A stochastic reconstruction strategy based on a stratified library of structural descriptors and its application in the molecular reconstruction of naphtha

Guangyao Zhao,Minglei Yang,Wenli Du,Feifei Shen,Feng Qian

Key Laboratory of Smart Manufacturing in Energy Chemical Process,Ministry of Education,East China University of Science and Technology,Shanghai 200237,China

Keywords:Novel stochastic reconstruction strategy Stratified library of structural descriptors Group contribution method

ABSTRACT Molecular reconstruction is a rapid and reliable way to provide molecular detail of petroleum fractions,which is required in the kinetic modeling of petroleum conversation processes at the molecular level.In the typical stochastic reconstruction method,the estimation of properties of pseudo molecules that are generated by Monte Carlo sampling depends on the building of predefined molecular libraries,which is expensive and inaccessible for certain petroleum fractions.In this paper,a novel stochastic reconstruction strategy is proposed,which is based on a stratified library of structural descriptors.Properties of pseudo molecules generated in the novel strategy can be directly estimated by group contribution method in the condition of lacking predefined molecular libraries.In this strategy,the molecular building diagram comprises two steps.First,the ring structure is configured by determining the number of rings.Different from the length of chain adopted in the traditional stochastic reconstruction method,in the second step,number of structural descriptors(SDs)for binding site and chain were determined sequentially for the configuration of binding site and saturated acyclic hydrocarbon chain.These structural descriptors for binding site and chain were selected from group contribution methods.To count the number of partial overlapping sections between structural descriptors for chain,two supplementary structural descriptors were created.All possible saturated structures of hydrocarbon chains can be represented by structural descriptors at the scale of property estimation.This strategy separates the building of a predefined molecule library from the stochastic reconstruction process.The exact structures of pseudo molecules represented by structural descriptors in this work can be determined with sufficient chemical knowledge.Fifty naphtha samples are tested independently to demonstrate the performance of the proposed strategy and the results show that the estimated properties were close enough to the experimental values.This strategy will benefit the molecular management of petrochemical industries and therefore improve economic and environmental efficiencies.

1.Introduction

Crude oils and their refined products are highly complex mixtures consisting of a large number of hydrocarbon molecules [1].The molecular composition of petroleum varies a lot depending on the origin of petroleum,which leads to wide distributions of their bulk properties.At the molecular level,petroleum fractions contain thousands of unique hydrocarbon species that can be regarded as collections of carbon atoms,hydrogen atoms,and heteroatoms under certain positional arrangements.Diverse positional combinations of atoms exist when the same number of atoms is provided.Each arrangement assembles a unique isomeric component.A statistically possible number of isomers grow exponentially with increasing carbon numbers,which causes exhausted molecular identities and concentrations in petroleum fractions to be difficult to reveal.

In recent decades,the most popular strategy used to study the conversion mechanism of petroleum fractions is lumping.Molecular components are classified into a few lumps on the basis of their carbon numbers and characteristic similarities.However,if petroleum fractions and kinetic models can be characterized at the molecular level [2-7],the prediction ability of kinetic models and the optimization for energy management can be significantly improved.Accordingly,researchers have investigated conversion mechanisms at the molecular level.Based on the molecular information of feedstocks,kinetic models at the pathway level have been proposed to predict the bulk properties and individual species of products and the operation conditions of refining units.

Analytic chemistry instruments,such as near-infrared spectrum instrument [8] (NIRS),nuclear magnetic resonance (NMR),mass spectrometry (MS),gas chromatography (GC),and high performance liquid chromatography (HPLC),play important roles in obtaining the molecular information of petroleum fractions.However,acquiring the molecular detailviainstrumental analysis is expensive and time consuming,which is a hindrance to the application of molecular information of petroleum in refinery operations.Therefore,computer-aided molecular reconstruction [9] of petroleum fractions has received attention as an alternative way to reflect petroleum fractions at the molecular level by generating sets of representative molecules that mimic the bulk properties of actual petroleum fractions.

Molecular-level reconstruction methods,including structureoriented lumping (SOL) [10],molecular type homologous series(MTHS) [11,12],stochastic reconstruction (SR) [13,14],and SRreconstruction by entropy maximization (SR-REM) [15,16],have been developed since the 1980s[17].These methods can be classified into deterministic and stochastic models.

