Molecularly Explicit Characterization Model (MECM) - ACS Publications

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Molecularly Explicit Characterization Model (MECM) for Light Petroleum Fractions Tareq A. Albahri* Chemical Engineering Department, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait

A method is developed for simulating undefined multicomponent mixtures such as petroleum fractions, coal liquids, and gas condensates using a preselected set of pure components. The molecularly explicit characterization model (MECM) uses routinely made measurements of a petroleum fraction’s bulk properties such as the ASTM D86 distillation, API gravity, Reid vapor pressure (RVP), and the paraffin, naphthene, and aromatic (PNA) content along with the pure components’ properties in an optimization algorithm to define the molecular composition of the petroleum fuel suitable for simulation purposes. The model is tested using a set of 68 pure components to characterize petroleum naphtha and simulate its separation in a distillation column. This model is found to be of better accuracy than the characterization methods currently used. The method has the flexibility to be tailored to use any set of pure components as desired and may further be used to predict the properties of petroleum fractions. Introduction A number of recent developments have required reengineering of key refining processes. One set of developments driving innovation is related to environmental regulations, such as the 1990 Clean Air Act in the United States which specifies, in part, the molecular composition of petroleum-based products (e.g., the limits of benzene and other aromatics in gasoline).1 This represents a great challenge to petroleum refiners since they have not traditionally considered their products on a molecular basis. Rather, they have modeled and marketed their products as volatility fractions (e.g., gasoline, kerosene, diesel, and fuel oil). Traditionally, petroleum refiners characterize petroleum fractions by their global physical properties such as ASTM D86 distillation, API, viscosity, H/C ratio, etc., using few laboratory tests. A more detailed characterization classifies the molecular structures of petroleum fractions as paraffins, isoparaffins, olefins, naphthenes, aromatics, and hydroaromatics.2 Contemporary simulation packages such as HYSYS, PROVISION, and ASPEN break down petroleum fractions into a number of pseudocomponents (boiling-point cuts) for the design of distillation columns and the simulation of many refinery processes. Although satisfying the needs of designers in the past, this form of lumping has several inherent limitations. These lumped models do not reflect the underlying chemistry since the actual composition of the lumps in terms of molecular components may change with overall processing and mask the true kinetics. The growing recognition that the performance of catalytic operations is governed by the molecular rather than bulk properties of the feed materials has resulted in the development of a new generation of more realistic models for petroleum processes that are molecularly explicit. However, all but one of these, because of the lack of molecular details, are models or single component studies and do not represent the true multicom* Tel: (+965) 481-7662 (7459). Fax: (+965) 483-9498. E-mail: [email protected]. Website: http:// www.albahri.info.

ponent feeds. What is needed is a molecularly explicit characterization model of petroleum fractions that will allow us to take advantage of these single component studies to simulate the processing of complex, multicomponent mixtures such as petroleum. This motivated the present approach aimed at the development of a molecularly explicit characterization model (MECM) that will allow the prediction of the molecular composition of petroleum fractions. Such molecular information is a direct input for molecular reaction models, which can subsequently be used to predict the molecular composition and properties for various different processing scenarios. Literature Review. In an effort to enhance the characterization of petroleum fractions, Riazi and Daubert2,3 developed three simple correlations for the prediction of the composition of petroleum fractions in terms of paraffin, naphthene, and aromatic content which was later modified by Nwadinigwe and Okoroji.4 This was followed by a more advanced method based on a twoparameter distribution model by Riazi to predict the complete property distributions of selected properties for a C7+ petroleum fraction using either the pseudocomponent or the single carbon number (SCN) groups approach.5,6 In the latter work, the fraction is divided into an infinite number of components along the true boiling point (TBP) distillation curve of the petroleum fraction. These methods are very useful but far from being considered molecularly explicit. The attempt to develop a molecularly explicit characterization model for petroleum fractions is not new. Shariati et al.7 used the chain of rotators group contribution equation of state (CORGC EOS) to characterize C6+ fractions using n-alkanes, n-cyclopentanes, and n-alkylbenzenes as model compounds. Each C6+ fraction was modeled using an ensemble of only three molecules which is insufficient for simulation purposes. Jabr et al.8 attempted to characterize petroleum naphtha by dividing it into five cuts with unified boiling ranges, the physical properties of which (namely Tc, Pc, MW, Hv, and ν20) are calculated using correlations from the literature. For each cut, representative chemical

10.1021/ie050150o CCC: $30.25 © 2005 American Chemical Society Published on Web 10/25/2005

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Figure 1. Simplified schematic representation of the MECM model.

components are assumed, the compositions of which are determined by solving a system of linear equations to arrive at the properties of the blend. However, the assumption that only five components or less can be used within each cut, since only five independent properties were considered, led the authors to use 9 true components and 16 pseudocomponents in a 25-component feed when testing the method on a debutanizer feed. This assumption is avoided in our method as will be explained below since the boiling point curve provides an infinite number of experimental data which can be used to estimate the composition of any number of pure components as desired. Neurock et al.9 devised a stochastic method using a general Monte Carlo algorithm to transform sets of analytical characterizations into molecular representations of complex petroleum feedstocks. Although the method was fairly accurate in representing the composition of 104 molecules in heavy oil and heavy gas oil, the method is impractical for use in detailed kinetic modeling with the computational power available today. Theory The proposed MECM model is based on the concept that the global properties of a petroleum fraction, such as the true boiling point, specific gravity, vapor pressure, etc., must be equal those calculated from the pure components contained in that petroleum fraction. When both bulk and pure component properties are available, the composition of the petroleum fraction may be simulated using optimization algorithms as simplified in Figure 1. The standard input global properties for the model are the true boiling point (TBP), the Reid vapor pressure (RVP) and the paraffin, naphthene, and aromatic (PNA) content. The internally calculated global properties are the molecular weight, the true vapor pressure at 37.8 °C, the specific gravity, the cubic average boiling point (CABP), the mean average boiling point (MeABP), the volumetric average boiling point (VABP), the weight average boiling point (WABP), the molar average boiling point (MABP), the Watson characterization factor (Kw), the refractive index, the carbon-to-hydrogen ratio (C/ H), the kinematic viscosity at 37.8 and 98.9 °C, the surface tension of liquid at 25 °C, the aniline point, the true and pseudocritical temperatures and pressures, the critical compressibility factor, the acentric factor, the freezing point, the heat of vaporization at the normal boiling point, the net heat of combustion at 25 °C, the isobaric liquid heat capacity at 15.6 °C, the isobaric vapor heat capacity at 15.6 °C, the liquid thermal conductivity at 25 °C, and the research and motor octane numbers. These global properties are calculated for the petroleum fraction using well established methods in the literature or from methods developed specifically for this purpose. The above input and analytically calculated internal properties are also calculated from pure com-

