Cong Nghe Che Bien Khi Thien Nhien Va Dong Hanh.diendandaihoc.vn

7/31/2019 Cong Nghe Che Bien Khi Thien Nhien Va Dong Hanh.diendandaihoc.vn

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Nguyn th Minh Hin

Cng ngh Ch bin

kh t nhin

v kh ng hnh

(Ti bn c sa cha v b sung)

Nh xut bn Khoa hc v k thut

H Ni 2004

Su tm bi:www.daihoc.com.vn


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Li Gii thiuLi Gii thiuLi Gii thiuLi Gii thiu

T thng 12 nm 1998 Nh my x lkh Dinh C, nh my x l khu tin ca nc ta chnh thc i vo hot ng, cung cp LPG phc v

cho cng nghip v dn dng. Cc d n Kh in m s I Vng Tu,

d n Kh in m s II C Mau v ang trin khai thc hin,

nhm s dng c hiu qu ngun nguyn liu kh thin nhin v kh ng

hnh ca t nc. Trc s pht trin ca ngnh cng nghip du kh ni

chung v ca ngnh cng nghip ch bin kh ni ring, nhu cu o to k

s v k thut vin hng nm ngy cng tng.

Cun Cng ngh ch bin kh thin nhin v kh ng hnh c bin

son nhm mc ch gii thiu cho cc k s, k thut vin v sinh vin

chuyn ngnh Cng ngh Ho du v kh nhng kin thc c bn v cc

phng php tnh ton hn hp cc hydrocacbon t C1 n C10 , H2O, CO2 ,

H2S, ... cc cu t chnh trong thnh phn kh t nhin v kh ng hnh,phc v cho vic tnh ton thit k cc qu trnh cng ngh x l kh. ng

thi cun sch cng cp n mt s qu trnh cng ngh chuyn ho kh

t nhin v kh ng hnh thnh cc hp cht ch yu s dng lm nguyn

liu cho cng ngh tng hp hu c - ho du.

Cun sch c chia lm ba phn:

Phn I: Thnh phn v tnh cht ca kh t nhin v kh ng hnh.

Trong phn ny gii thiu thnh phn, tnh cht v phng php tnh ton

cc i lng nhit ng ca hn hp kh t nhin v kh ng hnh. Trong

mi chng u c cc bi ton v d p dng lm sng t l thuyt, cngc cc kin thc c bn. Tc gi cng a vo trong phn ny cc th

thc nghim rt cn thit cho vic tnh ton thit k cng ngh.

Phn II: Cc qu trnh cng ngh c bn ch bin kh, bao gm cc

cng ngh lm sch kh khi cc tp cht (tch bi, lm ngt kh, sy kh) v

cc qu trnh cng ngh ch bin hin ang c s dng ph bin. l



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cc qu trnh cng ngh ngng t nhit thp, hp th nhit thp v

chng ct nhit thp. Tu theo thnh phn hn hp kh a vo ch bin

v yu cu mc tch cc cu t nh trc m la chn gii php cng

ngh thch hp. Ln ti bn ny c b sung cng ngh ca Nh my x l

kh Dinh C (B Ra Vng Tu).

Phn III: Chuyn ho kh t nhin v kh ng hnh, bao gm cc qu

trnh cng ngh c bn chuyn ho kh thnh kh tng hp, metanol,

amoniac, axetylen..., l nhng nguyn liu quan trng cho tng hp hu c -

ho du.

Mc d tc gi dnh nhiu n lc nhng do bin son ln u, nn

chc khng trnh khi cn thiu st. Rt mong cc bn ng nghip v bn

c gp b sung cun sch c hon thin hn trong cc ln ti bn

sau.

GS. TS. o Vn Tng



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Mc lc

Li gii thiu 3

Cc k hiu dng trong sch 9

Phn IThnh phn v tnh cht ca kh t nhin

v kh ng hnh 11Chng I

Gii thiu v kh t nhin v kh ng hnh 13

I.1. Thnh phn v cc c tnh ca kh t nhin v kh ng hnh 13I.2. Ch bin v s dng kh t nhin v kh ng hnh trn th gii 15I.3. Ch bin v s dng kh t nhin v kh ng hnh Vit Nam 17

Chng II

Cc tnh cht ca kh t nhin v kh ng hnh 19

II.1. Phng trnh trng thi ca cc hydrocacbon 19II.2. Gin pha h mt cu t 21II.3. Gin pha h nhiu mt cu t 24II.4. Cn bng pha lng hi 27II.5. Phng php gii tch xc nh hng s cn bng pha ca hn hp

cc hydrocacbon 31II.6. Phng php gin xc nh hng s cn bng pha ca hn hp

cc hydrocacbon 40II.7. ng dng ca hng s cn bng pha 51

Chng III

Cc thng s nhit ng ca cc hydrocacbonring bit v hn hp ca chng 55

III.1. Nhit si v p sut hi bo ho 55



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III.2. Cc i lng ti hn 58

III.3. Thng s acentric 72

III.4. Cc tnh cht ca hydrocacbon trng thi lng 73

Chng IV

Tnh cht ca h hydrocacbon v nc 77

IV.1. Hm m ca kh 77

IV.2. Cc phng php xc nh hm m ca kh 77

IV.3. nh hng ca nit v cc hydrocacbon nng n hm m ca kh 92IV.4. Hm m cn bng ca cc hydrat 93

IV.5. S to thnh hydrat 94

IV.6. D on kh nng to thnh hydrat 97

Phn IICc qu trnh cng ngh c bn ch bin kh 111

Chng V

Chun b kh ch bin 113

V.1. Lm sch kh khi cc tp cht c hc 113

V.2. Cc phng php hn ch s to thnh hydrat trong qu trnh ch

bin kh 116

V.3. Lm sch kh khi H2S v CO2 (lm ngt kh) 127

Chng VI

Ch bin kh bng phng php ngng t 131

VI.1. S ngng t nhit thp c chu trnh lm lnh ngoi 132

VI.2. S ngng t nhit thp c chu trnh lm lnh trong 143

VI.3. S ngng t nhit thp c chu trnh lm lnh t hp 147



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Chng VII

Ch bin kh bng phng php hp th 155

VII.1. S nguyn l cng ngh ch bin kh bng phng php hp th 155

VII.2. Cc thng s cng ngh ca qu trnh ch bin kh bng phng

php hp th nhit thp 159

VII.3. Cc phng trnh c bn tnh ton qu trnh hp th 162

VII.4. Cc s cng ngh hp th nhit thp hin i 166

Chng VIII

Ch bin kh bng phng php chng ct 176

Chng IX

Phm vi ng dng ca cc qu trnh ch bin kh 181

Phn III

Chuyn ho kh t nhin v kh ng hnh 185Chng X

Oxy ho ghp i metan 187

X.1. Xc tc v c ch qu trnh oxy ho ghp i metan 187

X.2. Cc thit b phn ng nghin cu qu trnh oxy ho ghp i metan 192

Chng XI

Cc cng ngh chuyn ho metan thnh kh tng hp 194

XI.1. C ch qu trnh 194

XI.2. Cc qu trnh cng ngh c bn 195

XI.3. Cc qu trnh cng ngh pht trin 202

XI.4. So snh v nng lng v gi c 204



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Chng XII

Cng ngh tng hp metanol 206

XII.1. Cng ngh tng hp metanol trc tip t metan 206

XII.2. Cng ngh sn xut metanol t kh tng hp 209

Chng XIII

Cng ngh tng hp amoniac 223

XIII.1. C s ho l ca qu trnh tng hp amoniac 223

XIII.2. Cng ngh tng hp amoniac 227

Chng XIV

Cng ngh tng hp axetylen 233

XIV.1. C s ho l ca qu trnh phn hu hydrocacbon sn xut

axetylen 233

XIV.2. Cng ngh sn xut axetylen 242

Ph lc 257

Ph lc 1.Hng s cn bng pha K 259

Ph lc 2. Cc h n v o v quan h gia chng 263

Ti liu tham kho 288



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Cc k hiu dng trong sch

Tha s acentric

T trng

H s hiu chnh i vi kh chua

i H s fugat ca cu ti

i H s hot ca cu ti

ai Hot ca cu ti

C3 Cc hydrocacbon parafin t propan tr ln

fi Fugat ca cu ti

fiK Fugat ca cu ti trng thi kh

fiL Fugat ca cu ti trng thi lng

fio Fugat ca cu ti tinh khit

fw Fugat ca hi nc

gi Khi lng ca cu ti

kHng s tc ca phn ngKP Hng s cn bng ca phn ng

Ki Hng s cn bng pha ca cu ti

Kr-k Hng s cn bng rn - kh

Mi Khi lng phn t ca cu t i

ni S mol cu ti

P p sut, MPa (h SI), psi (h Anh)P* p sut hi ca hn hp nhit T= 0,7TcPc p sut ti hnP

c

p sut gi ti hn (ca hn hp)Pci p sut ti hn ca cu tiPqt p sut quy tPr p sut rt gnPr p sut gi rt gn (ca hn hp)Q Hiu ng nhit, kJ/mol



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t Nhit , oC (h SI), oF (h Anh)

T Nhit tuyt i, K

Tc Nhit ti hn

Tc Nhit gi ti hn (ca hn hp)

Tci Nhit ti hn ca cu ti

Tr Nhit rt gn

Tr Nhit gi rt gn (ca hn hp)

v

i Nng phn th tch ca cu t i

Vc Th tch ti hn

Vc Th tch gi ti hn (ca hn hp)

Vci Th tch ti hn ca cu tiVi Th tch ca cu ti

Vr Th tch rt gn

Vr Th tch gi rt gn (ca hn hp)

W Hm m ca hn hp kh chua

W1 Hm m ca CO2

W2

Hm m ca H2SWhc Hm m ca hn hp cc hydrocacbon (kh ngt)

xi Nng phn mol ca cu t i

xi Nng phn khi lng ca cu ti

xw Phn mol ca nc trong pha lng

yw Phn mol ca nc trong pha hi

z H s chu nn

Cc ch vit tt

LPG (Liquefied Petroleum Gas) Kh ng hnh ho lng

LNG (Liquefied Natural Gas) Kh t nhin ho lng

CNG (Compressed Natural Gas) Kh t nhin nn



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phn I

Thnh phn v tnh chtca kh t nhin v kh ng hnh



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Chng I

Gii thiu v kh t nhin v kh ng hnh

I.1. Thnh phn v cc c tnh ca kh t nhin v

kh ng hnh

Nhng cu t c bn ca kh t nhin v kh ng hnh l: metan, etan,propan, butan (normal v izo ). Kh t nhin c khai thc t cc m kh,

cn kh ng hnh c khai thc t cc m du ng thi vi qu trnh khai

thc du m. Trong kh t nhin thnh phn ch yu l metan (chim n

98% theo th tch). Cc m kh t nhin l cc ti kh nm su di mt t.

Kh ng hnh nhn c t cc m du cng vi qu trnh khai thc

du m. Trong thnh phn ca kh ng hnh ngoi cu t chnh l metan

cn c etan, propan, butan v cc hydrocacbon nng vi hm lng ng k.

Thnh phn nhng cu t c bn trong kh thay i trong mt phm vi kh

rng tu theo m du khai thc. Ngoi ra trong thnh phn kh t nhin v

kh ng hnh cn c H2O, H2S cng cc hp cht cha lu hunh, CO2, N2

v heli.

Ngi ta cn phn loi kh theo hm lng hydrocacbon t propan tr

ln. Kh giu propan, butan v cc hydrocacbon nng (trn 150 g/m3) c

gi l kh bo (hoc kh du). T kh ny ngi ta ch c xng kh, kh

ho lng (LPG) v cc hydrocacbon cho cng ngh tng hp hu c. Cn kh

cha t hydrocacbon nng (t propan tr ln, di mc 50 g/m3) gi l kh

kh (hoc kh gy), c s dng lm nhin liu cho cng nghip v i

sng, lm nguyn liu cho cng ngh tng hp hu c, nguyn liu cho sn

xut phn m, sn xut etylen, axetylen, etanol ...Tr lng kh c th pht hin c tnh vo khong 1.300 t m3 kh. Tr

lng ny phn b trn ton lnh th nhng ch yu l cc b Nam Cn

Sn, Sng Hng, Malay - Th Chu. Trong cc bng I.1, I.2, I.3 di y cho

thnh phn kh t nhin v kh ng hnh khai thc c mt s m ca

Vit Nam.



