Formulario de TerRFmodinámica

8/10/2019 Formulario de TerRFmodinmica

1/7

Univ. Gutirrez Mamani ArielCarrera. Ing. Petrleo y Gas Natural

FORMULARIO ! "!RMOIN#MICA

IN"ROUCCI$N A LA "!RMOIN#MICA

flb

piemlb

g

N

smKg

g

g

amF cc

c .

.

174.3212

=

=

=

Presiones a%solutas mayores &ue la'resin atmos(ri)a

atmmanabs PPP +=

Presiones menores &ue la 'resinatmos(ri)a *va)i+

vacuometromanabs PPP =

Presin ,e un resorte'resin

t

Iresorte

t

resorteresorte

A

VK

A

FP

==

tA

FP=

PROPI!A!- "!RMOIN#MICA-

olumen es'e)i/)o regla ,eGi%%s

m

VV=

scomponentedemezclaPCG

componentesolounPG

..2

..3

+==

!)ua)in ,e Antoine volumenmolar

CT

BAPvap +

=ln n

VV=

PM

mn=

Cali,a,

( )

( )mezcl

sli

mezcla

satvap

satlisatvap

satlimezcla

satlisatvapmezcla

m

m!

m

m!

VV

VV!

V!V!V

=

=

=

+=

1

1

comprimidoliuidoVVV

orecalentadvaporVVV

vapoliuidomezclaVVV

subenocomprimidoliuidoVVsobresoorecalentadvaporVV

comprimidoliuidoPP

osubenfriadliuidoTT

orecalentadvaporPP

sobresaturoorecalentadvaporTT

asobresaturoorecalentadvaporTT

traba"osatlisatvap

satlisatvaptraba"o

satlitraba"osatvap

satlitraba"o

satvaptraba"o

sattraba"o

sattraba"o

sattraba"o

sattraba"o

ctraba"o

>>>

>>

>>

< >

>

!)ua)iones ,e esta,o

!)ua)in ,el gas i,eal

P

T#VT#VPT#nVP

===

alore ,e R

KKmol

mKPa

#lbmol

piePsiamo

flb

#lbmol

BT$

Kmol

cmatmKmol

%

Kmol

cal

3144.8

.731.10

.1545

.9869.1

057.82

082057.0

3144.8

9872.1

33

3

P

z#TV

#T

VPz ==

!)ua)in ,e an ,er 0aals( )

( )

( )

( ) #TbP

B#T

aPA

ABAzzBz

P

#Tb

P

T#a

V

a

bV

T#PT#bV

V

aP

c

c

c

c

==

=++

==

==

+

2

23

22

22

01

864

27

!)ua)in ,e Re,li)1 2 34ong

( )

( )

#T

bPB

T#

aPA

ABzBBAzz

P

#Tb

P

T#a

bVVT

a

bV

#TP

c

c

c

c

==

=+

==

+

=

5.22

223

5.22

5.0

0

08664.042748.0


2/7


!)ua)in ,e esta,o ,e -oave

( )

( )

( ) #TbP

B#T

PaA

ABzBBAzz

TTs

&&s

P

#Tb

P

#Ta

bVV

a

bV

#TP

c

c

c

c

c

==

=+

+=

+=

==

=

2

223

2

2

2

0

11

15613.055171.148508.0

0867.042748.0

Para le 56

c

r

r

c

T

TT

T

T

T=

>

=

5.2

30228.0exp202.15.0

!)ua)in ,e Peng 2 Ro%insn

( ) ( )

( ) ( ) ( )

#T

bPB

T#

PaA

BBABzBBAzBz

TTs

&&s

P

#Tb

P

T#a

bVbbVV

a

bV

#TP

c

c

c

c

c

==

=+

+=

+=

==

++

=

22

32223

5.0

5.0

2

22

0231

11

26992.054226.137464.0

0778.045724.0

!)ua)in ,el virial( ) ( ) ( )

( ) ( )

( ) ( )

( ) ( )22

2

2

2

32

''

........''1

.......1

.....

T#

BCTC

#T

BTB

PTCPTB#T

VPz

V

TC

V

TB

#T

VPz

V

TC

V

TC

V

TB#TVP

==

+++==

+++==

++++=

!)ua)iones ,e 'resin ,e va'or

( ) ( ) ( ) ( [

( )

( )

( )

(

( ) ( )

( )[ ]VPCTVPB

VPAP'c

TVPCT

VPB

VPAP'c

T

T

VPCVPBVPAP

P

'c

vap

vap

c

c

vap

+=

++=

=

++=

ln3.

lnln2.

1

1ln

1.

5.11

Mez)las

Fra))in molar en mez)la gaseosamez)la l7&ui,a

t

ii

n

n) =

t

i

i n

n! =

t

ii

F

F) =

t

ii

F

F! =

)(totalmezlcademolarflu"oF

especiedemolarflu"oF

t

i

Reglas ,e mez)la,o

% ,e mez)la

== ==n

i

ii

n

i

iimezcla b!b)b11

#obinsonPeng

*oaveK&onddlic+

,aalsderVan

Re

a ,e mez)la

K&odlic+

,aderVana)a!a

n

i

ii

n

i

iimezcla

=

=

== Re

2

1

21

2

1

21

*a8+ mez)la

( ) ( ) (

#obinsonPengsoave

aa))aa!!an

i

n

"

"i"i

n

i

n

"

"i"i"imezcla

== = == = 1 11 1

Prin)i'io ,e esta,os )orres'on,ientes

Com'onentes 'uros *'ro'ie,a,esre,u)i,as+

c

r

c

r

c

rV

VV

P

PP

T

TT ===


3/7


==

r

rrc

c

ccc

T

VPzz

#T

VPz

Mto,o ,e ley ersen( ) ( ) ( ) ( )

