Determination of Perturbed-Chain Statistical Association Fluid Theory

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Determination of PC-SAFT parameters for pure substances, SCN groups and petroleum fractions using the cubic EOS parameters Pouya Hosseinifar, and Saeid Jamshidi Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.5b03103 • Publication Date (Web): 22 Oct 2015 Downloaded from http://pubs.acs.org on October 23, 2015

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Industrial & Engineering Chemistry Research

Determination of PC-SAFT parameters for pure substances, SCN groups and petroleum fractions using the cubic EOS parameters Pouya Hosseinifar1, Saeid Jamshidi*, 2 1

2

MAPSA Technology Center, Tehran, Iran Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, Iran

Abstract New generation equation of state, perturbed-chain statistical association fluid theory (PC-SAFT), has attracted much attention to modeling the phase behavior of fluids using the molecular-based equations of state. A set of three pure component parameters is needed for non-associative compounds, conventionally determined by fitting vapor pressure and liquid density data, simultaneously. Unfortunately, experimental data are scarce and the number of pure substances is too large. Thus, it is indispensable for developing predictive methods to determine the pure component parameters. In the present paper, a new model has been developed to estimate PCSAFT parameters for different pure components, single carbon numbers (SCN) and petroleum fractions through the connection established between classical and molecular corresponding states theories and creating a relationship between cubic equations of state parameters (critical pressure, critical temperature and acentric factor) and PC-SAFT parameters. Accordingly, the proposed model requires five input parameters which are critical pressure (Pc), critical ∗ temperature (Tc), acentric factor (ω), mass density at 288 K ( ) and molecular weight (Mw). A comparison is performed between the proposed model and the old existing correlations used to estimate pure component PC-SAFT parameters. Moreover, experimental vapor pressure and liquid phase density data of 53 pure substances from 14 diverse families of compounds (in addition to data applied for the development of model) were collected to verify the accuracy of parameters estimated by the proposed model in the calculation of vapor pressure and liquid phase density. Experimental bubble pressure and liquid density data of three oil samples were also collected in order to check the reliability of the proposed model in the estimation of PC-SAFT parameters for SCN groups and petroleum fractions. Results of the comparison show that the proposed model is capable of estimating PC-SAFT parameters for both pure substances and SCN groups with average absolute deviations less than 1.21% and 1.05% of saturation pressure and liquid density, respectively. Keywords: Vapor pressure; Equation of state; Predictive method; PC-SAFT; SCN groups; Petroleum fractions

* Corresponding author, Tel.: +98 21 66166412, fax: +98 21 66022853. E-mail addresses: [email protected], [email protected]

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1. Introduction Precise predictive models for the calculation of thermodynamic properties and describing the fluid phase behavior of pure compounds and mixtures are of especial importance for the optimization and design of new processes in chemical and related industries. Over the years, many different approaches have been proposed including activity coefficient models and cubic equations of state for the calculation of phase equilibria. Two commonly used cubic equations of state, especially for hydrocarbon fluids, are Peng–Robinson1 and Soave–Redlich–Kwong2 equations applying the volume translation methods suggested by Peneloux and Rauzy,3 Yu and Lu,4 Tsai and Chen5 and Mathias and Naheiri6 to correct the predicted molar volumes. The accuracy of these models are usually restricted to specific types of systems and limited conditions. There are essential requirements for models which are capable of describing behaviors of complex fluids and macromolecules. Nowadays, molecular-based equations of state have been developed based on the principles of statistical mechanics. A concept lately proposed in such equations by Chapman et al.7 and Huang and Radosz,8,9 is the statistical associating fluid theory (SAFT). They have extracted the SAFT model from the first order thermodynamic perturbation theory (TPT1) of Wertheim.10-13 Over the past decade, several considerable attempts have been made in order to extend SAFT model to become more applicable for various types of fluids. A plethora of improvements and modifications of SAFT have been published which can widely cover miscellaneous pure components and complex mixtures. Walsh et al.14 could amend the dispersion term of SAFT to consider multipolar interactions. Jackson et al. and Green and Jackson15,16 proposed a simple form of original SAFT that is called hard sphere-SAFT (SAFTHS). Muller and Gubbins17 derived a modified SAFT for pure water which improves repulsive and attractive interactions through a Lennard-Jones18 potential function. Banaszak et al.19 developed a SAFT model for heteronuclear chains that is known as copolymer SAFT. Blas and Vega20,21 used a Lennard-Jones reference fluid22 instead of the hard-sphere fluid in the original SAFT. Gil-Villegas et al.23 substituted hard sphere reference fluid by some more accurate intermolecular potential functions such as square-well, Sutherland, Yukawa and soft repulsive fluids so that the attractive term of potential function would vary in a variable range called SAFT-VR. Recently, the Perturbed-Chain statistical associating fluid theory (PC-SAFT) has been developed by Gross and Sadowski,24,25 based on the second order perturbation theory of Barker and Henderson.26 PC-SAFT was introduced to describe the phase behavior of complex fluids especially systems with large differences in molecular weight such as polymer systems. Most SAFT models need five parameters for pure associative compounds among which three parameters are employed for non-associative fluids. These parameters are typically determined by the experimental vapor pressure and liquid phase density data over wide temperature ranges. Unfortunately, such experimental data are scarce and the number of pure substances is too large. Moreover, in many cases experimental data cannot even be measured for complex compounds and high molecular weight substances. Therefore, robust and predictive methods are required to estimate parameters of SAFT models for a wide range of components. Huang and Radosz8 suggested correlations of SAFT-HS parameters in terms of the average molecular weight for poorly characterized oil fractions. The correlations are given in terms of the different families, for instance n-alkanes, poly-nuclear aromatics, etc. Blas and Vega20 derived the equations estimating the molecular parameters of SAFT-VR for normal alkanes using their molecular weight. Similar expressions have also been proposed by Mccabe and Jackson27 for the prediction of SAFT-VR parameters. Kouskoumvekaki et al.28 developed a method for the estimation of pure-component PC-SAFT parameters for polymers. Ferrando et al.29 proposed a new 2 ACS Paragon Plus Environment

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methodology to determine association parameters (energy and volume) of PC-SAFT EOS for hydrogen-bonding molecules, using molecular simulation technique. Tihic et al.30 suggested different correlations to estimate PC-SAFT parameters for families of compounds in which molecular weight is needed as the input parameter. Although these linear correlations are able to estimate SAFT parameters for various substances, in most cases do not have sufficient precision and exhibit a large deviation in the estimation of molecular parameters. Another alternative which can present more accurate results for the parameter estimation is the group contribution approaches. Huynh and et al.31 developed a group contribution method to predict the pure component parameters of three version of SAFT: PC-SAFT, SAFT-VR and the original SAFT. In fact, they extended the method proposed by Tamouza and et al.32 for the calculation of saturation pressures and liquid densities of polyaromatic hydrocarbons. Burgess and et al.33 have also proposed a new group contribution method to calculate PC-SAFT parameters for alkanes, aromatics and cycloalkanes. Unfortunately, such methods cannot be used for a mixture with unspecified components and compositions such as SCN groups and petroleum fractions due to the need for the structural information of substances. In this study, we intend to develop a new model to predict PC-SAFT parameters for different pure components, SCN groups and petroleum fractions through creating a relationship between cubic equations of state parameters (critical pressure, critical temperature and acentric factor) and PC-SAFT parameters. PC-SAFT EOS can provide promising results in the prediction of fluid phase behavior and would be a good alternative to the cubic equations of state, especially for complex mixtures. A careful study has also been carried out by Leekumjorn and Krejbjerg,34 regarding the comparison of PC-SAFT and cubic equations of state. Their investigation showed that although the popular and widely used cubic equations of state can generally capture the phase behavior of different fluids, they don’t completely meet all requirements and expectations (for instance in predicting the gas compressibility factor and oil compressibility). However, we focused our attention to PC-SAFT model and strived to predict the molecular parameters of PC-SAFT using the cubic equations of state parameters. Such a connection has already been conducted between PC-SAFT parameters and critical properties by Polishuk,35 which leads to appearing critical point based PC-SAFT or CP-PC-SAFT. This method requires the critical constants and the triple point liquid density data for the numerical solution of complicated implicit equations to predict the pure component PCSAFT parameters. In the proposed model, a novel approach is applied connecting molecular parameters of PC-SAFT EOS to the critical properties of cubic equations of state. Afterwards, applicability of the proposed model are evaluated for pure substances from 14 diverse families of compounds and three oil samples. The results obtained from the proposed model are then compared against those of yielded by CP-PC-SAFT method and the old linear correlations previously proposed by Tihic and et al.30 2. Perturbed-Chain SAFT equation of state From PC-SAFT point of view, each molecule can be conceived as a chain comprised of freely jointed homogenous spherical segments. In fact, the chains are ingredients of a fluid which are characterized by three parameters for non-associative compounds. The three parameters are the number of segments per chain (m), the segment diameter (σ), and the depth of the pair potential (ε/k). All interactions between molecules are divided into two repulsive and attractive parts. A reference fluid without any attractive interactions should be defined to determine the repulsive contribution and attractive interactions can be considered as a perturbation to the reference fluid. In the framework of PC-SAFT proposed by Gross and Sadowski,24,25 the residual Helmholtz free energy is separated into hard-chain reference fluid and the dispersion contribution: 3 ACS Paragon Plus Environment


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= + Hard-chain reference contribution is given by: = − ∑ − 1 ln = ∑ =

ζ1 ζ2 ζ0 ζ3

( = #

1

+

+% $

ζ"!

# ζ3 $

&

) *

(1) (2) (3)

! ! + % ! − ζ0 & ln#1 − ζ3 $'

ζ"

ζ2

ζ"

+%

) *

&

,

(4)

,ζ!!

"

) + * # ζ $

) + * # ζ3 $ 3 ζn = . ∑ /0 , 2 ∈ 40,1,2,38 ? / 9 = :1 − 0.12 ) BC @A

ζ3

!

