A Method for Estimating the Normal Boiling Point of Heavy

Ind. Eng. Chem. Res. 2001, 40, 1781-1790

1781

A Method for Estimating the Normal Boiling Point of Heavy Hydrocarbons Suitable for a Group-Contribution-Based Equation of State Lucie Coniglio* and Armelle Nouviaire De´ partement de Chimie-Physique des Re´ actions, Ecole Nationale Supe´ rieure des Industries Chimiques de Nancy, Institut National Polytechnique de Lorraine, 1, rue Grandville, 54000 Nancy, France

In a previous work (Coniglio et al. Ind. Eng. Chem. Res. 2000, 39, 5037-5048), a cubic groupcontribution- (GC-) based equation of state (EOS) was developed for heavy hydrocarbons. Estimations of various thermophysical properties were obtained within the experimental accuracy from the triple point to 2 bar. The required inputs are the molecular structure of the compound and the experimental normal boiling temperature (Tb) or at least one vapor pressure measurement. This work presents a new GC method for estimating Tb values suitable for the cubic GCbased EOS of Coniglio et al. in order to obtain a purely predictive thermodynamic model. The performance of this purely predictive model is very satisfactory for all of the thermophysical properties investigated. Furthermore, excellent agreement between the Tb values estimated by the proposed GC method and experimental data (whenever available) is observed. Introduction The simulation, design, and analysis of products and processes require reliable and accurate information on thermophysical properties of pure components and mixtures. Unfortunately, the required properties (phase behavior, thermal properties, etc.) are generally not available for all components nor at all operating conditions of interest, and so, estimation procedures by thermodynamic models must be used. In the particular case of the chemical or petroleum/petrochemical industry, heavy (high-boiling) hydrocarbons (with molecular weights higher than 250) play an important role for at least three main reasons: (i) They significantly influence the phase behavior of crude oils or gas condensates although they occur in the mixture in rather small quantities. (ii) They occur in crude oils or gas condensates in considerable numbers (sometimes more than 100 heavy hydrocarbons) with various and sometimes complex molecular structures. Furthermore, the composition and identity of this class of components are often not properly defined. (iii) Their properties are generally not known experimentally. Considering all of these features, the most convenient thermodynamic models to be used for their simplicity and their performance are cubic equations of state (EOSs) with parameters estimated through the group-contribution (GC) concept. In the literature, the estimations of cubic EOS parameters are commonly based on the three-parameter corresponding state principle, which implies the use of the critical temperature, the critical pressure, and the acentric factor. These properties are, however, not known experimentally for most of high-boiling substances. Therefore, Coniglio et al.1 proposed a cubic GCbased EOS that does not verify the three-parameter corresponding state principle but rather involves pa* Author to whom correspondence should be addressed. Fax number: (+33) 3-83-37-81-20. Phone number: (+33) 3-83-1750-25. E-mail: [email protected]

rameters estimated by considering exclusively experimental properties that can easily be found for heavy (high-boiling) hydrocarbons. Various classes of thermophysical properties (such as vapor pressures, saturated liquid densities, heats of vaporization, saturated liquid heat capacities, and speeds of sound in saturated liquids) are estimated (correlated and predicted) within experimental uncertainty for a wide range of pressures (from the triple point to 2 bar). The required inputs of the GC-based EOS are, for each compound, the molecular structure and the experimental normal boiling exp is not known temperature (Texp b ). If the value of Tb (for example, for reasons of thermal decomposition of the compound), a simple procedure was also proposed by the authors to estimate it through the GC-based EOS ). The (the obtained values will be designated as TEOS b procedure requires the knowledge of at least one vapor pressure measurement. Even if the limit of the problem related to the estimation of the EOS parameters was delayed, however, the same problem reappears when no vapor pressure measurement is available. Consequently, the only real solution is to estimate the normal boiling temperature (Tb) through the GC concept (the obtained values will be designated as TGC b ). Successful GC methods for estimating Tb have been proposed recently.2,3 They perform very well and can be applied to a large variety of organic compounds (particularly, the Constantinou and Gani2 method). Concerning heavy (high-boiling) hydrocarbons, a higher degree of accuracy in Tb estimations, however, is required to obtain satisfactory results when calculating vapor pressures with the GC-based EOS proposed by Coniglio et al.1. The purpose of this work is to suggest a GC method for estimating Tb values of medium/heavy (high-boiling) and structurally complex hydrocarbons commonly found in crude oils or gas condensates, with a specific constraint: the GC method and the obtained Tb values should be particularly suitable for vapor pressure calculations with the cubic GC-based EOS developed by Coniglio et al.1 With this constraint, the proposed GC

10.1021/ie000723r CCC: $20.00 © 2001 American Chemical Society Published on Web 03/02/2001

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Ind. Eng. Chem. Res., Vol. 40, No. 7, 2001

method for estimating Tb should render the thermodynamic model of Coniglio et al.1 fully predictive (requiring as input only the molecular structure of the compound). Calculations of some other thermophysical properties (saturated liquid densities FL, heats of vaporization ∆vapH, saturated liquid heat capacities CPL, and speeds of sound in saturated liquids WL) will also be achieved in order to evaluate the accuracy of the obtained predictive thermodynamic model. The description of the proposed GC method for estimating Tb, and details on the database selected for the regression of the GC parameters, will be given in the next section. Typical results for Tb, vapor pressures (along with comparisons made with existing estimation methods of Tb), and the thermophysical properties investigated in this work (FL, ∆vapH, CPL, and WL) are shown in the Results and Discussion section, followed by our conclusions.