ponent data. The two methods are contrasted, and the difference is minimized using an optimization algorithm. The model output is a computationally generated explicit atomic detail of the petroleum feedstock. The outcome molecular ensemble retains the qualitative features expected to mimic the petroleum fraction for modeling purposes. The procedure as such is very similar to gas chromatography (GC) analyzers, which cannot possibly determine the composition of all the hundreds of molecules in a petroleum fraction, but rather the composition of a limited set of preselected representative molecules. Once these compounds are set, the same can always be used as part of a standard procedure to represent the composition of that fraction. Model Development. It has been shown5 that the average (global) physical property of the petroleum fraction, Θ, can be calculated by integration of the pure component properties along the true boiling point curve according to the following relation:

Θ)

∫01Θ(x) dx

(1)

where x is the fraction of volume vaporized in a TBP distillation, and Θ(x) is the property value at x. For a finite number of increments (components), the solution of the integral term in the above equation may be attained by calculating the area under the property distribution curve, and eq 1 may be approximated by the following expression representing that area: n

Θ)

Θi(x) ∆xi ∑ i)1

(2)

where n is the number of increments (or the number of the pure components in the molecular ensemble), ∆x is the increment size (i.e., volume fraction of the pure components), Θi(x) is the property value or a function thereof for the increment ∆xi (or the pure component). Since some pure component properties do not mix linearly, mixing rules may be applied to estimate the properties of the defined mixture. Therefore, in principle it is possible to use the above relation to predict the composition of the pure components, x, from the knowledge of the physical properties of these components and those of the mixture. In the proposed MECM model, a petroleum fraction is divided into a number of increments along the true boiling point (TBP) curve as shown in Figure 2. This is equal to the number of components in the molecular ensemble, the concentration of which is to be determined. To relate the API of a petroleum cut, for example, to that of the pure components within, the specific gravity (SG) at 15.6 °C is used (since API does not mix linearly), and the above property relation may be written as follows:

SG )

∫01SG(x) dx

(3)

For a finite number of components (n), this relation may be reduced to the following: n

SG )

(SG)i(xv)i ∑ i)1

(4)

where (xv)i is the volume fraction of molecule i in the ensemble. Similar relations may be produced for other

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Figure 2. Simulation of a true boiling point (TBP) curve using true components.

Figure 3. Chemical logic diagram for the methodology used to develop the MECM model.

properties which may be solved for the pure component concentrations, x, using an optimization algorithm. Methodology. The chemical logic diagram for this system is depicted in Figure 3 which illustrates the methodology used in developing the MECM model and the procedure followed for analyzing the simulation problem. The first step in this scheme consists of information gathering about a particular light petroleum fraction (in this case naphtha) from existing plants. To characterize the unknown hydrocarbon mixture, laboratory analyses are used to determine the RVP, PNA content, and TBP. These experimental procedures provide the input for the molecular feedstock simulation. Out of these three properties, the TBP must be available which is usually the case while the other properties, if not available, may be estimated using correlations from the literature. The other global prop-

erties of the petroleum fraction are calculated internally by the MECM model using methods in the literature. The second step in this scheme comprises selecting the pure compounds. The results of the above chemical analysis, in addition to some widely accepted rules from the literature, provide guidelines in selecting the pure compounds to be used for simulating the petroleum fraction. Gas chromatography (GC) analysis combined with literature data provides a better understanding of the structural composition of the petroleum fraction and is used as an additional basis for the selection of the pure components. For that purpose, naphtha samples were collected from local refineries and analyzed for composition in PIONA and detailed hydrocarbon GC analyzers. The second step in this scheme also comprises collecting the pure component properties from the property databanks of the API-TDB,10 AIChE-DIPPR,11 PGL,12 and others.13 In the absence of a certain property value for a molecule, common correlations for various physical properties, available in the literature,12 are used to estimate it. Estimation methods were also developed specifically for this purpose when reliable correlations were not available.14-17 The third step in this scheme comprises using widely accepted mixing rules from the literature to convert the predefined pure component data (molecular description, physical properties, and composition) into global properties (e.g., molecular weight, H/C ratio, etc.). The simulation outcome, molecular (boiling point) distributions, and average global properties are subsequently used to compare and contrast the experimental and analytical procedures described in step 1 above. The fourth step in this scheme comprises using an optimization algorithm that calculates the optimum molecular composition of the petroleum fraction. The objective function compares the global properties of the petroleum fraction (from step 1) with those of the molecular representation (from step 3) while incorporating additional constraints from structural relations within the petroleum fraction (namely PNA content) to improve the simulation output and provide the model with a general validity. For that purpose, it was essential to allow for not only the initial transformation of feedstock characterization information into a molecular representation, but also the inverse transformation of molecular representation into global properties. The fifth step in this scheme comprises the testing phase. To verify the validity and accuracy of the model, the simulated petroleum fraction was subjected to several separation tests. The results were compared with actual operating data from industrial distillation columns where the mixture is separated into a volatile fraction and a nonvolatile fraction. Error analyses are presented by comparing the model-predicted average properties and ASTM D86 distillation data for the molecular representation of both volatile and nonvolatile fractions with that from industry. The fifth step also comprises comparing the MECM model performance in simulating the actual petroleum fraction to the contemporary characterization methods currently employed in simulation packages that are widely used in the refining industry such as the HYSYS process simulator. To clarify the sensitivity of the column simulation to the feed characterization method, the HYSYS simulation is performed under the same conditions, but with feed modeled with two different


