Publications

NBSIR 79-1715

NAT'L INST. OF STAND & TECH R.I.C.

A11104 5 5 1 2 A

The Equation of State of Isobutane:

An Interim Assessment

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Center for Chemical Physics

Thermophysics Division

Washington, DC 20234

December 1978

Final

Issued September 1981 —QC

100

,1156

79-1715

1931

Prepared for Geothermal Energy Division

U.S. Department of Energy

20 Massachusetts Avenue, N.W.

Washington, DC 20545

NBSIR 79-1715

THE EQUATION OF STATE OF ISOBUTANE:

AN INTERIM ASSESSMENT

Meyer Waxman, Harry A. Davis,

J. M. H. Levelt Sengers and Max Klein*

°F stANX)ajrd8 Library

OCT 2 2 1981 cue. - tu

ic/oo

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Center for Chemical Physics

Thermophysics Division

Washington, DC 20234

*Presently at Gas Research Institute

Chicago, Illinois

December 1978

Final

Issued September 1981

Prepared for Geothermal Energy Division

U.S. Department of Energy

20 Massachusetts Avenue, N.W.

Washington, DC 20545

U.S. DEPARTMENT OF COMMERCE. Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS. Ernest Ambler. Director

Introduction

The design and preliminary costing of a binary geothermal energy

plant is an involved process requiring the combined use of a number of

correlations in an overall model for the plant's operation [SI 977a].

Some correlations relate component sizing to the operating parameters of

temperature and pressure. Others then relate component sizing to cost

of their manufacture. The basic operating temperature of a plant is

determined by the temperature of the operating well. Pressures and heat

exchanger temperature differences then depend in part on the properties

of the working fluid. The properties of the working fluid can therefore

play an important role in the plant design and costing. This must lead

one to conclude that fluid properties must be known within reasonable

accuracy limits for proper design and costing of potential plants.

The exact limits of uncertainties in fluid properties data which

can be tolerated in a design are not easy to assess. Thermodynamics

provides an extensive framework which connects the caloric and mechanical

properties of a fluid through the thermodynamic relations. It is generally

necessary, in applying these relations to specific design problems, to

perform mathematical manipulations on measured fluid properties to

produce data of the kind needed in the designs. These manipulations can

involve differentiation, integration (or combinations of the two) as

well as statistical fits of measured fluid property data to mathematical

forms. In such manipulations the original errors of measurement are

combined and transformed, often in non-linear ways, so as to affect the

design under conditions removed from those of the original property

measurements. This kind of propagation of the errors of measurement can

be difficult, if not impossible, to trace. One can, however, be sure

that, as a general rule, the original errors will become magnified in

these transformation processes. It is therefore essential that fluid
2 .

properties data be known with much better accuracy than the uncertainty

in the plant design from all other causes. An assessment of the effect

of errors in data measurement on a plant design can be made through

computer modelling. Errors of various kinds can be superimposed on

models of the measured fluid properties data and the effect of these

errors in a design observed. An attempt at this was made by Starling et

al . [S1977a]. Slightly different versions of the same model for isobutane

properties were used to illustrate data uncertainty. This made it

difficult to specify the precise nature of the errors being introduced

and hence the exact way in which design sensitivity to error was being

probed could not be determined. A more detailed analysis in which

errors are inserted directly has shown that certain kinds of errors can

indeed have a drastic effect on heat exchanger design and even design

feasibility [K1978]. In what follows we shall assume that the properties

of the working fluid must be known to perhaps an order of magnitude

better than the overall plant design uncertainty.

Isobutane is being widely considered as a prime candidate, either

as a pure fluid or as part of a fluid mixture, for the working fluid in

geothermal binary cycles. Although measurements of its properties

exist, there is considerable disagreement among the different sets of

measurements. Furthermore, these measurements have been made over

relatively limited regions of temperature and pressure. This combination

of problems has made it difficult to produce an overall correlation of

the properties of isobutane which might be used with a reasonable degree

of confidence. In fact, the two major recent correlations of the properties

of isobutane [S1977b-D1973] differ from each other by a considerable and

unacceptable amount.
3 .