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Bng I.1. Thnh phn kh b Cu Long (% theo th tch)

Rng (l 09)M

Thnh phn

Bch H

(l 09) Kh t do ng hnh

Rng ng

(l 09)

Ruby

(l 01)

Metan C1

Etan C2

Propan C3

Butan C4

Condensat C5+

N2CO2

H2S

76,82

11,87

5,98

1,04

0,32

0,501,00

84,77

7,22

3,46

1,70

1,30

76,54

6,89

8,25

0,78

0,50

77,62

10,04

5,94

2,83

0,97

0,330,42

78.02

10,67

6,70

1,74

0,38

0,600,07

Bng I.2. Thnh phn kh b Nam Cn Sn (% theo th tch)

M

Thnh phn

i Hng(05-1a)

Lan Ty(06-1)

Lan (06-1)

Rng i(11-2)

Hi Thch(05-2)

Mc Tinh(05-3)

Metan C1

Etan C2

Propan C3

Butan C4

Condensat C5+N2CO2

H2S

77,25

9,49

3,38

1,34

0,48

4,50

88,5

4,3

2,4

0,6

1,4

0,3

1,9

10,0

93,9

2,3

0,5

0,1

0,2

1,6

1,2

Cha o

81,41

5,25

3,06

1,47

0,55

0,08

5,64

0,00

81,00

5,20

2,8

1,50

4,70

0,11

4,40

89,44

3,80

1,48

0,71

0,54

0,15

3.88

Bng I.3. Thnh phn kh b Malay Th Chu (% theo th tch)

Thnh phn PM3 UNOCAL L Ty Nam

Metan C1

Etan C2

Propan C3Butan C4

Condensat C5+

N2CO2

H2S

77,91

6,86

4,091,98

0,42

0,80

7,86

89,65

2,74

0,400,17

0,05

2,14

4,38

89,42

4,26

2,381,12

0,32

0,34

1,88

24 ppm



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Hm lng CO2 b Sng Hng cao 75 85%. Hm lng H2S, CO2 rtnh trong kh ng hnh m Bch H, Rng, i Hng... l rt thun li choch bin v s dng, an ton thit b v khng gy nhim mi trng.

I.2. Ch bin s dng kh t nhin v kh ng hnhtrn th gii

Kh t nhin v kh ng hnh c khai thc t trong lng t l hnhp cc hydrocacbon ca dy metan gm c: metan, etan, propan, butan...Ngoi ra trong thnh phn ca kh cn c: He, N 2, CO2, H2S... S lng vhm lng cc cu t thay i trong nhng khong rng.

Metan l thnh phn chnh trong kh t nhin, c s dng ch yu lmnhin liu cho l nung v ni hi. Etan, propan, butan v hydrocacbon nngdng ch yu cho cng nghip tng hp hu c. V vy CHLB Nga v ccnc cng nghip pht trin, vic s dng hp l cc hydrocacbon c ngha rt to ln.

Kh ng hnh v kh t nhin l ngun chnh cung cp cc nguyn liu

quan trng cho cng nghip ho hc v ho du, v d etan. M t etan ch bin 40% etylen phc v cho sn xut nha tng hp, oxit etylen, chthot ng b mt, nhiu sn phm v bn sn phm ho hc khc (hin nay

ngi ta nh gi mc pht trin cng nghip tng hp hu c theo tngsn lng v nhu cu etylen). M do s dng etylen vi hiu qu cao vocui nhng nm 60 ca th k trc nn sn xut etan tng 24 31%. M v Canaa, vn chuyn etan ngi ta xy dng nhng h thngng ng dn khng l. V d nm 1977 hon thnh vic xy dngng ng di gn 3 ngn kilmet vn chuyn etan, etylen, propan vbutan t min Ty sang min ng Canaa v sang c M (cng sut ca

ng ng l 2,2 ... 2,4 triu tn/nm, p sut lm vic 10 MPa). cc ncTy u, sau khi tm ra cc m kh t nhin ln tng cng s quan tmn cc nguyn liu nhit phn nh, bi v s dng etan trong cng nghip

ho hc v cng nghip ho du hiu qu v c c s cn bng gia snxut v nhu cu etylen. Mt khc butadien v cc sn phm ph khc caqu trnh nhit phn benzin cng l cc nguyn liu rt cn thit.

Vic s dng etan cho php gim u t vo sn xut etylen, rt ngnthi hn xy dng cc dy chuyn cng ngh ho hc v ho du khp kn(etylen - polyetylen, etylen - ru etylic, ...), bi v khi nhit phn etan chohiu sut sn phm ph ti thiu (hiu sut etylen t etan l 70%, t benzin



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l 27%, t gazoil l 15%).

Thc t nhiu nc trn th gii cho thy rng, vi tr lng du vkh t nhin ln, c th t chc sn xut quy m ln c li nhun cao ccsn phm etan, kh ho lng (LPG, LNG), cc hydrocacbon khc, v nhinliu cho ng c. Do hiu qu cao ca nhin liu kh v s quan tm ngycng tng n cc sn phm ca n trn th trng th gii, nhiu nc khaithc du kh xy dng, m rng v trang b li cc nh my ch bin kh.

Trong nhng nm gn y cc nc Trung ng (Iran , rp Xut,

Baren, ...) d nh hon thnh chng trnh v khai thc, ch bin v vnchuyn kh ng hnh vi tng gi tr khong 33 t USD. Ngi ta cho rngiu cho php xut khu khong 46 triu tn LPG mi nm.

Mt trong nhng vn ca chng trnh l xy dng nhng nh myc cng sut ln sn xut etylen, polyetylen, styren, v cc sn phm ho

du khc. rp Xut d nh s t 8% tng sn lng th gii v nhng snphm . Trong nm 1978, cc nc t bn (tr M) u t 3,2 t la xy dng nhng nh my ch bin kh, chim khong 50% tng s u tcho cng nghip ch bin du.

Kh t nhin v kh ng hnh khng ch l nhin liu v nguyn liu

sn xut etan, propan, v cc hp cht khc. Khi lm sch v ch bin khngi ta cn nhn c mt lng ln lu hunh, heli v mt s sn phmv c khc cho nhiu ngnh kinh t quc dn. Canaa l nc ng th haitrong s cc nc pht trin v sn xut cc hp cht cha lu hunh t cngnghip ch bin kh t nhin. M ng u v sn xut heli, mt trongnhng sn phm quan trng nht trong cng ngh nghin cu v tr, nghincu kh quyn, k thut thm lnh, sc k, ...

M c 12 nh my sn xut heli vi tng sn lng 135 m3/nm. Nhucu v heli nm 1980 l 35 triu m3, n nm 1999 l 60 triu m3. Theochng trnh quc gia di hn, ton b s heli d tha t cc nh my ch

bin kh c bo qun di lng t cho n khi tr lng heli t kh tnhin v kh ng hnh cn s c mang ra s dng, bi v tch heli tkhng kh c chi ph cao hn rt nhiu.

Trong nhng nm gn y, nhiu nc c xu hng tng cng sut ccnh my ch bin kh. Ti cc nh my ch bin kh mi xy dng, ngi ta lp t cc thit b mi thc hin ng thi mt vi qu trnh cng nghch bin kh. C nhng nh my ti cc qu trnh cng ngh c bn c



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thc hin trong mt bloc. M v Canaa c dy chuyn cng ngh vicng sut 4 t m3/nm, nh gim vn u t, gim nhn cng phc v vtng tin cy ca cc nguyn cng trong nh my ch bin kh.

Tng cng sut cc nh my ch bin kh tng nhp pht trin cacng nghip ch bin kh. iu cn ph thuc rt nhiu yu t nh: cngngh ch to thit b, vn khai thc v vn chuyn kh, s dng nguynliu v sn phm. l nhng vn rt phc tp, gii quyt cn phixut pht t iu kin s dng hp l ngun ti nguyn kh t nhin v khng hnh ca tng nc.

I.3. Ch bin v s dng kh t nhin v kh ng Hnh Vit nam

Cho n nay Vit Nam ang khai thc 6 m du v 1 m kh, hnh thnh4 cm khai thc du kh quan trng:

Cm m th nht nm vng ng bng Bc B, gm nhiu m kh

nh, trong c Tin Hi C, tr lng khong 250 t m3 kh, bt ukhai thc t thng 12 nm 1981 vi trn 450 triu mt khi kh phc v cngnghip i phng. Vi cc pht hin mi trong khu vc ny, y l c snguyn liu cho cng nghip kh cc tnh pha Bc.

Cm m th hai thuc vng bin Cu Long, gm chui 4 m du:Bch H, Rng, Rng ng, Ru Bi, l cm quan trong nht hin nay, cungcp trn 96% sn lng du ton quc.

Hin nay m Bch H v m Rng c 21 gin khai thc ln nhang hot ng vi hn 100 ging khoan khai thc v bm p. Kh nghnh t c thu gom v a vo b bng ng ng dn di 110 km.

Thng 4 nm 1995 cung cp 1 triu m3 kh / ngy cho nh my in B Ra.

Nm 1997 tng ln 2 triu, ri 3 triu m3 kh / ngy cung cp cho nhmy in Ph M 2.1 v Ph M 2.1 m rng.

Thng 10 nm 1998 nh my x l kh Dinh C t mc thit k 4,2 trium3 kh / ngy.

Thng 12 nm 1998 bt u sn xut LPG. Hin nay mi ngy nh myDinh C gom, nn, x l kh t mc 4,6 ... 4,7 triu m 3 / ngy (khong 1,5 tm3 / nm) sn xut 800 tn LPG, 350 tn condensat.

ng thi khu vc ny cng v ang nghin cu tng cng sutchung ca h thng ln trn 2 t m 3 / nm.



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Cm m th ba vng bin Nam Cn Sn gm m du i Hng angkhai thc v cc m kh pht hin khu vc xung quanh l Lan Ty, Lan, Hi Thch, Mc Tinh v m du kh Rng i Ty... ang chun b avo khai thc.

Ring m kh Lan Ty - Lan vi tr lng xc minh l 58 t m 3 scung cp n nh lu di mc 2,7 t m 3 kh / nm.

Trong vi nm ti y khu vc ny s l cm khai thc v cung cp khln nht Vit Nam, m bo cung cp 5 n 6 t m 3 / nm.

Theo d kin ca PetroVietnam, trong khong thi gian t 2003 n

2010, cm m du kh vng bin Cu Long v Nam Cn Sn c th cungcp 6 n 8 t m3 kh / nm s l c s nguyn liu cho cm cng nghip dukh B Ra Ph M v Dung Qut.

Cm m th t ti thm lc a Ty Nam bao gm m Bunga Kekwa Ci Nc ang khai thc du, m Bunga Orkid, Bunga Parkma, Bunga Rayati khu vc tho thun thng mi Vit Nam - Malaysia s l khu khai thcv cung cp kh ln th hai v s l c s m bo s pht trin khu cngnghip du kh C Mau - Cn Th.

L PM-3-CAA bt u khai thc du t thng 8-1997. K hochpht trin kh v cc iu kin thng mi tho thun cho php hy vng

vic khai thc kh s c th bt u t cui 2003 vi sn lng khong 2,5 tm3/ nm cho hai pha trong thi gian t nht 15 n 17 nm, thm ch c th25 n 30 nm. V ngoi phn tr lng xc minh l 47 t m3 cn c phntim nng (khong 60 t m3) c th c xc minh trong nhng nm ti.

Cc l 46, 50, 51 lin k khoan 11 ging thm d, trong c 8ging pht hin du, c bit l kh. Nu c cc gii php thch hp, giiquyt cc kh khn (m nh, nhiu CO 2, ...) l 46 vi tr lng 15 ... 20 tm3 c th cung cp khong 1 t m 3 / nm.

L B + 48/95 + 52/97 giao thu cho UNOCAL c nh gi cth c ti 160 t m3, hy vng m bo cung cp di hn 2 ... 5 t m 3 / nm.

Ni chung kh t nhin v kh ng hnh ca Vit Nam cha rt t H 2S

(0,02 g /m3) nn l loi kh sch, rt thun li cho ch bin, s dng an tonvi thit b v khng gy nhim mi trng.

Vi tim nng v kh kh phong ph nh vy, nc ta c iu kin phttrin cng nghip du kh trn ton lnh th. Khai thc v s dng hp lngun ti nguyn thin nhin qu gi ny, trong tng lai ngnh cng nghipdu kh s l mt ngnh cng nghip pht trin mnh, ng gp ng k vos pht trin ca t nc.



