1 NGUYN TH THANH XUN B mn: Cng ngh ha hc Du v kh Nm hc 2011 -
2012 2 ng dng nhit ng hc compressor V, cPV, qV gas phase reactor V,
cPV, qV, V,Ahr, Agr, r pump V, cPL, qL,PSat decanter L, qL, oLL Ki
= xIi/xIIi distillation column V, L ,cPL, PSat, AhVL, Ki = yi/xi,
qL, oLS reboiler V, L, cpL, qL, L, AhVL, PSat, oLV heat exchanger
(gas) V, cpV, qV, V
3 Mc tiu mn hc Gii thiu cc nh ngha, cc hm nhit ng c bn, phng
trnh trng thi, ng dng vo phn tch cc hin tng ha l ca dng lu cht, c
bit trong lnh vc du kh ngdngmtphngphptnhphntchvnnhit ng t ra chn mt
m hnh nhit ng ph hp trong cng nghip - ng dng trong m phng 4 Gii
thiu chung Nhit ng hc l l thuyt vt l duy nht tng qut, trong kh nng
ng dng v trong cc c s l thuyt ca n, m ti tin rng s khng bao gi b lt
Albert Einstein Thut ng nhit ng hc (hoc nhit ng lc hc) c hai ngha:
Khoa hc v nhit v cc ng c nhit (nhit ng hc c in) Khoa hc v cc h thng
trng thi cn bng (nhit ng hc cn bng) Ban u, nhit ng hc ch mang ngha
th nht. V sau, cc cng trnh tin phong ca Ludwig Boltzmann em li ngha
th hai (nh lut ng nng trung bnh m hnh n gin v chuyn ng phn t). u im
ca phng php ng hc phn t l i su vo bn cht hin tng tuy nhin phi chp
nhn nhc im nh tnh chtgn ng ca nhng ktqu nh
lngvsphctpcacngvictnhton.Phngphpnhitnglchc khng kho st chi tit hin
tng xyra m ch tnh s bin i nng lng trong nhng hin tngy (t vic kho st
s bin i nhit nng thnh c nng). Cc nguyn l nhit ng lc hc rt cn thit
cho k thut cng nh cho vic nghin cu khoa hc ni chung 5 Cc khi nim H:
gm rt nhiu ht (nguyn t, phn t, vt cht) chuyn ng hn lon Vt l phn t
nghin cu theo quan im vi m, xem cc ht l cht im v p dng cc nh lut ng
lc hc ca Newton kho st chuyn ng ca cc phn t Nhit ng hc nghin cu trn
quan im v m, khng cn quan tm n cu trc phn t ca vt cht m ch da vo cc
nguyn l nhit ng tim ra mi quan h v nng lng m h trao i vi xung quanh
=> h kn, h m, h c lp Trng thi ca h: c trng bi cc thng s trng thi
(p, V, T), ch 2 trong 3 thng
snyclpcnthngscnlilphthuc,gia3thngscmtphng trnh lin kt chng li gi l
phng trnh trng thi. Ngoi ra cn c cc i lng khc c trng cho trng thi:
s ht N, ha th, entropy, ni nng, C hai kiu thng s trng thi : Loi
qung tnh (extensive), gm cc thng s ph thuc khong khng gian m h
chim, t lvilngvtchtnhV,N,S,U...=>sdngnhnhautronghcnbngcngnh khng
cn bng. Loicngtnh(intensive)khngphthucvokhongkhnggianhchim,khngtl
vi lng vt cht m c xc nh ti tng im trong h (T, p, )=> nh nhau ti
mi im trong h cn bng cn trong h khng cn bng th c th khc nhau t im
ny qua im khc. Pha: h m ti tt c cc tnh cht intensive ng nht nh nhau
ti mi im 6 Cc khi nim Trngthicnbng:Trongchc,trngthicnbngca
mtvtltrngthimvtngynivimthquy chiuquntnhnhtnh.Trongnhitnglchckhinim
trngthicnbngcamthltrngthimccthngs trng thi ca h khng thay i v trng
thi ca h khng thay i, trong h khng xy ra cc qu trnh nh dn nhit,
khuch tn, phn ng ha hc, chuyn pha.v.v...
Qutrnhchuncnbng:Khimthbinittrngthinysangtrngthi khc, mt chui cc
trng thi ni tip nhau xy ra, to nn mt qu trnh. Nu nhng
trngthinitipnhaunylnhngtrngthicnbng(binthinthngstrng thi theo thi
gian chm so vi khong thi gian gia hai trng thi k tip) th to mt ququ
trnh chun cn bng (chun tnh). Nhng qu trnh xy ra trong thc t khng
phi l nhng qu trnh chuncn bng nhng nu chng xyra cng chm bao nhiu th
cng gn ng l qu trnh chun cn bng by nhiu
Qutrnhthunnghch:Qutrnhthunnghchlqutrnhdinbintheochai chiu, trong nu
lc u qu trnh din ra theo mt chiu no (chiu thun) ri
saulidinratheochiungclitrvtrngthibanuthhiquami trng thi ging nh lc
h din bin theo chiu thun v khi h tr vtrng thi ban u th khng gy ra
mt bin i g cho ngoi vi . Mi qu trnh thun nghch u l qu trnh chun cn
bng7 Cc khi nim Ni nng: gm ton b cc dng nng lng trong vt nng lng
chuyn ng nhit (nhit nng), th nng tng tc gia cc phn t,
Nnglngbntrongphnt:thnngtngtcgiaccnguynt trongtng phn t, ng nng v th
nngtng tc ca cc ht cuto nn nguyn t (ht nhn v cc electron) v.v...
Khi nhit ca kh l tng thay i th ni nng ca kh cng thay i
=>cthlmthayininngcakhbngstraoinhitlng gia kh vi bn ngoi.