The combination of the potential importance of geothermal energy in

the national energy picture, the certain need to develop binary geothermal

cycles, the potential choice of isobutane as a working fluid, the disagreement

among published property measurements for isobutane and the differences

between the major correlations of its properties led to the establishment

of this project. The project has been aimed at carrying out a careful

and accurate assessment of the data situation for isobutane and at the

development of an accurate set of data sufficient in extent to produce a

correlation which might be used with confidence in plant design computer

programs. The project program has been designed to make maximum use of

existing information. Measurements have been made under conditions

which have been carefully selected to test the accuracy of published

data with special emphasis on those conditions for which there are major

discrepancies among literature values. The first phase of the effort

was to be the production of new data taken under such conditions as to

allow for di rect comparison with the best published data. This was to

be followed immediately by an assessment of the need for more extensive

measurements. This assessment would be expected to depend very strongly

on the relationship between our new measurements and the data published

by each of the earlier researchers. This was to lead to additional

measurements as required which in turn would be followed by a new correlation.

It was agreed that the areas of immediate need for assessment were

the vapor pressure, critical region and vapor and gas isotherms. This

first part of the program has essentially been completed and the results

are contained herein. We have chosen to present these results as an

informal report to sponsor at this time despite the fact that additional

data reduction and an important recalibration are still necessary. We

have done this in order to make our results available to interested
4 .

parties so that they can contribute to the decision process for establishing

the need for additional measurements. A paper will be submitted for

publication in the near future.

In what follows there will be separate discussions of our measurements

of vapor pressure and vapor isotherms and of our correlation of the

properties in the critical region. There is also a rather preliminary

comparison of some of the published correlations. Our results have now

made such a comparison of correlations somewhat academic, however.

Our work has shown that the vapor phase and vapor pressure data of Sage

and Lacey [SI 938, Ml 940] need to be omitted from any future correlation.

The large differences between our results and theirs leads us to expect

major revisions will be needed in those existing correlations which

included their data. Hence a detailed study of those correlations at

this time would not appear to be very useful.

Our work, although carried out over a rather limited set of conditions,

has already clarified the data situation considerably. We have been

able to correlate the data in the critical region thereby reducing the

pressure for new measurements. We have replaced the vapor pressure data

by new and accurate data, thereby removing a major source of confusion

in the isobutane literature. We have shown that, below the critical

point, the data of Connolly [Cl 962] are probably sufficiently accurate

to preclude redoing while the vapor pressure and vapor pressure data of Sage

et al. are not sufficiently accurate to be considered in any correlation.

In the following, each of the areas of work is described separately

in some detail and acknowledgements of assistance are included where

appropriate.
The Critical Region of Isobutane

There is a detailed set of critical -region PVT data in the temperature

range 134.60 to 1 35 . 1 5°C for isobutane reported by Beattie, Edwards and

Marple [B1949]. In addition, there is a block of supercritical PVT data

by the same authors [B1950] in the range of 150 to 300°C. We report

here a fit of the critical-region PVT data plus part of the 150°C isotherm

to a simple scaled equation of state called the Linear Model [SI 969

a,b]. The Linear Model is formulated in terms of parametric variables,

which are obtained by a transformation of the physical variables temperature

and density. The variables, adjustable and fixed parameters, transformation

equations and parametric functions are defined in Tables 1 and 2.

In fitting this model to the isobutane data, a transcendental

parameter transformation plus a non-linear least-squares fit have to be

effected. For the parameter transformation we use a procedure that

was recently documented by Moldover [Ml 978]. The non-linear fitting

routine is that developed by Bevington [B1969]. For the standard

deviations of the measured variables P,p,T we estimated

CT p

= ICf

4

MPa

aT

= 0.005 K (1)

3 a =0.001 mol /dm . p

The best fit we obtained had a reduced chi-square of 0.97 which is

quite satisfactory. The deviations of the experimental points from

the fitted surface are shown in Figs. 1 and 2. The best values for the

parameters obtained are listed in Table 3. In Table 4, we compare our

values of the critical parameters with those obtained by Beattie from the

same data set. The most striking result is the very considerable lowering
6 .

of the critical temperature, namely almost 0.3 K below that reported by

Beattie [ B1 94 9] . Part of the reason is the known phenomenon that splinedrawn coexistence curves are usually not sufficiently flat; the one

sketched by Beattie et al . is almost parabolic instead of roughly cubic,

which leads to an overestimate of T . It is, however, also possible

that the slope of the two-phase isotherms, caused by impurity, is interpreted

by our model as the finite compressibility of the one-phase region. Our

model is quite determined about this large decrease in the estimate of

T

c

; when we omit the 150°C isotherm, T

c drops by (.268+0.012) K instead

of (.278+009) K below Beattie's estimate, which is obviously the same

within error.