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Chng II

Cc tnh cht ca kh t nhin v kh ng hnh

II.1. Phng trnh trng thi ca cc hydrocacbon

Cc tnh cht vt l ca kh t nhin v kh ng hnh ph thuc vocc thng s ca hn hp v thnh phn ho hc ca n. Thnh phn ca h

nhiu cu t c th biu din bng nng theo khi lng (xi), theo mol(xi), hoc theo th tch (vi). Nh vy nu gi l khi lng ca cu t th itrong hn hp th nng phn khi lng ca cu t i s c biu dinbng biu thc sau:

= iii ggx (II.1)

Tng t, ni l s mol cu t th i trong hn hp kh th nng phnmol ca cu t thi s c biu din bng biu thc:

= iii nnx (II.2)

Vi l th tch cu t th i trong hn hp kh th nng phn th tch

ca cu ti c biu din bng biu thc sau:

= iii VVv (II.3)

Gia cc nng c quan h vi nhau v c th tnh chuyn i t nng ny sang nng khc.

Khi tnh ton cng ngh qu trnh ch bin kh, cn thit phi xc nhtnh cht nhit ng ca cc cht v hn hp ca chng nh entanpi, entropi,t trng, fugat.

xc nh cc i lng trn, ngi ta s dng phng trnh trng thixc nh quan h gia nhit , p sut v th tch ca h.

Vi h kh l tng chng ta c phng trnh trng thi:PV = nRT (II.4)

Tnh cht nhit ng ca kh t nhin, kh ng hnh v cc cu t cachng rt khc vi tnh cht ca kh l tng, c bit nhit thp v psut cao. V vy khng th s dng phng trnh trng thi kh l tng xc nh cc tnh cht ca chng. Do , c rt nhiu phng trnh trng thim t h kh thc.



19/292


Phng trnh Van der Waals:

(P + a/v2 ) (vb) = RT (II.5)

trong : a, b l cc hng s tng quan; vl th tch mol.

Phng trnh Benedict - Webb - Rubin (BWR): phng trnh c cha 8hng s:

P = RT+ ( B0RTA0C0/T2 ).2 + (bRTa).3

+ a6 + (c3/T2 ).(1 + 2 ) e2 (II.6)

trong : A0,B0, C0, a, b, c, v l cc hng s quan h;

P l p sut;Tl nhit tuyt i; l t trng mol.

Phng trnh Redlich - Kwong (RK):

)(5,0 bT

a

b

RTP

+

=

vvv

(II.7)

trong : a, b l cc hng s quan h; v l th tch mol.

Phng trnh Peng - Robinson (PR).

)()(

)(

bbb

Ta

b

RTP

++

=vvvv

(II.8)

trong : a, b l cc hng s quan h; v l th tch mol.

Cc phng trnh BWR, RK v PR cn c gi l cc phng trnhtrng thi lp phng v khi vit cho th tch chng cha m lp phng.

Cc hng sa, b l hm ca nhit ti hn Tc , p sut ti hn Pc v

tha sgi l tha s acentric. Tha sc xc nh t phng trnh sau:

= logPr 1 (II.9)

trong : Pr =P*/Pc (II.10)

P* l p sut hi T= 0,7Tc;Pc l p sut ti hn; Tc l nhit ti hn.

Tha sc s dng ph bin nh mt cng c hiu chnh s sailch trong phng trnh trng thi kh thc.

Ngi ta cn a ra thng s hiu chnh z v phng trnh trng thi cdng n gin:

PV = zRT (II.11)

trong z l hm s ca cc thng s ca cc phng trnh trng thi ni trn.



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Phng trnh trng thi c th vit li di dng:

zRT

MWP )).((= (II.12)

trong (MW) l khi lng phn t trung bnh ca hn hp kh.

Phng trnh (II.12) dng khi cn tnh ton t trng ca kh nhit Tv p sut P.

Cc hng s v cc thng s tnh ton c th tm c trong cc tiliu v trong cc s tay.

II.2. Gin pha h mt cu t

Trn hnh II.1 l gin pha ca cht tinh khit (h mt cu t) theo hba trc to P, V, T. Cc min tn ti hai pha: BDHG - lng v rn, FGIJ -rn v hi, HCI - lng v hi.

Hnh II.1. Gin P V T ca h mt cu t

Cc min ny vung gc vi trc nhit . Min ch c pha lng l minvch pha bn tri min HCI v lin k min BDHG. Min ch c pha hi lsn dc pha bn phi ca min HCI. Tt c cc min u ng ch ,

Th tch

Rn

LngRn+

Lng Lng+ Hi

Rn + Hi

psut

NH

tI

Hi



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nhng c bit quan trng l min HCI. Ngi ta c th biu din trn h hai

trc to P T hoc P V. Tt c cc min hai pha u vung gc vi trc

nhit nn s l cc ng cong trong to P T nh trn hnh II.2.

Hnh II.2. Gin P T ca h mt cu t

ng HD, HC v FH l cc ng cn bng, bao gm tp hp cc gitr p sut, nhit , ti c cn bng pha.

im H l im duy nht ti nhit v p sut xc nh ng thi tnti ba pha cn bng vi nhau. Ti ng cn bng nhit v p sutkhng i h c th chuyn pha bng cch thm vo hoc ly bt nng lngca h.

Dc theo ng FH khng tn ti pha lng, v pha rn thng hoa thnhhi. Dng CO2 rn ("nc kh") lm lnh l mt v d. HD l ng

cn bng rn lng. Trng thi nc 00C (320F) v p sut kh quynthuc ng ny. ng HD c th dc theo chiu dng hay chiu m tuthuc vo cht lng co ngt hay gin n khi lm lnh. Nng lng thay idc theo ng HD gi l nhit nng chy. Ti bt k gi tr P v T dc theong ny, trng thi ca h c th hon ton lng hoc hon ton rn hochn hp rn - lng tu thuc vo mc nng lng ca h. ng HD cgi l ng bo ho rn - lng hoc ng cn bng rn - lng.

ng HC l ng bo ho hoc cn bng gia hai pha lng v hi.

nhit

psut

im ba

Hi qu nhit hockh

Rn

Lng

Hi

Cht lng cht



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im C l im ti hn ng vi nhit ti hn TC v p sut ti hn PC. Tiim ny, cc tnh cht ca lng v hi tr thnh ng nht. i vi ncht, im ti hn c th c nh ngha l im m pha trn n, pha lngkhng th tn ti nh mt pha c lp. Ni cch khc, pha trn im ti hnkh khng th b ho lng bng cch nn p sut cao. Pha trn im C hc m t nh pha lng cht (dense fluid) khc vi pha hi v lng thngthng (liquid).

ng HC thng c gi l ng p sut hi. Cng c khi c gil ng cong im sng, v ng cong im bt ca n cht. Xem xt

qu trnh chuyn pha ng p trn hnh II.2. T "m" n "n" h trng thirn. H hon ton trng thi lng trong khong o - b. Ti "b", h trngthi lng bo ho. Bt k s cung cp nng lng s lm lng ho thnh hi nhit v p sut khng i. Ti "d", h trng thi hi bo ho. Tiptc tng nhit s nhn c hi qu nhit.

Ti cc gi tr p sut v nhit trn ng HC h c th tn ti honton trng thi lng bo ho hoc hi bo ho hoc hn hp lng hi. iukin h tn ti trng thi pha no ph thuc vo mc nng lng p sut v nhit xc nh.

Hnh vung "bfghd" trn hnh II.2 m t tnh cht pha quan trng khc

c xc minh bng thc nghim. Gi s trong bnh cha c ca s c y mt cht lng no . t bnh cha ti iu kin ca im b v chiuvo ca s cho d quan st. Tng p sut nhit khng i (nn ngnhit), i t "b" ti "f" nh sng s b m i. Ti mt im no (tng tnh khi chng ta nhy mt) nh sng hon ton bin mt. Khi ny, trongbnh cha c mt ci g ging nh hi nhng khng to bt nh vnthng thy. Ti "f" pha trn im ti hn C, h tn ti trng thi phath t, trng thi pha c bit khng th m t nh cc gic quan, thngc gi l pha lng cht (dense fluid) khc vi pha lng thng thng(liquid). Tuy nhin pha lng ny cng c th chy thnh dng v c sdng nh kh v lng thng thng. Pha lng ti "f" trng ging nh khnhng tnh cht li khc vi kh thng thng bn phi ng HC v phadi PC: n c t trng ln hn kh nhng chu nn cao hn lng thngthng.

T "f" c th thc hin qu trnh ng p ti "g", gim p ng nhit ti"h" v sau ng p ti "d". Nh vy chuyn t lng bo ho sang hibo ho m khng c s chuyn pha no c. C th i thng t "b" n "d"



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bng cch thm nng lng vo cht lng p sut khng i. Khi ny trongbnh cha s thy cc bt kh to thnh. Tip tc b sung nng lng lng schuyn thnh hi hon ton, khng c s thay i nhit khi i t "b"(lng bo ho) ti "d" (hi bo ho).

T im nhit ti hn tc trn trc nhit (hnh II.1) i ti im tihn C, tc l tip xc vi ng bao pha HCI. Cc ng nhit nmgia cc ng cong HC v CI bn trong ng bao pha tng ng vi psut khng i, l c trng c bn ca gin pha h 1 cu t. ngcong p sut hi ca cc hydrocacbon nh c a ra trn hnh III.1 v

III.2. l cc ng cong HC trn hnh II.2.

II.3. Gin pha h nhiu cu t

i vi h nhiu cu t, v tr ca cc ng cong trn gin pha phthuc vo thnh phn ca hn hp. Vi h mt cu t, ng bao pha HCIto thnh min l mt mt phng. i vi h nhiu cu t hn hp cc cht,ng bao pha to thnh khng phi mt mt phng m c chiu dy nhhnh ci li. Thnh phn l bin s phn nh chiu dy ca bao pha. Nuthay trc th tch trn hnh II.1 bng trc thnh phn v sau lp gin p sut - nhit phn lng - hi ca gin pha h nhiu cu t s nhn

c hnh II.3.

Hnh II.3. Gin pha in hnh h nhiu cu t

ng ABDE biu din qu trnh ngng t ng nhit suy bin inhnh trong cc m kh condensat. im A biu din pha lng cht (fluid)nm bn ngoi ng bao pha. Khi gim p sut ti im B, bt u qu

sut

Nhit

Min suy bin

im bt

im sng



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trnh ngng t. Tip tc gim p sut, lng lng hnh thnh nhiu hn, v cs i hng ca cc ng t l lng - hi (quality lines - cc ng nt ttrn hnh II.3). Min suy bin (retrograde region) c to bi cc im thayi dc ca cc ng ny. Trong min suy bin, s ngng t lng xy rakhi gim p sut hoc tng nhit (ngc vi s ngng t thng thng).Tip tc gim p sut, ra khi min suy bin, i t D ti E, lng lng gimdn cho ti khi t im sng (im E). Pha di im E khng cn trngthi lng, ch cn trang thi hi.

im ti hn C ca hn hp kh hydrocacbon lun lun pha bn tri

ca im N (cricondenbar - im ng vi p sut cc i s hnh thnh phalng v pha hi). V tr ca im C l quan trng nht, iu lin quan ns thay i hng ca cc ng lng hi bn trong ng bao pha. imti hn C i khi c th bn phi im N, nh biu din trn hnh II.4. Khi s c hai min suy bin. Nhng hnh II.3 biu din gin pha in hnhvi hu ht cc h nhiu cu t c tnh ton trong cc qu trnh cng ngh.

Hnh II.4.nh hng ca thnh phn n ngbao pha ca h bc hai etan - propan

Hnh II.5. V tr qu tch ti hn camt s h bc hai

Nhit Nhit

psut

psut



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Lu rng cc gi tr gi ti hn tnh ton c trong chng III khngphi l im C trn hnh II.3 tr trng hp ngu nhin. Trn hnh II.4 lgin pha ca h bc hai metan - propan, cho thy nh hng ca thnhphn n hnh dng v v tr ca ng bao pha. Hai ng cong ngoi cngl cc ng p sut hi ca metan v propan, bt u t im ti hn. Bang bao pha cn li l ca ba hn hp c t l thnh phn metan - propankhc nhau. ng nt t l ng ni tt c cc im ti hn trn ming bao pha, c gi l qu tch ti hn, bt u t im ti hn cametan, kt thc ti im ti hn ca propan. Nh vy v tr im ti hn trn

mi ng bao pha thay i theo thnh phn ca hn hp cc hydrocacbon.Hnh II.4 v II.5 cho thy nh hng ca thnh phn hn hp n v tr

v hnh dng ng bao pha. D on chnh xc v iu kin hnh thnh im btv im sng, im ti hn l rt quan trng khi tnh ton thit k cng ngh.

