Molecular reconstruction of vacuum gas oils using a general molecule library thr

Na Wang,Chong Peng,Zhenmin Cheng,Zhiming Zhou,*

1 School of Chemical Engineering,East China University of Science and Technology,Shanghai 200237,China

2 Dalian Research Institute of Petroleum and Petrochemicals,SINOPEC,Dalian 116000,China

Keywords:Vacuum gas oil Molecular reconstruction Model Algorithm Optimization

ABSTRACT Vacuum gas oil (VGO) is the most important feedstock for hydrocracking processes in refineries,but its molecular composition cannot be fully acquired by current analysis techniques owing to its complexity.In order to build an accurate and reliable molecular-level kinetic model for reactor design and process optimization,the molecular composition of VGO has to be reconstructed based on limited measurements.In this study,a modified stochastic reconstruction-entropy maximization (SR-REM) algorithm was applied to reconstruct VGOs,with generation of a general molecule library once and for all via the SR method at the first step and adjustment of the molecular abundance of various VGOs via the REM method at the second step.The universality of the molecule library and the effectiveness of the modified SR-REM method were validated by fifteen VGOs (three from the literature) from different geographic regions of the world and with different properties.The simulated properties (density,elemental composition,paraffin-naphthene-aromatics distribution,boiling point distribution,detailed composition of naphthenes and aromatics in terms of ring number as well as composition of S-heterocycles) are in good agreement with the measured counterparts,showing average absolute relative errors of below 10% for each property.

1.Introduction

In recent decades the world has witnessed a growing demand for light fuel such as gasoline and diesel on the one hand,and a continuous increasing of heavier and inferior crude oil supply on the other hand.It is therefore significant for the refining industry to efficiently convert heavy petroleum fractions into light fractions by thermal and catalytic cracking processes such as fluid catalytic cracking,hydrocracking and delayed coking [1-3].The conversion efficiency depends on the optimal operation of the reactor,which in turn relies on the reliable and accurate kinetic model.To circumvent the difficulty of quantifying individual species in the complex heavy fractions,a lumping technique is widely used in classical kinetic studies,in which hydrocarbon molecules are generally grouped into several lumps by physical properties such as boiling range[4-6].Nevertheless,these lumps cannot yet satisfactorily characterize the feedstock and product compositions as each lump contains a large number of molecules,and accordingly,the obtained kinetic model is restricted to specific feedstocks.Once some changes occur on the composition and properties of the feedstock,the rate parameters involved in the kinetic model cannot be feed-invariant.In this context,it is necessary to develop kinetic models at the molecular level [7].

The molecular-level kinetic models for chemical transformation of heavy petroleum fractions require the detailed molecular composition of feedstock as input.Unfortunately,current analysis tools cannot identify all species in the heavy fractions.In this case,the molecular reconstruction of feedstock is inevitably needed [8-10].To date,many molecular-level reconstruction methods have been developed,e.g.,stochastic reconstruction (SR) [11],structure-oriented lumping (SOL) [12],molecular typehomologous series (MTHS) [13],reconstruction by entropy maximization (REM) [14].Among them,the SR method is particularly suitable for reconstructing heavy petroleum fractions such as asphaltene [15-17] and residue [18-20].The MTHS and REM methods are suitable for light petroleum fractions as the former needs a detailed carbon number distribution [21] and the latter requires a complete molecule library [22],both of which can be accurately determined by modern analytic techniques for light fractions such as naphtha,but not for heavy fractions.Although the SOL method has been applied to heavy fractions [23,24],it suffers from too many variables,fewer constraints,and insufficient classification of types [10].When applying the SR method,the Monte Carlo construction procedure is placed within the optimization loop together with a huge number of molecules to be constructed,thus creating a substantial computation burden to restrict its practical application.