We conclude that barring impurity effects, the Beattie data are

consistent with a simple scaled equation to within estimated errors of

-4 3

10 MPa in pressure, 0.005 K in temperature and 0.001 mol /dm in density;

Beattie's critical constants, however, require major adjustments.
7 .

Vapor pressure of Isobutane

There are five sets of vapor pressure data for isobutane above 0°C

reported in the literature, those of Seibert and Burrell [SI 91 5], Dana

et al. [D1926], Sage and Lacey [SI 938], Beattie et al . [B1949] and

Connolly [Cl 962]. Four of these data sets are i ntercompared in Fig. 3,

the data set of Seibert and Burrell is too far off to be shown in this

figure.

It is clear that even the four data sets plotted scatter widely. At

the lower temperatures, they span a range of more than 0.1 bar on a

total pressure of only a few bars. This unsatisfactory state of the

data was our motivation in remeasuring the vapor pressure curve.

We have made our measurements on a "Research Grade" sample of

isobutane claimed to be 99.98% pure. We will discuss the impurity

content and the estimated impurity effects in a separate section of this

report.

We have made the vapor pressure measurements in our Burnett apparatus,

a detailed description of which was published elsewhere [W1971]. In

order to perform vapor measurements on a substance with elevated critical

temperature, such as isobutane, we had to make a number of modifications.

Our supply containers were placed above the gas handling system and the

supply was always tapped from the liquid phase which, in general, was

purer than the vapor. In order to inject the fluid, at room temperature,

into the sample cell at elevated temperatures, a volume pump was used so

that the liquid pressure could be raised sufficiently for transfer,

and injected in well -determined amounts. We began by using a 1 cc

sample from the injector at room temperature, and added fluid, as needed,

at elevated temperatures so as to maintain a two-phase situation. In

all cases, we measured near the vapor side of the phase boundary. In

several instances, we measured the vapor pressure with two different amounts of
8 .

_4 fluid. In general, the vapor pressure did not vary by more than 10

3

MPa. Only at 25°C, the pressure of two samples of, resp. ,1 and 5 cm -4

of liquid differed by 3x10 MPa.

The results of our vapor pressure measurements are summarized in

Table 5. We stress that our temperature values are preliminary; our

thermometer was calibrated several years ago, and a check of its icepoint

is needed before the temperature readings can be definitively assessed.

Such a check, however, can not be made before all the measurements are

completed. We have fitted our vapor pressure curve with a scaled form

that has proven very useful in other fluids [LI 972, HI 977]:

~ = 1 + A

1 AT* + A" | AT*

]

2~ 6 t A

2 (4T*)

2 + A

3

(aT*)

3

(2)

Here aT* = (T-T

c )/T . For the parameters P£

, T

c

, we used the values

obtained from our best fit to Beattie's PVT data (Table 3). Our data

are fitted by Eqn. (2) to within a few millibars. The coefficients

of the fit are listed in Table 6. The deviations from the curve are

listed in Table 5 and pictured in Fig. 3. We feel that the scatter of

the data reflects the variability due to impurity effects in samples of

varying 1 iquid-to- vapor ratios. The scatter of our data is far less

than that of the earlier data in the literature. At the higher temperatures,

our data show rough agreement with those of Beattie, Connolly and Dana.

At the temperatures below 60°C, however, our data follow a course of

their own and do not agree with any data reported previously. It is our

conviction that differences between authors are primarily due to differences

in sample composition. We have therefore worked out a model for small

impurity effects in isobutane, and present this in the next section.
9.

Impurity effects in Isobutane

The principal uncertainty in our measurements of the equation of

state of isobutane is sample purity. Our approach has been to obtain

the best sample cormercially available, to monitor sample composition

before and after the measurements, to develop a model for estimating the

effect of impurities known to be present, and to check our estimates by

measuring the vapor pressure at various fill densities. This approach

permits us to assign realistic error estimates to the vapor pressures we

report.

A. Sample composition

We have used Philips Petroleum samples. For preliminary work we

have used the instrument grade, claimed to be 99.5% pure. For the

definitive measurements we used research grade, claimed to be at least

99.9% pure.