approaches; the conventional approach employing the global properties of the fractions as criteria to select the pseudocomponents and the MECM approach employing the global properties of the fractions as criteria for the selection of the molecular ensemble. This necessitated the chemical analysis of some streams and the design information of some equipment. Feedstock Description. Conceptually, detailed characterization of each naphtha sample by GC could provide information about the inherent molecules. However, this approach can be complex, expensive, and time-consuming and thus undermine the motivation for building a simulation model. Furthermore, this method does not account for all the inherent molecular species from which 1500 have been so far identified in gasoline alone.18 Molecule-by-molecule separation and identification is a worthy goal that is nevertheless beyond present capabilities for naphtha not to mention heavier fractions. Recognizing that molecule-by-molecule measurements in petroleum feedstocks would be difficult, we sought to define and characterize the naphtha molecules in a simple mathematical way that would allow for the assembly for a molecular representation of a given feedstock. Since the ASTM D86 distillation test is more commonly used in the refinery than GC, we sought to utilize these traditional definitions of complex petroleum feedstocks based on available refinery and experimental separations that are used in daily refinery operations for achieving that objective. The computational description of the complex feedstock addressed the challenge of providing a unique identity to each of the ensemble molecules. The computational identification of each unique component is crucial not only to the description of complex feedstocks, but also for the development of molecular reaction models and the prediction of product properties. Model compounds of the selected molecular ensemble were based on conditional arguments calculated from initial boiling point considerations and basic structural logic. Selection of the components is performed by considering first that each petroleum fraction can be represented by a finite number of true components having boiling points within the boiling range of the petroleum cut. Straight run naphtha, for example, which is the typical feedstock for gasoline production, consists of material boiling between pentane and kerosene distillate, comprising chiefly paraffinic, naphthenic, and aromatic hydrocarbons with 3-11 carbon atoms per molecule.19 This corresponds approximately to a boiling range of 20-200 °C at 1 atm. These fractions are operationally defined, and therefore their exact boiling range is dependent upon the actual separation conditions. Therefore, the model compounds must be composed of normal- and iso-paraffins, naphthenes, and aromatics ranging in carbon number from C3 through C11. They must include such compounds as benzene, cyclopentane, cyclohexane, and homologous series of these. In addition, if more than one isomer for a compound exists in the fraction, then only one or two that best represents the physical and chemical properties of all the isomers would be selected. Another criterion relates to the order of carbenium and carbonium ions that are likely to form during the kinetic modeling of catalytic cracking mechanism on bifunctional zeolite catalysts, which is the focus of kinetic modeling. Consideration is also made

to the molecular product fraction (i.e., paraffin, naphthene, and aromatic content). Number of Molecules. The catalytic cracking of n-heptane alone is reported to undergo 2210 reactions and 336 intermediates.20 When the feed is a complex mixture, like naphtha or gas oil containing thousands of hydrocarbons, the number of components in the reaction mixture becomes enormous and the generation of reaction networks for each of the feed components becomes an overwhelming task. For that reason, predicting molecular compositions of 104 molecules in petroleum and its fractions9 is impractical for use in kinetic modeling. Therefore, an important challenge in modeling the refinery processes is the development of a reliable yet practical molecularly explicit characterization model for complex feedstocks where the number of components is not too excessive for computation power during kinetic modeling and rigorous phase equilibrium calculations or too diminutive for modeling purposes. The proposed model accounts for more or less 68 model compounds chosen in such a way as to account for the overall components that exist in the fraction. This reduced the number of parameters and resulted in large CPU savings. This number was arrived at by screening over 200 pure components based on our background knowledge of structural chemistry and relative volatility in addition to other criteria available in the literature.20-29 In that, special emphasis is placed on the important role the structure of the molecule plays in catalytic chemistry in petroleum refining processes. Special emphasis was also placed on some environmentally and economically significant compounds. Having satisfied the above criteria, the final molecular ensemble comprising 68 molecular species shown in Table 1 was used to simulate petroleum naphtha. Determination of Global Properties. The determination of the petroleum fractions’ global properties involves either accessing standard correlations or simulating various thermodynamic experiments. Several charts and correlations in the literature predict the physical, thermodynamic, and transport properties of undefined mixtures based on the boiling point, specific gravity, and some characterization factors. Examples of such charts and correlations are available in the APITDB10 and other references.3,5,6,12 The global properties used in the MECM model and their estimation methods are shown in Table 2. Two methods for each property are shown there. The first was used to obtain quick reliable answers during model development and solution using property estimation software packages such as PETROCHEM36 and EPCON API-TDB37 whenever possible in addition to some API procedures. The alternate methods were obtained from various sources including the API-TDB10and are shown in details in the Supporting Information. All the relevant API figures and procedures were digitized in order to automate the calculations for the purpose of carrying out the intended study.38 Aggregating the Molecular Ensemble. When molecular detail is available, it is possible to predict analytical results for multicomponent mixtures through simple accounting or methods for aggregating the molecules into lumped fractions. The properties in Table 2 calculated from global properties and aggregation of pure components must match; otherwise, model consistency and internal integrity are lost.

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Table 1. Molecular Ensemble Used To Characterize Petroleum Naphtha 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

propane isobutane n-butane 2-methyl butane (isopentane) n-pentane cyclopentane 2,2-dimethyl butane (neohexane) 2,3-dimethyl butane 2-methyl pentane 3-methyl pentane n-hexane methylcyclopentane 2,2-dimethylpentane benzene 2,4-dimethylpentane cyclohexane 2,2,3-trimethylbutane (triptane) 3,3-dimethylpentane 1,1-dimethyl cyclopentane 2,3-dimethylpentane 2-methylhexane cis-1,3-dimethylcyclopentane trans-1,2-dimethyl cyclopentane 3-methylhexane trans-1,3-dimethylcyclopentane 3-ethylpentane n-heptane ethylcyclopentane 2,2-dimethylhexane 2,5-dimethylhexane 2,4-dimethylhexane 2,2,3-trimethylpentane toluene 3,3-dimethylhexane

35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68

2,3-dimethylhexane 2-methyl-3-ethylpentane 2-methylheptane 3,4-dimethylhexane 4-methylheptane 3-methyl-3-ethylpentane 3-ethylhexane 3-methylheptane cis-1,3-ethylmethylcyclopentane trans-1,2-ethylmethylcyclopentane trans-1,3-ethylmethylcyclopentane 2,2,5-trimethylhexane n-octane cis-1,2-ethylmethylcyclopentane 2,3,5-trimethylhexane 2,2-dimethylheptane 2,4-dimethylheptane 2-methyl-4-ethylhexane 2,6-dimethylheptane 2,5-dimethylheptane 3,5-dimethylheptane ethylbenzene 3,3-dimethylheptane p-xylene m-xylene 2,3-dimethylheptane 3,4-dimethylheptane 4-ethylheptane 4-methyloctane 3-ethylheptane 2-methyloctane o-xylene 3-methyloctane n-nonane