Struynnnglngnichungcthchindihaihnhthc khc nhau: truyn nhit lng v
thc hin cng c hc. S truyn nhit lng l hnh thc truyn nng lng xy ra
trc tip gia nhngnguynthayphntchuynnghnloncutonnccvt ang tng tc
=> trc tip dn n s tng ni nng ca h ;
Sthchincnglhnhthctruynnnglnggianhngvtvm tng tc vi nhau => trc
tip dn n s tng mt dng nng lng bt k ca h (ng nng, th nng, ni
nng,...)8 U E E Ecin pot+ + = NNG LNG CA H THNG PdV W or W WPdV WdV
P Wrevrevext > > = =o o oooS TRAO I NNG LNG TRONG QU TRNH
CHUYN HA ( )Initial FinalQ W W U E E Ecin pot A+ + = + + A =
A:'Nguyn l 1 nhit ng lc hc 9 Nguynlthnhtcanhitnglchcchnhlnguynlbo
tonvbinhannglngpdngtrongccqutrnhclin
quannsbinininngsangcnngvnhitnnghoc sang cc dng nng lng khc v ngc
liQ W dUQ W Uo o + =+ = AS CHUYN HA TH TCH KHNG I (TRANSFORMATIONS
ISOCHORES) dT C Q dU Q UV V V V V= = = A oNN ON NHIT (COMPRESSION
ADIABATIQUE) U We adiabatiquA =S CHUYN HA P SUT KHNG I
(TRANSFORMATIONS ISOCHORES) ( )( )dT C dHH PV U QPV V P WP PP P PP
ext P=A = + A =A = A =10 CHNG I: CC NH NGHA, CC HM NHIT NG NGUYN L
II ENTROPIE - H thng c m t bi: V, U, n, i,- Tn ti mt tnh cht ca h:
Entropie tnh cht mang tnh cng tnh (extensive) TRONG QU TRNH CHUYN
HA ( )PdV W or W W TdS QTQdS dSthermique Echange dSTQdSdS dS
dSrevie ee i > > s> > =+ =o o o ooo011 CHNG I: CC NH
NGHA, CC HM NHIT NG NGUYN L II MI QUAN H GIA NI NNG V ENTROPIE } }
> s+ =+ = + = == =2121&1 1&PdV W TdS Qdl F PdV TdS
dUdvTPduTds dVTPdUTdS PdV TdS dUTdS Q PdV Wi ir ro o12 CHNG I: CC
NH NGHA, CC HM NHIT NG NGUYN L II P DNG VO IU KIN CN BNG 0 0 = = dQ
dWH C LP TH TCH V NI NNG KHNG I 0 0 = = dV dUENTROPIE CH C TH TNG 0
> dS13 CHNG I: CC NH NGHA, CC HM NHIT NG NNG LNG T DO HELMHOLTZ
ENERGY (A) ( )( )( )0 0.) , (.) , (.) (,,',''''= < = = A > =
> = A > + > + s+ + =dA m Equilibriu dATS U AConst V T TS U
WConst V T TS U d WConst T TS U W WTdS dU W W TdS QW W Q dUV TV TV
TToo o oo o o14 CHNG I: CC NH NGHA, CC HM NHIT NG ENTHALPIE T DO
GIBBS ENERGY (G) T, P = Const. ( ) ( )0 0','= < = + = + A > +
>A = =dG m Equilibriu dGTS H TS PV U GTS PV U W or TS PV U d WV
P W or PdV WP Too o15 dU CdT TPTPdVdH CdT TVTVdPdS CdTPTdVdS
CdTVTdPdA PdV SdTdG VdP SdTVVPPVVPP= +|\
|.|
((= + |\
|.| +
((= + |\
|.|= |\
|.|= = ccccccccdu cdT TPTPdvdh cdT TvTvdPds cdTPTdvds cdTvTdPda
Pdv sdTdg vdP sdTVVPPVVPP= +|\
|.|
((= + |\
|.| +
((= + |\
|.|= |\
|.|= = ccccccccS BIN THIN CA CC HM NHIT NG THEO T, P V V CHNG I:
CC NH NGHA, CC HM NHIT NG H U PVG H TSA U TS= += = CC HM NHIT NG C
BN 16 H U PVA U TSG U PV TS= += = + dU TdS PdVdH TdS VdPdA SdT
PdVdG SdT VdP= = += = +XYZYXZY XZX Ycccc=cccc=c c2cdYYZdXXZdZX
Ycccc+ =Maxwell: ccccccccUSHSTUVAVPV PS T= == = ccccccccHPGPVATGTSS
TV P= == = ccccccccTVPSTPVSS VS P= =ccccccccSVPTSPVTT VT P== 17 =
dU||.|
\|PPTVP CccdT||.|
\|+ T PPVPTVTccccdP= dHCPdT ||.|
\| +PTVT VccdP= dA||.|
\| PTVP SccdTTPVPcc dP= dGS dT+VdP= dSTCPdTPTVccdP18 = dU CV dT
||.|
\| + PTPTVcc dV = dH ||.|
\|+VVTPV Ccc dT ||.|
\|+ +V TTPTVPVcccc dV = dA S dT P dV = dG ||.|
\| VTPV Scc dT TVPVcc+ dV = dS TCV dT VTPcc+ dV 19 MT S H QU RT
RA T CC PHNG TRNH NHIT NG PT GIBBS-HELMHOLTZ PT CLAPEYRON( )dPdThTv
vV Lo oo o=A, ,Chng minh (*): ( )2 221 11 1THSTTS HTTGTGT TTGPP =
=|.|
\|cc+ =||||.|
\|ccTPTVV PP PV VPVTVTVPTPT C CHTTGORTHTTGUTTAORTUTTA|.|
\||.|
\| =|.|
\||.|
\| = =||||.|
\| =||||.|
\|=||||.|
\| =||||.|
