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Theses and Dissertations

1983

Joule Thomson effects for a hydrogen-methanemixtureRobert E. RandelmanLehigh University

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Recommended CitationRandelman, Robert E., "Joule Thomson effects for a hydrogen-methane mixture" (1983). Theses and Dissertations. 5155.https://preserve.lehigh.edu/etd/5155

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Joule Thomson Effects

for a

Jydrogen - Methane Mitture

by

Robert E. Randelman

A Thesis

in Candidacy for the Degree

Mas t'er of Science

in

Chemical Engineering

of

Department of Che~ical Engineering

Lebigh Uaiveristy

1983

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Joule Thomson Effects

for a

Hydrogen - Methane Mixture

by

Rob~rt E. Randelman

A Thesis

Candidacy for the Degree

Master of Science

1n

Chemical Engineering

of

Department of Chemical Engineering·

Leh~gh Univeristy

1983

This thesis is accepted and approved in partial fulfillment of the

requirements _for the degree of Ma~ter of Science.

------------------------- --Chairmen of Department

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ACKNOWLEDGEMENT

My d e e p e s t g r a t i tu d e mu s t .. b e ext e n d e d t o Dr • L eon a rd A • We n z e 1 · f o ·r· .

his guidance and aid in all phases of my graduate study. Without his

pra~tical understanding and

been completed.

sense of humor this ~ect would not have

~ thank also two people who helped in the reconstruction stages of

experimentation, Joseph Hojsak and Everitt White.

I am truly greatful for the support,· both monetary and moral,

provided by the Physics Department.

enlightening and possible.

. They made my graduate experience

Last, but certainly not least~ my graduate colleagues, Doug,

Morgan, Andrzej, Mark, Bill, Jay and Whitey; · Whose advice and

companionship made for an enjoyable experience.

This work is dedicated to my family. T~rough all the ·trials and \ .. .

tribulations, they always remained 1n my corner.

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1. 2. 3. 4. 5. 6 • 7. 8. 9.

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ABSTRACT I NTRODU'CTI ON HISTORICAL BACKGROUND. EXPERIMENTAL APPARAtUS PROCEDURE THEORETICAL BACKGROUND RESULTS and DISCUSSION AP·PENDIX A-LIST of REFERENCES

Table of Contents

iv

1 3 4 7

10

13 19 68

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~-- -·--·-·-·-~ --··----- ~---· --·-

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Figure 3.:.1: Figure 4-1: Fig_ure 7-1: Figure 7-2: Figure 7.!3:

-1,

1,

List·of Figures

DIAGRAM OF THE JOULE-THOMSON VALVE FLO~.PLAN OF APPARATUS EXPERIMENTAL ISENTHALPS MIXTURE A COEFFICIENTS: DATA vs.PREDIC~ED MIXTURE B COEFFICIENTS: DATA vs.PREDICTED

V

6 9

28 36 52

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Table 7-1: Table 7-2: Table 7-3: Tab'le 7-4: Table 7-5: Table 7-6: .Table 8-1:

List of Tables

NITROGEN ISENTHALP FOR 294.87K AND 135.83 ATM JOULE-THOMSON COEFFICIENTS FOR NITROGEN ISENTHALP EXPER1MENTAL ISENTHALPS: MIXTURE A EXPERIMENTAL ISENTHALPS: MIXTURE B MIX A JOULE-THOMSON COEFFICIENTS MIX B JOULE-THOMSON COEFFICIENTS TABLE of PARAMETERS

· vi

22 23 24 25 26 27 69

---:--::--::-·-_-.-:---

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I I

.I 1. ABSTRACT

. A s p 1 c i a· 11 y d e s i g n e d t hr o t t 1 in g v a 1 v e w a s em p 1 o ye d in a c 1 o s e d ·

recirculating system so as ·to ,measure the Joule.-Thomso.n· co.efficient of

-pure nitrogen and two. mixtures of hydrogen and methane. The mixtures

had· the compoi5ition of .• 127/ .873 mole fraction and .5657/ .4343 mole

fraction of hydrogen_/methane. The valve was designed to minimize

kinetic and· anisen~halpic effe·cts. Nitrogen was used: to check the·

reproducibility of the data obtained by correlating previous results to

present work over the pressure range 135 .83atm to 21.39atm and a

temperature range of 294.87K to 274,38K

Four exp e r i men t a 1 i s en t h a 1 p .s o f e a c h m ix tu r e we r e ob t a in e d o v er

the ~ranges of 74.83atm to 5.109atm and 245.60K to 133.57K. The

isenthalps · were fitted to a third. order polynominal an<l then this

' polynominal differentiated to obtain, the experimental coefficients.

Tlie experimental · coefficients were compared to· the Redlich Kwong

equation of state, as originally proposed, with the Prausnitz

modification and with the Soave modification, and to the Pe~g-Robinson

equation of state, The theoretical coefficients were obtained by using

the data points in the appropriate equation of state with mixing rule

or modification indicated • The data of Benham and Katz gave boundries

for the two phase ·region. 2 Th~ ex~erimental coefficients. were compared

to those obtained by Eakin, et. 6 a 1. .

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.. _.,_, ____ ·--~-~---

For the rich hydrogen mixtureJ the Peng-Robinson equation of state

·;gives excellent results when the Prausnitz correction for critical

·properties is employed. For the methane rich mixtureJ no equation of .. I

.'.~tate p~edicted the entire range adequately, and no recomendation for

ione nor the other can be made. \ It 1s apparent howeverJ that the

riginal Redlich-Kwong equation does correlate ~ell when the mixture is

ot ·on the verge of e~tering the two phase region. For all dataJ the

, eng-Robinson equation showed the lowest deviation at 3.36%. · Tbe

edlich-Kwong equation with the Prausnitz modification was next with

.28%J then the,Soav~ modifica·tion with 4.86% and fi~ally the original

edlich-Kwong equation with 6.51%

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INTRODUCTION

Joule Thomson coefficients are quite useful as a measure of the

pplicability 1

of equations of state and correlations to certain '

The pure ~omponents ~ methane and hydrogen have been studied

~xt~nsively, however, mixture data for this system 1s noticably absent

the literature,·· Hydrogen and methane are comparatively simple

gases, but the quantum interaction of the hydrogen in the

ixture causes effects that are usually not predicted by most equations

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·ecltaetdion of the Joule Thomson coefficient of the

the values of an equation of state gives a rough

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··easure of these. quantum effects. In a~dition, petter parameters for

he state equations could be derived so that other thermodynamic

roperties could be predicted with greater accuracy.

This investigation produces data from the region close to the

aturation curve· an-d strh1es to correlate the data to the

edlich- Kwong and Peng-Robinson equations of state. A mumber of

_ixing rules and modifications were used to represent the theoretical

. reatment. The obj_ective is to find the best equation of state and '

ixing rule by ·c_orrelating experimental coefficients to theoretical, so

this equation .and mixing rule could. be used to predict other

,hermodynamic functions for these mixt~res.

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3. HISTORICAL BACKGROUND

Thermodynamic analysis of the effects of throttling recieved

w id. e s pre ad at ten t i o ~ in the 1 at e n in e t e e t h century • Originally, the

in Ve S t i g at Or S Were inter'~ S t e d in the int er n a 1 energy O f' g a S e S , Jou le

carried out an experiment in 1845 with ·two large copper vessels

connected by a short pipe with a stopcock. One vessel was pressurized

w h i 1 e th e s to p c o ck ·w a ~ c 1 o s e d , t h.e o t he r w a s e v a cu a t e d • The s y s t em w a s

immersed in a water calorimeter and the stopcock was op~ned. The two

sides equilibrated with the rush of the high pressure gas to the vacuum

side, but no change in temperature was reco·rded for any gas. system

used. This was of course due to the high heat capac~tY of the copper.

In addition, the gas, as it is flowing, is in such a turbulent

condition that there is no uniformity of pressure or temperature.

William Thomson, later Lord Kelvin, modified the experiment to'

avoid these difficulties. He worked with Joule on a series of

experiments from 1852 to 1862. Th~ir original experiments we;e steady

flow systems that employed a cotton plug as an obstruction. Heat

losses were min'imal because they heavily insulated the .

p 1pe. They

deduced that frictiona.1 and kinetic effects were proportional to the

square of the flow velocity, and subsequently measured the molal

volume, presBue and temperature on both sides of. the plug. From this

data,. they calculated the Joule-Thomson coefficient. 7 It was not for

fif~y years, however, that reliable data were meas~red.

I

4

. i

Later in the 20th ceitury many investigators modified'the original

experi.ment. Hoxton9 revi.ews the deve'lopments of of this period.

The errors ~n a radial flow, porous plug apparatus include kinetic

effects, and the thermal effects of conduction, convection, and

radiation. Roebuct 17 critically analyzed these errors· and subsequently

produced a set of reliable data for many gases using a porous plug

apparatus.

The· use of valves, because of their ·heat capacity, had not been

s e r i o u s 1 y in v e s t i g a t e d u n t i 1 1 9 41 w he n Jo h n s ·on 1

O in t rod u c e d .

a ma Jo r

modification of the experim~nt by usi~g a valve constructed of ebony,

wood'and monel, It was this valve that Brazinsky 3 used as a model and

further refined the design, This valve, however, did not work well for

large pressure differences, Stockett 19 improved the v~lve further, by

using heavier gaug~ thermocouple wir~~ and inserting the wires directly

in the gas stream. There still existed a problem of heat conduction

through the high and low pressure sides of the valve. Ahlert1

remedied

t h i s p rob 1 em b y u s in g t e f 1 on s e a 1 s b e t we en t'h e s t a g e s and t h i s 1 a s t

modification proved to be quite successful in experimentation. This

was the valve used in ~his.work ·and is shown as figure 3-1.

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Figure 3-1: DIAGRAM OF THE JOULE-THOHSOU VA'LVJ',

Detail of Joule-Thomson Valve

Go., Ovtlct

lao.,i.0.049 "!di/ Type304 · Stam/eo Steel

Super Imulu1or, ·2ft turn~

l..ucite

?oJy~nco Nylon IOI

G,u!ntet

PreS$ure Tap

30 BWG copper­comtontdll th~macouple

NO~E: All maif>rtd! type 304-1,td,nft-t• ~t~e/ un~S3 oth•rwi1• · · ';4'~0 ttd. Ur::t si/v,:r Jo/d~d

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Cor,ctX thermo· couple jland

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4. EXPERIMENTAL APPARATUS

The initi~l phases of experimentation consisted of a great deal of

sys. t em . re bu i 1 d in g • · ·. The He is e gauge s were checked and recalibrated

using the Ruska apparatus and the thermocouples were calibrated with

the platinum resistance thermometer for the range of expermentation.

