Program BWRS

8/14/2019 Program BWRS

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DGE/ 1549- 3D i s t r i b u t i o n Category UC-66d

A COMPUTER PROGRAM FOR DETERMINING THETHERMODYNAMIC PROPERTIES OF LIGHT HYDROCARBONS

Dav id H. RiemerHarold R. JacobsRobert F B o e hDonald S. Cook

MECHANICAL ENGINEERINGUNIVERSITY OF UTAHSALT LAKE CITY, UT AH 84112D a t e Pub1 ished--July 1976NOTICE

sponsored by the United Ststea Government. Neitherthe United States nor the United Stat- EnergyResearch and Development Addnistmtion, nor any oftheir employees. nor m y of their mntnctorsSubconlnclon. or their employ- , mker anywarranty, expreu or implied. or anumes any Il iabaty 01 responsibility for the accuracy. cornpictenenor u rf u l n ea of m y informtion. apparatus. p r o d u a orpmcirr disclosed, r represents that its UIC would noti n f n n c privately owned right,.

?""si_.-PREPARED FOR T H E I >t p-ENERGY RESEARCH AND DEVELOPMENT ADMINISTRATIONUNDER GRA .IT E I 0-1 ) 1549

~~,~~~~DIVISION OF GEOTHERMAL ENERGY ~~~~~


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DISCLAIMER

This report was prepared as an account of work sponsored by anagency of the United States Government. Neither the United StatesGovernment nor any agency Thereof, nor any of their employees,makes any warranty, express or implied, or assumes any legalliability or responsibility for the accuracy, completeness, orusefulness of any information, apparatus, product, or processdisclosed, or represents that its use would not infringe privatelyowned rights. Reference herein to any specific commercial product,process, or service by trade name, trademark, manufacturer, orotherwise does not necessarily constitute or imply its endorsement,recommendation, or favoring by the United States Government or anyagency thereof. The views and opinions of authors expressed hereindo not necessarily state or reflect those of the United StatesGovernment or any agency thereof.


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DISCLAIMER

Portions of this document may be illegible inelectronic image products. Images are producedfrom the best available original document.


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ACKNOWLEDGEMENTS

This computer routine was developed t o use in program DIRGE0desc r ibed in Ana lys is of D irect Contact Binary Cycles fo r GeothermalPoweP Generation, ERDA Report DGE/1549-5 (September 1 9 7 6 ) .

The suppor t o f E RDA i s a p p re c i at e d .


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ABSTRACTT h i s program was written t o be used as a subrout ine. The program

determines the thermodynamics of 1i g h t hydrocarbons. The fol low ing1i g h t hydrocarbons can b e analyzed: Butane, Ethane , Ethyl ene , Heptane,Hexane, Isobutane, Isopentane, Methane, Octane, Pentane, Propane andPropylene.l ight hydrocarbons given any of the fo l lowing pa i r s o f s t a t e q u a n t i t i e s :pressure and qual i ty , pressure and enthalpy, pressure and entropy, tempera-ture and pressure, temperature and q&l i ty and temperature and s p e c i f i cvolume.dynamic cycle u t i l i z i n g a l i g h t hydrocarbon as the working f l u i d .St ar 1 ing-Benedict-Webb-Rubin equ ation o f s t a t e was used. This re p or tcon ta ins a brief des c r i p t i on , f lowcha r t, l i s t i n g and r equ ir ed equa t ions foreach subrout ine.

The subroutine can evaluate a thermodynamic state for the

These s ix pa i r s o f knowns allow the user to analyze any thermo-The


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NOMENCLATUREa

bBO

cO

C

hlh2h3h4h5h5h6cs 1cs2cs 3cs4cs5s6dDO

EOfhPS

c o n s t a n t i n SBWR e q u a t i o nc on s ta n t i n SBWR e q u a t i o n

I1 I 1 I 1 I 1

I 1 I t I t I t

I 1 I 1 I1 11

I 1 I 1 11 I 1

c o n s t a n t i n i d e a l gas e n t h a l p y e q u a t io nI1 I t 11 I 1 I 1 11

I1 I1 I1 I1 I 1 11

I1 I1 I1 I1 I 1 11

I1 I 1 I t 11 I1 11

I t I t I1 I t I1 11

I 1 I 1 I 1 I1 I 1 11

c on s t an t i n i d e a l gas en t r opy equa t ionI 1 I 1 I 1 I 1 I t 11

I1 I 1 I1 11 I1 11

I1 I t II I t I 1 11

I t I 1 I 1 I1 I 1 11

I1 I1 I 1 I t 11 11

c on s ta n t i n SBWR e q u a t i o nI t I1 I1 11

I1 I 1 I1 I1

f ugaci ye n t h a l p y ( B T U / l bmole)p r e s s u r e ( p s i a )en t ro py (BTU/l bmole)


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TABLE OF CONTENTSABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . iiNOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . v iINTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . 1DEVELOPMENT OF PROPERTIES . . . . . . . . . . . . . . . . . . . . 1PROGRAM DEVELOPMENT . . . . . . . . . . . . . . . . . . . . . . . . 2USE OF CARBON . . . . . . . . . . . . . . . . . . . . . . . . . . 3CARBON . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

