeotropic distillation sequences. The calculation of residue curves uses the assumption that the vapour and liquid are always in equilibrium. The computation of distillation lines assumes that the vapour and liquid leaving a tray are in equilibrium. In this work, the equations defining residue curves and distillation lines are extended to take into account mass transfer effects that occur in real distillation columns. A general relationship between the composition of the vapour and liquid leaving a tray at total reflux is developed and used to calculate the maps. The curvature of the residue curves and distillation lines changes, significantly affecting the shape of the maps. The consideration of mass transfer in azeotropic distillation columns produces quantitative changes in the behaviour of the liquid composition path for distillation columns at total reflux, and in some cases, a qualitative change in the products formed can also be observed. No change has been found in the bounds on the product composition at minimum reflux when mass transfer effects are taken into account. The pinch-point curves or distillation limits remain the same. Entrainers should be selected considering not only how much they modify the vapour–liquid equilibrium, but also how much they affect the multicomponent mass transfer that takes place in real distillation columns.

Homogeneous Azeotropic Distillation. 2. Design Procedure for Sequences of Columns

A graphical procedure based on residue-curve maps and distillation-line maps is developed for the synthesis of sequences of distillation columns for homogeneous azeotropic distillation. The feasibility of separation is determined by the overlap of product operation leaves defined as the feasible region containing all column profiles that lead to a desired product specification, which need not be a precise composition. Column sections may be constrained to operate within a subregion of the composition space, in which case the limit of operation is defined as a section boundary. Section boundaries for node-type and saddle-type products are established, and it is shown that they do not always coincide with simple-distillation or distillation-line boundaries. When the distillation line (or residue curve) and pinch-point curve from a desired product terminate at different nodes in the composition space, then distillation sequences using complex column arrangements can be proposed.

Homogeneous Azeotropic Distillation. 1. Design Procedure for Single-Feed Columns at Nontotal Reflux

Residue-curve and distillation-line maps are useful tools in the design of azeotropic distillation sequences. In this work we make use of residue-curve and distillation-line maps to develop a procedure for the design of single-feed columns at finite reflux. The procedure is noniterative with respect to the reflux and boil-up ratios, instead using an ‘operation leaf' formed by the total and minimum reflux conditions. The operation leaf bounds the possible liquid composition profiles in a column section and is calculated from the product composition. The overlap of operation leaves is a necessary and sufficient condition for column feasibility. Special cases of operation leaves where the liquid composition profile strays outside the leaf are also presented. ‘Open leaves', where the product distillation lines or residue curves and the pinch-point curves end at different nodes are introduced. These open leaves can be used to facilitate the crossing of total reflux boundaries at finite reflux using side-column flow sheets. The use of side condensers and reboilers is shown to reduce the capital penalty in the crossing of total reflux boundaries. The concept of operation leaves can be applied to the retrofit or reuse of existing distillation columns by defining stage composition lines that bound the composition space within the leaf achievable with a given number of stages.

Optimal Thermodynamic Approximation to Reversible Distillation by Means of Interheaters and Intercoolers

The purpose of this paper is to deal with the problem of heat and power integration on one side and the problem of minimizing heat exchange areas on the other side, in both conventional and nonconventional distillation columns. We consider the limiting case of columns operating at minimum reflux. The appropriate objective functions that one must consider are the entropy production rate and the total heat exchange area, respectively. This is done by means of optimal placement of a given number of interheaters (IHs) and intercoolers (ICs) in stripping and rectifying sections, respectively. To solve these problems, an appropriate thermodynamic model for both conventional and nonconventional distillative columns is formally presented. This model allows us to formulate an optimization problem involving thermodynamically reversible profiles in stripping and rectifying sections of the columns. Our approach differs from others previously reported in that multiple reversible profiles were identified for each section of the column which give rise to lower and upper bounds for the objective function of the minimization problem. In other words, we obtain two solutions for each column section: the first is a nonoptimal feasible one, and the second is an optimal but not necessarily feasible one. Finally, the comparison of our approach with a method based on pseudobinary reversible profiles is carried out. Optimizing with this curve, solutions will be generated with objective function values between our lower and upper bounds. Therefore, care would be taken in using a pseudobinary pinch point curve for the placement of intermediate heat-exchanger units especially when the difference between our upper and lower bounds for the objective function values is relatively great.

A Robust Method To Solve Mass Balances in Reversible Column Sections

Reversible composition profiles in azeotropic and reactive distillation were used as pieces of new methods for the prediction of product composition regions and minimum reflux in singleand multiple-feed columns. A simple and robust algorithm to solve the nonlinear equation system corresponding to mass and energy balances in a reversible distillation column section for highly nonideal mixtures is proposed. If a distillate (bottom) is specified, one additional variable has to be set to calculate a cross section in the rectifying (stripping) part. We initially use the concentration of the component to be eliminated in the section as the variable to be fixed. A former direct successive substitution (DSS) procedure used in a previous paper is here analyzed, and the conditions for convergence are discussed. A damped Newton-Raphson method (DNR) is an alternative also presented. The new algorithm involves an improved direct successive substitution (IDSS) outer loop and a bubble point temperature (BUTE) loop included. By assuming the liquid phase composition at the reversible section, solving BUTE, and using geometric considerations, a related “hypothetical” product composition can be calculated. The difference between the real and the “hypothetical” product composition is used to recompute the liquid phase. This method can be considered robust in view that it does not uses derivative calculations that cause numerical drawbacks in cases that maxima, minima, or turning points are reached. The initialization variables are the liquid mole fractions instead of temperatures and component flow rates, resulting in a more general case-independent method. The geometrical characteristics allow that the algorithm can be initialized in any arbitrary region of the concentration simplex. For constant relative volatility (CRV) mixtures, a small number of iterations are needed despite the start point selected. The convergence was found always satisfactory independently of the start point, even when inversions in volatility order of some components take place. Finally, a variant (secant) of imbedding homotopy continuation is proposed to efficiently trace the complete path of the reversible profile, using the IDSS algorithm as the corrector. This combination becomes necessary when multiple disjoint branches of a product pinch point curve must be computed in highly nonideal mixtures. Other approaches to the problem are mentioned and their results compared.