Elsevier

Chemical Engineering Science

Volume 143, 2 April 2016, Pages 105-113
Chemical Engineering Science

Slope curve method for the analysis of separations in extraction columns of infinite height

https://doi.org/10.1016/j.ces.2015.12.008Get rights and content

Highlights

  • A new “slope curve method” for the conceptual design of extraction columns is described.

  • The method easily finds all feasible product compositions.

  • Only LLE data needed as input.

  • Limitations by internal pinches can be quickly identified.

Abstract

A new method for the conceptual design of counter-current extraction columns, the slope curve method (SCM), is presented. It is a graphical method based on the equilibrium stage model and developed here for ternary mixtures. The well-known stage-to-stage construction in the ternary phase diagram is replaced by a concise representation in the so-called slope diagram. In that diagram, the slope curve represents the tie lines and operating lines represent material balances. Infinite column height is assumed so that for given feed and solvent composition, the only remaining degree of freedom is the solvent-to-feed ratio. Varying that parameter, all feasible solutions are obtained in the slope diagram. The corresponding product compositions can be reconstructed. Using the method, it is readily shown that internal pinches only occur for certain classes of mixtures, which can be readily identified based on an analysis of the shape of the slope curve. As the SCM yields a complete survey of all feasible solutions it is particularly suited for feasibility studies in conceptual design as well as for obtaining general insights in extractive separations.

Introduction

In the conceptual design of chemical processes, the feasibility of flow sheet options has to be evaluated. Before starting cumbersome flow sheet simulations with commercial simulators, it is convenient to consider material balances and thermodynamic property data (e.g. chemical equilibrium or separation limitations as azeotropes) to estimate flow rates and compositions of recycles and other process streams. A number of computer-aided methods for this task have been developed. Ryll et al., 2012a, Ryll et al., 2013, Ryll et al., 2014 developed a framework to assess the feasibility of entire flow-sheets and estimate the compositions of the process streams. The process units are assumed to achieve maximum performance, only limited by thermodynamic boundaries and material balances. A reactor attains maximum conversion (limited by the chemical equilibrium) and the separation units attain maximum separation efficiency. Distillation columns attain the products which follow from the /-analysis (Petlyuk and Avet׳yan, 1971, Serafimov et al., 1973), i.e. assuming infinite height and total reflux. The framework has been shown to be useful for the design on novel distillation-based processes, such as the production of trioxane (Grützner et al., 2007) or fuel additives (Burger and Hasse, 2013). It would be interesting to extend the framework to include other types of separation units of maximum separation efficiency as ideal crystallizers (Franke et al., 2008), absorption columns of infinite height (Burger et al., 2015) or extraction columns of infinite height (Minotti et al., 1996). In the present work this is done for the counter-current extraction columns of infinite height.

Minotti et al. (1996) were the first to study extraction columns of infinite height and systematically discuss pinch points in these columns. At the pinch points, the counter-current stream compositions are in liquid–liquid equilibrium, resulting in the absence of driving force for separation which leads to infinite column height. Minotti et al. (1996) distinguished two types of pinches: feed pinches that occur at the ends of the column and internal pinches (also called tangent pinches) that occur somewhere inside the column. Further, Minotti et al. (1996) proposed a geometric method for determining the minimal solvent/feed flow rate ratio and the extract composition for a given feed, solvent, and raffinate composition. Thereby, the method also determines the type of pinch that is limiting the separation. The method involves the solution of a set of non-linear equations for which a continuation method is used. It is non-iterative as long as ternary mixtures are considered. Samant and Ng, 1998, Samant and Ng, 1998 showed that the method is also applicable in some reactive systems with more than three components, when the components are coupled via the reaction stoichiometry and a suitable coordinate transformation is used. Recently, Redepenning et al. (2013) mentioned an independent method for determining the minimal solvent/feed flow rate ratio and the extract composition for a given feed, solvent, and raffinate composition for mixtures with more than three components but detailed presentation of that work is still not available.

In the present work a novel geometric method for the conceptual design of extraction columns in ternary systems is introduced which is called the slope curve method (SCM). For a given solvent and feed composition, the SCM enables finding all possible raffinate and extract compositions as well as the corresponding solvent/feed flow ratios. As infinite column height is always presumed here, these ratios are the minimal solvent/feed flow ratios for the considered specifications. In the following, we will simply refer to them as (S/F). In the SCM, contrarily to previously available methods, there is no need for specifying the raffinate composition, the SCM directly yields the solutions for all feasible raffinate compositions. (Of course, here and in the above instead of specifying the raffinate composition and determining the extract composition, also the extract composition could be specified and the corresponding raffinate could be determined). As the SCM yields a complete survey of all feasible solutions it is particularly suited for feasibility studies in conceptual process design as well as for obtaining general insights in extractive separations. It is used here for a general study on the occurrence of pinches in extraction columns. The following questions are answered: under which operating conditions do internal pinches occur? Can internal pinches occur in all systems, i.e. for all solvents or only for certain ones?

