Application of NEAT for the simulation of liquid–liquid extraction processes with poorly specified feeds

Funding information Horizon 2020 Framework Programme, Grant/ Award Number: 637077 Open access funding enabled and organized by Projekt DEAL Abstract The conceptual design of fluid separation processes is particularly challenging if the considered mixtures are poorly specified, since classical thermodynamic models cannot be applied when the composition is unknown. We have recently developed a method (NEAT) to predict activity coefficients in such mixtures. It combines the thermodynamic group contribution concept with the ability of NMR spectroscopy to quantify chemical groups. In the present work, we describe how NEAT can be applied to equilibrium stage simulations of liquid–liquid extraction processes with poorly specified feeds. Only a single C NMR spectrum of the feed is needed for predicting the distribution of a target component for different process parameters, such as temperature or extracting agent. The predictions from several test cases are compared to results that are obtained using the full knowledge on the composition of the feed and surprisingly good agreement is found.

spectrum of the mixture that yields the information on the groups, which is then used in the thermodynamic group contribution method modified UNIFAC (Dortmund). 18,19 In previous work, NEAT was applied for predicting the activity coefficients of target components in a variety of aqueous and nonaqueous poorly specified mixtures. 16,17 Test cases were studied, in which parts of the information on the speciation was deliberately ignored in NEAT. The agreement between the predictions with NEAT and results that were obtained using the full knowledge of the speciation was found to be very good.
Typical systems to which NEAT is applied are of the type (target component T + solvent S + unknown components U 1 …U N ). It has recently been shown that the application of NEAT is particularly simple if the ratios of the amounts of the unknown components remain unchanged, as this is, for example, the case when the target component T or the solvent S are selectively removed. 20 Then, only a single NMR spectrum is needed to predict the activity coefficient of the target component T for arbitrary variations of the amounts of T and S.
In the present work, we describe how NEAT can be used for the simulation of liquid-liquid extraction processes with poorly specified feeds. The applicability of NEAT for this purpose is demonstrated by considering single-stage liquid-liquid extractions with poorly specified feed mixtures of the type (target component T + solvent water W + unknown components U 1 …U N ) and pure extracting agents E. The composition of each studied feed mixture was known from sample preparation, but this information was only used for comparison and not for the predictions with NEAT in the present work. Based on a 13 C NMR spectrum of the feed and using modified UNIFAC (Dortmund), the partitioning of the target component between the extract and the raffinate phase was predicted using NEAT.
No experiments were carried out in the present work. The NMR spectra that were used for the evaluations of the present work were taken from an earlier work of our group. 16 The results of the liquidliquid equilibrium stage simulations are compared to predictions of the extraction process using modified UNIFAC (Dortmund) and the full information on the feed and good agreement is observed. The partitioning of the target component is predicted well with NEAT for different feed compositions, temperatures, extracting agents, and mass ratios of feed to extracting agent.

