Property estimation for design, simulation and analysis of biodiesel processsystems: Review and Implementation

Fabrıcio Rodrigues, Adilson J. Assis∗

aFaculdade de Engenharia Quımica, Universidade Federal de Uberlandia, Av. Joao Naves de Avila, 2121, Bloco 1K, Campus Santa Monica,CEP: 38400-901, Uberlandia, MG, Brazil

Abstract

Biodiesel is a very attractive alternative to fossil fuels in several aspects (e.g. sustainability), but requires economicefficient process in order to be viable. Therefore, the application of systematic methods for process synthesis, designand analysis is of special interest for biodiesel process systems. The success of most systematic approaches is based onphysicochemical properties values that are difficult (and sometimes impossible) to be experimentally obtained. Prop-erty estimation methods are a practical way to fulfill this gap, however the complex nature of the molecules involvedrequires the application of more refined theories to capture the intrinsic physicochemical behavior. To overcome thishudrle, an extensive review of the literature was performed in order to obtain the most representative compounds,experimental data for several properties and the state-of-the-art property estimation methods resulting in a computer-aided system to analyze (focusing on consistency checks) and selected the best estimation methods. The result isa robust set of estimation methods that provide the basis for biodiesel process systems simulation. The generatedknowledge and computational tools are, thus, integrated to develop a package that extends the original ChemSepcompound database, including more than additional 200 compounds (acylglicerydes, fatty acids, fatty acid methylesters and fatty acid ethyl esters) typically present in biodiesel process systems and implements the selected propertyestimation methods. The main advantage of the package is brought by the CAPE-OPEN capabilities of ChemSep thatenables the use of reliable physicochemical properties for biodiesel process systems in any process simulator that isCAPE-OPEN compliant.

Keywords: Property estimation, Biodiesel process simulation, CAPE-OPEN

1. Introduction

Biodiesel fuel has many advantages in comparison tofossil fuels. Biodiesel yields much more energy thanused in its production (372% more than bioethanol)(Hill et al., 2006), has good transportation propertiesdue to its low volatility (Krawczyk, 1996), can be pro-duced from many different renewable sources (Ma andHanna, 1999) and can be added, in small amounts(1-2w%), to regular diesel fuel with low lubricantproperties to yield an acceptable fuel (Gerpen, 2005).Nonetheless there are also many hurdles for its produc-tion and consumption, been the biodiesel price the mainhurdle as most existing processes can only deal withhigh value raw materials (Ma and Hanna, 1999; Zhanget al., 2003b).

∗Corresponding author. Tel.: +55 3291 4189 ramal XXXEmail address: ajassis@feq.ufu.br (Adilson J. Assis)

Although governments of many countries offer sub-sides to make the biodiesel production profitable thereis a very strong need to improve the process economics.The application of process synthesis and design tech-niques (Biegler et al., 1997) can contribute very muchto process profitability whilst amplifying the social andenvironmental benefits of biodiesel. Energy savings ofaround 50% and net present cost reductions of 35% havebeen achieved in industry (Siirola, 1996) and severalother examples of successful industrial applications andbest practices of process synthesis and design methodsand tools have been reported (Harmsen, 2004). How-ever, most, if not all, of these techniques require theknowledge of a set of physical and chemical proper-ties that are currently not widely available for the com-pounds involved in biodiesel systems.

The complex nature of some molecules (typicaltriglycerides have more than 50 carbons with manyunsaturations present) and the experimental difficulties

Preprint submitted to Bioresource Technology September 28, 2014

(and impossibilities) to obtain experimental data forsome properties (e.g. critical temperature due to degra-dation), requires the application of more refined theoriesto capture the physicochemical behavior of the involvedmolecules. Property estimation methods represent apractical way to fulfill this gap. Several methods havebeen developed and even though many authors have re-viewed the field (Su et al., 2011; Dıaz-Tovar et al., 2011;Chang and Liu, 2009), none of the discussions havegiven the proper focus to the property models behav-ior. For example, some property models fit very wellexperimental data for some compounds, but for othermolecules, that have no experimental data included, themodel presents inconsistencies (e.g. heat capacity de-creases with temperature increase) and a purely statisti-cal analysis of the methods deviations is, thus, not ableto identify.

Therefore, objectives of this paper are to discuss, as-sess and select property estimation methods, showingthat the analysis of the property models behavior pro-vides a powerful tool to select a proper estimation meth-ods in the face of scarce experimental data, and to im-plement the generated knowledge in a computationaltool that is CAPE-OPEN compliant providing a reliableenvironment for the application of process synthesis anddesign techniques to biodiesel process systems.

2. Computer-aided tools developed for the analysis

The compounds present in biodiesel process sys-tems can be summarized in short-chain alcohols (e.g.methanol, ethanol), glycerol, acylglycerides (AC), fattyacids (FA) and alkyl esters (AE). The properties ofshort-chain alcohols and glycerol are usually includedin common process simulators and databases, and a firststep for the analysis was the identification of 220 rel-evant compounds (29 fatty acids, 69 triglycerides, 40diglycerides, 15 monoglycerides, 29 fatty acid methylesters and 29 fatty acid ethyl esters). The next and moretime consuming step was an extensive literature reviewto gather information regarding compounds, importantproperties and state-of-the-art estimation methods. Tomanage and organize the information, a database wascreated in Microsoft Access and implemented in C# re-sulting in a software named BioPES (BIOdiesel Prop-erty Estimation System) that offers aids as illustratedin Figure 1 (the software can be obtained by the readerthrough contact with the authors).