A storage tank of two cubic feet held the experimental mixture.

The mixture was mixed from pure components supplied by the ~ir Products

and Chemicals, Inc.. Both components were at 99.97% purity, with the

impurity being nitrogen. From the storage tank, the gas was fed to a

two stage Corblin oil-driven diaphragm compressor that has a max1um

discharge pressure of 1600 PSI. Exiting the ·compressor,the gas passed

through a drier that contained Linde molecular . . s 1eve type 3A. No

components were· absorbed by the drier, however it tended to dampe11 the

pressure oscilla~ions that occurred from the staging of the compressor.

After l~aving the drier, the gas passed through a countercurr,ent coil

heat exchanger in which the hot high pressure ias was cooled by the low

pressure stream exiting from the JT valve. The gas then flows through

a constant temperature bath which brought the gas to the desired inlet

temperature ·Th e b a th con s is t e d o f a two g a 11 on dew a r 1 n w h i ch

Freon -11 w·a s u s e d a s the f 1 u id • The coo 1 ant was 1 i q u id n it r o gen , u s e d

both directly and through a coil immersed in the. freon, Real was

supplied by a resistance i-mersion blade •. The temperature control was

maintained by n Bayley Precision controller which activated the heatet

7

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blade when required. Bath agitation was maintained by a Fisher

variable stirrer or by the vaporiiation of the liquid nitrogen,

' After the contant temperature bath, the gas was transferred to the

JT valve by a heavily insulated copper t~be. The valve was enclosed in

a ·tank packed with copius imounts of a variety of insulative materials,

From either ·side of the valve, ·.there is a pressure tap and a Conax

gland for the thermocouples, Exiting the valve, the gas passed through

the heat exchanger, regulating valves and flow meter, then finally back

to the low pressure inlet of the· compressor to repeat the ·cycle, A

flow diagram of the system used is shown in figure 4-1.

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FLOW PLAN_ OF J-T APPARATUS

DRIER

vent .

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HIGH PRESSUR'E:

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HEAT --_;'EXCHANGER

electric heater

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potentio­meter

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LOW PRESSURE.

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5. PROCEDURE \

The system was charged with the mixture by first evacuating' the

apparatus to less than two m~Hg and then purging with 20 PSI of mixture

three times, The stor~ge tank was refilled to 175 PSI after the third

purging

Prior to starting the system, the water to the compressor was

turned on and the oil level checked~ The r~ference jupction for the

thermocouples was set up and' the temperature controller was turned on

to warm up. The constant temperature bath was set up and initially

liquid nitrogen was bubbled through so as to get the temperature 1n the . .,

approximate range required.

Compen~ator pumps and stages to the compressor were primed and the

oil level checked, A valve check of the operator board was carried out

to be sure the valves were set in the correct positions. The Heise

gauges were zeroed and the pot~ntiometer was balanced. The JT ~alve was

opened and the flow regulating valves were closed. The compressor was

started and a constant inlet flow was maintained so the interstage

pressure did not ~xceed 11 atmospheres. A pressure greater than this

causes undo strain to the thin metal diaphragms, , If that pressure is

exceeded, the diaphragms could crack or rupture causing oil to enter

·the system, This occured on the high pressure side once during

~peration and both high and low pressure diaphragms were replaced.

10

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-~- --------------------=:.:.:__ ___ . --~~.,;..;;;.;.,;- --. ···-"~- ,--··----··---·-

At start up of the cornprtssor, the· ·drier inlet valve was closed

8 n d the C i r CU lat i On 10 0 p by pa S S Va 1 Ve W a S Opened SO a S . t O CO n f i !I e the

gas to a s ma 11 reg ion u n t. i l the· comp r e s so r war rn e d up and i t was '. d e te rm in e d t ha t i t w a s n o t 1 o s in g p r 1 m e • There was a one in three

chance that prime was lost due to compensator ,pump valve clogging.

After warm up the bypass "as shut and the inlet opened. With the

regulating valves closed, the pressure increased rapidly. Gas inlet to

the compressor vas halted momentarily at near 400 PSI so that a sample

~ [ could be obtiined for later analysis.

~ f:. f After the pressure was about 100 PSI greater than desired for the l•

.experiment, the flow regulating valves were adjusted so as to get the

proper test. pressure. The entire system was then allowed to

equilibrate and usually did in under' three hours. Equilibrium was

determined when the pressure did not vary more than 5 PSI and the

temperature not more that 2.0K over a· period of thirty mintites

At this point the JT valve was partially closed so as to get

approximataly a 100 PSI kick down 1n pressure from high to low. After

cloaing, the system was allowed to equilibra~e again and usu~lly did in

about an ho\lr, ·nu r in g t h _is t i me t he in 1 e t pre s s u re and t em p e r a tu re

were held constant, and after e~u~libriumt the temperature and pressure

were recorded. Closing the valve further yielded another data point,

and this procedure was repeated five to seven times to generate the

isenthalp. Occasionally, the valve could not be closed very far

.11

·•., .. -·.,

because the temperature drop was enough·to cause a two phase c~ndition.

This condition was shown by the oscillation of the pressure while

temper~ture remained ne~rly constant. When. this effect· occurred, t~at

data _point was not use1 and other data were taken, O~nly when there- was

complet~ confidence that a truly single vapor phase existed was a data

point taken as accurate,

At the end of the exp~rimental session a shut down of the system

consisted of .opening the JT valve to equalize the pressure, The

temperature controller was shut down and a lid was placed over the

. constant temperature bath, A sample of gas was again ·withdrawn and the

re C i r CU 1 at in g g a S W a S d ire Ct e d b a Ck t O the St Ora g e . tank , r O S it i Ve

pressure was maintained in the system at all times, The compressor was

then shut off and the electrical panel shut down, The potentiometer

w a s, s e cur. e d and t h e b a t t e r i e s· d i s e n g a g e d , After the stages to the

compressor were cold to the touch the cooling water was shut off. and

the syste~ was secured,

~as analysis was done on~ Perkin Elmer 910 Gas Chromatagraph with

a 12 foot, 0~25 iqch 0,D, · stainle.ss steel column packed with

chromasorb. An Omega strip chart recorder with integrater was used to

record output from a thermal. conductivity detector, The method of

analy,is was obtained from a U.S. Bureau of Mines report11

12

-,.

6. THEORETICAL BACKGROUND

As with any thermodynamic problem it is best to start the analysis

and ultimate solution at the most fundamental point. For this case,

that point would· be th~ first law:

AH+ C6v2/2gc) + (g/gc)llz = Q - w

. '

We adopt as out system the JT valve itself, hence no work iw done,

We, by design, have minimized the effect of kinetic energy and heat

flow. Relative to the valve, the change' in potentia 1 energy is very

'small. From this analysis we obtain that the change in enthalpy must

be zero. 'Enthalpy is a state function, and we can write the exact differential thus:

. H=H(T,P,X)

We have neglected the composition differential because there 1s no

change in composition. The first differential is defined as the heat

capacity at constant pressure,Cp.

13

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The second differential can be determined . using the Haxwell

relations as:

hence since dH=O, we arrange the e~uation and the result:

-dT/dP = (1/Cp)*[ V-T(; V/ ~T)p]

This is the def in it ion of the Joule Thomson coefficient (.,..ll.)

the equations of state that are applied 1.n this work are the original

Redlich-Kwong 15 , the Redlich-Kwong with the Soave modif ication18

, and

the Peng-Robinson 13 • The mixing rules applied were the original

Redlich-Kwong·, and Chueh and Prausnitz 5 • The derivation of the heat

CBpacity equations and the Joule- Thomson expr~ssions for these

equations of state can be found i~ appendix A.

The equations of state are given as:

The Redlich-Kwong equation is given as:

P .= . RT / ( V - b ) - a / ( TO • 5 ! ( ! + b ) )

They gav~ the valu.es of the constants, a and b, as:

a= 0.42748 [R 2Tc 5f 2]/Pc

b=0.08664 [RTc/Pc]

These were for each pure component.

employed in the original work:

14

The mixing rules that were

., ./1

/

8 nt~ci=l $cj=l YiYj 8 ij

where a .. = (a,a,) 0 •5 . . lJ l J

b m = l.c i = 1 Y i b i

The parameter a, as described in the Van der Waals equation of

state, is an intermolecular· interaction cortstant. The b parameter 1s a

volume size constant.

Brief and Joffe 4 have shown that the pure co~Ronents and nixtures

of hydrogen and methane follow the Benedict-Webb-Rubin equation of

state satisfaitory with the constants Brief and Joffe calculated.

Redlich, Ackerman, et. al. 14 have calculated constants for the

Redlich-Kwong equation of state for methane, and their work has shown

excellent agreement.

The original mixing rules were refined by Chueh and Prausnitz 5

•

Their work was to derive a better equation for the constaµts by using

an adjustable parameter for the first empirical constants 1n the

original equations for "a" and "b". Gunn 8 and his co-workers proposed

a temperature dep~ndence of the critical properties for 4uantum iases.

These dependencies employed a correction utilizing the system

temperature and molecular weight of the qtiantum gas. The corrections

were used in the calculations except for the original Redlich;,. Kwong

values.

· 15

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f r· !

•/ .. ·

Chueh and Praunnitz proponed that:

a.·= 'l J

a= Sl R2Tc 2 •5/Pc a

b=8bRTc/Pc

( Sla • + Slb •) R 2T c , , 2 ' S / ( 2 Pc , , l. J .' lJ l]

Pc,, = Zc,, R Tc,, / Ve,, lJ lJ ' lJ lJ

Ve, ,1/J = lJ

0 5( vc~l/3 +Vc,1/3) • l J .

Zc,, = 0.291 - 0.08((8. + Sl.)/2 lJ' l J

Tc,· = ( Tc, Tc,) 0 •5(1-K, .) lJ l . J lJ

The constant K is a corr~ction factor for the deviation of the

geometric mean. The omega parameters are corrections for the

correlating constants th~t Redlich and Kwong originally used. For the

present work, the omega parameters ~ere identical to those that Redlich

and Kwon·g used. A list of parameters for methane and hydrogen are

supplied in tabl~ 8.1.

Giorgio Soave 18 proposed a tempera~ure dependence on the constant

. a and some changes in the correlating constants.

·a(T) = a(Tc)~'r(l(T)

b(T) = b(Tc)

a(.Tc) = 0.42747 R2Tc 2/Pc

.b(Tc)= 0.08664 R Tc/Pc

16

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,j ., !

' ,ii

. ,~'--·

~.- \ ----·------~----·--·-·-~·- ---· -·- ,It;

where mis the slope of the line obtained by ~lotting:

<r( T) vs. Tr O • S

The slopes have been correlated as:

m= .0.480 + 1.574W - 0.176 w2

·the cross coefficient is a,, = (a,a,)0.5(1-K, .) lJ 1 J lJ

Th~ mixing rules of the original Redlich-Kwong paper are then used.

