Optimizing the Polynomial to Represent the Extended True Boiling Point Curve from High Vacuum Distillation Data Using Genetic Algorithms

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1 A ublication of CHEMICAL ENGINEERING TRANSACTIONS VOL. 43, 015 Chief Editors: Sauro Pierucci, Jiří J. Klemeš Coyriht 015, AIDIC Servizi S.r.l., ISBN ; ISSN The Italian Association of Chemical Enineerin Online at Otimizin the Polynomial to Reresent the Extended True Boilin Point Curve from Hih Vuum Distillation Data Usin Genetic Alorithms Astrid L. Ceron Rodriuez *, Laura Plazas Tovar, Maria Reina Wolf Miel, Rubens Miel Filho School of Chemical Enineerin, University of Caminas, UNICAMP, Zicode , Caminas SP, Brazil Molecular distillation rocess has been used to obtain an extended true boilin oint (TBP) curve (above 565 C u to 700 C), comared with the results offered by traditional methodoloies like ASTM D 89 and ASTM D 536. This searation rocess has the advantae of oeratin under conditions that reduce the thermal decomosition of the oil. In this aer, olynomials to reresent the extended true boilin oint curve u to 565 C from molecular distillation data are roosed. The develoment is based on molecular distillation exerimental results of 14 atmosheric and 5 vuum oil residues obtained in Pilot and lab scale distiller in other works of the research rou at Searation Processes Develoment Laboratory (UNICAMP). The exerimental data were classified in seven different classes based on API density. In first instance, a database was built to erform an extension of the TBP curve of eh oil, usin the DESTMOL correlation to find the atmosheric temeratures that corresond to the distiller oeration temeratures. The results of the three methodoloies (ASTM D 89, ASTM D 536 and molecular distillation) were adjusted to a 3rd order olynomial as function of the cumulated mass ercent. The coefficients were otimized usin enetic alorithms. Finally, a variable analysis rocedure was develoed in order to determine the influence of the enetic alorithm arameters (oulation size and number of enerations) in the obtained resonse and imrove the averae absolute deviation ercent (%AAD). As a result, a third order fittin olynomial was found for every oil class, resentin %ADD lower than 3%. 1. Introduction The true boilin oint curve (TBP) reresents a charterization rocess of etroleum or crude oil, mostly used in refinin to determine the sub-roducts yield and rovide information about the oeratin conditions of oil searation (Arirov et al., 01). The TBP curve describes the mass (or volume) distilled frtion while increasin temerature. ASTM D 89 (010) and ASTM D 536 (003) methodoloies can be used in order to obtain the TBP curve of any oil u to 565 C (Behrenbruch and Dediama, 007). In order to overcome this limitation, the research rou at the Searation Processes Develoment Laboratory (UNICAMP) develoed a rocedure that allows oil frtion searation u to 700 C, by usin Molecular Distillation. The outcome of that research was the eneration of the DESTMOL correlation Eq(1) (Sbaite et al., 006), which converts Molecular Distiller oeration Temerature (TDM) at low ressure ( mmh) (Zuñia et al., 009) to equivalent atmosheric temeratures (TAE). This information is then used to calculate an extension of TBP curve TAE T = + + T T (1) DM DM DM In this work, charterization results for various oils obtained usin ASTM D 89 (010), ASTM D 536 (003) and Molecular Distillation methodoloies were used to enerate a correlation that reresents an extended TBP curve as a function of cumulative mass ercent distilled. The equation arameters were

2 estimated and otimized for eh oil usin a enetic alorithm and a Desin of Exeriments (DOE) technique, tryin to minimize the averae absolute deviation. Fiure 1 illustrates the imlemented methodoloy. Fiure 1. Block diaram of the imlemented methodoloy.. Extended TBP curve arameters otimization To estimate the correlation arameters of eh charterized etroleum, the PIKAIA sub-routine was imlemented in Fortran-90 lanuae (Comiler Visual Studio 008). This is a free cess enetic alorithm, develoed by Hih Altitude Observatory (Metalfe and Charboneau, 003)..1 Samlin classification The API density of eh crude oil, as well as the TBP curves obtained by standard methodoloies (ASTM D 89 (010) and ASTM D 536 (003)) were used as a criteria to classify the different vuum and atmosheric residues, in order to establish a sinle trend in the curve extension, which corresonds to Molecular Distillation. As a result, seven different rous were obtained, as shown in Table 1 and Fiure. In order to distinuish the atmosheric ( C+) and vuum ( C+) residues, they were named with different coded names comosed of one letter and the cut temerature. Table 1: Atmosheric and vuum residues classified cordin to API ravity of oriinal crude oil. A 400 C+ F 40 C+ N 40 C+ 19. B 400 C+ G 540 C+ O 565 C+ 4. P 400 C+ 5.6 C 400 C H 400 C+ K 400 C+ Q 40 C+ D 400 C+ I 400 C+ 0.0 L 400 C+.4 R 400 C E 565 C+ J 400 C+ M 550 C+ S 550 C+ Fiure. TBP data obtained by ASTM D 89 - D 536 and Molecular Distillation for eh rou in Table 1.