Figure 2: General molecules of saturated (a) fatty acids, (b) simpletriglycerides, (c) fatty acid methyl esters and (d) fatty acid ethyl esters.

3. Property estimation model analysis and practicalimplications

During the extensive literature review, several state-of-the-art property estimation methods were identifiedfor each of the selected properties. The methods can beclassified based on their approach to estimate the prop-erty, most of the methods are based on the group con-tribution approach and a complete classification of theestimation methods is presented in Tables 2 and 10.

The compounds analyzed are also classified in fattyacids (FA), acylglycerides, fatty acid methyl esters(FAME) and fatty acid ethyl esters (FAEE). The fourclasses of compounds can be divided in sub-classesbased on the number of unsaturations present in themolecule. For each of these subclasses there is a gen-eral structure form for each of the property estima-tion approaches. This general structure allows to writethe property estimation methods in a simplified waythat can substantially increase our understanding of themodel.

To organize and simplify the discussion, propertieswere classified in primary (depend only on the molecu-lar structure), secondary (cannot be explicitly calculatedonly from structural information and usually require theknowledge of other properties) and temperature depen-dent properties.

3.1. General Structure of the Compounds Involved inBiodiesel Process Systems

A general structure for each subclass of the involvedcompounds is derived as a basic means to understandand extrapolate the behavior of the property estimationmethods. In Figure 2 some classes of molecules arepresented in a generalized way, from this representa-tion is possible to draw generalized structures for eachof the approaches listed in Tables 2 and 10 as shownin Table 1 for a group contribution method based onthe UNIFAC groups and considering only first-order

2

Figure 1: Concept of BioPES

Table 1: General structure of saturated FA, simple TG, FAME andFAEE for a first-order group contribution method.

Class Group Contribution(Saturated) StructureFA 1.CCH3 + n.CCH2 + 1.CCOOH

TG 3.CCH3 + (3n + 2).CCH2 + 3.CCH2COO + CCH

FAME 2.CCH3 + n.CCH2 + 1.CCH2COO

FAEE 2.CCH3 + (n + 1).CCH2 + 1.CCH2COO

groups, such as Gani and Constantinou (1996); Mar-rero and Gani (2001). Other group-contribution meth-ods that use different groups than those defined in theUNIFAC group-contribution can easily be converted tothe proposed general structure as well as other classesof compounds, more information is given in Tables S1and S2.

At this point, it is possible to write any of the propertymodel functions in terms of general structures (such asthe ones presented in Table 1) which will greatly sim-plify the analysis of next section.

3.2. Primary and Secondary Properties

Primary properties are those that depend only of thechemical structure of the molecule considered. Theprimary properties considered are: critical temperature(Tc), critical pressure (Pc), critical volume (Vc), boilingpoint (Tb), melting point (Tm), standard Gibbs energyof formation (∆G f ) and standard enthalpy of formation(∆H f ). Secondary properties are those that cannot be

explicitly written only in terms of the chemical struc-ture and are often a function of other properties, the onlysecondary property analyzed is the acentric factor (ω).

Most of the estimation methods in the literature forprimary properties are of the group contribution type.They all assume that the groups have an additive contri-bution to the overall property value. Multi-level contri-butions are used as corrections for specific multigroup,conformational or resonance effects.

The methods in Table 2 represent selected methodsfor the estimation of primary properties. In Table 3 arepresented the experimental data points gathered for theevaluation of primary properties in which it is clear thelack of experimental data for acylglycerides for mostproperties.

3.2.1. Critical TemperatureAs presented in Table 2, five estimation methods are

analyzed for critical temperature, the property modelfunction of these methods is presented in Table 4. Ap-plying the general structure of saturated FAME in Ta-ble 4 the general property model functions shown inTable 5 are obtained (the property model functions forother classes of compounds are presented in Tables S3and S4). The estimation methods were checked against22 experimental data points, distributed within eachclass of compounds as presented in Table 3. The re-sults in terms of average absolute deviation (AAD =

1/n∑n

i=1 |Pexp − Pcalc|) and average relative deviation(ARD = 1/n

∑ni=1 100|Pexp − Pcalc|/Pexp) are presented

in Table 6. The CG method provided the lowest ARD,however no experimental data are available for acyl-glycerides further analysis is providential.

3

Table 2: Characteristics of the primary and secondary property estimation methods considered.

Property Estimation Method Approach

Tc

Fedors (1982)

Group-ContributionJoback and Reid (1987) (JR)

Tu and Liu (1996) (TL)

Gani and Constantinou (1996) (CG)

Marrero and Gani (2001) (MG)

Vc, Pc, Tb, Tm,∆G f , ∆H f

Joback and Reid (1987) (JR)Group-ContributionGani and Constantinou (1996) (CG)

Marrero and Gani (2001) (MG)

ω

Pitzer (1955) Correlation

Pitzer (1955) Definition

Lee and Kesler (1975) Pitzer expansion/Corresponding-states

Ambrose and Walton (1989) Pitzer expansion/Corresponding-states

Gani and Constantinou (1996) (CG) Group-Contribution

Marrero and Gani (2001) (MG) Group-Contribution

Table 3: Experimental data points per class of compounds for primary properties.

Number of data points

Tc Vc Pc Tb Tm ∆G f ∆H f

FA 18 19 8 24 71 18x 6

AG 0 0 0 11 29 0 0

ME 1 0 0 16 43 11 0

EE 3 0 0 15 43 3 0

Total 22 19 8 66 186 32 0

Table 4: Property model functions for the critical temperature.