The typical deterministic methods are the SOL and MTHS.The SOL method [10] was introduced to describe petroleum mixtures on the basis of predefined molecular libraries.Each molecule could be represented as a 22-dimensional vector of structural groups.Nickel and vanadium[18]were added in the SOL structural vector as extensional increments to characterize vacuum residue.The SOL method also provides a solid foundation to develop kinetic models of industrial processes [19-30] at the molecular level.The MTHS matrix [11] was proposed to represent the composition of petroleum fractions.Branched isomers were considered [31-33] to improve the accuracy in the estimation of the bulk properties of gasoline and diesel.In MTHS method,it was also assumed[33]that molecules in each homologous series follow a specific distribution based on their carbon number.Liuet al.[34] modified the MTHS matrix.Rows stand for pseudo component cuts,and columns still stand for homologous series.Wanget al.[35]imposed normal distributions to describe the molecular composition distribution of naphtha.Cuiet al.[36] reconstructed the petroleum gasoline fraction on the basis of a predefined molecular library with the assumption that the volume fraction in each series follows a gamma distribution.Renet al.studied the performance of the MTHS method between two ways of representation,namely,the gamma distributions against carbon number and boiling point[9,37].

Compared with deterministic methods,different strategies and frameworks have been developed using the stochastic strategy[38-46].From the point of their identical structural features,hydrocarbon species are treated as the assembly of substructures including rings and attached sidechains in stochastic sampling procedures.Neurocket al.first presented a stochastic approach[13,14]named SR method to characterize heavy residue feedstocks.As shown in Fig.1,the initial SR method treated each molecule as a collection of the structural attributes of molecular structures and imposed a probability density function (PDF) on each attribute.The types of PDFs varied in different molecular attributes,such as a histogram distribution for the determination of molecular families and a gamma distribution for ring numbers and the length of sidechains.Monte Carlo sampling with a quadrature method[47] was applied to generate an equimolar set of molecules from PDFs.The parameters for each PDF were adjusted in an optimization loop for simulated annealing to make the properties of generated mixtures close to those of actual samples.Pettiet al.examined the usage of CPU resource in SR method and suggested that[48] a sample size of 10,000 molecules could balance the simulation accuracy and computation expense.Zhanget al.extended a novel SR model on heavy vacuum residue fractions [49].The residue molecules were treated as a combination of approximately 600 building substructures.Denizet al.introduced a new structure parameter set for detailed ring and chain configurations into the SR method to improve the method performance in heavy petroleum fractions [50].Cuiet al.developed a gasoline molecular model based only on GC-FID (flame ionization detector GC gas chromatography) data [51].Fenget al.proposed a hybrid strategy combining structural units and a bond-electron matrix.

On the basis of the SR method,Hudebineet al.[15,52-54] presented a two-step molecular reconstruction algorithm by implementing the maximum entropy principle.The maximum entropy principle [55,56] provided PDFs with the best representativeness of the current state of knowledge.In the first step,a hydrocarbon mixture containing a set of equimolar molecules was generatedviathe SR method.The second step,termed ‘‘reconstruction by entropy maximization”,improved the performance of the set of generated molecules by imposing an objective function that was defined as the Shannon information entropy on the constraints of physiochemical properties.Pereiraet al.[57] proposed a cross-SR-REM method to reduce the computational burden of SR model.The experimental data from advanced analytical method were integrated [58],including GCxGC-FID,GCxGC-SCD (sulfur chemiluminescence detector,SCD),and NMR,into the SR-REM model.

In Fig.1,the SR method can be separated as two layers.The first layer focuses on the construction of pseudo mixture by Monte Carlo sampling.In the second,values of molecular properties are used as identities for molecular species in optimization loops.Predefined libraries of molecular substructures connect the two layers by determining the exact structures of pseudo molecules.Chemical analytical experiments are required to construct predefined molecular libraries.However,due to the high cost and time consuming of chemical analysis,it is not always accessible to obtain the momentarily changing molecular information of process streams in refineries.There are also limits for the current chemical analysis technology to reveal molecular details of heavy petroleum fractions.To capture the molecular information efficiently and accurately using the SR method in the condition of lacking predefined molecular libraries,this paper will propose a novel stochastic reconstruction strategy based on a stratified library of structural descriptors.The stratified library of structural descriptors that include structural attributes for cores,eight structural descriptors for binding sites and eleven structural descriptors for chains aim to construct pseudo molecules which can be directly recognized by the group contribution method [59].With adequate analytical knowledge,exact chemical structures of molecules can be transformed from the optimal pseudo mixture generated by the present SR method.