Hnh II.6.nh hng ca CO2,H2S n ng bao pha ca kh t nhin

psut

Nhit c) N2Nhit

b) H2S

Nhit a) CO2

psut

psut



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Cc tp cht khng hydrocacbon trong kh nh nc, CO2, H2S, N2 cnh hng ng k n ng bao pha. Nc c p sut hi thp v khngtan ln trong hydrocacbon lng nn ch nh hng n ng bao pha ca

hn hp iu kin nhit cao v p sut thp. nh hng ca H2S, CO2v N2 n ng bao pha c m t trn hnh II.6. CO 2 v H2S lm gimim p sut cc i tn ti hi v lng (cricondenbar) ca hn hp. Cc cut khc trong kh t nhin nh etan, propan v butan cng c nh hngtng t. Mt khc, N2 li lm tng im p sut cc i tn ti hi v lng(cricondenbar) ca hn hp v gim kh nng trn ln.

II.4. cn bng pha lng - hi

Nhiu qu trnh cng ngh c thc hin iu kin c cn bng phalng - hi nh cc qu trnh chng ct, hp th. Trn thc t, tnh ton ccqu trnh trn khng hon ton t c trng thi cn bng pha v thi giantip xc gia hai pha lng v hi cha thit lp cn bng. thuntin cho vic tnh ton, ngi ta cn a ra tha s hiu chnh.

Cn bng pha khng phi trng thi tnh m l cn bng ng, vn luntn ti s chuyn ng ca cc phn t t pha lng sang pha hi v ngc

li. Tc bay hi v ngng t l bng nhau.i lng c trng cho s phn b ca cc cu t gia cc pha iu

kin cn bng l hng s cn bng pha Kc xc nh bng phng trnh:

Ki =yi /xi (II.13)

trong yi l phn mol ca cu ti trong pha hi;

xi l phn mol ca cu ti trong pha lng.

Xt cn bng vt liu ca thp tch:

Ci l phn mol cu ti trong dng nguyn

liu vo thp tch;

yi l phn mol cu ti trong pha hi;xi l phn mol cu ti trong pha lng;

Ki l hng s cn bng pha lng - hi;

F l tng s mol nguyn liu;

V l tng s mol hi;

L l tng s mol lng;

F, Ci

V,yi

L, xi



27/292


Ta c phng trnh cn bng vt liu ca thp tch:

F = V +L

Vi cu ti no : F.Ci = V.yi +L.xi

Khi p sut P ca h di 400 kPa (600 psi) c th coinh kh l tng. Khi c th s dng p sut hi tnh p

sut cn bng pha. iu kin cn bng, tc bay hi catt c cc cu t phi bng tc ngng t, ngha l khng cs thay i thnh phn pha hi hoc pha lng. Do lc tc

dng theo c hai hng phi l bng nhau:

Py i =Pixi

trong : Pi l p sut hi ring phn ca cu t i no ti p sut P vnhit Tca thp tch.

T ta c: Ki =Pi /P (II.14)

iu kin cn bng pha c bn ca h l nhit , p sut v th ho hcca mi cu t phi bng nhau pha kh v pha lng:

PL =PK (II.15)

TL

=TK

(II.16)L = K (II.17)

Chnh lch th ho hc ca mt cu t no trong hai pha l ng lcca qu trnh chuyn khi gia cc pha. Tng t, chnh lch ca nhit lng lc ca qu trnh truyn nhit, cn chnh lch p sut l ng lc cacc qu trnh c hc. Cn bng ca h t c khi hiu s chnh lch t gi tr 0.

p sut cao hn, c th ti 3,5 MPa (500 psi), ngi ta s dng khinim fugat (k hiu l f) c lin quan n nng lng t do v cc khi nimnhit ng hc c s khc. Fugat c th nguyn p sut, c s dng hiu chnh vi h kh thc, v c lin quan vi tha s chu nn z, i khi fcn c gi l "p sut hiu chnh". Ngi ta cn s dng khi nim h s

fugat =f/P

i vi h kh thc, s thay i th ho hc t l vi s thay i cafugat hoc hot ca cu t , v vy cn bng ca fugat v hot cacng mt cu t trong cc pha khc nhau cng l du hiu cn bng:

Pyi

Pix

i



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fiL =fi

K (II.18)

aiL = ai

K (II.19)

Khi bit fugat ca cc cu t trong h, cng c th xc nh c hngs cn bng ca tng cu t, tc l xc nh c cn bng ca n. Phngtrnh cn bng pha l tng c dng:

0iK

0iL

i

ii

f

f

x

yK == (II.20)

vi 0iLf l fugat ca cu t tinh khit trng thi lng; 0iKf l fugat ca cut tinh khit trng thi kh.

Theo nh lut dung dch l tng (khc vi nh lut kh l tng)

fiL = 0iLf . xi v fi

K = 0iKf . yi

trong : fiL l fugat ca cu ti trong hn hp lng;

fiK l fugat ca cu ti trong hn hp kh.

Ti cn bng: fiL =fi

K

0iLf . xi = fi

K = 0iKf . yi

Do :0

iK

0iL

i

ii

f

f

x

yK ==

H s fugat ca hn hp bng:

=fi /P.Ci (II.21)

i vi cu t tinh khit Ci = 1, p sut ca h bng p sut hi bo hoca cu t p sut cho. Khi h s fugat ca cu t i tinh khit cdng:

vi0 =fi

0 /Pi0 (II.22)

H s hot :

= ai/ci =fi/ (c.fi*) (II.23)

trong fi* l fugat ca cu ti trng thi lng iu kin tiu chun;

c l nng dung dch.

Khi hng s cn bng ca h kh thc:



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Ki = iL /i

K (II.24)

hoc: Ki = iLfi* /i

KP

Ki = iLvi /i

k (II.25)

T cc phng trnh trng thi kh thc (BWR, PR, RK,...) c th xc

nh c i. l c s ca phng php gii tch tnh hng s cn bngpha ca hn hp hydrocacbon.

Phng trnh tnh ton fugat ca cu ti trong h kh thc nh sau:

PVVPlnRTfRT )d(ln iP

0ii += (II.26)

trong Vi l th tch mol ring phn ca cu ti;

V l th tch kh l tng: V =RT/P.

Phng trnh xc nh i c dng:

PP

RT

n

VRT

P

i

dln0

i

ijnP,T,

=

(II.27)

hoc

ln= ZVV

RT

n

P

RT

llnd

V jnV,T,

(II.28)

l biu thc tng qut nht xc nh hng s cn bng pha cahn hp hydrocacbon. Tnh ton bng cc phng trnh trng thi khc nhaus cho kt qu khc nhau. l v khi tnh ton cn phi gii cc phngtrnh trng thi kh thc c lin quan n cc quy tc, cc nh lut v cctha s hiu chnh khng phi l chnh xc hon ton cho mi hn hp. Mcn phi cho kt qu gn vi cc s liu thc nghim thu c. Vi cc

phn t hydrocacbon n gin s hiu chnh kh ph hp.Kt qu tnh ton vi cc parafin mch thng t etan ti decan l ng

n. Ring vi metan c s sai khc do p sut hi ca metan ln v tnhcht bt thng ca metan trong pha lng. Vi nit cng c s sai lch tngt. Hydrosunfit, nc v cacbon dioxit khc xa cc hydrocacbon do tnhphn cc ca chng. V vy vi cc hn hp kh c cha mt vi hoc tt c



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cc cu t k trn, tnh cht ca hn hp kh s rt phc tp, vic tnh toncn phi c s hiu chnh c bit.

C nhiu phng php khc nhau xc nh hng s cn bng pha cah nhiu cu t. Trong chng ny s ln lt nghin cu cc phng phpgii tch v phng php gin xc nh hng s cn bng pha ca hnhp cc hydrocacbon.

II.5. Phng php gii tch xc nh hng s cn

bng pha ca hn hp cc hydrocacbonc trng c bn ca phng php gii tch xc nh hng s cn

bng pha l s dng cc phng trnh trng thi khc nhau, tnh ton h sfugat v hot ca cc cu t.

Bn cht ca phng php ny l hng s cn bng pha c xc nhnh h s fugat.

Hin nay i vi h cc hydrocacbon, ngi ta thng s dng nht lcc phng trnh trng thi Benedict - Webb - Rubin (BWR), phng trnhRedlich - Kwong (RK), phng trnh Peng - Robinson (PR) nu phn

trn.II.5.1. S dng phng trnh RK xc nh hng s cn bng pha

T phng trnh trng thi RK:

)b(T

a

b

RTP

,

=

vvv50

(II.7)

trong : b = biyi (II.29)

bi = 0,0867 RTci /Pci (II.30)

d= diyi (II.31)

di = Ai + Bi (Tci

/T 1) + C i (Tci

/T 1)2 (II.32)

vi Ai , Bi , Ci l h s ca cc cu t ring bit.

Mt trong cc thng s trng thi a c thay th bng thng sd, trong

dph thuc vo nhit rt gn. Thng sdcn l hm ca thnh phn

hn hp. Cc gi tr ca n nhn c t x l cc s liu thc nghim xc

nh cn bng lng hi v entanpi ca h.



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Khi phng trnh RK c dng sau:

)( d

bdRT

b

RTP

+

=

vvv

(II.33)

Vic a thng s mi d thay th cho thng s a cho php nhn cphng trnh trng thi m t chnh xc hn cc tnh cht nhit ng cahn hp thc cc hydrocacbon trng thi kh v lng.

Gii cc phng trnh trn ta nhn c:

)mz(b

dmb

z

md)mz()mz(b

mb

+

+=

ii

ii 1lnlnln (II.34)

trong : m =Pb/RT; z y l thng s chu nn.

Thng s chu nn z c xc nh t phng trnh:

z3z2z (m2 + mdm) dm2 = 0 (II.35)

H sb, bi, d, di c xc nh t cc phng trnh (I.29 II.32). Cch s A i , Bi , Ci c trong bng II.1.

Bng II.1. Gi tr cc h s A i , Bi , Ci trong phng trnh (II.32)

Cu t A i B i C iMetan (T> 190,55K)

Metan (T< 190,55K)

Etan

Propan

izo-Butan

n-Butan

izo-Pentan

n-Pentan

n-Hexan

n-Heptann-Octan

n-Nonan

n-Decan

CO2

H2S

4,934

4,934

4,934

4,934

4,934

4,934

4,934

4,934

4,934

4,9344,934

4,934

4,934

3,500

4,260

8,00

7,39

8,30

8,82

9,30

9,35

9,40

9,50

10,00

10,5011,00

11,20

11,60

6,80

6,50

1,5

0,3

0

0

0

0

0

0

0

00

0

0

0

0



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Hng s cn bng pha ca nit ph thuc ng k vo bn cht cahydrocacbon m n ho tan:

iiNN 22

xdd = (II.36)

+

+=

2

11 22

NN

2

Ci

Cii

iN T

TB

T

TBAd (II.37)

Gi tr Ai , Bi , Ci i vi h bc 2 ca nit vi cc hydrocacbon, CO2 vH2S xem bng II.2.

Bng II.2. Gi tr cc h s Ai, Bi, Ci trong phng trnh (II.37)

Cc cu t A i Bi C i

Nit nit

Nit metan

Nit etan

Nit propan

Nitizo-butan

Nitn-butan

Nitizo-pentan

Nitn-pentanNitn-hexan

Nitn-heptan

Nitn-octan

Nitn-nonan

Nitn-decan

Nit CO 2

Nit H2S

4,934

4,350

2,960

2,030

1,790

1,300

1,100

1,0001,000

1,000

1,000

1,000

1,000

2,960

2,030

7,66

7,30

5,38

3,14

2,71

2,10

1,80

1,601,60

1,60

1,60

1,60

1,60

5,38

3,14

1,95

0

1,33

0

0

0

0

00

0

0

0

0

1,33

0

Sai s trung bnh gia gi tr hng s cn bng K nhn c bng tnh

ton v thc nghim trong khong nhit ( 180 ... +1400

C) v p sut n14 MPa vo khong 2 ... 7%.

II.5.2. Tnh ton hng s cn bng pha vi h nit v hydrocacbon

parafin t C1 n C10 bng phng php Kalasnhicov - Klimenco

Phng php Kalasnhicov - Klimenco da trn c s s dng phngtrnh Benedict - Webb - Rubin (BWR).



33/292


tin tnh ton, ngi ta a ra cc i lng rt gn:

v r = v /v c ; Pr =P/Pc ; Tr =T/Tc

vc , Pc ,Tc l cc i lng ti hn.

nh lut trng thi tng hp m t vi tt c cc cht, c tn ti trngthi ti chng c cng cc i lng rt gn.