Table 2. Characterization Methods for Describing Petroleum Fractionsa 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 a

property

symbol

method

alternative method

true boiling point distribution vapor pressure at 37.8 °C Reid vapor pressure cubic average boiling point mean average boiling point volume average boiling point weight average boiling point mole average boiling point Watson characterization factor molecular weight refractive index hydrogen content kinematic viscosity at 98.9 °C kinematic viscosity at 37.8 °C surface tension at 25 °C aniline point critical temperature. pseudocritical temperature pseudocritical pressure critical compressibility factor paraffins, naphthenes, and aromatics acentric factor freezing point heat of vaporization at NBP net heat of combustion at 25 °C isobaric liquid heat capacity at 15.6 °C isobaric vapor heat capacity at 15.6 °C liquid thermal conductivity at 25 °C API gravity research octane number motor octane number

TBP Pv37.8 RVP CABP MeABP VABP WABP MABP Kw MW RI H2 ν98.9 ν37.8 σ25 Ta Tctrue Tcp Pcp Zc PNA w Tf (∆Hv)Tb ∆Hc Cpl Cpv K API RON MON

Petrochem Petrochem experimental Petrochem Petrochem Petrochem Petrochem Petrochem Petrochem Petrochem Petrochem Petrochem Petrochem Petrochem Petrochem Petrochem API 4A1.2 API 4A1.2 API 4B1.2 API 6B1.4,5 EPCON EPCON EPCON EPCON API 14A1.1/2 EPCON EPCON Petrochem experimental ref 34 ref 35

API 3A1.1 API 5B1.1 ref 30 API 2B1.1 API 2B1.1 API 2B1.1 API 2B1.1 API 2B1.1 ref 10 ref 19 ref 2 API 2B2.1 ref 19 ref 19 API 10A1.5 API 2B2.1 ref 31 ref 31 ref 2 ref 31 ref 43 ref 32 ref 19 ref 19 ref 33 ref 10

References: API TDB,10 Petrochem Toolkit,36 EPCON.37

Molecular structure properties are computed by simply counting their occurrence with respect to composition. The averaged properties Θ are computed using weight, mole, or volume fractions as appropriate,19 where f(Θi) may be the property of pure component i or

any function thereof. n

Θ)

f(Θi)xi ∑ i)1

(5)


For the surface tension,10 average molecular weight, pseudocritical temperature, critical compressibility factor, acentric factor, vapor pressure, refractive index, aniline point, freezing point, and octane number, the simple mole average method is used. A simple mass fraction average method is used for the heat of vaporization, the net heat of combustion, Watson characterization factor, and the isobaric heat capacity for vapor and liquid, while volume fraction is used for the specific gravity. A detailed description of the methods of aggregating the molecular ensemble is shown in the Supporting Information. Concentration of Light Components. It is evident from experimental data that ASTM D86 distillation cannot account for the concentration of the components lighter than C5 due to evaporation at room temperature during the experimental procedure as well as sampling. The concentration of the light ends (n-butane and lighter) in naphtha is calculated using simple phase equilibrium calculations. First, the RVP for the petroleum fraction (naphtha) is converted into true vapor pressure (TVP) at 37.8 °C using the API method10 that has been digitized and incorporated into the MECM model. The TVP is then used to calculate the concentration of the light ends using simple bubble (boiling) point calculations the criteria of which is the following n

K′ixi ) 1 ∑ i)1

(6)

The vapor-liquid equilibrium constant (distribution coefficient) is simplified assuming ideal systems using Raoult’s law to the following relation

K′i ) Piv/Pt

(7)

where, Piv is the vapor pressure of the pure component i in the defined mixture and Pt is the true vapor pressure of the naphtha at 37.8 °C. Combining the above equations, we obtain the following simple relation: n

Pivxi ) Pt ∑ i)1

(8)

which can be used to calculate the mole fraction of the light ends using an optimization algorithm. Model Solution It is difficult to determine the composition of the molecules in the ensemble by solving a system of linear equations.8 The maximum number of independent equations that can be formulated is equal to the number of independent properties available in Table 2, which is 30. It is not possible to solve for the mole fractions of the 68 components in the molecular ensemble by solving a system of 30 linear equations since the problem is indeterminate. A better approach is to find the mole fractions based on minimizing the difference between the global properties of the petroleum fraction and the properties calculated from the molecular ensemble using optimization techniques for the reasons discussed below. Optimization Algorithm. The distribution of the molecular ensemble is determined in terms of volume fractions by minimizing the following objective function

which is based on the least-squares method where i is n

S)

∑ j)1

P

((Tbj - T′bj) × W0 × 100/Tbj)2 +

((Yi ∑ i)1

Y′i) × W1 × 100/Yi)2 (9) the index number of the physical property, j is the index number of the molecule, P is the total number of physical properties considered (shown in Table 2) except boiling point, and n is the total number of molecules. Yi is the value of the global property i for the petroleum fraction determined experimentally or calculated using generalized correlations with the global properties as input parameters. Y′i is the value of the global property i for the petroleum fraction calculated from aggregating pure components in the molecular ensemble using mixing rules. T′bj is the boiling point of pure component j, and Tbj is the boiling point value on the petroleum fractions’ TBP curve corresponding to component j. W0 is the weighting factor for the boiling points, and W1 is the weighting factor for all other properties. S is the objective function to be minimized. The objective function (eq 9) is taken as the sum of the square of the percent error between the observed global (experimental or otherwise predicted from experimental) properties of the petroleum fraction and those calculated from mixing the components of the molecular ensemble. The objective function consists of two parts. The first compares the boiling point of the pure component to the boiling point on the TBP curve of the petroleum fraction corresponding to the concentration (or the mid cumulative volume percent) of that component as illustrated in Figure 2. By minimizing the objective function, we reduce the difference between the two boiling points by manipulating the composition of the molecular ensemble in the simulated mixture until each molecule’s boiling point matches that on the TBP curve. The second part of the objective function compares all the other global properties of the petroleum fraction (e.g., specific gravity, RVP, molecular weight, and paraffin, naphthene, and aromatic content, etc., shown in Table 2) obtained experimentally or predicted from experiment and those from aggregation of the molecular ensemble. By minimizing the objective function, we reduce the difference in these properties for the petroleum fraction and the molecular ensemble while the composition of the molecular ensemble simulating the petroleum fraction is calculated. As such, the feed is characterized using a molecular ensemble with average physical properties close to that of the petroleum fraction. In the above objective function, both Y′i and T′bj are a function of the composition. The first utilizes the molecular composition in mixing rules while the second is a polynomial fit of the TBP curve of the petroleum fraction in which the composition is expressed in volume percent as follows:

T′bj ) aΨj + bΨj2 + cΨj3 + dΨj4 + e

(10)

where a, b, c, d, and e are constants estimated by regression from the TBP curve of the petroleum fraction and Ψj is the cumulative volume fraction at the midvolume percent of component j given by the following

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equation with xv as the volume fraction j-1

Ψj )

∑

k)1

xvk +

xvj 2

(11)

The mathematical fitting of the TBP curve in eq 10 is a source of an unlimited number of boiling point values to be compared with those of an unlimited number of molecules. Hence, there will always be an equal number of variables both independent (boiling points) and dependent (concentrations), using the true boiling point distribution alone, regardless of the number of molecules chosen. Therefore, no matter how many molecules are used in the ensemble, it is always possible to find a feasible solution. It is evident that the sum of the squares of the percentage errors of the boiling points in the first part of the objective function (eq 9) is very much larger than that of the other properties in the second part. This is because the number of molecules, n, in the ensemble is 68 which is much larger than the number of properties P (28 properties). For that reason, a weighting factor is used in each part of the objective function to give an equal account of the other properties which will otherwise be overwhelmed by the errors from the boiling points of such a large number of molecules. Weighting factors associated with each term in the objective function were arrived at by trial and error which produced the best fit of experimental measurements. The optimum weighting factors W1:W0 values of 25:1 produce a very good reproduction of the TBP curve as well as the other global properties of the naphtha (e.g., the API gravity, molecular weight, and paraffin, naphthenes, and aromatic content, etc.). In the event that the number of molecules in the ensemble is reduced, W1 must also be reduced to accommodate the changes and produce the minimum error possible. Once the optimum values of the weighting factors are determined, they are kept constant as part of the procedure since they are a function of the number of both molecules and properties considered. Finding Global Minimum. Nearly all classical nonlinear optimizers are guaranteed only to find a locally optimal solution. To find a globally optimized solution, using for example the nonlinear GRG local optimization module, an alternative approach is usually used. The optimization program is run several times from judiciously chosen but different starting points, and the best solution found will be the best estimate of a globally optimized solution. Making use of this multistart technique is often used to get an estimate of the solution’s uniqueness.8 Although it is argued that the model outcome in terms of molecular distributions and predicted average global properties has very little sensitivity to variations in feed molecular representation8 we sought to employ a global optimization algorithm to ensure uniqueness of the results and avoid lengthy trial-and-error procedures as well as errors resulting from a nonjudicial initial assumption. The optimization algorithm, written in an MS EXCEL macro, is applied using the PC version of Frontline Systems Premium Solver Platform 6.0 software package39 using the multivariable nonlinear large-scale global optimization (LGO) solver engine in order to search for the unknown vector (xi) that minimizes the objective function (S) in eq 9 and satisfies the constraints. Convergence was achieved in about 10 s for

each case on a Pentium IV-3.0 GHz PC. The global optimization algorithm calculates the objective function and then alters the concentration of the pure components until the global minimum is found. This point represents the optimal concentrations which best fit the basic analytical data and quantitatively represents the naphtha sample. As such, the program always predicts the same composition for a specific sample, and solution uniqueness is achieved. Model Testing To verify the validity and accuracy of the model, the simulated petroleum fraction was subjected to several separation tests, the results of which were compared with actual operating data from industrial distillation columns used as naphtha splitters. For that purpose, naphtha samples and experimental results were obtained from local petroleum industry. Experimental data on the boiling point distribution for petroleum naphtha feed and vapor and liquid streams during distillation were available. The samples were obtained from naphtha splitters, the feed of which was saturated debutanized naphtha produced from hydrocracking of heavy gasoil. A total of nine naphtha samples were collected to assess model performance against experimental data and for error analysis. Three samples were collected for each naphtha splitter: one for the feed, one for the light naphtha product, and one for the heavy naphtha product. Detailed descriptions of these samples are provided in tables in the Supporting Information. The two naphtha splitting columns operated by the local refinery were identical. The distillation tower has 30 stages (excluding the reboiler and the condenser), and the feed enters as saturated liquid on tray 14. The relevant operating conditions such as flow rates, temperature, and pressures in addition to the distillation column hydraulic parameters and design specifications are presented in Table 3. The naphtha splitting column is simulated using HYSYS process simulator40 using the above design and operating information with the following assumptions: (1) Vapor and liquid outlet streams from each stage are in thermal and phase equilibrium throughout the 30 theoretical stages. (2) Tray vapor hold-ups are negligible. (3) Reflux enters the column as a saturated liquid. (4) Simulation calculations were done using fixed design parameters at steady-state conditions using the Peng-Robinson thermodynamic equation of state. To test the MECM model, two sets of data were used as input to the HYSYS simulation model. In one set, the naphtha was characterized in terms of bulk properties (API, RVP, PNA, and ASTM D86 distillation), while in another that information was used in the MECM model to generate a molecular ensemble that simulates naphtha and is used as the feed. After the separation test, the MECM model-predicted molecular distributions are converted back into global properties (API, RVP, PNA, and ASTM D86 distillation) and compared with products of the experimental data. The model performance in simulating the actual petroleum fraction is, in addition, compared to products from the HYSYS simulation package which uses the contemporary method of feed characterization. Error analyses are presented by comparing the model-predicted ASTM D86 curve developed from the molecular composition with that

Ind. Eng. Chem. Res., Vol. 44, No. 24, 2005 9293 Table 3. Operational and Design Data for an Industrial Naphtha Splitter operating conditions

value

design specifications

value

feed naphtha flow rate light naphtha product flow rate heavy naphtha product flow rate reflux flow rate feed temperature overhead temperature reflux temperature reboiler temperature pressure of condenser overhead pressure reboiler pressure