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(5) (6) (7)

Where is the mean segment number in the mixture; is the Helmholtz free energy of the hard-sphere fluid, ( is the radial distribution function of hard-sphere fluid and / is the temperature dependent segment diameter. The dispersion contribution of the Helmholtz free energy is expressed as: , G − D ,G , HHHHHHHHH HHHHHHHHHH = −2DE F, I E, F, (8) I = >1 +

+ 1 −

,MK ,NK ! +,K" ,K L B O K, KP! R)* HHHHHHHHH , G = ∑ ∑( Q Q( ( >@A B ( R)* , HHHHHHHHHH , G , = ∑ ∑( Q Q( ( >@A B ( ( = , # + ( $ JK ,K ! KL

G( = SG G( #1 − T( $ E F, = ∑.UM F . E, F, = ∑UM V F = M + > V = VM + >

B + >

B V + >

B>

B>

B ,

,

,

(9)

(10) (11) (12) (13) (14) (15) (16)

B V,

(17) , HHHHHHHHH Where I is an abbreviation for the compressibility expression, G and HHHHHHHHHH , G , are also abbreviations for intermolecular segment-segment interactions between two chains. Conventional combining rules are used to calculate PC-SAFT parameters for a pair of unlike segments. Integrals of the perturbation theory are introduced by E and E, as simple power series in density where coefficients and V are related to the chain length according to eq 16 and eq 17. The universal PC-SAFT model constants M , , , , VM , V and V, have been determined by Gross and Sadowski,25 are given in Table 1. More details about PC-SAFT model can be found in the original paper.25 3. Development of the proposed model Several attempts have been made to present an accurate method which is capable of predicting PC-SAFT parameters based on physical properties of substances such as molecular weight. Most of the existing correlations have merely employed molecular weight as an input parameter that decreases abilities of models in the diagnosis of diverse molecular structures, especially if two different components have the same molecular weights. In this work, we strived to make a relationship between PC-SAFT parameters and cubic EOS parameters by applying molecular 4 ACS Paragon Plus Environment

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weight and mass density. For this purpose, a connection between macroscopic and microscopic theories of corresponding states should be established, upon which the proposed model will require to take critical pressure, critical temperature, acentric factor, molecular weight and mass density as input parameters, in order to estimate all three PC-SAFT parameters (m, σ and ε/k). 3.1. Two parameter classical and molecular theories of corresponding states Classical or macroscopic theory of corresponding states was developed based on the mathematical properties of the macroscopic equation of state and from the principle of continuity of gaseous and liquid phases at the critical point. According to this theory there exists a universal function for volume, temperature and pressure which can be expressed as: W> , X

A

, B=0 Z

XY AY ZY

(18)

Where subscript c refers to the critical point. In other words, if the equation of state is written based on reduced variables for any fluid, that equation will also be credible for any other fluid. Similarly, molecular or microscopic theory of corresponding states, was expressed using mathematical properties of potential energy function. The potential function can be written in the dimensionless form as a universal function of the dimensionless distance of separation between molecules given by: [)* = W > B (19) R \

In this equation, G is the energy parameter, denotes the distance parameter characteristic of the interaction between two molecules and ]( is the potential energy of a pair of molecules. Calculating the canonical partition function of a system will lead for the macroscopic thermodynamic properties to appear which can be employed in the definition of reduced quantities used in the molecular corresponding states theory36 as follows: )

)

= W ∗ > R , _\" B (20) ∗ Where, W is a universal function which depends only upon the nature of the potential function in eq (19), k is Boltzmann’s constant and N is the number of molecules. This theory is analogous to the classical theory of corresponding states and therefore a connection between the parameters of one theory and those of the other can be established. There exist two independent parameters (an energy parameter and a distance parameter) in the microscopic corresponding states theory and there are three parameters (` , 9 and a ) in the macroscopic theory that only two of them are independent, because the compressibility factor at the critical point is the same for all fluids (b = a ` /d9 ). Hence, macroscopic critical properties can be related to molecular parameters through the connection between classical and molecular corresponding states theories, upon which three proportions are concluded: R ∝ 9 (21) @ ∝ ` (22) R ∝ a (23) @\" Since, critical temperature can be regarded as a measure of the kinetic energy of the fluid, the proportionality between energy parameter (G/T) and critical temperature (Tc) is reliable. The critical volume can also be considered as an indicative of the size of the molecules, so the proportionality between distance parameter ( ) and critical volume (` ) is reasonable. According to the classical corresponding states theory, the compressibility factor (b ) is the same for all fluids and a ∝ 9 /` . Hence, the proportionality of the critical pressure to the ratio (G/T ) is also credible. Z\" R

@A

^

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3.2. Relating PC-SAFT parameters to macroscopic parameters From the classical corresponding states theory, it can be concluded that ` ∝ 9 /a . The ratio 9 /a is able to determine through dividing eq (21) by eq (23), which is expressed as 9 /a ∝ . This proportionality can also be confirmed by the combination of eq (22) and ` ∝ 9 /a , that gives 9 /a ∝ . On the other hand, in PC-SAFT model each molecule is described by a chain comprised of m spherical segments and such proportion can be written for a chain as follows: A ∝ > Y B (24) ZY

Another expression will also be obtained from the multiplication of eq (21) and eq (24) which is given by:

∝ > R

@

AY ! ZY

B

(25)

It should be noted that, PC-SAFT parameters for a large variety of compounds have been determined by Gross and Sadowski24,25 and Tihic et al.30 through fitting experimental vapor pressure and liquid phase density data. In this study, experimental data regarding 14 different groups were collected,25,30 in order to develop the proposed model. As given in eq (25), a proportionality between molecular parameters of PC-SAFT model and macroscopic parameters of the cubic EOS has been appointed. Accordingly, the ratio #9 , /a $/ G/T was plotted versus molecular weight for the collected data and a linear trend was observed for each specific group as illustrated in Figure 1. Such trends are also observable for eq (24) if the ratio 9 /a / is plotted against molecular weight of different families of compounds. Therefore, eqs (24) - (25) can be written in the below forms: AY /ZY ≈ ghi + j (26) \" AY ! /ZY

\" R/@

≈ gk hi + j k

(27)

As indicated in Figure 1, in spite of concentrating data on different straight lines, a dispersing behavior is still remained and the correlation coefficients are not accurate enough. A portion of errors arise due to the fact that the theories of corresponding states expressed by eqs (18) and (20) are two-parameter theories limited to simple and symmetric molecules. For more complex molecules, it is necessary to apply at least one additional parameter to construct a three parameter theory of corresponding states. Therefore, all proportionalities concluded by two parameters corresponding state theory are not able to accurately describe the behavior of complicated and asymmetric molecules. In order to rectify this difficulty, five adjustable variables were defined in eq (26) which can easily be assessed through an optimization process and make the model applicable to complicated fluids. Rearranging eq (26) and defining new adjustable parameters leads to the following expression: = l

AY /ZY

rL

mno pq r! +n" s

nu

t

(28)

Similarly, eq (27) can be rewritten in terms of six adjustable variables by substituting eq (28) in eq (27) as follows:


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y w

R

@

=

∗ 9 ∗

w

AY ! /ZY

(29) o x {Y /|Y u m! pq " +L s w wz r r! ~r C L :r } v o q " Where , … , in eq (28) and , … , . in eq (29) are the adjustable coefficients, which should be tuned to the experimental data of each families of compounds. 3.3. Relating the first order perturbation theory to the attractive term of the cubic EOS In the previous section, two equations were extracted from the proportionality of the molecular and macroscopic parameters. Another equation will also be required to estimate the number of segments in a chain. For this purpose, a connection between attractive term of the PengRobinson EOS and the first order perturbation theory was performed. The absolute value of temperature dependent attractive term existing in PR EOS is given by: ||Z = 9, (30) In this equation, 9, is the temperature dependent function and the parameter is a constant relating to critical properties. The proportion ∝ #9 , /a $ can be resulted from the definition of constant . Comparing this proportionality to eq (25) gives ∝ G/T and the following expression is concluded by substituting ∝ G/T in eq (30): R ||Z ∝ > B × ∗ 9 ∗ , (31) @ In order to keep constant the influence of temperature on attractive forces, the constant temperature T* = 288 K was considered to account for all temperature dependent parameters. Hence, the superscript * indicates the value of a parameter at T* = 288 K. The choice of T* = 288 K is based on the temperature upon which specific gravity is defined, because the mass density at 288 K will be required as an input parameter in the proposed model and can easily be calculated in this temperature. According to Peng-Robinson equation of state the temperature dependent function at T* is defined by: , = 1 +

−0.176,

+ 1.574 + 0.48 %1 − A &' A∗ Y

,

(32)

Where ∗ denotes the temperature dependent function at the constant temperature T* = 288 K and is the acentric factor. On the other hand, all attractive forces in PC-SAFT framework are expressed in the term of perturbation contribution to the Helmholtz free energy of the system as follows:

o ! = @_A + @_A (33) @_A Where g and g, are the first and second order perturbation terms, respectively. The first order perturbation term was only considered for the purpose of relating PC-SAFT attractive term to that of Peng-Robinson EOS, which for a pure fluid of homo-nuclear chains its absolute value is expressed as below:

Z A

@_Ao ∗ = 2D >A ∗ B ∗ , @ E∗ F∗ , (34) * ∗ ∗ In the above equation, is the total number density at T = 288 K, F is the packing fraction at T* = 288 K and E∗ is an abbreviation defined by eq (14). Although eq (30) and eq (34) are different in dimensions, both of them can be considered as a measure of attractive forces and their ratio exhibits a regular trend. This ratio is obtained by dividing eq (30) by eq (34) as follows:

R



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|||

=

|||

= §∗ ¨∗ K∗ ,

|o /@_A ||¡¢£¤¥{

¦ ∗ #\" R/@$

,-/A ∗ §∗ ! \" R/@ö∗ K ∗ , ∗

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(35)

The term 2D1/9 is always constant for all substances and can be omitted from the ratio. The simplified form of eq (35) is given by: |o /@_A ||¡¢£¤¥{

¦∗

(36)

o

Similar to the same procedure previously performed for eqs (26) and (27), calculated values of eq (36) were plotted against molecular weight for different families of compounds and a fairly good linear behavior was observed for each group, upon which the following expression can be written: ¦∗ ∝ g© hi + j © (37) ∗ ∗ ∗ § ö K ,

Furthermore, the new adjustable variables were defined for the enhancement of model estimation power. So, eq (37) can be rewritten in terms of adjustable parameters as below: ¦∗

§∗ ö∗ K ∗ ,

∝ mª hi «! + ª s

«L

(38)

Rearrangement of eq (38) gives the following equation: ¦∗ E∗ F∗ , = ¬L §∗ m«o pq ¬! +«" s

(39)

Regarding to eq (14) and eq (16), an expression can be drawn out for the left hand side of eq (39) as presented below: , E∗ F∗ , = M + − 1 + > − 3 + B , (40) M = ∑.UM M F∗ (41) . ∗ = ∑UM F (42) . ∗ , = ∑UM , F (43) Where M , and , are the constant coefficients given in Table 1, F ∗ is the packing fraction at T* = 288 K and m is the number of segments in a chain. Substituting eq (40) in eq (39) gives: , ¦∗ M + − 1 + > − 3 + B , = (44) ¬L

§∗ m«o pq ¬! +«" s

The aforementioned equation can be expressed as a second-degree polynomial in terms of the segment number, as follows:

M + + , , − l + 3, +

¦∗

¬L

§∗ m«o pq ¬! +«" s

t + 2, = 0

(45)

The conditions of roots and the number of real roots in eq (45) depend upon the determinant ∆ (delta), which is defined by: ∆= l + 3, +

¦∗

¬L

§∗ m«o pq ¬! +«" s

,

t − 8, M + + ,

(46)

It is assumed that ∆> 0 and eq (45) has two real roots. The authenticity of this assumption can be guaranteed by determining the adjustable variables ª , … , ª° so that, the first term in eq (46) will sufficiently enlarge to overcome the second term. The greater real root of eq (45) was considered as an appropriate equation to estimate the number of segments in a chain as follows: =

z±o +±! +

²∗

¬L + √∆ ³∗ :¬o }q ¬! ~¬" C

,± +±o +±!