Phng trnh trng thi tng hp c dng:

f(v r , Pr ,Tr) = 0 (II.38)

C th pht biu nh sau: Nu c hai hay nhiu cht ph hp vi

phng trnh trng thi tng hp, c hai trong s ba i lng rt gn bngnhau, th chng cng s c i lng rt gn th ba nh nhau. Cc cht tuntheo nh lut trng thi tng hp c gi l cc cht tng t nhau v mtnhit ng hc. Trn c s nh lut ny c th xc nh tnh cht ca mtcht nu bit tnh cht ca cht tng t v mt nhit ng.

V d khi bit P v Pc ca mt cht, c th xc nh P1 ca mt chtkhc nu bit Pc1 ca n:

P1 =Pr .Pc1m ta bit: Pr =P/Pc.

nh lut trng thi tng hp m t kh tt tnh cht ca cc hydro-

cacbon dy parafin. iu c gii thch do s khc nhau rt t gia cngthc phn t ca cc hydrocacbon thuc cng mt dy ng ng, hay nicch khc v chng c cng cng thc tng qut CnH2n+2.

Mc sai lch ca kh thc vi nh lut kh l tng c xc nhbi thng s chu nn z trong phng trnh:

PV = zRT

nh lut trng thi tng hp gi thit thng s chu nn ti im tihn zc i vi tt c cc cht l nh nhau. Tuy nhin cc s liu thc nghim chng t rng zc i vi cc cht khc nhau c gi tr khc nhau, i via s cc cht kh zc = 0,2 ... 0,3.

Cc hng s vt l ca cc hydrocacbon t C 1 n C12 v mt s kh ctrong bng II.3.

Nguyn nhn gy nn s sai lch l do hnh dng phn t kh thckhng c dng hnh cu nh ngi ta gi thit. Thng s acentric ca ra c trng cho mc sai lch hnh dng phn t so vi m hnhhnh cu. Khi phng trnh trng thi tng hp c dng:

f(vr ,Tr , Pr , ) = 0 (II.39)



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Bng II.3. Hng s vt l ca cc hydrocacbon C1 ... C12 v mt s kh

Nhit ti hn p sut ti hnCu t Khi lng

phn tzc

0R K psi MPaEMR Tha s

acentric

C1C2C3izo-C4n-C4izo-C5n-C5n-C6n-C7n-C8n-C9n-C10 n-C11 n-C12

16,04330,07044,09758,12458,124

72,15172,15186,178

100,205114,232128,259142,286156,302170,338

0,290,290,280,280,27

0,270,270,260,260,260,250,250,240,24

343550666734765

829845913972

10241070111211501185

191305370408425

460470507540569595618639658

666707617528551

491489437397361332305285264

4,604,884,253,653,80

3,393,373,012,742,492,292,101,971,82

14,1924,3734,6344,7444,24

55,3055,2765,5875,8886,1996,53

106,86117,17127,50

0,01040,09790,15220,18520,1995

0,22800,25140,29940,34940,39770,44450,48980,53500,5620

N2CO2

H2SO2H2H2O

28,01644,010

34,07632,000

2,01618,015

0,290,28

0,280,290,30

0,235

227548

672278

601165

126304

373155

33647

4931071

1300731188

3199

3,407,38

8,965,041,30

22,06

9,7114,44

20,288,694,23

0,03720,2667

0,09480,0216

0,22020,3443

Phng trnh trn thng c ng dng xc nh cc thng s nhitng ca cht dng:

a = a0 + .a (II.40)

trong : a l thng s nhit ng ca kh thc cn xc nh;

a0 l thng s nhit ng ca cht gi thit tun theo nh lut v l

hm ca cc i lng rt gn;a l h s hiu chnh s sai khc ca kh thc so vi kh gi thit

tun theo nh lut, v cng l hm ca cc i lng rt gn.

Trn c s s dng phng trnh Benedict - Webb - Rubin (BWR) trn, a vo cc i lng rt gn, Kalasnhicov v Klimenco nhn cphng trnh c dng:



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+

++

++=

5ir

2ir

ir

ir54

ir

ir

3ir

32ir

21

Kiln

T

P

T

Pcc

T

P

T

c

T

ccf

2i2

ir

2ir

2ir

11

ir

1095

ir

ir

2ir

8

ir

76 )1(

+++

+++ N

T

P

T

c

T

cc

T

P

T

c

T

cc (II.41)

trong :i

iii

M

yMN

= ;

Pc l p sut ti hn; Tc l nhit ti hn;Pri , Tri l cc i lng rt gn ca cu ti.

Mi l khi lng phn t ca hydrocacbon (i vi nit, cng nhn gitr khi lng phn t tng ng l 11).

c1 .. . c11 l cc hng s c a ra trong bng II.4 (vi cc hydrocacbont C2 n C10 , cc hng sc1 .. . c11 l chung cn vi nit v metan l ring).

Hng s cn bng pha c tnh theo phng trnh:

P

fK

Ki

*Li

Li

i

= (II.42)

Bng II.4. Gi tr cc h s c1... c11 trong phng trnhKalasnhicov - Klimenco

H s N2 CH4 Hydrocacbon C2 n C10

c1

c2

c3

c4

c5

c6

c7

c8

c9

c10

c11

0,1827448

0,5567094

0,1628858

0,3695996

0,5736230

0,2494726

1,395258

0,9883554

0,2979147

2,302971

4,256129

0,06557467

0,2533226

0,07441288

0,06095239

0,04814230

0,01650733

1,233154

0,7383944

0,6241929

3,262881

4,255619

0,4567890

0,7364150

0,09020270

0,04647840

0,001388500

0,7589850

1,341610

0,0004026500

0,8807840

1,276069

0,5362179



36/292


Fugat ca cu t tinh khit trong pha lng trng thi tiu chun *Lif

c xc nh theo phng trnh:

2i6i5

(1)ii

(0)ic

L*i lnlnlnln i

aa

PPf

++++= (II.43)

trong : 3i42i3i2

i

10iln

aaa

aa ++++=

ic

rii y.T

TT

==

i l tha s acentric ca cu ti;a0 .. . a6 l cc tha s ca phng trnh. Gi tr ca a0 ... a4 c a ra

trong bng II.5. Gi tr a5, a6, i c a ra trong bng II.6.

Bng II.5. Bng gi tr cc h s a0... a4

a0 a1 a2 a3 a4

ln(0 ) (C2 ... C10)

ln(1 ) (C2 ... C10)

10,6147

0,968095 6,52897

7,08812

7,39448

23,3047

3,46229

22,7035

0,678062

5,36108

Bng II.6. Bng gi tr cc h si, a5, a6Cc cu t a5 a6 i

Nit trong C1 ... C10

Metan

Etan

Propan

izo-butan

n-butan

izo-pentan

n-pentan

Hexan

Heptan

Octan

Nonan

Decan

935

559

650

510

394

394

326

326

272

233

213

185

166

475

209

328 240

152

152

117 117

90,6

65,5

62,8 49,2

40,6

0,105

0,152

0,192

0,200

0,206

0,252

0,298

0,349

0,392

0,450

0,479



37/292


i vi nit v metan, tha s acentric nhn gi tr = 0, v phng

trnh tnh fugat *Lif trn (II.43) c thm cc s hng sau:

i vi nit:

=

=

+N

2ii

N

2iiCN i2

x

x.a

(II.44)

i vi metan:

=

=

+N

3ii

N

3iiCC i1

x

x.a (II.45)

trong aN2Ci l h s c tnh n nh hng ca dng mi n*LN2

f ;

aC1Ci l h s c tnh n nh hng ca dung mi n*LC1

f .

i vi etan v cc hydrocacbon nng hn, ngi ta tha nhn trng thilng ca cht tinh khit iu kin p sut v nhit ca h l trng thitiu chun.

Phng trnh tnh h s hot ca cc cu t trong pha lng Lk c

dng:

==

+=N

1iiiik

2i

N

1iik

Lk )(2)(ln Sxbbxbb (II.46)

trong :

+++ 3i2i1i xxx .... i < k

+++ +++ 3i2i1i xxx .... i > k

bi l h s, gi tr c cho trong bng II.7.Ch sk trong phng trnh trn ch cu t no trong dy ng ng

ngoi tr metan.

Phng trnh trn c p dng vi cc cu t C2 (t etan tr ln). Khi nng ca nit (thng khng qu 10%) c tnh tng vi nng metan.

Si =



38/292


i vi nit v metan, phng trnh xc nh hot c dng:

=

=

=

= 2N

3iiN

3ii

N

3iiCC

LC 1

.

lni1

1x

x

xb

(II.47)

=

=

=

= 2N

2i iN

2ii

N

2iiCN

L

N

1

.

lni2

2

x

x

xb

(II.48)

Cc h s tnh ton xem bng II.7.

Bng II.7. Gi tr cc h s trong phng trnh tnh fugat

Cu t aN2-Ci

bN2-Ci aC1-Ci bC1-Ci bi

Nit

MetanEtanPropanizo-Butann-Butanizo-Pentann-Pentann-Hexann-Heptann-Octann-Nonan

n-Decan

0

0,601,602,002,502,502,602,602,602,602,152,152,15

0

0,601,001,000,950,950,850,850,720,600,500,350,20

0

00,450,650,660,720,740,800,850,890,930,890,85

0

00,450,470,480,440,400,350,310,360,400,250,21

0

00,450,540,630,630,680,680,730,770,790,810,82

II.5.3. Tnh hng s cn bng pha theo phng php Starling

Hng s cn bng pha c xc nh bng cng thc:

iK

i

iL

ii

xf

xfK = (II.49)



39/292


Nu k hiu l t trng mol ca hn hp, A0, B0, C0, b... l cc thngs ca phng trnh; kij l cc thng s tng tc ca cu ti v cu tj, thphng trnh xc nh fugat ca cu t i c dng sau:

++= RTBBRTxRTfRT )()ln(ln 0i0ii

+

j

3ij2

1/20i0j

ij1/2

0i0j )(1)(

)(1)(2 kT

CCkAA +

+

5ij4

1/20i0j

4ij3

1/20i0j

)(1T

)()(1T

)(k

DE

k

DD

+

+

T

ddaaRTbb

1/3i

21/3

i21/2

i2

2 )(3)(3)(3

2

+

+ 1/3i22

51/3i

21/3

i2 ))((

5

3)(3)(3

5

T

da

T

dd.aa.

.++

+ +

+

2

)exp()exp(1)(3 2

2

2

2

21/3i

2

T

cc

++

4222

21i

2

21/3

2

11)exp(1

2

/

T.

c(II.50)

Kt qu tnh ton bng cc phng php khc nhau v so snh vi ktqu thc nghim nhn c cho thy sai s khng qu 5%. Phng php tnhton cho kt qu ph hp i vi h c cha N2 , CO2 v H2S.

II.6. Phng php gin xc nh hng s cn bngpha ca hn hp cc hydrocacbon

Khi tnh ton bng tay xc nh hng s cn bng pha, ngi ta thng

s dng cc phng php gin . Trong thc t tnh ton hng s cn bng phaca h hydrocacbon t C1 n C10 v N2 , ph bin nht l s dng cc phngphp NGPA (Natural Gas Processors Association)v phng php Neyrey.

II.6.1. Xc nh hng s cn bng pha theo phng php NGPA

y l mt trong nhng phng php gin n gin v chnh xc hnc xc nh Ki i vi h hydrocacbon t C1 n C10 v nit. Trong



40/292


phng php ny Ki ca cc hydrocacbon c xc nh bng cc gin ph thuc vo nhit , p sut ca h v p sut quy t. Trn cc gin trc honh l p sut ca h, cn trc tung l hng s cn bng pha ca cut no trong h. Trong h trc to ny ngi ta xy dng cc ngng nhit, chng gp nhau ti mt im tng ng vi gi tr hng s cnbng pha K = 1 v p sut chnh bng p sut quy t ca h. Trn hnh II.1a ra gin hng s cn bng pha Kca cc hydro-cacbon ti cc nhit v p sut khc nhau.

Hnh II.1. Hng s cn bng K cc nhit v p sut khc nhau

i vi cc hn hp khc nhau c cng gi tr p sut quy t th gi trhng s cn bng ca cc cu t ring bit c gi tr bng nhau ti cc gi trp sut v nhit bng nhau. V vy p sut quy t c s dng nh mtthng s c tnh n nh hng ca thnh phn hn hp n gi tr hng s

cn bng pha ca h. p sut quy t c xc nh bng phng php Heddlen.

Nhit khng i

p sut

K

11



41/292


Theo Heddlen, h nhiu cu t c gi thit l h gi bc hai gm ccu t nh v cu t nng, trong cu t nng c c trng bng nhit ti hn trung bnh v p sut ti hn trung bnh ca tt c cc cu t cn litrong h, tr cu t nh.