\|cccccccccccccccc2 22211(*): CHNG I: CC NH NGHA, CC HM NHIT NG
2.2.20 p dng nguyn l nhit ng vo cu t tinh khit Tnh cn bng pha
Enthalpie t do : C th vit:hay: => dg1 = dg2 = 0 (g ch ph thuc P
v T, khng i) dN1 = -dN2 Suy ra vi mi dNN1, T, P, v1,h1, g1, ... N2,
T, P, v2,h2, g2, ... dN 0 s dG02 1s + dG dG( ) ( ) 02 2 1 1s + g N
d g N d02 2 2 2 1 1 1 1s + + + dg N dN g dg N dN g( ) 01 2 1s dN g
g2 1g g ==> 2.2.21 Phng trnh Clausius-Clapeyron Clapeyron :
Clausius : ooov ThdTdPAA=( ) RhT dP do oA =/ 1ln=constante v
vvRTPhL VV Biu thc ny kh p dng v bin thin entropie trong iu kin
trng thi bo ha rt kh xc nh. Mt khc ta c:vDo vy:2.2.23
Clausius-Clapeyron ln(P) - 1/T l mt ng thng 2.2.24 Kh l tng: Phng
trnh trng thi T : Rankine hay Kelvin Nu v l th tch mol l R l hng s
kh l tng: R=8,3145 J/mol-K= 8,314 MPa-cm3/mol-K R = 1,987 cal/mol-K
R = 82,058 atm-cm3/mol-K RT Pv =#25 S BIN THIN CA CC HM NHIT NG CA
KH L TNG THEO NHIT , P SUT HOC TH TCH du cdTdh c dTds cdTTR
dvvcdTTR dPPda RT dvvsdT ou da RTd vdg RT dPPsdT ou dg RTd Pc c
RVPV PTTP V# ## ## # ## # ## # ## #lnln=== + = = = = = =R =
8,314J.mol-1K-1 R = 1.987cal.mol-1K-1 = 83.145 bar.cm3. mol-1K-1 =
82.058 atm.cm3. mol-1K-1 2.2.26 Nhit dung ring ng p ca kh l tng
2.1.1. Le gaz parfait -Kh l tng l h khng c tng tc gia cc phn t kh
vi nhau m ch c tng tc ni phn t, do vy nhit dung ring Cp ca kh l tng
ch ph thuc vo cu trc ca phn t xem xt v khng ging nhau i vi nhng phn
t kh khc nhau.-i vi phn t kh n gin, c th tnh chnh xc t phng tnh vt
l phn t : Vi kh c 1 nguyn t : c R cal mol KP#= ~ 525 / Vi kh c 2
nguyn t c R cal mol KP#= ~ 727 / -Nhn chung Cp ph thuc T theo mi
quan h sau : c a bT cT dTP#= + + + +2 3. . .(Passut & Danner)
ou ( ) ( )c B CDTDTEFTFTP#= +
(((+
(((sinh cosh2 2 (Aly & Lee, 1981) 2.2.27 Hot p (fugacity) ca
cu t tinh khit Enthalpie t do l mt hm nhit ng c bn thit lp cn bng
pha i vi kh l tng: i vi kh thc: f: hot p (fugacity)f RTd dgTlnA=P
RTd dg ln#T =2.2.28 Fugacity ca cu t tinh khit Fugacity c th nguyn
nh p sut. Fugacity ca kh l tng: H s hot p : P fA=# ln ln ln ln#T
TRTdPfRTd P RTd f RTd dg dg = = = } } } }= =||.|
\|cccc= P P PTTPd RTPfd RT dPPgPgdg dg0 0 0#0#T Tln ln ( )}
}|.|
\| = =P PdPPRTv dP v v RT0 0#lnRT PvRTPvRT dvvRTP RTV + |.|
\|+ =}ln ln0 1 = P khiPf2.2.29 Fugacity ca cu t tinh khit C th
rt ra t cc h thc quan h: Trong pha hi p sut thp: Hay:nu P 5bar v B
Lp bng tnh: Trong pha lng hay Xc nh Po 300 K Tnh f o = fv ti P = P
o Tnh vL o
Tnh fL ( )} }|.|
\| = =P PdPPRTv dP v v RT0 0#lnRT ln = vi-RTPi| \ | . | i (Pi-
Pi - 1)|||.|
\|}+PPvdPRToo1expvf = fLfL=fvoexp + vLo(P-Po)RT2.2.31 Nguyn tc
tnh mt tnh cht nhit ng Trng thi l tng + hiu chnh v trng thi l tng
Khi nim hm d (RES rsiduelle) Kh l tng+Cc tnh cht rsiduelle 2.2.32
Tnh ton mt tnh cht nhit ng trong pha hi ( ) ( )+ =0 0#, ) , P T X P
T XTrng thi kh l tng Hm d ( ) ( ) | |+ 0 0#0#, , P T X P T X( ) ( )
| |+ 0# #, , P T X P T X( ) ( ) | | P T X P T X , ,# Vi gi trkhi
bit trng thi i chng (T0, P0), tnh c X# (T0, P0)
Thng thng: Vi gi tr tnh t mi quan h cc hm nhit ng ca kh l tng Vi
gi trtnh t mi quan h cc hm nhit ng ca kh l tng ( ) 0 ,0 0#= P T XVi
trng thi l tng ( ) ( ) | |+ 0 0#0#, , P T X P T XdTTXPTT00}cc=( ) (
) | |+ 0# #, , P T X P T X( )0 0#, P T XdPPXTPP}cc=0# Cn lu nu X=U
ou X=H,Gi tr ny bng 0 Cc hm nhit ng ca kh l tng 34 du c dTv##=dh c