Fig.1.The framework of traditional SR method [14].

In Section 2.1,we discuss the novel SR strategy.In Section 2.2,the stratified library of structural descriptors is introduced to generate pseudo molecules.In Section 3,the application of the novel SR strategy in the molecular reconstruction of naphtha is presented.In Section 4,the novel SR strategy is tested with fifty naphtha samples.Lastly,a conclusion is given in Section 5.

2.Methodology

2.1.The novel stochastic reconstruction strategy

A novel stochastic reconstruction strategy based on a stratified library of structural descriptors is proposed in Fig.2.In this novel SR strategy,molecular substructures including core,binding site on core and chain are represented by a stratified library of structural descriptors.Each structural descriptor is imposed with a probability density function.Based on the proposed stratified library of structural descriptors and molecular compositions in Naphtha,a building diagram comprising two steps is designed to generate feasible pseudo molecules.In the first step,the number of each type of ring is determined for the configuration of core.In the second,the structure of binding site on core is determined by the number of eight structural descriptors,and the structure of chain is configured by nine structural descriptors.These structural descriptors for binding site and chain were selected from the group contribution method [59-61].Therefore,molecular properties of each pseudo molecule can be directly calculated by the group contribution method[59-61].Due to the partial overlapping section between nine structural descriptors for chain,two supplementary structural descriptors were created for the purpose of estimating properties of pseudo molecules in this work.Bulk properties of the pseudo mixture are estimated by mixing rules and compared with corresponding experimental data through an objective function.The differential evolution algorithm is applied to minimize the objective function by tuning parameters of PDFs on structural descriptors.

The advantage of the novel SR strategy lies in that molecular properties of Pseudo Molecules generated by Monte Carlo Sampling (PMMCS) can be directly calculated by high performance properties estimation methods in the condition of lacking predefined molecular libraries.In traditional SR method,to calculate molecular properties of PMMCS,molecular species should be determined from predefined molecular libraries based on the number of structural attributes in PMMCS.

The traditional SR incorporates two scale of molecular information,the scale of molecular species and the scale of molecular properties.At the first scale,molecular species are basic elements for the petroleum mixture.Define a mixture S containing t molecular species as follows:

where each s stands for a molecular specie in the mixture S.tis the number of molecular species in the mixture.

The second scale is on the scale of molecular properties.Define a set of molecular properties:

where eachpstands for a molecular property,such as the boiling point temperature and density.nis the number of properties involved in SR method.

By applying the molecular properties estimation methods,each molecular specie in the mixture S can be represented as the collection of molecular properties:

However,different estimation methods provide different values for same molecular properties of the molecule.Different molecular species can also have the same values of molecular properties under the same estimation methods.We deleted repeated molecular species at the scale of molecular properties in Eq.(4) and define the concept,pseudo molecular specie,to represent the mixture S as follows:

Fig.2.The novel SR strategy in this work.

where ps is defined as the pseudo molecular specie.Each psi,represented as a vector of molecular properties,stands for a unique representation of molecular species under the properties estimation methods seti.ris the number of ps in the mixture S.Therefore,at the scale of molecular properties,the ps,rather than the molecular specie,is used as the identity for molecules in the mixture S.Properties estimation methods play the role to map molecular species at the first scale to pseudo molecular species at the second scale.

Lacking predefined molecular libraries,there is only molecular information at the scale of molecular properties in the present SR method.PMMCS are directly transformed into pseudo molecular species using properties estimation methods.Since the improvement of properties estimation methods can enhance the performance of SR method,high performance properties estimation methods should be employed in the present model.

In this work,the group contribution method by Ganiet al.[59-61] is involved in the SR model to estimate the basic properties of pure components.Denizet al.[62]demonstrated that this method has a lower prediction error in the boiling point of pure components compared with other group contribution methods in molecular reconstruction.To enable the group contribution method to recognize PMMCS,we proposed a stratified library of structural descriptors to construct PMMCS in Section 2.2.

