A PC-SAFT model for hydrocarbons II: General model development

Accepted Manuscript A PC-SAFT model for hydrocarbons II: General model development Bennett D. Marshall, Constantinos P. Bokis PII:

S0378-3812(18)30362-5

DOI:

10.1016/j.fluid.2018.09.002

Reference:

FLUID 11936

To appear in:

Fluid Phase Equilibria

Received Date: 13 May 2018 Revised Date:

23 July 2018

Accepted Date: 3 September 2018

Please cite this article as: B.D. Marshall, C.P. Bokis, A PC-SAFT model for hydrocarbons II: General model development, Fluid Phase Equilibria (2018), doi: 10.1016/j.fluid.2018.09.002. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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A PC-SAFT model for hydrocarbons II: General model development

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Bennett D. Marshall* and Constantinos P. Bokis

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ExxonMobil Research and Engineering, 22777 Springwoods Village Parkway, Spring TX 77389

Abstract

This is the second paper in a series which describes the development of a general PC-

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SAFT hydrocarbon model. In instalment I, a new treatment of aromaticity was included in the PC-SAFT equation of state by mapping aromatic π-π attractions onto a dipolar free energy. In this paper we include this aromatic-polar map into the development of a generalized thermodynamic model for hydrocarbons. The characterization model incorporates heteroatom

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polarity as well as aromaticity. The minimum level of input to the model is boiling point, molecular weight, and specific gravity. If a specific molecular structure is known, the model

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formalism accommodates inclusion of various aromatic and heteroatom functional groups. We demonstrate by comparison to pure component properties of defined hydrocarbon molecules that the new approach is of nearly quantitative accuracy. We also demonstrate how the use of the polarity contributions allows for accurate prediction of non-idealities in mixture phase equilibria. *Author to whom correspondence should be addressed: [email protected]

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I: Introduction

The thermodynamics of complex hydrocarbon mixtures is of fundamental importance in

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the petrochemical industry. Cubic equations of state (EoS) are the industry workhorse methodologies to predict petroleum phase equilibria. The general approach is to provide a boiling point curve and average gravity (SG or API) from which petroleum pseudo-components

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can be generated. Cubic EoS are then used to predict the phase equilibria of these pseudocomponents. This method works well for mixture calculations so long as the pseudo-components

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are of a similar molecular class. However, if some of the pseudo-components are polar or highly aromatic, this approach may significantly under-predict mixture non-idealities.

Recently there has been substantial interest in the application of statistical associating fluid theory (SAFT) to model petroleum[1-7]. The SAFT[8-14] class of EoS have a molecular

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basis and are grounded in statistical mechanics. Molecules are represented as chains of m spheres of diameter sigma σ and attractive energy ε. The chain treatment allows for accurate description of mixtures with large size asymmetries or high molecular weight molecules, where a traditional

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cubic EoS would lose accuracy. The true power of SAFT is realized through the inclusion of contributions for hydrogen bonding and long range dipolar attractions. These polar contributions

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introduce new energy scales of attraction which allow for accurate prediction of mixture phase equilibria.

In this work we will focus on the long range dipolar contribution that allows for the

incorporation of heteroatom polarity and aromaticity in a general hydrocarbon framework. The polar contribution brings in an additional parameter αp = mxpµ2 that describes the polar strength

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of the molecule[15], where µ is the dipole moment, and xp is the fraction of segments in the

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molecule that are polar. Figure 1 illustrates a possible molecular model for 2-pentanone.

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Figure 1: Possible model representation of 2-pentanone

In a companion paper[15] we demonstrated that with SAFT, aromatic π-π interactions can be mapped onto a dipolar free energy. It was demonstrated that this allows for more accurate

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phase equilibria predictions in multi-component mixtures.

Our goal in this paper is to describe a general formalism to characterize hydrocarbon molecules or pseudo-components in such a way that exploits the full predictability of the PC-

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SAFT EoS[11]. While there has been success in development of group contribution approaches[16-20] for PC-SAFT parameters, parameterization in terms of petroleum variables

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has proven more challenging. We will begin by construction of a hydrocarbon model (no heteroatoms) that requires an input of specific gravity, molecular weight, and boiling point. The outputs of the model are the PC-SAFT parameters (m, σ, ε, and αp ) to be used in the PC-SAFT EoS. We validate the approach by comparison to liquid density and vapor pressure data over a wide temperature range for 330 hydrocarbon molecules. We show that the new approach is of nearly quantitatively accurate. We also demonstrate how the inclusion of the aromatic-polar map

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allows for accurate predictions of mixture phase behavior involving aromatics and paraffins in the absence of binary data to tune the model.

