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, 6, d' - r'v '! ,.3 Equation fits ASTM distillations H. Dhulesia, Compagnie Frangaise des P6troles (TOTAL), Paris, France 4P 't-\ \ ASTM DISTILLATIoN cURVES of refining fractions can a/: e adequately described by an empirical equation. The equa- 220 ,on is suitable for insertion in models used for ontimiiins on optimi optimizing r operation of refining processes such as distillation, F FCC, catalytic reforming, hydrotreating, etc. The equation Itakes ing, the form of: ,^-,fpzoo f V:ll-e\o/ -rrf I )x100 (1) rJ I 180 where Zis volume percent distilled at temperature ?] o and e 0 are the constants of equation and are determined from the 6 data of ASTM distillation curve. 7"* is the dimensionless o temperature defined as: E 160 ra+ =I-T Tt-7, e) where 7l and T1 are, respectively, the initial and final boiling point temperatures of ASTM distillation. By defining di- mensionless temperature, the constants of Eq. 1 are in- variant with respect to unit of temperature. a Laboratory data Eq. 1 with DETERMINATION OF CONSTANTS - o= 0.592, Constants a and B are calculated such that Eq. 1 fits the B = 1.804 laboratory data of ASTM distillation. To obtain the best fit- o 20 80 100 oistiuea,oluo .,t., ting, the sum of square of errors for prediction should be vllrme minimum. Let 21, 72, ..., T, and. Vr, Vz, ..., V,be the data Fig. 2-ASTM distillation curve for gasoline from FCCU. of ASTM distillation test. The values of o and 6 should min- imize the following function: andananalyticalsolutionisextremelydifficulttoobtain'A numerical method, employing the Newton-Raphson tech- , = t-[{'-,el " 1oo - z,]' (3) niqu:. has been developed to resolve the above problem. In This problem of minimization is non-linear optimization, o g o E o .t l E 6 .o € ,o i-?.1- a Laboratory data a Laboratory data Eq. 1 wirh 1 with - a = 0.622, -Equation B = 2.722 Volume dislilled, o/o Volume distilled, qo Flg. 1-ASTM distillation curve for feed to FCCU. Fig. 3-ASTM distillation curve for LCO from FCCU. Hydrocarbon Processing, September'l 984 179 :r:ndFE{i!:a}E .t'/ suBRouTlNE ASTMFT (TEMB VOL, NB NMAX, ALPHA, BETA, NCON, IERR) {: it:;tnt I ll' A Fof-:TF:Ail V SlJtrF:0t'l lflE lo {l/rl [lll.Arf TfiF cl]NSTANTS,AI-FHA i iil! til:ll, Ir IHE rill LFlICirl- li{]UAtI0il DI:SCtItiIl{(; ASIH DISTII'LATI0N L lll:fl rlll (l(lf!lili,fllli ilit { Al ( lJl nl! D ll:;1il[ rllE l rinOF:ATORY DAtA OF nr;tf 0t.:ilt,t nlIOfl i\lrl lill llrrlJ (,1 l'ilinffltF::i IL t11 . -.A Ftt-Al. .lliliAa (l(rrllAllllflL Al;lh Dltl ll L,ATI0l{ lfH[Fl:lA]tlREi 0il ANY lJlllI) ItihF(1 ) :;IrOul D !t lllf IillrlAl !0It lN[ ft]lNT ]Ehf'(ilf ) SHOI]LD II TH[ FINNI IOILIN6 FOINT Vl)L. - ...A RI]AL AIRAY COI{IAINI}iG TI]F VOI UilE Z DISTILL.€D {]OFRT]SF'OIIDIN{; TO IHE At.IRAY TEHF' Nr'. - ^.,..NUillIF 0r l 0INl]i IIF A-!Th DISIIt.I ATION. NF SIIOIJLD I'E GREATER TI]AN:] FIJT I-ESS THAN 22 NilAX.....NUiEER OI: hAXIilIJH ITERAIIT}I.IS ALLOUED TO CALCULATE THE CONSTANTS ALF'IIA....FIRST CONSTAI{T OF THE EiPJRICAL EGUATION OF ASTi DISTILLATlON CATCULATED FY THIS SUFROIJTINE TII]IA.. -..SECOND CONSTANI OF THE EHF'IRICAL EGUATION OF ASTil DISTILLATION CAT(:ULATED AY THIS SUFROUTINE I L:0N... -.{UhFF:R OT ITfFiATIONS REQI'IFED IN CALCULATING THE CONSTANTS IEITR..".