D e s c r i p t i o n . . . . . . . . . . . . . . . . . . . . . . . . . 5V ar ia b l e Symbol Tab l e . . . . . . . . . . . . . . . . . . . . 5Log ic D iagram . . . . . . . . . . . . . . . . . . . . . . . . 9C o m p u t e r L i s t i n g . . . . . . . . . . . . . . . . . . . . . . 15 ENTH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

D e s c r i p t i o n . . . . . . . . . . . . . . . . . . . . . . . . . 24Equa t ions . . . . . . . . . . . . . . . . . . . . . . . . . . 24Va r ia b l e Symbol T ab le . . . . . . . . . . . . . . . . . . . . 24Log ic D iagram . . . . . . . . . . . . . . . . . . . . . . . . 26C o m p u t e r L i s t i n g . . . . . . . . . . . . . . . . . . . . . . 27

ENTR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28Description . . . . . . . . . . . . . . . . . . . . . . . . . 28Equa t ions . . . . . . . . . . . . . . . . . . . . . . . . . . 28Va r ia b l e Symbol T ab le . . . . . . . . . . . . . . . . . . . . 28Log ic D iagram . . . . . . . . . . . . . . . . . . . . . . . . 30C o m p u t e r L i s t i n g . . . . . . . . . . . . . . . . . . . . . . 31

FUGAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32D e s c r i p t i o n . . . . . . . . . . . . . . . . . . . . . . . . . 32E q u a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . 32Var iable Symbol T.able . . . . . . . . . . . . . . . . . . . . 32Log ic D iagram . . . . . . . . . . . . . . . . . . . . . . . . 34 C o m p u t e r L i s t i n g . . . . . . . . . . . . . . . . . . . . . . 35


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INVERT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 6 D e s c r i p t i o n . . . . . . . . . . . . . . . . . . . . . . . . . 3 6 Va r i ab le Symbol Tab le . . . . . . . . . . . . . . . . . . . . 36Log ic D iagram . . . . . . . . . . . . . . . . . . . . . . . . 37 C o m p u t e r L i s t i n g . . . . . . . . . . . . . . . . . . . . . . 39

PHKNOW . . . . . . . . . . . . . . . . . . . . . . . . . . . J . . . 40D e s c r i p t i o n . . . . . . . . . . . . . . . . . . . . . . . . . 40Equat ions . . . . . . . . . . . . . . . . . . . . . . . . . . 40Va r i ab le Symbol Tab le . . . . . . . . . . . . . . . . . . . . 40Logic Diagram . . . . . . . . . . . . . . . . . . . . . . . . 42C o m p u t e r L i s t i n g . . . . . . . . . . . . . . . . . . . . . . 43

PRES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45D e s c r i p t i o n . . . . . . . . . . . . . . . . . . . . . . . . . 45 V ar ia b l e Symbol Ta b le . . . . . . . . . . . . . . . . . . . . 45Equa t i ons . . . . . . . . . . . . . . . . . . . . . . . . . . 45Log ic D iagram . . . . . . . . . . . . . . . . . . . . . . . . 47C o m p u t e r L i s t i n g . . . . . . . . . . . . . . . . . . . . . . 48

PRESAT . 49Descr i t on . . . . . . . . . . . . . . . . . . . . . . . . . 49Equa t i ons . . . . . . . . . . . . . . . . . . . . . . . . . . 49V ar ia b l e Symbol Tab le . . . . . . . . . . . . . . . . . . . . 49 Log ic D iagram . . . . . . . . . . . . . . . . . . . . . . . . 52C o m p u t e r L i s t i n g . . . . . . . . . . . . . . . . . . . . . . 54

PRINTC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56D e s c r i p t i o n . . . . . . . . . . . . . . . . . . . . . . . . . 56Va r i ab le Symbol Ta b le . . . . . . . . . . . . . . . . . . . . 56 Logic D i a g r a m . . . . . . . . . . . . . . . . . . . . . . . . 57 C o m p u t e r L i s t i n g . . . . . . . . . . . . . . . . . . . . . . 58

PSKNOW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60D e s c r i p t i o n . . . . . . . . . . . . . . . . . . . . . . . . . 60Equa t i ons . . . . . . . . . . . . . . . . . . . . . . . . . . 60Va r i ab le Symbol Tab le . . . . . . . . . . . . . . . . . . . . 60Log ic D iagram . . . . . . . . . . . . . . . . . . . . . . . . 62C o m p u t e r L i s t i n g . . . . . . . . . . . . . . . . . . . . . . . 64