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Upon completion of the base hydrocarbon framework, we incorporate contributions for the heteroatoms oxygen, nitrogen, and sulfur. Addition of heteroatoms shifts the hydrocarbon correlations for m and σ, and also adds a polarity contribution. We demonstrate that the resulting

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model allows for accurate predictions of pure component properties of these polar components, as well as prediction of mixture non-idealities when these polar molecules are mixed with non-

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polar hydrocarbons.

In this work we specifically employ the simplified PC-SAFT[14] form with the Jog and Chapman[12] dipolar term. The specific model was discussed in detail in paper I of this series[15]

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II: Base hydrocarbon models

In this section we develop basic models for m, σ, ε, and αp of hydrocarbon molecules

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without heteroatoms. There have been several such attempts in the literature[3, 7]. A typical approach is to obtain a database of PC-SAFT parameters m, σ, ε, and then develop separate

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correlations for the specific quantities m, mε, and mσ3. A common mistake in developing these correlations is the separate correlation of m and mσ3. The molecular volume, which sets the liquid phase density, is determined by mσ3. If one correlates these two quantities separately, random errors in each correlation will be magnified and it will be impossible to develop truly accurate models.

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Yan et al.[7] realized this and attempted to solve the problem by fixing σ to the value of an n-alkane of equal molecular weight. This σ was imposed, refitting the remaining parameters m and ε, and then developing correlations for these quantities. While PC-SAFT sphere diameters σ

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are typically close in size, small variations can result in substantial changes in model predictions.

In our model we take another approach. We use PC-SAFT parameters for 330

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hydrocarbon molecules as our database. The molecular classes are outlined in Table 1. The parameters explicitly include aromaticity contributions as dictated through the aromatic-polar

given by

α p , A = mx p µ 2 = 2.17 n A =

2.17 NA 6

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map described in [15]. Using this methodology the polar strength of an aromatic molecule is

(1)

where nA is the number of aromatic rings, and NA is the number of aromatic carbons in the

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molecule. The polar strength is given in units D2 (Debye squared).

We begin the development of our model with the correlation of the chain length m in

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terms of specific gravity SG and molecular weight MW. Hosseinifar et al.[3] proposed that PCSAFT parameters should scale with the refractive index RI and molecular weight. Modifying the

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results of Vargas and Chapman[21], Hosseinifar et al. proposed the following form for the refractive index

RI ≈

3 + 2 SG 3 − SG

(2)

Using this approach, Hosseinifar et al. proposed a series of 7-constant correlations for the model parameters. One drawback to this approach is that the large number of parameters in the

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correlation produces unpredictable extrapolation to high molecular weights. The model parameters are largely determined from lower molecular weight molecules, so controlled extrapolation to high molecular weight is crucial. We face a similar limitation – although our

# of molecules

Linear + branched alkanes

125

Linear + branched alkenes

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Linear + branched alkynes

Molecular weight range

44.1 – 507.0

42.1 – 280.5

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Molecular class

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of components are of lower molecular weight.

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component library contains n-alkanes up to C36 and multi-ring aromatics up to C18, the majority

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42.1 – 138.2

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42.1 – 252.5

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40.1 – 82.1

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68.1 – 108.2

Alkyl benzenes

36

78.1 – 302.5

Poly-nuclear aromatics

41

116.1 – 230.3

Alkyl naphthenes Linear + branched dienes

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Cyclic alkenes + cyclic dienes

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Table 1: Distribution of molecules in parameter library

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Employing the RI scaling approach introduced by Hosseinifar et al., we develop a correlation for the chain length m. However, we do so in a much simpler 3-parameter model  3 + 2 SG  m = 0.0925   3 − SG 

−1.4459

(3)

MW 0.9834

The three parameters were adjusted to the m values for all molecules in our library. The results of this regression are given in the parity plot shown in Fig. 2

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Figure 2: Correlation parity plot for chain length through Eq. (3)

Overall, Eq. (3) is able to correlate the values of m very well with an average deviation of 2.3%. We note that several molecules within the data set were parameterized from very limited data, and this will result in variations of m and σ from any definitive trend. Much of the scatter

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observed at small m results from small highly branched molecules.