9300 BPD (43100 kg/h) 4450 BPD (19500 kg/h) 4870 BPD (23680 kg/h) 4000 BPD (17640 kg/h) 142 °C 88 °C 40 °C 142 °C 0.70 bar 0.70 bar 0.745 bar

number of trays tray efficiency number of trays (enriching section) number of trays (stripping section) tray (tower) diameter (enriching section) tray (tower) diameter (stripping section) tray type tray weir height (enriching/stripping) tray weir length number of passes (enriching/stripping) distance between trays

30 75 16 14 167.64 cm 167.64 cm valve trays 101.6/88.9 mm 76.2 mm 1/2 610 mm

Figure 4. Comparison of feed naphtha TBP with that simulated from pure components.

from analysis of the actual operating plants as well as HYSYS simulation. Results and Discussion The molecular ensemble in Table 1 was used to compute molecular distribution results, the boiling point distribution of which was estimated by fitting to the petroleum fractions TBP curve. Figure 4 compares the overall experimentally measured boiling point distribution with that predicted from the MECM simulation. The components’ results demonstrate an almost exact match with the TBP curve to within statistical errors. This was to be expected in that the input distribution was directly derived from the experimental distribution. It is noticed that the two TBP curves do not match exactly. There is a small deviation due to optimization of other properties as well (i.e., API, PNA content, etc.) in addition to the boiling points. To illustrate the finegrained molecular detail of the output, the molecular distribution for 68 species used to simulate a naphtha feed for one case is shown in Figure 5. Applying the MECM methods and correlations to determine the petroleum fractions’ properties, shown in Table 2, the PNA compositions and physical properties of the naphtha splitter feed fraction are estimated and tabulated in Table 4. The same properties estimated from aggregation of the molecular ensemble are also shown in the same table. The results demonstrate an almost exact match which was to be expected in that the ensemble properties were directly derived from these global properties. Feedstock product quality was compared through experimental distillation analysis. The HYSYS model calculations simulated the fractionation process and produced an overall distillation curve for the light and heavy naphtha products. The combined MECM-HYSYS model calculations simulated the fractionation process

as well. As evidence of the ability of the MECM model to determine molecular and global product properties, the discrete boiling points for each component are plotted as a function of temperature to reconstruct the TBP and ASTM D86 distillation curves. The experimental and simulation-derived distillation curves for both methods are contrasted in Figure 6. The MECM model results for the light and heavy naphtha products correlated better with the experimental ASTM D86 distillation data than those using the pseudocomponent method incorporated in the HYSYS process simulator. This indicates how good the feed modeling and characterization by the proposed technique are. Error Analysis. Error analyses were performed by converting the model-predicted molecular distribution back into ASTM D86 distillation data and compared with those of actual operating units and simulation packages used in the refining industry. As an illustrative example, Table 5 lists the percent relative deviations for the light naphtha product of the steady-state simulation of the naphtha splitter column with both feeds. It is noticed that the percent deviations for the steady-state simulation of the naphtha splitter column with the feed characterized by global properties and the pseudocomponent approach are greater than those with the feed characterized by the proposed MECM technique. The relative deviations are presented with respect to experimental data for only one case. Notice that when using the pseudocomponent feed characterization approach, only the boiling point distribution of the product is computed while the other properties are not predictible. The standard deviation between experimentally determined ASTM D86 distillation data and those simulated for all the samples (total of six product samples) using the MECM computationaly simulated distillation was 8.1 °C with an average percentage error of 1.8%. Differences between the experimental and simulated results may be caused by inconsistencies in the data provided by the analytical tests, approximations made during construction of the MECM model including the choice of the molecular ensemble, and inherent errors in the various correlations used. This standard deviation of 8.1 °C is better than the reported value in the literature of 20.8 °C using stochastic algorithms.9 The standard deviation between experimentally determined ASTM D86 distillation curves and those simulated for the same six product samples using the conventional method of feed characterization and the pseudocomponent model was 14.3 °C with an average percentage error of 3.4%. This shows that rough feed characterization results in high errors in the simulation results which make the application of the MECM model more suitable and advantageous.

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Figure 5. Calculated composition of representative pure components.

We have assumed an ideal system in calculating the concentration of the light components in the petroleum fraction although the system is nonideal. This simplifying assumption was used because the concentration of the components lighter than pentane such as propane and butane (all of which are paraffins and may be considered an ideal solution) is very small and is of minor significance in our work. This assumption has proven to be adequate as shown by the final results both in terms of modeling physical separation and product property estimation. Properties of the Molecular Representation. Using the resultant molecular distributions for the naphtha splitter products, along with the physical properties of the pure components and the aggregation scheme described above, the calculated global properties for the naphtha top product for one case are shown in Table 6. The percent deviation of these estimated properties from those obtained experimentally or estimated from experimental is shown in the same table. The fit between the experimental and stimulation results is quite good. This small deviation indicates how the estimated molecular distributions are representative of the undefined petroleum mixture.

Simulation Time. The steady-state HYSYS simulation of the splitting column for each feed system was run on a Pentium IV personal computer running at 3.0 GHz. The CPU time of the simulation with the feed characterized as in the proposed technique with 68 components is about 7 s. The HYSYS simulation time for feed characterized using global properties is at an average of 2 s. Results with the conventional characterization and pseudocomponent method are about onethird of the reported CPU of the improved model. The time expended by the MECM model to characterize the petroleum naphtha feed into a molecular ensemble is on the order of 10 s. The time expended to aggregate the product molecular ensemble into light or heavy naphtha product and recalculate the global properties is on the order of 3 s. It is worth mentioning that the molecular representation of Table 1 is not unique, and various other molecules can be employed since the model outcome has very little sensitivity to variations in feed molecular representation.8 One advantage of the model is the ability to tailor the number and type of model components as desired by the user, the limitations being only the computation power available and the intended use