Method Critical temperature model function

Fedors Tc = 535log(∑

i NiTc1i)

JR Tc = Tb[0.584 + 0.965∑

i NiTc1i − (∑

i NiTc1i)2]−1

TLTc = [6.26897.10−6 + 2.56086.10−3( 1

2x + 1√

x )]−1

where x = −0.160864 +∑

i NiTc1i

CG Tc = 181.28ln[∑

i NiTc1i +∑

j M jTc2 j]

MG Tc = 181.6716ln[∑

i NiTc1i +∑

j M jTc2 j +∑

k MkTc3k]

4

Table 5: General property model functions for the critical temperature estimation of saturated FAME.

Method Generalized critical temperature model function for saturated FAME

Fedors Tc = 232.3475ln(10.12 + 1.34n)

JR Tc = −2799.4737Tb[(n + 25.5806)(n − 70.0568)]−1

TL Tc = [6.26897.10−6 + 0.001286.1438+0.9172n + 0.00256

√6.1438+0.9172n

]−1

CG Tc = 181.28ln[15.4897 + 3.492n]

MG Tc = 181.6716ln[16.7104 + 3.4607n]

Table 6: Tc estimation methods experimental analysis.

Method AAD ARD

Fedors 14.41 (5.46 - 27.59) 2.05 (0.77 - 4.16)

JR 13.18 (1.92 - 28.68) 1.81 (0.28 - 3.57)

TL 13.74 (5.94 - 25.05) 1.95 (0.84 - 3.77)

CG 4.39 (0.25 - 11.31) 0.64 (0.03 - 1.70)

MG 18.09 (5.17 - 33.63) 2.57 (0.73 - 5.09)

Regardless of experimental data, the generalized crit-ical temperature model functions for each compoundclass are a way to gain a deeper understanding of theestimation method. Figure 3 presents the Tc estima-tions vs the number of carbons (NC) (note that NC , n)for saturated fatty acids (a) and saturated simple triglyc-erides (b) with carbon number. The Tc vs. NC curveof each estimation method deviate considerably in bothcases. For saturated fatty acids, there is a considerableamount of experimental data suggesting the CG methodas the more accurate, the same happens for fatty acidmethyl and ethyl esters as shown in Figures S1 and S2.It is clear from Figure 3 (b) that the JR method providesa completely different curve compared to the other esti-mation methods even when experimental boiling pointsare used (see Figure S2). The JR method generalized Tc

model function for saturated simple triglycerides is:

Tc =−311.0526Tb

(n + 11.67678)(n − 20.202233)(1)

In this case NCFA = n + 3 and therefore the modelwill return negative value for Tc for triglycerides formedfrom FA with NC higher than 23, such as Trilignocerin(C24:0, C24:0, C24:0). Therefore, the JR method is not

recommended for use.The CG and MG methods provided almost the same

estimations (the difference is always smaller than 8 Kfor AG, ME and EE; and about 25 K for low NC FA,the difference decreases as NC increases), TL and Fe-dors methods are qualitatively similar to CG and MGpredictions but overestimate CG and MG methods onabout 50 K. The same is also observed for other groupsof compounds as shown in Figure S1.

Based on this analysis, we recommend the CGmethod for the Tc estimation due to its confirmed use-fulness as a thermodynamic parameter for the calcula-tion of secondary and temperature dependent properties.

3.2.2. Critical PressureDifferently from Tc, the Pc model functions of all

methods have the following form:

Pc = A +1

(B +∑

i NiPc1i)2 (2)

where, A and B are additional adjustable parameters ofthe property estimation models. The generalized formfor each of the subclasses of compound has the follow-ing model form:

Pc = A +1

(B1 + C.n)2 (3)

where, B1 combines the adjustable parameter B and thegroup-contributions that are independent of n and C arethe group-contributions dependent of n.

The AAD and ARD for JR, CG and MG were cal-culated based on 19 experimental data points, and, aspresented in Table 3, only FA are represented by thedata. Figure 4 (a) presents the estimated Pc values forsaturated fatty acids showing that the estimation meth-ods differ very little, the same happens for FAME andFAEE as shown in Figure S2 and Table S2.

5

Figure 3: Tc estimations behavior with NC for (a) saturated fatty acids and (b) saturated triglycerides.

The estimations differ significantly only for acylglyc-erides. Equations 4, 5 and 6 are the generalized modelfunctions for JR, CG and MG, respectively, applied forsaturated simple triglycerides.

Pc =1

(0.2347 + 0.0288.n)2 (4)

Pc = 1.3705 +1

(0.24782 + 0.0318.n)2 (5)

Pc = 0.0519 +1

(0.2325 + 0.0261.n)2 (6)

where, in this case, n is equal to the number of car-bons of the fatty acid that constitutes the triglyceridesubtracted by three. From these equations, it is possibleto identify two different regions:

• if NCFA <= 9 then Pc(MG) > Pc(CG) > Pc(JR)

• else NCFA > 9 then Pc(CG) > Pc(MG) > Pc(JR)

The same analysis is applied for all other classesof compounds and the identified regions are describedin Table S4. Our final recommendation is to use theCG method for FA, FAME and FAEE as it performedslightly better to the experimental data. However, aproper recommendation for acylglycerides is highly de-pendent of the situation, but based on the regions iden-tified and presented in Table S4 it is possible to selecta models to provide a high, a low and a intermediateestimation.

Table 7: Critical pressure estimation methods analysis.

