Correlation for Vapor Pressure of Mixture

Transcription

1 Availale online at Proceedings Vol. 6 pp th Annual Conference for Postgraduate Studies and Scientific Research Basic Sciences and Engineering Studies - University of Khartoum Theme: Scientific Research and Innovation for Sustainale Development in Africa Correlation for Vapor Pressure of Mixture Ali A. Raah, Nagi A. Osman Department of Chemical Engineering, Faculty of Engineering, University of Khartoum Khartoum, Sudan ( raahs@yahoo.com) Astract: This paper aims to find empirical equation to calculate the vapor pressure of the mixture of crude oil from Sudan and taking advantage of some of the PVT properties that are measured experimentally. Where the data is retrieved from many fields and different wells to get the relationship etween vapor pressure and properties availale Emphasis was placed on thermodynamic properties have a direct effective on the vapor pressure, and has to take useful of the density of the mixture at the oiling pressure measured in the laoratory to calculate these properties using the equations are availale in advance (Raiza Duert) and then use the method of regression analysis using the Excel program to find a relationship etween vapor pressure and properties calculated on the asis of the density at the oiling of the mixture and the molecular weight of the mixture. Where the results were compared with some of the empirical equations used to calculate the vapor pressure of some of the world raw materials used other properties of non-thermodynamic properties as a function of vapor pressure. The study found positive results in dependence on the thermodynamic properties of a direct impact on the vapor pressure and through the use of some statistical metrics to compare other equations which proved the quality of the idea where the error etween the measured pressure and the calculated error rate dropped Keywords:Merowe Dam; Specific Water Consumption S.W.C; Routing, Operation Rule Curve; Megawatt INTRODUCTION The ule point is essential in reservoir simulation and in design of transport and separator equipment.there are asically one experimental method and threetheoretical methods for ule point pressure of reservoir fluid. Constant mass expansion tests (CME) is the experimental test for ule point pressure. The prediction methods are correlation and equation of state. The availale correlations of the prediction of ule pressure include Standing, Lasater, Glas, Stunn and Farshad, Vazquez and Beggs, AL Marhounand Hanafy et al correlation. All these correlation incorporate four input feature from datasets (1) reservoir temperature, (2)API (3) gas specific gravity and (4) solution gas oil ratio. The first three parameters are readily availale from composition analysis. The fourth parameter is determined experimentally from differential lieration test. Hence, these models are not predictive, as experimental phase equilirium data are needed.hence these correlations are used only to verify experimental data. Quick prediction of the ule point pressure with minimum information remained difficult task. The ule point pressure can e predicted from equation of state using ule point calculation procedure. There are a numer of equations of state availale such as PR, SRK,However, all of the availale cannot e used as a quick procedure for the prediction of ule point pressure of reservoir fluids. It is the purpose of this paper is to provide correlation for the prediction of mixture vapor pressure. The equation, with data of compositional analysis only, facilitates the calculation of ule point pressure. The Model The vapor pressure of mixtureis considered to e a function of critical temperature, critical pressure, ule point temperature, centric factorand gas oil ratio as P P(, Tc, Pc, T,, Rs ) (1) 202

2 The parameters in the mixture characterization procedure are calculated directly from measured gas oil ratio data for the hydrocaron fractions. In turn the critical temperature, critical pressure, ule point temperature is function of density at ule point pressureas given y Riazi and Dauert (1987), equation (3) The molecular weight of mixture are calculate y using equation (2) mixture a exp 1.008M M mixutr mixutr...(2) f e M c dm M......(3) wherea to f, are constants for ule point temperature as follows Tale (1) Parameter A c D f E T (k) To calculation critical temperature and critical pressure is function of specific gravity and ule point temperature as given y Riazi and Dauert: a exp f e M c dm M......(4) where a to f, are constants for critical temperature and critical pressure as follows y tale (2) Tale (2) Parameter A C D f E P c * * T c * Hence equations(1) and(2) can e written as P P( P, T, T,, R, M, ) c c Thea centricfactor in this work calculate as function in (T c, P c ) y using equation (6) Where: Pc 3log Tc 7 1 T.. (6) ω = Acentric factor P c = Critical pressure, psia T c = Critical temperature, Rᴼ T c = Normal oiling point, Rᴼ S W (5) Using the principles of corresponding state equation (5) can e reduced further to P P( P, T, T, R,, ) (7) c c There are many formulations for vapor pressure such as Antoine and Wagner equations of vapor pressure of pure components. In this work is adoptedthe model y using Microsoft Excel(regressionlogarithmic) to express vapor pressure of mixture. s Ln P = a + lnt c T c P c e R S d ω f (8) Where: P = The ule point pressure (ar) T c = Critical temperature k P c = Critical pressure ar T P = The ule point pressure k R s = Gas oil ratio (scf/st) ɷ = a centric factor 203