To force all molecules to follow the same parameter trend, we now refit the parameters σ and ε subject to the m correlation given in Eq. (3), and to the aromaticity contribution from Eq.

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(1). The regression is performed by adjusting σ and ε to match liquid densities ρ and vapor pressures Psat from temperatures which correspond to Psat = 1torr to 90% of critical temperature.

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Table 2 lists average absolute deviations over all components and temperatures for both the original parameter set as well as the modified parameter set resulting from the enforcement of Eqns. (1) and (3).

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AAD Psat

AAD ρ

Original

0.32%

0.15%

Modified

2.7%

0.6 %

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Parameter set

Table 2: Average absolute deviations using original and modified parameter sets

Although enforcing Eq. (3) results in slightly higher errors in vapor pressure and density

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predictions, the benefits of this choice will soon become apparent. With the modified parameter set, Eq. (3) represents an exact model for the chain length m. Now we correlate mσ3 from the

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modified parameter set to the same fitting form as Eq. (3). When we adjust the three correlation parameters, we do so to minimize the objective function defined as the average deviation between model and “data” values of σ (not mσ3). Equation (4) gives the new correlation. −0.97677

MW 1.0408

(4)

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 3 + 2 SG  mσ 3 = 2.8872   3 − SG 

Equation (4) represents a very tight correlation with an average deviation between correlation predictions of σ and “data” of 0.04%. The parity plot comparing correlation predictions to data

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can be seen in Fig. 3. The highest observed errors are for the largest values of σ which correspond to multi-ring aromatics pyrene (1.12%), chrysene (1.87%), triphenylene (1.25%) and

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noroborane (1.03 %).

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Figure 3: Parity plot for sigma correlation Eq. (4) vs. modified parameter set

Furthermore, dividing Eq. (3) into Eq. (4) and taking the cube root shows that σ ~ MW0.019 and increases very slowly with molecular weight. This is a very important feature in a parameter model meant to be used for high molecular weight molecules.

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At this point, within the context of our modified parameter set, we have a perfect correlation for m and a nearly perfect correlation for σ. All that remains is the development of a model for ε. We first note that, when developing pseudo-components from a boiling point curve,

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the boiling point temperature Tbp is known. If PC-SAFT parameters are needed for some new defined compound, Tbp may or may not be known a priori. However, if it is unknown there are

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several classical and quantum group contribution approaches which can be used to estimate this quantity.

With Tbp known, we treat the unknown parameter ε as a thermodynamic variable and

perform a constant temperature T = Tbp and pressure P = 1 atm flash. That is, we fit the parameter ε to the vapor pressure at Tbp. The conditions for equilibrium are

µ L = µV

PL = 1 atm

PV = 1 atm T = Tbp

(5) 9

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Equation (5) states that at equilibrium the chemical potentials, pressures, and temperatures of both phases must be equal. These equations provide the required information to solve for the three unknowns which are ε and the density of each phase. While we are not necessarily

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interested in the densities, they are required to evaluate the PC-SAFT chemical potentials and pressures.

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A benefit of this approach is that it is the solution of a small set of equations, not a parameter optimization. Given that the number of equations is fixed at three, a very fast

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Newton’s method numerical solution can be constructed using an analytical inverse of the Jacobian matrix. This calculation only needs to be performed once to determine the ε of a component. In the case of pseudo-components within process simulators, the ε would be

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determined once at simulation initialization and would remain fixed.