SATC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65D e s c r i p t i o n . . . . . . . . . . . . . . . . . . . . . . . . . 65 Va r i ab l .e Symbol Table . . . . . . . . . . . . . . . . . . . .Logic Diagram . . . . . . . . . . . . . . . . . . . . . . . . 66C o m p u t e r L i s t i n g . . . . . . . . . . . . . . . . . . . . . . 6765

i v


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I N T R O D U C T I O NTh is sub rou t i ne compu tes the thermodynami c p ro pe r t i e s o f 1i ht

hydrocarbons.a p p l i c a t i o n s s u c h t h a t i t may be used t o d e te rm in e t h e p r o p e r t i e s o f l i g h thydrocarbons i n any thermodynamic c y c le i c l u d i ng, as t h e au th ors deve l opedi t , e v a l u a t in g b i n a r y f l u i d cy c le s .b ox b y t h e u s e r w i t h a l i m i t e d b ac kg ro un d i n p r o g r a m i n g o r t h e p r og ra mmay be mod i f i e d t o meet th e users requ i rements . Th i s manual was w r i t t e nt o a s s i s t t h e u se r i n wh icheve r manner he i n tend s t o use th i s p rogram.DEVELOPMENT OF PROPERTIES

The s u b ro u t i n e was d e v e lo p ed t o a l l o w f o r a w id e ra n g e o f

T h i s r o u t i n e ca n b e t r e a t e d as a b l a c k

The b a s i c e q u a t i o n u se d i s t h e Starling-Benedict-Webb-Rubb e q u a t i o no f s t a t e , w hic h i s a p re s s ur e e x p l i c i t e q u a t i o n o f t h e f orm :

P =

h =

s =

Rn f =

2 3 4 2P R T + (BoRT-Ao-Co/T +Do/T -Eo/T )p + (bRT-a-d/T)p3 + a (a + d / T )p 6

@ (BoRT-2Ao-4Co/T 2 + 5D0/T 3 6E0/T 4 ) p + @ / 2 (2bRT-3a-4d/T)p 22+ar$/5(6a+7d/T)p5 + C@/ ( yT 2) (3 -( 3+yp2/2-y2p4),

bRen (pRT) -@(BoR+2Co/T3 3D0/T 4 + 4E0/TS)p- @/2(bR + d/T)p22YPa@dp5/(5T2) + 2 @C /(yT3 ) (1 - (1 +yp2 /2 )e - + CS1 + C S 2 T

+ Cs3T2 + CS4T3 + CsgT4 + Cs6T5

Rn (PRT) + 2/(RT) (BRT-Ao-Co/TZ + Do/T3 - E0/T4)p + 3/(2RT)2(bRT-a-d/T)p + 6a/ RT) (a- d/T ) p 5 + C/(yRT3) ( 1 ( 1 yp2/2-y2p4)

Ie-YP .)


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2

Recal l tha t a thermodynamic s ta te requires t h a t two properties be known andfor s a t u r a t i o n s t a t e s p r e s s u r e and temperature are dependent.an ideal power cycle the fo l lowing processes are employed, constant entropy(turbine, compressor and pump), con stan t entha lpy (expansion val ve) ,consta nt pressu re (heat exchanger).proc esses, pr op er ti es must be determined w i t h one of the fo l lowing pa i r s

For eva lua t ing

In o rde r t o de te rmine p rop er t ie s fo r these

of knowns: temperature and pre ssu re, temperature and q u a li ty , pre ssu reand quality, pressure and enthalpy,and pressure and entropy. Sincepressure i s a func t ion o f de ns ity and temperature,when pre ssu re a nd tempera-ture are known a search technique must be used t o f i n d t h e d e n s i t y . Oncethe dens i ty i s k n o w n the remaining pr op er tie s may be ca lc ul at ed .s ta tes a re de f ined by the e q u a l i t y o f pressu re and fu gaci ty a t the sametemperature and both saturated 1 i q u i d and vapor densi t ies .

S a t u r a t i o n

When th es a tu r a t i o n p r e s s u r e i s known, a three variable search on temperature ands a tu r a t e d 1 i q u i d and vapor densi t ies i s requ i red . When the sa tu ra ti o ntemperature i s known a two var iab le sea rch i s required on t h e s a t u r a t e dl iq uid and vapor de ns i t ie s . Having completed e i t h e r o f t h e s e s e a r c h e s ,t h e r em a i n i n g p r o p e r t i e s may b e c o m p u te d b y u s i n g t h e s a t u r a t e d l i q u i dand vapor dens i t i e s . The cases of pressure and entropy or enthalpy asknowns re qu ire a two va ria bl e search sin ce both pres sur e and entropy oren tha lpy a re func t ions o f ' temperature and den si ty . This search i s usedonly i n the compressed l i q u i d or superheated regions .i t e r a t i o n t e c h n iq u e i s used for searches i n CARBON beccuse o f i t s genera l ly

The Newton-Raphson

r a p i d convergence.PROGRAM DE V E L0PME NT

Subrout ine CARBON was written i n FORTRAN V for t h e U N I V A C 1108 se r ie scomputer b u t should be easily adapted t o any s imi la r FORTRAN compiler.