dTP##=ds cdTTRdvvcdTTRdPPV P## #= + = daRTvdv s dT# #= dgRTP dP s
dT# #= c c RP V# # =2.2.35 L hiu chnh so vi trng thi l tng : ( ) (
) | | P T X P T X , ,#( ) dPPXPXP T XPTTres}||.|
\| =0#,ccccVic tnh ton cc gi tr d cn mt phng trnh dngty theo mi
quan h ca cc hm nhit ng v ph thuc duy nht vo 3 thng s trng thi PVT
TPXccHm d 36 TNH TON CC HM D (RESIDUAL PROPERTY) }}(((
||.|
\|cc|.|
\|cc=(((
||.|
\|cc|.|
\|cc=VTTresPTTresdVVXVXV T XanddPPXPXP T X#0#) , () , (ENTHALPY
D dPTvT v P T hTvT vPhPPresP T}((
|.|
\|cc =|.|
\|cc =|.|
\|cc0) , (NI NNG Ddv PTPT vvRTP T u v P T uPTPTvuvvV T}((
|.|
\|cc=|.|
\|= |.|
\|cc=|.|
\|cc, , ) , , (# #37 NI NNG Ddv PTPTPRTv P T u v P T uvv}((
|.|
\|cc=|.|
\|= # #, , ) , , (((
|.|
\|= |.|
\|= +((
|.|
\|= =|.|
\|= PRTv P T u vvRTP T u vvRTP T u v P T uPRTv P T u v P T u# #
# # # ## #, , , , , , ) , , (, , ) , , (0 ( ) ( )( ) ( )} +((
|.|
\|cc= + = + = + =vvRT Pv dv PTPT P T h P T hRT Pv u u h hRT u h
Pv u h, ,,## ## #38 NNG LNG T DO D( )( )( )( )RTPvRT dvvRTPPRTv P T
a v P T aPRTvRTvdvRTPRTv P T a vvRTP T avRTPvaPRTv P T a vvRTP T a
vvRTP T a v P T aPRTv P T a v P T advvRTP vvRTP T a v P T
avRTPvaPvavvvTvTTln , , , ,ln , , , ,, , , , , , , ,, , , ,, , ,
,,# ## # # #### # # # # ## ## ####|.|
\|+ =|.|
\|= = =((
|.|
\|= |.|
\|= = =||.|
\|cc((
|.|
\|= |.|
\|= +((
|.|
\|= =|.|
\|= |.|
\|+ =|.|
\|= = =||.|
\|cc =|.|
\|cc}}}39 NNG LNG T DO D( )( ) ( )( ) ( ) RT PvRTPvRT dvvRTP P T
g P T gRT Pv a a g gRT a g Pv a gRTPvRT dvvRTPPRTv P T a v P T avv
+ |.|
\|+ = + = + = + =|.|
\|+ =|.|
\|= }}ln , ,,ln , , , ,## ## ## #( )}|.|
\| == =||.|
\|cc=|.|
\|ccPresTTdPPRTv P T gPRTvPgvPg0##,,2.2.40 Tnh ton cc hm d ( )
dv PTPT P T uvvres}||.|
\| =cc,( ) RT Pv dv PTPT P T hvvres +||.|
\| =}cc,( ) dPTvT v P T hPPres} ||.|
\| =0,cc( ) dPPvPTvT P T uPT Pres} ||.|
\|+ =0,cccc( )RTPvRT dvvRTP P T avresln , |.|
\|+ =}( ) dPPRTv P T gPres}|.|
\| =0,( ) RT PvRTPvRT dvvRTP P T gvres + |.|
\|+ =}ln ,( ) dPPRTvP T sPPres} ||.|
\|+ =0,cc( )RTPvR dvvRTPP T svvresln , +||.|
\| =}cc2.2.41 p dng tnh enthalpie Tnh trng thi kh l tng Vi Th
nguyn s dng l J/kmol Trng thi i chng c th chn bt k Tnh enthalpie d
55443322 1 0#T h T h T h T h T h h h + + + + + =( )55443322 1 0 ref
ref ref ref ref refT h T h T h T h T h h h + + + + =2.2.42 Bi tp
Tnh ethalpie ca ethane theo nhit (T=200 400K) Hng dn Tnh Enthalpie
trng thi kh l tng Enthalpie d Enthalpie = H l tng + H d Tnh
enthalpie trng thi l tng 43 55443322 1 0#T h T h T h T h T h h h +
+ + + + =( )55443322 1 0 ref ref ref ref ref refT h T h T h T h T h
h h + + + + =h1h2h3h4h5 J/kg19,040,060,000,000,00
J/kmol572,4387501,8065650,000685-0,0000010,000000 S dng cng thc: Vi
cc h s:Chn trng thi i chng T=298,15oC Tnh href theo n v J/kg chuyn
i thnh J/kmol Tnh enthalpie d Phngtrnhtrngthicaethanetrongiu kin
pha hi c th theo phng trnh Viriel Vi B (cm3/mol) c tnh nh sau: (T
K) 44 P =RTv+BRTv2B(T) = 78,48 5,245 x 104T5,133 x 106T28,002 x
108T35,510 x 1019T8Tnh enthalpie d (tt) Enthalpie d ti mt iu kin
(T, P) nht nh c tnh theo phng trnh: Hoc theo phng trnh: 45 hres(T,
P) = (TcPcTv}v P)dv + Pv RT( ) h TP vPvTPTdvresT vv, = +|\
|.|}ccccTnh enthalpie d (tt) Th tnh mol c tnh da vo phng trnh
Viriel: Phng trnh ny c 2 nghim: Nghim c gi tr ln hn tng ng vi trng
thi pha hi Nghimcgitrnhhntngngvitrngthigilngv phng trnh Viriel khng