(47)


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Another adjustable variable ª is also added to eq (47) in order for it to be more flexible in the optimization process and the final form of the equation is the absolute value of eq (47) to the power of ª as: = µµ

z±o +±! +

²∗

³∗ :¬o }q ¬! ~¬" C

,± +±o +±!

¬L + √∆

«u

µ µ

(48)

The packing fraction at T* = 288 K, required to calculate M , and , in eqs (41)-(43) is obtained from the combination of eq (6) and eq (7) as:

F∗ = ∗ :1 − 0.12 ∗ BC (49) . @A The term in the above equation can be substituted by the same expression as given in eq (28), which leads for five additional adjustable parameters to appear in the estimation of m as indicated below: -

R

F = . l ∗

-

∗

AY /ZY

¬¸

m« pq ¬¶ +«· s ∗

«o

t

:1 − 0.12 @A ∗ BC R

(50)

In eq (50), denotes the total number density. The molar density in units of mol/m3 is achieved from the total number density as ∗ /¹ × 10M and the mass density at T* = 288 K is given by: ∗ =

§∗ pq ×M!L _¤

(51)

∗

In this equation, indicates the mass density in units of g/cm , ¹ = 6.022 × 10, mol-1 is Avogadro’s number and hi is the molecular weight. Rearranging eq (51) yields a useful relation to calculate ∗ , based on molecular weight and mass density at 288 K as follows: § ∗ _¤ ∗ = º × 10 ,° (52) p 3

q

This relation can be substituted in all the above equations where total number density is presented. 3.4. Optimization of the model constant coefficients As previously discussed, pure component PC-SAFT parameters have been reported for a large number of compounds in the literature.25,30 These parameters were employed as real values in order to assess the constant coefficients of the proposed model for 15 diverse groups indicated in Table 2. About 80% of the available data was used for optimization while the remaining 20% was employed to validate the proposed model. The Nelder-Mead optimization algorithm37 was applied to minimize the following objective function: »W = _ ∑_ U %

¼) ¼)¡ ¼)¡

,

&

(53)

Here, ¹ is the number of real data points, ½ represents the ¾ ¿ real data point which can be substituted by each of three , G/T and . Similarly, ½ denotes the calculated parameter corresponding to ½ . Developing relations given in eq (28), eq (29) and eq (48), for the estimation of , G/T and encompass five , … , , six , … , . and ten ª , … , ªM adjustable parameters, respectively that should be tuned to the available real data. All equations were separately implemented in eq (53) and the model constant coefficients were determined for each family, exclusively. Moreover, one set of constant coefficients was also assessed for single carbon number (SCN) groups and petroleum fractions used in reservoir fluids analysis. It is assumed that SCN groups contain paraffinic, naphthenic and aromatic compounds (PNA). 9 ACS Paragon Plus Environment


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Physical properties for these pseudo components have been reported in many studies, such as Whitson,38 Riazi and Al-Sahhaf39 and Katz and Firoozabadi.40 The real PC-SAFT parameters of the three mentioned families (PNA) were collected among available data to optimize the model constants for pseudo components. Indeed, petroleum fractions can be considered as SCN groups described by their properties such as molecular weight and mass density. Although, these pseudo components are hydrocarbon mixtures with unspecified components and compositions, each constituent within them will impress total physical and critical properties of petroleum fractions. Therefore, the proposed model will be able to estimate PC-SAFT parameters for such pseudo components if the model adjustable parameters are optimized based on all pure component PCSAFT parameters existing in petroleum fractions. Table 3 indicates optimized values for constant coefficients required to estimate that should be applied to obtain the segment diameter () after estimating the number of segments. Table4 and Table5 represent optimized values for adjustable parameters given in eq (29), eq (48) and eq (50) needed to estimate G/T and .

4. Results and discussion The new proposed model has been accurately evaluated, in order to estimate the pure component PC-SAFT parameters. For this purpose, real values of PC-SAFT parameters reported in the literature25,30 were compared to those predicted by the proposed model for all different groups of pure substances and petroleum fractions. Average absolute errors for each case is presented in Table 6. Furthermore, another comparison was also performed between PC-SAFT parameters estimated by the old existing correlations suggested by Tihic et al.30 and the real PC-SAFT parameters for all mentioned groups, the results of which are given in Table 6. According to Table 6, the total error occurred in results estimated by the old correlations (Tihic et al.) is 12.23% for the number of segments (), 5.78% for the segment diameter () and 11.86% for the depth of the pair potential (G/T). The corresponding results obtained from the proposed model indicated a notable reduction in the level of errors, so that the total error would decrease to 2.68% for the number of segments (), 1.39% for the segment diameter () and 2.26% for the depth of the pair potential (G/T). Although, the proposed model requires more input parameters in the prediction of PC-SAFT parameters in comparison to the old linear correlations, its outcomes are more accurate. 4.1. Verification of the model reliability for pure substances In order to check the reliability of the proposed model, about 53 elected pure components from all families of compounds were employed to calculate their vapor pressures and liquid phase densities. Initially, PC-SAFT parameters for all collected substances were estimated using the proposed model, and the vapor pressures and liquid densities were then calculated for each component in a wide range of temperatures. Experimental vapor pressure and liquid phase density data of pure substances extracted from the DIPPR correlations41 were compared to those obtained from the PC-SAFT equation of state in three different cases. In the first case PC-SAFT parameters were estimated by the proposed model; in the second case PC-SAFT parameters were determined by Tihic et al.’s correlations and in the third case PC-SAFT parameters are assessed by fitting experimental data. All comparison results are presented in Table 7. Although accurate experimental data on thermodynamic properties (such as vapor pressure and liquid density) of light or medium molecular weight alkanes have been measured, the experimental investigation of heavier alkanes are difficult, especially at high temperatures above 600 K. In most cases, more than one set of PC-SAFT parameters have been reported for heavy alkanes due to existence of nuance differences among the measured experimental data used to optimize PC-SAFT 10 ACS Paragon Plus Environment

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parameters. The proposed model is capable of estimating PC-SAFT parameters for heavy alkanes up to Hexatriacontane in wide temperature ranges, while linear correlations suggested by Gross and Sadowski,24,25 have only verified chosen normal alkanes from ethane to normal eicosane. Table 7 shows the average absolute errors in the estimation of vapor pressure and liquid phase density for five selected alkanes are 2.21% and 0.93%, respectively. Similarly, the same comparisons were also carried out for other families of compounds, the results of which are given in Table 7. The total error in the calculation of vapor pressure and liquid phase density of all 53 selected pure components are: 1.21% and 1.05% for the proposed model, 5.67% and 5.39% for Tihic et al.’s correlations, 0.99% and 0.91% for fitted parameters, respectively. Moreover, coexisting density curves were plotted for four different substances (ethane, i-C5, benzene and toluene) in order to check the shape of phase envelops created by proposed model parameters compared to the experimental data as illustrated in Figures 2-3. It is clearly observable that the parameters estimated by the proposed model could well capture the experimental data and exhibit sensibly more accurate shapes of phase diagram in comparison with old existing correlations. Another evaluation was also conducted to compare the results of the proposed model, Tihic et al.’s correlations and fitted parameters for all 274 pure substances existing in the data base, in addition to comparison previously performed between the mentioned approaches for 53 pure substances to check the model validation. The average absolute deviations in the prediction of saturation pressure and liquid phase density were calculated using PC-SAFT equation of state for all three methods and it was found that the proposed model considerably yields better results compared to Tihic et al.’s correlations. In the next step, the estimation power of proposed model was compared against CP-PC-SAFT method for 28 pure components existing in the data base as given in Table 8. PC-SAFT parameters were once estimated by the proposed model and once again were determined using CP-PC-SAFT method. Afterwards, both estimated parameters were employed to calculate the saturation pressures and liquid densities. Figures 4-5 illustrate the average absolute errors in predicting the saturation vapor pressures and liquid densities when PC-SAFT parameters are estimated by the proposed model, fitted to the experimental data and calculated by CP-PC-SAFT method for 28 pure substances at the temperature ranges given in Table 8. These figures indicate that despite the simple nature of proposed model in comparison with CP-PC-SAFT approach, the results are more accurate for the prediction of both saturation pressures and liquid densities. However, Polishuk35 has also noted that a major drawback of CP-PC-SAFT approach is a poor accuracy of predicting the vapor pressures of heavy compounds away from their critical points. 4.2. Verification of the model reliability for reservoir fluids Due to the fact that the natural gas and crude oil mixtures contain more than thousands of different components, no attempt is usually made to diagnose all the hydrocarbons beyond C5 and therefor SCN groups are used in the analysis of reservoir fluids. In order to describe a multi component system consisting of well-defined components and SCN groups thermodynamically by an equation of state, all EOS parameters for SCN groups must be determined. In the proposed model, critical pressure, critical temperature, acentric factor, mass density at 288 K and molecular weight are needed to estimate PC-SAFT parameters for SCN groups and plus fraction in a reservoir oil sample. Experimental values of specific gravity and molecular weight are usually measured for petroleum fractions and SCN groups, but their critical properties should be estimated. Several methods and correlations have been developed to calculate critical properties of petroleum fractions and SCN groups based on their physical properties, including investigations by Twu,49 Kesler and Lee,50 Riazi and Daubert,51 Cavett,52 Edmister,53 Korsten,54 11 ACS Paragon Plus Environment


