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

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1 1561 A ublication of CHEMICAL ENGINEERING TRANSACTIONS VOL. 43, 015 Chief Editors: Sauro Pierucci, Jiří J. Klemeš Coyright 015, AIDIC Servizi S.r.l., ISBN ; ISSN The Italian Association of Chemical Engineering Online at DOI: /CET Otimizing the Polynomial to Reresent the Extended True Boiling Point Curve from High Vuum Distillation Data Using Genetic Algorithms Astrid L. Ceron Rodriguez *, Laura Plazas Tovar, Maria Regina Wolf Miel, Rubens Miel Filho School of Chemical Engineering, University of Caminas, UNICAMP, Zicode , Caminas SP, Brazil astridceron@feq.unicam.br Molecular distillation rocess has been used to obtain an extended true boiling oint (TBP) curve (above 565 C u to 700 C), comared with the results offered by traditional methodologies like ASTM D 89 and ASTM D 536. This searation rocess has the advantage of oerating under conditions that reduce the thermal decomosition of the oil. In this aer, olynomials to reresent the extended true boiling 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 grou 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, using the DESTMOL correlation to find the atmosheric temeratures that corresond to the distiller oeration temeratures. The results of the three methodologies (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 using genetic algorithms. Finally, a variable analysis rocedure was develoed in order to determine the influence of the genetic algorithm arameters (oulation size and number of generations) in the obtained resonse and imrove the average absolute deviation ercent (%AAD). As a result, a third order fitting olynomial was found for every oil class, resenting %ADD lower than 3%. 1. Introduction The true boiling oint curve (TBP) reresents a charterization rocess of etroleum or crude oil, mostly used in refining to determine the sub-roducts yield and rovide information about the oerating conditions of oil searation (Argirov et al., 01). The TBP curve describes the mass (or volume) distilled frtion while increasing temerature. ASTM D 89 (010) and ASTM D 536 (003) methodologies can be used in order to obtain the TBP curve of any oil u to 565 C (Behrenbruch and Dedigama, 007). In order to overcome this limitation, the research grou at the Searation Processes Develoment Laboratory (UNICAMP) develoed a rocedure that allows oil frtion searation u to 700 C, by using Molecular Distillation. The outcome of that research was the generation of the DESTMOL correlation Eq(1) (Sbaite et al., 006), which converts Molecular Distiller oeration Temerature (TDM) at low ressure ( mmhg) (Zuñiga 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 using ASTM D 89 (010), ASTM D 536 (003) and Molecular Distillation methodologies were used to generate a correlation that reresents an extended TBP curve as a function of cumulative mass ercent distilled. The equation arameters were Please cite this article as: Ceron Rodriguez A., Plazas Tovar L., Wolf Miel M.R., Miel Filho R., 015, Otimizing the olynomial to reresent the extended true boiling oint curve from high vuum distillation data using genetic algorithms, Chemical Engineering Transtions, 43, DOI: /CET154361

2 156 estimated and otimized for eh oil using a genetic algorithm and a Design of Exeriments (DOE) technique, trying to minimize the average absolute deviation. Figure 1 illustrates the imlemented methodology. Figure 1. Block diagram of the imlemented methodology.. Extended TBP curve arameters otimization To estimate the correlation arameters of eh charterized etroleum, the PIKAIA sub-routine was imlemented in Fortran-90 language (Comiler Visual Studio 008). This is a free cess genetic algorithm, develoed by High Altitude Observatory (Metalfe and Charboneau, 003)..1 Samling classification The API density of eh crude oil, as well as the TBP curves obtained by standard methodologies (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 single trend in the curve extension, which corresonds to Molecular Distillation. As a result, seven different grous were obtained, as shown in Table 1 and Figure. In order to distinguish 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 cording to API gravity of original 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+ Figure. TBP data obtained by ASTM D 89 - D 536 and Molecular Distillation for eh grou in Table 1.