p dng cho pha lng46 Z =1+Bvou PvRT=1+BvPv2RT- v- B=0v=1 1+ 4 BPRT2P
RT47 CHNG I: CC NH NGHA, CC HM NHIT NG Tnh ton cc tnh cht nhit ng
ca pha lng: h T P h T P h T P hh T P h T P h T P h v TvTdPL vL v
LLP PPRESRES( , ) ( , ) ( , )( , ) ( , ) ( , )##o o o oo o occo= +
= + + |\
|.|
(((}AAEnthalpy ca pha lng Enthalpy t do v fugacity iu kin cn bng
g TP g TP gf TP f TP f PvRTPdPRTL VL VVP( , ) ( , )( , ) ( , ) expo
o oo o o oo= == = =|\
|.|
((((((}048 CHNG I: CC NH NGHA, CC HM NHIT NG Tnh ton cc tnh cht
nhit ng ca pha lng: =||.|
\|=((
=||.|
\|= ||.|
\|==||.|
\|}}}}o oooooooof dPRTvf (T,P) fRT) P (P vdPRTvdPRTvf (T,P) fdP
vf(T,P) fRTPPLLLPPLPPLLPPLLexpexp exp: ) ( Poynting chinhhieudoi
khong v xemexplnL trng thi lng qu lnh Bi tp: Tnh enthalpie ha hi ca
thylbenzne 180C Cho bit Tc = 617,1 K Pc = 35,14 bar Zc = 0,263 w=
0,301 Dng phng trnh Clapeyron : Tnh th tch mol lng p dng phng trnh
Rackett vi ZRA = 0,29056 0,08775e Th tch mol pha hi tnh t phng trnh
Viriel : H s Viriel tnh t nh l Tsonopoulos p sut hi bo ha tnh theo
nh lut Antoine : Vi T tnh bng K v P tnh bng mmHg. d ln Pod 1 / T (
)= AhoRAZo( )ln ln,vvT ZLcr RAo|\
|.| = 12 7v=RTP+Bln Po=16,01953279,47T 59,95Phn tch gin cc tnh
cht nhit ng ca ethylene p dng cc nguyn l nhit ng vo hn hp Hn hp l
tng: tun theo nh lut Raoult HC cng h Hn hp khng l tng: sai lch (m
hoc dng) vi nh lut Raoult; hn hp ng ph; hn hp lng lng khng tan; hn
hp lng-lng-hi HC c p sut hi bo ha gn nhau HC- nc p dng cc nguyn l
nhit ng vo hn hp Cc hot ng trng thi 1 pha (lng/hi) ca hn hp tng t
nh i vi cu t tinh khit trng thi cn bng pha, hot ng ca hn hp hon ton
khc vi cu t tinh khit i vi hn hp l tng: Quy tc pha Gibbs Gin pha
PT, Txy, Pxy nh lut Dalton v Raoult, nh lut Henry Quy tc pha Gibbs
F = N - u + 2 Trong : F:s bc t do N:s cu t trong hn hp u: s pha Quy
tc pha Gibbs cho php xc nh s lng cc thng tin cn bit c th nhn bit
hon ton h Quy tc ny ch p dng i vi cc tnh cht intensives (nhit , p
sut, thnh phn mol trong hn hp) 1.2.541.2. Les mlanges idaux Quy tc
pha Gibbs V du 1: Cu t tinh khit (N=1), Mt pha (u=1) F=2: H ch c xc
nh khi bit gi tr p sut v nhit (2 thng s intensives) V d 2: Cu t
tinh khit (N=1), Hai pha (u=2) => F=1 : H c xc nh khi bit p sut
hoc nhit ; ng cong p sut hi bo ha cho php xc nh gi tr cn li
1.2.551.2. Les mlanges idaux Quy tc pha Gibbs V d 3: Hn hp 2 cu t
(N=2), Mt pha (u=1) => F=3: ngoi p v T, cn bit thm thnh phn mol
V d 4: Hn hp 2 cu t (N=2), Hai pha (u=2) => F=2: hoc bit p, T s
tnh c thnh phn pha; hoc bit T v thnh phn 1 pha s tnh c tt c cc thng
s khc ! Khng c ngha l s xc nh c lng tng i ca mi pha (thng s
extensives)! 1.2.561.2. Les mlanges idaux Gin pha
ivihnhp,theoquytcphaGibbs,sbctdo cahtngrtnhanh.Ginphaphicbiudin
trong mt h khng gian gm N+1 chiu, tng ng vi h c N cu
t.ngin,chngtasxemxthgm2cutv biu din trong khng gian 3D. Cc gin pha
: PT; Txy et Pxy 1.2.571.2. Les mlanges idaux Le diagramme de
phases 1.2.58 Gin pha Gin PT : 020406080100120-100 -50 0 50 100 150
200Pressure, barTemperature, CCourbe de bullePoint CritiqueCourbe
de rose1.2.591.2. Les mlanges idaux Gin PT ca h thane - heptane p
sut hi bo ha ca thane p sut hi bo ha ca heptane 1.2.601.2. Les
mlanges idaux Gin PT ca h thane - heptane ng si ca hn hp 77,1% mol
thane im ti hn ca hn hp ng sng ca hn hp 77,1 % mol thane 1.2.611.2.