The temperature dependence of the critical properties· of the

hydr~gen cari be expressed as:

Tc= Tc 0 / [1 + (cl/mT)]

Pc·= Pc 0 /[ 1 + (c2/mT)]

cl and c2 are empiiical constants that equal 2l_.8K and 44.2K

respectively.

· The equation of state proposed .by Peng and Robinson13

1s qu·ite

similar to the Redlich Kwong equation.

P= ( RT/(V -b))- [ a(T)/V(V+b) + b(V -b)]

were a(T) = ·a(Tc)*a(T)

a(Tc)=0,45724 ·R 2Tc 2/Pc

U(T)O.S~ 1 + k(l-tr 0 •5 )

k= 0.37464 + 1.54226"1 -·0,26992"12

· 17

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.)

The cross coefficient_ aij = (1-6)(,aiaj')O.S the 6 must be ,.determined

empiric~ll~. There exists no reporting of 6 f6r .this mixture. It was

' calculated ~sing P~V-T data that was obtained from Mueller,Leland and

Kobayashi 12 .

The b parameters were given by Peng and Robinson as:

b(T)=b(Tc)= 0.07780 RTc/Pc

The mixing rules are the same as those used 1n the Redl:ich-Kwong

original paper,

18

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,. ' 7, RESULTS and DISCUSSION

One can see from the graph£ of the·. isentha:lps that the <fata

. ' present smooth curves and the subs~quent differentiation to obtain the

Joule- T~omson co~fficients yields interesting results. With the

approximate 50/50 mixture one can see that· the Peng-Rot in sen c.urve:;

correlate quite closely. to the data. The general trend is that as one

goes , from the original Redlich-Kwong equation to . the Prausnitz

modification to the Soave modification and finally to the Peng-Robi~son

equa~ion, the agreement gets bett~r betw~en predictiori and data.

Interestingly enough for the hydrogen rich mixture, the data f.all orr

both sides of the predicted. None of the equations yields very good

correlation . 1n howe:ver at higher pressures the all pressure ranges,

agreement is better than at low. This leads to the belief that the

e qua t ions over correct for the· qua n tu t1 int er a c t ions at 1 ow p re s sure .

T.he error associated with the hydrogen rich mixtures a,re: 8.72% for

the original· Redlich-Kwong equation, vith a range of -17 .50 tc 1.38;

4.21% for the Prausnitz modification, with a range of ~9.24 to ,9.33;

4.89% for the Soave modification, with a range of ,-1.86 to .16.25; ~nd

the Peng- Robinson e~uation with 3.21% with a range. of -1.18 t6 11.38 •

The run "3l>" is in doubt because of the high error, but is reported.

'fhe metlrnne rich mixture showed, overall, excellent aqreeE.ent.

there is a clear pattern that as one progresses to a later equation or

mod~fication, thri correlation is improved. The Peng-Robinson eq~~tion

19

,, ,.·

'i·

i

I:

i ,,1· i

' ' . r

( '.

'\!

it ':/J

./ :\I I_.;':' ' I ,I" j

('

--_ . ., ... ,._ -~~-. - r ~: -~--::--:·,·~.:-__ :.: -,J..~ ••

,·

/

. . ·-. ..,, ... -·~ -. ~ ... ~, _l.- .• -;,,_;·· .• ~0.(:..- .:;:::_·_;';- -·· --~.': --~-~-· ·.:. :.,··;: . _, .--~ ~:· .. :.:: .·• - ..;..,-:_.:;,-, ;, . ,,,_'

,· -- ·-· , ..... :·;._,., . .-:.":: .. ..:..',: .;.,.·.'

r c.g ion.

Kwong w1.th a ranee of -l0.00 to 15,(W; l,G§:l !(.d' l?\"~u1s;n:iitt7,. -:~ftli: ,r rl111,:.~ I

of -9.43 to 15.68; 3.33% for Soave vltb a r&ate ~f -n~~~l ,~ ,· I

It is believed that vith the wetfuzme ricfu ~iz~~rE ~EI tfu~

is so slight; however, the hydrogen

the equations all under correct at low p=essure, then over ~cr~e~t ~;

high pressure.

. . approach , but also pressu~e by a ~olecnler radii c~ncept.

parameter takes into account the criticil ?roperties ic it& ~ef£rrit£c~~

however, most correlations t:ha t use tfuie to·

parameters are only weak functiQ,ns.

formulate the empirical constant~.·

Agreement t () the Eakin data

repo~t the coefficients, one had to differenti5te their d3ta.

cd,tat.ion,

,,,'.i ·,

)'. ! ·1 I

.265 k/atm,

Errors associated with the experimental' work are due to inaccuracy

in the pressure and temperature readings or calibrations. The Heise

gauges, even with· a reliable calibration curve, exhibit errors due to

hysteresis and readability. These errors are. estimated by the

recomendation of ·the manufacturer to be 3 PSI and results 1n an error

1n the Joule Thomson coefficients on the order of ~.4%.

The platinum resistance thermometer gave a teinperature error in

the thf}rmocouples of ·o.Ol4K. This error caused an error 1n the

Joule- Thomson coefficient of 0.02%.

errors are, unfortunately, unavoidable.

21

-These temperature and pressure

\;

! ' i'

I: I

Table 7-1: NITROGEN ISENTHALP FOR 294.87K AND 135.83 ATM

Press. ATM Temperatfrre,K ------- ---------------------------------------------

Randelman Ahlert Din Strobridge Roebuck 135.83 294.88 294.90 298.84 294.99 107.59 291.21 291.21 291.06 291.54·

82.84 287.21. 287.44 287.11 287.93 ·'

73.59 285.93 285.81 285.48 286.43 62.17 283.37 283.76 283.33 284.45 283.76 44. 9 2 280.03 280.30 279.82 281.18' 280.31 31.58 277.09 27 7. 3 7 276.92 278.43 277.33 21.39 274.93 275.00 274.54. 276 .• 48 · 274.91 o.oo 269.55 269.58 269.25 271.04 269.33

. 2 2

i' I' ( ,.,

• ·--·--~-.. p _____ , ·~ --· ,-----------·-·· ••• ---·-

I I

i' ! ! ': : ;

: .i 'I : ~

! l !

l

't

''

[. i

i, ! ' i I

:1 ' ',

, ···..;.;.....ji - . -~------ -

Table 7-2': JOULE-TllOMSON COEFFICIENTS FOR NITROGEN ISEHTHALP

For Isenthalp at 294.lSK and 135.83 ~TM

Pr;essure,ATM Coefficient K/ATH

----------- ------------------------------------------------Randelman Ahlert Din Strobridge Roebuck

135.83 0.110 0 .• 116 0.119 0.110

10.7 .59 0.143 0.142 0.147 0.134

82.84 0 .17 2 0.167 0.173 0.158

73.17 0.183 0.177 0.182 0.167

62.17 0.196 0.190 0.194 0.180 0.189

44.92 0.216 0.210 0.212 0.199 0.213

31.58 0.231 0.227 0.226 o. ·215 0.231

21.39 0.243 0.240 0.237 0.227 0.246

o.oo 0. 271 0. 26 8. 0.259 0.254 0.276

23

'",,If/, ·, • , ' ,' r .• t ' ' ' ,, • ' · , , · -. ·1 ' ,,< · < , • ', • ,,,t· . ••• L!-~ - --

l i I

I I. I !

j t' t l: I;

• ! I

i: I' '! ti ! '.

. ' I

'. :

", " ' ,· Table 7-3:. EXPERIMENTAL ISENTHALPS: MIXTURE A

for .127 / .873 mole fraction

Pressure(atm)

6 6 .. • 3 2 7 59.199 51.244 47 .625 44.230 40.842 34.014

54.429 50.009 44.229 38,791 31.299 25.512 18~636

lA

3A

Temperature

219.44 213.48 208.68 204.03 200.88 197.53 190.31

270.18 216.91 211.72 207.55 200.50 193.31 185.52

(K)

24

hydrogen/methane

Press.(atm)

47.636 41. 26 4 34.769 27.141 20.485 13.764 3.402

71.429 62.934 54.431 42.182 30.967 19,407

5.109

2A

4A

Temp,(K)

198.22 192.64 185.08 17.8. 7 4 167.72 155,92 133.57

245.60 238.20 235.33 227.38 215.06 203.07 182.98

l

i I '

I : I I I

I

I ' ' ; i

It I : ' 1

I

I ! l I ! l !

!

' i t . !

Table 7-4: EXPERIMENTAL ISENTHALPSi MIXTURE B

for • 565'7 I .4343 mole fraction hydrogen/methane

lB 2B

Pr-es sure (at m) Temperature (K) P r e s s • ( a· t m )

68.027 199.54 71. 42 9 61.572 198.68 63.272 57,l~68 196.09 ·s 5. 448 50.148 194.96 47.621 43 • 8 8 6 192.59 40.148 38.817 191.21 25.854 33.002 188.85 13.535

3B 4B

74.830 215.25 51.020 65.660 212.43 43.2-07 54.422 210.85 35.378 44.565 206.97 30.279 34.017 203.22 24.153 20.333 198.85 18.369 5.446 192.58 11.568

25

... ,- .. - - . --------~-,--------~--- --- -

Temp. (K) 181.63 178.71 176.62 173.86 170.96 164.19 157.87

204.00 202.00 199.12 197.61 195.72 193.17 190.62

i I I :

I I : I

I

!

l ! ' ! ;

i t

I· I t ii

t i; I."·· 1-· ! ' I I I

I I

_·;~- .r-- ~-:.. .. :'-- ~·

I'

... Table 7-5: MIX A JOULE-THOMSON COEFFICIENTS

Joule Thomson Coefficients

Data RK Dev. RP Dev. RS Dev. PR Dev. -.67566 .66341 1 .-81 .65697 2.76 .67862 -0.44 .66526 1.54 .76475 ·• 7 4010 3.22 .73277 4 .18 .75634 1 .10 .74265 2.89

.• 87535 .82743 5.47 .81905 6.43 .84485 3.48" .83277 4.86 .92957 .88641 4.64 .87744 5. 61 .90501 2.64 .89227 4.01 • 98265. .93756 4.59 .92798 5.56 .9569.9 2.61 .94469 3.86 Mix 1A

1.03776 .99322 4.29 .98307 5 .. 27 1.01360 · 2.33 1.0018 3.47 1.15532 1.12000 3.05 1.10870 4 .04· 1.14190 1 .16 1.1316 2.05