Table 1. Description of the GC-Based EOS1 Used in This Worka P)

Equation of State a(T) RT with vcorrected ) v - c(T) - 2 v - b v + 2bv - b2

Temperature-Dependent Parameter a T x T a(T) ) a(Tb) exp f1(m) 1 - f2(m) 1 Tb Tb with f1(m) )

[

{ [ ( )]

C2

(xC2 - y)

] [ m-

C1y

(xC2 - y)

[

[ ( ) ]}

]

y

(2)

, f2(m) )

] [

C1 x 1 m(xC2 - y) (xC2 - y)

]

(3)

1 x ) 0.4, y ) , C1 ) 0.787820, and C2 ) -16.2469 x Covolume b 7

b ) bCH4S/Vw,CH4

Development of the New GC Method The equations of the GC-based EOS used in this work1 are listed in Table 1 (eqs 1-8). The cubic EOS is of the Peng-Robinson4 type and uses the combination cubic EOS-consistent volume correction introduced by Peńeloux et al.5 and Rauzy.6 The three EOS parameters, a, b, and c, have been modified to fit the estimation of heavy (high-boiling) hydrocarbon properties. The temperature dependence of the energy parameter a is expressed through a modified version of the analytical form proposed by Melhem et al.7 The estimation of the covolume b is related to the van der Waals volume (Vw) calculated by Bondi’s GC method8 by taking methane as the reference for evaluating the proportionality between the two properties (b and Vw). The shape parameter m has a role similar to that of the acentric factor in the temperature-dependent parameter a. The temperature dependence of the volume correction c has been expressed through an exponential form. The normal boiling temperature (Tb) is taken as the reference temperature (instead of the conventional critical temperature) in the two temperature-dependent parameters a and c. The covolume b, the shape parameter m, and the value of the volume correction at Tb, c(Tb), are calculated through homogeneous GC methods, i.e., through the same calculation procedure. Indeed, the property estimation of a compound from its molecular structure is considered to be a collection of two types of contributions: (i) the contributions of basic functional groups and (ii) the contributions of structural corrections that account for various intramolecular effects. Contrary to the case of basic functional groups, there can be molecular structures that do not need any structural correction. The identifications of the basic functional groups and of the structural corrections are exactly the same as the ones defined by Bondi 8 for the estimation of the van der Waals volume. However, for the shape parameter m, which characterizes the shape of the molecule, new structural corrections had to be identified. For the hydrocarbons investigated (those currently found in crude oils or gas condensates, including alkanes, naphthenes, alkylbenzenes and condensed polynuclear aromatics), seven basic functional groups and three structural corrections (six for the shape parameter m) were required. Proposed Model. Let τbj be the contribution to Tb of the jth basic functional group which occurs Nj times, and let δτbk be the contribution to Tb of the structural

(1)

with

S)

∑V

3

+

w,jNj

j)1

bCH4 ) 26.80 cm3 mol-1

∑δV

w,kIk

(4)

k)1

Vw,CH4 ) 17.12 cm3 mol-1

and

Shape Parameter m 7

m ) C3 + S - C5 ln(1 + C4S2)

S)

with

∑

6

MjNj +

j)1

∑δm I

k k

k)1

(5a)

C3 ) 0.30048, C4 ) 0.08425, and C5 ) 0.88/xC4 for five hydrocarbons (cyclopentane, cyclohexane, isopropylcyclopentane, benzene, toluene) 7

m ) C3 + S - C5 ln(1 + C4S2) + ∆m

S)

with

∑M N j

(5b)

j

j)1

Temperature-Dependent Volume Correction c c(T) ) c(Tb)[1 + Ro(1 - Y) + βo(1 - Y)2] + (-1 + x2)b with T Y ) exp 1 (6) Tb

(

)

Ro ) R1Tb2 + R2, βo ) β1Tb + β2,

(7)

R1/10-6 ) 1.89213, R2 ) -0.25116, β1/10-3 ) 2.20483 and β2 ) -1.22706 7

c(Tb) ) RbTb + βbm2 - S

with

S)

3

∑C N + ∑δC I j

j

k k

j)1

(8a)

k)1

Rb ) 0.27468 and βb ) -50.94930 for cyclopentane and cyclohexane 7

c(Tb) ) RbTb + βbm2 - S + ∆c

with

S)

3

∑C N + ∑δC I j

j)1

j

k k

k)1

(8b)

a

Vw,j, Mj, and Cj are the contributions of the jth basic functional group to the van der Waals volume, to the shape parameter m, and to the volume correction at Tb, respectively. δVw,k, δmk, and δCk are the structural corrections related to the kth intramolecular effect for the estimation of the van der Waals volume, the shape parameter m, and the volume correction at Tb, respectively. Nj is the number of groups of type j, and Ik is the number of structural corrections related to the intramolecular effect of type k in a compound.

correction related to the kth intramolecular effect with Ik occurrences in a compound. The proposed GC model for the estimation of Tb takes the form

b 2 TGC b ) A0 + B0(ln S) + C0 m

(9a)

Ind. Eng. Chem. Res., Vol. 40, No. 7, 2001 1783

Figure 1. Normal boiling point in terms of number of carbon atoms for n-alkanes: +, experimental values of Tb; ×, values of Tb estimated through the GC-based EOS developed by Coniglio et al.1 and the knowledge of vapor pressure measurements; s, values of Tb calculated by the proposed GC method.