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The s u b r o u t i n e a l l o w s t h e u s e r t o u se t h e p r o gr am a t tw o l e v e l s , f i r s tas a " b l a c k b o x" ( t h e m a in t e x t d e s c r i b e s t h e u s e and g e n e ra l developmentof t h e p r og r am ) , s ec on d t h e p ro g ra m may be m o d i f i e d t o b e s t s u i t t h e u s e rsneeds ( t h e r e m a i n i n g t e x t c o n t a i n s a m ore c om p le t e d e s c r i p t i o n o f eachs u b r o u t i n e ) .and as a means o f t r a c in g any po ss i b l e p rob lems .v a r i a b l e d e s c r i p t i o n t a b l e s , f l o w ch a r t s , e q u a ti o ns and a b r i e f d e s c r i p t i o no f a l l s ub ro ut in es .U SE OF CARBON

S u b r o u t in e s were used t h r o u g h o u t t o a l l o w f o r e ac h m o d i f i c a t i o nT h i s r e p o r t c o n t a in s

I n o rd e r t o use CARBON t h e u s e r mu st su p p l y t o t h e p ro gr am t h e f o l l o w i n gi f ormati n :

1. The p rocess f o r wh i ch p r op er t i e s a re t o be de te rm ined (CYCLE)The a l l ow ab le va lues o f CYCLE a re th e f o l l o w in g p a i r s o f knowns:TP - temperature and pressureTX - t e mp e ra tu r e a nd q u a l i t yTV - t empera tu re and dens i t yPH - p r e s s u r e a n d e n t h a l p yPS - p r e s s u r e a n d e n t r o p yPX - p r e s s u r e a n d q u a l i t y

These a r e t h e o n l y a l l o w a b l e v a lu e s o f CYCLE an d t h e o r d e r i s i m p o r t a n t ,i.e., PT o r SP, e tc ., a r e i l l e g a l and w i l l genera te an e r r o r t e r m in a t io no f CARBON.

2. The v al ue o f t h e f i r s t known s p e c i f i e d b y t h e v a l ue o fCYCLE (FGIVEN) .The value o f th e second known sp e c i f ie d by th e va lue o f CYCLE.( SGI VEN ).


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44. Light hydrocarbon type. Acceptable val ues o f L FT Y PE are ISOB,

ISOP, B U T , P EN T, METH, ETH, ETHYL, P R O P , H E X , H E P T , O C T andPROPYL.Print s e l e c t o r - i f NPRIN = 0 , then do not print o u t r e s u l t s ,. otherwise p r i n t r e s u l ts.

CARBON w i l l return the fo l lowing information:1. Enthalpy (Btu/l bm)2. Entropy (BTU/l bmoR)3. Qua l i ty - a p p l ie s t o s a t ur a t io n s t a t e s ,

4.5.6.7.8.9.

10.11.12.

te r than onethen superheated vapor region and i f less than one thencompressed 1 q u i d region.Specif ic volume (f t3 / lbm)Temperature ( O F )Pressure (psia )S a tu r a t e d 1 i q u i d enthalpy (Btu/lbm)S a tu r a t e d 1 q u i d entropy (Btu/ l brr; R)S a tu r a t e d 1 q u i d s p e c if ic vol ume ( f t /1 bm)Satura ted vapor enthalpy ( B t u / l bm)Satura ted vapor entropy (Btu/ l b m o R )Satura ted vapor specif ic volume ( f t /1 bm)

3

3A typ ica l ca l l on CARBON would l ook l ikeCALL CARBON ( I TP ' , TEMP, PRESS, ISOB I , H ,S V ,T ,P NPRIN ,SL ,HL ,VL ,SV ,HV,W, Q U A L )T h i s ca l l on CARBON eval ua tes p rop er t ie s f o r I sobu tane g i ven temperature ,

( T E M P ) and pressure (PRESS).independent of the ca l l in g program excep t f o r the passage of the aboveparamete rs , the re fo re , no e x te r n a l v a r i a b l e s need be placed i n common.

Subrout ine CARBON was w r i t t e n so as t o be


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5

CARBONDes c r p t i on

CARBON i s the main ro uti ne fo r determining th e thermodynamic pr op er t ie sof 1 ight hydrocarbons. The r o u t i n e s e l e c t s t h e a p p r o p r i a t e c o e f f i c i e n t s f o rt h e p a r t i c u l a r l i g h t hydrocarbon to be evaluated. CARBON then determinesi f t he two s t a t e qu an t i t i e s spe c i f i ed accord ing t o t he va lue of C Y C L E a r el e g i t i m a t e q u a n t i t i e s .grea te r than one or l ess than zero for va lues of CYCLE equal t o TX o r PX.

A n example of an i l le g al qu an t i ty would be qu a l i t i e s

O n c e t h e s e t e s t s a r e s a t i s f i e d CARBON then determines the region t o whichthe poin t cor responds , i . e . , compressed l iqu id , sa tura t ed l iqu id-vaporequi 1 i br i um o r superheated vapor. Having determi ned th e reg ion , CARBONs e l e c t s the proper subrout ines t o determine the remaining thermodynamics t a t e p r o p e r t i e s .VARIABLE SYMBOL TABLEABST absolute temperature di fference between O F and OF = 459.6BTOLER lower tolerance on s a t u r a t i o n and convergence testsBUT 1-d imensiona l a r ray conta in ing the required coe f f i c i e n t s fo r

ButaneC

CH

CONVRcs

1-d imensiona l a r r ay conta in ing the coe f f i c i e n t s t o theSta r1 ing-Benedict-Webb-Rubin equ ation o f s t a t e f o r th el ight hydrocarbon to be evaluated1-dimensional a r r ay con t a i n i ng t he coe f f i c i en t s t o t he i dea l gasenthalpyconvers ion fac tor = 0.185057 B t u i n / l b - f t1 -d imensional a r ray conta in ing the co ef f i c i en t s t o the ideal gasentropy