.92185 .92225 -0.04 .91293 0~97 .94171 - 2.15 .92508 -0.35 :.95425 1.0318 -8.12 1 .0212 -7.02 1.0529 -10.34 1.0368 -8.65" 1.0590 1 . 1 7 1 0 - 1. 0 • 5 8 1 • 1 1 5 8 -9.43 1.1939 -12.74 1 . 1780 -11.23

. Mix 2A · 1.2744 1.3209 -3.64 1.3076 -2.59 ,1 .3422 - 5.40 1.3317 -4.49 1 • 5441 1.5516 -0.48 1 . 5363 0.50 1.5689 - 1.60 1.5572 .... 0.85-

N 1.8935 1.8410 -2.77 1.8238 3.68 1.8380 2.93 1.8278 3.47 O' 2.5841 2.5424 -1.62 2.5211 · 2.44 2.4081 6.81 2.4054 6.92

.74761 , .73880 1.18 .73132 2 .18 .75387 -0.84 .74744 0.02

.78144 .78494 -0.45 .77701 0.57 .80092 -2.49 .79555 -1. 80

.84045 .85576 -1.82 .84716 -0.80 .87312 -3.89 .86904 -3.40

.9n·125 · . 92 1 9 5 ..,. 1 . 1 7 . 91 2 8 0 -0 .17 .94036 -'3. 1 9 .93866 -3.01 Mix 3A 1 .0331 1.0319 0.12 1.0219 1 . 08 1 ·. O 511 -. -1. 74 1 .0529 -1.92

1 • 1 464 1.1439 0.22 1 .1331 1 . 1 6 1 . 1 624 -1.39 1 • 1 667 -1.77 1.3029 1 . 281 4 1.65 1 .2698 2.54 1. 291+7 0.63 1.3043 -0.11

.54671 .54059 1.12 .53507 2. 13 .55049 -0.69 .54930 -0.47 .58381 .60619 -3.83 ·.60004

.65058 .65753 -1.07 .65096 -2.78 .61755 -5.78 .61672 -5.64 -0.06 .66981 -2.96 .67265 -3.39 .79887 .75773 5.15 .75039 6.07 .98860 .77221 3. 34' .78015 2.34 Mix 4A. - .89951 9.01 .89112 9.86 .91602 1 • 23 81 1 .0646 14.01 1.0553 14.77

7.34 .92819 6. 11 1.6226 1.0787 12.88 1.0990 11 • 24 1 ._3791 15.00 1.3681 15.68 1.36?2 15.74 1.4020 13.59

-~.- - -. - .-- ' -~ --;..+_.....:.-cfu

-

..

Table 7-6: MIX B JOULE-THOMSON COEFFICIENTS-

Joule Thomson Coefficients

Data RK Dev. RP Dev. RS Dev. PR Dev.

.27354 .30514 '"'."11.55 .28543 -4.35 • 26341 3.70 .27424 -.255

.30008 .32554 - 8.48 .30513 -1.68 .28307 5.66 .29568 __ 1.46

.32676 ~35011 _.··7.15 .32880 -0.64 .30697 6.06 .32147 1. 62-·

.34419 . 36.543 - .: 6. 1 7 • 34373 0 .13 . .32213 6.41 .33819 1.74

.36517 • 384 7-1 - 5.35 .36248 ·0. 7 4 .34141 6.50 .35957 1.53 Mix 4B

.38503 .40695 - 5.69 .38407 0.25 .36363 5.56 .38384 0.31

.40844 • 43215· -' 5.80 .. 40864. -0·.05 .38921 4.71 .• 41233 ....;.0.95

.20178 .23710 -17.50 .22043 -9.24 ,.19984 0.96 . 20842. -3.29

.24045 .25752 - 7 .10 .23998 0 .19 .21874 9.03 .22837 5.02

.28342 .27929 .1.46 .26101 7.91 .23931 15.56 .25116 11 • 38

.31712 .30689 3.22 .28754 9.53 .26570 16. 21 .27929 11 • 93 N .34904 .33753 3.30 .31715 9 .14 .29559 1 5. 31 .31172 10.69 Mix 3B -.J

.'38408 .37859 1 ~ 43 .35707 .. 7.03 .33670 12.34 .35736 6.95

.41402 .43403 - 4.83 .41111 0.70 .39308 5.06 .42002 .:..1_. 45

.28460 .33096: -16.289 .30802 -8.23 .28672 -0.75 .28433 0.09

.30936 .36~27 -17.11 .33768 -9 .16 .31511 -1.86 .31303 -1 • 19

.33829 .39209 -15.90 .36607 -8. 21 .34247 -1.23 .34136 -0.91

.37232 .42667 -14.60 .39908 -7.19 .37463 . -0. 62' .37460 -0.61 '

.40955 .46331 -13.13 r. .• 43416. -6.01 .40912 -0 .10 .41046 -0.22 Mix 23

.49366 .54805 -11.02 .51565 -4.45 .48997 0.75 .49494 -0.26

.57975 .49494 - 9 .. 46 .59930 -3.37 .57332 1 • 11 .58351 -0.65

.26167 .28714 '"'." 9.73 .267t6 -2. 21 ·• 24606 5.96 .25124 .3. 98

.27151. .30191 -11.19 • 281 5 -3.73 .25975 4.33 .26609 1 • 99

.28066 .31796 -13.29 .29692 -5.79 .27469 2. 13 .28116 -0 .18

. 30229 .33646 . -11 . 30 .31478 -4.13 .29225 3.32 .30039 o.63 Mix 1·B

.32640 .35798 - 9.67 .33544 -2.77 .31275 4. 1 8 . 32208 1.32

.34960 .37404 -=6-~97 .35089 -0."37 .32832 6 .10 .33899 3.05

.38049 .39639 - 4 .18 .37254 2.09 .35002 8.00 .36219 4. 81

.. --- . --~-- --~---------· -- -- ---------~- ---------- -----·'· -·-----·· --- .. ··--~----,-·-·- . ..

' I I

I i: t• I.

I. l · !: i

I:. I

I

Figure 7-1: EXPERIMENTAL ISENTHALPS

',

\ ! i

I

·,~- --·~-· -. -

,(: /f• ! 1,/· :p, :I·'

l' I

,',L

' I'

. ~ r

,..._, ~ -w a:: ::, I--< a:: w

. 0.. E Lu· ,_

. ... . 0 .-X g (\I

(\J

"" d 0 ex,

-(\I

0 0 oq-

(\I

0 0 ·O

.-(\I

0 0 lO

0 (\J

0 0 (\J

0 (\I

0 o· ex,

O')

0 0 ~-0') -0 0 0

MIX lA ISRNTIIALP

·-··

O') -+-----...--------..i---·--------r-------..--------. 3.4. ODO. 42., ODD. so .. 0.0.0. 58., O.OD 66,00.0 74,DDO 82., 0.00

PRESSURE CAJM) .

. 28

:I .,·

I .. :,

., ,., i i-i ,. ,,, i": I

r· 1: l l-l L

f' I;,

\:; 1··

V

I;

LJJ ~ ::> I-<

-~ LJJ

. -d .-x 0 a t,...,

0) ....

·d 0

. 0) . 00 .-

0 0

00

0 0 M

.-

0

" lf)

<D .-

a.. ~ [JJ ·O

0 ,.._ I-·

0 0 0)

,q-.-

0 q

',.\ { ,·',·,,,, ?, ... ; '

MIX 2A ISENTIJALP

1,,;.

I : I

•\

. I 1·· I; 'I j ' I I

0 0 M M-f-1-----...--------------------=..-------.------,

43., O.OD. 51 .ooo. ... 3.,00D. 11 • O.OD. l 9. O.OD 27. 0.00 3.5. O.OD.

PRESSURE

29

CA.TM)

! ' . I I ' I I I I i !

i:

. i

-~ .....,

LLJ 0::: :,

\. ' t-< ~ LLJ 0... ~ LLJ t-

[ Ii

• ~·-···"· __ -_. ___ ··."""1::::~~- .• ~.,;.:......-...~ •• - ... ~-·---.--.,, -- _··_

. .-

d -X Q Q 1/)

(\J (\J

0 0 0

(\J , (\J

0 0 If)

(\J

0 0 0

.-(\J

0 0 If)

0 (\J

0 0 0

0 (\J

0 0 If)

0) -0 0 0

0, ...

0 0 V)•

MIX 3A ISENTIIALP

' )

I

~ -l-.;.....----....----------------------------1. 66,000 50., ODD 58,000

1 B. 0.00. 26,0DD 3.4. 0.0.0. 42. ODD.

PRESSURE CA J M)

.30

'I i'

}

'

. -- --- - •- - ·- -~ ---· - --~------­ -----~

f}

t: I

l

,-,.

~ ~

w ~ :) I-

< ~ w a.. E w I-

... 0 ..., X 0. Q co

Q 0 00

I"? C\I

0 0 0

I"? C\I

0 0 C\I . C\I C\I

0 0 ,q-

C\I

0 0 cO

0 C\I

0 0 CX)

0)

0 0 0

0) ...

0 0 C\I

MIX 4A ISENTDALP

CX) -+-,_ .... __________ ,---_____________________ __,

... o .. 00.0. 2.,0DD 4,00.0 6,000

· . PRESSURE (AJ M)

31

8 .. ODO 1 0. 0.0.0 1 2., O.OOX.1 0 1.

i,, I

l~--·--··. -.1-. ~....,- .... _._ .. _··---_·· .. ~-,-- ·---·----~---· ·._. - "~'- .•

- -- -·· - .. .----· ··-- ..... ;::_ ~..;...._..:.· -~·-:- .. -. ------~---1-~X..:-~ry--

i

ti I

r-I ,.

~-

I !

!. ,: ! L f. '· [,, !·, , .. ':

i.

,I

r [' I

f 1·

t f' I ,, f. \

[' f, ~

r t I I

. , t

-~ ._.,

I.LI a:: ::, I-.< a: w a.. E I.LI I-

... 0 .-

g ~· d (\J

a 0 (\J

0 (\J

b 0 0

0 (\J

0 0 ro m .-

0 0 <.O

0) ..,..

0 0 ,q-

m ....

0 0 (\J

m .-

0 0 0

m -0 o. ro

MIX 1B ISEN'flIALP

00-i---------------------------.------------.-

3.3., O.OD., 41., ODO. 49. 0.00. 57,0.0.0 65,000 73., ODO 8.l ., 0.00

PRESSURE (ATM)

32 I

',

! ,.

•

·r r; t, i:: !. ,-,,

~: ~ ._..

[: LJJ f.~ ~ f~ :::> j;._ ;.~ t-i < ;.

'· ~ I'

C w 1·'. a... ;~ E F u.i 1, I I-[: ,:

i I ['.

l.