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and Hosseinifar and Jamshidi.55 In this study, Hosseinifar-Jamshidi method was used for determination of petroleum fraction physical properties required to estimate PC-SAFT parameters through the proposed model. Furthermore, a condensate sample (Oil 1), a black oil sample (Oil 2) and a gas sample (Oil 3) were selected to calculate their bubble pressures and liquid densities using PC-SAFT equation of state. All three samples were characterized with the proposed model and the estimated PC-SAFT parameters are given in Table 9. These parameters were then employed to predict the bubble pressure and liquid phase density of samples by applying PC-SAFT model. Experimental bubble pressure at reservoir temperature and liquid phase densities measured in the differential liberation test (DL) were compared to results predicted by PC-SAFT equation of state for all three samples, upon which the average absolute errors for the bubble pressure calculations are 9.23%, 10.77% and 7.57% for Oil 1, 2 and 3 respectively. Similarly, the average absolute errors in predicting the liquid densities are 8.42%, 9.14% and 6.45% for Oil 1, 2 and 3 respectively. It has to be noted that, the plus fractions contain large concentrations of high molecular weight components which cause many difficulties in their characterization. This problem leads to produce a considerable amount of error in the prediction of bubble pressure, liquid density and other properties. One solution to overcome the problem is splitting the plus fractions into single carbon numbers through an appropriate method to achieve the more accurate characterization of plus fractions, but here PC-SAFT parameters of plus fractions were estimated using the constant coefficients determined for the SCN groups and petroleum fractions and the created deviations were declined by considering PC-SAFT parameters of plus fraction as adjustable parameters must be tuned to the experimental data of reservoir fluids for reduction of errors arising due to the difficulties in characterizing the plus fractions. Table 9 indicates tuned PC-SAFT parameters for plus fractions along with parameters previously estimated by the proposed model. In fact, estimated parameters for plus fractions can be employed as a good starting point in the tuning process in order to achieve the new adjusted parameters. The results obtained by PC-SAFT equation of state in predicting the bubble pressure and liquid phase density for three oil samples before and after tuning process showed that the parameter tuning process for plus fractions could significantly reduce error values, such that average absolute errors in the prediction of bubble pressure would decrease to 0.11 %, 0.21% and 0.14% for Oil 1, 2 and 3 respectively, and the corresponding error values for liquid phase density would reduce to 1.11%, 1.36% and 0.51% for Oil 1, 2 and 3, respectively. Table 10 shows the detailed results of calculations in all pressure steps of differential liberation simulation before and after parameter tuning of plus fractions for each oil samples along with their average absolute errors. It should be mentioned that the model constant coefficients determined for SCN groups and petroleum fractions have been optimized based on the pure component data of paraffinic, naphthenic and aromatic compounds. Hence, the proposed model may exhibit a significant deviation in the estimation of PC-SAFT parameters for heavy oil samples containing high concentrations of poly aromatic, resin and asphaltene compounds. In such cases, the parameter tuning process for plus fractions can sensibly reduce error values. 4.3. Sensitivity of the proposed model with respect to the input parameters According to eq (28), eq (29) and eq (48), the proposed model takes critical pressure, critical temperature, acentric factor, mass density at 288 K and molecular weight as input parameters to estimate PC-SAFT parameters. The accuracy of output results obtained from PC-SAFT equation of state severely depend on its input parameters. The influence of PC-SAFT parameters accuracy on modeling the phase behavior has been verified for many systems in the literature.25,30 In this 12 ACS Paragon Plus Environment

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section, we intend to evaluate how much estimated PC-SAFT parameters by the proposed model can be affected by the errors occurred in the measurement of the required input parameters. Besides the effect of input parameters, the values of the model constant coefficients may impress the sensitivity of model. As can be seen in Tables 3-5, there exists an obvious difference between the adjusted values of the constant coefficients for various groups (especially the values of ª in Table 5) that will definitely influence model sensitivity. Therefore, in order to verify the sensitivity of the proposed model, a specified range of error was deliberately provided for each input parameter from -30% up to +30%, while other parameters were kept constant with their real values. Figures 6-8 illustrate the average absolute errors in the estimation of PC-SAFT parameters due to deviations provided for each input parameter for all groups. It is worth noting that, critical properties, mass density and molecular weight are measurable and available with high accuracy for a large number of pure substances. According to Figures 6-8 the maximum level of uncertainty which may occur in the measurement of input parameters is usually less than 10% that leads to errors below 4% in the estimation of PC-SAFT parameters for all families of compounds, compared to the situation when real values of input parameters have been applied for the estimation of PC-SAFT parameters. The importance of the model sensitivity becomes mainly apparent in the case of SCN groups and petroleum fractions, because the measured molecular weight for petroleum fractions can contain a high level of uncertainty (sometimes about ±25%). In addition, critical properties and specific gravity of petroleum fractions that must be estimated by the proper correlations may include different considerable uncertainties, depending on the method which has been used. It is observable from the Figures 6-8 that, model constant coefficients for petroleum fractions have been optimized in such a way that the sensitivity of model be the lowest with respect to its input parameters. Hence, PC-SAFT parameters being estimated by the proposed model will be less affected by deviations resulting from the measurement or calculation of the input parameters as much as possible. More explanations about the use of sensitivity analysis results indicated in Figures 6-8 are presented in supporting information section, in order to enhance the estimation power of proposed model. 5. Conclusion The model presented in this paper, has been developed based on the connection established between macroscopic and microscopic corresponding states theories and the comparison which was carried out between the attractive term of PC-SAFT model and the similar term in PengRobinson equation of state, in order to derive the relationships which are capable of estimating PC-SAFT parameters for pure components and SCN groups. The proposed model requires five input parameters that are critical pressure, critical temperature, acentric factor, mass density at 288 K and molecular weight. A comparison was made between the estimation power of the proposed model and the old existing correlations used to estimate PC-SAFT parameters. Results reveal that the proposed model could noticeably enhance the estimation accuracy of PC-SAFT parameters. The performance of model was also evaluated in the estimation of PC-SAFT parameters for 53 pure components belonging to 14 different families of compounds, among which vapor pressures and liquid phase densities were calculated and compared to the experimental data. Furthermore, the applicability of the proposed model was studied to estimate PC-SAFT parameters for SCN groups (petroleum fractions) and estimated parameters were then employed to calculate bubble pressures and liquid phase densities of three oil samples. The results indicate that the proposed model presents accurate estimations of PC-SAFT parameters for different pure components and SCN groups. 13 ACS Paragon Plus Environment


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Supporting information Additional guiding information are also provided in this section in order to increase the accessibility of the proposed model in the estimation of PC-SAFT parameters and making it easier to use. These information are available free of charge via the internet.

Acknowledgment We would like to express our deepest gratitude to MAPSA Technology Center for its technical and financial support.

Nomenclature A = Helmholtz free energy, J a = reduced Helmholtz free energy aj(m), bj(m) = functions defined by eqs 16 and 17 d = temperature-dependent segment diameter, Å ( = site-site radial distribution function of hard chain fluid I1, I2 = abbreviation defined by eqs 14 and 15 k = Boltzmann constant, J/K kij = binary interaction parameter m = number of segments per chain m = mean segment number in the system Mw = molecular weight, g/mol N = total number of molecules Pc = critical pressure, bar T = temperature, K Tc = critical temperature, K xi = mole fraction of component i Greek Letters ]( = potential energy of a pair of molecules ε = depth of pair potential, J ζn = abbreviation (n=0 …, 3) defined by eq 6, Ån-3 η=packing fraction ρ = total number density of molecules, 1/ Å3 ρm = mass density, g/cc σ = segment diameter, Å ` = molar volume, m3/mol 14

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` = critical molar volume, m3/mol ω = acentric factor Superscript C = calculated property disp = contribution due to dispersive attraction exp = experimental property hc = hard-chain hs = hard sphere res = residual quantities R = real value sat = property at saturation condition (~) = used for reduced quantities (*) = property at 288 K



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References (1) Peng, D. Y.; Robinson, D. B. A New Two-Constant Equation of State. Ind. Eng. Chem. Fundam. 1976, 15, 59. (2) Soave, G. Equilibrium constants from a modified Redlich-Kwong equation of state. Chemical Engineering Science. 1972, 27, 1197. (3) Peneloux, A.; Rauzy, E. A consistent correction for Redlich-Kwong-Soave volumes. Fluid Phase Equilibria. 1982, 8, 7. (4) Yu, J.; Lu, B. A three-parameter cubic equation of state for asymmetric mixture density calculations. Fluid Phase Equilibria. 1987, 34, 1. (5) Tsai, J.; Chen, Y. Application of a volume-translated Peng-Robinson equation of state on vapor-liquid equilibrium calculations. Fluid Phase Equilibria. 1998, 145, 193. (6) Mathias, P.; Naheiri, T. Application of a volume-translated Peng-Robinson equation of state on vapor-liquid equilibrium calculations. Fluid Phase Equilibria. 1989, 47, 77. (7) Chapman, W. G.; Gubbins, K. E.; Jackson, G.; Radosz, M. New reference equation of state for associating liquids. Ind. Eng. Chem. Res. 1990, 29, 1709. (8) Huang, S. H.; Radosz, M. Equation of state for small, large, polydisperse, and associating molecules. Ind. Eng. Chem. Res. 1990, 29, 2284. (9) Huang, S. H.; Radosz, M. Equation of state for small, large, polydisperse, and associating molecules: extension to fluid mixtures. Ind. Eng. Chem. Res. 1991, 30, 1994. (10) Wertheim, M. S. Fluids with highly directional attractive forces. I. Statistical thermodynamics. Journal of Statistical Physics, 1984, 35, 19. (11) Wertheim, M. S. Fluids with highly directional attractive forces. II. Thermodynamic perturbation theory and integral equations. Journal of Statistical Physics, 1984, 35, 35. (12) Wertheim, M. S. Fluids with highly directional attractive forces. III. Multiple attraction sites. Journal of Statistical Physics, 1986, 42, 459. (13) Wertheim, M. S. Fluids with highly directional attractive forces. IV. Equilibrium polymerization. Journal of Statistical Physics, 1986, 42, 477. (14) Walsh, J. M.; Guedes, H. J. R.; Gubbins, K. E. Physical Theory for Fluids of Small Associating Molecules. J. Phys. Chem. 1992, 96, 10995. (15) Jackson, G.; Chapman, W. G.; Gubbins, K. E. Phase Equilibrium of Associating Fluids. Spherical Molecules with Multiple Bonding sites. Mol. Phys. 1988, 65, 1. (16) Green, D. G.; Jackson, G. Theory of phase equilibria for model aqueous solutions of chain molecules: water + alkane mixtures. J. Chem. Soc., Faraday Trans. 1992, 88, 1395. (17) Muller, E. A.; Gubbins, K. E. An Equation of State for Water from a Simplified Intermolecular Potential. Ind. Eng. Chem. Res. 1995, 34, 3662. (18) Kolafa, J.; Nezbeda, I. The Lennard-Jones fluid: an accurate analytic and theoretically-based equation of state. Fluid Phase Equilibria. 1994, 100, 1.