with 7

S)

∑ j)1

15

τbjNj +

∑ δτb Ik

k)1

k

(9b)

A0/K ) 258.257, B0/K ) 49.6530, and C0/(K cm3 mol-1) ) -1.35746(2 - x2). The parameters b and m are, respectively, the covolume and the shape parameter involved in the GC-based EOS of Coniglio et al.1 (Table 1, eqs 4 and 5, respectively). Equations 9a and b are shown in Figure 1 in terms of number of carbon atoms (up to NC ) 100) for (experimentally determined) n-alkanes. Values of Texp b (estimated through the whenever available or TEOS b GC-based EOS of Coniglio et al.1 and the knowledge of vapor pressure measurements) are also reported. Similar pictures are obtained for other classes of hydrocarbons in homologous series (n-alkylcyclopentanes, nalkylcyclohexanes, or n-alkylbenzenes). The very good exp EOS values agreement observed between TGC b and Tb /Tb for light to heavy (high-boiling) hydrocarbons confirms the suitable analytical form of eqs 9a and b. The basic functional groups and the structural corrections (identification and contributions) are given in Table 2. The identification of the basic functional groups is exactly the same as the one defined for the three parameters involved in the GC-based EOS used in this work [covolume b, shape parameter m, and volume correction c(Tb); see Table 1]. New structural corrections, however, had to be defined for Tb in order to capture a finer description of the molecular form of a compound and, thus, various intramolecular effects that were found to influence the property (such as blocked rotation encountered in nonaromatic branched systems or in biphenyl structures and steric crowding encountered in cis branching naphthenes or in aromatic systems with ortho disubstitutions). Whereas structural corrections 1, 2, 6, 7, and 15 are common to the shape parameter m estimation technique, structural corrections 3-5 and 8-14 had to be introduced specifically for Tb. Their identification (with the exception of

structural corrections 3-5, which derive from the GC method proposed by Constantinou and Gani2) is not predicated on any theoretical basis (such as the principle of conjugation operators in the ABC framework used by the Constantinou and Gani2 method or ab initio quantum mechanics used in the work of Wu and Sandler9) but rather is aimed to achieve accurate Tb estimations. The proposed method with the defined structural corrections (15 of them for the investigated hydrocarbons) is able to distinguish among some isomers found in paraffinic, naphthenic or aromatic systems. As also found by Coniglio et al.1 for the estimation of the shape parameter m, five hydrocarbons of low molecular weight had to be treated individually (cyclopentane, cyclohexane, isopropylcyclopentane, benzene, and toluene). Three of them occur first in different homologous series (cyclopentane, cyclohexane, and benzene) and, therefore, exhibit a particular behavior as compared to that of the derived branched compounds (for example, n-alkylcyclopentanes, n-alkylcyclohexanes, and n-alkylbenzenes, respectively). For these five compounds, the TGC b expression (eq 9a) has to be corrected whose values are given in by adding the term ∆TGC b Table 3. Finally, an important note should be made regarding the method for determining the occurrences of structural corrections 3-5, 8, 10-12, and 14 (if they exist in a compound). Structural corrections 3-5 and 14 have to be treated in an extensive way, i.e., as many times they appear in a compound (for example, for 2,3,4trimethylpentane, I3 ) 2; for 2,2,3,4,4-pentamethylpentane, I4 ) 2; for 2,2,3,3,4,4-hexamethylpentane, I5 ) 2; for o-xylene, I14 ) 1; and for 1,2,3-trimethylbenzene, I14 ) 2). On the other hand, structural corrections 10-12 have to be treated as for basic functional groups (for example, for diphenylmethane, I10 ) 1; for 2,2-diphenylpropane, I12 ) 1; and for diphenylethane, I10 ) 2). Furthermore, structural correction 8, which is commonly valid for compounds such as cis-1,2-dimethylcyclopentane, also has to be applied to condensed naphthenes in cis conformations such as cis-decaline or cishydrindane. Application Examples. To illustrate the proposed GC method for estimating Tb, sample assignments of the basic functional groups and of the structural corrections are provided for various chemically feasible hydrocarbons in the Supporting Information (Appendix I, Table A1). All of these examples were chosen so that structural corrections exist in their molecular form (which is not the case for many other investigated hydrocarbons). The Tb estimations along with the experimental data are also reported. We propose here to estimate Tb of a hypothetical hydrocarbon built with chemical blocks chosen to illustrate most of the structural corrections involved in the proposed GC method. The developed formula of the selected hypothetical hydrocarbon is shown in Figure 2. The assignments of the basic functional groups and of the structural corrections are given in Table 4, together with the Tb value estimated by the proposed GC method. Selection of the Database. The successful character of a GC method depends not only on its own definition (analytical expressions and group identification) but also on the number and reliability of the measurements selected to fit the GC parameters (the latter, indeed,

1784


Table 2. Basic Functional Groups and Structural Corrections for the Estimation of the Normal Boiling Temperature group alkyl

(sp3

CH3 CH2 CH C

τb

group

0.803931 1.77186 2.56070 3.32912

ACH ACsubstituted ACcondensed rings

carbon atom)