2 3


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6

I CYCLE

DDCRITDHDDDH DTDLDPDDDPDTDSDDDSDTD VETA

EHTYLF G I V E N

HHEPT

Type o f ca lcu la t ion to be made, C Y C L E has the fo l lowing poss ib lpairs of knowns:1 .2.3 .

temperature and pressure = T Ptemperature and qual i ty = TXtemperature and specific volume = TV

4.5.6 .d e n s i t y (1bmole/f t3)c r i t i c a l d e n s i t y ( 1bmol e / f t 3 )

p ressu re and qua l i ty = PXpressure and entropy = PSpressure and enthalpy = PH

a h ( P , W a pa h ( P , I / a~s a t u r a t e d 1iqu id dens i ty (1bmoap( P S T ) / aPa P ( P , T I / a Tas( P, I / a Pas(P , T I a~

3e / f t ' 1

3saturated vapor density ( lbmole/f t )1-d imens iona l a r ray con ta in ing the requi red coe f f i c ie n t s f o rEthane1-d imens iona l a r ray con ta in ing the requ ired c oe f f i c ie n ts fo r EthF i r s t k n o w n passed to C A R B O N , i .e . , temperature for values ofCYCLE o f TP, TX and TV and pressure for values o f CYCLE of PX,PS and PHenthalpy (BTU/l bm)1-dimens onal array containing the r e q u i r e d c o e f f i c i e n t s f o rHeptane


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8

QUALRSS G I V E N

S LsvTT C R I TTRTTOLERVVLvvMUX ISOB

X I S O P

XMETH

qua l i t yuniversa l gas constant 10 .7335 psia-f t / lbmoleentropy (BTU/l bm oR)second known pas sed t o CARBON, i . e . , q u a l i t y for values o f CYCLEof TX and PX, p r e s s u r e f o r CYCLE = TP, sp ec i f ic volume f o rCYCLE = TV, e n th a lp y f o r CYCLE - PH and entropy for CYCLE = PSs a t u r a t e d l i q u i d entropy (BTU/lbm OR)saturated vapor entropy (Btu/lbm0R)temperature ( O F )c r i t i c a l t e m p e r a t u r e ( O F )temperature (OR)upper to lerance on sa tura t ion and convergence tes tsspecif ic volume ( f t /lbm)

3s a t u r a t e d l i q u i d s p e c i f i c voluw ( f t / l b m )sa tura ted vapor specif ic volume ( f t / l b m )mol ecul a r weigh t

3

3

3

1-d imens iona l a r ra y con ta in ing th e requ i red co ef f ic ien t fori sobutane1 -d ime ns io na l a r r a y c o n ta in in g t h e r e q u i r e d c o e f f i c i e n t s f o risopentane1-dimensional ar ra y conta in ing the r e q u i r ed c o e f f i c i e n t s f o r methan e


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vL>

I

n


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10c 27-

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T= F t 1 I NP = S S 1; C PiT R = T 4 i C S T

I --A 1 > ' -


21/94

11

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22/94

12

PPINTC

RETUPN


23/94

1 3

TEMSAT

1 I

t


24/94

14

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PRES

ttt1

ENTH

EIITR

PRINT:

RETURN

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26/94


27/94

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29/94

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30/94

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31/94

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32/94

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33/94

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34/94

24

ENTHDes c r i pti n

ENTH c a l c u l a t e s t h e e nt ha l py and i t s d e r i v a t i v e s w i t h r e sp e ct t odens i t y and t em per a t u r e g i ven t em per a t u r e and dens i t y .c a l c u l a t e d by c om p u ti ng t h e i d e a l gas en t ha lpy and t he en t ha lpy depa r t u r e

The en th al py i s

f r o m t h e i d e a l g a s e n t h a l p y b y u s i n g t h e Starling-Benedict-Webb-Rubinequa t ion o f s t a t e .EQUATIONS

h ( p ,T) = (CONVR/WM) ( ( Bo*R*T-2*Ao-4*Co/T 2 + 5*D0/T 3 6*E0/T 4 ) P + 1 2(2*b*R*T-3*a-4*d/T) p2+a/5( 6*a+7*d/T) p5+c(y*T2) (3- ( 3 9 * P 2 / 2 - y Z

ah P T) = (CONVR/WM) ( BoR+8*Co/T3-1 5*D0/T4 + z ~ * E , / T ~ ) ~ +/2 (Z*b*R+4*d/T 2 2paT -7*a*d*p5/5*T2-2*c/ (y*T3) (3- (3+1 2*y*p2) -y 2 4p ) exp( -y*p2) ) )+2*c *T + 3*Ch4*T 2+4*Chs*T 3+5*Ch6*T 4