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(19) Banaszak, M.; Chen, C. K.; Radosz, M. Copolymer SAFT equation of state: Thermodynamic perturbation theory extended to hetero bonded chains. Macromolecules. 1996, 29, 6481. (20) Blas, F. J.; Vega, L. F. Prediction of Binary and Ternary Diagrams Using the Statistical Associating Fluid Theory (SAFT) Equation of State. Ind. Eng. Chem. Res. 1998, 37, 660. (21) Pamies, J. C.; Vega, L. F. Vapor−Liquid Equilibria and Critical Behavior of Heavy nAlkanes Using Transferable Parameters from the Soft-SAFT Equation of State. Ind. Eng. Chem. Res. 2001, 40, 2532. (22) Johnson, J. K.; Zollweg, J. A.; Gubbins, K. E. The Lennard-Jones Equation of State Revisited. Mol. Phys. 1993, 78, 591. (23) Gil-Villegas, A.; Galindo, A.; Whitehead, P. J.; Mills, S. J.; Jackson, G.; Burgess, A. N. Statistical associating fluid theory for chain molecules with attractive potentials of variable range. J. Chem. Phys. 1997, 106, 4168. (24) Gross, J.; Sadowski, G. Application of perturbation theory to a hard-chain reference fluid: an equation of state for square-well chains. Fluid Phase Equilibria. 2000, 168, 183. (25) Gross, J.; Sadowski, G. Perturbed-Chain SAFT: An Equation of State Based on a Perturbation Theory for Chain Molecules. Ind. Eng. Chem. Res. 2001, 40, 1244. (26) Barker, J. A.; Henderson, D. Perturbation Theory and Equation of State for Fluids. II. A Successful Theory of Liquids. J. Chem. Phys. 1967, 47, 4717. (27) Mccabe, C.; Jackson, G. SAFT-VR modelling of the phase equilibrium of long-chain nalkanes. Phys. Chem. Chem. Phys. 1999, 1, 2057. (28) Kouskoumvekaki, I. A.; von Solms, N.; Lindvig, T.; Michelsen, M. L.; Kontogeorgis, G. M. Novel Method for Estimating Pure-Component Parameters for Polymers: Application to the PCSAFT Equation of State. Ind. Eng. Chem. Res. 2004, 43, 2830. (29) Ferrando, N.; Hemptinne, J. Ch.; Mougin, P.; Passarello, J. Ph. Prediction of the PC-SAFT associating parameters by molecular simulation. J. Phys. Chem. B. 2012, 116, 367. (30) Tihic, A.; Kontogeorgis, G. M.; von Solms, N.; Michelsen, M. L. Applications of the simplified perturbed-chain SAFT equation of state using an extended parameter table. Fluid Phase Equilibria. 2006, 248, 29. (31) Huynh, D. N.; Benamira, M.; Passarello, J. Ph.; Tobaly, P.; Hemptinne, J. Ch. Application of GC-SAFT EOS to polycyclic aromatic hydrocarbons. Fluid Phase Equilibria. 2007, 254, 60. (32) Tamouza, S.; Passarellob, J. Ph.; Tobaly, P.; Hemptinne, J. Ch. Group contribution method with SAFT EOS applied to vapor liquid equilibria of various hydrocarbon series. Fluid Phase Equilibria. 2004, 222, 67. (33) Burgess, W. A.; Tapriyal, D.; Gamwo, I. K.; Wu, Y.; McHugh. M. A.; Enick, R. M. New Group-Contribution Parameters for the Calculation of PC-SAFT Parameters for Use at Pressures to 276 MPa and Temperatures to 533 K. Ind. Eng. Chem. Res. 2014, 53, 2520. (34) Leekumjorn, S.; Krejbjerg, K. Phase behavior of reservoir fluids: Comparisons of PC-SAFT and cubic EOS simulations. Fluid Phase Equilibria. 2013, 359, 17. (35) Polishuk, I. Standardized Critical Point-Based Numerical Solution of Statistical Association Fluid Theory Parameters: The Perturbed Chain-Statistical Association Fluid Theory Equation of State Revisited. Ind. Eng. Chem. Res. 2014, 53, 14127. (36) Prausnitz, J. M. Molecular thermodynamics of fluid-phase equilibria, Prentice-Hall, Inc., Englewood Cliffs, New Jersey 1969. (37) Nelder, J. A.; Mead, R. A Simplex Method for Function Minimization. The computer journal. 1965, 7, 308. 17 ACS Paragon Plus Environment


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(38) Whitson, CH. Characterizing hydrocarbon plus fractions. Soc Petrol Eng J. 1983, 23, 683. (39) Riazi, M. R.; Al-Sahhaf, T. A. Physical properties of heavy petroleum fractions and crude oils. Fluid Phase Equilibria. 1996, 117, 217. (40) Firoozabadi, A.; Katz, D. L. Predicting phase behavior of condensate/crude-oil systems using methane interaction coefficients. J. Petrol. Technol. 1978, 30, 1649. (41) DIPPR Table of Physical and Thermodynamic Properties of Pure Compounds, AlChE, New York, 1998. (42) Vargaftik, N. B. Tables of Thermophysical Properties of Liquids and Gases; John Wiley & Sons: New York, 1975. (43) Daubert, T. E.; Danner, R. P.; Sibul, H. M.; Stebbins, C. C. Physical and Thermodynamic Properties of Pure Chemicals: Data Compilation; Taylor & Francis: Washington, D.C., 1989. (44) Ruzicka, K.; Majer, V. Simultaneous Treatment of Vapor Pressures and Related Thermal Data between the Triple and Normal Boiling Temperatures for n‐Alkanes C5–C20. J. Phys. Chem. Ref. Data. 1994, 23, 1. (45) American Petroleum Institute Research Project 44. Selected Values of Properties of Hydrocarbons and Related Compounds; Texas A&M University: College Station, Texas, 1973. (46) Von Solms, N.; Michelsen, M.L.; Kontogeorgis, G.M. Computational and Physical Performance of a Modified PC-SAFT Equation of State for Highly Asymmetric and Associating Mixtures. Ind. Eng. Chem. Res. 2003, 42, 1098. (47) Voutsas, E.C.; Pappa, G.D.; Magoulas, K.; Tassios, D.P. Vapor liquid equilibrium modeling of alkane systems with Equations of State: “Simplicity versus complexity”. Fluid Phase Equilibria. 2006, 240, 127. (48) VDI-Wa¨rmeatlas, VDIGesellschaft Verfahrenstechnik und Chemieingenieurwesen (GVC), Du¨ sseldorf, Germany, 1994. (49) Twu, C.H. An internally consistent correlation for predicting the critical properties and molecular weights of petroleum and coal-tar liquids. Fluid Phase Equilibria. 1984, 16, 137. (50) Kesler, M.G.; Lee, B.I. Improve Prediction of Enthalpy of Fractions. Hydrocarbon Process. 1976, 55, 153. (51) Riazi, M.R.; Daubert, T.E. Characterization parameters for petroleum fractions. Ind. Eng. Chem. Res. 1987, 26, 755. (52) Cavett, R.H. Session on computer applications, in: Proceedings of the 27th Midyear Meeting of the API Division of Refining, San Francisco, 15 May, 1962. (53) Edmister, W.C.; Lee, B.I. Applied Hydrocarbon Thermodynamic, vol. 1, second ed., Gulf Publishing Company, Houston, TX, 1993. (54) Korsten, H. Internally Consistent Prediction of Vapor Pressure and Related Properties. Ind. Eng. Chem. Res. 2000, 39, 813. (55) Hosseinifar, P.; Jamshidi, S. Development of a new generalized correlation to characterize physical properties of pure components and petroleum fractions. Fluid Phase Equilibria. 2014, 363, 189.


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Graphical Abstract



T2c /Pc Ф= mσ3 ε/k 1

Normal Paraffins (Ф) Iso Paraffins (Ф-0.02)

0.9

Cyclo Alkanes (Ф+0.1)

0.8

Ф + Family number

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Nitro Alkanes (Ф+0.1) 0.7

Alkenes (Ф+0.2)

0.6

Alkynes (Ф+0.05) Aromatics (Ф-0.05)

0.5

Ploy Nuclear Ar (Ф-0.08)

0.4

Plasticizers (Ф-0.15)

0.3

Halogenated HC (Ф-0.1) Ethers (Ф+0.25)

0.2

Esters (Ф+0.3) Ketones (Ф+0.4)

0.1

Sulfides (Ф+0.5)

0 0

50

100

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Molecular weight (Mw) Figure 1. The ratio of the macroscopic parameters to the molecular parameters (Ф) versus molecular weight for different families of compounds (Family number is shown in the legend for each family).


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60

Ethane (EXP data) Iso-Pentane (EXP data) Benzene (EXP data) Toluene (EXP data) Fitted to EXP data Estimated by Proposed model Estimated by Tihic et al.’s Corr

50

40

P (bar)

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30

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Density (Kg/m3) Figure 2. Coexisting density curves at different pressures and corresponding saturation temperatures from triple point up to critical point when PC-SAFT parameters are determined by proposed model(─ ─ ), Tihic et al.’s Corr (▪▪▪) and fitting experimental data (──) for ethane, i-C5, benzene and toluene.



700

Ethane (EXP data) Iso-Pentane (EXP data) Benzene (EXP data) Toluene (EXP data) Fitted to EXP data Estimated by Proposed model Estimated by Tihic et al.’s Corr

600

500

T (K)

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400

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Density (Kg/m3) Figure 3. Coexisting density curves at different temperatures and corresponding saturation pressures from triple point up to critical point when PC-SAFT parameters are determined by proposed model(─ ─ ), Tihic et al.’s Corr (▪▪▪) and fitting experimental data (──) for ethane, i-C5, benzene and toluene.


