New Correlation for Calculating Critical Pressure of Petroleum Fractions

Transcription

1 IARJSET ISSN (Olie) ISSN (Prit) Iteratioal Advaced Research Joural i Sciece, Egieerig ad Techology New Correlatio for Calculatig Critical Pressure of Petroleum Fractios Sayed Gomaa, PhD 1, 2 Miig ad Petroleum Egieerig Departmet, Faculty of Egieerig, Al-Azhar Uiversity, Cairo, Egypt 1 Petroleum Egieerig ad Gas Techology Departmet, Faculty of Egieerig, British Uiversity i Egypt 2 Abstract: Critical pressure is oe of the most importat physical properties of the petroleum fractios, which commoly cosidered i compositioal modelig studies ad phase behavior calculatios. This paper presets a compariso study amog te differet correlatios used to calculate the critical pressure of udefied petroleum fractios. A ew correlatio was developed for calculatig the critical pressure of petroleum fractios as a fuctio of the umber of carbo atoms with a average error of % ad correlatio coefficiet of Keywords: Critical pressure, petroleum fractios, Compositioal Modelig Studies, Phase Behavior Calculatios. INTRODUCTION Katz ad Firoozabadi [1] preseted a geeralized set of physical properties for the petroleum fractios C6 through C45. The tabulated properties iclude the critical properties, average boilig poit, specific gravity, ad molecular weight. The authors geerated these properties by aalyzig the physical properties of 26 codesates ad crude oil samples. These geeralized properties are give i Table A-1. Ahmed [2, 3] correlated Katz-Firoozabadi-tabulated physical properties with the umber of carbo atoms of the fractio by usig a regressio model. The geeralized equatio has the followig form: P c = a 1 + a 2 + a a a 5 (1) a 1 = a 2 = a 3 = a 4 = a 5 = Udefied Petroleum Fractios Nearly all aturally occurrig hydrocarbo systems cotai a quatity of heavy fractios that are ot well defied ad are ot mixtures of discretely idetified compoets. These heavy fractios are ofte lumped together ad idetified as the plus fractio, e.g., C 7 fractio [2, 4]. A proper descriptio of the physical properties of the plus fractios ad other udefied petroleum fractios i hydrocarbo mixtures is essetial i performig reliable phase behavior calculatios ad compositioal modelig studies. Frequetly, a distillatio aalysis or a chromatographic aalysis is available for this udefied fractio. Other physical properties, such as molecular weight ad specific gravity, may also be measured for the etire fractio or for various cuts of it [3, 5]. To use ay of the thermodyamic property-predictio models, e.g., equatios, of state, to predict the phase ad volumetric behavior of complex hydrocarbo mixtures, oe must be able to provide the acetric factor, alog with the critical temperature ad critical pressure, for both the defied ad udefied (heavy) fractios i the mixture. The problem of how to adequately characterize these udefied plus fractios i terms of their critical properties ad acetric factors has bee log recogized i the petroleum idustry [3, 5]. Riazi ad Daubert [6] developed a simple two-parameter equatio for predictig the physical properties of pure compouds ad udefied hydrocarbo mixtures. The proposed geeralized empirical equatio is based o the use of the molecular weight ad specific gravity of the udefied petroleum fractio as the correlatig parameters. Their mathematical expressio has the followig form: P c = am b γ c EXP dm + eγ (2) a = b = c = d = e = Edmister [7] proposed a correlatio for estimatig the acetric factor of pure fluids ad petroleum fractios. The equatio, widely used i the petroleum idustry, requires boilig poit, critical temperature, ad critical pressure. The proposed expressio is give by the followig relatioship: ω = 3 log p c T c T b 1 1 (3) The Edmister equatio ca be rearraged to solve for the critical pressure as follows: log p c = log ω + 1 (T c T b ) 1) (4) Cavett [8] proposed correlatios for estimatig the critical pressure of hydrocarbo fractios. The correlatios Copyright to IARJSET DOI /IARJSET

