Subscriber access provided by UNIV OF SCIENCES PHILADELPHIA
Thermodynamics, Transport, and Fluid Mechanics
Application of modified NRTL models for binary LLE phase characterization Younas Dadmohammadi, Solomon Gebreyohannes, Brian J Neely, and Khaled A M Gasem Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b00683 • Publication Date (Web): 25 Apr 2018 Downloaded from http://pubs.acs.org on April 25, 2018
Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.
Page 1 of 21 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Industrial & Engineering Chemistry Research
Application of modified NRTL models for binary LLE phase characterization
Younas Dadmohammadi Solomon Gebreyohannes Brian J. Neely
Oklahoma State University School of Chemical Engineering Stillwater, OK 74078-0537
Khaled A. M. Gasem* University of Wyoming Department of Chemical & Petroleum Engineering Laramie, WY 82071
* email:
[email protected] Phone: 405-766-2845
1
ACS Paragon Plus Environment
Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Abstract Phase characterization of liquid-liquid mixtures is required in numerous chemical process calculations. The original non-random two-liquid (NRTL) model is used widely in describing liquid-liquid equilibria (LLE). Application of this model, however, is affected by (a) lack of reliable parameters, (b) a wide range of acceptable parameter values, and (c) highly correlated parameters. Recent modifications of the NRTL model, the two-parameter modified NRTL, “mNRTL2”, and the one-parameter NRTL, “mNRTL1”, address these issues and show promising results for characterizing LLE systems. The accuracy of these two modifications was tested in our previous studies using a comprehensive vapor-liquid equilibria (VLE) experimental database [1] and a representative LLE database [2]. In the current study, the efficacy of these modified NRTL models is assessed for the proper characterization of LLE phase conditions and attributes, including phase stability, miscibility, and consolute point coordinates. For the systems considered, the modified NRTL models produce good LLE characterization results in comparison to those of the original NRTL; albeit, the results from the mNRTL2 model are more precise than those of the mNRTL1 model Key words: liquid-liquid phase equilibria; modified NRTL model; stability; miscibility; consolute point coordinates
2
ACS Paragon Plus Environment
Page 2 of 21
Page 3 of 21 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Industrial & Engineering Chemistry Research
1.
Introduction
Characterization of phase equilibria of liquid mixtures is important in numerous industries where practitioners are concerned with separation of fluid mixtures. In handling liquid-liquid equilibria (LLE) of a given mixture, interest exists in determining the number of coexisting phases, the stability of phases present, the composition of each phase, and the critical (consolute) coordinate(s) for the mixture investigated. These concerns in LLE modeling have been the subject of intensive investigation for the past two decades. Research in this area intensified gradually to meet demands for higher process efficiency, lower operational costs, and handling process bottlenecks [3]. Numerous LLE modelling studies appear in the literature [see, e.g., [4-9]]. In many of these studies, the non-random two-liquid (NRTL) and universal quasichemical (UNIQUAC) models were used to correlate the experimental mutual solubilities of a variety of LLE systems. The models are also routinely used to characterize the LLE immiscibility, and determine the critical solution temperature for targeted systems. Equation of states are also used in LLE characterization. For example, Fotouh et al. [5] studied the perturbation theory and van der Waals one-fluid theory for predicting the liquid-liquid immiscibility for highly asymmetric mixtures. Similarly, Boshkov et al. [10] studied closed-loops of liquid-liquid immiscibility in binary mixtures, as predicted by the Redlich-Kwong (RK) equation of state (EOS). They reported that liquid-liquid phase behavior is highly sensitive to molecular interactions as indicated by the required interaction parameters. Other research has focused on developing algorithms for characterizing the phase behavior of LLE systems using activity coefficient and EOS models. For example, Yushan et al. [11] developed an algorithm to determine LLE compositions using the tangent-plane distance function approach for stability analysis. The NRTL and UNIQUAC activity coefficient models were used to express the Gibbs free energy functions for the LLE systems investigated. Similarly, Sofyan and coworkers [12] developed three different algorithms combining the methodology of Gibbs energy minimization and the iteration function method with an extended phase-check procedure were used for multiphase equilibrium calculations. The Peng-Robinson EOS was successfully employed in those studies. In spite of its practical importance, LLE has not been studied as extensively in the literature as vapor-liquid equilibria (VLE). The disproportionate need for VLE measurements and models, and difficulties in developing generalized models for LLE property predictions are key reasons in this regard. Further, the experimental determination of LLE compositions can often be carried out on an ad hoc basis, which produces large experimental uncertainties and weakens the incentive for data correlation [13]. The current study focuses on the application of the NRTL model and two recent modifications of the NRTL model (two-parameter modified NRTL (mNRTL2) and one-parameter modified NRTL (mNRTL1)) to a variety of LLE systems. The accuracy of these two modifications were evaluated in previous studies using a comprehensive VLE database [1] and a representative LLE database [2]. Our primary objective is to examine the efficacy of these models in determining the LLE phase conditions and attributes of binary mixtures, including phase stability, miscibility, and consulate point coordinates. The current work is a continuation of recent efforts by the Thermodynamics Group at Oklahoma State University to develop reliable parameter generalizations for the NRTL model [14]. 2.