; ' t 1\ 1.;

I , .. ~ I

'I r

1: I

I· t·

l

: ,:: : ... : ; ·.,.'-,-· - -__ __ ---= .,.,...:..,...--,---·.-- - -~---

. . ~ d ->< 0 d o,

00 .....

q 0 LI) . 00

0 0

00 -0 0

""' "'--.o o· n

"'--0 0 en

tO -b 0 LI)

<.O -'o ·O

.-

<.O

0 0 "'-

MIX 2D ISENTIIALP

1/') -4----------------......-;.......,.---------------.-

13., 000 23 .. O.OD. 3.3., 00.0. 43 .. ODO 53.. ODO.

P 6 ES SURE CA .TM)

33

63 .. ODD 73 .. 0.00.

I I

.1 '

I· ·, I ,,

·( ..

--···,,

I !~

t It I I ' I

r " I

j: t '· i', 1,

r:

,..,, ~ .....,

i i• ,.,: w i,

i L I'

a:: ::> I-'

< I

I, I

I'

! 1' i

a:: w a..

' ~

L w

I I-

fi

l·' f ['.

r' f.

I

i ti [I

[

' I ,

l'

\

... d -:>< q 0. 0

0 0 0

0 0 0

n (\I

0 0 0

0) -0 0 0 . l!) .-

0 0 ·o .. .... -0 0 0

0 0 0

n

0 0 0

... , 'I

'1 MIX 3 8 I SENTilALP

I,

--

--'-----..;._------------.~-----.-------.------. O .• O.OD. 2 .. 000. 4. 000. 6. 0.00.

P.RESSURE (A Tt1)

34

B:. 0.00 1 O .. O.OD 12.o.oox10 1.

:l !

.I i,t

; .·,, , .. ,,, .. , :,: (,., ,,. ,, i', !

'!j .. 1.,

• 1:

l I 'I

I , I

., '

'

·::\',, 111'.

!,i,

,.... ~

I:

.....

Lu ! ~

::) I-< ~ Lu

i a.. ~ Lu

: I-

1·

i i I

' ! ' i !: /'.

i<

I f !:

. ---=--- ·- -- --- --- . -- ---------------------·--· - --- --- -----

d

X Q 0 <.O . d (\I

0. 0 ..., . . 0 (\I

0 0 (\I

0 (\I .

0 .0 0 . 0

. (\I

0 0 00

0)

0 0 <.O

0)

0 0 ."'f

0) -0 0 (\I

0) -0 0 0 .

MIX 4B ISENTHALP

/ . O'l--+------,-------r------.~----....-------.-----1 .-.

1.1., 0.0.0. • .1 9, 0.00 27,0.0.0 3.5,00.0 43 .. ODO

·· PRESSURE (A.TM) .

35

S 1., ODD 59 :o.o.o.

I ·I

•• I

····1 fi

1

, ..

'•1

li~ ..

Figure 7-2: MIXTURE A COEFFICIENTS: DATA vn.PREDICTED

i.

I I

- - • - --::---J.-- ... _

ii I

,! :i " •1

" ]'

ii, ,' 'i p

f,. Ii I'

i' I'

i

I

(

0 oqo (\J

.-

0 tO ...

0 ro 0 .. . -

0 0 0

.-

o. (\/

O"l

0 -..i·

, 00

0 lO "-

0 ro C)

0 0 tO·

34 ,.000 42,000

JOUI,JZ-'1'1101,lfiON COJWI1ICJE!frS

JtIWJ.,lCil··KWotW ono. vs. DNJ'A

50,000 58,000 66,000

(ATM) PRESSURE

RUN 1 A

DATA 0

PRED I CTI!D /.1

74,000 82,000

" ~;

,:1 1.

., •\; ,. .,, ' ·1 ,. ,,

I({ ,,

\ .. fl·. I· i' ,. I

,. ,, ,( ' "· r,,

(:1 I. ,I'

I, I. I

. N :, .. I-

0 ~· (\I

-

0 l{) .-

0 00 .o .-

·z ~ , l/) .m :) .

<( er: Q...

~!o ·I ' ,q· ~ ·oo

i . U' I-: -:) :

0 l{)

"-

0 00 l{)

0 Q (0.

34,000 .. 42 .poo

..

50,000

JOULH-'fllOJ.lf;ON C0Ef1FJ.CIEN1'S

R-K rnAUSNITZ vs. DA1'A .

58,000 66,000

.PRESSURE (ATM)

RUN 1A 37

DATA 0

PREDICTED /j

. .

74,000 .!

82,000

'! 'I I I !

' I I I I

I I,

'

i. ,, .1, !i I :, !,·,

~

~ 1...:.. ~ '-.~

·• ..__

l w ?c

j 0 U)

~ I

re

u I-

I -:, [, t.,

-0 <O .-

0 CJ'J 0

.-

0 0 0

-

0 N m

0 ~· ro

0 <O t,...

.o ro tO

0 0 tO

34,000 42,000

JOULE-Tll01,1SON COBFI•'I CI ENTS

R.:.K SO AVE VS. J)ATA

50,000 58,000 66,000

PRESSURE (ATM)

RUN lA 38

DATA . 0

PlmD I CTED LJ

74,000 1 .

82,000

'· 1. ,, I.

I I I

I.

' I I' ,.

j, ··1

i '

: I [, ,, 1: JI .,, I

/:1

!: ,,

;r

:,

,: f

i,

i I

I 1:

.,

., -- - -· --- ---- - - ·-·---- - -

... ··-- ·--·-· ___ , ___ .__ ____ ~ ,-1----~

0 oq•

(\I

.-

D ,(0,, ... -

'·D ro D ....... z .-

I-<( ·, ~ D

D

"" 0

z 0 U)

z m o. 0

(\J

m a= (!) z w a.. D

I ~ I (X)

U'. I

I-·. J

D tO "-

0 . ro

(!)

D 0 c.o '

,34.000 42,000

JOULE-TIIOUSON COEFFICIENTS

PENG-RODINSON.VS, DATA

50,000 58,000 66,000

PRESSURE (ATM)

RU.N 1 A

DATA 0

PREDICTED A

7A, 000 82,000

~

/

I I ( I. I

!: 'i 'I

'I ' ·1

·i

'i

i,

ii 1: .Jl ,:

r ,I

i ,1·1

(II .

'./'i· 1.,. [''

(' (

L I" I I :h' jl ·1·'. ,•,

t !' !·.i·' ' i

i' I'·

l · I I

h L /,., , I

i:: I I i \·:, 1:. I I• I I.

1r I

l·i: ,:· I' i I:. 1::

I: u, iii il i ;, .1

I i

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0 0

. (\I

n

0 0 ro (\I

0 0

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I (\I.

~

~:

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' 0 0

~ ~ (\/ -(!j z 0 0 3:1 0,

! lO •

~ l •· 0

w a; L') cc 0

u I--:,

0 0 (\J

.-

0 0 ro

0 ,0

,q·

0 0 0 ..

JOULE-TUOMSON COEFFICIENTS

REDLICll-KWONG ORG. VS. DATA

DATA CJ

PREDICTED A

0-+------,.--------------.-...:..~-----.-------1 3,000 11 ; 000 19,000 27,000 35,000 43,000 51,000

PRESSURE (A TM)

:1 I

'!

'i ·1

'I i

,I

•I

'

. ' I

'I : I

I:

' '

•• 1

·i' i I

I II

I

i I,

I I,

i.

i~

J

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--~-·-----~..--,-. ........... _ ... ~=--·-------.......-=------_..,,..~------·-----·---~· ............ --... .--. .._~_,__,....,_..,,..,_·.,ff.--- ...• ~ •. -~.

,-...

2 I-<(

' ~ .._,

·N . J-z U') ::, <( a:: ~

~ •I 0::

u J-J

0 0 (\/

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0 0 00

(\I

0 0 ,q·

(\I

0 0 0

(\I

0 0 <D •

.-

0 0 C\I

.-

0 0 00 .

.. '

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0 0 0

JOULE-THOT,!SON COEFFI CJENTS

R-K PRAUSNITZ VS, DATA '

DATA 0

PREDICTED /J

i.

..

0 -+-------------r----~-------r----~--~-.-~----------r---~..--~--i-----~~~l

3,000 1-1 • 000 19,000 . 27,000 43,000 51 , 000

PRESSURE (A TM)

RUN 2A 41

, I · 1

i; I ; I

'., I .. I

~i i ti 1

, l l fl 11· .;; I ,1:

: i' I r

,, :,

If

......... ~

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w ·:c

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0 U)

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u I-. "?

i; ....

··· ... ·.-~· ·- :·~ . - ...

0 0 (\/

n

0 0 00

(\/

0 0 ~-(\/

0 0 0

(\/

0 0 <.O

0 0 (\/

.-

0 0 00

0 0 ~·

0 0 0 .

JOULil-TttOMSON COEFFICIENTS

R-K SOAVE VS, DAJA

DATA 0

·PREDICTED ~

'' -+-~---~~-.--~~~~.....-~~~~ .......... ~~~~~...,......~~~~·~~~---,

:S,000 11 , 000 19,000 27,000

PRESSURE 35,000

(ATM)

RUN ·· 2A 42

S 1 . 000

'. 'i

I j

I I i

'I

I

I.! I

! : ; I' I I: I

i: li I: i i

: '! I i

i ' I I

. I I

i. 1· '·'

i

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---~--r---·

( ' :

,;1

" ,, y

" ,.

\

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<,

~ I-<t

' ~ ..._,, z 0 V)

z m 0 ~

tO z w Cl..

u I--.,

0

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r,,

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(\I

0 0 ,q•

('J

0 0 0

('J

0 0 <!:>

.-

0 0 (\J

.-

0 o. 00

0 o· . ..q•

JOULE-THOMSON COEJJFICIENTS

PENG-ROBINSON VS. DATA

DATA 0

PREDICTED ~

0 0 0 • o·-1-------------~~--..-.._~~----~---~--~~..;...-,-.,---~~--.

. . 35. 000 · 43. 000 !-;i, 000

3,000 11 , 000 19. 000 · 27,000

PHESSUHE (ATM)

RUN 2A· 43.

'' '

I I

ii

I

I.

1 ~ ,!',

I.

' '

I. ': II I. !'1

1:

' ''

I 1., I•, ;, '

i, '

i ,,

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-- -~.-- _. -· - -

•l .;,.,

0 oq-

n .-

0 (0 (\/

-0 CX) ...

<Dlo . z (\/ 0 Q;

3: ... ~ \ d ll,J 0

n:: .; l!) . 0:: 0

u 1--,

0 tO CX)

0 CX)

""' '

18,000.