For monitoring the sample composition we used a gas chromatograph

provided with a gas sampling valve. We used prepared standard mixtures

containing known proportions of lower hydrocarbons for calibration of

the gas chromatograph trace. Our measurements are qualitative only and

we estimate our compositions to be accurate to perhaps 20%.

The impurities found in our isobutane supply are listed in Table 7.

In no case were we able to distinguish the n-butane peak. Although the

two butane peaks, when present in aomparable amounts, separate easily in

our column, in actual samples the n-butane peak is swamped by the large

isobutane tail.

In our experiments, samples are always taken from the liquid phase

for measurement. When samples are analyzed after the measurements,

varying compositions are found, probably due to fractionation in the gas

handling system. Typical impurity compositions would be 300 ppm propane

and 30 ppm Ng.
10 .

B. Model for estimation of impurity effects.

We have used a simple model first developed by Keesom [K1901] to

estimate impurity effects. The model is based on the assumption that

isobutane and slightly impure isobutane obey a principle of corresponding

states. A binary mixture of composition x will have pseudocritical

parameters that are slightly different from the critical parameters of

the pure host

T

cx V1 + «>

P cx

- P

X

(1 + ex) (3)

Vcx

* V

c

(1 + {a- B}x)

The mixture parameters a,B are estimated from the critical parameters of

the pure components 1 and 2.

Here 1 is the host, 2 the impurity. Keesom developed these estimates on

the basis of the so-called Clausius equation of state, a modification of

Van der Waal s' s. (The values assumed for the interaction parameters

are, as is usual in any mixture model, the weakest link).

The impurity effect on the vapor pressure is obtained by expanding,

for small x, the conditions for 2-phase equilibrium in a mixture.

Define a parameter k as follows
n.

T

dP

k = Ca 7 dT B][z

v‘

Z

L

] {5)

Here Pa is the vapor pressure of the pure host, Zy, the compressibility

factors PV/RT of the vapor and liquid of the pure host. In our calculations,

dP

, a from the correlation by

dT

Das et al . [D1973]. Then, the dew point pressure P

d

of the impure system

of overall concentration x is given by

we have accepted values for P , Zy, Z^

< p dP a

} = 1^

P a

X VZ

L

( 6 )

Likewise, the bubble-point pressure P^ is given by

P x a

( 7 )

For a mixture of overall composition x, with a fraction, b, of molecules

in the liquid phase, the vapor pressure P is given by

P -

CT

1-e

be

k +(l-b)

J

VZ

L

( 8 )

C. Results.

We have used the model to calculate the effect of one percent of a

known impurity on the vapor pressure of isobutane. We have done the

calculations at three temperatures, namely 300, 350 and 400 K. We have

considered four different impurities, namely nitrogen, ethane, propane and

n- butane. We have calculated the impurity effect at four liquid-vapor
12 .

ratios, namely dew point, 1 cc of liquid on 50 cc total, critical

density and bubble point. The results of our calculations are summarized

in Table 8. In Table 9, we estimate the effect on our measurements due to

the known impurity concentrations in our experiment. The known impurities

_3 contribute small amounts, not exceeding 10 MPa (0.01 bar) to the

vapor pressure, amounts that increase in absolute, but decrease in

relative magnitude as the temperature increases.

The large differences between our own and the preceding data sets

(Fig. 3) can not be explained by impurity in our sample. The departure

of Connolly's data from our own has the general appearance that a volatile

impurity in Connolly's data would take. The departure of Beattie's data

from ours, however, cannot be explained solely by a large amount of

n-butane present in Beattie's data, even though such an impurity would

escape Beattie's way of checking for impurities.
13 .

PV isotherms for isobutane vapor

We have measured two isotherms in the vapor phase of isobutane. One

isotherm was measured at 104.444°C (220°F) at which temperature PV data

were available from two sources, namely Connolly [Cl 962] and Sage and

Lacey [SI 938]. Another isotherm was measured at 1 21 . 11 °C (250°F) at

which temperature Connolly had measured the PV relation [Cl 962]. At

each temperature, three series of three or four Burnett expansions were

performed. The pressures were measured on a Ruska gas-lubricated piston

gage which had been calibrated at the National Bureau of Standards. For

the cell constant, we assumed the values previously determined by expansions

using helium [W1 979] . The data were analyzed using a nonlinear leastsquares formulation of the Burnett problem based on a density virial

expansion [W1973]. The results are given in Tables 10 and 11. Note

that the significance of the virial coefficients deteriorate rapidly

with order with the fourth having no significant figures. The numbers

contained in Table 10 are nevertheless essential to the reproduction of

the experimental data and, because of the statistical correlation between

the vi rials listed, all figures presented must be used. This is true

despite the fact that some of these have no significance for "stand

alone" virial coefficients.