Method Pc AAD Pc ARDJR 0.72 (0.21 - 1.32) 3.44 (0.91 - 8.80)CG 0.66 (0.11 - 1.31) 3.09 (0.64 - 7.75)MG 1.07 (0.17 - 2.13) 5.10 (0.96 - 9.88)

Table 8: Critical volume estimation methods analysis

Method Vc AAD Vc ARDJR 10.71 (0.17 - 22.5) 1.81 (0.03 - 5.07)CG 10.06 (0.32 - 21.85) 1.73 (0.06 - 5.08)MG 12.73 (0.32 - 24.77) 2.04 (0.06 - 5.05)

3.2.3. Critical Volume

All the critical volume model functions are linear andthere is essentially no difference from JR, CG and MGas shown in Figures 5 and S4.

3.2.4. Boiling Temperature

Experimental data for Tb and Tm are much moreavailable than for the other primary properties. The esti-mations for the CG and MG methods are very good ex-cept with a reservation for acylglycerides, as shown inFigure 6. Table 9 gives the calculated AAD and ARD,suggesting the MG method as the most accurate.

6

Figure 4: Pc estimations behavior with NC for saturated fatty acids.

Figure 5: Vc estimations behavior with NC for saturated triglycerides.

Figure 6: Tb estimations behavior with NC for (a) saturated FA and (b) saturated triglycerides (JR estimations are above 1000 K).

7

Figure 7: Tm estimations behavior with NC for (a) saturated FA and (b) saturated triglycerides (JR estimations are above 1000 K).

Table 9: Boiling point estimation methods analysis.

Method Tb AAD Tb ARDJR 0.72 (0.21 - 1.32) 3.44 (0.91 - 8.80)CG 0.66 (0.11 - 1.31) 3.09 (0.64 - 7.75)MG 1.07 (0.17 - 2.13) 5.10 (0.96 - 9.88)

3.2.5. Melting TemperatureSimilarly to Tb there is a considerable amount of ex-

perimental data for Tm, the JR method strongly over-estimate the experimental values while the estimationsobtained from CG and MG fit well the data except fortriglycerides (there is no data for di- and monoglyc-erides) as shown in Figure 7. It is difficult do determinefrom a theoretically point of view the reasons for the de-viations for triglycerides. The group-contribution mod-els may be missing one or several important groups thatare very important for triglycerides. On the other handthe definition of many other groups would also increasethe complexity of the models which is also a not desir-able situation. Here we define two new second-ordergroups for the MG method, one only to account for thetriglyceride form and another to incorporate a proper de-scription of unsaturations present in triglycerides. Themodified MG-Tm for TGs is:

Tm = 143.5706 ln(∑

i

Tm1k + C1.NC + C2.NDB

)(7)

where, C1 and C2 are given by Equations 8 and 9,NC is the number of carbons of the triglyceride and NDB

is the number of double bonds of the triglyceride. Theimproved estimations are shown in Figure 8.

Figure 8: New CG-Tm estimations for triglycerides with up to threeunsaturations.

C1 =

0.643364 − 0.18376.NC , if NC is even2.559501 − 0.2099.NC , if NC is odd

(8)

C2 =

−5.21927, if NC is even−4.08173, if NC is odd

(9)

3.2.6. Standard Enthalpy of FormationA considerably good amount of experimental data is

available for ∆H f regarding FA and FAME, the estima-tion methods agree well with the experimental data (seeFigure 9. For acylglycerides the estimations methodsdeviate little with the deviation increasing with the num-ber of unsaturations, the highest deviation was betweenJR and MG: about 80 K for Trioctadecatrienoin (C18:3).

8

Our recommendation is to use CG method, however onemust consider that:

∆H f JR > ∆H f CG > ∆H f MG (10)

3.2.7. Standard Gibbs Energy of FormationNo experimental data is available for ∆G f , neverthe-

less it is demonstrated in Figures 10 that all the meth-ods have precisely the same qualitative behavior. JRprovides a considerably lower estimation and there isno significant difference between CG and MG methods(the largest difference encountered is about 27 kJ/molfound for TGs with many unsaturations).

3.2.8. Acentric FactorThe acentric factor is the only secondary prop-

erty considered in this work, it was originally definedby Pitzer (1955) as:

ω ≡ −log10

[lim

Tr→0.7(Pvap/Pc)

]− 1 (11)

According to Poling et al. (2001) there are two use-ful procedures to estimate the acentric factor. One is touse an accurate equation for Pvap and obtain (or esti-mate) the critical properties, the second approach is touse group-contribution methods such as CG and MG.Based on experimental data points for Pvap, Tc and Vc,it is possible to derive 12 true experimental values forthe acentric factor from Equation 11 (11 for FA and 1for FAME), Figure 11 presents the estimation curvesfor FA (the calculated MAE and MAPE are also pro-vided in Table S5) in which it is clear the accuracy of theacentric factor calculations derived directly from Equa-tion 11. The calculations used the Pvap model by Ceri-ani et al. (2013) and CG for the critical properties, Fig-ure 12 shows the influence of the estimation methodsfor Tc and Pc demonstrating that the Tc method chosenis crucial while changing the Pc method has little effectin the acentric factor calculations.

Based on experimental values for Pvap available forall the classes of compounds analyzed, the Pvap modelby Ceriani et al. (2013) is considered a very accuratemodel and our recommendation is to use this methodand CG for the critical properties in Equation 11. Theonly relevant uncertainty is regarding Tc, thus, in caseof inconsistencies the methods by Fedors (1982) and Tuand Liu (1996) can offer alternative values.

3.3. Temperature-dependent PropertiesSecondary properties are those that depend on

the chemical structure and also of other proper-ties/variables. The secondary properties considered are

Figure 11: Acentric factor estimation curves for FA.

Figure 12: Effect of the critical properties estimation method in theAcentric factor estimation curves for FA.

9

Figure 9: Hf estimations behavior with NC for (a) saturated FA and (b) saturated FAME.