Figure 4: Parity plot for ε calculated versus modified parameter library

As a test, we calculated ε using this approach and compared to our modified parameter

library. The overall agreement between ε calculated through Eq. (5) and the “data” ε from the modified parameter library is stunning. The average deviation over the component set is only 0.26%. The very tight parity plot is illustrated in Fig. 4. 10

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To complete our characterization model, a correlation is needed to estimate the number of aromatic carbons NA in the event that structural information is not available. This relation must depend only on MW, Tbp, and SG, as this is the only information that will be available for

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pseudo-components being generated from a boiling point curve. We first introduce the structural Watson-K factor (Wk) which gives a crude measure of the aromaticity of an oil sample[22] Tbp (R )

1/ 3

SG

(6)

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Wk =

Roughly, aromatics molecules tend to have Wk < 11, paraffinic molecules Wk > 12 and

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naphthenic molecules 11 < Wk < 12. We propose the following simple form for the fraction of carbons that are aromatic fA

0.5(1 − tanh (α 1 (Wk − α 2 ))) for Wk < 11.3 and SG > 0.85 NA  fA = = NC   0 Otherwise

(7)

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where we estimate the number of carbon atoms NC from MW and NA using the simple relationship (MWk is the molecular weight of atom k)

(8)

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MW ≈ N C (MWC + 2 MWH ) − MWH × N A

The conditions Wk < 11.3 and SG > 0.85 are meant to exclude non-aromatics. In Eq. (8) we

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account for the fact that an unbranched aromatic carbon will have one less hydrogen than an unbranched paraffinic carbon. Solving Eqns. (7) – (8) for NA we obtain NA =

MWf A MWC + 2 MWH − MWH f A

(9)

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We adjust the constants αj to best reproduce NA for all hydrocarbon molecules in our library which contain at least 1 aromatic core to obtain an AAD = 13%. These constants are listed in

α1

α2

0.472

11.2

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Table 3.

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Table 3: Constants to evaluate fA correlation

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We make no claim that this correlation is of quantitative accuracy; however it is suitable for our needs here. Ultimately, the purpose of NA is to include effects of liquid phase nonidealities which may exist between paraffinic and aromatic molecules. Since the dipole term is calculated prior to performing the flash dictated by Eqns. (5), any deficiencies in the estimation of NA will be absorbed into the calculation of ε. However, these deficiencies are rather small as

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the AAD of estimated ε for all aromatics in our library is 0.26% when the known NA is used to evaluate Eq. (1). Upon use of Eqns. (7) and (9) this error increases only slightly to 0.37 %.

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As a quick summary, we have developed a very simple parameter model for PC-SAFT which includes the effects of aromaticity. The PC-SAFT parameters m, σ and αp are calculated

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by the relations (3), (4) and (1) and ε is determined from the boiling point flash Eqns. (5). If only SG, MW, and Tbp are known, the number of aromatic carbons can be estimated by Eq. (9). We will call this new approach ExxonMobil petroleum characterization (EMPETRO). Figure 5 gives a visual outline on the required steps to evaluate EMPETRO.

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Figure 5: Outline of steps to evaluate EMPETRO parameter model

In general, for petroleum pseudo-components, SG and Tbp will be model input, with MW

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evaluated by correlation[23, 24] from these quantities.

III: Validation of hydrocarbon model

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In this section we perform a severe test of the characterization model developed in

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section II. We generate pseudo-data for defined components using ExxonMobil correlations for each molecule (which are fit to multiple data sources for most species present). We generate vapor pressures and liquid densities for each pure component in a temperature range which corresponds to T(Psat = 10 torr) to 90% of the critical point. If the correlation was not developed over this full range, we restrict the temperature range such that we do not extrapolate the correlations. We then compare this pseudo-data to PC-SAFT predictions with parameters estimated through EMPETRO.

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In Table 4 we report the AAD (average absolute deviation) in Psat and AAD in ρ. When we evaluate EMPETRO, we use correlation predicted NA through Eqns. (7) and (9); meaning no structural information was included to influence model predictions. Comparing Tables 2 and 4

Psat

ρ

n-alkanes

2.0%

1.2%

Aromatics

3.3%

Overall

2.8%

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AAD

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shows that EMPETRO gives a very good representation of the modified parameter set.

1.3%

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1.0%

Table 4: Average absolute deviations over hydrocarbons

Another advantage of our approach is the inclusion of the aromatic-polar map as described by Eq. (1). The inclusion of this term permits the separation of aromatic π-π attractions

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from standard dispersion forces experienced by non-aromatic molecules. This results in more accurate predictions of multi-component phase equilibria in the absence of binary interaction

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parameters (kij = 0).