Adsorption is generally a problem in these kinds of measurements on

the vapor side below the critical temperature. We checked for the

presence of adsorption by using the cell constant as a free parameter.

The values we obtained this way agreed with our previous helium results

to + 1 part in 20,000, with the values obtained for density and compressibility

factor in the cases of fixed N and free N, respectively, agreeing with each

other to 1 part in 5000 over the entire range of the vapor isotherm thereby

indicating that the effect of adsorption is negligible.
14 .

We have not yet estimated the effect of impurities on the vapor

isotherms. Previous work for ethylene using our model [HI 978] indicates

that those effects are relatively small.

Our results are compared with those of Connolly and of Sage and

Lacey in Fig. 4. The compressibility factors, compared at the same

density, agree with those of Connolly, at 104.44°C and at 121.11°C, to

within 0.002 in Z. The difference with Sage and Lacey, at 104.44°C, is

very large, of the order of 0.01 in Z. Thus, our data confirm those of

Connolly but put those of Sage and Lacey into serious question.

Some Comparisons Among Published Correlations

There have been a number of correlations of the properties of

isobutane published. We have selected three correlations for intercomparison

on the basis of their availability, because of their extent and since

the properties of isobutane were of major importance to the correlator

in each case. Each correlation used a version of the Benedict, Webb,

Rubin (BWR) equation for the pressures as a function of the density.

For several reasons this could not be expected to result in identical

correlations. First of all, where there is extensive disagreement among

data sets, as there is for isobutane, a correlation can be expected to

be extremely sensitive to the data selection process. Secondly, there

are significant differences among the particular versions of the BWR

equation used. Finally, one author was also interested in a generalized

version of the BWR equation which would be simultaneously applicable to

a number of hydrocarbons. An indication of the differences to be expected

can be had from the differences between two similar versions produced by

the same group [SI 977b, S1977c]. While the differences are sufficiently

small so as not to affect an overall plant design [SI 977a] they are

nevertheless significant.
15 .

Table 12 contains comparisons between the vapor pressures predicted

by the correlations and the measurements of Waxman and Davis reported

herein. It should be noted that Das et al . and Starling et al . [SI 977b]

are much closer to the new values of Waxman and Davis reported herein

than are Starling et al. of [SI 977c]. The former pair of correlations

differ from each other by an excessive amount, however, with each differing

from Waxman and Davis in a systematic manner.

Table 13 contains a comparison between the two correlations of the

compressibility factor for the saturated volume. The differences between

the two correlations are certainly excessive.

Table 14 contains comparisons of the second virial coefficients of

the two correlations. It also contains experimental values taken from

Table 10 and from the literature. Here, the results of Starling et al

are much superior to those of Das et al

Table 15 shows a comparison between the data of Waxman and Davis

and the correlation of Starling et al . [SI 977b] for T = 104.44°C. The

former have been extrapolated to the vicinity of the saturation boundary.

Differences are systematic and increase with the increasing effects of

non- idealities, approaching 5% near saturation. The extrapolation of

the data of Waxman and Davis can be expected to contribute negligible

error since the contribution of each term in the virial series to the

compressibility factor is almost an order of magnitude less than that of

the preceding term, becoming approximately 1* for the fourth virial.

The relationship between the correlation of Starling et al . [SI 977b] and

the data of Waxman and Davis at 121.11 is very nearly identical with

Table 15.

It is clear, even from the rather cursory comparison carried out

here, that the correlations are in rather violent disagreement and that
16 .

neither is adequate for the task of predicting the properties of isobutane

for use in plant design models. Wherever one or the other correlation

is moderately close to experiment in any particular region of pressure

and temperature can only be due to fortuitous circumstances since each

correlation leans heavily on inaccurate data. This belief is reinforced

by the overall large differences between the correlations. It will

obviously be essential for a new correlation to be developed once an

adequate set of data has been produced.