Figure 10: Hf estimations behavior with NC for (a) saturated TG and (b) 3-unsaturations TG.

10

Table 11: Heat Capacity.

Classes of Generalized formula for

Compounds d from Eq. 12

Sat. FA 5.06 + 0.41 NC

Sat. TG −27.59 + 0.41 NC

Sat. FAME −5.39 + 0.41 NC

Sat. FAEE −4.98 + 0.41 NC

vapor pressure (Pvap), liquid density (ρL), liquid heat ca-pacity (CL

p), liquid viscosity (µL) and heat of vaporiza-tion (∆Hvap), which are all temperature dependent andfor some models also dependent of critical properties.The methods considered are listed in Table 3.

Analysis regarding experimental data have alreadybeen given by Su et al. (2011) for all the temperature-dependent properties considered here, similar resultsbased in our database is provided in Tables S6 and Fig-ures S7-10. Our analysis is, therefore, focused on thegenerality and inconsistencies of the property modelstaking advantage of the general structure of the involvedcompounds presented in Section 3.1.

3.3.1. Heat CapacityFour models are analyzed for cp and two of these

were found to be inconsistent.The method by Kolska et al. (2008) is ultimately

given by the following quadratic function:

cp = a + b T + d T 2 (12)

where a, b and d are given by the group contributions.This model equation must not have a negative value forthe parameter d, otherwise it can potentially lead to cp

decreasing with an increase in temperature. Applyingthe generalized structures, presented in 3.1, the general-ized formulas for the parameter d are obtained and arepresented in Table 11.

It directly comes from the general formulas that themodel by Kolska et al. (2008) is potentially inconsistentfor:

• simple saturated TG with NC smaller than 51.

• saturated FAME with NC smaller than 14.

• saturated FAME with NC smaller than 15.

Examples of the inconsistencies are presented in Fig-ures 13. The same inconsistencies happen for the

Figure 14: Heat Capacity Stuff.

classes of compounds, specially when unsaturations arepresent (see Figures S40-50).

The cp model by Morad et al. (2000) also presents in-consistencies. This method is based on the Rowlinson-Bondi equation, requiring knowledge of the criticalproperties and the acentric factor and it is argued thatto apply this method to acylglycerols and vegetable oilsone can use a simple molar average of the required prop-erties to represent the mixture properties. For example,following the analysis the critical temperature of a sim-ple triglyceride is:

Tc,mix =∑

i

xiTci (13)

where Tci is the critical temperature of the compoundi and xi is the composition of the compound i in themixture. This assumption does not introduces any prob-lems for moderate temperatures, however note that thecritical temperature of a triglycerides is not simply themolar average of the fatty acids that compose it. In Fig-ure 14 one can see that about Tr = 0.8, the value for cp

estimated using the method by by Morad et al. (2000) isindeterminate (in this point Tr,mix = 1).

The methods that do not present inconsistencies havealmost identical estimations and the method by Cerianiet al. (2009) is recommended for use as it can describea larger number of molecules than the method by Zonget al. (2009).

3.3.2. DensityThree models are analyzed for the density estima-

tion (see Table 10), the model by Ihmels and Gmehling(2003) (version GCVOL-OL-60) exhibits a very simi-lar inconsistency found for the method by Kolska et al.

11

Table 10: Secondary property estimation methods considered and their characteristics.

Property Estimation Method Approach

cp

Kolska et al. (2008) Group-Contribution

Morad et al. (2000) Rowlinson-Bondi Equation

Ceriani et al. (2009) Group-Contribution

Zong et al. (2009) Fragment-based

Hvap

Tu and Liu (1996)Group-ContributionBasarova and Svoboda (1995)

Ceriani et al. (2013)

ρ

Halvorsen et al. (1993) Rackett Equation + Correction Term

Ihmels and Gmehling (2003) Group-Contribution

Zong et al. (2009) Fragment-based

PvapCeriani et al. (2013) Group-Contribution

Zong et al. (2009) Fragment-based

Figure 13: Heat Capacity Stuff.

12

Table 12: Density inconsistency for the method by Ihmels andGmehling (2003).

Classes of Generalized value for

Compounds c from Eq. 14

Sat. FA 0

1-Unsat. FA -0.0002878

2-Unsat. FA -0.0005756

3-Unsat. FA -0.0008634

4-Unsat. FA -0.0011512

(2008). The density estimation model proposed by Ih-mels and Gmehling (2003) can be represented in the fol-lowing model equation:

ρ =MW

A + B T + C T 2 (14)

The quadratic function in the denominator of Equa-tion 14 is the molar volume of the substance and as thevolume must decrease with an increase in temperature,a potential inconsistency may appear if the parameterC is negative. Applying the general structure presentedin 3.1, the model equations in Table 12 are obtained.

Therefore if the model by Ihmels and Gmehling(2003) wrong profiles like the one in Figure 15 can beobtained.

A last consistency test for molar volume estimationmethods is:

limTr→1

(Vm) = Vc (15)

It can be seen in Figure 15 that the method by Zonget al. (2009) does not return the a Vc near from those pre-dicted by the group-contribution methods and, thus, ourfinal recommendation is to use the model by Halvorsenet al. (1993).

3.3.3. Vapor PressureVapor pressure is one of the most important proper-

ties for process simulation, only two estimation mod-els are analyzed, namely Zong et al. (2009) and Ceri-ani et al. (2013). Both methods have consistent estima-tions with experimental data for all the classes of com-pounds analyzed (see Table S8 and Figure S11). Fortriglycerides, the methods are both in good agreementin the reduced temperature range of 0.4-0.7, howeveroutside this range no experimental data is available andthe models estimations deviate very much from each

Figure 15: Density Stuff.