Trn hnh II.2 l gin biu din cc gi tr hng s cn bng K cametan p sut quy t Pqt = 800 psi

= 5,5 MPa (1 psi = 6894,76 Pa).

Hnh II.2. Hng s cn bng pha ca metan Pqt = 800 psi (5,5 MPa)

p sut quy t ca h c coi l p sut ti hn ca h gi bc 2 nhit ca h theo ng cong ti hn ca h gi bc 2 cho. Nu nhit ca h thp hn nhit ti hn ca cu t nh th p sut quy t nhn

gi tr p sut ti hn ca cu t nh. p sut quy t c xc nh theo gin, trn biu din cc ng cong ti hn ca cc h bc 2.

Trnh t tnh ton nh sau:

p sut, psi

K=yx



42/292


1) Cho gi tr p sut quy t Pqt.

2) Vi gi tr p sut quy t cho theo gin tng ng (v d trnhnh II.2 i vi metan p sut quy t ca h l 800 psi), xc nh hng scn bng pha ca mi cu t nhit v p sut ca h.

3) S dng gi tr hng s cn bng pha va nhn c, tnh ton thnhphn pha lng cn bng xicb theo phng trnh:

=+

=i i i

ii 1)1(1cb Ke

Cx (II.51)

trong : Ci l thnh phn hn hp ban u, mol/mol (mol cu ti/mol hn hp).e l phn mol pha hi ca hn hp, tnh bng phng php lp vi

cc gi tr phn mol ca pha hi e chn trc cho n khi biuthc (II.51) tho mn.

4) Chia pha lng cn bng thnh h gi bc 2, trong cu t th nhtl cu t nh nht trong h, c nng bng hoc ln hn 0,1% mol, cncu t th hai l tt c cc cu t cn li.

5) Tnh ton nhit ti hn v p sut ti hn ca cu t gi th hai ckhi lng l khi lng trung bnh ca cc cu t cn li:

=

=

=N

2iii

N

2icii

ci

2

Mx

TMx

T (II.52)

=

=

=N

2iii

N

2icii

c

i

2

Mx

PMx

P (II.53)

6) Trn hnh II.3 l cc gin m t cu t gi th hai ca h tngng cc gi tr nhit v p sut ti hn xc nh im 5).

7) p sut quy t theo gin c xc nh nh sau: Sau khi xydng ng cong ti hn i vi trng hp ang xt ti gi tr tng ngvi nhit ca h, gi tr trn trc tung l p sut quy t ca h cn tm.

8) So snh gi tr p sut quy t vi gi tr cho ban u. Nu hai gitr khng trng nhau, lp li cc php tnh t im 2) n im 7), vi gi trp sut quy t mi. Lm cho n khi gi tr Pqt tnh ton v gi tr Pqt chnban u trng nhau vi sai s 8 ... 12% l c th chp nhn c.



43/292


Hnh II.3. Gin xc nh p sut quy t ca h hydrocacbon

44

Nhit , 0F

psut,psi

p sut quy t 2120F

Nhit ti hn cacu t gi - nng



44/292


Khi h hydrocacbon p sut 1,6 ... 2 MPa, nh hng ca p sut quyt n gi tr K khng ng k. V vy p sut thp c th khng cn xcnh gi trPqt v s dng gin xc nhK gi tr Pqt bt k.

Trn c s kt qu nghin cu, ngi ta a ra phng php chn Pqt n gin qu trnh tnh ton nh sau:

Khi tnh ton s cng ngh ch bin kh ng hnh c hm lngC3 = 150 ... 640 g/m

3 bng phng php ngng t nhit thp, tu thucvo p sut v nhit ti cng on tch, c th chn gi tr Pqt nh sau:

Pqt= 2000 psi khi p sut ca h xp x 2 MPa, T= 200C.Pqt = 1500 psi khi h c P = 2 ... 5 MPa, T= 0 ... 40

0C.

Pqt = 1000 psi khi h c P = 2 ... 5 MPa, T= 40 ... 700C.

Trong tnh ton qu trnh tch etan, p sut quy t trn nh ct c thly bng 1000 psi, cn y ct bng 800 psi.

tnh ton im sng cho kh kh nhn c t thp tch etan lmvic p sut 5 ... 6 MPa (chnh l p sut trn ng ng dn kh i sdng), hng s cn bng pha c xc nh p sut quy t Pqt = 1500 psi.

Trong s cng ngh ch bin kh ng hnh bng phng php hp

th nhit thp, ngi ta s dng cht hp th l hn hp hydrocacbonphn on benzin hoc keroxen. Khi tnh ton c th chn gi tr p sut quyt nh sau:

Vi qu trnh hp th s dng cht hp th nh c khi lng phn t100, chn Pqt = 2000 psi. Khi s dng cht hp th c khi lng phn t140 ... 160, chn Pqt = 4000 psi. Trong thc t ngi ta kim tra chnh xccaPqt chn theo thnh phn pha lng a di cng ca thp hp th.

tnh im sng ca kh nhn c t nh thp hp th, ngi tatnh hng s cn bng cng p sut quy t nh khi xc nh hng s cnbng trong thp hp th. i vi qu trnh tch etan thc hin trong thp hpth bc hi, p sut quy t trong phn hp th c chn nh trong thp hpth; cn trong phn bc hi ca thp, th khi s dng cht hp th nh chnPqt = 1000 psi, khi s dng cht hp th 140 ... 160 th chnPqt = 2000 psi.

Vi qu trnh nh hp th thc hin p sut 0,4 ... 2,0 MPa, chn gitr Pqt khng nh hng n kt qu tnh ton hng s cn bng. Hng s cnbng pha ca cc cu t nng c xc nh t hng s cn bng pha bitca cc cu t nh bng cch: Trn trc honh l gi tr khi lng phn t



45/292


ca hai hoc ba cu t nh c gi tr hng s cn bng pha K, cn trctung l gi tr logarit K ca cc cu t , qua cc im nhn c ngthng. Gi tr logarit K ca cu t nng c xc nh tng ng vi khilng phn t ca n.

Hng s cn bng pha ca CO2 c xc nh theo cng thc:

6242 HCCHCOKKK =

II.6.2. Xc nhKbng phng php Neyrey

Neyrey a ra mt phng php n gin v chnh xc xcnh hng s cn bng pha ca cc hydrocacbon parafin v olefin trongkhong rng nhit v p sut.

C s ca phng php l s ph thuc tuyn tnh ca logarit hng scn bng pha (lgK) vo nhit si ca cu t. Hng s cn bng pha Kc xc nh nh ba gin .

Trn gin th nht (hnh II.4), l cc ng ng p, tng ng vicc gi tr p sut quy t khc nhau. T gin xc nh c gi trhng sK0 tng ng vi gi tr P v Pqt .

Hnh II.4. Gin xc nh hng sK0

p sut, psi

K0



46/292


Trn gin th hai (hnh II.5) c hai thang gi tr nhit lm vic vgi tr thng sS song song vi trc tung, cn trc honh l gi tr p sutquy t, trong gin l cc ng ng p sut lm vic. T gin ny xc

nh gi tr thng sS l hm ca T, P v Pqt .Trn trc honh xc nh gitr Pqt , t k ng vung gc, ct ng ng p tng ng vi p sutca h. T giao im k ng nm ngang cho n khi ct trc tung. T giaoim trn trc tung ni vi im tng ng vi nhit lm vic ca h trnthang nhit , giao im ca ng k ny vi thang S cho ta gi tr thngsScn tm.

Hnh II.5. Gin xc nh thng sS

Theo gin th ba (hnh II.6) xc nh gi tr hng s cn bng Knhsau: Trn trc tung l gi tr K0 (xc nh t gin th nht trn hnh II.4)v K0/10 , cn trn trc honh l gi tr S (xc nh t gin th hai) cah cho. T gin xc nh im c to (S, K0/10). Qua im v

p sut quy t, psi

Nhit

0F

p sut lm vic ca h



47/292


im (0, K0) trn trc tung k ng thng. T cc im trn cc trc honh(trc nhit si hoc trc cc cu t) tng ng vi nhit si hoc tnca cu t cho, k ng vung gc ct ng thng k trn, gi tr cagiao im chnh l gi tr hng s cn bng pha ca cu t tng ng.

Hnh II.6. Gin xc nh hng s cn bng pha

Thng sS

Metan

Etan

Propylen

Etylen

Propan

n-Butan

izo-Butan

izo-Pentan

n-Pentan

Hexan

Heptan

Octan

Nonan

Decan

Hng

scnbngphaK

Nhit si,0F

0oF

100

50

200

100

0

100

300

400

0 62 4 8 10

12

100

60

20

40

10

6,0

2,0

4,0

0,2

0,4

1,0

0,6

0,1

0,06

0,02

0,04

0,01

0,005

0,004

0,001

0,002



48/292


Sau khi xc nh c K cng kim tra gi tr Pqt chn tng t nhtrong phng php NGPA ni trn.

Tm li trnh t xc nh hng s cn bng pha theo phng php Neyreynh sau:

1) T gin hnh II.4 xc nh K0 tng ng vi P v Pqt .2) T gin hnh II.5 xc nh gi tr S.3) T gin hnh II.6 xc nh gi tr K.4) Kim tra gi tr Pqt c chn tng t nh phng php NGPA.

Bng II.8 di y so snh chnh xc ca cc phng php xc nhhng s cn bngK.

Bng II.8. So snh chnh xc ca cc phng php xc nh K

Phng php tnh Sai s trung bnh

Myers v Lenoir

NGPA

Rzaca

Winn

Neyrey

7,0

8,5

9,3

10,0

7,8

II.6.3. V d tnh hng s cn bng

V d II.1.Tnh hng s cn bng ca hn hp c thnh phn cho trong

bng di y P = 3,4 MPa (hay 493,1 psi);T= 300C (hay 220F).

a) Tnh theo phng php NGPA

1) Chn p sut quy tPqt = 1500 psi.

2) Theo gin NGPA, vi p sut quy t 1500psi v cc thng s ca h, xc nh c hng scn bng pha i vi tt c cc cu t: KC

1 = 3,45;

KC2

= 0,46; KC3

= 0,113; Kn-C4

= 0,034 ; Kn-C5

= 0,0095.

3) Xc nh thnh phn pha lng cn bng theophng trnh (II.51):

1)1(1

N

1i

N

1i i

ii =

+=

= = Ke

Cx

Cu t C i

CH4

C2H6

C3H8n-C4H10

n-C5H12

0,8745

0,0586

0,03720,0212

0,0085

1,0000



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Tnh ton bng phng php lp xc nh gi tr ca e khi bit phn molca pha kh. Kt qu nhn c thnh phn pha lng xi (mol/mol) nh sau:C1 l 0,2635; C2 l 0,1199; C3 l 0,2321; n-C4 l 0,2480; n-C5 l 0,1365 vie = 0,9467.

Pha lng va tnh c chuyn thnh h gi hai cu t. Cu t nh lmetan, cn cu t th hai l cc cu t cn li ca h. T phng trnh(II.52) v (II.53) tnh nhit v p sut ti hn ca cu t th hai a ra trn tnh cTc2 v Pc2. Kt qu tnh ton c xem bng II.9 di y.

Bng II.9. Kt qu tnh ton

Cu t x i M i x iM i Tci x iM iTci Pci x iM iPci

CH4

C2H6

C3H8

n-C 4H10

n-C 5H12

0,2635

0,1199

0,2321

0,2480

0,1365

30

44

58

72

3,60

10,21

14,39

9,83

90,3

106,6

306,0

386,0

325,08

2109,39

4403,34

3794,38

707

614,3

549,5

486,3

2545,2

6272,0

7878,53

4780,33

1,0000 38,03 10632,19 21476,06

Kt qu nhn c Pqt = 1500 psi. Kt qu tnh ton trng vi gi tr Pqtchn ban u. Nh vy cc hng s cn bng xc nh c l ng.

b) Tnh theo phng php Neyrey

1) Theo gin (K0 P) chn Pqt = 1500 psi v P = 500 psi xc nh

cK0 = 7.

2) Theo gin xc nh thng sSvi: Pqt = 1500 psi,P = 500 psi, T=

220

F, S= 1,7.3) T gi tr K0 v S trn gin (KS), Tbng phng php m t

trn xy dng ng thng, t xc nh hng s cn bng pha ca cccu tKC

1= 3,5 ; KC

2= 0,465 ; KC

3= 0,114 ; Kn-C

4= 0,032 ; Kn-C

5= 0,0080.

Kim tra gi tr Pqt chn tng t nh trong phng php NGPA.