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8

Average absolute errors % [∆Psat ]

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7

Proposed model CP-PC-SAFT Fitted to Exp data

6 5 4 3 2 1 0

Figure 4. A comparison between the average absolute errors (AAD %) in predicting the saturation vapor pressures when PC-SAFT parameters are estimated by the proposed model, CP-PC-SAFT method and fitted to the experimental data for 28 pure substances at the temperature ranges given in Table 8.



8 7

Average absolute errors % [∆ρ]

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Proposed model CP-PC-SAFT Fitted to Exp data

6 5 4 3 2 1 0

Figure 5. A comparison between the average absolute errors (AAD %) in predicting the liquid phase densities when PC-SAFT parameters are estimated by the proposed model, CP-PC-SAFT method and fitted to the experimental data for 28 pure substances at the temperature ranges given in Table 8.



15 10

Pc

5 0

Tc

Mw Petroleum fractions

Normal Paraffins Iso Paraffins Cyclo Alkanes Nitro Alkanes Alkenes Alkynes Aromatics Ploy Nuclear Ar Plasticizers Halogenated HC Ethers Esters Ketones Sulfides

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

Average absolute errors % [∆ε/k]

Page 25 of 41

Figure 6. A sensitivity analysis for the proposed model with respect to the input parameters in the estimation of (ε/k) for different families of compounds and SCN groups: [∆ε/k] indicates the percent of average absolute error arisen due to deviations deliberately created in each input parameter from -30% up to +30%.



ω Pc

15 10

Tc

5 0 Normal Paraffins Iso Paraffins Cyclo Alkanes Nitro Alkanes Alkenes Alkynes Aromatics Ploy Nuclear Ar Plasticizers Halogenated HC Ethers Esters Ketones Sulfides Petroleum fractions

Average absolute errors % [∆m]

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

Page 26 of 41

SG

Mw

Figure 7. A sensitivity analysis for the proposed model with respect to the input parameters in the estimation of (m) for different families of compounds and SCN groups: [∆m] indicates the percent of average absolute error arisen due to deviations deliberately created in each input parameter from -30% up to +30%.



ω

15 10

Pc

5 0 Normal Paraffins Iso Paraffins Cyclo Alkanes Nitro Alkanes Alkenes Alkynes Aromatics Ploy Nuclear Ar Plasticizers Halogenated HC Ethers Esters Ketones Sulfides Petroleum fractions

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

Average absolute errors % [∆σ]

Page 27 of 41

Tc

Mw

Figure 8. A sensitivity analysis for the proposed model with respect to the input parameters in the estimation of (σ) for different families of compounds and SCN groups: [∆σ] indicates the percent of average absolute error arisen due to deviations deliberately created in each input parameter from -30% up to +30%.



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

Table 1. Universal PC-SAFT model constants for equations 16 and 17.25 ¾ M , VM 0 0.910563145 -0.308401692 -0.090614835 0.724094694 1 0.636128145 0.186053116 0.452784281 2.238279186 2 2.686134789 -2.503004726 0.596270073 -4.002584949 3 -26.54736249 21.41979363 -1.724182913 -21.00357682 4 97.75920878 -65.25588533 -4.130211253 26.85564136 5 -159.5915409 83.31868048 13.77663187 206.5513384 6 91.29777408 -33.74692293 -8.672847037 -355.6023561

V -0.575549808 0.699509552 3.892567339 -17.21547165 192.6722645 -161.8264617 -165.2076935


Page 28 of 41

V, 0.097688312 -0.255757498 -9.155856153 20.64207597 -38.80443005 93.62677408 -29.66690559

Page 29 of 41

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


Table 2. Families of compounds used in this study. Correlation No. of Groups name Number compounds 1 Normal Paraffins 20 2 Iso Paraffins 23 3 Cyclo Alkanes 21 4 Nitro Alkanes 14 5 Alkenes 23 6 Alkynes 15 7 Aromatics 20 8 Ploy Nuclear Aromatics 25 9 Plasticizers 25 10 Halogenated HC 15 11 Ethers 15 12 Esters 27 13 Ketones 17 14 Sulfides 14 15 Petroleum fractions (P, N, A data)* 186 Total pure substances 274 * All paraffinic, naphthenic and aromatic data used to develop model for petroleum fractions.



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

Table 3. Optimized values of model constant coefficients required to calculate (mσ3). Correlation , ° Number 1 1.356782 0.491799 2.462146 -10.76028 0.161737 2 0.834897 0.572323 5.414184 -6.217822 0.254886 3 1.039288 0.285719 1.096325 -7.694455 0.339245 4 0.744700 0.432444 3.166139 -6.113175 0.303755 5 0.128198 0.462419 9.963644 -1.351749 0.846776 6 3.054124 0.982979 9.620007 -5.305202 0.157084 7 0.531718 0.491857 4.804565 -2.887083 0.538495 8 0.076522 0.933208 7.355429 -11.21669 0.157994 9 0.265498 0.718961 5.723064 -3.012450 0.459506 10 0.060142 0.274624 2.108762 -3.694221 0.855419 11 -0.11233 0.197888 3.631975 -2.253053 0.919014 12 0.899968 0.216207 1.291184 -4.063468 0.616397 13 1.210594 0.058180 1.197051 -2.471722 0.941361 14 0.547698 0.291565 2.793177 -2.632505 0.727770 15 1.709315 0.093896 0.373366 -8.776440 0.409845


Page 30 of 41

Page 31 of 41

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


Table 4. Optimized values of model constant coefficients required to calculate (ε/k). Correlation , ° . Number 1.301730 10.318684 0.840739 32.891731 -7.705554 0.358170 1 1.933458 3.448115 0.791412 24.371376 -8.333815 0.477454 2 2.688539 3.842781 0.866931 18.888650 -7.992011 0.477633 3 0.417630 -0.448225 0.472307 63.164156 -1.851481 0.562435 4 1.196233 0.824368 0.267977 14.878680 -1.562925 0.875216 5 0.604549 9.520453 0.537607 1.0535600 -5.439126 0.368069 6 1.647928 4.369317 0.620709 40.884767 -4.316491 0.396884 7 0.771889 1.182164 0.838912 45.566782 -6.849476 0.349728 8 2.361144 0.587350 1.001275 83.440116 -8.000053 0.231714 9 1.436638 2.088896 0.466200 21.266987 -3.788710 0.383941 10 2.782671 3.513605 0.538353 23.678706 -6.017443 0.290112 11 2.633455 6.765670 0.716853 6.4369800 -4.655047 0.448676 12 1.306793 1.259840 0.415688 24.145970 -1.251793 0.839419 13 1.655047 4.742744 0.505466 18.350275 -2.900171 0.569170 14 15 2.516360 6.707332 0.304540 3.7756230 -13.30190 0.240197



1 2 3 Table 5. Optimized values of model constant 4 5 Correlation ª ª, ª 6 Number 7 1 9.8236740 -0.727208 -0.026361 8 2 11.436567 2.361066 7762.8093 9 3 19.687774 -2.222776 -2.244149 10 4 -21.55169 -0.491634 -0.424123 11 5 145.73737 -1.079309 -8.318561 12 13 6 -37.82452 -0.843737 -3.102143 14 7 -70.58489 -1.353408 -3.742032 15 8 -58.97166 -1.170469 3.064888 16 9 899.18081 -1.678195 -2.509344 17 10 15.711823 -1.167256 -2.180341 18 11 46.759459 -2.470173 -1.177438 19 20 12 43.736325 -1.281663 -2.844007 21 13 -109.0936 10.711733 178.38100 22 14 -24.65015 -1.174129 -2.645111 23 15 74.48655 -7.543290 -4.473790 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

coefficients required to calculate (m). ª°

41.54699 0.946700 7.486196 7.550112 1.543735 4.437946 4.710042 4.925265 8.385086 7.637415 -5.336915 4.217732 0.260971 4.572863 3.386119

ª

0.022865 -1.36469 -0.368790 -0.850995 0.354631 -0.753091 -0.636405 0.952969 -1.457865 -0.703668 -0.131372 0.725315 -1.152626 -0.375305 -0.440970

ª.

22.641210 -8.287227 27.779710 67.399760 -41.42223 117.22114 25.659548 18.475331 -87.06441 164.02061 64.019395 14.712732 356.17011 -44.10965 10.00833


Page 32 of 41

ªN

-0.427497 1.370476 -2.112532 -2.224376 -0.525893 -1.421395 -1.240361 -0.705127 -0.881079 -2.379812 -3.790555 -1.151975 -9.372800 -2.170408 -26.9705

ªJ

16.004634 -301.74361 -1.037761 -0.595067 13.605871 -12.38595 -0.652302 1.694163 -6.341534 -0.739087 7.771025 -0.143266 -1.370164 -5.364318 -0.55257

ªË

0.465784 1.025400 -33.99798 -5.279674 1.816992 1.093445 -4.934414 2.635819 2.631454 -7.768888 25.025343 -0.189572 -2.104285 1.398888 -7.140960

ªM

-226.7309 -0.794711 0.981149 -7.427911 -2.947231 -3.513082 -31.06013 2.647243 -2.459287 -6.30796 -0.098546 1.877847 1.477557 -28.14246 -1.767310

Page 33 of 41

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


Table 6. Average absolute deviations (AAD %) in the estimation of PC-SAFT parameters using the proposed model compared to that estimated by the old existing correlations. m (AAD %) σ (AAD %) ε/k (AAD %) Correlation Tihic et al.’s Tihic et al.’s Tihic et al.’s Number Proposed Corr Proposed Corr Proposed Corr Corr30 Corr30 Corr30 1 3.23 1.44 0.77 0.52 3.36 1.49 2 14.8 2.69 3.75 1.13 3.68 1.59 3 8.29 3.74 2.15 1.02 5.14 1.88 4 11.4 3.08 15.7 2.05 21.2 3.46 5 11.2 3.77 2.32 1.41 9.62 2.52 6 12.3 2.15 3.89 1.67 8.65 3.74 7 19.4 1.68 1.68 0.6 17.4 0.76 8 7.49 2.18 2.65 1.58 6.04 1.49 9 25.7 3.49 15.2 2.31 24.8 2.97 10 17.8 2.15 11.4 1.25 36.1 2.25 11 11.7 1.14 9.06 0.87 9.32 2.64 12 5.19 2.78 1.61 1.09 3.09 1.59 13 14.2 3.43 8.89 2.84 12.6 3.62 14 8.59 3.82 1.94 1.25 5.11 1.68 15 3.94 2.88 3.21