Conclusion

This report contains a partial assessment of the equation-of-state

data and the existing correlations for isobutane. We have reached the

following conclusions:

(a) vapor pressure

Below 60° C our data disagree with all other data in the literature

by amounts of the order of 0.007 MPa (1 p.s.i.) for vapor pressures that

are all below 1 MPa. We have shown that the known impurities in our

sample cannot have caused the discrepancies with the earlier data.

Above 60°C, our data agree modestly, to within 0.005 MPa, with those of

Beattie, on vapor pressure going up to 3 MPa.

(b) vapor phase

Our PV measurements at 104.44 and 121.11 C confirm the virial data

of Connolly to 0.002 in Z. Our results at 104.44°C depart strongly from

the data of Sage and Lacey, by as much as 0.01 in Z.

(c) critical region

We were able to correlate the critical -region data plus the 150°C

isotherm of Beattie et al . with a scaled equation that has proven very

useful in other fluids. The principal result of the fit is a considerable

decrease of the critical temperature from the value reported by Beattie.
17 .

We feel that this strong decrease may be due in part to small impurity

effect; the main reason, however, lies in the fact that the coexistence

curve is much flatter than Beattie had assumed. We are of the opinion

that there is a good chance that Beattie's data in the supercritical

region are sound.

(d) correlations

With existing large discrepancies between data sets, it is to be

expected that the results of correlations depend heavily on the data

sets chosen and the weights assigned. We have indeed found that there

are large discrepancies between the correlation of Das et al. and that

of Starling, running as high as 10% in Z in the vapor phase near the

phase boundary even reasonably far from critical.
18 .

Assessment of further work

From our point of view, the following work will be required as a

minimum in order to establish the equation of state of isobutane.

(a) A check of Beattie's supercritical data at at least one

temperature.

(b) Further spot checks of Sage and Lacey's data.

(c) Spot checks of the saturated liquid densities and of some

densities in the liquid phase.

(d) A recalibration of our thermometers

.

We realize that there may be a need for caloric data to supplement

the equation of state data in regions of technical interest. We suggest

that this need be assessed by the interested parties. Independent of the

outcome, the following work will be unavoidable.

(e) After the new data are obtained, the thermodynamic behavior of isobutane

will have to be reformulated, with close interaction between the

experimenters, correlators and users of the data.
Acknowl edgements

1 r.

, •

Frances Balfour performed the non-linear least-squares

fit of Beattie's PVT data to the Linear Model scaled equation. Mr. W.

Dorko provided advice, help and standard samples for gas-chromatographic

analyses. Professor J. Kestin provided valuable comments and suggestions

for the measurement program.
References

[B1 949] J.A. Beattie, D.6. Edwards and S. Marple, Jr., J. Chem. Phys.

17, 576.

[B1 950] J.A. Beattie, S. Marple, Jr. and D.G. Edwards, J. Chem. Phys.

18, 127.

[B1 969] P.R. Bevington "Data Reduction and Error Analysis for the

Physical Sciences", McGraw Hill, New York.

[Cl 962] J.F. Connolly, J. Phys. Chem. _66_, 1082.

[D1 926] L.I. Dana, A.C. Jenkins, J.N. Burdick and R.C. Tim, Refrig.

Eng. 12_, 387.

[D1973] T.R. Das, Ch. 0. Reed, Jr. and P.T. Eubank, J. Chem. Eng.

Data _1_8, 253.

[HI 977] J.R. Hastings and J.M.H. Levelt Sengers, Proc. 7th Symp.

Thermophys. Prop. ASME, Ared Cezairliyan, Editor, p. 794.

[K1 978] H.E. Khalifa, private communication.

[ K1 901] W.H. Keesom, Comm. Phys. Lab. Leiden, No. 75.

[LI 972] J.M.H. Levelt Sengers and W.T. Chen, J. Chem. Phys. 56_, 595.

[Ml 978] M.R. Moldover, J. Res. N.B.S. 83_, 329.

[Ml 940] W.M. Morris, B.H. Sage and W.N. Lacey, Trans. Am. Inst.

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[SI 938] B.H. Sage and W.N. Lacey, Ind. Eng. Chem. 30, 673.

[SI 969a] P. Schofield, Physical Review Letters 22, 606. yd l T

[SI 969b] P. Schofield, J.D. Litster and J.T. Ho, Phys. Rev. Letters (y(\V Y HY

23, 1098.