Hudebineet al.[25] proposed a SR-REM two-step molecular reconstruction algorithm,which made use of the ability of SR to generate appropriate molecules at the first step and the flexibility of REM to adjust the molecular composition at the second step.The SR-REM method has advantages over the sole SR method in both computation time and accuracy,and has been applied to different fractions including light cycle oil (LCO) [25-27],vacuum gas oil(VGO) [28-30],and vacuum residue [31-33].However,this method is still time-consuming if the oil samples that belong to the same fraction but with different properties are reconstructed individually (one-by-one) by the SR-REM method.Indeed,this strategy has been used in most previous studies.If a general molecule library specific to a given petroleum fraction is first built by the SR method,and then any sample from this fraction is reconstructed by the REM method based on this molecule library (a modified SR-REM method),the computational burden will be greatly reduced.To the best of our knowledge,to date only two studies have used this modified method to reconstruct LCO [25]and vacuum residue fractions [32].de Oliveiraet al.[32] reported that the computation time to reconstruct a VR fraction varied from several hours to one day by the traditional SR-REM method,which was greatly reduced to a few seconds using the modified SR-REM method.

The present work aims at reconstructing the molecular composition of VGOs via the modified SR-REM method.First,a general molecule library is built by the SR method using four VGO samples derived from different geographic regions of the world.In this step,two objective functions that contain different constrained properties are applied and compared: one with basic properties such as density,elemental composition and boiling point distribution,and one with not only the basic properties but also the detailed composition of naphthenic and aromatic rings as well as Sheterocycles.Next,the general molecule library is used to rebuild the above four VGOs by the REM method.The universality of the molecule library is examined by reconstructing eight other VGOs.Finally,this molecule library is applied to rebuild the VGOs reported in the literature,which further validates the effectiveness of the modified SR-REM method.Considering that the VGO fraction is the most widely used feedstock for hydrocrackers in refineries,this study lays a solid foundation for molecular-level kinetic modeling of VGO hydrocracking and subsequent reactor modeling and optimization.

2.Description of the Modified SR-REM Algorithm

The modified SR-REM two-step algorithm for molecular reconstruction of the VGO composition is shown in Fig.1.At the first step,four VGO samples from different geographic regions with different properties are individually reconstructed by the SR method to generate a set of molecules (or molecule library),and then the generated four molecule libraries are united into a general molecule library.At the second step,the REM method is applied to adjust the molar fractions of molecules in the general molecule library,aiming at fine-tuning the properties of the generated mixture.Next,we will make a brief description of the SR-REM algorithm.More detailed information is available elsewhere[25,26,32,34].

2.1.Stochastic reconstruction (SR)

The SR method assumes that any molecule in the VGO feedstock is an assembly of different structural attributes according to certain probability distribution functions (PDFs).These structural attributes include type of molecules,number of side chains,number of benzene rings,number of naphthenic rings,type of heterocycles (thiophene,pyrrole and pyridine),etc.,as listed in Table 1.Although oxygen-containing species such as furans and phenols are also identified in VGO,they are less relevant for subsequent refinery modeling purpose and thus excluded from molecular reconstruction [34].Each molecule is constructed by Monte Carlo sampling of the PDFs of the structural attributes based on a building diagram (Fig.2),which is repeatedNtimes to obtain a virtue mixture.Nis set to 10000 in this work,as previous studies have shown that a sample size of 5000-10000 molecules can guarantee the prediction accuracy[32,35,36].Worthy of mention is the use of structural attributes to differentiate aromatic cores with different configurations,i.e.,phenanthrene and anthracene (for triaromatics),pyrene and chrysene (for tetraaromatics),and perylene and benzopyrene (for pentaaromatics).The difference in the structural configuration of aromatic cores with multiple rings has recently been taken into account for heavy petroleum fractions such as asphaltene [17] and vacuum residue [37],but very few studies have been reported for VGO.Recently,Denizet al.[38] reported that consideration of different configurations for aromatic cores was favorable for better fit of VGO through increased model flexibility.

The range of values and the number of parameters of PDFs of structural attributes are presented in Table 1,which are determined by referring to previous studies [34].In addition,several chemical rules are used:(1)only single-core structures are allowed for naphthenes and aromatics;(2)only cyclohexane rings are considered for naphthenes;(3) aromatic species contains up to five benzene rings and two cyclohexane rings;(4)only one heterocycle such as thiophene,pyrrole or pyridine is allowed;(5)only one nonmethyl branch is considered in the case of multiple alkyl branches;and (6) multiple branches are located as far as possible from each other on the parent structure.In total,there are 17 structural attributes with 27 associated parameters that need to be estimated from the experimental properties of VGO.It should be noted that the gamma distribution is normally associated with two parameters,i.e.,a shape parameter and a scale parameter.However,in the case of paraffin chain length and alkyl branch carbons,the scale parameter can be derived from the shape parameter and thus,the number of parameters is reduced to 1 [32,34].