2 IARJSET ISSN (Olie) ISSN (Prit) Iteratioal Advaced Research Joural i Sciece, Egieerig ad Techology received wide acceptace i the petroleum idustry due to their reliability i extrapolatig coditios beyod those of the data used i developig the correlatios. The proposed correlatios were expressed aalytically as fuctios of the ormal boilig poit i F ad API gravity. Cavett proposed the followig expressio for estimatig the critical pressure of petroleum fractios: log p c = b 0 + b 1 T b + b 2 T b 2 + b 3 API T b + b 4 T b 3 + b 5 API T b 2 + b 6 API 2 T b + b 7 API 2 T b 2 5) i b i E E E E E E-9 Kesler ad Lee [9] proposed a correlatio to estimate the critical pressure of petroleum fractios. This relatioship use specific gravity boilig poit as iput parameters for their proposed expressios: l p c = γ ( γ γ 2 ) 10 3 T b + ( γ γ 2 ) 10 7 T b 2 ( γ 2 ) T b 3 (6) Wi [10] developed coveiet omographs to estimate various physical properties icludig molecular weight ad the pseudocritical pressure for petroleum fractios. Sim ad Daubert [11] developed aalytical relatioships that closely matched the moograph graphical data. The authors used specific gravity ad boilig poit as the correlatig parameters for calculatig the critical pressure of the udefied petroleum fractio: p c = T b γ (7) Watasiri et al. [12] developed a set of correlatios to estimate the critical properties ad acetric factor of coal compouds ad other udefied hydrocarbo compoets ad their derivatives. The proposed correlatios express the critical ad physical properties of the udefied fractio as a fuctio of the fractio ormal boilig poit, specific gravity, ad molecular weight. These relatioships have the followig forms: l p c = T c V c M T c T b M (8) Willma ad Teja [13] proposed correlatio for determiig the critical pressure of the -alkae homologous series: p c = Li ad Chao [14] developed a correlatio to estimate the critical pressure as a fuctio of molecular weight: p c = C 1 + C 2 M + C 3 M 2 + C 4 M 3 + C 5 M (9) C 1 = C 2 = C 3 = C 4 = C 5 = Sacet [15] preseted a correlatio to estimate the critical pressure from the molecular weight. This correlatio has the followig form: p c = 653 exp M (10) Proposed correlatio A ew correlatio was developed by use of the liear ad oliear regressio aalysis ad ca be expressed as: P c = a 0 + a 1 l() + a 2 l() 2 + a 3 l() 3 + a 4 + a a a 7 / (10) With the coefficiets a 0 through a 7 havig the followig values: a 0 = a 1 = a 2 = a 3 = a 4 = a 5 = a 6 = a 7 = Statistical Error aalysis The statistical error aalyses were used to check the accuracy of the critical pressure correlatios developed by Ahmed, Reazi- Daubert, Li, Cavett, Kessler-Lee, Wi- Sim, Watasiri, Willma, Sacet ad this study. The accuracy of correlatios relative to the experimetal values tabulated by Katz-Firoozabadi-tabulated is determied by various statistical meas. The criteria used i this study were average percet relative error, average absolute percet relative error, miimum/maximum absolute percet relative error, stadard deviatio, ad the correlatio coefficiet. Average Relative Error This is a idicatio of the relative deviatio i percet from the experimetal values ad is give by: Copyright to IARJSET DOI /IARJSET E i E i is the relative deviatio i percet of a estimated value from a experimetal value ad is defied by: / E i = p c exp p c cal p c exp i 100

3 IARJSET ISSN (Olie) ISSN (Prit) Iteratioal Advaced Research Joural i Sciece, Egieerig ad Techology The lower the value of E i the more equally distributed are the errors betwee positive ad egative values. Average Absolute Relative Error This is defied as: E i ad idicates the relative absolute deviatio i percet from the tabulated values. A lower value implies a better correlatio. Stadard Deviatio Stadard deviatio s x is a measure of dispersio ad is expressed as: s 2 x = E i 2 / /( 1) A lower value of stadard deviatio meas a smaller degree of scatter. Correlatio Coefficiet The correlatio coefficiet, r, represets the degree of success i reducig the stadard deviatio by regressio aalysis. It is defied as: r 2 = 1 Where p c cal p c exp p c avg = 2 / p c cal p c avg p ci exp The correlatio coefficiet lies betwee 0 ad 1. A value of 1 idicates a perfect correlatio, whereas a value of 0 implies o correlatio at all amog the give idepedet variables. Compariso of Correlatios Statistical Error Aalysis Average relative error, average absolute relative error, stadard deviatio, ad correlatio coefficiet were computed for each correlatio. Table 1 presets the compariso of errors relative to the experimetal critical pressure calculated from two correlatios. The correlatio for critical pressure of this study achieved the highest correlatio coefficiet accuracy of , as preseted i Table 2. Table 1 Compariso of critical pressure calculated by correlatios from this study ad others Experimetal Reazi Li Cavett Ahmed Sayed / 2 Copyright to IARJSET DOI /IARJSET