2.2.The stratified library of structural descriptors

Hydrocarbon molecules in petroleum can be classified into cyclic and acyclic hydrocarbons.In the traditional SR method,cyclic molecules are generally regarded as the assembly of cores and side chains,or the assembly of cores,side chains and binding sites.Each part of the molecule is labeled by structural attributes,such as the number of aromatic ring and aliphatic ring and the length of chains.Acyclic molecules are generally determined by the length of chains.However,the group contribution method is not able to directly recognize PMMCS which are represented by structural attributes.Based on structural characteristics of hydrocarbon molecules and the group contribution method,we proposed a stratified library of structural descriptors for the construction of PMMCS,which contains three groups of structural descriptors to represent cores,chains and binding sites respectively.

2.2.1.Structural descriptors for cores

Structural descriptors in the first group are structural attributes of cores.In petroleum,the large number of molecular components mainly lie in the isomerization on chains.The number of core species is much less than that of chain species,so it is accessible to build predefined libraries of cores.Structural attributes are used as labels to mark these cores in predefined libraries.The definition of structural attributes depends on exact structures of cores in predefined libraries.Commonly used structural attributes in SR method are the number of aromatic rings,naphthenic rings and so on.These structural attributes are also adopted in this work for cores.By determining the value of each structural attribute,the core can be identified from predefined libraries.

Table 1 gives an example to show the identification and the properties calculation of the core.Three structural attributes are involved,including the number of five-membered naphthenic ring,six-membered naphthenic ring and aromatic ring.If we set the number of aromatic rings as one and two other structural attributes as zero,the core will be benzene.

Through dividing a full molecule into functional groups in the group contribution method,the molecular property is calculated by Eqs.(6)-(8).

whereFi,jis the frequency ofith functional group injth substructure,CVi,jstands for the contribution value ofith functional groupon a specific property,NFjis the number of functional groups injth substructure,is the contribution value ofjth substructure.Contribution values of substructures such as core,binding site and chain on properties of the full molecule are calculated in Eq.(6)by contribution values and frequencies of functional groups they contain.In Eq.(8),the property of the full molecule is estimated by the contribution value of the full molecule.In Table 1,benzene can be regarded as the combination of six functional group aCH,which is a specified functional group in group contribution method[59].The contribution value of benzene on boiling point temperature of the full molecule is calculated by Eq.(6).

Table 1The dentification and the contribution value on boiling point temperature of the core

Fig.3.A binding site for core.

2.2.2.Structural descriptors for binding site on core

The binding site for core is the position on a ring where a sidechain is attached.In this work,a structural descriptor used to represent the binding site consists of two parts.The first part is the binding site on the ring and the second part is the first position on the sidechain beside the binding site.As shown in Fig.3,the atom C on benzene and the functional group CH on sidechain,which are both marked using red color,constitute a structural descriptor for the binding site.

In this work,molecules are assumed to have less than three binding sites,and only one side chain exists in each binding site.In Table 2,eight structural descriptors and their contribution value on boiling point temperature are listed,including Caro-CH3,Caro--CH2,Caro-CH and Caro-C for aromatic ring,and CHcyc-CH3,CHcyc-CH2,CHcyc-CH and CHcyc-C for naphthenic ring.

2.2.3.Structural descriptors for chains

Eleven structural segments (SGs) are adopted as structural descriptors to represent saturated hydrocarbon chains.The structural formula of each SG is shown in Table 3.SGI-Vcan be regarded as certain arrangements of basic functional groups CH3,CH2,CH,and C.Partial overlapping is permitted among SGI-V.There are two types of partial overlapping sections among SGI-V.As shown in Fig.4(a),we define the overlapping section -CH(CH3)-as SGX.Likewise,SGXIis created to represent the overlapping section-C(CH3)2-in Fig.4(b).Since the contributions of functional groups in partial overlapping sections are counted repeatedly in the estimation of molecular properties by the group contribution method,it is necessary to count the frequencies of partial overlapping sections to remove the redundancy.The formulas of SGVI,SGVII,SGVIII,and SGXIare CH3,CH2,CH,and C.The frequencies of SGVI,SGVII,SGVIII,and SGXIare calculated as follows.

Table 2Structural descriptors for binding sites and their contribution values on boiling point temperature

Table 3The eleven structural descriptors

Finally,the frequencies of eleven SGs form the expression of saturated hydrocarbon chains.Since overlapping sections SGXand SGXIhave been taken into account in the calculation of frequencies of SGVI-IX,the frequencies of SGI-IXare enough to estimatethe properties of molecules represented by SGI-XI.Therefore,only the frequencies of SGI-IXare determined in the building diagram in Fig.7.