Figure 6 illustrates the near quantitative accuracy of EMPETRO in the prediction of the

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naphthalene / dodecane binary VLE. Again, when EMPETRO is evaluated, we use correlation predicted NA through Eqns. (7) and (9); that is, no structural information was included to influence model predictions. EMPETRO allows for the accurate prediction of both pure component vapor pressures as well as the azeotrope. It is the inclusion of the aromatic-polar map that allows for the quantitative prediction of the azeotrope. This is demonstrated in Fig. 6 by the inclusion of PC-SAFT predictions using literature parameters without the aromaticity correction

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(dashed curve). While the literature parameters do qualitatively predict the azeotrope, they

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underpredict the non-idealities.

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Figure 6: Comparison of model predictions to experimental VLE data (red circles)[25] for the naphthalene / dodecane binary at P = 0.133 bar. Blue curve gives EMPETRO predictions and dashed curve gives predictions using literature parameters[11, 26] Representation of precise data for defined molecules provides the ultimate test of a

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generalized hydrocarbon model. If a PC-AFT model accurately represents all molecules (and binaries) which constitute petroleum, it will necessarily be accurate for the petroleum mixture.

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The reverse is not true. A parameter model could reasonably represent petroleum, but be inaccurate in the pure component limit. It is a requirement of our model that it accurately reduces to the pure component limit.

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Figure 7: Binary VLE predictions (curves) using EMPETRO with NA predicted by correlation Eq. (9), compared to experimental data (red circles). References: Propylbenzene / nonane[27],

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benzene / decane[27], benzene / methylcyclopentane[28], phenanthrene / hexadecane[29]

Figure 7 further highlights the accuracy in the prediction of binary phase equilibria using

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EMPETRO for low MW binaries such as benzene / methylcyclopentane to the high MW binary phenanthrene / hexadecane. Finally, Fig. 8 displays Txy diagrams for the multi-ring aromatic

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binary phenanthrene / anthracene. For each comparison EMPETRO gives nearly quantitative accuracy, using only Tbp, MW, and SG to develop the model parameters.

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IV: Inclusion of functional groups

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Figure 8: Same as Fig. 6. Data from ref[30]

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At this point we have neglected any contribution of heteroatoms. We have demonstrated that the thermodynamics of hydrocarbon fluids can be accurately described with simple parameter correlations. It is the simplicity of the approach which results in the accuracy,

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predictability, and broad applicability. Addition of heteroatoms represents a significant complication. However, as we modify the approach, we must ensure that in the absence of

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heteroatoms the model reduces to the form developed in section II.

Heteroatoms will contribute to the parameter models in several ways. First, additional

polarity contributions will accompany these atoms. To incorporate these additional polarity contributions, we define the total polar strength of a molecule as the sum over the polar strength of functional groups

α p = m∑ nk x p ,k µ k2 = ∑ nkα p ,k k

(10)

k

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where nk is the number of functional groups of type k in the molecule, and αp,k is the polar strength of a functional group of type k.

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For any given functional group (ethers, aldehydes, etc…) the polar strength is obtained as follows. For a representative molecule in the series (say 2-butanone for ketones), the parameters m, σ, ε, and αp are obtained by fitting the equation of state to saturated liquid densities, vapor

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pressures, and binary vapor liquid equilibrium data with a reference alkane. The binary data with the alkane is included to help separate the polar and non-polar contributions to the free energy.

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Hence, this polar strength yields the best predictability for multi-component phase equilibria. As all polar functional groups share an alkane reference, the polar-polar interactions between functional groups will be on equal footing. This consistency of treatment allows for a degree of model insight that might not be possible otherwise.

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Equation (10) will likely be accurate so long as functional groups are widely separated on a molecule. If two functional groups are in close proximity, Eq. (10) may over-predict the polar contribution; in this situation it may be advisable to define the two functional groups which

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are in close proximity as a new functional group.

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In determining modifications of the parameter correlations m and mσ3 we consider perturbations to the base hydrocarbon correlations in the form (where the subscript k represents group k)

m = mHC + ∑ nk f k( m ) k

(

mσ 3 = mσ 3

)

HC

(11)

+ ∑ nk f k(σ ) k

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The leading terms in these expressions are the base hydrocarbon correlations Eqns. (3)-(4). The second term on the RHS gives the first order correction for functional groups where f(a) is a to-

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be-determined constant.