JOULR-TllOMSON COEFFICIENTS

REDLICH-KWONG ORG. vs·. DA.'~A

26,000 34,000 . 42,000 50,000

PRESSURE (ATM)

RUN 3A 44

DATA 0

PREDICTED 6

58,000 66,000

,, '' ' i ,, ,· ,, !, II t·

,. •I,

1: ,, ,, I

i

., I

Ir i! V '•. r

' ! i, I

I, I

I: i i

I,

if. I ,,

I! [,

I.: .. L .·,

,,:,

,, :•:1,,' ; ;:;f:-t..!:.

:) ,

',l

,., ,1

'. ' '

,-.. ~

· l-<(

' Y. ..._,

N I-z U) ::> <( cc a..·.

' ~I

•I 0:::

0 tO (\J

.-

0 00 .-.-

0 0 .-

0 (\J 0 '.

0 ...,. O'l

' l .

u I­~ 0

tO 00

0 00

"'·

0 0 "'- .

18. ooo· 26 .·ooo

J'OULH-TJIOMSON COEFFICIENTS'

R-K PUAUSNITZ VS, DATA

'34. 000 42,000

· PRESSURE

50,000

(A TM)

RUN 3A .45

DATA 0

PREDICTED f;J

58,000 66,000

I 'I I'

I i:

I :

' ; !. I /

; il ' 1' I I lr

l . I

f I t

i t I

I '. I I I ' I ' I I I

I I , I

,. ,, lil

,,' ,I,

']: i'

I ,,

,I . I

!t: F I;.·. :i I.

r i: I.' J, I,'

ii I'

II' i

!· :1

: '

i" I

( i,

___ :·1,-: ·-·: .. ··-~~-.--::- --·----. -~ .......... .--- ..

w ~ 0

! lf)

.-

0 tO (\I

.-

0 ro .-

.-

..

! •\~. b ~ ~­I , 0)

0: i .

l I , u;

r r-: f "'")

I 0 w GO

0 O· "-

\

18,000 ·

JOULE~TllOMSON COEFFICIENTS

R-K SOAVH VS,. DATA

26,000. ,.34,000 42,000 ·so.ooo

PRESSURE (ATM)

RU·N 3A 46

DATA 0

PRHDICTED·Ll

58,000 G6,0DO

I :,.

ii ,I H. 11·

! , I

I

: ! '· I

I•

• I ! j\

: ; I

: ' ; .I

' i

o I

,:

I , 1: I

t .', ,;

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! :i 1 ·

I I

; :i I ''' t '.

, ·.

1: I' \,

i I

I; I 1,

!·

1.: !·, ,, !'', 1,/'

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1·

/1.,

,:=-:----· -------. ·-- ·~------'---- ------·-----

\

,...

0 tO (\J

0 0 "-·

18,000

..

JOULE-TilOMSON COEFFICIENTS

PENG-RODINSON VS. DATA

26,000 34,000 42,000 so.ooo 58,000 G6,000

PRESSURE (ATM)

RUN 3A 47

;,.

I

·' \ ~ I-<! ;, ~ .._., z 0 l/)

·z _, m 0 ~

<.!) z· w a..

I

I u· I-J

0 c.o (\I

0 00 .-

•· .-

0 0

-

0 (\I ; •

0

0 '<,j"

0)

0 tD 00

0 ·OO "-

0 0 "-·

. 18,000

..

26,000

JOlJLE-TilOMSON COEFFICIENTS

PENG-ROBINSON VS. DATA

34,000 42,000

PRESSURE

50,000

(ATM)

RUN 3A 47

I, '

DATA 0

PREDICTED I::,.

1,, 1: .t

!1 I

' I 1:

': ·I

; I

58,000 G6,000·

;1 ·'

I I

''

i: 'i ·1 r

;:i ,I

i ;,, .

!'·

I

i' I

,, .. l:i I i, :,

1! i;

!., I,

!i,· I! I I, I!; l/1 i/ ;.= i !(, .

I

--~- ... ~--· --·-·-

0 0 (\J

·n

0 0 00

(\J

0 0 ..,. N

0 0 0

N

0 0 lO

0 0 N

0 0 00

0 0 ~-

0 b 0

JOULE-TTIOMSON COEFFICIENTS

REDLICll-KWONG ORG, vs~ DATA

--· -------------- - ·-­·- ·------·-·-

-DATA 0

PREDICTED !J.

..

0 -1-------...------.....-------"T"""'-----..--------,,-----'----, 0,000 2,000 4,000 6,000

PRESSURE

"8. 000

(A TM)

RUN~ 4A 48

10.000 12.ooox10

i. ,, ,;'

i I,: ,j: I

I' !

. i : Ii '· • i

: ! ! • 1'!

! ! ! : ! l

! :.:-1 J I'. I ·1 I ';' ! ; /!

! ':; I

I ,, I I

l · : I ; : I '.

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t ; 'i ! '

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l

I

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r

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r"

~

-~

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N I--z V) :> <C O'.:

0 l? (\I

n

0 0 00

"'

0 0 ,q-

"'

0 0 0

"'

0 0 tO

.-

Cl.·.

~ -• cc' (.) I-?;

0 0 (\J

.-

0 0 00

0 o· ~-

0 o· 0

., . .,

. JOULR-'fl10t,fS0Ii COEftJ7ICIENTS

R-K PRAUSNITZ VS. UATA

0 -t--__,-------~---·--:-1 8,000 (i.000

0,000 2.000 4.000

PRESSURE (ATM)

RUN 4A. l~9

DATA 0

. ,PREDICTI1D A

10.000 12.ooox10

'i

, I

'. I

; 'i

i i i I I I

I

'' I

i I I

I 11

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I

::,

•. •,,

)

., -:,1

, ,-..

0 0 ('\I

n

Q 0 00

('\I

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, (\J

0 ~o

·O ·1-. . <( ,: ~' ~, w ~ 0 U')

f

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0:: I

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0 0 (0 . .-

.o 0 (\J

• .-

0 0 00

0 0 "It'

0 0 0 .

JOUJ...11-TIIOM 80N COEFF I.Cl ENTS

R-K SOAVE VS. DATA

DATA 0

PREDICTED fl

0 ...-t--------------=----------------------1 0,000 2,000 4,000 6,000 ·' 8,000 10,000 12.ooox10

PRESSURE (ATM)

RUN 4A 50

i i i I

I I

" I

i

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I.·

II:: I• !'t:

1;: I

\;: j. <'

/

0 0 (\I

0 0 00

(\J

.o ·o

-q-

z 0 O· l/) 0

I.O z ro 0 0:: ·'

0 t!) 0

z (\J

lJ..1 .-Q..

u I- o -:> 0

00

0 0 "11'

0 O· 0 •

0

0,000

JOULE-TUOMSON COEFFICIENTS

PENG-RODINSON VS. DATA

-·~···-."'··--r

2.000 4.000 6,000 8,000

'PHESSURE "(ATM)

RUN 4A 51

DATA 0

PREDICTED 6

10.000 12.ooox10

'. ,I

' ' ; .

i i

! . \: i

; I : I

! i

. I I

: i l

'i : I i I

., I

' .,

i I

I .1

! . Ii ! '

I I

'· J:· ·c,· ..

: .. I ·;I· 1i, ,, it; I ;'i th i I

:::!: ..

l: j~~~ ••

i

f ., I. L 1,

Figure 7-3: MIXTURE. B COEFFICIENTS: DATA vs.PREDICTED

'i

I 11

11

_ .I

I I. I I

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·1· 'l \•_i I

'" I I

. ' ·O w

0

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0 OJ ~-

O::· 0

0 ·~ 0:: • 0

f{o 1, OJ

(\I

0 ·"'l:f' (\I

0 0 (\I

,I

J0ULE-'11I0l,1SON COEFFJCIENn:

. RHDLI en-KWONG OIW. vs. DATA

i: : I

i

DATA 0 1·

PREDICTED A

41 .ooo 49,000 57,000 65,000 73,000 81 , 000 J3,000·

PRESSURE (A TM)

RUN lB 52

------·------- -~-----·····

i. ; ' :·

II; :

1_: '

Ii. ilJ I

'),'i il ! ·' i:, I I. 1_:,. I l:, . I :1• . I

i t1·: _:) i · , I I ,:,

~

t""'

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' ~

z U) ::> ~ ~ Q.

~ •I ex:

I u l-J

0 ('I ti)

0 00 ~-

0 0 -..i-

o. ([)

M

0 (\I

n .

0 00 (\I

0 'If" (\I

0 O· (\I.

JJ,000 41,000

JOULE-THOMSON COEFFICimrrs

R-K PRAUSNITZ vs:· DATA

49,000 57,000

PRESSURE

65,000

(ATM)

R·UN 1 B 53

DATA 0

PREDICTED/.)

·,

73,000 ,,81 , 000

1.

,. ,, i

I•

!

\. I

,, I ,, 'r

l1 II ! '

;:. '

i . I

I : I : I I I

:\

IJ' I' II

1l1 , • c· . !,! 1.

:1 i

i!·· ,'.i '.

ii,! (,, I

'' .

~

!~

'I

C 1· l: I i; [;

t l, (,

I, I' r·: I·

l'. b , .. t ('

,-...

2 I-

. :<(

'-~

I.....,

w ~ 0 (j).

I

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rt.

u ~ J.

0

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0 00 ..,.

0 ~ ~-

0 0 -q·

0 (0 f')

0

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0 00

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0 'q'

C\I

0 0

"' •

33,000

JO ULE-'1'11 OJ,! so N ·co Ell FI CI ENT:;

R-K· SOAVE VS, DATA

.. . '

41,000 49,000 57,000

PRESSURE

65,000

(A TM)

RUN lB

DATA 0

PJtEJ>ICTED

73,000

ti

81,000

I I )'

j

' I

.\

' I' I I

I' I:

l: i I .. i

I I I I I

11 l I

I

' I '

I I

! ' I

I ,

l I I

! i

l

i

I I

i 1·,

! '·

z

0 (\I II)

0 OJ oq·

0 0 ~

. · 0 0 ~ (/) (0 : z 10

i

l,i Ii Ii i; 1:

0 "('\I

10

0 CX) ('\I

0 "Cf' ('\I

0 0 N

33,000 41 ~000

JOU l,Il-'l'Jl(H1 f;C)N COEFFICIENTS

PENG-JtonINSON vs. DATA

49,000 57,00~ 65,000

'PRESSURE CATM)

RUN 18 55

DATA 0

PREDICTED /Ji • I

i:.'

i I

· l j

, I

.,

i

' i L. ! • :{

j. j,

I

i I 1:

'Y I; r: I I•

F ' 1·

j; I

11 I I I

;, I

73,000 81,000

1

11'.: .

I/;: '.I' . I , . .

1,'. 11· I , . . ,/ i'i I. ii,i I,

ii ,! I

,.·

i /

11

"''" ·~· ,.,- .... -. ~-. ;•, .::,';

':~

' l .,,l

0 ~· 00

0 lO t-..