'h2 h3ah( ,T = (CONVR/WM) ( Bo*R*T-2*Ao-4*C /T2 + 5*Do/T3-6*Eo/T4+( 2*b*R*TaP 0 2 3 3 5-3*a-4*d/T)p+c1(6*a+7*d/T)p4 + C/(y*T2) (5*y*p+59 p -2*y p )

exp (-Y*P'))VARIABLE SYMBOL TABLEC

CH

CONV R

1 -d im e ns io na l a r r a y c o n t a i n in g t h e c o e f f i c i e n t s t o t h e SBWR eqio f s t a t e1 -d im en sio na l a r r a y c o n ta i n i n g t h e c o e f f i c i e n t s f o r t h e i d e a lgas en t ha lpyc o n v e r s i o n f a c t o r = 0.185057 B t u - i n / l b - f t 3

3 t i


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25

DDHDDDHDTHTTE RM1TERM2TERM3TERM4

3d e n s i t y ( lbmol e / f t )W , T )aP

entha lpy B t u / l b m )temperature O R )in te rmedia te va lueinte rmedia te va luei ntermedi a t e Val ueinte rmedia te va lue

WM mol ecul a r weight


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26

IC(4 *R 'T - 2 . 9 * C ( 2 ) - 4.0*:(6 /7"2 + 5 . 0 * C ( 8 ) /T"3 - 6 . O 'C ( 9 / T+ * 42 . f l*C(3 +R* l 3 . O* C( l ) - 4 . 0 * C ( 7 ) / Tt ( l J ) * ( G . O * C ( l 4 7.0*C(7)::)C ( 5 * ( 3 . 0 - ( 3 .0 + O . S ' C ( l l * D + * 2 - C ( l l ) + ' 2 * D * * 4 ) +E X P ( - C( l l ) * U * * ? ) ) / C ( 1 1 )TEHfII*D 4 TERll:*D**2/2.0 + T i R 1 4 3 * D * * 5 / 5 . 0 + TERE;'J/T W( 5 . 1 1 r C ( l l ) * D 4 5 . 0 * C ( l l ) * * ? * D * * 3 - 2 . 5 * C ( l l ) + + 3 *BlDD T E H r i l + TERX:+D 4 TERM3*D"d + C ( 5 / ( i ( l l ) ' T * * Z +J"5) +E XP( - C ( 1 1 'D+*Z)' E R f l l = ( C ( 4 j . R 4 3 . 0 f C ( 6 ) / T * + 3 - 1 5 . 0 * C ( b ) / T * + 4 + 24.0.C / 9 ) / T + * 5 ) 2' E R N = 0:5*(i?.O*C(3)*S + 4 .0*C( 7 ) :? **2 )*D*+2

~ : 4- z . v T E R ~ ~ ~ / T * * ~'ERI 3 = - C ( 1 0 * D 9 * 5 * 7 . 3 'C ( 7 ) / ( T * * 2 ' 5 . 0 )tI = H*CO lL'R/LIIl + C t l ( 1 ) + C H ( 2 ) T + C H ( 3 ) * T * * Z + C H ( 4 ) *1 * * 3 * U I ( S ) * T * * 4 + C H ( 6 * T * + 5+ 2 . O + C t l ( 3 ) * T 4 3 . 9 * C H ( 4 ) ' i g * 2 4 C i ( S ) * T " 3 * 4 . 04 5 . O * C H ( 6 ) * T * * 4

DH9D = DtiI)D*CO:IVR/'.JIlW5T = ( T E R l I + T E C l l P 4 TER M 3 + :ERY4)*CONVR/ W + C H 2 )

tR ETU R ' I


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38/94

ENTRDESC RI PT I ON

ENTR c a l c u l a t e s the entropy and i t s d e r i v a t i v e s w i t h r e s p e c t t otemperature and densi ty g ive n densi ty and temperature .calculated by computing the ideal gas entropy and the en t ropy depar tu refrom the ideal gas entropy by using t h e S ta r1 ng-Benedict-Webb-Rubinequat ion o f s t a t e .

The en t ropy i s

EQUATIONSS ( p,T) = (CONVR/WM) (-RRn (p*R*T) - (Bo*R + 2*CoT 3 3*D0/T 4+4*E0/T 5 ) p

-1/2 (b*R+d/T 2 2p +a*D*p5/(5*T2)+2*c/(y*T3) (1-(1+1/2*y*p2)e x P ( - Y * P 2 ) ) ) + c s , + cs2*T + Cs3*T 2 + Cs4*T 3 + Cs5*T4+Cs6*T5

28

a T COP.I.VR/WM) ( - R / T - (-6*Co/T4+1 2*DoT5-20*Eo/T6)p+ d*p2/T3-2*a* d p 5 / ( 5*T3) -6*C/Cy*T4) ( 1- 1+1/2*y* p 2 ) exp (-y*p2) ) )

+2*Cs3*T + 3 Cs4*T2 + 4*Cs5 *T 3+5*CS6*T4cs2

aSP = C O N V R / W M ) ( -R/p-( Bo*R+2*Co/T3-3*Do/T4 + 4*D0/T5) - ( b*R+d/T2)p+a*d*p 4 4T + 2*C/T 3( p+y*p3)exp ( -y*p2) )