A) Sulfur

Equations (10) and (11) provide a general methodology to include functional groups. In

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this sub-section, we demonstrate the application of this methodology to include sulfur as a functional group. Sulfur exists in petroleum as mercaptans, sulfides, thiophenes etc…. In a

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typical petroleum characterization, which gives the percentage of sulfur, the actual type of sulfur will be unknown. Initially in this work we consider sulfur to mean mercaptans or sulfides in linear and branched chains (no cyclics or aromatics). We then parameterize the model with this assumption. Once completed, we demonstrate that the methodology also works well for

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thiophenes, even though they were not included in the model development.

The polar strength of mercaptans and sulfides was set to an average value of the polar

(12)

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α p , S = 2.7

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strengths for both mercaptans and sulfides

With this parameter fixed, all other parameters m, σ, and ε were regressed to vapor pressures and liquid densities in the temperature ranges T(Psat = 1 torr) to 90% of the critical point. Our sulfur library consist of non-cyclic mercaptans (76.2 ≤ MW ≤ 174.3) and sulfides (62.1 ≤ MW ≤ 118.2), 40 molecules in total. We first develop the correction for the m correlation, as with the hydrocarbon models, we then refit the parameters of all 40 molecules subject to this m correlation and the polar strength in Eq. (12). 19

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AAD Psat

AAD ρ

Original

0.11%

0.05%

Modified

1.33%

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Parameter set

0.4%

Table 5: Average absolute deviations using original and modified parameter sets for sulfur

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molecules with a single sulfur atom

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As shown in Table 5, the modified parameter set, which was subject to an imposed m correlation, provides an accurate representation of the vapor pressure and liquid densities. From this modified parameter library we develop the correlation for mσ3. Equation (13) summarizes the model for sulfur containing hydrocarbons

(13)

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m = mHC − 0.05 N S ; mσ 3 = (mσ 3 )HC − 0.41N S

As with the base hydrocarbon model, the σ correlation is very tight with an AAD of 0.2%.

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When performing calculations involving S atoms, Eqn. (7) is no longer valid due to the fact that heteroatom containing molecules can have low Wk in the range of aromatic molecules.

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Therefore, it is not possible to discriminate between non-aromatic sulfur containing compounds and aromatic compounds that do not contain sulfur. Therefore, we assume that if information is provided on the fraction of various heteroatoms, that fraction of aromatic carbon will also be provided. In the following calculations, when we report model results for sulfur containing compounds, it is assumed that the number of aromatic carbon is also provided. This is in contrast

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to the results of section III, where the number of aromatic carbons was estimated using Eqns. (7) and (9).

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To validate the parameter model, we perform the same test as performed in section III, where we generate saturated liquid densities and vapor pressures from temperature ranges T(Psat = 10 torr) to 90% of the critical point. As previously, if the correlations were not developed over

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this full range, we restrict the temperature range such that we do not extrapolate the correlations. The results are shown in Table 6, and the agreement is quite good.

AAD

Psat

1.6%

ρ

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1.4%

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Table 6: Average absolute deviations over 40 hydrocarbons with a single sulfur atom

Figure 9: Model VLE predictions (blue curves) versus experimental data (red circles) for benzothiophene / dodecane[31] Figure 9 shows binary VLE predictions using EMPETRO for the non-ideal binary benzothiophene / dodecane. This binary is particularly interesting, since benzothiophene is 21

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composed of two functional groups - an aromatic ring and a sulfur atom embedded in a cyclic ring. Also, no thiophenes were included in the model development, so this represents a pure prediction. As shown, the model predicts the location of the azeotrope observed at these

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conditions.

B) Oxygen and nitrogen

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Inclusion of oxygen into the parameter model is complicated by the fact that the properties of oxygen containing molecules are strongly dependent on the type of oxygen. For

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example, alcohols hydrogen bond while ethers, ketones, and aldehydes do not (although they do not self-associate, they can cross-associate with other species). In addition, ketones and aldehydes have much stronger dipole moments than ethers. To properly describe oxygen, model parameters need to be developed for each of these functional groups. In this work we focus

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solely on ethers and carbon-oxygen double bonds meant to describe ketones and aldehydes; we denote this functional group a C=O group. The coefficients for ethers in Eq. (11) were developed from 11 non-cyclic ether molecules (46.1 ≤ MW ≤ 130.2). The coefficients for the C=O group

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were determined from 8 non-cyclic ketones (58.1 ≤ MW ≤ 100.2).