Les mlanges idaux Gin PT ca h thane - heptane Tp hp cc im ti hn
1.2.621.2. Les mlanges idaux Gin PT ca h thane - heptane
Cricondenbar:pmax ti cn tn ti 2 pha 1.2.631.2. Les mlanges idaux
Gin PT ca h thane - heptane Cricondentherme Vng ngng t ngc
1.2.641.2. Les mlanges idaux Gin pha 1.2.651.2. Les mlanges idaux
Gin Txy 01020304050607080901000 0,2 0,4 0,6 0,8 1Temperature,
CComposition, Mole Fraction PROPANE, (P = 5.0 bar)T-X-Y Plot for
PROPANEand PENTANEBubble PointDew PointNhit si ca cu t tinh khit (
5 bar) 1.2.661.2. Les mlanges idaux Gin Txy T-X-Y Plot for PROPANE
and PENTANE01020304050607080901000 0.2 0.4 0.6 0.8 1Composition,
Mole Fraction PROPANE, (P = 5.0 bar)Temperature, CBubble PointDew
PointChn mt thnh phn bt k ca h v phn tch 1.2.671.2. Les mlanges
idaux Gin Txy T-X-Y Plot for PROPANE and
PENTANE01020304050607080901000 0.2 0.4 0.6 0.8 1Composition, Mole
Fraction PROPANE, (P = 5.0 bar)Temperature, CBubble PointDew
PointKhi T thp, hn hp trng thi lng. Tuy nhin T hn hp vn ln hn T si
ca cu t nh 1.2.681.2. Les mlanges idaux Gin Txy T-X-Y Plot for
PROPANE and PENTANE01020304050607080901000 0.2 0.4 0.6 0.8
1Composition, Mole Fraction PROPANE, (P = 5.0 bar)Temperature,
CBubble PointDew PointLIQUIDE 1.2.691.2. Les mlanges idaux Gin Txy
T-X-Y Plot for PROPANE and PENTANE01020304050607080901000 0.2 0.4
0.6 0.8 1Composition, Mole Fraction PROPANE, (P = 5.0
bar)Temperature, CBubble PointDew Point trng thi si, s c 1 pha hi
xut hin c thnh phn pha (y) cn bng vi lng c th c c trn ng sng
LIQUIDE 1.2.701.2. Les mlanges idaux Gin Txy Cn bng vt cht c vit di
dng: ( ) F y F x zi i i+ = 1Vi L VVN NNF+= l thnh phn mol bc hi.F c
th tnh t quy tc Leviers: i ii ix yx zF=1.2.711.2. Les mlanges idaux
Gin Txy T-X-Y Plot for PROPANE and PENTANE01020304050607080901000
0.2 0.4 0.6 0.8 1Composition, Mole Fraction PROPANE, (P = 5.0
bar)Temperature, CBubble PointDew PointGia ng si v ng sng tn ti 2
pha. LIQUIDE 1.2.721.2. Les mlanges idaux Gin Txy T-X-Y Plot for
PROPANE and PENTANE01020304050607080901000 0.2 0.4 0.6 0.8
1Composition, Mole Fraction PROPANE, (P = 5.0 bar)Temperature,
CBubble PointDew PointLIQUIDE Thnh phn pha lng (x)c trn ng si
1.2.731.2. Les mlanges idaux Gin Txy T-X-Y Plot for PROPANE and
PENTANE01020304050607080901000 0.2 0.4 0.6 0.8 1Composition, Mole
Fraction PROPANE, (P = 5.0 bar)Temperature, CBubble PointDew
PointLIQUIDE Thnh phn pha hi (y)c trn ng sng 1.2.741.2. Les mlanges
idaux Gin Txy T-X-Y Plot for PROPANE and
PENTANE01020304050607080901000 0.2 0.4 0.6 0.8 1Composition, Mole
Fraction PROPANE, (P = 5.0 bar)Temperature, CBubble PointDew
PointLIQUIDE p dng quy tc Leviers: Thnh phn mol hi1.2.751.2. Les
mlanges idaux Gin Txy T-X-Y Plot for PROPANE and
PENTANE01020304050607080901000 0.2 0.4 0.6 0.8 1Composition, Mole
Fraction PROPANE, (P = 5.0 bar)Temperature, CBubble PointDew
PointLIQUIDE p dng quy tc leviers Thnh phn mol lng 1.2.761.2. Les
mlanges idaux Le diagramme Txy T-X-Y Plot for PROPANE and
PENTANE01020304050607080901000 0.2 0.4 0.6 0.8 1Composition, Mole
Fraction PROPANE, (P = 5.0 bar)Temperature, CBubble PointDew
PointLIQUIDE Ti nhit im sng, ton b h trng thi hi.Thnh phn pha hi ng
nht vi thnh phn ca h Thnh phn ca nhng git lng cui cng c trn gin
1.2.771.2. Les mlanges idaux T-X-Y Plot for PROPANE and
PENTANE01020304050607080901000 0.2 0.4 0.6 0.8 1Composition, Mole
Fraction PROPANE, (P = 5.0 bar)Temperature, CBubble PointDew
PointLIQUIDE T cao, (c th thp hn T si ca cu t nng) ton b h trng thi
hi1.2.781.2. Les mlanges idaux Gin pha 1.2.791.2. Les mlanges idaux
Gin Pxy: 1. nh lut Dalton Nu ti nhit T, p sut hi bo ha ca cu t A l
Thnh phn pha lng l v pha hi l Ta c Vi P l p sut tng ca h oAPoA A AP
x P y =AxAy1.2.801.2. Les mlanges idaux Gin Pxy: 2. nh lut Raoult V
tng thnh phn mol trong pha hi bng 1, ta c: p sut h l cn bng tuyn
tnh ca cc gi tr p sut hi bo ha ca cc cu t c trong h Ch rng nh lut
Raoult ch ng vi phn mol, khng p dng cho phn khi lng oi iP x
P=1.2.811.2. Les mlanges idaux Gin Pxy P-X-Y Plot for PROPANE and
PENTANE02468101214160 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9
