The calculation of ternary vapor-liquid system equilibrium by using P-R equation of state

Transcription

1 The alulaton of ternary vapor-lqud syste equlbru by usng P-R equaton of state Y Lu, Janzhong Yn *, Rune Lu, Wenhua Sh and We We Shool of Cheal Engneerng, Dalan Unversty of Tehnology, Dalan 11601, P.R.Chna Correspondene should be addressed to ynzhaq@al.dlptt.ln.n Abstrat: By usng P-R equaton of state (EOS), the phase equlbru haratersts was sulated for a syste onssted of hydrogen-hexane-dylopentadene (DPD). In order to prove the auray of the sulaton, dfferent αfuntons and xng rules were respetvely used to odfy the P-R EOS. The olar onentratons n vapor and lqud phase alulated was ontrasted wth that of the experental data ted n lteratures. The applablty and auray of eah odfed oeffent for the syste ontans hydrogen at dfferent redued paraeter ondtons were presented. So ths approah ay be used to predt the equlbru behavors of a hgh-pressure vapor-lqud syste. Keywords: Solublty, phase equlbru behavor, hydrogen, sulaton Introduton: The vapor-lqud equlbru data of ternary syste s one of the ost portant paraeters for the desgn of the heal proess. In therodynas, the sulaton of phase equlbru based on the study of experents s the an ethod to resolve ths knd of proble. The researh of phase equlbru behavor s a knd of very portant work n superrtal flud extraton, gas-antsolvent, heal reaton and any other proesses. Generally, P-R EOS has already been onsdered as the ost effent way to sulate the equlbru behavor of a syste subeted to hgh pressure (espeally for the syste ontans lqud phase). The sulaton of bnary syste by P-R EOS s very aurate, and any referenes [1-3] reported ths knd of odel. But when t s onern to ternary syste or low teperature syste that ontans hydrogen, the alulated value does not onde wth the experental data very well. And the lterature about the sulaton of ternary syste by P-R EOS s not very uh, and the auray s relatvely low. So several αfuntons and xng rules were presented to odfy the P-R EOS. Calulaton: The hydrogen-hexane-dpd syste was alulated wth Peng-Robnson EOS. RT a( T ) p = v b v( v+ b) + b( v b) (1) RT at ( ) = α () p 1

2 0.5 α = [1 + (1 )] (3) k T r k ω ω = (4) b RT p = (5) The followng are xng rule and obnng rule: = a x x a (6) = b x x b (7) b b + b = (8) a = (1 k ) a ( T) a ( T ) (9) The P-R EOS was orgnally desgned to odel hydroarbon systes usng one nteraton paraeter k, and t was obtaned by regressng the experental data. To odfy the equaton, any αfuntons and xng rules were presented [4]. And we use the followng funton as the xng rule nstead of funton (8). b b + b = (1 l ) (10) where l s also an nteraton paraeter. And we use funton (10) as the xng rule to alulate the equlbru data of the ternary syste oposed of H -hexane-dpd. In ths syste, k and l used n alulaton are k 1 = , k 13 = , k 3 = , and l 1 = , l 13 =0.074, l 3 = [5].Fgure 1 to showed the hexane ole fraton n the gas phase fro to 6 MPa, the DPD ass ontent (wt) was 7% and 5%, at 313K and 343K respetvely. The average devaton (AAD%) of the hexane ole fraton n the gas phase at 313K s 5.1% and at 343K s 13.4%. But the AAD% of lqud phase s ore than 0%. And the AAD% s defned as: al exp α α AAD % = 100 (11) exp α

3 Fg.1 Coposton of hexane n the gas phase for DPD n lqud feed at 7 wt% Fg. Coposton of hexane n the gas phase for DPD n lqud feed at 5 wt% Harens and Knapp [6] presented one αfunton as the followng to prove the P-R EOS: 3

4 1 α = [1 + k (1 T ) k (1 )] (1) r Tr Tan gave the k 1 and k value of hydrogen. That s k 1 = and k = By usng the equaton (1), we get a ore aurate result that the AAD% of hydrogen n lqud phase at 313K s 5.4% and at 343K s 8.6%.Fgure 3 and 4 shows that the hydrogen ole fraton n the lqud phase usng funton (1) nstead of funton (3). Fg.3 Coposton of hydrogen n the lqud phase for 7 wt% DCPD Conluson and dsusson: The phase equlbru behavor for the ternary syste hydrogen-hexane-dpd were sulated by usng P-R EOS at pressure fro to 5 MPa and teperature at 313K and 343K. Fro fgure 1 to 4, t an be onluded that f we are the equlbru behavor n the gas phase of the syste oposed of hydrogen-hexane-dcpd, we an use funton (3), otherwse we the better use funton (1). It was also found that usng the P-R EOS odel to alulate the equlbru behavor s aurate. And usng P-R EOS norporate wth a odfed αfunton to sulate the equlbru behavor of a ternary syste an get a satsfatory result. Lst of sybols: Letters a, b onstants n P-R EOS T teperature (K) P pressure (MPa) T r redued teperature 4

5 Fg.4 Coposton of hydrogen n the lqud phase for 5 wt% DPD x ole fraton n lqud phase k onstants n P-R EOS y ole fraton n gas phase ω aentr fator k,l paraeter n xng rule Subsrpts 1 hydrogen hexane 3 DPD Referenes: [1] Melhe, G.A., A odfed Peng-Robnson equaton of state, Flud Phase Equlbra, Vol. 47, 1989, p189 [] Ln, H.M., Peng-Robnson equaton of state for vapor-lqud equlbru alulatons for arbon doxde + hydrogen xtures, Flud Phase Equlbra, Vol.16, 1984, p.151 [3] A. Kordkowsk, A.P. Shenk, R.M. Van Nelen, C.J. Peters, Volue expansons and vapor lqud equlbra of bnary xtures of a varety of polar solvents and ertan near-rtal solvents, J. Superrt. Fluds, Vol.8, 1995, p.05 [4] Yao S, Guan Y, Zhu Z., Investgaton of phase equlbru for ternary systes ontanng ethanol, water and arbon doxde at elevated pressures, Flud Phase Equlbra, Vol.99, 1994, p.49 [5] Meng-Shyang, Chung-Sung Tan, Solublty of hydrogen n a xture of n-hexane and dylopentadene fro 313 to 363 K and fro.0 to 5.5 MPa, Flud Phase Equlbra, Vol.93, 1994, p.33 [6] Harens, A and Knapp, H., Three-paraeter ub equaton of state for noral substanes, Ind. Eng. Che., Funda., Vol.19,1980, p.91 5