3 . Genetic Alorithm alication: obtainin the equation arameters. The enetic alorithms are comutational methods used to find otimized solutions emulatin a rocess of natural evolution (Kothari, 01). These alorithms are very sensitive to variations in their confiuration arameters: Poulation size, number of enerations, crossover robability and mutation rate (Azadeh et al. 010). As mentioned before, in this case the PIKAIA sub-routine was imlemented, usin the redefined values for mutation rate and crossover robability (0.005 and 0.85) and varyin the oulation size and number of enerations, aimin to find the coefficients of olynomial that fits eh dataset. The otimized equation was a 3 rd order exression in function of cumulative mass ercent Eq(). ( ) ( ) 3 T = A+ B % D + C % D + D % D () Where: T is the= Boilin temerature ( C) % D is the = cumulative mass ercent distilled.3 Desin of Exeriments to estimate the alorithm arameters. The STATISTIC 7 software from Statsoft Inc. was used to develo a DOE in order to determine how the oulation size (T) and number of enerations (N) influence on the results, quantified by the averae absolute deviation Eq(3). 1 n Tical, T iref, % AAD = 100 i= 1 (3) n Tiref, Where: n is the= number of data oints Ti,cal is the= Ti calculated ( C) Ti,ref is the= Ti exerimental ( C) Previously, a sensitive analysis was erformed, in order to define a valid rane for T and N arameters. As a result, the ranes that exhibited an %AAD less than 10 % were reselected to feed the DOE. Table shows the DOE inut ranes. The central comosite desin ( lus a central oint) was the exeriment desin chosen to do the statistical analyses. Table. Preselected arameter ranes Codified Level Ftor Ftor Poulation Size X Number of Generations X Poulation Size X Number of Generations X ,0 Poulation Size X Number of Generations X Poulation Size X Number of Generations X Poulation Size X Number of Generations X Poulation Size X Number of Generations X Poulation Size X Number of Generations X Results From the P test results, the aroriate ftors and combinations were established for eh scenario, takin into count the maximum confidence levels (Table 3). The selected results (in bold, Table 3) satisfied the followin conditions: An Effect less than 0.05 at 95 % confidence, less than 0.1 at 90% confidence or less than

4 0.15 at 85 % confidence. In all cases, the codified ftor that corresonds to the size of oulation (X1) is the arameter that resents a bier influence, as exected for any enetic alorithm (Roeva et al., 013). Table 3: T and N effects in %AAD. Confidence Ftor Effect P Confidence Ftor Effect P Mean Mean % X1(L) X1(L) X1(Q) % X1(Q) X(L) X(L) Mean X1(L)*X(L) X1(L) Mean % X1(Q) X1(L) % X(L) X1(Q) Mean X(L) % X(L) X1(Q) % Mean X(L) X1(L) Mean X1(Q) X1(L) % X1(L) X(Q) X1(Q) X1(L)*X(L) X(L) In eh case a rediction model was enerated, in order to reresent mathematically the intertion between the T and N arameters and the %ADD. These models were verified usin a variance analysis (ANOVA), where the valid models are chosen deendin on the F-test (i.e., models which the Calculated F is reater than the Critical F) (Table 4). Fiure 3 shows the surfe resonses for the different rous of etroleum. Table 4: Valid Statistic Models for %AAD as function of T and N and F-Test results Prediction Model % AAD T 0.04T N T N %Exlained Variation Calculated F F Test Critical F = F4;4;0.010=4.10 % AAD = T T F3;5;0.015=.79 % AAD T T N = F3;5;0.015=.79 % AAD = T T F3;5;0.010=3.6 % AAD = T 0.01T F3;5;0.005=3.6 % AAD T T N = F3;5;0.005=5.40 % AAD T T N = F5;3;0.005=9.07 Finally, based on the surfe resonses, the critical oints that corresond to the minimization of the %ADD value were defined. These arameter values were used to run the enetic alorithm aain. The %ADD values calculated under these conditions were very close to the rediction model results (Table 5), validatin the whole analysis. The aroriate equation arameters (otimized equations) that describe the extended TBP are listed in Table 5. Profiles of the extended TBP equations are resented in Fiure 4, where the different trends resented in eh equation roves the different comositions or frtion distributions which deends on the tye of crude oil.