τb aromatic

structural corrections and occurrences

1.39979 3.06025 3.57473 δτb

normal alkanesa I1 = N(-0.5) for NC g 7 C branched alkanesb I2 = NC,P + Nsubst. - 6 for NC e 8 I2 = 2 for NC > 8 nonaromatic branched systems I3 ) occurrence of CH(CH3)-CH(CH3) structure I4 ) occurrence of CH(CH3)-C(CH3)2 structure I5 = occurrence of C(CH3)2-C(CH3)2 structure naphthenes (five- or six-membered rings) I6 ) occurrence of five-membered ring I7 ) occurrence of six-membered ring I8 ) (-1)∑lλ-l per cis double branching [1-2 or 1-3] in five- or [1-2, 1-3, or 1-4] in six-membered ringsc aromatic systems I9 ) occurrence of CH3-AC structure I10 ) occurrence of CH2(noncyclic)-AC structure I11 ) occurrence of CH2(cyclic)-AC structure I12 ) occurrence of [CH(noncyclic)-AC or C(noncyclic)-AC] structure I13 ) occurrence of substitution in position 2, 2′, 6, or 6′ in biphenyl structure I14 ) occurrence of R-vicinal noncyclic disubstitution condensed polynuclear aromaticsd I15 ) 1 for naphthalene and derived compounds I15 ) (-1)R0.15(NC,2 + 2NC,3) for other compounds (phenanthrene, pyrene, ...)

-1.57503 -0.209878 0.161289 0.454852 1.21475 -1.93623 -1.25952 0.166022 -0.678644 -0.913446 -0.542889 -1.24178 -1.30161 0.231818 -1.17975

a N ) Number of carbon atoms in the molecule. b Branched alkanes with neither quaternary carbon atoms nor substituted neighboring C carbon atoms. NC,P is the number of carbon atoms in the main chain, and Nsubst. is the number of substitutions in the molecule. c λl ) position of the lth cis branching. d R ) number of aromatic rings in the molecule; NC,2 and NC,3 ) number of condensed aromatic ring carbon atoms in common with two or three rings, respectively.

Table 3. List of Compounds Requiring the Corrective Term ∆TGC b for the Estimation of the Normal Boiling Temperature compound

∆TGC b

cyclopentane cyclohexane isopropylcyclopentane benzene toluene

3.65 -12.27 9.39 -13.10 -6.32

have to be regressed on all of the experimental data). Furthermore, these data should cover a large number of classes of compounds. As far as we are concerned in this work, the classes of compounds should be commonly found in crude oils or gas condensates (paraffins, naphthenes, alkylbenzenes, and condensed polynuclear aromatics), and each of them should cover various molecular structures (including complex ones). The selected hydrocarbons should also be medium to heavy (high-boiling) compounds with a major proportion of heavy ones in order to increase the predictive abilities of the method. However, few Tb measurements are available in the literature for heavy (high-boiling) hydrocarbons because of thermal decomposition. Moreover, one should keep in mind that the proposed GC method for estimating Tb should satisfy a constraint (which is actually the real objective of this work) of achieving suitable vapor pressure calculations with the GC-based EOS of Coniglio et al.1 Therefore, the selected database comprises 135 compounds for which experimental values of Tb are known (hydrocarbons of category I, Texp b /K ) 300-600) plus 55 much heavier (higher-boiling) compounds for which measured values of Tb could not be found in the

literature, so that they had to be estimated with the procedure proposed by Coniglio et al.,1 i.e., with their GC-based EOS and the knowledge of at least one vapor pressure measurement (hydrocarbons of category II, /K ) 430-750). Indeed, the procedure showed TEOS b very good performance for the estimation of Tb and also vapor pressures over extended temperature ranges. Typically, the errors in Tb (as reported by the authors for hydrocarbons of category I) were never greater than 0.3 K, regardless of the experimental datum on the saturation curve (from 0.1 × 10-5 to 2 bar), and vapor pressures (PS) were calculated within the experimental accuracy of this type of measurements (1% for PS values ranging from 0.1 × 10-5 to 0.01 bar, 0.5% for PS values ranging from 0.01 to 0.06 bar, and 0.3% for PS values ranging from 0.06 to 2 bar). Values of Tb obtained by ) are given in the the Coniglio et al.1 procedure (TEOS b Supporting Information (Appendix II, Table A2) for the 55 hydrocarbons of category II selected in our database (the deviations in vapor pressures, along with the references for the data, are also reported). Concerning the 135 hydrocarbons of category I, most of their experimental values of Tb (Texp b ) are from ebulliometric vapor pressure measurements made around 1945 by the NBS/American Petroleum Institute.10 Regression. The optimization algorithm used for the regression of the GC parameters (contributions of the basic functional groups and of the structural corrections, plus the A0, B0 and C0 constants) is the NewtonRaphson approach. The objective function was to minimize the sum of squares of the differences between the EOS and TGC Texp b /Tb b (eq 9) values.