Fig.4.Partial overlapping sections (a) SGX and (b) SGXI among SGI-V.

Fig.5 shows the chemical structures of three saturated hydrocarbon sidechains and the way to count the number of eleven SDs in each sidechain.SGI-V,,CH*and C*are marked with unique colors.SDXand SDXIexist in the areas with overlapping colors.In Fig.5(a),the frequencies of SGI-V,SGXand SGXIare all equal to 1.The frequencies of,CH* and C* are 2,2,1 and 1,respectively.The frequencies of SGVI,SGVII,SGVIIIand SGIXare calculated as-1,2,0 and 0 using Eqs.(9)-(12),as shown in Table 4.In Fig.5(b),the frequencies of SGI-V,SGXand SGXIare 1,1,1,1,1,0 and 2.The frequencies of,CH* and C* are 2,2,1 and 1.Therefore,the frequencies of SGVI,SGVII,SGVIII,SGIXare derived as-2,2,1 and -1.In Fig.5(c),there is 1 SGI,1 SGIVand 1 SGX.The frequencies of other SGs are shown in Table 4.

Fig.5.Three saturated hydrocarbon sidechains:(a)sidechain 1,(b)sidechain 2,(c)sidechain 3.

In Eqs.(6)-(8),the frequencies and properties of SGI-IXare needed to calculate the properties of a saturated hydrocarbon chain.Table 5 shows the properties of SGI-IX,including the carbon number,the hydrogen number and the contribution values on boiling point temperature.The carbon number and hydrogen number in each SG are determined by counting.The contribution value of each SG on boiling point temperature is derived from the contribution values of functional groups in group contribution method[59].

A full molecule in Fig.6 is formed by three substructures including the core in Table 1,the binding site in Fig.3 and the sidechain in Fig.5(c).In Table 6,the boiling point temperature of the full molecule is calculated by Eq.(8)with the sum of contribution values of three substructures.TBPstands for the boiling point temperature.Tb0is a constant parameter in the group contribution method [59].To estimate the boiling point temperature.

Fig.6.The full molecule.

3.Application of the Novel Strategy in Molecular Reconstruction of Naphtha Samples

To study the performance of the novel strategy,we test fifty naphtha samples that are selected from a database of Chinese refinery.Table 7 specifies the range of fifty naphtha samples.In Table 7,properties include density,distillation curve and mass fractions of hydrocarbons with different carbon numbers in normal paraffins,isoparaffins,naphthenes and aromatics.

To apply the novel strategy in the reconstruction of naphtha samples,it is necessary to confirm the predefined rings and building diagram for the construction of pseudo molecular species.Based on the range of bulk properties in Table 7,predefined rings in this work are selected.The library includes cyclopentane,cyclohexane,decalin,benzene,tetralin and naphthalene.Heteroatomcontaining hydrocarbons are not considered in this work because the naphtha samples in this work only contain limited sulfur.

The sampling steps in the building diagram are shown in Fig.7.The building diagram starts at Distribution 1 to determine the type of each molecule to be built.The type of each molecule varies among normal paraffins,isoparaffins,naphthenes,and aromatics.In the case of normal paraffins and isoparaffins,the step to determine the ring is skipped.If the paraffin is normal,the chain length is determined in Distribution 2.Otherwise,the number of SGI-IXthat constitute the branched chains is determined using Distributions 8-16 sequentially.As for naphthenes,Distribution 3 is adopted to determine whether the ring is cyclopentane,cyclohexane or decalin.For aromatics,two parameters in the Distribution 4 are used to determine whether the ring is benzene,tetralin or naphthalene.In the configuration of side chains in ringcontaining molecules,structural binding sites are determined in Distribution 5.The structure of normal side chains is determined using Distribution 6 and Distribution 7.The number of SGI-IXare then determined using Distributions 8-16.This work assumes that each generated mixture contains 1000 molecules.

Fig.7.The building diagram in the molecular reconstruction of naphtha.-

The type of distributions and the number of parameters are listed in Table 8.Histogram distribution and gamma distribution are adopted on the basis of the existing chemical knowledge on naphtha components [29].In each homologous series,the gamma PDF is used to simulate the distribution of weight fraction against carbon number.

Based on the structural descriptors in Section 2.1 and the building diagram,a vector in Table 9 is created to represent the pseudo molecules species in this application.All pseudo molecular species are represented in this form as presented in Table S1 in Supplementary Material.