3 The parametersaoveare otained using equation (2) and (5) and using the data direction. Experimental Data Experimental PVT data were supplied y the Ministry of Energy and Mining, Sudan, for a numer of wells representing different reservoirs. The data include compositional analysis of single caron numers of up to Eicosanes plus (C20+) and Hexatriacontanes plus (C36+) and PVT of CME of ottom hole samples. The data also include ule point pressure,reservoir temperature, and specific gravity of the reservoir fluid. Tale 3:The Data Description for ule Point Pressure Numer of Data Properties Min Max MEDIAN 65 Reservoir temperature ( F) Bule point pressure (psig) density at P (gm/ml) Specific gravity (centipoises) Formation volume Total gas oil ratio (scf/stb) Gas oil ratio at P (scf/stb) Gas specific gravity (air = 1) Molecular weight API

4 Tale 4: Summary of Calculate Parameters using Equations 2, 3, 4 and6 NO P(ar) Spec. Gravity Mw T C (K) T (K) P c (ar) Centric factor

5 Comparison of correlations Statistical Error Analysis Mean Asolute per- cent error, minimum /maximum asolute per- cent error, standard deviation and correlation coefficient were computed for each correlation Tale (5) shows the statistical error analysis results of the ule-point pressure correlations. This work correlation gives low values of Mean Asolute Per-cent Error (MAPE) and standard error of percent and 0.235percent, respectively. Lower value of MAPE indicates a etter accuracy of the correlation. The correlation coefficient of the correlation is almost equal to 1.0(0.995). This shows that a good agreement exists etween experimental and calculated ule point pressure. In comparison withother known correlations, this work correlation gives lowest AAPRE and standard Error. This shows that this work correlation predicts etter ule point pressure for Sudanese crude oil than any other known correlations. Tale5: Summary of Statistical Measures for P for Common Correlations Correlation Crude Oil MAPE (E a ) MPE(E i ) Ea max Ea min R 2 Standing California Marhoun Middle Eastern Glaso s North Sea Petrosky and Farshad Gulf of Mexico Dolka& Omer U.A.E Hanafy et al Egyptian Marhoun Saudi Araian Vasquez-Beggs API API AdAlshakoor, Ali and Nagi Sudanese RESULTS AND DISCUSSION The parameters of mixture for samples 1 to 33 is calculated using equation (2), (3), (4) and (7). The regression analysis is facilitated using the Microsoft excel. The results of regression with respect to the constants of equation (8) shown Tale (6) shows the statistical parameters of regression Tale 6: The constant a to f of equation (8) Constants a B C d f e Value

6 Tale 7: The Vapor Pressure of Mixture for TheSample 1 to 33Otained to Develop Correlation Equation (8) No Rs (scf/stb) T C (k) T ( k) P c (ar) Ω P (ar)meas P (ar) calc E a Ea max Ea min MAPE

7 Tale (6) shows The Vapor Pressure of Mixture for The Sample 1 to 31Otained Using Equation (8) is Validated NO Rs (scf/stb) T c (K ) P c (ar ) T (K ) Ω P (ar) measuring P (ar) Calculate E a E a max E a min MAPE 11.3 THROUGH THE STUDY CAME TO THE CONCLUSION FOLLOWS: 1- Acute shortage of data and not availale in large and one of the prolems faced Search 2. The presence of more than one field, and more than well in addition to the diversity of geographical locations led to a variation in the readings of the data and the existence of differences in each 3. Has to take advantage of the measured data within the narrow represented y the density at a pressure oiling point in addition to the 208

