Elsevier

Fluid Phase Equilibria

Volume 529, 1 February 2021, 112867
Fluid Phase Equilibria

Revisiting the treatment of cross-association interactions in oxygenate mixtures with the polar PC-SAFT equation of state

https://doi.org/10.1016/j.fluid.2020.112867Get rights and content

Abstract

In this work a new approach to the cross-association of non-self-associating (NSA) oxygenates with carbonyl oxygens within polar PC-SAFT is developed. Aldehydes, esters and ketones fall into this class of NSA molecules. The challenge in developing such an approach is that predictability of phase behavior of NSA species with alcohols is desired, while at the same time, there is the requirement that the approach must be able to reproduce the phase behavior in aqueous systems. To meet these two criteria, the hydrogen bonding parameters of the NSA oxygenate are adjusted to accurately reproduce the phase behavior with water. With the hydrogen bonding parameters fixed, binary interaction parameters between NSA oxygenates and alcohols must be adjusted to achieve accurate phase behavior. However, as shown in this work, these binary interaction parameters are predictable solely on the basis of alcohol and NSA oxygenate molecular weights. A simple correlation of the binary interaction parameter between these two classes is developed, allowing for accurate representation of the phase behavior with alcohols in absence of phase behavior data to tune the model.

Introduction

Modern process scoping, design and optimization is dominated by computer process simulations. At the heart of the process simulation lies the thermodynamic model. Nearly all calculations which are performed in a process simulation rely on the accuracy of the underlying thermodynamic model.

Dr. Constantine (Costa) Tsonopoulos, for whom this special issue is dedicated, was the manager of the thermodynamics group in Exxon Research & Engineering and dedicated his career to thermodynamics for industrial applications. Under his guidance, the group developed a number of mixture thermodynamic models that can generally be grouped into cubic equations of state and activity coefficient models. The activity coefficient models are generally used by ExxonMobil researchers for the development of chemical processes with highly non-ideal interactions. These activity coefficient models require expert support for the development of the model parameters and deployment within a process simulation environment.

In contrast, engineers and researchers rarely use activity coefficient models for hydrocarbon processes; instead, they typically rely on the cubic equation of state (EoS) approach. The cubic EoS are used extensively throughout the corporation and the industry for a very wide range of applications and conditions. Unlike the activity coefficient methods which normally require a thermodynamics expert to determine the appropriate binary parameters, the majority of applications of cubic EoS are typically applied “off-the-shelf”, while, at the same time, the expectation is that they are accurate enough for process design and optimization. To accomplish this, great care must be taken to ensure the EoS predicts quantitatively accurate vapor pressures, and when binary interaction parameters are an absolute requirement, that they can be accurately estimated if they are lacking in the binary parameter library. Of course this requirement cannot be met for certain classes of non-ideal interactions for which the activity coefficients approaches are required.

More recently, the authors implemented and deployed a version of the statistical associating fluid theory (SAFT) class of EoS. SAFT methods employ perturbation theories to construct the various free energy contributions. The resulting Helmholtz free energy is given as the following sum,A=Ahc+Aat+Adp+Aas

Specifically, in this work, PC-SAFT [1] is employed for the dispersion contribution to the free energy Aat, the hard chain contribution Ahc is evaluated with the simplified mixing rule of von Solms et al. [2], long ranged polarity Adp is evaluated with the Jog and Chapman [3] polar free energy, and hydrogen bonding Aas is evaluated with the standard SAFT form [4] which has been rearranged [5] such that each molecule is described by some number of acceptor na and donor nd hydrogen bonding sites. The basic equations of the theory are reviewed in Appendix A.

The overarching goal of the development of a SAFT-based approach was (and remains) to deploy an EoS methodology which can be applied to complex phase behavior, which is normally handled by activity coefficient methods, in such a way that it can be employed without extensive interactions with experts from the thermodynamics groups. Hence, a single EoS methodology which can be applied across the refining, chemicals and upstream applications which makes design quality predictions out of the box, without expert thermodynamics support. This is the dream.