1Composition, Mole Fraction PROPANE, (T = 40.000 C)Pressure,
barBubble Pointng si l ng thng! 1.2.821.2. Les mlanges idaux Gin
Pxy ng sng tnh d dng t nh lut Dalton: PP xyA AAo=1.2.831.2. Les
mlanges idaux Gin Pz P-X-Y Plot for PROPANE and
PENTANE02468101214160 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1Composition, Mole Fraction PROPANE, (T = 40.000 C)Pressure,
barBubble PointDew Point1.2.841.2. Les mlanges idaux Gin Pz P-X-Y
Plot for PROPANE and PENTANE02468101214160 0.1 0.2 0.3 0.4 0.5 0.6
0.7 0.8 0.9 1Composition, Mole Fraction PROPANE, (T = 40.000
C)Pressure, barBubble PointDew PointVng c p sut cao trng thi lng
Vng c p sut thp trng thi hi 1.2.851.2. Les mlanges idaux Gin Pxy
Tng t gin Txy, trn gin Pxy ta c th xc nh: Thnh phn pha lng cn bng t
ng si Thnh phn pha hi cn bng t ng sng p dng quy tc leviers xc nh
lng lng v lng hi Bi tp p dng Xy dng gin cn bng pha ca hn hp
benzen-toluen 1atm, xem hn hp l l tng. Nhit si ca benzen v toluen:
80,1C v 110,7C p sut hi bo ha tnh theo pt Antoine : (T tnh bng K et
Ps tnh bng mm Hg) i vi benzne, A=15.9008; B=2788.51; C=-52.36 i vi
tolune, A=16.0137; B= 3096.52; C= -53.67 p dng vo chng ct: Xc nh cc
gi tr nhit cn thiu trong trng 86 n Po=A-BC+ TTemprature (C) PoBz
(mm Hg) PoTOL (mm HG) KBzKTOLxBzyBz 1.2.871.2. Les mlanges idaux nh
lut Henry nh lut Raoult: khng th p dng khi mt trong nhng cu t trng
thi qu ti hn. Khi l hng s Henry y gi l quy c khng i xng oA A AP x P
y =oB B BP x P y =B B BH x P y =oA A AP x P y =BH1.2.881.2. Les
mlanges idaux Cc iu kin p dng nh lut Henry bay hi gia cc cu t khc
nhau nhiu (kh lng) ha tan rt thp trong dung mi Hn hp thc Sai lch m
so vi nh lut Raoult Sai lch dng so vi nh lut Raoult Nc - ethanol im
ng ph thay i theo p sut Tch bng chng ct 90 Nc - HC 91 92 CHNG II:
TNH TON CC TNH CHT NHIT NG CA CC CU T GII THIU Cc i lng v tnh cht
cn thit: - Cc thng s ti hn - p sut hi bo ha Cc loi lc tng tc: - Cc
lc c hng - Cc lc cm ng - Cc lc phn tn - Lin kt Hydro - Lc ht gia cc
phn t -Lc y gia cc phn t NH LUT TRNG THI TNG NG(LOI DES TATS
CORRESPONDANTS)S HIU CHNH THEO CU TRC CC PHNG TRNH TRNG
THI(QUATIONS D'TAT) 93 CHNG II: TNH TON CC TNH CHT NHIT NG CA CC CU
T NH LUT TRNG THI TNG NG(LOI DES TATS
CORRESPONDANTS)nhlutnyrtratnhnxtthcnghimlsbinthincahsnn (facteur de
compressibilit (Z)) ch ph thuc vo cc gi tr Tr, Pr, v nu chng ta chp
nhn nguyn tc ny tinh ton Z, th ta cng c th s dng n tnh cc tnh cht
rsiduelles khng th nguyn khc (hres/RT, sres/R, cP(res)/RT,,
...)SSAIKHCVINHLUTKHLTNG(HAYCCGITRD
(RSIDUELLESXRES))CHPHTHUCVOCCTHNGSTIHN
THNGQUACCGITRTHUGN(Tr,Pr,vr)MKHNGPHTHUC VO BN CHT CA CU T NGHIN
CU.94 CHNG II: TNH TON CC TNH CHT NHIT NG CA CC CU T NH LUT TRNG
THI TNG NG(LOI DES TATS CORRESPONDANTS)( )h TP v TvTdPv Z
RTPhRTTPZTdPTPZTdPvRT PdP ZdPPRESPPRESPPrr rPPrPPrrrrr( , )ln=
|\
|.|
((= = |\
|.|
((= |\
|.|
(((= |\
|.| = }} }} }cccccc00 00 011Ta cung co:V d: 95 CHNG II: TNH TON
CC TNH CHT NHIT NG CA CC CU T NH LUT TRNG THI TNG NG(LOI DES TATS
CORRESPONDANTS)Gii hn: nh lut ny ch l gn ng bc nht, thng gy ra sai
s ln c bit l nhngvnggnimtihn,phalngcngnhkhitnhtonpsut hi, t xut hin
thm nhng s hiu chnh khc nhau theo Zc hoc e.Zc: H s nn ti hn e: H s
quay (Facteur acentrique) eeo o08 , 0 291 , 0) 7 , 0 ( 1 log10 ==
=cr r rZT P P96 CHNG II: TNH TON CC TNH CHT NHIT NG CA CC CU T NH
LUT TRNG THI TNG NG(LOI DES TATS CORRESPONDANTS)Cc hiu chnh s dng
Zc Phng trnh Rackett: ( )( ) | |7 / 21 1 ,7 / 2,ln 1 lnrTccc Lc
rcLZPRTvZ Tvv += =||.|
\|oo( )| |vRTPZZL ccRaTRac,/. .oe== =+ 1 12 7029056 008775nu Z
Zsai scua phng phap la2.4%,hoc sdu ng cac giatrZtcac ngn hang
dliuRa cRaNhit ha hi theo phng php Watson 38 , 0,11||.|
\|=AAo rroTThhoo97 CHNG II: TNH TON CC TNH CHT NHIT NG CA CC CU
T NH LUT TRNG THI TNG NG(LOI DES TATS CORRESPONDANTS)Cc hiu chnh s
dng facteur acentrique e (Pitzer, 1955) Xc nh e: Tc, Pc v p sut hi
bo ha (Po) Tr=0,7 ( ) |.|
\| + = ~1 137lg11lg73TTPPTTPPccbcbceeo( ) ( )( )( )8 3 2) 1 (8 3
2) 0 () 1 ( ) 0 (008 . 0 423 . 0 331 . 0063 . 0000607 . 0 0121 . 0
1385 . 0 33 . 01445 . 0r r rrr r r rrr rccT T TT FT T T TT FT F T
