New Correlation Predicting Molecular Weight of Petroleum Fractions

Introduction

Petroleum fractions are complex mixtures of thousands of hydrocarbon compounds and can be categorized roughly into several special fractions, e.g. liquefied petroleum gas (LPG), straight run gasoline, naphtha, gas oil, diesel etc., according to their boiling range [1]. In order to obtain the detailed molecular composition distribution in the petroleum fractions, during the past decade several modern analytical techniques such as gas chromatography (GC), gas chromatography-mass spectrometry (GS-MS), nuclear magnetic resonance (NMR) have been developed. However, all these straightforward methods are time-consuming, so rarely applied in simulation process [1]. Several empirical modelling and correlations developed to predict molecular weight of petroleum fractions as a function of critical and pseudo properties. Katz and Firoozabadi presented a generalized set of physical properties for the petroleum fractions C6 through C45 [2]. The tabulated properties include the average boiling point, specific gravity, molecular weight and critical properties. These tabulated properties generated by analyzing the physical properties of 26 condensates and crude oil samples as given in Apendix-1. Ahmed correlated Katz-Firoozabadi physical properties with the number of carbon atoms of the fraction by using a regression model [3, 4]. The generalized concluded mathematical model has the following form:

𝑀= 𝑎1 + 𝑎2𝑛+ 𝑎3𝑛2 + 𝑎4𝑛3 + 𝑎5 𝑛 ⁄ (1) where:

𝑎1 = −131.11375𝑎2 = 24.96156𝑎3 = −0.34079022

𝑎4 = 0.002494118𝑎5 = 468.32575

Nearly all naturally occurring hydrocarbon systems contain a quantity of heavy fractions that are not well defined and are not mixtures of discretely identified components. These heavy fractions are often lumped together and identified as the plus fraction, e.g., C7+? fraction [3, 5]. A proper description of the physical properties of the plus fractions and other undefined petroleum fractions in hydrocarbon mixtures is essential in performing reliable phase behavior calculations and compositional modeling studies. Frequently, a distillation analysis or a chromatographic analysis is available for this undefined fraction. Other physical properties, such as molecular weight and specific gravity can measured for the entire fraction or some cuts [6, 7]. To use any of the thermodynamic property-prediction models, e.g., equations, of state, to predict the phase and volumetric behavior of complex hydrocarbon mixtures, one must be able to provide the acentric factor, along with the critical temperature and critical pressure, for both the defined and undefined (heavy) fractions in the mixture. The problem of how to characterize these undefined plus fractions in terms of their critical properties and acentric factors has been long recognized in the petroleum industry [4, 7]. Riazi and Daubert [8] developed a simple two-parameter equation for predicting the physical properties of pure compounds and undefined hydrocarbon mixtures. The proposed generalized empirical equation based on the use of the molecular weight and specific gravity of the undefined petroleum fraction as the correlating parameters. Their mathematical expression has the following form:

𝑏𝛾𝑐𝐸𝑋𝑃(𝑑𝑇𝑏+ 𝑒𝛾+ 𝑓𝑇𝑏𝛾) (2) where: a=581.96 b=-0.97476 c=6.51274 d=0.000543076 e=9.53384 f=0.00111056 Kesler and Lee proposed a correlation to estimate the molecular weight of petroleum fractions [7]. This relationship use specific gravity boiling point as input parameters for their proposed expressions:

𝑀= 𝑎𝑇𝑏

𝑀 = −12272.6 + 9486.4γ + (4.6523 −3.3287𝛾)𝑇𝑏 + (107 𝑇𝑏)(1 −0.77084𝛾−0.02058𝛾2) ⁄ (1.3437 −720.79 ) 𝑇𝑏 + (1012 𝑇𝑏

3)(1 −0.80882𝛾−0.02226𝛾2) ⁄ (1.8828 −181.98 ) (3)

𝑇𝑏

Winn developed convenient nomographs to estimate various physical properties including molecular weight and the pseudocritical temperature for petroleum fractions [9]. Sim and Daubert developed analytical relationships that closely matched the monograph graphical data [10]. The authors used specific gravity and boiling point as the correlating parameters for calculating the molecular weight of the undefined petroleum fraction:

2.3776𝛾−0.9371 (4) Hall and Yarborough proposed a correlation for determining the molecular weight as follow [11];

𝑀= 1.4350476 × 10−5𝑇𝑏

𝑀= (40𝑣𝑐𝛾0.7935)1/1.15 (5) Silva and Rodriguez proposed a correlation for determining the molecular weight with the following formula [12]

𝑀= 64.2576𝐸𝑋𝑃( 𝑇𝑏−460

447.08723) (6) Sancet presented the following expression to estimate the molecular weight of petroleum fractions [13]:

𝑀= 4.075 + 𝐸𝑋𝑃(𝑇𝑐+ 778.5

383.5 ) (7) Sancet presented the following expression to estimate the molecular weight of petroleum fractions [13]:

𝑥/𝜌20 (8) 𝑥= 1.52869 + 0.06486 ln(𝑇𝑏(1078 −𝑇𝑏) ⁄ ) In this study, a new correlation was developed for calculating the molecular weight of undefined petroleum fractions as a function of boiling point with an average error of 0.4%, standard deviation of 0.6% and correlation coefficient of 0.99991, where the proposed mathematical formula represented as follow 𝑀= 0.01077𝑇𝑏 𝑀= a (1 + exp (𝑏−𝑐𝑇𝑏)1/𝑑 (9) a=2238.880249b=0.836856c=-0.001215 d=0.225397

Statistical Error Analyses

The statistical error analyses were used to check the accuracy of the developed molecular weight correlations and the published one. The accuracy of correlations relative to the experimental values tabulated by Katz- Firoozabadi determined by various statistical means. The

criteria used in this study were average absolute relative error, standard deviation, and the correlation coefficient.

Evaluation of the Developed Correlation

Average absolute relative error, standard deviation, and correlation coefficient were computed for each correlation. Table 1 presents the comparison of errors relative to the experimental molecular weight calculated from two correlations. The correlation for molecular weight of this study achieved a high correlation coefficient accuracy of 0.99991 with absolute average relative error of 0.4 % and standard deviation of 0.6 % as presented in Table 2.

Conclusions

From this paper, one may conclude that: 1. This paper presents a comparison among eight different correlations used to calculate the molecular weight of undefined petroleum fractions.

2. New correlation was developed for calculating the molecular weight of undefined petroleum fractions. 3. Deviations from experimental values of molecular weight indicated as average absolute percent relative error, and the standard deviation were lower for this study than for calculated values based on the other correlations except Ahmed correlation. 4. The developed correlation has high accuracy where the correlation coefficient of the proposed correlation in this study is closer to one. Nomenclature 𝑝𝑐= critical pressure, psia 𝑇𝑐= critical temperature, °R 𝑇𝑏= boiling point, °R 𝜔 = acentric factor M = molecular weight 𝛾 = specific gravity 𝑣𝑐= critical volume, ft3/lb-mol 𝑛 = no of carbon atoms