4 IARJSET ISSN (Olie) ISSN (Prit) Iteratioal Advaced Research Joural i Sciece, Egieerig ad Techology Table 1 Cot.: Compariso of critical pressure calculated by correlatios from this study ad others Kessler Wi-Simm Edmister Watasiri Willma Sacet Copyright to IARJSET DOI /IARJSET

5 IARJSET ISSN (Olie) ISSN (Prit) Iteratioal Advaced Research Joural i Sciece, Egieerig ad Techology Table 2 Statistical accuracy of critical pressure correlatios AARE, % SD R 2 This study(sh4) Ahmed Reazi Li Cavett Kesler Wi-Simm Edmister Watasiri Willma Sacet CONCLUSIONS REFERENCES From this paper, oe may coclude that: 1. This paper presets a compariso amog ie differet correlatios used to calculate the critical pressure of udefied petroleum fractios. 2. New correlatio was developed for calculatig the critical pressure of udefied petroleum fractios. 3. Deviatios from experimetal values of critical pressure idicated as average percet relative errors, average absolute percet relative errors, ad the stadard deviatios, were lower for this study tha for calculated values based o Ahmed, Reazi- Daubert, Li, Cavett, Kessler-Lee, Wi-Sim, Watasiri ad Willma, Sacet correlatios. 3. The developed correlatio is more practical tha Edmister correlatio, which is a fuctio of critical temperature ad acetric factor that i tur eed two correlatios to be calculated. 4. The correlatio coefficiet of the correlatios of this study are closer to oe tha that of other correlatios. Nomeclature p c = critical pressure, psia T c = critical temperature, R T b = boilig poit, R ω = acetric factor M = molecular weight γ = specific gravity v c = critical volume, ft 3 /lb-mol = o of carbo atoms 1. Katz, D.L., Firoozabadi, A., Predictig phase behavior of codesate/crude-oil systems usig methae iteractio coefficiets. J. Petrol. Tech. (November), Ahmed, T., Hydrocarbo Phase Behavior, Gulf Publishig Compay, Ahmed, T., Equatios of State ad PVT Aalysis Applicatios for Improved Reservoir Modelig, Amsterdam: Elsevier, secod editio Daesh, A., PVT ad Phase Behavior of Petroleum Reservoir Fluids, Elsevier Sciece & Techology Books, Whitso, C. H. ad Brule, M. R., Phase Behavior, SPE, Texas, Riazi, M.R., Daubert, T.E., Characterizatio parameters for petroleum fractios. Id. Eg. Chem. Fudam. 26 (24), Edmister, W.C., Applied hydrocarbo thermodyamics, part 4, compressibility factors ad equatios of state. Petroleum Refier. 37 (April), Cavett, R.H., Physical data for distillatio calculatios vapor-liquid equilibrium, Proceedigs of the 27th Meetig, API, Sa Fracisco, pp Kesler, M.G., Lee, B.I., Improve predictio of ethalpy of fractios. Hydrocarb. Process. (March), Wi, F.W., Simplified omographic presetatio, characterizatio of petroleum fractios. Petroleum Refier. 36 (2), Sim, W.J., Daubert, T.E., Predictio of vapor-liquid equilibria of udefied mixtures. Id. Eg. Chem. Process. Des. Dev. 19 (3), Watasiri, S., Owes, V.H., Starlig, K.E., Correlatios for estimatig critical costats, acetric factor, ad dipole momet for udefied coal-fluid fractios. Id. Eg. Chem. Process. Des. Dev. 24, Willma, B., Teja, A., Predictio of dew poits of semicotiuous atural gas ad petroleum mixtures. Id. Eg. Chem. Res. 226 (5), Li, H. M. ad Chao, K. C., Correlatio of critical properties ad acetric factor of hydrocarbos ad derivatives, AIChE Joural, Vol. 30, No. 6, Vov. 1984, PP Sacet, J., Heavy Factio Characterizatio. I: SPE , 2007 SPE Aual Coferece, November 11 14, Aaheim, CA Appedix 1: Table A-1 C Tb SG K M Tc Pc ω Vc , , Copyright to IARJSET DOI /IARJSET

6 IARJSET ISSN (Olie) ISSN (Prit) Iteratioal Advaced Research Joural i Sciece, Egieerig ad Techology , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , Copyright to IARJSET DOI /IARJSET