Ind. Eng. Chem. Res., Vol. 44, No. 24, 2005 9295 Table 4. Comparison of Petroleum Fractions’ Global Properties and Internal Relations Calculated from Analytical Methods as Well as Aggregation of Pure Components Using MECM Model (Naphtha Splitter Feed) Case 1

a

property

experimental or predicted from experimental data

MECM simulationa

% error (or deviation)

specific gravity vapor pressure at 37.8 °C, bar Reid vapor pressure, bar cubic average boiling point, °C mean average boiling point, °C volume average boiling point, °C weight average boiling point, °C mole average boiling point, °C Watson characterization factor molecular weight, g/mol refractive index hydrogen content, wt frac kinematic viscosity at 98.9 °C, mm2/s kinematic viscosity at 37.8 °C, mm2/s surface tension at 25 °C, dyne/cm aniline point, °C critical temperature, °C pseudocritical temperature, °C pseudocritical pressure, bar critical pressure, bar critical compressibility factor paraffins content, mol % naphthenes content, mol % aromatics content, mol % acentric factor freezing point, °C heat of vaporization at NBP,b J(abs)/g net heat of combustion at 25 °C, J(abs)/g isobaric liquid heat capacity @ 15.6 °C, J(abs)/g K isobaric vapor heat capacity @ 15.6 °C, J(abs)/g K liquid thermal conductivity @ 25 °C, J(abs)/s m2 K/m

0.704 0.7308 0.5585 83.9 81.4 85 85.7 79.6 12.44 99.23 1.3919 0.155 0.34 0.51 19.89 52.2 257.2 251.7 31.03 33.78 0.2772 72.13 21.35 6.52 0.285 -102.6 327.31 44136 2.183 1.683 0.1090

0.701 0.7308 0.5585 76.8 75.4 78 80.2 74 12.25 90.78 1.3915 0.154 0.305 0.482 19.03 60 253.6 248.1 31.57 34.27 0.2677 72.07 21.80 6.12 0.274 -105.9 325.17 44192 2.049 1.611 0.1149

-0.44 0.00 0.00 -1.98 -1.69 -1.94 -1.53 -1.60 -1.52 -8.52 -0.03 -0.90 (-0.035) (-0.028) -4.35 2.39 -0.68 -0.68 1.76 1.43 (-0.0095) (-0.06) (0.45) (-0.4) (-0.011) -1.91 -0.65 0.13 (-0.134) (-0.072) (0.0059)

From aggregation of pure components. b At 0 bar and MeABP.

Conclusion

Figure 6. Comparison of ASTM D86 distillation curves for light and heavy naphtha products from naphtha splitter column.

of the simulation whether be it physical separation, property estimation, or kinetic modeling. This factor is very attractive for application in environmental and technical studies aimed at increasing efficiencies and improving economics through increasing octane number and optimizing catalyst design. Moreover, the larger the number of components is, the less sensitive the result is to their variation.8 However, execution time increases with the number of components, and a tradeoff is selected when satisfactory accuracy is obtained.

It was an objective of this work to develop a method for simulating undefined multicomponent mixtures, such as petroleum fractions in general and light petroleum fuels such as naphtha and gasoline in particular, that will provide compositional information that is more suitable than the current methods to enhance the characterization and thus the prediction performance of simulation packages. We have developed a technique that combines routine analytical tests and a molecularly explicit modeling approach to provide quantitative insight to naphtha structure. This permitted easy accounting of molecules (their precise atomic configuration) and the distribution of each component which enabled the direct estimation of the physical and chemical properties thereof. The molecular distribution for a hydrocarbon-plus fraction is predicted with good accuracy, when at least one bulk property is available (namely, ASTM D86 distillation temperatures). However, distributions can be predicted more accurately if, in addition to TBP data, RVP and PNA are available. The method has been used to predict molecular distributions of feed, vapor, and liquid products in distillation of three petroleum naphtha samples, and predicted boiling point distributions were in good agreement with the experimental data. Lumping and delumping schemes of C5+ samples for the proposed distribution model are also presented. Estimated properties using these lumping schemes are in excellent agreement with the experimental data. The results suggested that optimization techniques can lead to lowend and high-end details in the distributions of the

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Table 5. Comparison of Experimental and Simulated Analytical Results Using MECM Model (Light Naphtha Product) Case 2 property

experimental

API RVP, bar paraffins, mol % naphthenes, mol % aromatics, mol % ASTM D86 Distillation, °C IBP 5 vol % 10 vol % 30 vol % 50 vol % 70 vol % 90 vol % 95 vol % FBP

84.8 0.855 92.76 7.24 0.00 48 52 55 62 67 71 77 80 90

HYSYS simulation

58 64 68.5 79.5 88 93 98 100 106

deviation (% error)

3.1 3.7 4.1 5.2 6.2 6.4 6.0 5.7 4.4

MECM model simulation


83.7 0.834 91.3 8.7 0.01

(-1.1) (-0.021) (-1.46) (1.46) (0.01)

49.4 51.7 53.6 59.2 63.9 67.8 72.8 75.6 80.6

0.4 -0.1 -0.4 -0.8 -0.9 -0.9 -1.2 -1.3 -2.6

Table 6. Comparison of Petroleum Fractions’ Global Properties and Internal Relations Calculated from Analytical Methods as Well as Aggregation of Pure Components Using MECM Model (Naphtha Splitter Light Naphtha Product) Case 1

a

property

experimental or predicted from experimental

MECM simulationa


specific gravity vapor pressure at 37.8 °C, bar Reid vapor pressure, bar cubic average boiling point, °C mean average boiling point, °C volume average boiling point, °C weight average boiling point, °C mole average boiling point, °C Watson characterization factor molecular weight, g/mol refractive index hydrogen content, wt fraction kinematic viscosity at 98.9 °C, mm2/s kinematic viscosity at 37.8°C, mm2/s surface tension at 25 °C, dyne/cm aniline point, °C critical temperature, °C pseudocritical emperature, °C pseudocritical pressure, bar critical pressure, bar critical compressibility factor paraffins content, mol % naphthenes content, mol % aromatics content, mol % acentric factor freezing point, °C heat of vaporization at NBP,b J(abs)/g net heat of combustion at 25 °C, J(abs)/g isobaric liquid heat capacity at 15.6 °C, J(abs)/g K isobaric vapor heat capacity at 15.6 °C, J(abs)/g K liquid thermal conductivity at 25 °C, J(abs)/s m2 K/m

0.6757 0.717 0.683 60.9 58.9 61.7 61.9 57.9 12.47 81.2 1.3775 0.1559 0.28 0.39 17.77 51.1 231.1 225.6 32.54 35.85 0.2790 86.28 10.64 3.08 0.263 -112.2 343.95 44,170 2.255 1.675 0.1065