Figure 2. Developed formula of a hypothetical hydrocarbon built with chemical blocks chosen to illustrate most of the structural corrections involved in the GC method proposed for estimating the normal boiling temperature. Table 4. Estimation of the Normal Boiling Temperature of a Hypothetical Hydrocarbon (see Figure 2) through the Proposed GC Methoda Basic Functional Group Assignment (Occurrences) CH3 (15), CH2 (13), CH (13), C (1) ACH (30), ACsubstituted (16), ACcondensed rings (24) Structural Correction Assignment Related to Tb (Occurrences) Branched Alkanes: CH(CH3)-CH(CH3) structures (I3 ) 2) Naphthenes: five-membered rings (I6 ) 2) + six-membered rings (I7 ) 2) + cis double branching [1,2]a, [1,3]b and [1,4]c in six-membered ring (Ia8 ) +1, Ib8 ) -1, and Ic8 ) +1) + cis double branching [1,2]d and [1,3]e in five-membered ring (Id8 ) +1 and Ie8 ) -1) Aromatic Systems: CH3-AC structures (I9 ) 3) + CH2(noncyclic)-AC structures (I10 ) 4 because the CH2(noncyclic)-AC structure has to be counted only once) + CH2(cyclic)-AC structures (I11 ) 3) + [CH(noncyclic)-AC + C(noncyclic)-AC] structures (I12 ) 2) + substitutions in positions 2 and 6′ in biphenyl structure (I13 ) 2) + R-vicinal noncyclic disubstitutions (I14 ) 3) block block Condensed Polynuclear Aromatics: Ipyrene ) 1.2 because R ) 4, NC,2 ) 4, and NC,3 ) 2; plus Inaphthacene ) 0.9 15 15 block because R ) 4, NC,2 ) 6, and NC,3 ) 0; plus Icoronene ) -2.7 because R ) 7, N ) 6, and N ) 6 C,2 C,3 15 Structural Correction Assignment Related to the Covolume b (Occurrences) Ring Systems: one free cyclopentyl ring plus one free cyclohexyl ring (I1 ) 2) + one cyclopentyl ring condensed to one cyclohexyl ring in cis conformation (I2 ) 2) + two methylene rings (cyclopentyl ring and cyclohexyl ring) condensed to an aromatic system (I3 ) 2) Structural Correction Assignment Related to the Shape Parameter m (Occurrences) Ring Systems: two cyclopentyl rings (I3 ) 2) + two cyclohexyl rings (I4 ) 2) + one tert-butyl group attached to an aromatic ring (I5 ) 1) block block Polynuclear Aromatics: three condensed polynuclear aromatic blocks (Ipyrene ) 1.2 plus Inaphthacene ) 0.9 plus 6 6 coronene block I6 ) -2.7) Result 3 -1 TGC b /K ) 1073.28, covolume b/(cm mol ) ) 1351.13, shape parameter m ) 1.63531 a Concerning the covolume b and the shape parameter m,1 the basic functional group assignments and occurrences are identical to those provided for Tb; structural corrections, however, are different.

Results and Discussion The results related to property X will be expressed in terms of percent average relative deviations [δr(X)%] or average absolute deviations [∆(X)]. Details for the databases related to vapor pressures (PS), saturated liquid densities (FL), thermal properties (heats of vaporization, ∆vapH, and saturated liquid heat capacities, CPL), and speeds of sound in saturated liquids (WL) are given by Coniglio et al.1 Normal Boiling Temperature and Vapor Pressures. Results were grouped into two categories according to the databases to which they are related: hydrocarbons of category I or of category II (see Selection of the Database section). A comparison with two successful and recent GC methods2,3 for estimating Tb is made for this property (Table 5) and also for vapor pressures calculated with the GC-based EOS of Coniglio

et al.1 combined with the various Tb estimation techniques (Table 6). It is worth mentioning that this comparison should be considered cautiously as all tested methods do not have the same applicability range and were not developed by considering a common database. Particularly, the Constantinou and Gani2 method is valid for a wide range of organic compounds (including oxygen, nitrogen, halogens, and sulfur-containing substances). The Avaulleé et al.3 method is valid for hydrocarbons and also sulfured compounds, whereas the proposed method is valid only for hydrocarbons. Nevertheless, the possibility of extending the proposed method to larger classes of organic compounds should be realized by leaving unchanged the GC parameters related to hydrocarbons and introducing into the method new parameters for only the contributions of the functional groups that are missing to describe the molecular structure of the new compounds. In that sense, Tb esti-

1786


Table 5. Deviations in the Normal Boiling Temperature. Comparison between Experimental Values (Hydrocarbons of Category I) or Values Estimated through the GC-Based EOS of Coniglio et al.1 (Hydrocarbons of Category II) and Values Calculated by Various GC Methodsa hydrocarbons of category Ib

hydrocarbons of category IIc

δr(Tb)%

δr(Tb)%

class of hydrocarbons

NH

d

d

ref 2

ref 3

this work

NH

ref 2

ref 3

this work

normal alkanes branched alkanes cyclopentanes cyclohexanes alkylbenzenes polynuclear aromatics overall

13 38 18 21 32 6 128

1.35 0.94 1.01 1.17 0.86 4.46 1.17

0.69 1.17 1.03 0.79 0.91 0.91 0.96

0.47 0.59 0.61 0.71 0.44 0.69 0.57

12 3 1 6 22 11 55

4.64 2.85 0.06 2.51 3.78 5.13 3.98

0.23 1.62 0.41 0.71 2.33 1.12 1.38

0.39 0.91 0.40 0.35 0.97 0.73 0.71

a Constantinou and Gani,2 Avaulle ´ e et al.,3 and this work. b Hydrocarbons for which the experimental value of Tb is available in the literature. c Hydrocarbons for which the value of Tb determined experimentally could not be found in the literature; it was then estimated through the GC-based EOS of Coniglio et al.1 with the knowledge of vapor pressure measurements. d Number of hydrocarbon compounds.