8 4. Benefited from the pre-existing relationship () at the expense of the critical temperature and critical pressure and temperature at the oiling point and the calculation of molecular weight 5- Considered thermodynamics of the factors mentioned properties to affect direct impact on the vapor pressure of the crude mixture a,, c coefficients of the aove equation having the following values:a = = c = Al MarhounCorrelations (1988) (Middle Eastern crude oil) c d e S g 0 P ar T 6- Compare the results proved the high quality of which was otained compared with the linear correlations exist, which depends on the properties availale in the data 7. Use the properties thermodynamics direct link characteristic proven APPENDIX A: PVT CORRELATIONS StandingCorrelations (1981) Standing (1981) expressed the graphical correlation y the following expression P = 18.2 [(Rs/γ g ) 0.83 (10) a 1.4] where T temperature, R γ o stock-tank oil specific gravity γ g gas specific gravity a e coefficients of the correlation having the following values: a c e d With Where a = (T 460) (API) P =ule-point pressure psia T =system temperature, R Glaso s Correlations (North Sea crude oil)(1980) log (P )= log(p* ) [log(p* )] 2 where P* is a correlating numer and defined y the following equation: where: RS P t API g R s gas soluility, scf/stb tsystem temperature, F. a γ g average specific gravity of the total surface gases (air = 1) c The Petrosky-Farshad Correlations (Gulf of Mexico crude oil) P R g s (10) X Where the correlating parameter X is X = (10 4 ) (API) (10-5 ) (T - 460) where P =pressure, psia T =temperature, R Al-Marhoun 1985 (Saudi Araian Oil) P X X Where s g o X R T In this work(2015) (Sudanese crude oil) 209

9 Ln P = a + lnt c T c P c e R S d ω f where P = The ule point pressure (ar) T c = Critical temperature k a ecoefficients of the correlation having the following values: P c = Critical pressure ar T = The ule point pressure k R s = Gas oil ratio (scf/stb) Ω = a centric factor Constants A B C D F E Value Dokla and OsmanCorrelations (United Emirates crude oil) E a = 1 n d n d i=1 E i P = R s γ γ g T APPENDIX B: Statistical Error Analysis 1. MEAN PERCENT ERROR(MPE): It is the measure of the relative deviation from the experimental data, defined y: E r = 1 E n i d i=1 WhereE i is the relative deviation of an estimated value from an experimental value. E i = x exp x est 100 i = 1,2.. n x d exp 2. MEAN ABSOLUTE PERCENT ERRO(MAPE)R: It measures the relative asolute deviation from the experimental values, defined y: n d 3. MINIMUM AND MAXIMUM MEAN ABSOLUTE PERCENT ERROR: To define the range of error for each correlation, the calculated asolute percent relative error values are scanned to determine the minimum and maximum values. They are defined y: n E a max = max d i=1 Ei 4-STANDARD DEVIATION: n E a min = min d i=1 Ei Standard deviation, (sx), of the estimated (otained from the correlation) relative to the experimental values can e calculated using the following equation: Symol x represents physical properties.a lower value of standard deviation means a smaller degree of scattering. The accuracy of the correlation is determined y the value of the standard deviation, where small value indicates higher accuracy. The value of standard deviation is usually expressed in percent. 5. THE CORRELATION COEFFICIENT: It represents the degree of success in reducing the standard deviation y regression analysis, defined y: r 2 n xy ( x)( y) = n x 2 ( x) 2 n y 2 ( y) 2 SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R

10 Square Standard Error Oservations 33 ANOVA Df SS MS F Significa nce F Regression E-21 Residual Total Coefficien ts Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept X Variale X Variale X Variale X Variale X Variale E RESIDUAL OUTPUT Oservation Predicted Y Residuals

11 E REFERENCES [1]. Riazia, M. R. and Dauert, T. E., Characterization Parameters for Petroleum Fractions, Ind. Eng. Chem. Res., 1987, Vol. 26, No. 24, pp [2]. Glaso, O., Generalized Pressure-Volume- Temperature Correlations, JPT,May 1980, pp [3]. Marhoun, M. A., PVT Correlation for Middle East Crude Oils, JPT, May 1988, pp [4]. Standing, M. B., Volumetric and Phase Behavior of Oil Field Hydrocaron Systems, pp Dallas: Society of Petroleum Engineers, [5]. Sutton, R. P., and Farshad, F. F., Evaluation of Empirically Derived PVT Properties for Gulf of Mexico Crude Oils, SPE Paper 13172, presented at the 59th Annual Technical Conference, Houston, Texas, [6]. Vasquez, M., and Beggs, D., Correlations for Fluid Physical Properties Prediction, JPT, June 1980, pp