Table 4The frequencies of eleven structural descriptors in three saturated hydrocarbon sidechains in Fig.5

Table 5The number of carbon atom and hydrogen atom and the contribution values of nine structural descriptors on boiling point temperature

The vector contains three parts of structural information for core,binding site for ring and chain respectively.The frequency of Ring stands for the type of ring.There are three types of rings in this work,namely cyclopentane,cyclohexane and benzene,which are designated as one,two and three.If the pseudo molecule belongs to paraffin,the frequency of Ring is zero.In the second part of this vector,B1,B2,B3 and B4 are Caro-CH3,Caro-CH2,Caro-CH and Caro-C for aromatic ring,and CHcyc-CH3,CHcyc-CH2,CHcyc--CH and CHcyc-C for naphthenic ring.In the part for chain,SGI-XIare structural descriptors for branched chains.n-CH2andn-CH3stand for the number of functional groups CH2and CH3in normal chains.Fig.8 shows the structural formula of a pseudo molecule generated in this work.The ring in this molecule is cyclopentane.For the binding site,there exist a CHcyc-CH2and a CHcyc-CH.The molecule has a normal chain that contains a CH2and a CH3and a branched chain that only contains a SGIV.The vector of the molecule is shown in Table 9.

Table 6The calculation of the boiling point temperature of full molecule

Table 7The range of bulk properties of fifty naphtha samples

Table 8The arrangement of distribution types

Table 9The vector to represent pseudo molecules

Fig.8.The structural formula of a pseudo molecule.

To obtain the optimal pseudo mixture by adjusting the PDFs parameters,an objective aiming at minimizing the relative error of the bulk properties of naphtha samples between experiment and mixing rules is presented in Eq.(13).The differential evolution algorithm [63] is adopted to find the optimum solution.

where the subscriptiis the index of involved properties.wiis the weight factor.Giis the normalized relative error,calculated by Eq.are values of bulk properties obtained by mixing rules and experiment.

Bulk properties involved in the objective function are basic properties and true boiling point (TBP) distillation curve.Basic properties include average boiling point temperature,average molecular weight,critical pressure,critical temperature,C/H ratio,WastonKfactor and refractive index.The adopted methods to estimate properties and the mixing rules are listed in Table 10.

For bulk properties of naphtha samples,values of density and D86 distillation curve are obtained by experiments.The TBP distillation curve is obtained from the D86 distillation curve by the method API 3A1.1[65].Other properties are estimated on the basis of density and distillation curve [32].

For properties of pure compounds,boiling point temperature,critical pressure,and critical temperature of molecules are estimated using the group contribution method [59].Molecular weight and C/H ratio are calculated by counting the number of atoms.Density,refractive index,and Watson K factor are predicted using empirical correlations in Table 10.The contributions of molecules to the compositions of chemical families are recorded through the inspection of their structures.

4.Results and Discussion

4.1.Comparison of estimated and measured values of bulk properties

Table 11 provides a comparison of average relative errors(AREs)between the measured and predicted values of fifty naphtha samples.The reconstruction model in this paper can accurately estimate the properties of these naphtha samples.The maximumARE does not exceed 1.2%.For basic properties,the relative errors of average boiling point,average molecular weight,specific gravity,critical pressure and critical temperature are 0.084%,0.52%,0.98%,0.72% and 0.69%.The relative errors of C/H ratio,Watson K factor and refractive index are 0.44%,0.82%,0.23%,respectively.Since the values of the TBP initial point and 10% point in Centigrade are close to 0,small changes of the TBP initial point and 10%point can lead to larger relative errors compared with other distillation points.In this paper,the values of TBP points in the objective function are in Kelvin.The relative errors of all points in the TBP distillation curve are less than 1.2%.The relative errors of weight fractions of normal paraffin,isoparaffin,naphthene and aromatic(PINA) are all 0 because the values of PINA are used as prior knowledge.

Table 10The methods to estimate properties and mixing rules(Eq: equations in the reference Riazi,2005 [64],API: API TDB,1997 [65])

Table 11The average relative errors and the range of relative errors of fifty tests between measured values and predicted values

Fig.9 shows a comparison between the basic properties of estimated mixtures and their corresponding experimental values.The properties of fifty predicted mixtures agree well with those of the experimental ones.The relative errors(REs)of basic properties are all below 4% for the fifty samples.As shown in Fig.10,the predicted distillation curves fit with the experiment.In Fig.10,it can be found that the estimation values of several samples are the same at certain distillation points,especially below the 50%point.The reason is there are fewer molecular species when the boiling point temperature is low.