Table 6. Estimation of Vapor Pressures with the GC-Based EOS of Coniglio et al.1 by Using Various GC Methods for Calculating the Normal Boiling Temperaturea (i) Information by Class of Hydrocarbons hydrocarbons of category Ib

hydrocarbons of category IIc

δr(PS)% d

δr(PS)% d

class of hydrocarbons

NP

ref 2

ref 3

this work

NP

ref 2

ref 3

this work


496 805 398 606 844 236 3385

28.36 12.89 12.41 20.46 13.03 >50 22.00

9.55 13.89 13.70 10.49 12.66 9.98 12.04

7.28 7.40 7.56 9.74 5.40 8.57 7.40 (1.94)e

190 82 15 119 519 196 1121

>50 >50 1.03 >50 >50 >50 >50

6.52 32.06 7.07 15.52 49.70 26.45 32.83

10.61 18.54 6.95 6.85 19.33 17.60 16.00 (1.97)f

(ii) Information by Pressure Range hydrocarbons of category I

hydrocarbons of category II

δr(PS)%

δr(PS)%

pressure range (bar)

NP

ref 2

ref 3

this work

NP

ref 2

ref 3

this work

(0.1 × 10-5) - 0.01 0.01-0.06 0.06-2 (7)

378 236 2771

49.05 28.80 17.73

15.49 11.57 11.61

11.64 7.67 6.80

775 222 124

>50 >50 49.77

37.40 24.52 19.10

17.34 14.12 11.04 exp

a

Constantinou and Gani,2 Avaulleé et al.,3 and this work. b Hydrocarbons for which the experimental value of Tb (designated as Tb ) is available in the literature. c Hydrocarbons for which the value of Tb determined experimentally could not be found in the literature; it was then estimated through the GC-based EOS of Coniglio et al.1 with the knowledge of vapor pressure measurements (values designated EOS exp EOS as Tb ). d Number of vapor pressure measurements. e Deviation obtained by using Tb values. f Deviation obtained by using Tb values. Table 7. Estimations of Various Thermophysical Properties by the GC-Based EOS Developed by Coniglio et al.1 Combined with the GC Method Proposed in This Work for Calculating the Normal Boiling Temperaturea,b class of hydrocarbons (category I)

NPc

δr(FL) (%)

NPc

δr(∆vapH) (%)

NPc

δr(CPL) (%)

NPc

δr(WL) (%)


270 213 68 87 329 54 1021

0.81 0.90 0.72 0.70 0.89 1.26 0.86 (0.51)

120 77 14 139 151 102 603

0.70 1.02 0.44 1.26 0.86 1.37 1.02 (0.66)

212 444 122 416 177 83 1454

0.58 2.62 2.99 1.87 1.47 1.75 1.95 (1.96)

133 164 6 40 343

10.11 8.99 7.04 10.35 9.55 (9.35) exp

Deviations obtained from experimental values of Tb are given in parentheses. b FL/number of compounds ) 117; Tb /K ) 310-604; exp exp T/K ) 273-604. ∆vapH/number of compounds ) 69; Tb /K ) 310-615; T/K ) 260-650. CPL/number of compounds ) 69; Tb /K ) 310exp c 610; T/K ) 120-460. WL/number of compounds ) 28; Tb /K ) 300-560; T/K ) 200-470. NP ) number of experimental data points. a

mations as obtained with the actual version of the proposed method would not change. Therefore, all general conclusions that will be drawn in the following should be restricted to hydrocarbon compounds. Finally, it should be pointed out that, for hydrocarbons of category II, the comparison of the Tb estimates calcu-

lated by the Constantinou and Gani2 and Avaulleé et al.3 methods (Table 5) has been provided for guidance in better understanding the deviations in the vapor pressures obtained for the same category of hydrocarbons (Table 6). Indeed, as no experimental values of Tb are available for these compounds, the comparison of


Figure 3. Estimation of saturated liquid densities through the GC-based EOS developed by Coniglio et al.1 combined with the proposed GC method for calculating the normal boiling point. (a) Comparison with the estimations obtained by using experimental values of Tb for (a1) n-propylcyclopentane and (a2) n-pentadecane. (b) Results for some heavy hydrocarbons. s, Tb calculated by the proposed GC method; - - -, experimentally determined Tb; patterns, experimental data for FL.11

the Tb estimation techniques was made by considering as reference values those calculated with the procedure proposed by Coniglio et al.1 (i.e., with their GC-based EOS and the knowledge of at least one vapor pressure measurement). The following conclusions summarize our observations:

(i) Considering first hydrocarbons of category I, the Constantinou and Gani2 and Avaulleé et al.3 methods exhibit Tb estimations with roughly the same accuracy [for the compounds as a whole, δr(Tb) ) 1.17% and 0.96%, respectively], with the exception of the condensed polynuclear aromatics for which Avaulleé et al.3 performs much better (by around 3.5%). A significant difference in accuracy is observed, however, when vapor pressures are calculated with the Tb estimates obtained by the two methods and the GC-based EOS of Coniglio et al.1 [for the data as a whole, δr(PS) ) 12% with Avaulleé et al.,3 whereas δr(PS) ) 22% with Constantinou and Gani2). This result shows that Tb is a very sensitive “parameter” in the EOS used,1 as is the critical temperature in any cubic EOS. This feature is particularly significant for very low vapor pressures ranging from 0.1 × 10-5 to 0.01 bar (see Table 6ii for information by pressure range). (ii) Considering again hydrocarbons of category I, better accuracy in Tb estimation is observed with the proposed method [overall deviation of δr(Tb) ) 0.57%], which results in significant improvement in the vapor pressure calculations (with the EOS) when compared to the application of the Constantinou and Gani2 or Avaulleé et al.3 techniques [overall deviation with the proposed method of δr(PS) ) 7.4%]. Of course, the deviation in the vapor pressures is larger than the one obtained by using the experimental value of Tb [overall deviation of δr(PS) ) 1.9%]. It can be concluded, however, that the performance of the proposed method is very good, with no particular failure for all of the investigated hydrocarbons. (iii) Considering now hydrocarbons of category II, larger deviations in Tb as well as vapor pressures are obtained with the three approaches (Constantinou and Gani, 2 Avaulleé et al.,3 and the proposed one). These compounds indeed have higher molecular weights (higher Tbs) and more complex molecular structures than those of category I. Furthermore, their vapor pressure measurements range mainly from 0.1 × 10-5 to 0.01 bar and can exhibit large experimental uncertainties and discrepancies (from 2 to 10%, see Coniglio et al.1). Nevertheless, the performance of the proposed method is still satisfactory for all of the investigated hydrocarbons of category II [overall deviations of δr(Tb) ) 0.71% and δr(PS) ) 16%, half as large as those obtained with the Avaulleé et al.3 method]. Other Thermophysical Properties. Estimations related to saturated liquid densities (FL), thermal properties (heats of vaporization ∆vapH and saturated liquid heat capacities CPL), and speeds of sound in saturated liquids (WL) obtained with the GC-based EOS of Coniglio et al.1 and the GC method proposed in this work for calculating Tb are summarized in Table 7. All of the results concern hydrocarbons of category I (i.e., compounds with experimentally known Tb values). Details on the databases related to FL, ∆vapH, CPL, and WL are given by Coniglio et al.1 As could be expected, the properties for which the estimation of Tb has a significant impact are saturated liquid densities and heats of vaporization. Indeed, FL and ∆vapH are, respectively, of orders zero and one, whereas CPL and WL are of order two, if order is defined as the degree of derivation of the EOS leading to the property calculation. The performance of the proposed method for the two properties FL and ∆vapH is nevertheless very good [overall deviations of δr(FL) ) 0.9% and

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are shown in Figure 3 for saturated liquid densities and in Figure 4 for heats of vaporization. As can be seen, very good estimations are obtained, particularly for heavy (high-boiling) hydrocarbons. Concerning CPL and WL, similar accuracy is obtained by using values of Tb either estimated from the proposed exp GC method (TGC b ) or experimentally determined (Tb ) [overall deviations of δr(CPL) ) 1.9% and δr(WL) ) 9.5% with TGC b values and δr(CPL) ) 2.0% and δr(WL) ) 9.3% values]. This overall tendency is also obwith Texp b served for each class of hydrocarbons investigated. Conclusion

Figure 4. Estimation of heats of vaporization through the GCbased EOS developed by Coniglio et al.1 combined with the proposed GC method for calculating the normal boiling point. (a) Comparison with the estimations obtained by using experimental values of Tb for (a1) n-hexane and (a2) trans-decaline. (b) Results for some heavy hydrocarbons. s, Tb calculated by the proposed GC method; - - -, experimentally determined Tb; patterns, experimental data for ∆vapH.11-14

δr(∆vapH) ) 1.0%, whereas these deviations were δr(FL) ) 0.5% and δr(∆vapH) ) 0.7% when the experimental values of Tb were used]. Furthermore, the quality of the property calculations (FL and ∆vapH) obtained with the proposed method (and the EOS) is essentially the same regardless of the class of the compound concerned (paraffins, naphthenes, or aromatics). Typical results

A new GC method for estimating the normal boiling temperature Tb, particularly suitable for vapor pressure calculations with the cubic GC-based EOS proposed by Coniglio et al.,1 has been developed. At this stage of this work, the applicability range of the method are mediumto high-molecular-weight (high-boiling) and structurally complex hydrocarbons commonly found in crude oils or gas condensates (alkanes, naphthenes, alkylbenzenes, and condensed polynuclear aromatics). More precisely, their Tb values range from 280 to 750 K. Another feature of the new GC method is that it distinguishes among some isomers found in paraffinic, naphthenic, or aromatic systems. The combination of the proposed GC method with the GC-based EOS of Coniglio et al.1 leads to a purely predictive thermodynamic model requiring as a single input the molecular structure of the compound. Other thermophysical properties such as saturated liquid densities (FL), heats of vaporization (∆vapH), saturated liquid heat capacities (CPL), and speeds of sound in saturated liquids (WL) were also calculated in order to evaluate the accuracy of the predictive thermodynamic model. Very satisfactory estimations were obtained over a wide range of pressures (from the triple point to 2 bar) for all properties [overall deviations of δr(PS) ) 9.5%, δr(FL) ) 0.9%, δr(∆vapH) ) 1.0%, δr(FL) ) 2.0%, and δr(WL) ) 9.6%]. Furthermore, no failure of the purely predictive thermodynamic model was detected for the investigated hydrocarbons (even for condensed polynuclear aromatics). Finally, the excellent agreement observed between the Tb values estimated by the proposed GC method and the experimental data (whenever available) indicates that the new approach can also be used separately from the GC-based EOS of Coniglio et al.1 as a property estimation method [overall deviation of δr(Tb) ) 0.6%, i.e., ∆(Tb) ) 2.38 K]. Because of its purely predictive, reliable, and accurate features, the GC-based EOS of Coniglio et al.1 combined with the proposed GC method for estimating Tb can be a helpful tool in computer-aided product or process design. Supporting Information Available: Appendix I, a table (Table A1) that gives sample assignments of the basic functional groups and of the structural corrections involved in the GC method proposed for the normal boiling temperature for various chemically feasible hydrocarbons. Appendix II, a table (Table A2) that gives for the hydrocarbons of category II selected in the database of the work presented in this paper the estimation of the normal boiling temperature from the procedure proposed by Coniglio et al.1 Also provided is a comparison of the percent average relative deviations