5 Fiure 3: Surfe resonses for statistical rediction models as function of T and N. Table 5: Calculated %AAD: rediction model and enetic alorithm results. Parameters T N Otimized Equations % 0.603% % Predicted Value (%ADD) Alorithm Result (%AAD) T = + D D + D T = + D D + D % % % T = + D D + D % % % T = + D D + D % % % T = + D D + D % % % T = + D D + D % % % T = + D D + D % % %

6 Fiure 3: Calculated Extended True Boilin Point curves by otimized equations. 4. Conclusions Due to the PEV curves follow a 3rd order trend, revious work develoed an alebraic and statistic arohes, roducin mathematical exressions statistically consistent. However, the adjustable arameters were not otimized. The scoe of this work was the otimization of the arameters aforementioned, usin enetic alorithms, exloitin their effectiveness solvin search and otimization roblems. The otimal conditions for the enetic alorithm (number of enerations (N) and oulation size (T) arameters) can be established by imlementin a central comosite desin for eh of the oil tyes, determinin the minimum Averae Absolute Deviation. As exected, the oulation size was the alorithm arameter with a reater influence on the enetic alorithm results. PIKAIA sub-routine was used to otimize the equation arameters that fit the extended TBP curves defined by 3 rd order olynomials, findin a sinle trend for eh crude oil with %ADD less than 3%. References Arirov G., Ivanov S., Cholakov G., 01, Estimation of crude oil TBP from crude viscosity, Fuel, 97, ASTM Standard D 89, 010, Standard test method for distillation of crude etroleum, ASTM International, United States. ASTM Standard D 536, 003, Standard test method for distillation of heavy hydrocarbon mixtures (Vuum ot still method), ASTM International, United States. Azadeh A., Layeh L., 010, Otimal model for suly chain system controlled by kanban under JIT hilosohy by interation of comuter simulation and enetic alorithm, Australian Journal of Basic and Alied Sciences, 4, Behrenbruch P., Dediama T., 007, Classification and charterization of crude oils based on distillation roerties, Journal of Science and Enineerin, 57, Celis O.J., Plazas Tovar L., Jardini Munhoz A.L., Sieel C., Miel Filho R, Wolf Miel M.R., 011, Comutational aroh for studyin the laser radiation thermal crkin rocess of heavy etroleum frtion: otimization of laser oerational conditions, Chemical Enineerin Transtions, 4, Kothari D., P., 01, Power System Otimization, CISP Proceedins, Metalfe T., Charbonneau P., 003, Stellar structure modellin usin a arallel enetic alorithm for objective lobal otimization, Journal of Comutational Physics, 185, Nedelchev, A., Stratiev, D., Ivanov, A., Stoilov, G., 011, Bolin Point Distribution of Crude Oils Based on TBP and ASTM D-86 Distillation Data, & Coal, 53(4), Roeva O., Fidanova S., Parzycki M., 013, Influence of te oulation size on the enetic alorithm erformance in case of cultivation rocess modelin, Federated Conference on Comuter Science and Information Systems, Sbaite P., Batistella C.B., Winter A., Vasconcelos C.J.G, Wolf Miel M. R., Miel Filho R., Gomes A., Medina L., Kunert R., 006, True boilin oint extended curve of vuum residue throuh molecular distillation, Science and Technoloy, 4, Zuñia L., Lima N., Wolf Miel M. R., Miel Filho R., Batistella C., Manca D., Manenti F., Medina L., 009, Modelin and simulation of molecular distillation rocess for a heavy etroleum cut, Chemical Enineerin Transtions, 17,