Table 1 Mathematical description of structural attributes

During the molecular reconstruction process,the properties of each molecule are calculated either directly by its structure(chemical formula,molecular weight,etc.) or by group contribution methods (liquid density at 20 °C and normal boiling point [32]).The average density of the mixture is calculated using the linear mixing rule.After that,the calculated bulk properties of VGO are compared with the analytical data through an objective function.The parameters of the PDFs are optimized using a simulated annealing algorithm to minimize the objective function.The objective function is defined as the average of the relative residuals between the experimental and simulated properties:

Fig.1.Flow diagram of the molecular reconstruction of VGOs by a modified SR-REM algorithm.

whereXi,expandXi,simare the experimental and simulated values of thei-th constrained property,respectively,andNpis the number of constrained properties in the objective function.Note that the relative residuals are not squared,with the aim of avoiding the amplification of the background noise available in the objective function derived from the Monte Carlo-based sampling method [32].In this study,two objective functions are considered in order to evaluate the effect of constrained properties on the simulation result.The constrained properties in the first objective function are some basic properties,including density,elemental analysis (C,H,S and N),paraffin-naphthene-aromatics (PNA) distribution and boiling point distribution.The second objective function is an extension of the first objective function,which contains not only the basic properties,but also the detailed composition of naphthenic and aromatic rings (i.e.,1-5 rings) as well as S-heterocycles.A Fortran code is implemented on an Intel®Core(TM) i5-6500 based computer,and the CPU time required for each stochastic reconstruction is about 12 h.

Fig.2.Molecule building diagram for VGOs.

2.2.Reconstruction by entropy maximum (REM)

The SR method generates a set of representative molecules,whose molar fractions are determined by the REM method that is based on the principle of maximum Shannon entropy [39].The information entropy (H) to be maximized is expressed as:

whereyjis the molar fraction of thej-th molecule,Nmis the number of molecules,μ is the Lagrange multiplier associated with the mass balance constraint,λiis the Lagrange multiplier associated with thei-th property,andXj,iis the coefficient of thej-th molecule for theith property.Further information on the REM method and its calculation procedure can be found elsewhere[40-43].Compared to the SR method,the CPU time for REM is greatly reduced,being only around 2 min.

3.Characterization of Vacuum Gas Oil

Twelves VGO samples with different properties (Table 2) were characterized.The liquid density at 20 °C was measured by ASTMD4052.The elemental composition(C,H,S and N)was determined by ASTM D5291/D1552.The boiling point distribution was acquired by simulated distillation according to ASTM D6352.The hydrocarbon-type distribution and S-heterocycles were analyzed by two-dimensional gas chromatography with a flame ionization detector and a sulfur chemiluminescence detector,respectively.

Table 2 Physicochemical properties of twelves VGO samples

Table 3 Experimental and simulated properties of four VGO samples by the SR method

4.Results and Discussion

4.1.Construction of a general molecule library for VGOs

Four samples used for constructing a general molecule library for VGOs originate from Saudi Arabia(VGO-1),China(VGO-2),Iran(VGO-3) and Venezuela (VGO-4),which represent the main VGO fractions in the world.It can be seen from Table 2 that the four samples have different characteristics,e.g.,the nitrogen content of VGO-1 is the lowest among the four samples,the viscosity of VGO-2 is the lowest,and the density and sulfur content of VGO-3 are the lowest.