3 1563. Genetic Algorithm alication: obtaining the equation arameters. The genetic algorithms are comutational methods used to find otimized solutions emulating a rocess of natural evolution (Kothari, 01). These algorithms are very sensitive to variations in their configuration arameters: Poulation size, number of generations, crossover robability and mutation rate (Azadeh et al. 010). As mentioned before, in this case the PIKAIA sub-routine was imlemented, using the redefined values for mutation rate and crossover robability (0.005 and 0.85) and varying the oulation size and number of generations, aiming 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= Boiling temerature ( C) % D is the = cumulative mass ercent distilled.3 Design of Exeriments to estimate the algorithm 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 generations (Ng) influence on the results, quantified by the average 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 range for T and Ng arameters. As a result, the ranges that exhibited an %AAD less than 10 % were reselected to feed the DOE. Table shows the DOE inut ranges. The central comosite design ( lus a central oint) was the exeriment design chosen to do the statistical analyses. Table. Preselected arameter ranges 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, taking into count the maximum confidence levels (Table 3). The selected results (in bold, Table 3) satisfied the following conditions: An Effect less than 0.05 at 95 % confidence, less than 0.1 at 90% confidence or less than

4 at 85 % confidence. In all cases, the codified ftor that corresonds to the size of oulation (X1) is the arameter that resents a bigger influence, as exected for any genetic algorithm (Roeva et al., 013). Table 3: T and Ng 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 generated, in order to reresent mathematically the intertion between the T and Ng arameters and the %ADD. These models were verified using a variance analysis (ANOVA), where the valid models are chosen deending on the F-test (i.e., models which the Calculated F is greater than the Critical F) (Table 4). Figure 3 shows the surfe resonses for the different grous of etroleum. Table 4: Valid Statistic Models for %AAD as function of T and Ng and F-Test results F Test %Exlained Prediction Model Calculated Variation Critical F F % AAD = T T N T N F4;4;0.010=4.10 g g % AAD = T T F3;5;0.015=.79 % AAD T T N g = 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 g % AAD T T N g = F3;5;0.005=5.40 = 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 genetic algorithm again. The %ADD values calculated under these conditions were very close to the rediction model results (Table 5), validating 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 Figure 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 1565 Figure 3: Surfe resonses for statistical rediction models as function of T and Ng. Table 5: Calculated %AAD: rediction model and genetic algorithm results. Parameters T Ng Otimized Equations % 0.603% % % % % % % % % % % % % % % % % % % % Predicted Value (%ADD) Algorithm 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 1566 Figure 3: Calculated Extended True Boiling Point curves by otimized equations. 4. Conclusions Due to the PEV curves follow a 3rd order trend, revious work develoed an algebraic and statistic arohes, roducing mathematical exressions statistically consistent. However, the adjustable arameters were not otimized. The scoe of this work was the otimization of the arameters aforementioned, using genetic algorithms, exloiting their effectiveness solving search and otimization roblems. The otimal conditions for the genetic algorithm (number of generations (Ng) and oulation size (T) arameters) can be established by imlementing a central comosite design for eh of the oil tyes, determining the minimum Average Absolute Deviation. As exected, the oulation size was the algorithm arameter with a greater influence on the genetic algorithm results. PIKAIA sub-routine was used to otimize the equation arameters that fit the extended TBP curves defined by 3 rd order olynomials, finding a single trend for eh crude oil with %ADD less than 3%. References Argirov 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., Layegh L., 010, Otimal model for suly chain system controlled by kanban under JIT hilosohy by integration of comuter simulation and genetic algorithm, Australian Journal of Basic and Alied Sciences, 4, Behrenbruch P., Dedigama T., 007, Classification and charterization of crude oils based on distillation roerties, Journal of Science and Engineering, 57, Celis O.J., Plazas Tovar L., Jardini Munhoz A.L., Siegel C., Miel Filho R, Wolf Miel M.R., 011, Comutational aroh for studying the laser radiation thermal crking rocess of heavy etroleum frtion: otimization of laser oerational conditions, Chemical Engineering Transtions, 4, Kothari D., P., 01, Power System Otimization, CISP Proceedings, Metalfe T., Charbonneau P., 003, Stellar structure modelling using a arallel genetic algorithm for objective global otimization, Journal of Comutational Physics, 185, Nedelchev, A., Stratiev, D., Ivanov, A., Stoilov, G., 011, Boling 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 genetic algorithm erformance in case of cultivation rocess modeling, 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 boiling oint extended curve of vuum residue through molecular distillation, Science and Technology, 4, Zuñiga L., Lima N., Wolf Miel M. R., Miel Filho R., Batistella C., Manca D., Manenti F., Medina L., 009, Modeling and simulation of molecular distillation rocess for a heavy etroleum cut, Chemical Engineering Transtions, 17,