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II.7. ng dng ca hng s cn bng pha

C 3 loi bi ton s dng hng s cn bng pha K tnh ton:

- Tnh ng cong im bt trn ng bao pha.

- Tnh ng cong im sng trn ng bao pha.

- Tnh cc thnh phn lng hi ti cc gi tr P v T bt k bn trongng bao pha.

II.7.1. Xc nh im bt

im bt c nh ngha l iu kin m ti hi c ngng t honton thnh lng, ch tn ti duy nht mt bt kh. Phn mol ca pha lngchnh l phn mol ca hn hp.

iu kin hi c ngng t hon ton:

Kixi = yi = 1 (II.54)


1) Chn nhit khi bit p sut (hoc chn p sut khi bit nhit ).

2) Tm cc gi tr Ki P v T cho v chn.

3) Nhn Ki tm c bc 2 vi xi tng ng (biu thc II.54).

4) Nu tng cc gi tr Kixi nhn c bc 3 bng 1 c ngha l gi

tr T (hoc P) chn l ng. Nu khng th lp li t bc 1 n bc 3cho n khi Kixi = 1 th kt thc.

V d II.2.

Cu t xi K i K ixi

CO2 1,25 1,50 1,880

H2S 0,50 0,41 0,210

C1 21,36 3,48 74,330

C2 36,78 0,58 21,330

C3 10,21 0,16 1,630

i-C4 6,38 0,063 0,400

n-C4 9,84 0,043 0,420i-C5 2,63 0,017 0,040

n-C5 4,01 0,012 0,048

C6 3,90 0,0036 0,014

C7+ 3,14 0,00033 0,001

Xc nh im bt ca hn hp cthnh phn cho trong bng 4 MPa(580 psi). Coi phn on C7+ c tnhcht tng t C8.

Tnh lp vi cc gi tr T c

chn sao cho Kixi = 1 (hoc 100).Trong bi v d ny nhit ng l

T = 140C (70F). Kt qu tnh ton vigi tr Tng cho trong bng.

100,30



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II.7.2. Xc nh im sng

im sng c nh ngha l ton b h trng thi hi v ch tn tiduy nht mt git lng rt nh. Trong trng hp ny thnh phn ca hnhp bng thnh phn pha hi yi. Nh vy iu kin h hon ton trngthi hi:

yi/Ki = xi = 1 (II.55)

V d II.3.

Cu t yi Ki yi /Ki =xi

CO2 1,25 4,83 0,26H2S 0,50 2,38 0,21C1 21,36 6,36 3,36C2 36,78 2,84 12,95C3 10,21 1,57 6,50i-C 4 6,38 1,02 6,25n-C4 9,84 0,86 11,44i-C 5 2,63 0,55 4,78n-C5 4,01 0,49 8,18C6 3,90 0,28 13,93

C7+ 3,14 0,097 32,37

Xc nh im sng ca hn hp

c thnh phn cho trong bng 4 MPa(580 psi). Coi phn on C7+ c tnhcht tng t C8.

Tnh lp vi cc gi tr T c

chn sao cho yi / Ki = 1 (hoc 100).Trong bi v d ny nhit ng lT = 1530C (307,40F). Kt qu tnhton vi gi tr T ng cho trongbng.

100,23

Hn hp a ra trong hai v d trn l kh bo. Phn trm mol ca metanthp. Ch rng trong ct Kixi i vi metan c gi tr ln nht. Nu phnmol metan ln hn s c nh hng rt ng k n kt qu nhn c.

Vi v d xc nh im sng, gi tr trong ct yi /Ki ca C7+ c gi trln nht. Tnh ton im sng vn km chnh xc hn so vi tnh tonim bt, trn thc t i vi kh gy, cha rt t cc cu t nng, sai s caphp tnh cng ln.

II.7.3. Tnh thnh phn lng hi bn trong ng bao pha

Mc ch ca php tnh ny xc nh thnh phn pha lng v pha hi trng thi cn bng trong h hai pha, cn bng vt liu ton h:

F = V +L (II.56)

Cn bng vt liu vi tng cu t:

FC i = Vy i +Lxi (II.57)

trong : F l s mol nguyn liu vo thp tch;



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V l s mol pha kh nhn c tF mol nguyn liu;

L l s mol pha lng nhn c tF mol nguyn liu;

Ci l phn mol cu t i trong dng nguyn liu;

yi l phn mol cu t i trong dng khV;

xi l phn mol cu t i trong dng lng L;

Gi sF = 1, ta c Ci =yiV +xiL

ng thi, theo nh ngha hng s cn bng pha c yi = Kxi, t

ta c:

i

ii

KVL

Cx

+= ;

( )i

ii

KLV

Cy

+= (II.58)

Tng phn mol ca tt c cc cu t phi bng 1, do :

1=+

= i

ii

KVL

Cx ;

( )1=

+=

i

ii

KLV

Cy (II.59)

Bng phng php lp, chn cc gi tr L hoc V sao cho cc biu thctrn l ng.

Mt khc, c th vit yi xi = 0

( )( ) =+

= 0

11

1

i

iiii

KV

KCxy (II.60)

Biu thc (II.60) l biu thc tng qut nht thng c s dng tronglp trnh tnh ton trn my vi tnh.


1) Tm K gi tr p sut v nhit ca h hai pha (iu kin ca thptch).

2) Chn V hocL.

3) Tnh cc biu thc (II.59) hoc (II.60).

4) Nu biu thc tho mn, th php tnh hon thnh.

Nu cha ng th lp li t bc 2 n bc 4.

5) Tnh thnh phn phn mol trong pha lngxi v trong pha hi yi.

6) Tnh s mol ca cu ti (c k hiu l Yi) trong V mol pha hi.

Tnh s mol ca cu ti (c k hiu l Xi) trong L mol pha lng.



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V d II.4.

Tnh thnh phn v lng mol pha lng, pha hi ca thp tch 4 MPa(580 psi) v 1000C (2120F). Thnh phn nguyn liu Ci cho theo phn trm

mol, ngha l Ci = 100.

Trc ht xc nh Ki ca cc cu t trong h. Cc gi tr nhn cin vo ct Ki (ct th 3 trong bng)

Trong bc 2, chn V (hoc L). Tnh cc s hng trong cc biu thc(II.59) hoc (II.60). Php tnh lp c thc hin cho n khi cc biu thc

(II.59) hoc (II.60) c tho mn. Trong v d ny, gi tr ng caV = 0,770. Kt qu tnh c ghi trong bng II.10.

Bng II.10. Kt qu tnh ton ca v d II.4.

Cu t Ci Ki yi x i xi yi Xi Yi

CO2 1,25 4,050 1,139 0,373 1,512 0,086 1,164

H2S 0,50 1,740 0,236 0,319 0,554 0,073 0,427

C1 21,36 5,950 21,974 4,439 26,413 1,021 20,338

C2 36,78 2,160 22,535 19,427 41,962 4,468 32,311

C3 10,21 1,030 0,299 9,979 10,279 2,295 7,915i-C 4 6,38 0,600 3,688 9,220 5,532 2,282 4,260

n-C4 9,84 0,490 8,264 16,203 7,940 3,727 6,114

i-C 5 2,63 0,280 4,250 5,903 1,653 1,358 1,273

n-C5 4,01 0,240 7,348 9,668 2,320 2,224 1,786

C6 3,90 0,120 10,646 12,098 1,452 2,783 1,118

C7+ 3,14 0,031 11,987 12,370 0,383 2,845 0,295

100,00 0,000 100,000 100,000 23,000 77,000

Cn bng vt liu ca thp tch:F = V +L = Yi +L = Xi

trong : Yi =yiV ;

Xi =xiL .



54/292


Chng IIIthng s nhit ng ca cc hydrocacbon

ring bit v hn hp ca chng

Khi tnh ton nhit ng hc ca qu trnh ch bin kh, ngi ta thngs dng cc i lng nhit ng sau: p sut, nhit , chu nn, th tchring, trng lng ring, entanpi, entropi, nhit dung, dn nhit, nht.Trong chng ny s xem xt tnh cht nhit ng ca cc hydrocacbonring bit v hn hp ca chng, v trnh by mt s phng php xc nh

cc tnh cht . p sut, th tch, nhit v h s chu nn thng nmtrong phng trnh trng thi. Nhiu tnh cht ca cc hydrocacbon c xcnh trn c s l thuyt trng thi tng hp, v vy cn phi bit cc thngs ti hn ca cc cu t v hn hp ca chng.

III.1. Nhit si v p sut hi bo ho

Nhit si ca hydrocacbon t C 1 n C10 c xc nh bng thcnghim, s liu a ra trong bng III.1.

Nhit si ca cc hydrocacbon parafin tinh khit t C 1 n C20 iukin tiu chun c th tnh chnh xc n 1 K theo phng trnh:

7,232121)1()05,03,193( 91,0s += nnnT (III.1)

trong n l s nguyn t cacbon trong phn t hydrocacbon.

p sut hi bo ho ca hydrocacbon tinh khit c th xc nh theophng trnh sau khi bit Ts , Tc ,Pc :

hlgP = [ 0,01500 + 1,397.(Th)2 + 0,581(Th)]. )

11(

hT (III.2)

trong : Ph =Pbh/Pc

= 0,1018 + 0,3806. 0,02861. 2

=Th.lg(0,96784 .PC).(1 Th)

Th =Ts/Tc

p sut hi bo ho ca cc cu t ring bit c th xc nh bng phngphp n gin hn, l phng php gin , trong ngi ta s dnggin ph thuc p sut hi bo ho vo nhit (hnh III.1 v hnh III.2).



55/292


Bng I II.1. Cc tnh cht ho l ca hydrocacbon v N2, CO2, H2S

Nhit si Cc thng s ti hn

Nhit Cu t

Cng

thc

Khi

lngphn t

0C K0C K

p sut,MPa

Th tch ring,

cm 3/g

H s

n

Metan

Etan

Propan

Butan

izo -Butan

Pentan

izo -Pentan

Hexan

Heptan

Octan

NonanDecan

Nit

Cacbondioxit

Hydrosunfua

CH4

C2H6

C3H8

C4H10

C4H10

C5H12

C5H12

C6H14

C7H16

C8H18

C9H20 C10H22

N2

CO2

H2S

16,043

30,070

44,097

58,124

58,124

72,151

72,151

86,178

100,205

114,232

128,259142,286

28,010

44,010

34,080

161,49

88,63

42,07

0,5011,73

36,074

27,852

68,740

98,427

125,665

150,798174,112

195,798

78,477

60,341

111,66

184,52

231,08

272,65

261,42

309,074

301,00

341,89

371,577

398,815

423,948447,272

77,352

194,673

212,809

-82,60

32,28

96,67

152,01

134,98

196,50

187,24

234,20

267,00

295,61

321,41344,4

149,89

31,05

100,4

190,55

305,43

369,82

425,16

408,13

469,65

460,39

507,35

540,15

568,76

594,56617,5

126,26

304,20

373,6

4,61

4,88

4,25

3,80

3,65

3,37

3,38

3,01

2,74

2,49

2,292,10

3,40

7,38

9,01

6,1985

4,9126

4,5568

4,3945

4,5256

4,3071

4,2759

4,2759

4,2572

4,2572

4,20104,1885

3,2147

3,1723

0,2

0,2

0,2

0,2

0,2

0,2

0,2

0,2

0,2

0,2

0,20,2

0,2

0,2

0,2

56



56/292


Hnh III.1.p sut hi bo ho ca cc hydrocacbon nh nhit thp

Hnh III.2.p sut hi bo ho ca cc hydrocacbon no mch thng

Nhit , 0C

psut,kPa

Nhit , 0C

p

sut,kPa



57/292


III.2 Cc i lng ti hn

Cc i lng ti hn: Tc , Pc , Vc ca cc hydrocacbon ring bit nhnc bng thc nghim xem bng III.2.