FRTBP + = =+ = eD on h s B : |.|
\| =PRTv B98 CHNG II: TNH TON CC TNH CHT NHIT NG CA CC CU T NH
LUT TRNG THI TNG NG(LOI DES TATS CORRESPONDANTS)Bi tp ng dng : Xc
nh e, nhit si, Zc, ZRa, p sut hi v th tch lng bo ha ca nC5 50oC 99
CHNG II: TNH TON CC TNH CHT NHIT NG CA CC CU T NH LUT TRNG THI TNG
NG(LOI DES TATS CORRESPONDANTS)Phng php Lee v Kesler (1975) Bn cht
ca phng php: XRES(Tr,Pr) bin thin tuyn tnh theo e Ni suy tuyn tnh
cc gi tr XRES(Tr,Pr) da vo cc gi tr tng ng ca hai cu t i chng: Cu t
so snh nh (e = 0), l cc cu t CH4, Ar hoc Kr Cu t so snh nng,
n-octane, c e = 0.3978 Tnh cht th tch ca hai cu t ny c m t bi phng
trnh trng thi Bndict, Webb v Rubin c pht trin: rr rr r rrr rccrr r
r r r r rTdd DTcTcc CTbTbTbb BTv PZRTv Pvv v v TcvDvCvBZ2133 213423
212 2 2 345 2: nhitvao c phu thu D C, B, sthng Cacexp 1+ =+ = ==
=||.|
\|||.|
\|+ + + + + = |100 CHNG II: TNH TON CC TNH CHT NHIT NG CA CC CU
T NH LUT TRNG THI TNG NG(LOI DES TATS CORRESPONDANTS)Phng php Lee v
Kesler (1975) Thng sCu t so snh nh Cu t so snh nng Thng sCu t so
snh nh Cu t so snh nng b10.11811930.2026579c300.016901
b20.2657280.331511c40.0427240.041577
b30.154790.027655104.d10.1554880.48736
b40.0303230.203488104.d20.6236890.0740336
c10.02367440.0313385|0.653921.226
c20.01869840.05036180.0601670.03754 Cc thng s ca phng trnh trng thi
Bndict, Webb v Rubin 101 CHNG II: TNH TON CC TNH CHT NHIT NG CA CC
CU T NH LUT TRNG THI TNG NG(LOI DES TATS CORRESPONDANTS)Phng php
Lee v Kesler (1975) Phm vi ng dng: - Xc nh cc tnh cht d
(rsiduelles) khng th nguyn cc nhit v p sut cho: Z, hRES/RT, sRES/R,
(CP-Cp#)/R, ... - 0.3 Tr 4v0 Pr 10 - C th s dng i vi hn hp bng cc
xc nh cc thng s "gi ti hn" (Pseudo-critique)
Cc bc tnh ton: - Xc nh cc thng s thu gn (Tr, Pr, vr) ca cu t m
ta mun s dng phng php. - Xc nh cc tnh cht rsiduelles nh phng trnh
trng thi ( y ly v d l facteur de compressibilitZ) Z(0) ca cu t c e
= 0 (mtane) v Z(R) ca n-octane c e = 0.3978 tng ng vi cc thng s thu
gn (hoc tra bng) - Thc hin ni suy tuyn tnh theo e ( )( )( ) ( )( )(
)Z Z Z Z Z ZRRA + = + = eee0 0 0102 CHNG II: TNH TON CC TNH CHT
NHIT NG CA CC CU T NH LUT TRNG THI TNG NG(LOI DES TATS
CORRESPONDANTS)Phng php Lee v Kesler (1975) ln ... ln .... ln .PTT
TTT Trrr rrr roe= ++ +|\
|.|5927146 09648128862 0168347152518156875134721 0 4357766 Phng
php ny cng cho php tnh ton Po theo biu thc sau: Tnh ton n nhit bc
hi theo phng trnh Watson: 38 , 0,11||.|
\|=AAo rroTThhoo103 CHNG II: TNH TON CC TNH CHT NHIT NG CA CC CU
T NH LUT TRNG THI TNG NG(LOI DES TATS CORRESPONDANTS)Xc nh cc thng
s "gi ti hn" (Pseudo-critique) ca hn hp Quy tc Kay (1936) = =i c i
m c i c i m cP z P T z T, , , ,zi: Nng phn mol, C th p dng cho e
Phng php Lee-Kesler ==||.|
\| +=ii i mm cm cm c m ci jj c i cj c i cj im cm cxvRTZ PT Tv vx
xvTe e,,, ,, ,33 / 1,3 / 1,,,2133 / 1,3 / 1,,, ,,,, ,2085 . 0 2905
, 0 085 . 0 2905 , 0||.|
\| += = ==i jj c i cj i m cm m c i i ci ci ci c i cv vx x vZ
ZPRTZ ve e104 CHNG II: TNH TON CC TNH CHT NHIT NG CA CC CU T Ch yu
c s dng ch yu tnh s v cP, ngoi ra cng c s dng tnh cc thng s ti hn
do phn ny khng cn phi cp nhiu thm thm v cc gi tr ny c th tham kho
trong ngn hng d liu sn c: Ly v d: S HIU CHNH THEO CU TRCC N C N Cs
N s N s RPoi P ioij PjojPoi P ioij Pjoj= += + A AA AA A, ,, ,''
lnoooy:va 'lasong gop vaphn hiu chnh c tham khaotrong cac stay hoc
cac ngn hang dliuN :Snhom loai iN :Snhom hiu chnh loai j:Mc i xng
ni cua phn t(Tra bang) hoc tnh theo tng gc - CH ,mi gc co = 3ij3105
CHNG II: TNH TON CC TNH CHT NHIT NG CA CC CU T S HIU CHNH THEO CU
TRCp dng tnh ton cc thng s ti hn ( )( ) A + =A A + =i i ci i i icv
N mol cm vT N T NTT5 . 17 /965 . 0 584 . 032NhmAT (K)AV (cm3.mol-1)
Nhm mch thng -CH30.014165 -CH2-0.018956 >CH-0.016441 >CCCCTc:
Hyperbole: Kh l tng Phng trnh Clapeyron: Xa im ti hn: 2 gi thit -Th
tch lng Vl c th b qua -Pha hi c th xem l kh l tng Phng trnh
Clapeyron tr thnh: 122 I. CN BNG LNG HI Phng trnh Clapeyron sau khi
ly tch phn: Phng trnh Antoine: V d: i vi H2O i vi Ethane 123 I. CN
BNG LNG HI I.1.2. Gin Enthalpy Hnh 2: Gin enthalpy ca Ethane Khi
P