A naphtha sample is selected to present a detailed comparison between the experiment and simulation.Table 12 indicates that the bulk properties of the generated mixture are close to those of the sample.The relative errors of average boiling point,specific gravity,Watson K factor and refractive index are less than 0.71%.The relative errors of average molecular weight,critical pressure,critical temperature and C/H ration have much high relative errors,namely,1.0%,2.4%,0.94%,and 2.4%,respectively.The relative errors in distillation curve points are all less than 0.85%.As shown in Fig.11,the estimated distillation curve fits well with the distillation temperatures by experiment.

Table 12The comparison of bulk properties of the naphtha sample between experiment and simulation

Fig.9.Parity plots for the predicted basic properties of fifty naphtha samples by the molecular reconstruction model:(a)average boiling point,(b)specific gravity,(c)critical pressure (kPa),(d) critical temperature,(e) average molecular weight,(f) C/H ratio,(g) Watson K factor,(h) refractive index.

Fig.10.Parity plots for the predicted TBP distillation curve of fifty naphtha samples by the molecular reconstruction model:(a)initial point,30%,50%,(b)70%,90%,end point.

Fig.11.The TBP distillation curve comparison between measurement and prediction.

Fig.12 shows comparisons of detailed mass fractions of homologous series between experiment and prediction.The predicted mass fraction in each chemical family follows a basically similar trend of gamma distribution with the measurement.In normal paraffins and isoparaffins,the experimental values of C5 and C10 are larger than the predicted values.On the contrary,the experimental values of C7 and C8 are smaller than the predicted values.The experimental values of other homologous series are close to the predicted values.In naphthenes,there are relatively larger derivations at C6 and C7 compared with the values at C8 and C9.The predicted values in aromatics fit well with the experimental values.

4.2.Analysis on unique molecular components in naphtha samples

In this work,naphtha samples are regarded as the collection of pseudo molecular species in Eq.(4).Based on the constraints of bulk properties in Table 7,372 pseudo molecular species are generated in the molecular reconstruction of each naphtha sample.

Fig.13 depicts the distribution of 372 pseudo molecular species in each homologous series.Paraffins,naphthenes,and aromatics have 239,97,and 36 components,respectively.The numbers in each homologous series follow an exponential trend against carbon number because of the nature of isomers.In naphthenes and aromatics,the numbers are relatively smaller compared with paraffins because the types of unique sidechains for naphthenes and aromatics are limited when the total carbon number of a full molecule is less than 11.

In this work,the identity of molecules is determined by their properties.Fig.14 presents the pseudo molecular species in each homologous series by their specific gravity and boiling point temperature.These points in each coordinate system can be regarded as the projection of true molecular species on the scale of molecular properties.

Fig.12.The detailed mass fractions comparison in (a) normal paraffins,(b) isoparaffins,(c) naphthenes and (d) aromatics.

Fig.13.The number of pseudo molecular species by homologous series.

True molecular species adopted in the molecular reconstruction of naphtha samples by Renet al.[9] and van Geemet al.[30] are compared with the pseudo molecular species in this work.Because the naphtha samples in works by Ren and van Geem and in this work have different ranges of boiling point temperature and carbon number,Table 13 only count the true molecular species that fall into the ranges of properties in Table 7.In Table 13,TMS stands for the true molecular specie and PMS stands for the pseudo molecular specie.‘‘If all included”stands for if the pseudo molecular species in each homologous series by Ren or by van Geem are all included in the pseudo molecular species in corresponding homologous series generated in this work.There are 194 and 105 true molecular species in the works by Ren and van Geem.By representing true molecular species as the collections of structure descriptors defined in Section 2.2,126 and 87 pseudo molecular species are obtained respectively.Since different true molecular species may have same expression by structure descriptors,the number of pseudo molecular species in each homologous series are not greater than the number of true molecular species.The number of pseudo molecular species in each homologous series by Ren and van Geem are not greater than the number in this work.In each homologous series,all pseudo molecular species by Ren and van Geem are included in the pseudo molecular species in this work,which shows the molecular reconstruction model in this work is able to generate pseudo molecular species which cover representative true molecular species in the molecular reconstruction of naphtha samples in the condition of lacking predefined molecular libraries.