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

Page 34 of 41

Table 7. Pure component PC-SAFT parameters determined by the proposed model, Tihic Corr and fitting experimental data for 53 elected pure substances from various families of compounds and the percent of average absolute deviations (AAD %) in the calculation of vapor pressures and liquid phase densities using PC-SAFT model. Estimated by proposed model AAD % Proposed Tihic et al.’s Fitted to T range Components References 30 model Corr Exp data [K] m [-] σ [Å] ε/k [K] Ì Ì Ì a ¿ a ¿ a ¿ Normal Paraffins Tetradecane (C14H30) 5.9603 3.9238 254.27 2.39 1.93 2.55 2.31 2.03 1.21 279-580 42-45 Heptadecane (C17H36) 6.9920 3.9614 254.84 2.98 0.74 2.19 0.97 2.11 0.61 295-736 42-45 Docosane (C22H46) 8.7062 3.9929 256.19 2.31 0.88 2.47 1.11 1.88 0.73 400-700 46 Octacosane (C28H58) 10.782 4.0156 255.39 1.48 0.34 1.34 0.75 1.26 0.57 460-720 46 Hexatriacontane (C36H74) 13.487 4.0380 253.30 1.93 0.77 1.57 0.67 1.19 0.66 500-700 47 Iso Paraffins 2,3,3-Trimethylpentane 3.0187 4.1129 260.51 1.12 0.43 3.95 3.07 0.98 0.24 180-570 DIPPR (42) 2,2-Dimethyloctane 4.0445 4.0222 251.01 0.94 1.31 4.21 3.86 0.81 1.06 255-540 DIPPR (72) 2,3,4-Trimethylpentane 3.2397 4.0222 256.62 0.24 0.36 4.36 4.16 0.34 0.48 170-560 DIPPR (43) 2,2-Dimethyl-33.4263 4.0860 261.23 0.77 1.61 5.11 3.91 0.67 1.23 250-530 DIPPR (190) ethylpentane Cyclo Alkanes Cyclobutane 2.0988 3.6309 254.45 0.48 0.92 3.34 4.07 0.39 0.88 185-490 DIPPR (102) Cyclopropane 1.9049 3.4591 233.49 0.81 0.98 5.49 4.78 0.84 1.04 145-395 DIPPR (101) Isopropylcyclohexane 3.2779 4.0487 277.92 0.17 0.66 3.90 4.44 0.64 0.73 185-625 DIPPR (150) Decylcyclohexane 6.0327 4.0083 281.23 0.69 1.95 4.73 5.52 0.97 1.39 280-750 DIPPR (158) Nitro Alkanes Nitroethane 2.9556 3.2322 290.55 0.77 1.98 5.77 6.24 0.73 1.21 185-590 DIPPR (1761) 2-Nitropropane 3.1188 3.3249 289.95 1.93 1.46 6.81 8.45 1.44 1.01 171-590 DIPPR (1763) o-Dinitrobenzene 6.4010 3.0559 302.08 0.69 0.93 6.33 7.91 0.65 0.87 390-831 DIPPR (2741) Acetonitrile 1.9693 3.3648 344.90 1.84 0.41 7.62 6.16 1.56 0.62 275-470 DIPPR (1772) Alkenes 1,2-Butadiene 2.2818 3.5892 238.59 0.63 1.27 7.44 6.57 0.62 1.11 230-400 DIPPR (302) 2,3-Dimethyl-1-butene 2.9389 3.7686 245.61 1.38 0.82 6.66 5.92 1.29 0.78 120-500 DIPPR (230) 2,3-Dimethyl-1,32.7005 3.7841 257.70 0.34 0.98 5.72 7.14 0.41 0.54 220-470 DIPPR (319) 34 ACS Paragon Plus Environment

Page 35 of 41

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

butadiene Alkynes 1-Propyne 3-Hexyne Ethyne Aromatics Toluene o-xylene tert-Butylbenzene p-tert-Butylstyrene Ploy Nuclear Aromatics 1-Butylnaphthalene 1-Propylnaphthalene Indene Plasticizers Dimethyl maleate Diethyl phthalate Dibutyl phthalate Methyl oleate Halogenated HC Methyl chloride 1,1,1-Trichloroethane Chlorobenzene m-Dibromobenzene Ethers Dipropryl ether p-Dioxane Vinyl methyl ether Esters Benzyl acetate Decyl acetate Hexyl acetate Isobutyl acetate


2.4826 2.8836 2.4870

3.1269 3.7261 2.7578

202.70 247.58 174.03

0.74 0.86 1.93

0.57 0.44 2.18

8.51 6.56 5.93

6.98 5.22 7.49

0.77 0.55 0.98

0.63 0.37 1.64

170-400 175-540 195-300

DIPPR (402) DIPPR (406) DIPPR (401)

2.8150 3.1490 3.4461 3.8919

3.7169 3.7520 3.9508 4.0705

285.69 289.95 289.50 290.64

0.81 0.87 1.96 2.18

0.43 1.03 0.91 1.18

8.66 5.41 6.75 7.51

7.37 3.94 4.22 5.97

0.99 0.93 1.55 2.20

0.83 1.88 0.89 1.44

178-594 248-630 270-590 300-600

42,43,48 42,43,45 DIPPR (521) DIPPR (621)

4.7224 3.8091 2.7985

3.8503 4.1398 3.8989

330.73 338.48 333.21

0.46 0.98 1.032

0.37 0.87 2.69

4.33 3.91 2.87

2.97 2.13 3.71

0.51 0.67 0.93

0.29 0.54 2.72

255-790 270-780 272–687


5.0101 6.8395 7.7275 9.6672

3.2679 3.4630 3.6572 3.6265

262.83 262.72 260.55 240.45

0.35 0.42 2.44 2.87

0.93 1.38 0.67 1.14

9.51 8.79 14.2 12.9

10.1 12.4 11.6 9.92

0.44 0.23 2.11 2.07

0.82 0.97 0.95 0.86

255-675 270-755 238-781 295-760

DIPPR (2387) DIPPR (2375) DIPPR (2376) DIPPR (1362)

1.9287 2.4924 2.6929 2.8806

3.2299 3.7242 3.7157 3.9138

236.56 295.5 293.83 364.00

0.67 0.39 0.28 0.82

1.66 0.72 0.55 0.66

10.4 9.01 11.5 8.42

13.8 11.8 10.9 6.96

0.56 0.46 0.14 0.89

1.33 0.54 0.39 0.74

175-416 270–540 230–630 385–680

43 DIPPR (1527) DIPPR (1571) DIPPR (1678)

3.4998 2.8714 2.6740

3.6483 3.4153 3.3130

234.16 275.88 218.44

0.25 1.87 0.73

0.03 1.59 0.36

5.75 6.32 4.98

4.61 5.53 3.74

0.22 0.32 0.67

0.13 0.91 0.23

150–530 305-525 220-390


4.3738 6.8862 4.8449 4.0834

3.6331 3.5898 3.5678 3.4837

278.18 235.55 236.93 233.85

0.95 3.51 1.19 2.34

1.88 0.41 0.71 0.92

2.29 3.64 2.15 3.81

1.93 1.47 0.99 2.21

0.72 2.16 0.84 1.79

0.94 0.31 0.55 0.89

255-700 260-675 195-615 175-560




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

Ketones 2-Ethylhexanal 4.8416 3.5412 236.37 0.88 0.94 4.97 5.19 2-Methylpropanal 3.5488 3.1626 236.65 0.76 1.32 3.25 5.59 p-Tolualdehyde 4.3618 3.4241 280.17 1.56 2.89 2.92 4.84 Glutaric anhydride 4.0893 3.2052 350.06 1.74 2.67 3.77 5.09 Sulfides Carbon disulfide 1.7029 3.6201 328.11 0.87 0.63 5.88 4.97 Diethyl disulfide 3.1372 3.7818 297.77 0.59 0.77 4.39 6.14 Methyl-n-propyl sulfide 2.8048 3.6909 267.83 0.44 0.48 3.27 3.69 Methyl ethyl sulfide 2.5442 3.6474 258.86 2.64 1.34 6.71 4.33 * The number between parentheses after DIPPR is the chemical ID in DIPPR compound list.


Page 36 of 41

0.74 0.87 1.42 1.56

0.80 1.33 2.72 2.34

200-600 210-505 290-680 330-830


0.71 0.45 0.52 1.88

0.26 0.68 0.37 1.17

165-550 175-640 160–565 168-533


Page 37 of 41

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


Table 8. PC-SAFT parameters estimated by the proposed model, fitted to the experimental saturation pressure and liquid density data and molecular parameters determined by CP-PC-SAFT method for 28 pure components. CP-PC-SAFT method Components

Methane Ethane n-Propane n-Butane n-Pentane n-Hexane n-Heptane n-Octane n-Nonane n-Decane Undecane Dodecane Tridecane Tetradecane Pentadecane Hexadecane Nonadecane Benzene Toluene Chlorobenzene Bromobenzene o-Xylene m-Xylene p-Xylene Ethylbenzene n-Propylbenzene n-Butylbenzene Cyclooctane

Proposed model

Fitted to Exp data

m [-]

σ [Å]

ε/k [K]

m [-]

σ [Å]

ε/k [K]

m [-]

σ [Å]

ε/k [K]

T range [K]

1.0008 1.5636 2.4144 2.4826 3.0642 3.5108 4.0703 4.4548 4.851 5.2701 5.7146 6.0121 6.6436 7.0429 7.3172 7.5878 8.1124 2.5443 3.7053 3.3927 3.6271 3.7275 4.1504 4.1207 3.8282 4.5000 4.7130 2.7949

3.7476 3.5741 3.3918 3.6504 3.6242 3.6558 3.6352 3.6787 3.7047 3.7219 3.7309 3.7698 3.7339 3.7515 3.7862 3.8190 3.9469 3.6471 3.4007 3.4877 3.4631 3.5773 3.4609 3.4794 3.5539 3.5017 3.5939 4.1022

142.51 185.39 184.37 209.45 212.53 218.24 220.49 225.29 229.27 232.26 234.68 238.24 237.90 240.58 243.43 246.37 254.17 274.07 249.54 275.31 284.75 265.23 250.19 250.47 257.27 252.05 256.99 303.67