27.027.0

,27.0,,,

=

+=

zz

PT(zPTzzPTz

c

rrcrrcrr

Mto,o ,e Pitzer Curl( ) ( ) ( ) ( )

0

,27.0,,, 1

+=

&

TPz&zTPz&PTz rrcrrrr

Mez)la ,e )om'onentes

Pro'ie,a,es 'seu,ore,u)i,as*'seu,o)riti)as+

pc

pr

pc

pr

n

i

cii

n

i

ciipc

n

i

cii

n

i

ciipc

P

PP

T

TT

P!P)P

T!T)T

==

==

==

==

==

11

11

#TzVP mezclamezcla =

Mto,o ,e Ly,esen( ) ( )

( ) ( )

==

==

==

=+=

==

=+=

n

i

ii

n

i

iimezcla

mezcla

mezclamezcla

n

i

cii

n

i

ciiPc

PcPc

mezclaPcmezclamezcla

&)&!&

&

TPz&TPzz

z)z!z

zz

(zPTzz

11

PrPr

1

PrPr

11

27.0PrPr

0

,,

27.027.0

27.0,

9ALANC! ! !N!RGIA!:'resin 'reliminar ,el %alan)e ,eenerg7a

( ) ( ) ( )

dt

denergia,-energiamenergiam sistsalent =+

9alan)e ,e materia9alan)e molar

( )

dt

dmmm sistsalent =

( )

dt

dnnn sistsalent =

!)ua)in )ontinui,a,

VelAmV

VelAnV

VelAm ttt

===

-m

-

t

m

tiempo

masam ===

"ra%a;o ,e )om'resin y e:'ansinVPd,PdV, ==

Pro)eso isotrmi)o )on un gas ,ial )on(uerzas motri)es in/nitesimales " -

ocomprimidoliuido***

orecalentadvapor***

vaporliuidomezcla***

traba"osatlisatvap

satlisatvaptraba"o

satlitraba"osatvap

>>>

>>

>>

( )

satlisatvap

satlimezcla

satlisatvapmezcla

**

**!

*!*!*

=

+= 1

Prin)i'io ,e esta,os )orres'on,ientes

1

2

1

2*21

1221

2

1

2

1

2*

11221

2

1

*

11221

lnln

lnln

2

2

2

1

P

P#

T

TCp

#

*

#

*#***

*P

P#

T

TCp****

*P

dP#

T

dTCp****

rr

rr

r

P

P

T

T

r

+

==

+==

+==

9alan)e ,e entro'7a )omo ,esigual,a,

9alan)e ,e entro'7a 'ara sistemaa%ierto en rgimen transiente o noesta)ionario

( )

( )sistsuspsalent

sist

suspsalent

*ndt

d

T

-n*n*

*mdt

d

T

-m*m*

++

+

-istema a%ierto en rgimenesta)ionario o 'ermanente no e:istea)umula)in

( )

( )

( ) 0

0

0

++

+

+

suspsalent

susp

salent

susp

salent

T

-**

T

-**n

T

-**m

-istema )erra,o

( ) ( )

( ) ( )sist

susp

sist

susp

sist

susp

sist

susp

*dt

d

T

-*

dt

dm

T

-

*ndt

d

T

-*m

dt

d

T

-

!/)ien)ia

!&ui'os &ue entregan tra%a;o

idealturbinaTurbinarealturbina

idealturbina

realturbina

idealturbina

realturbina

idealturbina

realturbinaTurbina

idealturbina

realturbinaTurbina

idealturbina

realturbinaTurbina

,,

,

,

,

,

,

,

,

,

,

,

..

.

.

.

.

.

.

.

.

.

.

*

100*

=

===

==

!&ui'os &ue )onsumen tra%a;o

2

2

2

2

100*

.2

.2

.2

.2

.

.

.

.

.

.

=

=

==

==

c

idealsal

c

realsal

Bomba

c

idealsal

c

realsal

Tobera

idealBomba

realBombaBomba

idealBomba

realBombaBomba

Compreso

Compreso

Compresor

idealCompresor

realCompresor

Compresor

g

Vel

g

Vel

g

Vel

g

Vel

,

,

,

,

,

,

,

,


7/7


Pro'ie,a,es resi,uales )on e)ua)iones,e esta,o

!)ua)in ,e an ,e 0aals

( )

=

=

=

=

z

#TbP

z#

*

z

TPa

zTT#T

/

V

a#TVP

V

a

bV

Tb

#T

/

r

C

r

r

1ln

11

2

!)ua)in ,e Re,li)1 34ong

++

=

++

=

V

b

b#T

a

V

bz

#

*

V

b

b#T

az

T

T

#T

/

r

cc

r

1ln2

1ln

1ln5.1

1

5.1

5.1

!)ua)in ,e -oave

( )

( )

++

=

+=

+++

=

V

b

b#T

(

V

bz

#

*

Ta&&(

V

b(a

b#Tz

T

T

#T

/

r

r

cc

r

1ln1ln

15613.055171.148508.0

1ln1

1

2

!)ua)in ,e Peng Ro%insn

( )

( )

++

=

+=

+++

=

Vb

Vb

b#T

(

V

bz

#

*

TTa&&(

(ab#T

zT

T

#T

/

r

r

cc

r

414.01

414.21

ln828.2

1ln

2699.054226.137464.0

41.01

41.21ln

828.2

11

2

Formulario de TerRFmodinámica

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