0.6734 0.703 0.676 56.9 56.4 57.4 58.5 55.9 12.51 83.2 1.3797 0.1597 0.2718 0.425 17.49 65.4 227.4 225.4 32.50 36.27 0.2688 86.23 9.98 3.79 0.2517 -99 330.83 44,520 2.139 1.806 0.1100

-0.35 -1.92 -1.01 -1.20 -0.74 -1.26 -1.01 -0.60 0.35 2.47 0.16 2.44 (-0.0082) (0.035) -1.56 4.42 -0.74 -0.03 -0.14 1.15 (-0.0102) (-0.05) (-0.66) (0.71) (-0.0113) 8.23 -3.81 0.79 (-0.116) (0.131) (0.0035)

From aggregation of pure components. b At 0 bar and MeABP.

various molecular products. Therefore, the use of optimization can be more appropriate than other techniques and reduce the differences between the experimental and simulated data. This work further demonstrates that the complex nature of petroleum fuels may be modeled by a limited set of representative pure components. Considering the difficulty and complexity of accounting for the thousands of compounds in petroleum fuels and the limitations of the conventional pseudocomponent technique, the proposed method can be an effective alternative. It was found that through proper characterization of feed composition the MECM model does improve the accuracy of prediction over more traditional methods. The developed methodology is a useful tool in representing a broad range of different petroleum feedstocks

in terms of molecule structures, provided a relatively simple set of experiments are performed to characterize the attributes of the feed. This molecularly explicit simulation of feedstock structure is direct input for molecular reaction models which can ultimately be used to map out the changing molecular population with respect to various processing conditions. Advantages of Molecular-Level Characterization. The MECM model proves to be a powerful tool for simulating the composition of petroleum fuels. The model requires limited information from readily available lab analysis and simple analytical characterizations to describe the feedstock. The real benefit of the MECM approach over the currently used pseudocomponent approach is clear when modeling refinery processes. The MECM has the added advantage that it will follow the


distribution of molecular products, including environmentally and economically significant compounds such as benzene, naphthalene, and high-octane-number compounds, as the reactions progress, thus enhancing the information content of the model predictions. The mathematical model that captures these product distributions can help optimize operations and reduce costly and time-consuming experimental programs and will potentially lead to an increase in operational efficiencies and a reduction in cost and pollution. The model has the ability to tailor the number and type of components in the molecular ensemble as desired by the user, the limitations being only the computation power available and the intended use of the simulation. The MECM model advances the current characterization methods for undefined multicomponent mixtures such as petroleum fractions which will be useful not only for the modeling of physical separations but also the kinetics modeling of the chemical and catalytic processes in the oil refining industry. The computerized procedure can be combined with or incorporated in simulation packages such as HYSYS, Provision, and ASPEN, making the pseudocomponent procedure used there obsolete. Furthermore, the level of atomic detail offered by the MECM model allows both molecular reaction kinetics and molecular properties (molecular weight, H/C ratio, viscosity, boiling point, etc.) to be deduced straightforwardly. The model provides a foundation for developing molecular-based property relationships and incorporating well-established correlations to estimate mixture properties, which is an essential need of future process models, and the capability of predicting physical and performance properties of undefined multicomponent hydrocarbon mixtures. This feature is currently lacking in contemporary simulation packages (e.g., HYSYS and ASPEN) which cannot predict the properties of petroleum during processing once it has been broken down into pseudocomponents. Future Outlook. The results of this work will be of benefit for the future modeling of the various aspects of petroleum refinery processes which require detailed knowledge of both the molecular composition and structure of the petroleum fraction feeds, intermediates, and products for the proper modeling of the physical separations and chemical reactions of refinery processes. One aspect may include the simulation of gasoline production processes such as catalytic reforming, alkylation, isomerization, and (Fischer-Tropsch) gasoline synthesis as well as the blending of the feeds and products of these processes for optimal gasoline production. Another aspect pertains to the prediction of the properties of petroleum fuels from distillation data41 since, except for the TBP, the availability of other properties is not essential and can be estimated using the MECM model. Yet another aspect includes simulating heavier petroleum fractions such as kerosene as a pretext for the future molecular-level characterization of crude oil. Work is currently in progress to optimize the number of components in the molecular ensemble using a mixed integer programming (MIP) model to arrive at a practical minimum number that can still represent the chemical and physical behavior of the petroleum fraction with acceptable performance. Ranges of errors produced for distribution of various properties are expected to vary but slightly according to the number of components chosen.9

Acknowledgment This work was supported by Kuwait University, Research Grant No. EC04/01. It has been partially presented at the 227th National Meeting of the American Chemical Society.42 Supporting Information Available: Additional details and tables involving global properties estimation methods for the MECM model and methods for aggregating the molecular ensemble (RTF). This material is available free of charge via the Internet at http:// pubs.acs.org. Nomenclature ∆xi ) increment size of component i on the distillation curve API ) API gravity FBP ) final boiling point IBP ) initial boiling point K′ ) vapor-liquid equilibrium constant (distribution coefficient) MW ) molecular weight n ) total number of components in the molecular ensemble NBP ) normal boiling point P ) total number of physical properties except boiling point Pvi ) vapor pressure of the pure component i in the mixture PNA ) paraffins, naphthenes, and aromatics Pt ) true vapor pressure of petroleum fraction RVP ) Reid vapor pressure S ) objective function SG ) standard specific gravity for liquid at 15.6 °C T ) temperature T’bi ) normal boiling point of pure component i Tbj ) boiling point value on petroleum fractions’ TBP curve corresponding to component j TBP ) true boiling point curve TVP ) true vapor pressure Wi ) weighting factor for all properties but the boiling points W0 ) weighting factor for the boiling points x ) mole fraction xi ) mole fraction of component i xvi ) volume fraction of component i xw ) weight fraction xwi ) weight fraction of component i Y′i ) value of the global property i for the petroleum fraction calculated from aggregating pure component in the molecular ensemble using mixing rules Yi ) value of the global property i for the petroleum fraction determined experimentally or calculated using global correlations with the bulk properties as input parameters Θ ) any thermophysical property Θ(x) ) property value at volume percentage x Θi(x) ) property value of component i Ψj ) cumulative volume fraction at the mid-volume percent of component j on the TBP curve

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Received for review February 6, 2005 Revised manuscript received August 10, 2005 Accepted September 15, 2005 IE050150O

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