13

Figure 17: Heat of Vaporization e etc/Octanoic acid.

other as shown in Figure 16 (in a representative exam-ple for Trioctanoin, for more information see FiguresS11-S30). The predictive power of Pvap for temper-ature ranges outside the experimental data is speciallycumbersome, as shown in the Appendix 2 fitting curvesto Pvap using a number of experimental data will po-tentially overestimate the Pvap for temperatures abovethe range of experimental data. From Figures 16 andS11-30, it is of no doubt that the model by Cerianiet al. (2013) has used experimental data points for awider range of reduced temperatures than the model byZong et al. (2009), also Ceriani’s method is a group-contribution model and is capable of predicting Pvap

for a much higher number of molecules than Zong’smethod. Therefore, we recommend the model by Ce-riani et al. (2013) to be used.

3.3.4. Heat of Vaporization

None of the methods analyzed exhibited inconsisten-cies. Su et al. (2011) analyzed the methods by Basarovaand Svoboda (1995) and Ceriani et al. (2009) and it isclaimed that the method by Ceriani et al. (2009) pro-vides profiles in which the Hvap increases with temper-ature. Recently, a updated model has been proposedby Ceriani et al. (2013) and using this model we didnot find any inconsistencies as shown in the profile ofFigure 17. The agreement of the estimations with ex-perimental data is provided in Table XX suggesting themodel by Ceriani et al. (2013) as the best estimationmethod.

Table 13: Hvap Error (statistics).

Classes of Generalized value

Compounds for c from Eq. 14

Sat. FA 0

1-Unsat. FA -0.0002878

2-Unsat. FA -0.0005756

3-Unsat. FA -0.0008634

4-Unsat. FA -0.0011512

4. Computational Implementation of the Frame-work

The selected property estimation methods are of al-most no use if these are not computationally avail-able to be used in a process simulator or other re-lated tool. Modern computational Chemical Engineer-ing tools (software) are very much influenced by theCAPE-OPEN interoperability standard, which has pro-posed a component (piece of software) architecture andclear interface standards. The idea was to make BioPESCAPE-OPEN compliant. Nevertheless, the simulatorused in our research group is COCO (CAPE-OPEN toCAPE-OPEN) that is based on ChemSep van Baten(2007) where an easiest work path was encountered.ChemSep already has an efficient software architecturethat enables the incrementation of custom compoundsdatabase.

4.1. ChemSep Important Features

ChemSepTM has a component that manages the in-formation regarding pure compounds, named PCDman-ager, in which the user can perform several tasks such asaccess pure compound properties, add a new compound,insert and update correlation parameters for temperaturedependent properties. Among these tasks, some are ofcritical importance for the accomplishment of this work:export compound to file and import compound from file.ChemSep-LiteTM has 432 compounds in PCDmanagerand by choosing one of these compounds and exportingit to a file one encounters a simple text file that can bedivided in:

1. Compound Identifiers (Name, Formula, CAS,Smiles and Family)

2. Pure Compound Primary Properties (Critical Prop-erties, Molecular Weight, Boiling Point and Melt-ing Point, to name a few).

14

Figure 16: Vapor pressure e etc.

3. Parameters for 17 Pure Compound TemperatureDependent Properties (Solid Density, Liquid Den-sity, Vapor Pressure and Heat of Vaporization, toname a few).

4. Additional Pure Compound Parameters for Calcu-lation of Mixture Properties and Molecular Prop-erties (UNIQUAC r and q, Chao-Seader acentricfactor, Chao-Seader solubility parameter)

5. Group Contribution Data (UNIFAC, UNIFAC-LLE, ASOG and Modified UNIFAC, to name afew)

Therefore, to add compounds to ChemSepTM system-atically, all that is required is to create such text filesholding all the required information and then add thecompounds through PCDmanager using the text file.The process to increment ChemSepTM is further ex-plained in Figure 18.

An additional difficulty to the process is that the tem-perature dependent correlations are based on a set of 35defined model forms1. Unfortunately, no estimationsmethods have the defined model forms, for instancesome of the methods are based on group contributionplus a correction term. To overcome this issue a param-eter estimation procedure was developed in MS Excel.

4.2. Parameter Estimation ProcedureEven though the estimation methods/models were not

directly constructed in any of the defined equation formsavailable in ChemSep, all of them do follow at leastone of the 35 defined model forms as shown in the Fig-ures 19 and 20 for liquid density and heat of vaporiza-tion, respectively.

1The model forms are the same used in the DIPPR databankand a complete list can be found at http://www.chemsep.com/

Figure 19: Pamitoleic acid liquid density values generated usingHalvordensen et al. (1993) and a nonlinear regression using the model

form number 105[y = A

B[1+(1−T/C)D]

].

Figure 20: Pamitoleic acid heat of vaporization values generated usingCeriani et al. (2013) and a nonlinear regression using the model form

number 106[y = A(1 − Tr)B+C Tr+D T 2

r +E T 3r

].

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Figure 18: Process to export a file compound from BioPES to ChemSep.

Therefore, all that is necessary is to obtain the pa-rameters for 5 temperature dependent properties for allthe 232 compounds that means to perform at least 1362nonlinear regressions. All the necessary data can begenerated on BioPES and the nonlinear regressions areeasily done on Excel through the development and ap-plication of appropriate macros systematicaly callingExcel Solver. The process to obtain the property es-timation model parameters in a model form compatiblewith ChemSepTM is summarized in Figure 21 with a fewmore details.