It is shown that, only by analyzing the liquid–liquid equilibrium of a given system, it can be decided using the SCM whether internal pinches occur. Furthermore, it is shown here, that for certain systems only feed pinches can occur, whereas for other systems internal pinches may occur, no matter what composition the feed has. These insights are particularly useful in conceptual design. If, e.g., a system is considered in which internal pinches are never present, the design problem can be treated with much simpler methods.

Section snippets

Liquid–liquid equilibria

For applying the SCM, global information on the liquid–liquid equilibrium (LLE) in the studied system is needed, which can be obtained from any thermodynamic model. We will use the UNIQUAC model (Abrams and Prausnitz, 1975) in our examples and restrict the entire discussion to ternary systems. Concentrations in ternary systems are depicted here in the non-cartesian symmetric triangular map introduced by Gibbs. Other forms like Cartesian coordinates representing concentrations of two arbitrarily

Slope diagram, slope curve, operating lines

The slope curve method (SCM) is based on a representation of the material balance line segments and tie lines of the stage-to-stage construction (cf. Fig. 1) in a suitable diagram, the so-called slope diagram.

The first step is only introduced for convenience: an arbitrary Cartesian x,y-coordinate system is defined to replace the Gibbs ternary phase diagram by a linear transformation. Fig. 2a gives an example for a particularly attractive choice of the Cartesian coordinates: the binary axis BC

Analysis of extractive separations in ternary systems

The SCM is applied in the following to study the limitations of extractive separations in exemplary ternary mixtures. In all examples the pressure is 1 bar and the temperature is 298 K. The UNIQUAC model is used to determine the liquid–liquid equilibrium. The UNIQUAC parameters are reported in Table 1. The algorithm to numerically calculate the slope diagram and the product curves in arbitrarily fine discrete steps is described in the supporting information.

Conclusions

Extraction columns at infinite height are limiting cases of real extraction columns. The study of columns of infinite height yields limiting parameters of mode which are of practical interest. The product compositions of columns of infinite height depend strongly on the type and the location of composition pinches in the column. This work presents a novel graphical method, the slope curve method (SCM), to analyze ternary mixtures with respect to extractive separations in columns of infinite

Nomenclature

List of symbols
ai,jbinary UNIQUAC-parameter
bijbinary UNIQUAC-parameter
by-intercept
mslope
Mmixing point
Nnumber of stages
ṅmolar flow rate
ppressure
qUNIQUAC-parameter
rUNIQUAC-parameter
Ttemperature
xBmole fraction component B
xmolar composition vector
Δintersection point for all material balance lines

Abbreviations
AAacetic acid
CFchloroform
cpcritical point
CTCcarbon tetrachloride
Eextract phase
EFethyl formate
EGethylene glycol
EtOHethanol
Ffeed
LLEliquid–liquid equilibrium
prefpreferred
Rraffinate phase
Ssolvent
Empty Cell

Acknowledgment

The authors gratefully acknowledge financial support from “Stiftung Rheinland-Pfalz für Innovation” (Project no. 961-386261/1107). J.B. thanks BASF SE for financial support.

References (18)

There are more references available in the full text version of this article.

Cited by (9)

  • Integration of graphical approaches into optimization-based design of multistage liquid extraction

    2020, Computers and Chemical Engineering
    Citation Excerpt :

    More recently, Kaul et al. (2018) proposed a hierarchical framework to systematically design extractive separations. In this framework, the authors employed pinch-based short-cut models with piece-wise linearized thermodynamics based on the Slope Curve Method (SCM) (Burger et al., 2016). Even though the available simulation-based methods are capable of rigorously simulating the system, these techniques face limitations when the goal is to structurally optimize the liquid extractors.

  • Short-cut method for assessing solvents for gas cleaning by reactive absorption

    2020, Chemical Engineering Research and Design
    Citation Excerpt :

    The choice of the number of stages is again somehow arbitrary. We prefer to use the assumption of infinite number of stages in both columns which has been shown to be very useful for conceptual design of distillation processes (Ryll et al., 2012, 2013, 2014; Burger et al., 2016). Removing the arbitrariness establishes safer ground for comparisons and yields the possibility to draw general conclusions.

  • Hierarchical design of extraction-distillation processes using short-cut apparatus models with piece-wise linearized thermodynamics

    2018, Chemical Engineering Science
    Citation Excerpt :

    For large (S/F), R is located at the tie line pointing to S and a solvent pinch occurs (Rmin in Fig. 3). There are some ternary mixtures for which an internal pinch may occur (Burger et al., 2016). In case of an internal pinch, neither Emax nor Rmin are obtained.

  • In situ measurement of liquid-liquid equilibria by medium field nuclear magnetic resonance

    2017, Fluid Phase Equilibria
    Citation Excerpt :

    The corresponding peak assignment is listed in Table S1 in the Supplementary Information. By means of a coordinate transformation the tie lines and thus the LLE phase behavior can be illustrated using the slope curve method (SCM) which is described in detail by Burger et al. [28]. The resulting slope curve diagrams for every non-reactive system investigated in this work are presented in the SI as well.

View all citing articles on Scopus
View full text