VARIABLE SYMBOL TABLEC 1-dimensional arr ay con ta in ing the c o e f f i c i e n t s t o the SBWR equat ion

o f s t a t e2 3CONV convers ion fac to r = 0.185037_-BtUurin / l bmft

CS 1-dim ensional a r ra y c o nt ai ni ng the c o e f f i c i e n t f o r the idea l gasentropy

D d e n s i t y ( 1bmol e/f t3)


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29

DSDT

T temperature ( O R )TERM1 in te rm ed ia te Val ueTERM2 in termediate valueTERM3 in termediate values entropy ( B t u / l bmoR)WM molecular w eigh t


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30

START7


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32

FUGACFUGAC c a l c ul a te s t h e f u g a c i t y and i t s d e r i v a t i v e s w i t h r e s p ec t t o

t em per a t u r e and dens i t y g i ven t em per a t u r e and dens i t y . The f u g a c i t y i scomputed us ing the Starling-Benedict-Webb-Rubin e q u at io n o f s t a t e .E Q U A T I O N?,nf(p,T) = An (p*R*T) + 2/(R*T)(Bo*R*T-Ao-Co/T 2+Do/T 3 Eo/T 4 > P

+ 6 4 ( 5*R*T) ( a+d /T) p5+C (y*R*T3) ( 1- ( 1+y*p 2 Z Y2, P4)exp (-Y*P2))

+ 31 2*R*T) ( b*R*T-a-d/T)p2

2 3 4af o = f ( p , T ) * ( l / d +2 (R*T) (Bo*R*T-Ao-Co/T + Do/T - E o / T )aP+3/( R*T) (b*R*T-a-d/T)p + 6*a/ (R*T) (a+d/T)p4+C/( R*T3)*y( 3*y*p+3*y2 **p3-Z Y3 5p 1- exP(-Y*P 2 1)

af (p,T) = f(p,T) * ( 1/T+2/(R*T2)(Ao + 3*Co/T2-4*Do/T4)p + 3/(2*R*T2) (a+2*d/T)p2aT 2 2 4 2-6*a/ ( 5*R*T2) (a+Z *d/T) p5 -3*c/ (y*R*T4) (1- ( 1 y*p /2-y *p ) exp ( -y*p ) )VARIABLE SYMBOL TABLEC

DDFDDDFDT

TERM1TE RM2

1 -d im e ns io na l a r r a y c o n t a i n i n g t h e c o e f f i c i e n t s t o t h e S t a r 1 n g -Benedict-Webb-Rubi n e qu at i on o f s t a t ed e n s i t y (1b m o l e / f t 3 )% ( P T )aP

f ugaci yu n i v e r s a l g a s c o n s t a n t = 10.7355 p s i a - f t / lbmole"Rtempera ture ( O R )i n t e r m e d ia t e Val uei n t e r m e d i a t e v a l u e

3


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33

TERM3 intermediate valueTERM4 intermediate value


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34

S T A R T(7T E R M 2 = : {3 );R'T-C( 1 ) - C( 7 ) / TTERM 3 = C ( l ) + C ( ? ) / TTERM 4 = l . f l - ( l O - O. S* C ( 1 1 ) * 3 " 2 - C [ 1 1 ) * * 2 ' P * 4

C .CPf -3 1 1 ) ' @ ' * 5 1F = L O G ( U h R * T i+ 2 i O o ?f % l i O / t R * T ) + 3 . 0 * O * * 7 ~

F = E X I ' ( I )DFDD F + ( l . O / D t 2 . 0 * T E R K l / { R L T I - 3 . O * T E R V 2*3/

T E A 1 2/(2.fl*R*:)+C.O*C( 10). XRI 3 * Dc * 5 /(5.0aR+T)+C(5)* T E RM C / ( C ( l l ) * R * T * * 3 )

t R *T ) + G .O * C ( 1 0 ) * C + * 4 * T F R u 3 / ( 9 * T + C ( S ) /( R a t ( 1 1 * T ** 3 ) *( 3.G*C( 11:.*3+ .3*t( 11)**?*9* + 3- 2. 0' O t* 5* C ( 1 1 * * 3 ' * i P ( - C ( 11) D " 2 ) ,TERM 1 C( 2 ) +3.0*C( 6)/T"2-J. 0C 8) T* * 3 + 5 . 0 *

T E R I l 2 = C { l - 2 . 3 * C ( 7 / TC ( O ) / T * * 4OFDT = F*( 1 .O/T+2 .0* T E Y 4 1 * D / ( T * * Z * R ) + 3 . 0 *T f R l l 2 'D0*2/(2 .O*~ 'T"2) -6 .3 .C( 13). T E W I 22 ' D k ' 5 / ( S . D * R * T * * 2 ) - 3 . 0 * C ~ S ) ~ T E R M 4/C( 11)*R*T * *4 ) )

RETURN


45/94

-. . . . . .. . . -. ..-. . . - .. . . .