Within the SAFT class of EoS, it is the partitioning of the interactions between dispersion, polar and hydrogen bonding energy scales which gives the methodology predictive power. Over the course of the last 30 years there has been 100’s of papers which demonstrate how to parameterize classes of polar molecules to achieve accurate predictions of phase behavior in binary mixtures within SAFT. In general, one chooses how to distribute the energetic degrees of freedom across dispersion, long ranged polar and hydrogen bonding energy scales to achieve maximum predictability for a certain class of binary phase behavior.

What is often left unaddressed in these papers, is how the decisions one makes to describe a certain class of binary interactions affects another class of binary interactions. A good example of this is the polar treatment of organic solvents. It has been extensively demonstrated [3,[6], [7], [8]] that accounting for long ranged polarity in polar molecules allows for the accurate description of saturated hydrocarbon / polar solvent phase behavior. This predictability is a result of a certain partitioning of the cohesive energy of the polar solvents among polar and non-polar energy scales. But now what happens if this same polar solvent parameter set is applied to predict phase behavior with aromatics, alkenes, dienes and alkynes? As has been recently demonstrated [9,10], the approach will predict far too much non-ideality. Therefore, putting out one fire for the solvent / saturates class of interactions, you create another fire in the solvent / unsaturates class of interactions. The reason for this, is that the dipole moment of the polar molecules polarizes the π bonds of the unsaturates. This results in an increase in induction forces as compared to the corresponding saturated molecules. The situation can be resolved [9,10] by allowing the unsaturated species to interact with the polar degrees of freedom of the polar solvent.

This provides a single example of a general problem which is encountered when applying the SAFT EoS in the context of a general thermodynamics package in process simulations. When applying the polar and hydrogen bonding contributions to the theory, one has to be careful to ensure that the resulting parameterization is sufficient for all classes of possible interactions. We follow the general guidelines

  • 1

    If a molecule can interact with long ranged polar and / or hydrogen bonding interactions, the interaction must be allowed

  • 2

    Stay true to hydrogen bond stoichiometry

Let us consider alkenes for instance. Generally, alkenes are thought as non-polar molecules. However, when mixed with polar and hydrogen bonding species, the π bond of the alkene will, as described above, interact with the dipole moment of a polar molecule, as well as receive hydrogen bonds [11] from hydrogen bond donors such as alcohols, organic acids and water. If the promise of SAFT predictability is to be realized on an industrial scale, all of the interactions must be accounted for. Remember, in any given process simulation, any molecule can be with any other molecule at any condition. In our description, we allow alkenes to have a single hydrogen bond acceptor site [5] as well as a phantom dipole. Phantom dipoles [9] where recently proposed as a means to represent induction forces between polar molecules in π bonds.

Another example is the proper accounting of cross-association interactions between self-associating (SA) molecules (alcohols, water, etc.…) and non-self-associating (NSA) molecules which receive hydrogen bonds. Examples of NSA molecules include ethers, ketones, aldehydes, esters, aromatics, alkenes, alkynes, and organic solvents such as acetonitrile, dimethylformamide (DMF), n-methyl-2-pyrrolidone (NMP), and sulfolane.

The NSA challenge has been the subject of several studies [12], [13], [14], [15], [16], [17], [18]. As NSA molecules do not hydrogen bond in pure fluids, the hydrogen bonding energy εAB and bond volume κAB are often chosen to best reproduce mixture data with SA molecules. A problem that we ran into with this approach, was that if the NSA hydrogen bonding parameters were chosen to give the best predictability with alcohols, the theory could not then be accurately applied to water (even with adjusting a binary interaction parameter). This same effect was observed by Cripwell et al. [12] who developed an NSA association scheme for ketones using SAFT VR-Mie. They were able to demonstrate reasonable predictability with alcohols, but the approach severely failed for mixtures with water. This result is not easily workable in the context of a commercially deployed thermodynamics package. An unfortunate fact is that where there are oxygenates, there is usually water somewhere near. Cripwell et al. [12] employed a physically consistent association scheme for ketones, in that the carbonyl oxygen had a single hydrogen bond acceptor site. This is in contrast to how these NSA molecules are commonly treated [13] with the 2B scheme (1 acceptor and 1 donor) and self-association negated by setting the self-hydrogen bond energy εAB to zero. While physically consistent, the hydrogen bonding scheme of Cripwell et al. [12] did not allow for the correct hydrogen bond stoichiometry. The carbonyl oxygen can accept two hydrogen bonds instead of one. While this difference may not be important for phase equilibria with alcohols, it is extremely important for phase behavior with water. Another approach based on group contribution SAFT (GC-SAFT) [17,18] was shown to give good results for oxygenates and alcohols and reasonable results with water by employing additional binary interaction parameters for the cross-species hard sphere diameter, and cross hydrogen bonding parameters.