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Nitrogen is a much simpler atom than oxygen, in the sense that nitrogen molecules do not typically strongly self-associate (hydrogen bond). In the implementation of nitrogen into the parameter model, we assume that it belongs to an amine. To develop model parameters, we fit parameters to the following list of molecules: propyl amine, diisopropyl amine, dipropyl amine, pentyl amine, hexyl amine, dodecyl amine, hexadecyl amine, 2-aminobutane, and diethyl amine.

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Inclusion of oxygen and nitrogen into the parameter model follows the same approach as that described for sulfur. Like sulfur, for each group we add a correction to the base hydrocarbon

are summarized in Table 7.

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models, as well as add a polarity contribution. The final model results including all hetero atoms

αp,k (D2)

f k(m )

Aromatic ring

2.17

0

Sulfur

2.7

-0.05

-0.41

Ether (C-O-C)

1.75

0.24

-3.8

C=O

4.9

0.2

-1.2

Nitrogen

1

0.3

0

f k(σ )

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0

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Table 7: Functional group parameters

For ethers and C=O we have performed our standard pure component validation scheme as discussed in section III. The results are given in table 8. Again, EMPETRO is demonstrated

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table 5.

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to be accurate. No aldehydes were included in the development of the C=O parameters listed in

AAD

Ethers

Ketones

Aldehydes

Psat

0.84%

0.97%

1.31%

ρ

0.86%

1.8%

2.08%

Table 8: Average absolute deviations over 15 ethers, 8 ketones and 9 aldehydes

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Figure 10 shows Pxy diagrams for tetrahydrofuran (THF) / hexane. This represents a severe test of the model since no cyclic ethers were included in the model development and, given the small size of the molecule, the oxygen accounts for a significant portion of the

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molecular weight. Hence, the oxygen imposes a very substantial modification to the hydrocarbon backbone. As observed, the model accurately predicts both the pure component vapor pressures as well as the azeotrope resulting from liquid phase non-idealities induced by the polarity of

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THF. We conclude our analysis with Fig. 11, which compares model predictions and data for the binary methyl isobutyl ketone (MIBK) / heptane. EMPETRO accurately predicts the MIBK /

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hexane azeotrope.

Figure 10: Model predictions (curves) versus experimental VLE data[32] (red circles) for the

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tetrahydrofuran / hexane binary

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Figure 11: Model predictions (curves) versus experimental VLE data (red circles) for the MIBK / heptane[33] binary

V: Summary

We have developed a generalized hydrocarbon characterization model (EMPETRO) for

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the PC-SAFT EoS. We specifically employ the simplified PC-SAFT[14] form with the Jog and Chapman[12] dipolar term. The PC-SAFT parameters m and σ are calculated through the relations (3) and (4) with heteroatom corrections given in Table 7, and ε is determined from the

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boiling point flash Eq. (5). The polar strength of a molecule is given through the general relation

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Eq. (10). If a boiling point of the molecule is unknown, one can employ a variety of group contribution approaches to estimate Tbp.

The new approach was shown to be of nearly equal accuracy to the base PC-SAFT model

with molecule specific parameters. The magnitude of this advance is difficult to overstate. The result of this study demonstrates that, if one provides SG, MW, and Tbp of an unknown hydrocarbon molecule, the EMPETRO model will return PC-SAFT parameters that will

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accurately predict liquid densities and vapor pressures over a very wide temperature range. In addition, the polarity contributions allow for accurate mixture predictions.

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Equations (10) and (11) provide a general formalism to introduce additional functional groups and interactions among these functional groups. Future work will focus on the extension of this methodology to include additional functional groups. Also, we have not yet allowed for

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hydrogen bonding contributions. Therefore, future work will also focus on development of a

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hydrogen bonding parameter model such that alcohols can be included.

References:

4. 5. 6. 7. 8. 9.

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