46/94

36

I N V E R TDESCR IPTI N

I N V E R T so l ves a sys tem of t h r e e e q u a t i o n s i n t h r e e unknowns b yG a us sia n e l i m i n a t i o n .TEMSAT. INVERT is used i n t h e t h r e e v a r i a b l e se arch i nVARIABLE SYMBOL TABLEC i n t e r m e d i a t e v a l u eDX(1)DX(2)

ApL to be so lved forApv t o b e s o l v e d for

D X ( 3 ) AT t o b e s o l v e d forF(1)F( 2)

F, v alu e of f i r s t e qu at io nF va lue o f second equat ionF v a lu e o f t h i r d e q u a ti o n

2F( 3) 3I i n d e x3 i n d e xK i n d e xL indexM indexN i n d e xW w o r k i n g a r r a y c o n t a i n i n g t h e c o e f f i c i e n t m a t r i x a n d t h e f u n c t i o n

v e c t o rXJACOB c o e f f i c i e n t m a t r i x


47/94

37

S T A R T

tY E S

YES


48/94

38

YES

1 m K = K + I

t


49/94


50/94

40

PH KNOWDESCRI PT I ON

PHKNOW uses a two va ria bl e Newton-Raphson i te r a t i o n technique t o f indthe dens i ty and temperature given pressure and enthalpy in the superheatedvapor or compressed l iquid regions.EQUATIONSP ( P T ) - 'knownh ( P T ) - known

= o= o

VARIABLE SYMBOL TABLEB T O L E R lower tolerance on saturat ion and convergence tes tsD dens i t y (1bmol e/ft')

a h ( P J )a Pa h ( P T I

a T

. DHDDDH DTDLASTDPDDDPDTH known enthalpy (BTU/l bm)HCAL

l a s t dens i t y ca l cu l a t ed , t o be used i n next i t e r a t i o n.,P( P T Ia PN P J )a T

ca l cul a t e d enthalpy (BTU/l bm)


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41

1L IMITPPCALTTLASTTTOLERX JACOB

indexm a x i m u m number of i t e r a t i o n s a llo we d i n any one searchknown pressure ( p s i a )cal cul a ted pressure (psia )temperature O R )l a s t tempera ture ca lcu la t e d , t o be used i n n e x t i t e r a t i o nupper tolerance on saturat ion and convergence testsJacobian o f pressure and enthalpy


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42

tPRFSUTUENTH

I f

1 . 1- I = I + lP H Y W : F4 I L O

DIDLAST - ( ( P C 4 L - P ) M D T -(HCAL-H)D P D T ) / X J A C O BT = T L A S S T - ( ( H C A L - H ) o P D D - ( P c A L - P ) RETURN

Y cstD = D L A S T / l O . ONo

f

T = T L A S T / l O . O

6


53/94

PRES

43

I

. _.

I


54/94

*4*i4*iYY**4Y***ini*ui*Y*Y*

49****i*YiY4*

x00uoWWaCwc


59/94

49

P RESATDESCRIPTION

PRESAT uses a two va ria ble Newton-Raphson i te r a t i o n technique t o f i n dt he sa tu ra t ion p ressu re and the sa tu ra t ed l i qu id and vapor dens i t i e s g iventemperature.vapor phases m u s t be equal .

A t equ i l ib r ium the pressure and fugaci ty of the l i q u i d and

EQUATIONSI

- m p T )aPJacobian = (

J iacobianL LVARIABLE SYMBOL TABLEBTOLER lower to le ran ce on sa tu ra t io n and convergence te s t sDFFDDL a f ( PL T 1


60/94

50

DFLDTDFPDDL

DFPDDV

DFVDDV

DLDL LASTDPLDDL

DPLDT

DPVDDV

DPWDT

D VDVLASTFFFLFPILIMITM2PPLPV

s a t u r a t e dl a s t l i q u

1 i qu id d e n s i t y ( 1bmod dens ty ca l cu la t ed

e / f t 3 )t o be used i n n e x t i t e r a t on

3saturated vapor densi ty ( l bmol e / f t )l a s t va por d e n s i t y c a l c u l a t e d , t o be used i n n e x t i t e r a t i o nd i f f e r e n c e i n f u g a c i t i e s - f (pL ,T ) - f (pv,T)l i q u i d fu g a c i t y f (pL ,T )d i f f e r e n c e i n pressu res P(pL,T) - P(pv,T)indexmaximum number of i t e ra t ions a l lowed i n any one searchu n i t number fo r p r i n t e dp re s s u re (p s i a )1 i q u i d pressure P(PL,T) ( p s i a )vapor pressu re P(pv T) ( p s i a )

S


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51

T temperature ( O R )TTOLER upper to1 erance on sa tu ra ti on and convergence t e s t sX JACOB Jacobian


62/94

r -

52

FUCiAC

FP = PL - PVF F = FL - FVDFPDnV -DPVDDVDFPDDL = D P L D D LDFFDD'J = - OFVDDVOFFDOL = D F L O D LX JACOi3 * DFP DDV'DFFDDL -DFPDDL DFFDDVD V = D'JLAST ( F P ' D F F D 3 L - F T ' D F P D D L ) iD i = DCLAST-( FF 'DFPDDV-FP*DFFDDV)/XJACOBXJACOR

P R E S A T F A I L ETD CONVERGC

tcETURN


63/94

53

D K A S T DV

YDV = OVL4ST/lO.O

bL , 0.0OL = 0 L L AST; I O . O

FUCACrFUGACr

23FTURN


64/94

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Documents

Program BWRS