The nonlinear regression was only accepted when thecoefficient of correlation was higher than 0.99 resultingin 227 compounds with all the correlation parametersdetermined. An example of the results for Trimyristinis given in Table 14.

4.3. Compound Text Files Generation and CompoundsAddition to ChemSep

After obtaining the property estimation model param-eters in an model form compatible with ChemSepTM allthe requirements to accomplish the task defined in Fig-ure 2 (create the compound text files and import them onPCDmanager) are met. The compound text file genera-tion was done through BioPES using the .NET Frame-work and, using these files, the compounds were finallyadd to ChemSep using the “Import from File” feature.At this point, the only step to be accomplished was tosave the work. The file generated contains 660 com-pounds (432 originally included and 228 add in thiswork) with several reliable, constant and temperaturedependent, physical property values ready to be used ina distillation column simulation using ChemSepTM oran entire plant simulation using COCO simulator or anyother simulator that is CAPE-OPEN compliant such asAspen PlusTM. The final file containing all the informa-tion can be obtained via email contact to the authors.

downloads/docs/ChemSepTutorial_PCDManager.pdf

Figure 22: COCO flowsheet configuration GUI showing some of theCompounds added in this work.

4.4. Results and Discussion for the Computational Im-plementation of the Framework

The implementation was successfully loaded onCOCO simulator as shown in Figure 22 and, as an initialvalidation, the biodiesel production process from wastecooking oil (triolein) proposed by Zhang et al. (2003a)simulated on HYSYS was reproduced as represented inFigure 23.

The simulation results were exact the same as thosereported by Zhang et al. (2003a). It should be men-tioned that Triolein (the compound representing thewaste cooking oil) is usually the only triglyceride foundin most of the commercial simulators and the advan-tage in using the implementation developed here is thatother compounds present in the waste cooking oil canbe included in the analysis, resulting in a more detaileddescription of the system. Furthermore, any other bio-diesel production systems composed by the 228 com-pounds included in the framework can be approachedusing the reliable property estimation methods.

5. Conclusions

The extensive review of the property estimationmethods for the compounds involved in biodiesel pro-

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Figure 21: Process to obtain the property estimation model parameters in an model form compatible with ChemSepTM in four steps.

Table 14: Nonlinear Estimation Results for Trimyristin.

Property Eq. Number Eq. Form A B C D E

Liquid Density 105 y = A

B[

1+(1−T/C)D] 0.289 0.443 808.4 0.5848 -

Vapor Pressure 101 y = eA+ BT +C ln(T )+D T E

194.2 -29241 -22.028 0.0002 -0.375

Heat of Vaporization 106 y = A(1 − Tr)[

B+C Tr+D T 2r +E T 3

r

]0.289 0.443 808.4 0.5848 -

Liquid Heat Capacity 2 y = A + B T 1.01.106 1530.5 - - -

17

Figure 23: Simulation of the biodiesel production process from triolein proposed by Zhang et al. (2003) using COCO simulator and the frameworkimplemented in this work.

cess systems shows the importance of consistency testswhen building property models. Nevertheless a ro-bust framework for the estimation of many propertieswas successfully built. One subject of substantial im-portance not addressed in this work is phase equilib-ria and chemical reactions, but are addressed elsewhereby Likozar and Levec (2014) and ??. The successfulcomputational implementation described shows the ca-pabilities of integrating several different methods andtools towards a common objective. One may realize thatthe computational implementation developed here has aconsiderable resemblance to the CAPE-OPEN standard,even though the former is not as elegant as the later, eachof the tools used are specialized in a certain task and thecommunication between the different tools were care-fully controlled by the author’s strategy.

List of Symbols

∆G f Standard Gibbs Energy of Formation (J/mol)

∆H f Standard Enthalpy of Formation (J/mol)

Ci Contribution of the group i in the property func-tion

Pc Critical Pressure (bar)

Tb Boiling Temperature (K)

Tc Critical Temperature (K)

Tm Melting Temperature (K)

Vc Critical Volume (cm3/mol)

AAD Average Absolute Deviation

AE Alkyl esters

AG Acylglycerides

ARD Average Relative Deviation (%)

BioPES A software developed in this work (BiodieselProperty Estimation System)

CG Gani and Constantinou (1996) property estima-tion method

FA Fatty acids

FAEE Fatty acid ethyl esters

FAME Fatty acid methyl esters

JR Joback and Reid (1987) property estimationmethod

18

MG Marrero and Gani (2001) property estima-tion method using the updated parameters byHukkerikar et al. (2012).

TL Tu and Liu (1996) method for critical tempera-ture estimation

Appendix A. Supplementary data

Supplementary data associated with this ar-ticle can be found, in the online version, atftp.feq.ufu.br/Adilson/supplementarydata.pdf.

References

Ambrose, D., Walton, J., 1989. Vapour pressures up to their criticaltemperatures of normal alkanes and 1-alkanols. Pure and AppliedChemistry 61 (8), 1395–1403.

Basarova, P., Svoboda, V., 1995. Prediction of the enthalpy of vapor-ization by the group contribution method. Fluid phase equilibria105 (1), 27–47.

Biegler, L. T., Grossmann, I. E., Westerberg, A. W., 1997. Systematicmethods of chemical process design. Vol. 796. Prentice Hall PTRUpper Saddle River, NJ.

Ceriani, R., Gani, R., Liu, Y., 2013. Prediction of vapor pressure andheats of vaporization of edible oil/fat compounds by group contri-bution. Fluid Phase Equilibria 337, 53–59.