| APPLICATION OF NEAT
A comprehensive description of the NEAT method and its application for predicting activity coefficients in poorly specified mixtures is given in Reference 17. Therefore, the method itself is not described in detail here. We focus on the description of the new application of NEAT for equilibrium stage simulations. The methodology of the present work is shown in Figure 1a.
In the present work, single-stage liquid-liquid extraction processes are considered. In all cases, a poorly specified mixture is considered as feed F that is mixed and equilibrated with an extracting agent E in the extraction unit as schematically shown in Figure 1b.
All mixtures that are considered as feed in the present work are of the type (T + W + U 1 …U N ). Here, T denotes the target component, of which the nature and mass fraction in the feed are assumed to be known. W denotes the solvent water, of which the mass fraction in the feed does not have to be known as it can be obtained from NEAT using a mass balance. 17 For the remaining components U 1 …U N , which are called unknown components here, no information on the nature and concentration is used in NEAT. Quantitative 13 C NMR spectroscopy and modified UNIFAC (Dortmund) were used in NEAT for the determination of the nature and concentration of the chemical groups in the unknown components and the calculation of activity coefficients, respectively. The application of NEAT requires the assignment of chemical groups to chemical shift regions in an NMR spectrum.
The assignment that was used in the present work is the same as the one that was used in our previous work 17 for aqueous mixtures and is given in Table S.2. To use modified UNIFAC (Dortmund) for the calculation of activity coefficients, the chemical groups of the unknown components that are identified with NMR spectroscopy have to be lumped to mean unknown components. In our previous work, 16,17 all identified groups in the studied mixture were simply lumped to a single mean unknown componentŨ, to which a molar mass of MŨ = 150 g/mol was assigned. It was shown that this arbitrary assignment of the molar mass is not critical for the prediction of the activity coefficients of the target components in many cases. Hence, each poorly specified feed F was considered as pseudo-ternary mixture of the components T, W, U, and a thermodynamic model of the pseudo-ternary mixture was obtained from NEAT. The model can be straightforwardly extended by adding further known components, in our case the extracting agent E. Since only aqueous feeds were studied, the extracting agents were selected such as to exhibit a miscibility gap with water, compare  Once the thermodynamic model of the pseudo mixture is available, process simulations can be done with ease. Here, the liquid-liquid extraction process is simulated. The distribution of the (pseudo) components T, W,Ũ, and E on the coexisting phases in liquid-liquid equilibrium at constant temperature T was calculated from the isoactivity relations: T A B L E 1 Overview of the single-stage liquid-liquid extraction processes that were studied in the present work where b T 0 and b T 00 denote the molality of T in the raffinate 0 and in the extract 00 , respectively, and n T 00 and n T F denote the mole number of T in the extract 00 and in the feed F, respectively. The molalities b T in both phases were calculated referring to the mixed solvent (W + E): where m W and m E denote the mass of water W and extracting agent E, respectively.
The predictions for K T and Y T obtained with NEAT for the poorly specified feed are compared to results that were obtained in the same way but using information on the full speciation of the feed. To obtain these results for the fully specified mixtures, also modified UNIFAC gives poor results for the activity coefficients in the studied systems, the predictions with NEAT based on modified UNIFAC (Dortmund) will also be poor. The same holds for subsequent predictions of phase equilibria. However, for the predictions with NEAT, also any other group contribution method can be used. Table 1 gives an overview of the studied feed systems, extracting agents, and the parameters that were varied in the equilibrium stage simulations, which were the temperature T and the mass ratio of extracting agent to feed m E :m F . For each feed system and the selected process paramters, compare Table 1, five mixtures with constant ratio of target component to water and different amounts of unknown components were considered. For the predictions with NEAT, the feed F was always considered as poorly specified mixture and characterized using a single 13 C NMR analysis, whereas the extracting agent E was always assumed to be known. In the present work, only pure extracting agents were considered.

| RESULTS AND DISCUSSION
In the following diagrams, results for the partition coefficient   In practice, more than one unknown component may be present and lumping them together into a single mean unknown component in NEAT might cause problems. In the following, an approach to relax this constraint by introducing more than one mean unknown component is presented and tested using five-component feed mixtures from System VI (1,4-butanediol + water + cyclohexanone + acetonitrile + methyl acetate) and System VII (acetone + water + xylose + acetic acid + methyl acetate), where the target component is either (T = 1,4 butanediol) or (T = acetone).
The extracting agent is (E = 1-octanol), the is temperature 298 K, and the mass ratio of extracting agent E to feed F is m E :m F = 1:1 in all cases.
First, the results for the case that all unknown components are lumped together into a single mean unknown component are discussed. They are shown in Figure 6 as open symbols. The plot in Figure 6 is the same as in the previous figures. The results that were obtained with NEAT are good.
For both systems, a fair agreement with the results based on the full specification of the feed is obtained both for the partition coefficient K T and the extraction yield Y T of the target component T. That is, it could help in the assignment of chemical groups to different mean unknown components, which is expected to improve the predictions with NEAT. More information on the definition of several mean unknown components are given in the Supporting Information.

| CONCLUSIONS
The NEAT method, which was introduced recently by our group, enables calculating activity coefficients of target components in poorly The unknown components can be handled in different ways. In the simplest case, they are lumped together into a single mean unknown component, but also several mean unknown components can be introduced based on the NMR results.
In the examples that were studied here, the differences between the results of these two approaches were not large.
The results of this work demonstrate the potential of NEAT for the conceptual design of liquid-liquid extraction processes for systems with poorly specified mixtures, for example, regarding the selection of suitable extracting agents. The quality of the results that are obtained by NEAT is, however, limited by the quality of the underlying thermodynamic group contribution method. The NEAT approach can not only be used together with modified UNIFAC (Dortmund) but in principle together with any group contribution method. It should be possible to extend the application of NEAT also to other separation processes, such as crystallization and distillation.

ACKNOWLEDGEMENTS
Open access funding enabled and organized by Projekt DEAL.

CONFLICT OF INTEREST
None.