0 00 lO

0 (\I If)

0 "q"

·"<it'

0 lO I'?

0 00 (\I

0 0 C\I

1 :5, 000, 23,000

J'OULH-TJJOMSON COEFFICIENTS

REULICII-K\'/ONG OIW. vs·. DATA

33,000 43,000

PRESSURE

53,000

(A TM)

·RUN 28 56

DATA 0

PUHDI CTED /)

I 63,000 7·3'. DOD

':: ,.

I •

t l i

f I 11

I t·

• I

I I

,i • ,.

I,

i: ! t'.,

]·. )

!I . 1q : i}, II,_

1 1 ~---•••- -- ~ --H ; ._.,___ _ __ -_-_--_-_. -_-___ :.;.:___.:..=======~!!!!!!!___.,;;;;;:;;;;:=

.,.

,-·~·- ,-·,.~ .. ; .

. ,

'

I' \: t'; , .. i:' I'

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!

,·

r-1'

t h i,,

'· 1:· I-•

......... ~-:

I-<(

'

0 0 c.o

0 ti) ti)

0 0 ti)

0 ~. ti). .. ~-'--' . N I--z (/) :J <( a; a. ~ •I

c::

u I--:>

0 0 ~-

0 lf) I")

0 0 I")

0 ti) N

0 0 N

13,000 23,000

.·, ..

JOlIT,E-TIIOMSON COEFFICIENTS

R-K PRAUSNITZ VS. DATA

33,000 43,000

PRESSUBE

..

53,000

(ATM)

.... RUN. ·2s 57

DATA 0

I

~ PREDICTED

i

I I

: I I

I I

63,000 73,000

I

,, I•• ;.1

i' i· 1·. I t:,

I

! 1 •

! I ,

i: i1·-._;.

Ii lj, /1 I

·---_--::--:_--·--~---------:-_:;--:- __

i: ~-\·

0 C} (f)

0 lf) lf) .

0 0 11)

0 . 11)

"<;!"

0 0 "<;!"

0 If).

n

0 0 I"?

0 . I/)

C\I

. O· o· ~ .

13,000 23,000

.'?'

JOULE-TIIOHSON COEFFICIENTS

R-K SOAVE- VS. DATA

33.000 43,000 53,000

'PRESSURE (A TM)

RUN 28

DATA 0

PRE.DI CTED 4

63,000 73,000

. I

r.

! l. I I

\,' ' .

i

i ·l . I

I

l ! i' i;

I

I

j .~ ' I ,, 1.,

!

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(· I

'• ,, I

I'

""' :E I-<( .,

[,/ ~ I '-"

z ~ ·1

0 \ ~! r'

i Ul I z I, 1: I·

l· ill

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0

:: a: tO z:

, w a.

u. I-

r, ~ 1:

\i r: ,, \'

!1

0 0 ct)

0 ti) ti) .

0 0 ti)

0 ti)

"ii"

0 0 ,q·

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0 0 f")

0 · II> (\I

0 0 (\I

1:S,000 23,000

J'OULE-TJIOf.lSON COEFFICIENTS.

PENG-IlOilINSON VS, DATA

DATA 0

PREDICTED {j

'l

·!·

33,000 43,000 53,000 63~000 73,000

·PRESSURE (ATM)

RUN 2B

'I• J,'

i:: ,,I ,,; 'I

I

11. l(i' ,;,.I' I:.

,, ,,

I'

), I

1: ': Ir !

ili i1··: 1, i

·1

f

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I l: i i

0 (\I I/}

0 00 'If"

0 ,0 ,q-

0 (0

n

0 (\I I")

0 ro (\I

0 .,,. (\I

0 0 (\I

0,000 2,000

J'OULE-TIIOMSON COEFFICIENTS

REDLICII-KWONG ORG. VS. DATA

4,000 6, 000·. 8,000

PRESSURE (A TM)

R'UN 3B

DATA 0

PREDICTED A

. I

10·.000 12,000XlO

j !

; ; I

I·! :

: '

i i

. \'

Ii I Ii I

I' I i I , I

l j i I

!/ii I :: I

i ;

I i I

..

,,

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i I

,.' ,, ··' J '

0 (\I 1/)

0 00 ..,.

·o . "It"

oq·

,...._ ~ l- 0 <( 0

' 'V

~ ._,

N l-' z U) :> <( ~ n.

I

·~

·I 0::

(.)

I:... J

0 (0

n .

0 . (\J

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0 00 (\J

0 'q"

(\J

0 0 (\I. •

0,000 2.000

JOULE-THOMSON COEFFICIENTS

R-K PRAUSNITZ VS, DATA

4.000 6,000 8,000

PRESSURE ·(ATM)

R.UN 38

DATA 0

PREDICTED fi

10,000 12.ooox10

I

I 1, i' I

:1 •I

;, ; : j; >· i: .. ! :•

i' ' I, I, ! : ' Ii . I

1 l ; I

I ! i ! 'I I : I

I' ! ;

0 00 n

0 0 f")

0 lO (\J

;o : C\I . C\I I •

0 ro

0 0 -

0,000 2,000

JOULE-THOMSON COEFFICIENTS

R-K SO AVE vs·. DATA

I

4.000

•

I '6,000

I 8,000

PRESSURE (ATM)·

RUN. 38

DATA. O

PREDICTED h

I ,o.ooo 12.ooox,o

i

j, .;

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1 !.

I i ; I I ; j : I I I l

I 1 l

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1

1: . i ' ,

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"-"' { z i 0

tn z

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m 0 0::

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w 0. ·•

·:~ u l--:, ,,

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0 (\I II)

0 ()'..)

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0 ~ ...,. •

0 0 ...,.

0 (0. (")

0 (\I (")

0 ()'..) (\J

•

0 . -.i-

(\J

•

0 0 (\J

0,000 2.000

JOULE-TIJOMSON COEFFICHrnTS

P~NG-ROilJNSON VS. DATA

4,000 6,000 8,000

PRESSURE (A r·M) ' ' .

RUN 38 63

DATA 0

PREDICTED

10,000

6

I I

'i

! :

:

i

' '

:;i ·~ ;. i, I

i l I 1

I i

Ii I

·1 i: , I

' 12.ooox10

I !·

!: I .

I .• :_ . ·'

ii : ii;; . ~ ' \ ,

iir r -ii ;

0

"' lf)

C}

00 ~-

0 '<t" ,q·

,0 t!) tO

z·': Q.·· ~: ~

" \ . ., D

i O·· w~ cc: •

0 0:: o. . I .u ~ .. r. (\J

-:) : .

0 ~ ('\I ..

0 0 ('\I

, , . ood

JOULE-nmr.tSOH COEFFICIENTS i I •

1IBDLICII-K'70NG onG. vs. DATA

0 DATA

/1 PREDICTED

-r-··-- I

19;'QOO ·· -27,000

I c,

35,000 43,000

( A'T M)

51,000

'PRESSURE

RUN 48

. '

ii .1

. ,. 59,000

',!,

I.

', I

,. '' ]•I

I' : I ''

,I

I (.

0 (\J lf).

0 CJ)

~-

0 0 "'4·

0 lO !'0

0 (\J f'"")

0 CJ)

(\J

0. ""= (\I

0 0 (\I

JOULE-11IOi,ISON COEFFICIENTS

R-K PHAUSNITZ VS. DATA

~ '@.

"

•

I ··--·--r

1 l • 000 19,000 27,000 :~s. ooo 43. ooo

PRESSURE- (ATM)

RUN 4B 65

\ I

t 1 I'

l

DATA 0

PREDI C'IBD ,A .,

-'·. ! ' I

I

I I

.i.

t i

:] ,. _,

'i • 'I ::, I ,. ,,1 ~-

l ' i,

I -:-...-1 -----i I I

\ ! 51,000 59,000

!

,. ;(

(

r .... -2. F-<(

'-~

' '-' w ~ 0 U)

~ I ~.

u ,_ .. ')

l? 00 ~·

0 ~ ~-

0 0 ~-

0, (t) •

n

0 (\I n

0 00 (\I

o· ~ (\I

0 0 (\/,

(].

1 l , 000 19,000

--~·---~·----•'-·--- -~.

J'OU~,E-'flJOf.fSOH COEFFICIENTS

R-K SOAVE VS, PATA

DATA 0

PREDICTED ~

.. -~-r --i

?.7,000 3S,OOO 43. 000 51. 000 59. uoo

PRESSURE: (AT 1'1)

RUN 4.8 66.

I

!

l

; ' . .

; ' •' :I • 'I I. ii ... i r t ,·

. I

I . ) ~

~ I-~ ....... ~

"--""

z 0 (/)

.z m 0 cc U)

z (JJ 0..

u! 1--: ~:

0 (\I tr)

0 00 ,q·

0 -.;t' ,q·

0 0 ...-i·

0 lO n

.

0 (\I M .

0 00 (\I

·o "It" ('J

O· ·o.

(\I

t

-, .. 11.000 1 9. 000

-----------....... ---~-- -

JOULE·-TIJOl,lSON COEFFIClE!ffS

PENG-Il0BIN80N VS. DATA

DATA O

PREDICTED {j

·--r ___ ..: ·--.,-~----r-··--~·i

27,000 35,800 43,000

( A Tt1)

RUN 48 67

51 , 000 59,000

I I .. t

i j

:, I ,,

,; ,j

:1 .,

·J l I

.J ~ I

8, APPENDIX A

l

! ,'i

f ''.• ! '· ;, :

I '

68 I I I f, I

:; \i ii

/' ·1 I·

/ i

I I

! l !

:1 ·r ·1.

I

!·,

I

'I.,'

Tc(K)

CH4 190.65

H2 43.6

K,, = 0.03 lJ

6,. = 0.1481+4 lJ

Table 8-1: TABLE of PARAMETERS

Data from ~~ed, et. a116

Pc(atm)

-------45.4

·20. 2

Sla

0.4278

0.4278

-----··-0.0867

0.0867

0.013

0.000

R= 82.057 (atm-cc/gmole-K)

IDEAL ]EAT CAPACITY

Cp 0 =A+ BT+ CT2 + DT 3

A

Cll4 4.598

H2· 6 .483

--------1.245

0.2215

(cal / gmole-K)

Cxl0 6

--------2.860

-3.298.

69

T(K)

Dxl0 9

-------·---2.703

1 • 8 26

' ! i !., I

. i

'~ ··:

'' ~I•

'.;

' ... ,,,.--. '·-. ····-. - - . \ • J ·--· --- -~ ------- --··~•· -·--- ··--·------~------·,---- .

Development 6f Expressions

Heat Capacity and Joule Thomson Coefficient

The· :general differential expressions for the heat capacity or .. Joule Thomson coeffidient · cin be stated as:

. fo~ (T(B¥)p- V)

C p.