A Supplementary Material is provided to list the 372 pseudo molecular species represented by structural descriptors.The 194 true molecular species by Ren and 105 true molecular species by van Geem are also given in Table S2 and Table S3 in the Supplementary Material.

5.Conclusions

This paper proposed a novel stochastic reconstruction strategy based on a hierarchical library of structural descriptors.In the novel strategy,structural descriptors,rather than structural attributes of molecular substructures,are adopted to represent pseudo molecules in Monte Carlo sampling.The hierarchical library includes three groups of structural descriptors.In the first group,the structural attributes of rings,such as the number of naphthenic rings and aromatic rings,are used as structural descriptors to determine the structure of rings in molecules.The second group contains eight structural descriptors to represent the binding site for naphthenic ring and aromatic ring.The third group contributes to construct saturated hydrocarbon chains by eleven structural descriptors.

Fig.14.Pseudo molecular species represented by specific gravity and boiling point temperature in each homologous series:(a)C3P,(b)C4P,(c)C5P,(d)C6P,(e)C7P,(f)C8P,(g) C9P,(h) C10P,(i) C11P,(j) C12P,(k) C5N,(l) C6N,(m) C7N,(n) C8N,(o) C9N,(p) C10N,(q) C11N,(r) C6A,(s) C7A2,8(t) C8A,(u) C9A,(v) C10A and (w) C11A (The Xcoordinate: specific gravity,the Y-coordinate: boiling point temperature/K).

The novel SR strategy is tested with fifty naphtha samples under limited bulk properties,including basic bulk properties,distillation curve,and detailed mass fractions by homologous series.Basic bulk properties comprise average boiling point temperature,density,average molecular weight,critical properties,WatsonKfactor,and refractive index.The model can generate mixtures whose bulk properties are close to those of the fifty naphtha samples.The relative errors of basic properties and distillation curve are under 4.1%.The mass fractions of the detailed homologous series are compared between experiment and prediction to validate the model.The result shows that the model has good performance in the prediction of molecular compositions.

372 pseudo molecular species,including 239 paraffins,97 naphthenes and 36 aromatics,are generated in the molecular reconstruction of each naphtha sample.To verify the applicability of pseudo molecular species in this work,true molecular species that are in the ranges of properties in Table 7 are collected from the work of Ren and the work of van Geem respectively.It is foundthat true molecular species by Ren and van Geem are all covered by 372 pseudo molecular species in this work,which shows the pseudo mixtures generated in this work can reflect the information of true molecular species in naphtha samples in the condition of lacking predefined molecular libraries.This strategy separates the building of a predefined molecule library from the stochastic reconstruction process.The exact structures of pseudo molecules represented by structural descriptors in this work can be determined with sufficient chemical knowledge.

Table 13The number of molecular species in each homologous series in the works by Ren [9] and van Geem [30] and in this work

Declaration of Competing Interest

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

Acknowledgements

The authors are grateful for the support of International(Regional) Cooperation and Exchange Project (61720106008),National Natural Science Fund for Distinguished Young Scholars(61925305),and National Natural Science Foundation of China(61873093).

Supplementary Material

Pseudo molecular species generated by the novel building diagram in this paper;True molecular species in the work of Ren;True molecular species in the work of van Geem.Supplementary data to this article can be found online at https://doi.org/10.1016/j.cjche.2021.12.020.

Nomenclature

CVcorecontribution value of core on a specific property

CVfullmoleculecontribution value of the full molecule

CVsubstructurejcontribution value of thejth substructure on a specific property

CVi,jcontribution value of theith group contribution group in thejth substructure

FCH* frequency of CH*

frequency of

frequency of

FC* frequency of C*

FSGfrequency of a structural segment

Fi,jfrequency of theith group contribution group in thejth substructure

Girelative error of theith property

Propertyfullmoleculea specific pure molecular property

Tb0a constant to estimate the boiling point temperature in group contribution method,K

TBPboiling point temperature,K

wiweight factor for relative error of propertyi

Superscripts

ithe property estimation methodi

Subscripts

aro aromatic,Caromeans the C atom on aromatic ring

cyc cyclic,CHcycmeans the C-H group on aliphatic ring

nthe number of properties involved in SR method.

I-VI roman numerals used to count the index of structural descriptor 1 to 11

ithe functional groupior the involved propertyi

jthe substructurej

tthe number of molecular species in the mixture S