When the first objective function is applied,the analysis data(columns labeled ‘‘exp”,Table 3) of density,elemental composition,PNA distribution,and boiling point distribution are well simulated by the synthetic mixture (columns labeled ‘‘sim-1”,Table 3).Unfortunately,however,as far as the detailed composition of naphthenic and aromatic rings are concerned,remarkable deviations are observed between experimental and simulated data.Taking VGO-1 as an example,although the experimental and simulated contents of aromatics(53%(mass)vs.51%(mass))are close to each other,the simulated distribution of aromatics in terms of ring number(37.5%,8.3%,1.6%,0.3%and 0.1%(mass)for mono-,di-,tri-,tetra-and penta-aromatics,respectively) is different from the experimental distribution (18.2%(mass),10.2%(mass),6.7% (mass),4.4%(mass) and 1.8%(mass),respectively).A similar result is obtained for naphthenes.In addition,the simulated content of Sheterocycles(3.2%(mass))is quite different from the experimental value(11.7%(mass)).Therefore,the first objective function does not yield a molecule library that can satisfactorily represent the VGO fractions.

Fig.3.(a) Carbon number distribution and (b) molecular weight distribution of the general molecule library.

Table 4 Experimental and simulated properties of four VGO samples by the REM method using a general molecule library

Next,the second objective function is applied to construct a molecule library for VGO.The simulated properties are also listed in Table 3 (columns labeled ‘‘sim-2”).It seems that the second objective function gives a slightly poorer simulation of the basic properties of the four VGOs as compared to the first objective function,which is mainly due to more constrained properties in the second objective function for global optimization by simulated annealing.Nevertheless,the simulation results about the distribution of aromatics and naphthenes as well as the content of S-heterocycles are greatly improved when the second objective function is used.Taking the content of S-heterocycles as an example,the experimental data for four samples from VGO-1 to VGO-4 are 11.7%(mass),9.1%(mass),5.3%(mass)and 5.7%(mass),respectively,which deviate from the simulated data obtained with the first objective function (3.2% (mass),1.3% (mass),7.1% (mass) and 6.0% (mass),respectively) but close to the data obtained with the second objective function (14.1% (mass),9.6% (mass),5.4% (mass)and 5.4% (mass),respectively).It is therefore concluded from the comparison of the results of the two objective functions that,the second objective function that contains both the basic properties and the distribution of naphthenic and aromatic rings is appropriate to construct a molecule library for VGO fractions.

By applying the second objective function,four molecule libraries are constructed individually for the four VGOs.Note that although the number of Monte Carlo sampling is 10000 for each VGO,the number of molecules (each molecule is unique) in the final molecule library is less than 10000 due to repetition of some molecules during sampling.The number of molecules in each library (from VGO-1 to VGO-4) is 1571,1644,1507 and 1670,respectively.The four libraries are then united together by rejecting identical molecules,which finally yields a general molecule library for VGOs.The general library contains 3023 molecules with a gamma distribution within the carbon number range of 9-45(Fig.3(a)),whose molecular weight distribution by PNA family is shown in Fig.3(b) and Table S1 (Supplementary Material).The molecular weight range of the general molecule library is 105-63 0 g·mol-1,which is close to those reported for VGOs in the literature,e.g.,160-580 g·mol-1[34] and 150-700 g·mol-1[44].The aromatic species account for a major proportion of the molecule library (74.0%),followed by naphthenes (20.6%) and paraffins(5.4%).Considering that the aromatic hydrocarbons are more complex in structure than naphthenic and paraffinic hydrocarbons,more structural attributes are required to describe the aromatic hydrocarbons (Table 1),which results in the largest contribution of aromatics to the general molecule library.The most abundant species in the aromatic and naphthenic families have molecular weights of 355-380 g·mol-1,which shift to 380-480 g·mol-1for paraffins.Next,the general molecule library consisting of an equimolar set of 3023 molecules is used to reconstruct VGOs by the REM method.The properties used in REM are the same as those in the second objective function of the SR method.