,· (~) We can express aT p

Therefore:

C =-T(~) v ·p (~P) .

. JV t - V

The heat capacity can be expressed as: ~

J d2P T _._("' ,;.2) dV

·O'T V V

. Clearli with the .prbper derivatives the expressions could be

· solved. These expressions were then applied .to the Redlich­

Kwong equation of state, both original and with the Soave

modification; and to'the Peng-Robinson equation of state.

•·

70

. l

i i' !:: i:l f '.! I j

! i I I i ·! : l

I i I

I ! I I • I

·I

I I

!

.:I II ·{

: ·1

I I r,

r

_, .....

~;.~ :., ......... "';'"···-.... --~ic-:~ ... - · · .. . -.·.--...::.~---~~.-.-:--.-...

--····-·-

- ~--~-~~-c.-::a.::"'..........:--. __.,1:;.,.,.~=:::.1 ...... ..'..! -~-~,,2~~w~~-,

Expres~ions for Heat Capacity and Joule Thomson Coefficient­

Redlich-Kwong: Original

a . P=RTb - -T-o~.5~V(V+b) (V+b)

V- . 0.75a 1n V· . _ Co _ R +T1 • 5b C - p -p 2 R 0.5a )

T( V-b. + T1 .5(V+b)V.

RT + 2a + ab _{V-b) 2 _To. 5 (V+b) 2y To. 5v 2-(V+b) 2

-RT._ 0.5a + RTV _ 2a _ ab

C. = V-b ~ T0 • 5 (V~b)V (V-b) 2 T0.5(V+b) 2 T0 • 5 (V+b) 2V p _ RT + 2a

· · (V-b)~ T?· 5 (V+b) 2V + ab

T0.5v2(V+b)2

With the Soave modifacationp a is not a constant, but a £unction 0£ temperature.

am-' ( T) = ~ ~ y1. y . ( 1 -K

1. J. ) ( a . a . a . ( T) a • (T) '5 O ~ 5

-:-:. -" J . C 1 CJ 1 .J

0 2 2 -1 ·a

1.= .42747 -R T. P.

C C1 CJ.

a. (T)= ( 1. + (ni. (1. -Tr. 0.5)) ) 2 1 . 1 1 .

m. (c.c,) =. 0. 480 + 1 • 57 c.:>4 ··.- 0. 176:Cy. 2 1 . ~ -1

dP =- ( R/v-b)dT - (V(V+b) r-1 da (t) m

·--...---,-. -~------··-~-.,':~,,,,."" .... ___ ..... __ ._ --,.----------···--·------ -·-·---·· •--·-· -·----·-- - --- . -·- ·-· ·- - . - . . .

1~{

i if t r :: r

i' ~-~·

=· ~:,.:,2...,:,),L~c:.c,, .. , : ,c

..L.,....C,.t~\,-'C;)">>:"' .·3'",§':,.).K_-:.;,;'~~ .. "; .• ,...;.~-rn-: .. -- ., .. ~-::;:;.,,-...~~,-··

We can express the derivative 0£ am(t) as: Z * Q

Z=~~ ~iyj(1_~Kij)(aciacj·)o.5 . ~

m.m. Q= -.5mi.- .5mimj ._ .•. 5(mj±1Jlimj)

(Tc.T)O.S 1i6 T)0.5 l. . . j

+ l. J (Tc1T~j)0.5

...., N

Hence:

dP ·= R/(V-b) dT . .

(Z*Q)/(V(V+b)) . .

dP = ( -RT ) + dV (V-b)2

( 0-vv-. (V(V+b))~)(2V+b)

a:2p

dT 2 . -·z dQ/(V(V+b))

.25m. + .25m.m. dQ~ l. . l. J

. (Tei 0~5T1 .5) +·

.25mj .+ .25mimj

. (Tc.o.5T1.5) J .

Now by dirgct substitution we obtiin:

C = c0 p . p R T(dp)·2

dT

(dP) dV

. ---·--·--_.·- -.~ -~-----.e -.. w--•r-·, ... , . . ,-,: ........ ..,.~--~-l'f'i': .. ·r-- - -···-·---·· ·- ·.

TZdQ_ 1n (V+b) b V ·

•,

...

4=

-·-

.. '

dP dP (-T(dT) - V(a:v)

~p (*)

-...J • w

,·.0:.::_.--;:...,.,r;~:i.:.:c_~ :r~,-- ,...~;;;, .. ,. :. ____ ,.-- .-·

A similar procedure £or the Peng-Robins9n equation of state:

p .... RT V-b

a

(V+b)V + b(V-b) .

dP _ =fil 2 DPV= dV - (V-b)

+ a(2V'+2b) ~

(V(V+p)+(V-b)b) 2

dP R . ( ( ) ( ) ) -1 da -DPT= dT = V-b)2 - V V+b + b V-b dT.

a~'~ y .. y. a:·. c.,, J. J J. J

( • • ) - I -J.. = J a . . = a c . . a .

J.J J..J. J.

( ·~-)- _ C( - - )0.5 J.,J a .. - a .. a ..

1.J 1.J. JJ .

C = ( 1 • - 6 .. ) J..,

acii . J

- 0.45724 t R Tc.) 2 / . J.

Pc-= i.

a' i = ( 1 + K . ( 1 - Tr? • 5 ) ) 2 . -J. J.

. 2 K:l . = '·0.37464 + 1.54226(,Ji -. 0.26992Wi

daij dT .i- = Daij=

( ·-·) . di - K (( , )0.5)(T T)-0.5 J.-J acii a ·i - - i · acii a :i.i · - "··· _ ci

,-

(i;'j) 0.5(ac~iacjj)-0·5c (a'jda'i + a'ida•j>.ca•iaij)-0 •5

...... ·'--::._~·-:~ -~

>~

•

..

, .

f I~

'

_. ~-

-~- ~ -=-~ -:-::.~ . ..,_ ·.--:-~--:-·_

· ·2~r;;-•.._.. ... ~- __ .:_:._··.·:-i~·'-"·-~-'"'··::.-,·

Q = ~~yiyj daij

_D;PT_ = (V~b) - (V(V+b) + b(V-b) )-1 Q

2 D4PT = d ! = -(V(V+b)+b(V-b) r-1 ~~

dT .

. DQ = . ~~ = ~~ yiy j (~2ai,j

dt2

d2a.·.= ac .. d2a'. 1.J 1.J 1.

) = 'E~~yiyj .,.. "J

"~.,_.,.::-.... ~;;:;:,,_~~~·~-': .... -:

d2aij ·

k a'~.5 K.

( · · ) d2 · ( i 1 ) ( 0. 5 . _J_ )

1.=J a .. = ac. · O 5 -1 5 - _-: ... Q 5 1 t:::

J.J J.J Tc. • T • ·Tc .• T • J. J.

(i#j) d2a .. =· (0.50)((a' .a' .)-0.5(a' .d2a.·. + 2da' .. da' "j .. J.J J. J. J J.J. J.J. J

+ a' . d2a' . ) J. J

+ ( ' d ' + t d ' ) 0 5 ( . t ' )-1. 5·( ' d. t + t d. ' ) ) a . a . a . a .. -. • a . a . · a . a . a . a .

J J. J. J J. J J. J J 1.

Substituting into the equations we obtain:

. C = C 0

p p R - T((DPT) 2 /DPV) + T{DQ)_(~b2 )--0.5 ln( (2V+b+(8b.2

)0.5) (2V+b-(~b2)0.5)

AL= (_;(T (DPT)) (V(DPV~)/(Cp(DPV))

'l!"'""~•-,.--"<"''.#-..,,-~~~1:"'-,.;:r,-~-::---"'"'":".-.,._~ ~ ~--- __ ._,__ .. ..., __ J_:-...,..-,.~1·-MO' .... ,..,___~ . ..- •.• ,. .... ,-~ ,......, ..... ,.-..._-,---:""-·•.--~·--~·-I .-.,.- -,~-. ..... --h••._•,•• ~--~,-• '°?"'•-"••, •,, •. ,~_., •. -,,.-•

' I

i· i

9. LIST, of REFERENCES

1 •

2 •

LIST OF REFERENCES

Alhert,R.C., Ph.D. Thesis, Lehigh University·, Bethlehem, Pa, 0964)

Benham,A.L. and I<atz,D.L., "A.LCh,E, Jour."J..,33,(1957)

3, ·Brazinsky, I., M.A. Thesis, Lehigh University, Bethlehem, Pa, (1960)

4. Brief,A. and Joffe,J, 11 Jour. Chem. Eng. Data "li,1,(1970)

5. Chueh, P.H., and Prausnitz, J.M., 11 Ind, Eng. Chem. Fund." &.,492,(1976)

6, Eakin,B,E,,Devaney,W.E, and Bailey,N,L.~ ~ Proc~ of 54th Gas Processors Conv~ -Enthalpy Measurements of Synthetic Gas Mixture." Gas Pro. Assoc.,52,(1976)

7. Epstein, P.S,,Textboolc Qf Thermodynamics, J,Wiley:London, 70,1937.

8, Gunn,R;D., Chueh,P,L, and Prausnitz, J.M. ,"A,I.Ch,E, .Jour.", li,5,937 ,(1966)

9. Hoxton, L.G., "Physical Review" Series 2,.Ll_,938,(1919)

10. Johnston, ILL. "Joi.tr, Amer. Chem. Soc.",ill,23102,(1949)

11. · Kim, A.G. and· Douglas, L.J. 11 U.S. Burea·u of Mines: Report of Investigation",RI7903 , U.S. Dept. of Interior, (1974)

12. · Muller,W.H,,Leland,T,W. and Kol,ayaShi, R.," A,I.Cb,E, Jour.", ll,2,267 ,(1961)

13. Peng, D.Y, and Robinson, D.B., "Ind. Eng. Chem. Fund.",li 59, (1976)

14. Recilich,O,,Ackerman,F.S, et. al.,"Ind, Eng. Chem. Fund." !,4,(1965)

15, Redlich, O. and Kwong, J.W.S.," Chem, Rev. ",4li,233,(1949)

75

. ' !:

l.

I / 1

l f,

!'

16. Reed,R.C.,Prausnitz,J.M. and Sherwood,T.K., The Properties tl Gases and Liquids ,3rd.,McGraw-Hill:New York,629,1977.

17 II . d

• ·Roebuck, J.R., Proc. Amer. Acad. Arts an Science",60

527,(.1925)

18. Soave, G.," Chem. Eng. Sci.",ll, 6, 1197, (1972)

19. Stockett, A.L., Ph.D. Thesis, Lehigh University, Bethlehem, Pa.

(1965)

'76

i

~-