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					                                                                                                                                      ,    6,
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             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,




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                                                                       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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