Ceriani, R., Gani, R., Meirelles, A. J., 2009. Prediction of heat capac-ities and heats of vaporization of organic liquids by group contri-bution methods. Fluid Phase Equilibria 283 (1), 49–55.

Chang, A.-F., Liu, Y., 2009. Integrated process modeling and prod-uct design of biodiesel manufacturing. Industrial & EngineeringChemistry Research 49 (3), 1197–1213.

Dıaz-Tovar, C.-A., Gani, R., Sarup, B., 2011. Lipid technology: Prop-erty prediction and process design/analysis in the edible oil andbiodiesel industries. Fluid Phase Equilibria 302 (1), 284–293.

Fedors, R., 1982. A relationship between chemical structure andthe critical temperature. Chemical Engineering Communications16 (1-6), 149–151.

Gani, R., Constantinou, L., 1996. Molecular structure based esti-mation of properties for process design. Fluid Phase Equilibria116 (1), 75–86.

Gerpen, J. V., 2005. Biodiesel processing and production. Fuel pro-cessing technology 86 (10), 1097–1107.

Halvorsen, J., Mammel Jr, W., Clements, L., 1993. Density estimationfor fatty acids and vegetable oils based on their fatty acid compo-sition. Journal of the American Oil Chemists’ Society 70 (9), 875–880.

Harmsen, G., 2004. Industrial best practices of conceptual processdesign. Chemical Engineering and Processing: Process Intensifi-cation 43 (5), 671–675.

Hill, J., Nelson, E., Tilman, D., Polasky, S., Tiffany, D., 2006. Envi-ronmental, economic, and energetic costs and benefits of biodieseland ethanol biofuels. Proceedings of the National Academy of Sci-ences of the United States of America 103 (30), 11206–11210.

Hukkerikar, A. S., Sarup, B., Ten Kate, A., Abildskov, J., Sin, G.,Gani, R., 2012. Group-contribution+ (gc+) based estimation ofproperties of pure components: Improved property estimation anduncertainty analysis. Fluid Phase Equilibria 321, 25–43.

Ihmels, E. C., Gmehling, J., 2003. Extension and revision of the groupcontribution method gcvol for the prediction of pure compound liq-uid densities. Industrial & engineering chemistry research 42 (2),408–412.

Joback, K. G., Reid, R. C., 1987. Estimation of pure-component prop-erties from group-contributions. Chemical Engineering Communi-cations 57 (1-6), 233–243.

Kolska, Z., Kukal, J., Zabransky, M., Ruzickaa, V., 2008. Estimationof the heat capacity of organic liquids as a function of temperatureby a three-level group contribution method. Industrial & Engineer-ing Chemistry Research 47 (6), 2075–2085.

Krawczyk, T., 1996. Biodiesel-alternative fuel makes inroads but hur-dles remain. inform 7 (8), 800–815.

Lee, B. I., Kesler, M. G., 1975. A generalized thermodynamic correla-tion based on three-parameter corresponding states. AIChE Journal21 (3), 510–527.

Likozar, B., Levec, J., 2014. Transesterification of canola, palm,peanut, soybean and sunflower oil with methanol, ethanol, iso-propanol, butanol and¡ i¿ tert¡/i¿-butanol to biodiesel: Modellingof chemical equilibrium, reaction kinetics and mass transfer basedon fatty acid composition. Applied Energy 123, 108–120.

Ma, F., Hanna, M. A., 1999. Biodiesel production: a review. Biore-source technology 70 (1), 1–15.

Marrero, J., Gani, R., 2001. Group-contribution based estimation ofpure component properties. Fluid Phase Equilibria 183, 183–208.

Morad, N. A., Kamal, A. M., Panau, F., Yew, T., 2000. Liquid spe-cific heat capacity estimation for fatty acids, triacylglycerols, andvegetable oils based on their fatty acid composition. JOURNAL-AMERICAN OIL CHEMISTS SOCIETY 77 (9), 1001–1006.

Pitzer, K. S., 1955. The volumetric and thermodynamic properties offluids. i. theoretical basis and virial coefficients1. Journal of theAmerican Chemical Society 77 (13), 3427–3433.

Poling, B. E., Prausnitz, J. M., John Paul, O., Reid, R. C., 2001. Theproperties of gases and liquids. Vol. 5. McGraw-Hill New York.

Siirola, J. J., 1996. Industrial applications of chemical process synthe-sis. Advances in chemical Engineering 23, 1–62.

Su, Y.-C., Liu, Y., Diaz Tovar, C. A., Gani, R., 2011. Selection ofprediction methods for thermophysical properties for process mod-eling and product design of biodiesel manufacturing. Industrial &Engineering Chemistry Research 50 (11), 6809–6836.

Tu, C.-H., Liu, C.-P., 1996. Group-contribution estimation of the en-thalpy of vaporization of organic compounds. Fluid Phase Equilib-ria 121 (1), 45–65.

van Baten, J. M., 2007. An introduction to coco. In: The 2007 AnnualMeeting.

Zhang, Y., Dube, M., McLean, D., Kates, M., 2003a. Biodiesel pro-duction from waste cooking oil: 1. process design and technologi-cal assessment. Bioresource technology 89 (1), 1–16.

Zhang, Y., Dube, M., McLean, D., Kates, M., 2003b. Biodiesel pro-duction from waste cooking oil: 2. economic assessment and sen-sitivity analysis. Bioresource technology 90 (3), 229–240.

Zong, L., Ramanathan, S., Chen, C.-C., 2009. Fragment-based ap-proach for estimating thermophysical properties of fats and veg-etable oils for modeling biodiesel production processes. Industrial& engineering chemistry research 49 (2), 876–886.

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