^AN INTEf,[I] VAFIATILE THAT, ON RETIJRN, CONTAINS AN ERFOR SICNAL. lF IERfi IS ilOT ZCRO,THEN EITHER THE INFUT DATA ARE INCI]RRIC] OR lIiI FFOGRAh FAILS TO CALCULATE THE CONSTANTS )F IEFIR .. I, IhI:N NF' IS NI]T 3 ( NF ( 2? IF JIFF = ?, THEN oNE (]f vol(I) Is LESS THAN ZERo IF IEFR ' 3, THEN ONT: OF VOL(I) IS GFEATER THAN IOO (llll.rl) r...11,1) IF IFFIi = 4, THEN VllL(I) IS NOT EXFRESSED IN FEFCENTAGE !i(-rlll ') . rl(i,1) IF IERk " 5, I HEN TEHF { 1 ) IS Nol IFF l(l tr1L.i (l I i,{;1 II- IFHR = 6. THEN lfhF(Nf ) Is Nol FFP (tt i,irt ., (t I n(;L lF IERR = 7, llifl{ SoLIJTION lS NOT CETAINED FOR GMN XHA fri LLLl = 1 I )' ), f;lt - -1 rrIHtiNs t0N TE}IP ( NF ), VOL ( NP), X ( 2, ! ), Xl ( ?, 3 ), X?( 2 ), XOLD ( CK ( ? ll (]il(1,1)^{;l.o) ^l:1, Itl ilLl . 1 lL:({1(:1,1r-l,f-l)) lf LAI:1 . 1 Il rll.l Ll.1 ) LLI Il) !1) l{lr. I . KFt rlcl I t.l t,nL.l t(lti.l l(tLnl,,' I lIr f,(,4 It (tl]l1.Nt.4\ L.((r) ; r.lr[(/1) ll:( Il)l(1.tiQ.0) ill((1 ) -- O-/rtjK(1 ) tr(I|[]-NE.O) t;t(i:t) 1.3rc((:t) If (lllfi?-i:Q.0) C((l) . O.7rCK(l) Il (ul(i1).1 I.CKHIN) C{(l) = C(ilIN Ir (Cll(:l).Ll -CXiIll) CX(2) = CXdIN l:f:((11((1 ).II.C(HAx) CK(1 ) = CKhAX IF(CK(?).Gr.CKHa,X) C((:) .. CkiAX 50 D0 60 II = 1,: X(II,1) = X(II,1) - CK(II)rxl(II,1)/X2(II) 60 coNt tNUE. IfLA{;l - 0 ll-LA1;! = 0 Ifl iG3 = 0 Llr,AG4 = o Ir {il.llQ. I ) GO rO lO LF(AIIS(XOLD(1 )-X(1,1)),t.l.CLIn1) IFL'if,1 = 1 It(AtlS(Xol D(-') X(:,1)).LT.CLIil) IfLAf,3 = t tF (Ali(xl ( 1 ,1 ) ).Ll.CLIilf) If-t ACi = I lF(nls(x1(:,1 )).Lt.{lLIrl) Itl AG4 - t ll (fFI-AGr.NE.o.AND.IFLAGI,llE.0) Grl lu SO IF( Il A63.r{E.O.AND. lf!.4G4.ilE.0) G0 T0 80 ao c0Nr Ir{uE IiITUFN 8D ALfllA - X(1,1) !tirt = x(:,1) |lCt)N = N fit I lJliN t ilD this numerical method, the function F is minimized with re- spect to d. and P. The procedure of the numerical method is cbmplex and is not discussed here but the listing -of this method as a subroutine, ASTMFI in FORTRAN IV (see box) is given with necessary exPlanation of input and outPut data. EXAMPLES As shown in Figs. I to 4, the numerical method success- fully fits Eq. t to ASTM distillation data of the feed and products of FCC unit of Lindsey Oil Refinery, CFP/FINA, England. Optimum values of constants o and p are-significantly-d-if- I to 4). Eq. I h-q!9e1 successfully ferent for each case (Figs. integrated in CnpiO-RO model of FCCU for blending ASTV distillation curves of fresh feed, recycle LCO and re- cycle HCO for the total feed to the reactor. I r f't The author l Hasmukh Dhulesia is with the Wrational Re- search Department of Compagnie Franqaise des Pdtroles (TOTAL), frris, where he is rcspon' sible for sottwarc of automatic computer control of FCCIJ with static and dynamic optimizations. a Laboratory dala Dr. Dhulesia obtained his BSc (Hons.) degree Eq. 1 wrlh - r' - 0.683, in Chemistry from M.S. University ol Baroda, iJ = 3.296 BSc degree in Chemical Technology from Kan- & '- pur lJnivasity, and MSc and PhD degrees ir - Chemical Engineering from tho llnivarsity ol Manchester lnstitute ( Science and-Technology. He is authot of several papers on hydrodf-.2 Fis. 4-ASTM distillation curve for mixed product of HCO and namics and afficiencies of distillation ttays. slu-rry from FCCU. 180 Hydrocarbon Processing, September 1984 -\'.

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