1.0000 1.5996 2.0541 2.3841 2.6847 3.0759 3.4556 3.8276 4.1924 4.5525 4.9081 5.2595 5.6109 5.9603 6.3049 6.6509 7.6747 2.4653 2.8150 2.6929 2.6696 3.1490 3.1657 3.1723 3.1511 3.3438 3.5570 2.9204

3.6854 3.5260 3.5568 3.5877 3.7675 3.7920 3.8150 3.8351 3.8531 3.8715 3.8859 3.9007 3.9118 3.9238 3.9356 3.9461 3.9795 3.6478 3.7169 3.7157 3.8244 3.7520 3.7666 3.7689 3.7599 3.8535 3.9288 4.0082

152.34 191.42 207.50 219.55 227.94 234.32 239.03 242.78 245.90 248.08 250.08 251.68 253.08 254.27 254.69 254.70 255.52 287.35 285.69 293.83 326.29 289.95 285.19 284.52 286.55 286.80 287.56 303.47

1.0000 1.6069 2.0020 2.3316 2.6896 3.0576 3.4831 3.8176 4.2079 4.6627 4.9082 5.3060 5.6877 5.9002 6.2855 6.6485 6.9809 2.4653 2.8149 2.6929 2.6456 3.1362 3.1861 3.1723 3.0799 3.3438 3.7662 2.8856

3.7039 3.5206 3.6184 3.7086 3.7729 3.7983 3.8049 3.8373 3.8448 3.8384 3.8893 3.8959 3.9143 3.9396 3.9531 3.9552 3.9675 3.6478 3.7169 3.7367 3.8360 3.7600 3.7563 3.7781 3.7974 3.8438 3.8727 4.0117

150.03 191.42 208.11 222.88 231.20 236.77 238.40 242.78 244.51 243.87 248.82 249.21 249.78 254.21 254.14 254.70 255.65 287.35 285.69 312.11 334.37 291.05 283.98 283.77 287.35 288.13 283.07 307.03

97-300 90-305 85-523 135-573 143-469 177-503 182-623 216-569 219-595 243-617 247-639 263-685 267-675 279-580 283-708 291-723 305-758 278-562 178-594 230-630 242-670 248-630 225-619 286-616 178-617 173-638 185-660 290-640


References DIPPR (1) DIPPR (2) DIPPR (3) DIPPR (5) DIPPR (7) DIPPR (11) DIPPR (17) DIPPR (27) DIPPR (46) DIPPR (56) DIPPR (63) DIPPR (64) DIPPR (65) DIPPR (66) DIPPR (67) DIPPR (68) DIPPR (71) DIPPR (501) 36,37,42 DIPPR (1571) DIPPR (1680) 36,37,39 DIPPR (506) DIPPR (507) DIPPR (504) DIPPR (509) DIPPR (518) DIPPR (160)


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

Table 9. PC-SAFT parameters of SCN groups and plus fractions estimated by the proposed model for selected oil samples. Oil 1 Oil 3 Comp mol % Mw m [-] σ [Å] ε/k [K] Comp mol % Mw m [-] σ [Å] ε/k [K] N2 0.29 28.01 1.2053 3.3130 90.960 H2S 0.68 34.08 1.6490 3.0550 229.84 CO2 2.28 44.01 2.0729 2.7852 169.21 N2 0.18 28.01 1.2053 3.3130 90.960 C1 42.85 16.04 1.0000 3.7039 150.03 CO2 3.41 44.01 2.0729 2.7852 169.21 C2 6.55 30.07 1.6069 3.5206 191.42 C1 34.43 16.04 1.0000 3.7039 150.03 C3 5.18 44.10 2.0020 3.6184 208.11 C2 9.67 30.07 1.6069 3.5206 191.42 i-C4 1.44 58.12 2.2616 3.7574 216.53 C3 7.14 44.10 2.0020 3.6184 208.11 n-C4 2.84 58.12 2.3316 3.7086 222.88 C4 4.89 58.12 2.4862 3.6450 240.60 i-C5 1.49 72.15 2.5620 3.8296 230.75 C5 3.64 72.15 2.7779 3.6945 249.17 n-C5 1.74 72.15 2.6896 3.7729 231.20 C6 3.54 84.00 2.9632 3.7694 252.20 C6 3.09 84.00 2.9632 3.7694 252.20 C7 2.51 96.00 3.1215 3.8057 261.74 C7 4.26 96.00 3.1215 3.8057 261.74 C8 3.16 107.0 3.2670 3.8242 270.28 C8 4.58 107.0 3.2670 3.8242 270.28 C9 3.22 121.0 3.4725 3.8652 273.82 C9 3.65 121.0 3.4725 3.8652 273.82 C10 2.36 134.0 3.6632 3.8993 276.09 C10 3.08 134.0 3.6632 3.8993 276.09 C11 1.95 147.0 3.8512 3.9319 277.64 C11 2.35 147.0 3.8512 3.9319 277.64 C12 1.31 161.0 4.0451 3.9568 280.40 C12+ 14.33 329.5 6.5691 4.1060 289.28 C13 1.90 175.0 4.2285 3.9785 283.43 C14 1.76 190.0 4.4212 3.9950 287.22 Tuned parameters (C12+) 6.7556 4.2310 295.44 C15 1.45 206.0 4.6241 4.0114 290.65 Oil 2 C16 1.24 222.0 4.8257 4.0283 293.16 Comp mol % Mw m [-] σ [Å] ε/k [K] C17 1.02 237.0 5.0106 4.0388 296.25 N2 0.300 28.01 1.2053 3.3130 90.960 C18 0.87 251.0 5.1787 4.0473 299.02 CO2 0.148 44.01 2.0729 2.7852 169.21 C19 0.76 263.0 5.3249 4.0547 301.06 C1 2.559 16.04 1.0000 3.7039 150.03 C20 0.67 275.0 5.4781 4.0607 302.91 C2 3.181 30.07 1.6069 3.5206 191.42 C21 0.67 291.0 5.6611 4.0606 307.24 C3 4.931 44.10 2.0020 3.6184 208.11 C22 0.58 305.0 5.8243 4.0692 309.00 C4 4.635 58.12 2.4862 3.6450 240.60 C23 0.63 318.0 5.9750 4.0710 311.71 C5 4.776 72.15 2.7779 3.6945 249.17 C24 0.56 331.0 6.1279 4.0772 313.26 C6 4.925 84.00 2.9632 3.7694 252.20 C25 0.56 345.0 6.2897 4.0832 314.91 C7 5.009 96.00 3.1215 3.8057 261.74 C26 0.53 359.0 6.4453 4.0854 317.29 C8 5.071 107.0 3.2670 3.8242 270.28 C27+ 4.71 581.0 9.5532 4.3821 275.62 38 ACS Paragon Plus Environment

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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

C9 4.660 121.0 C10+ 59.805 430.0 Tuned parameters (C10+)


3.4725 7.9111 8.0697

3.8652 4.1866 4.2145

273.82 289.04 292.99

Tuned parameters (C27+)


10.341

4.4731

280.88


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

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Table 10. Comparison of liquid phase density and bubble pressure predictions to experimental data measured in the differential liberation test (DL) for three oil samples before and after parameter tuning process of plus fractions. Samples

Oil 1

Oil 2

Pressure Calculated values steps [bar] Before tuning After tuning Liquid phase density (Ì ) [g/cm3] 414.61 0.744 0.689 387.03 0.741 0.686 359.46 0.733 0.683 338.78 0.724 0.681 326.38 0.718 0.679 304.32 0.715 0.677 283.64 0.730 0.674 262.96 0.727 0.672 252.89 0.735 0.669 221.61 0.753 0.681 180.25 0.786 0.696 138.89 0.803 0.708 90.640 0.823 0.728 42.390 0.847 0.749 1.0132 0.903 0.787 Bubble pressure (aÍÎÍÍÏ ) [bar] 276.24 253.17 Liquid phase density (Ì ) 355.53 327.41 302.32 276.61 251.93 226.84 202.03 177.28 170.94 150.95 120.97 90.990

[g/cm3] 0.655 0.651 0.647 0.643 0.638 0.624 0.623 0.622 0.621 0.636 0.657 0.673

Experimental values

0.714 0.710 0.707 0.702 0.698 0.694 0.690 0.685 0.687 0.696 0.711 0.743

AAD % Before tuning After tuning

0.694 0.690 0.687 0.684 0.682 0.679 0.676 0.673 0.671 0.687 0.705 0.722 0.744 0.776 0.813

7.20 7.39 6.70 5.85 5.28 5.30 7.99 8.02 9.54 9.61 11.49 11.22 10.62 9.15 11.07

0.72 0.58 0.58 0.44 0.44 0.29 0.30 0.15 0.30 0.87 1.28 1.94 2.15 3.48 3.20

252.89

9.23

0.11

0.718 0.716 0.713 0.710 0.707 0.703 0.699 0.696 0.695 0.705 0.721 0.737

8.77 9.08 9.26 9.44 9.76 11.24 10.87 10.63 10.65 9.79 8.88 8.68

0.56 0.84 0.84 1.13 1.27 1.28 1.29 1.58 1.15 1.28 1.39 0.81


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61.000 0.691 31.020 0.718 1.0132 0.757 Bubble pressure (aÍÎÍÍÏ ) [bar] 189.35

Oil 3

Liquid phase density (Ì ) [g/cm3] 295.08 0.663 246.08 0.657 221.54 0.654 197.07 0.651 187.28 0.650 182.39 0.649 180.39 0.649 148.06 0.650 123.52 0.660 99.050 0.670 74.510 0.681 49.970 0.692 25.500 0.705 15.720 0.711 5.860 0.732 1.0132 0.757 Bubble pressure (aÍÎÍÍÏ ) [bar] 194.05

0.758 0.789 0.829

0.751 0.770 0.800

7.99 6.75 5.37

0.93 2.47 3.62

171.3

170.94

10.77

0.21

0.699 0.693 0.690 0.687 0.686 0.686 0.687 0.699 0.709 0.719 0.730 0.742 0.756 0.763 0.776 0.798

0.701 0.695 0.692 0.689 0.688 0.687 0.687 0.702 0.712 0.725 0.735 0.748 0.761 0.770 0.783 0.806

5.42 5.47 5.49 5.52 5.52 5.53 5.53 7.41 7.30 7.59 7.35 7.49 7.36 7.66 6.51 6.08

0.29 0.29 0.29 0.29 0.29 0.15 0.00 0.43 0.42 0.83 0.68 0.80 0.66 0.91 0.89 0.99

180.65

180.39

7.57

0.14


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