In a previous manuscript [5] we developed a general NSA scheme for aromatics and alkenes in the context of liquid-liquid equilibria with water. This same NSA scheme was shown [19,20] to give very accurate predictions for the phase behavior of unsaturated hydrocarbons with alcohols. In this work we develop an NSA approach for species with a carbonyl functional group: ketones, aldehydes and esters. Per the second guideline presented above, we assign each carbonyl oxygen two hydrogen bond acceptor sites. The fact that the carbonyl groups do not have any hydrogen bond donor sites, prevents the carbonyl containing molecules from self-associating.

A “water first” approach is taken, meaning the hydrogen bonding parameters of the carbonyl groups are determined to best describe the phase behavior with water. This is in contrast to the Cripwell et al. and GC-SAFT approaches described above, which took an “alcohol first” approach. The hope is that using a “water first” approach we can construct a methodology which gives a good representation of aqueous phase behavior using a single binary interaction parameter. When applying the approach to alcohol-carbonyl phase behavior, the carbonyl hydrogen bonding parameters are non-optimal, and a binary interaction parameter kij is frequently required to achieve quantitative accuracy. However, we propose a justifiable kij correlation on the basis of alcohol and carbonyl molecular weights. The resulting kij correlation is demonstrated to result in the accurate representation of alcohol-carbonyl phase behavior.

Section snippets

Model development and analysis: aqueous systems

In this section the hydrogen bond parameterization strategy for NSA molecules containing a carbonyl oxygen is developed and analyzed. The non-hydrogen bonding parameters of the NSA molecules consist of the chain length m, segment diameter σ, dispersion energy ε and the polar strength αp = mxpμ [2]. The polar strength groups two separate parameters used in the Jog-Chapman [3] approach, the dipole moment μ and the fraction of polar segments xp. It is the polar strength which provides the “charge”

Model development and analysis: phase behavior with alcohols

As discussed in the introduction, the main goal of this manuscript is the development / deployment of a thermodynamic model which can make accurate predictions out of the box, without further tuning. In Section 2, the hydrogen boding parameters of the oxygenate species where chosen to give the best phase behavior with water. In addition, binary interaction parameters are generally needed to get accurate predictions of phase behavior. As difficult as aqueous systems are, at least there is only

Summary and conclusions

In this work a new approach to the treatment cross association of non-self-associating (NSA) species containing a carbonyl oxygen was developed. Given both the prevalence and modeling difficulty of oxygenate / water phase behavior, the association parameters of the NSA species were optimized to their phase behavior with water. The approach was shown to give a good description of aqueous phase behavior. Across the board accuracy of an equation of state for aqueous systems is currently not

Dedication

Both of us authors have held Dr. Tsonopoulos's position in ExxonMobil Research & Engineering in recent years, and we have first-hand experience of the vast amount of research and development of thermodynamic technology for the corporation, that has been used for decades. We feel fortunate to have followed in his footsteps and humbled by his legacy. He was a visionary, an influential integrator, and a true gentleman.

CRediT authorship contribution statement

Bennett D. Marshall: Conceptualization, Methodology, Software, Investigation, Writing - original draft, Formal analysis. Constantinos P. Bokis: Investigation, Writing - review & editing, Formal analysis, Funding acquisition.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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