4.2.Reconstruction of VGOs by REM

Prior to REM of any VGO sample,the above general molecule library is reduced by eliminating the molecules with a normal boiling point lower than the initial boiling point or higher than the end boiling point of the VGO [22].Table 4 compares the experimental and simulated properties of four samples from VGO-1 to VGO-4.Comparing with the simulated results obtained from the SR method (Table 3),it is apparent that,after the REM step using the general molecule library,a remarkable improvement is achieved in the properties of the four VGOs.,i.e.,density,elemental composition,boiling point distribution,and PNA distribution including detailed composition of naphthenic and aromatic rings as well as S-heterocycles.In addition,eight other VGOs (from VGO-5 to VGO-12) with different properties can be well reconstructed by the REM method using the above generated molecule library,as summarized in Table S2.For all the twelve samples from VGO-1 to VGO-12,the average absolute relative error of all properties for each VGOis calculated to be 5.7%,5.4%,5.4%,4.0%,4.4%,4.6%,5.4%,4.2%,2.9%,3.3%,7.7%,and 4.5%,respectively.The errors for the first four VGOs that are used for generating the molecule library are generally comparable to those for the other eight VGOs,demonstrating the reliability of the general molecule library.

Fig.4(a-h) shows the parity plots of simulated versus experimental values for basic properties of the twelve VGOs.The average absolute relative errors for most basic propertiesare smaller than 5% except for sulfur and nitrogen contents(6.5% and 7.1%,respectively).Moreover,the simulated boiling points are very close to the experimental values(Fig.4(i)).Even regarding the detailed distributions of naphthenes and aromatics in terms of ring number as well as the content of Sheterocycles,the average absolute relative errors are smaller than 10%(Fig.S1).Therefore,the approach to reconstruct the molecular composition of VGOs from a general molecule library with the REM method is justified.

Finally,this molecule library is applied to reconstruct VGO samples in the literature.As listed in Table 5,sample A (VGO-A,from Canadian oil sands heavy crude) [34],sample B (VGO-B,fromCanadian oil sands bitumen)[29]and sample C(VGO-C,from Middle Eastern light crude) [34] have different properties: VGO-A and VGO-B are characteristic of no or only a very small amount of paraffins with the former rich in aromatics and the latter rich in naphthenes,while VGO-C has comparable amounts of paraffins,naphthenes and aromatics.Unfortunately,the detailed distribution of naphthenes in terms of ring number is not available in the literature for the three VGOs,but instead the13C NMR spectrum is provided.In this case,the constrained properties associated with the ring number distribution of naphthenes have to be removed from Eq.(2) when applying the REM method with the general molecule library.The simulated properties are presented in Table 5,which are close to the experimental data.In addition,the13C NMR spectrum data that are not used as constrained properties during the molecular reconstruction are generally predicted.For some13C NMR data,e.g.,the aliphatic CH2group,there exists a relatively large difference between experimental and predicted values,which is probably caused by the lack of detailed distribution of naphthenes in the objective function.In summary,the molecular reconstruction of VGOs is fulfilled successfully by the REM method using the general molecule library.It should be noted that the molecule library generated in this study is restricted to VGOs with no or a very small amount of resins;otherwise,6+-ring naphthenes and aromatics should be taken into account at the SR step.

Table 5 Experimental and simulated properties of literature reported VGOs

5.Conclusions

The molecular composition of VGO was constructed by a modified SR-REM algorithm,where a general molecule library was first built by the SR method and then used to adjust the molecular composition of any VGO by the REM method.It was noteworthy that the general molecule library was built only once and for all,such that the computational burden was greatly reduced as compared to the conventional SR-REM algorithm.During construction of the molecule library from four VGOs differing in the geographic regions and in the physicochemical properties,it was found that the constrained properties in the objection function affected the simulation results.The commonly used properties such as density,elemental composition,PNA distribution and boiling point distribution were not adequate to generate an appropriate molecule library for VGO.Detailed compositions of naphthenes and aromatics in terms of ring number as well as S-heterocycles were also required.The general molecule library consisted of 3023 unique molecules with a gamma distribution within the carbon number range of 9-45,in which aromatics accounted for the largest proportion.With this general molecule library,eleven other VGOs including three from the literature were rebuilt by the REM method.A good agreement was achieved between the simulated and experimental properties,demonstrating the universality of the molecule library and the effectiveness of the modified SRREM method for the molecular reconstruction of VGO.

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

We thank Dr.Jinwen Chen for helpful discussion.This work was supported by the National Natural Science Foundation of China(21978093).

Supplementary Material

Supplementary data to this article can be found online at https://doi.org/10.1016/j.cjche.2021.06.007.