Vi cc hydrocacbon t C1 n C15 c th xc nh nhit ti hn

(chnh xc ti 1 K) theo phng trnh:

7,1901)(645,2

1)391,7(0,785c

++

=

n

nT (III.3)

trong n l s nguyn t cacbon ca cu t.p sut ti hn ca hydrocacbon t C 1 n C20 (tr C18) c th xc nh

chnh xc ti 0,05 MPa theo phng trnh:

1,2c 977,7

49,51

nP

+= (III.4)

trong n l s nguyn t cacbon ca cu t.

xc nh th tch ti hn ca cc hydrocacbon t C 3 n C16 (chnhxc n 4 cm3/mol) c th p dng phng trnh:

Vc = 58,0 n + 22 (III.5)

Khi khng th tm c cc i lng ti hn ca hn hp trong ccbng s liu, chng ta c th tnh ton bng nhiu cch khi bit cc ilng thc ca cc cu t. Cng tng t nh vy, cc thng s a, b, c, ...trong cc phng trnh trng thi cng c xc nh bng cch c bit ivi hn hp. Cc ng thc c mt cc thng s ca hn hp c gi l ccnh lut kt hp hoc nh lut hn hp. Khi tnh ton khng quan tm ndng chnh xc ca n m da trn c s gi thit rng cc tnh cht ca hnhp l trung bnh cng tnh cht ca cc cu t ring bit to thnh hn hp.

nh lut c p dng vi cc phng trnh trng thi Van der Walls,Redlich - Kwong, Peng - Robinson xc nh thng sa v b nh sau:

= i jij1/2jijim )(1)( kaaxxa

=i

iim bxb

trong : am , bm l thng sa, b ca hn hp;ai , aj l thng sa, b ca cu ti v j;



58/292


xi , xj l phn mol ca cu ti v jtrong hn hp;kij l thng s tng tc bc hai.

Nh vy cc thng sam v bm ca hn hp c xc nh trn c s ccthng sa v b ca cc cu t tinh khit. Vi cc phng trnh trng thi nitrn, nh lut hn hp l tng ca cc cp bc 2. V d hn hp bn cu ts gm c 6 cp bc 2...

Thng s tng tc bc hai kij khng phi l thng s l thuyt m lthng s thc nghim c s dng hiu chnh trong cc phng trnh

trng thi.Cc gi tr ti hn tm c t cc nh lut hn hp khng phi l cc

gi tr thc, m l cc gi tr gi ti hn, thng c k hiu l Tc v Pc.Nh vy gi tr gi ti hn khng phi l mt im trn ng cong cn bngpha, n ch l thng s tng quan s dng khi nim trng thi tng hp.Trng thi tng hp l trng thi c cng cc thng s rt gn (hnh III.3).

Hnh III.3.p sut hi v p sut rt gn ca metan v propan

Cc thng s gi ti hn c th c xc nh theo nh lut Kay:

==i

iicci

iiccv c.TTc.PP

trong ci l phn mol ca cu t trong hn hp; Pciv Tci l cc gi tr ti

hn ca cu t.

Cc gi tr ti hn ca cc hydrocacbon xem bng III.2.

Nhit , 0C

Metan

Propan

-150-200 -50-100 50 1000

10

1

100

1000

10000

psut,kPa

a

Propan

Metan

0,20 0,40 0,60 0,80 1,000,0001

0,0010

0,0100

0,1000

1,0000

Nhit rt gn, T

psutrtgn,

Pr

b

P

PCPr =

T

TCTr =



59/292


Chia gi tr p sut v nhit thc cho cc gi tr gi ti hn, ta c gitr cc i lng gi rt gn ca hn hp:

cr

T

TT

= ;

cr

P

PP

= (III.6)

nh lut Kay cng c th p dng tnh khi lng phn t hiu dngca hn hp.

V d III.1

Tnh h s chu nn z ca kh c thnh phn v cc thng s ti hn chotrong bng III.2 p sut P = 13,94 MPa (2021 psi) vT= 331 K (5950R).

p dng nh lut Kay xc nh c cc i lng gi ti hn ca hnhp kh. Kt qu tnh theo h n v quc t v n v Anh a ra bng III.2.

Bng III.2. Thnh phn v cc thng s ti hn ca hn hp kh

H Anh H mt MWCu t yi

Pc cP Tc cT Pc cP Tc cT MW MW

N2

CO2

H2S

C1

C2

C3

izo-C4

n-C4

0,0046

0,0030

0,1438

0,8414

0,0059

0,0008

0,0003

0,0002

493

1071

1300

666

707

617

528

551

2,3

3,2

186,9

560,4

4,2

0,5

0,2

0,1

227

548

672

343

550

666

734

765

1,0

1,6

96,6288,6

3,2

0,5

0,2

0,2

3,40

7,38

8,96

4,60

4,88

4,25

3,65

3,80

0,02

0,02

1,29

3,87

0,023

-

-

-

126

304

373

191

305

370

408

425

0,6

0,9

53,6

160,7

1,8

0,3

0,1

0,1

28,016

44,010

34,076

16,043

30,070

44,097

58,124

58,124

0,13

0,13

4,90

13,50

0,18

0,04

0,02

0,01

1,0000 758 392 5,23 218 MW = 18,900

Tnh ton cc i lng gi rt gn ca hn hp theo cc h n v quc

t (h mt) v h n v Anh:

H mt: 521218

331672

235

9413rr ,T,

,

,P ====

H Anh: 521392

595672

758

2021rr ,T,P ====

T gin h s chu nn Katz (hnh III.5) c z = 0,8.



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Hnh III.4. Gin Katz xc nh h s chu nn cc gi tr p sut thp

Hschu

nnz

Hschunnz

p sut gi - rt gn p sut gi - rt a) b)61



61/292


Hnh III.5. Gin Katz xc nh h s chu nn cc gi tr p sut cao

p sut gi - rt gn Pr

Nhit gi - rt gn T r

p sut gi - rt gn Pr

H

schunnz



62/292


T phng trnh trng thi:

V

MWzRTPV == v

ta nhn c cng thc tnh t trng thc ca kh nhit Tv p sut P:

zRT

)P).(MW(=

trong MWl khi lng phn t.

Thay vo cng thc trn ta c t trng thc ca kh:

12033100831080

90189413=

=

,,

,, kg/m3.

V d III.2

p dng cc phng php tnh h s chu nn z ca kh c cha H2S vCO2.

C hai phng php ph bin l phng php Robinson v phng phpWichert. Chng ta s dng phng php Wichert. Trong phng php ny,tc gi s dng cc thng s gi ti hn Pc v Tc c xc nh bng

nh lut Kay v gin Katz. Ngoi ra tc gi cn s dng h sc xcnh t gin trn hnh III.6. H sc s dng hiu chnh cc thngs gi ti hn xc nh t nh lut Kay i vi kh chua. Gi tr cc thngs gi ti hn sau khi hiu chnh c s dng xc nh p sut rt gnPr v nhit rt gn Tr theo gin Katz.

H mt: 556,0cc = TT

556,0)1(c

ccc

+

=

BBT

TPP

H Anh: = cc TT

+

=

)1(c

ccc

BBT

TPP

trong : Pc v Tc l thng s gi ti hn c hiu chnh, t tnhc Pr = P/Pc v Tr = T/Tc , v s c dng trong gin Katz xcnh z.

Pc v Tc l cc thng s gi ti hn c xc nh t nh lut Kay;



63/292


xc nh t gin trn hnh III.6;

B l phn mol H2S trong kh.

C th xc nh theo gin trn hnh III.6 hoc theo biu thc:

= 120(A0,9A1,6 ) + 15(B0,5 B4) (III.7)

trong : tnh theo 0R bng 1,8 K;

A l phn mol H2S v CO2 trong kh;

B l phn mol H2S trong kh.

Vi cc s liu thnh phn kh nh v d III.1, t gin trn hnhIII.6 hoc t biu thc (III.7) c = 21.

Hnh III.6. Gin xc nh h s hiu chnh

% H 2S

%C

O2



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Tnh ton theo cc h n v quc t (h mt) hoc h n v Anh:

H mt: cT = 218 0,556 21 = 206,3 K

cP = 0560218562014380218

3206235

,,,

,,

+

= 4,92 MPa

H Anh: cT = 392 21 = 3710R

cP = 218562014380392

371758

+

,,= 713 psi

t : rP = 2,8 v rT = 331/206,3 = 1,6, do z = 0,83.=

331008310830

90189413

,,

,,= 115 kg/m3.

V d III.3

i khi cn phi tnh ton t trng ca hn hp kh khi c sn rt tthng tin. Ngi ta s dng gin trn hnh III.7 biu din cc tnh chtgi ti hn ca kh t nhin tnh ton gn ng.

Vi s liu tng t nh v d III.1, nhng khi lng phn t ca hnhpMW= 18,90 (cc thng s khc khng bit).

T trng tng i ca hn hp kh (so vi khng kh, khng kh = 1):

0,6528,97

18,90k ==

T gin ta c: Tc = 208 K (3750R)

Pc = 4,62 MPa (670 psi)

T tnh cc i lng rt gn ca hn hp:

H mt: 3,024,62

13,95

cr ==

= P

PP

1,59208

331

cr === T

T

T

H Anh: 3,02670

2021

cr ==

= P

PP

1,59375

595

cr ==

= T

TT



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Hnh III.7. Gin cc tnh cht gi ti hn ca kh t nhin

T gin trn hnh III.4 v III.5 xc nh c z = 0,825 v:

=

3310083108250

90189413

,,

,,= 116 kg/m3

Nhng phng php khc xc nh h s z

Cn c mt s phng php khc xc nh h s chu nn z. Nichung phng php xc nh z t cc phng trnh trng thi c ng dngkh rng ri khi khng cn phi tnh ton tht chnh xc. Cc ng thc thcnghim c pht trin tnh h s chu nn z vi cc hn hp kh cbit hoc hn hp kh trong phm vi hp, cho kt qu kh chnh xc nhng

Pc'

psi

Tc'OR

T trng tng i, khng kh = 1

Tc'

K

Pc'

MPa



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khng tng qut. V d biu Katz p dng tt khi tnh ton vi kh ngt(nh khi tnh ton thit k ng ng dn kh ngt chng hn), nhng likm ph hp vi kh c cha lng nh H2S, CO2 v N2. Bng III.3 di ya ra cc s liu so snh kt qu tnh h sz vi hn hp kh c thnh phnnh trong cc v d trn khi c thm cc h s hiu chnh.

Bng III.3. So snh cc kt qu tnh z

Cc phng php tnh z

Katz

Katz vi h s

th Pc, Tc

Phng trnh trng thi SBV

Phng trnh trng thi SRK

Phng trnh trng thi PR

0,80

0,83

0,825

0,83

0,85

0,81

Vi kh t nhin v kh ng hnh c th xc nh h s chu nn theophng trnh:

z = 0,990 + (Pr 0,0681) / ( 26,481Tr2 + 49,11Tr 25,17) (III.8)

vi chnh xc 0,5% trong khong gi trPr = 0,35 ... 1,5 ; Tr = 1,2 ... 1,8.

Cn ni chung thc t thng tnh ton theo cc gin ph thuc ca zvo cc i lng rt gn nu trn.

T trng ca cc hydrocacbon t C1 n C10 p sut kh quyn ca ra trn cc gin tng ng trong khong nhit thp (hnh III.8) vtrong khong nhit cao (hnh III.9). Gi tr to tng ng vi cchydrocacbon trn hnh III.9 c cho trong bng III.4.

T trng ca kh nn c tnh theo phng trnh:

+=

imii

i

ii

)( vvx

Mx

d (III.9)

trong : v i l th tch mol ca cu ti , m3/kg.mol;

v m l th tch m ca hn hp, tc l i lng cho bit tng thtch ca cc cu t ring bit ln hn th tch hn hp cachng, m3/kg.mol.



67/292


Hnh III.8. Gin xc nh t trng hydrocacbon lng p sut kh quyn trong v ng nhit thp

Bng III.4. Gi tr to v khong nhit tnh t trng ca cchydrocacbon lng p sut kh quyn

Cc to (hnh III.8) Khong nhit , 0CHydrocacbon

x y Hnh III.8 Hnh III.9

n-Pentanizo -Pentann-Hexan

n-Heptann-Octan

n-Nonann-Decan

2,192,072,332,452,652,742,80

0,610,431,532,272,893,363,73

90 ... 050 ... 10

90 ... 0

90 ... 0

50 ... 0

50 ... 0

10 ... 3010 ... 20

10 ... 60

10 ... 90

10 ... 120

10 ... 120

10 ... 140

Nhit,0C

Metyl xyclohexan

Etan

Metan

Etylen

PropanPropylen

2-Metyl propann-Butan

2,2-Dimetyl propan Buten-1Pentan2-Metyl butan

Hecxen-1

n-Nonann-Octan

3-Etyl pentan2,2,4-Trimetyl pentan

n-Heptann-HexanPenten-1

Ttrng,kg

/m3



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Hnh III.9. Gin xc nh t trng hydrocacbon lng p sut kh quyn trong vng nhit trung bnh v cao

Ngoi ra ngi ta cn c th xc nh cc thng s ti hn v gi ti hnca hn hp theo cc gin khi bit gi tr nhit si trung bnh ca hn

hp: T nhit si trung bnh mol xc nh nhit gi ti hn.

T nhit si trung bnh

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