Phase equilibrium models
The Gibbs equilibrium criteria for a closed system require that:
3
ACS Paragon Plus Environment
Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
=
Page 4 of 21
(1)
=
(2)
= = 1,
(3)
= = 1,
(4)
subject to mass balance constraints. Where T and P are the system temperature and pressure, respectively, and is component partial fugacity. Here, the superscripts “I” and “II” denote the liquid coexisting phases, the subscript “i" signifies the component index, and N is number of components in the mixture. To determine the conditions that satisfy the above equalities, a model is required to evaluate the partial fugacity of each component in each phase. Following the split approach formulation, Equation 3 is rewritten in terms accessible variables: where is the liquid activity coefficient, and is the liquid mole fraction for phases ′ and ′′, respectively.
Numerous activity coefficient models have been presented in the literature based on different theories and derivations of the excess Gibbs energy. Local-composition models like the NRTL have proven superior to other models for characterizing the binary liquid-liquid equilibria with sufficient accuracy for design purposes. In this work, we examine the efficacy of the NRTL model and its modifications in determining the LLE phase conditions and attributes of binary mixtures, including phase stability, miscibility, and consolute point coordinates. 2.1.
Non-Random Two-Liquid (NRTL) model
Wilson’s local-composition concept [15] and Scott’s two-liquid solution theory formed some of the basis for developing the NRTL model by Renon and Prausnitz [16]. Unlike the original Wilson’s model, the NRTL is applicable to partially miscible as well as completely miscible systems [17]. Further, the model resulted in higher precision in representing stability, immiscibility, and consolute coordinates of LLE systems compared with other literature models [6, 8, 9, 11, 18, 19]. The original NRTL excess Gibbs energy model for a binary system is as follows:
=
! "!
+
$ ! "!
(5)
where the model parameters % and & are defined as:
% = exp*−, & - & % = exp *−, & and
& =
/
=
0 & &
=
/
=
0
(6)
(7)
where R is the universal gas constant, 2 is an energy parameter characterizing interactions between molecules 1 and 2, and , is the non-randomness factor in the mixture. To be consistent with the DECHEMA database [20], the non-randomness factor, , , was kept constant as 0.2 for all binary systems in this work. Further, in our previous work [14], we found variations in , to have a limited effect on VLE and LLE property predictions and in reducing overall prediction errors [14]. Therefore, in this study the original NRTL model was limited to two interaction parameters (3 and 3 ) to be regressed from mutual solubility data [1]. The interaction parameters of the original NRTL are highly correlated. In the following sections, we present our recent modifications of the NRTL model [1]. The first model (mNRTL2) recasts the original NRTL model parameters in a manner that decreases the correlation between the
4
ACS Paragon Plus Environment
Page 5 of 21 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Industrial & Engineering Chemistry Research
parameters and narrows the range of acceptable parameter values. In the second model (mNRTL1), pure-component properties are used to generalize one of the parameters of the proposed model for LLE systems; thus, we obtain a one-parameter model which eliminates the parameter correlation problem. 2.2.
Modified Non-Random Two-Liquid: mNRTL2 and mNRTL1
Typically, in applying the NRTL model, three parameters are determined through regression of experimental data for a specific binary system. In a binary system, the NRTL model parameters are designed to account simultaneously for pure-component liquid interactions, g11, and g22, and mixed-component liquid interactions, g12 and g21. As stated earlier, the main disadvantages of the NRTL model are the strong parameter correlation between the two parameters a12 and a21 and wide range of acceptable values. To reduce the parameter correlation and narrow down the range of acceptable values in the NRTL model parameters, two modified NRTL models, mNRTL1 and mNRTL2, were developed in our previous work [21, 22]. Equations 8 and 9 present the model parameters for the modified NRTL: 34 = 524 − 244 6 = 24 71 −
88 98
: = 24 51 − ;4 6 = 24
