Department of Energ oltecnco d Mlano Va Lambruschn - 05 MILANO Eercses of Fundamentals of Chemcal rocesses rof. Ganpero Gropp Eercse 8 Estmaton of the composton of the lqud and vapor streams etng a unt wth a supercrtcal component A mture of hdrogen, n-heptane, n-heane and n-butane (molar composton reported n the table) s sent to a unt. A B C 0.0 n heptane 0.30 5.8737 9.3 5.5 n heane 0.0 5.83 97.55 8.78 n butane 0.0 5.78 5.90 3. For each spece, A, B and C are the parameters of Antone s equaton for the estmaton of the vapor pressure. he mture s ntall at 0 bar. Assumng deal gases, deal lqud mture and assumng that s absent from the lqud phase ( s an n component), estmate: the dew temperature of the mture at 0 bar the vaporaton rato and the composton of the lqud and vapor streams obtaned n a unt mantaned at a temperature of 350 K and at a pressure of 0 bar. Re-estmate the unt (vaporaton rato and outlet streams composton) assumng that the dssolves n the lqud phase accordng to the enr s law. he enr s constant of vares wth the temperature and the composton of the lqud mture, accountng the data reported n the table and the equatons lsted below. 0,(98K) [bar] DES /R n n heptane 8.8 73. n n heane 05.7 397.7 n n butane 77. 8.0
Varaton of the enr s constant wth the temperature for n the -th spece: s bar, s K DES 98K ep 0,, R 98 Varaton of the enr s constant wth the composton of the lqud mture: NC m,, Antone s equaton: SA s mmg, s K SA B A C
Soluton s absent n the lqud phase. hs case s ver nterestng, snce ts results can be convenentl assumed as frst attempts for more comple cases. It s possble to verf the presence of a lqud phase under the operatng condtons of the unt b comparng the dew temperature of the mture at wth the temperature of the unt. Assumng deal gas and deal mtures, the equaton for the dew pont s: NSpece ( Dew ) Gven that the supercrtcal component s absent from the lqud phase ( = 0), the equaton ncludes onl the speces (for whch a uraton temperature does est): N CondensableSpece ( Dew ) ( Dew ) ( Dew ) 7 ( 7 Dew ) he dew temperature s equal to 7.98 K, hgher than that of the unt. It s concluded that a lqud phase s formed n the unt, at the equlbrum wth the vapor phase. he vapor phase s alwas present due to the presence of the supercrtcal spece. ence, the bubble temperature of the mture cannot be defned. Once the formaton of the lqud phase s verfed, the value of the vaporaton rato s determned b followng the same procedure shown for the Rachford-Rce equaton. he materal balances are consdered for all the speces, whle the equlbrum condtons are consdered eclusvel for the speces:... N, spece... N spece 0... N... N spece spece supercrtcal supercrtcal From these equatons, one obtans:... N... N spece spece 0... N... N spece spece supercrtcal supercrtcal 3
B combnng the stochometrc relatons of e, t results: NSpece NCondensableSpece NSupercrtcalSpece 0 Eq. Snce the temperature and the pressure of the unt are nown, the onl unnown value of Equaton s the vaporaton rato. In the present case, Equaton leads to the followng form: 0 he solvng value s = 0.85. he correspondng compostons for the lqud and the vapor phases are: 0.8307 0.0000 n heptane 0.08 0.553 n heane 0.07 0.3 n butane 0.09 0.035 It s nterestng to note that the Rachford-Rce equaton n the presence of supercrtcal components can be obtaned b consderng that the equlbrum constant for the mass transfer between the lqud and the vapor phase s nfnte n the case of supercrtcal components., wth 0 (supercrtcal) he lmt of the Rachford-Rce equaton for tendng to nfnte s n fact: lm NSupercrtcalSpece NSupercrtcalSpece From whch Equaton s obtaned.
s present n the lqud phase. Under the assumpton of deal gas and deal mtures, the presence of n the lqud mture s accounted for va the enr s equaton. he equlbrum constant for the mass transfer between the vapor and the lqud phase has a fnte value also n the case of the supercrtcal compound, and the Rachford-Rce equaton can be appled n ts general form. NSpece m,... N spece he enr s coeffcent for n the lqud mture m s defned as a functon of the composton of the components. he followng formulas are appled: NC, m,, m ep,, 7, 7 he enr s coeffcents for dssolved n each ndvdual spece are estmated at the temperature b applcaton of the followng equaton: 0,, R DES 98K ep 98 From whch, t s obtaned: 0, (98 K) [bar] DES /R, (350 K) [bar] n n heptane 8.8 73. 879.79 n n heane 05.7 397.7 85.00 n n butane 77. 8.0 87.0 In order to rearrange the Rachford-Rce equaton bac to the onl unnown value, the molar fractons of the components n the lqud phase must be epressed as a functon of ther feed composton and of the vaporaton rato tself. 5
7, 7 7,,, ep m spece... N B substtutng ths latter equaton nto the Rachford-Rce, the fnal solvng equaton n the onl unnown s obtaned: 0 Eq. NCondensableSpece he equaton s solved for = 0.75. It s worth to note that the soluton obtaned under the assumpton of the absence of from the lqud phase ( = 0.85) s a ver good frst attempt to solve the current case. he compostons of the lqud phase and of the vapor phase are: 0.003 0.83 n heptane 0.55 0.080 n heane 0.307 0.0 n butane 0.035 0.09