in the vapor pressures obtained (a) by considering TEOS b values and (b) by considering values of Tb suggested in the literature (not experimentally determined). This material is available free of charge via the Internet at http://pubs.acs.org. Nomenclature a ) temperature-dependent energy parameter of the cubic equation of state a(T) ) function taken as a model for the temperaturedependent parameter a a(Tb) ) value of the function a(T) at the normal boiling temperature b ) covolume of the cubic equation of state bCH4 ) methane covolume calculated from the critical properties c ) volume correction of the cubic equation of state c(T) ) temperature-dependent volume correction of the cubic equation of state c(Tb) ) value of the temperature-dependent volume correction c(T) at the normal boiling temperature C1, C2 ) constants characteristic of the function a(T) C3, C4, C5 ) constants involved in the estimation method related to the shape parameter m Cj ) contribution of the jth basic functional group to c(Tb) Ik ) occurrences of the structural correction related to the kth intramolecular effect involved in the estimation of a specific pure-component property through the groupcontribution concept m ) shape parameter Mj ) contribution of the jth basic functional group to the shape parameter m NC,2 ) number of condensed aromatic ring carbon atoms in common with two rings NC,3 ) number of condensed aromatic ring carbon atoms in common with three rings Nj ) number of basic functional groups of type j involved in the estimation of a specific pure-component property through the group-contribution concept NP ) number of property measurements for a specific database P ) pressure PS ) vapor pressure T ) temperature Tb ) normal boiling temperature (normal boiling point) ) normal boiling temperature as estimated by the TEOS b group-contribution-based equation of state of Coniglio et al.1 and the knowledge of vapor pressure measurements exp Tb ) normal boiling temperature determined experimentally TGC ) normal boiling temperature as estimated by the b group-contribution method proposed in this work τbj ) contribution of the jth basic functional group to the normal boiling temperature v ) molar volume Vw ) van der Waals volume of a molecule Vw,CH4 ) van der Waals volume of methane Vw,j ) contribution of the jth basic functional group to the van der Waals volume estimated by Bondi’s method8 W ) speed of sound in a fluid x, y ) powers of function a(T) Superscripts exp ) experimental cal ) calculated GC ) group contribution EOS ) equation of state

Subscripts b ) boiling corrected ) property calculated by a cubic equation of state corrected with a volume correction L ) related to the saturated liquid r ) relative S ) saturation vap ) molar property of vaporization Greek Symbols R ) number of aromatic rings in a molecule R1, R2 ) parameters involved in the calculation of Rb Rb, βb ) parameters expressed in terms of the normal boiling temperature in the estimation of c(Tb) β1, β2 ) parameters involved in the calculation of βb δmk ) contribution of the structural correction related to the kth intramolecular effect for the estimation of the shape parameter m δCk ) contribution of the structural correction related to the kth intramolecular effect for the estimation of c(Tb) δτbk ) contribution of the structural correction related to the kth intramolecular effect for the estimation of the normal boiling temperature δr(X) ) percent average relative deviation in the property NP exp |(Xexp - Xcal X, δr(X) ) (100/NP)∑i)1 i i /Xi )| δVw,k ) contribution of the structural correction related to the kth intramolecular effect for the estimation of the van der Waals volume by Bondi’s method8 ∆c ) corrective term required for two hydrocarbons (cyclopentane and cyclohexane) in the estimation of c(Tb) ∆m ) corrective term required for five hydrocarbons (cyclopentane, cyclohexane, isopropylcyclopentane, benzene, and toluene) in the estimation of the shape parameter m ∆TGC ) corrective term required for five hydrocarbons b (cyclopentane, cyclohexane, isopropylcyclopentane, benzene, and toluene) in the estimation of the normal boiling temperature ∆vapH ) molar heat of vaporization ∆(X) ) average absolute deviation in the property X, ∆(X) NP ) (1/NP)∑i)1 |Xexp - Xcal i i | F ) density

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Vapor Pressures of Some Pure Substances in the Normal and LowPressure Region; Elsevier: Amsterdam, 1984. (11) Thermodynamics Research Center. TRC Thermodynamic TablessHydrocarbons; Texas Engineering Experiment Station, The Texas A&M University System: College Station, TX, 1987. (12) Kudchadker, A. P.; Kudchadker, S. A.; Wilhoit, R. C. Anthracene and Phenanthrene; API Monograph Series; API Publication 708, American Petroleum Institute: Washington, D.C., 1979. (13) Majer, V.; Svoboda, V. Enthalpies of Vaporization of Organic Compounds; IUPAC Chemistry Data Series 2; Blackwell: Oxford, U.K., 1985.

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Received for review August 7, 2000 Revised manuscript received January 5, 2001 Accepted January 10, 2001 IE000723R

A Method for Estimating the Normal Boiling Point of Heavy

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