[SI 91 5] F.M. Seibert and G.A. Burrell, J. Am. Chem. Soc. 37 , 2683.

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Improvement of Geothermal Binary Cycles —Phase II," Report

0R0-4944-7, The University of Oklahoma School of Chemical

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[SI 977c]

[W1971]

[W1973]

[W1979]

K.E. Starling, C.M. Sliepcevich, L.W. Fish, K.M. Goin,

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K.L. Zemp, "Development Working Fluid Thermodynamic Properties

Information for Geothermal Cycles-Phase I," Report ORO-5249-

2, The University of Oklahoma School of Chemical Engineering

and Materials Science, Norman, Oklahoma 7301 9.

K.E. Starling, L.L. Lee, K.C. Mo, C.M. Turi , K.M. Goin, U. Lee,

T.J. Lee, K. Zemp, B. Batson, P. Plumb and K. Brunsman,

"Self Consistent Correlation of Thermodynamic and Transport

Properties," Report GRI/AGA/BR-11 1-1/77-36, University of

Oklahoma School of Chemical Engineering and Materials Science,

Norman, Oklahoma 73019.

M. Waxman and J.R. Hastings, J. Res. N.B.S. 75C , 165.

M. Waxman, H.A. Davis and J.R. Hastings, 6th Symp. Thermophys.

Prop. ASME, 1973, 245.

M. Waxman and H.A. Davis, Adv. of Chem. 1979.
Table 1

Definition of reduced variables

Critical-point constants 3 adjustable parameters

pressure P

c

vol ume v

c density p c - 1/V

C temperature V K

Reduced quantities

pressure P* = P/P

c temperature a'T* = (T-T )/T

density Ap* = (p-p

c )/pc
Table 2

Definition of parameters

Critical exponents a, g, y, 6

coexistence-curve exponent s = .355

critical-isotherm exponent 6 = 4.32

Y

= 3 (. <5— 1 ) a = 2-s(6+1)

2

Linear-Model parameters a,k,b

2 three constants: a,k,b

a,k are adjustable

b

2 is calculated from b2 = ——

( 5 - 1 ) (

- 2 3 ) Parametric variables r,9

two parameters r,e for each data point

They are calculated from the transformation

AT* = r(l-b

2

e 2

)

Ap* = r

e ke

Free energy function f ( 6

)

f(e) = f

Q + f

2

e 2 + f

4

e 4

f

_ B(<S-3) - Day

0

2b*

4

( 2— ct) (l-a)a

. . 8(6-3) - b

2

a(1-26)

2

2b2

(l-a)a

f

4

- -(l-26)/2a

Pressure

* *

P*

- VT > + Panom

P*nom =

rB<S a0 O- 0 ^) + r2_a ak{

2

(1 -e

2

) - f

(

0 )

}

P* _

= -r

2 " a

ak f(l) anom Analytic Background

A*(T*) = -1 + A*(aT*) + A*(aT*)

2 + A*(aT*)

3

* *

A-j ... A^ are adjustable

(1-phase)

(2-phase)
Table 3

Linear-Model parameters for the critical region of isobutane

Critical-point constants

P

c = (3.6306+0.0006) MPa

P c= (3.906+0.002) mol /dm

3

T

c = (407. 851+0. 005) K

Critical exponents (fixed)

a = 0.100

6 = 0.355

y = 1.19

6 = 4.352

Linear-model constants

a = 20.787+0.16

k = 1.44096+0.009

o

b

2 = 1.3909 (fixed)

Analytic background

A* = 7.1318+0.04

A* = - 198.12+43

A* = 4722+1100
Table 4

Critical Parameters of Isobutane obtained from

data of Refs [B1 949, B1 950]

as reported in [B1949]

P c (3.648+0.005) MPa

3

P c 3.80 mol/dm

T (134. 98+0. 05 )°C

From fit to scaled equation

(3.6306+0.0006) MPa

(3. 906+0. 002) mol/dm3

(134.701+0.009) °C
Table 5

Vapor pressure of -99.98% pure sample of isobutane.

Preliminary temperature values prior to thermometer calibration.

Temperature, °C Pressure, MPa P -P

exp calc

(10"4

MPa)

25.000 0.3500 -2

30.000 0.4043 +2

35.000 0.4641 +1

40.000 0.5304 +1

45.000 0.6032 -3

50.000 0.6836 -3

55.000 0.7725 +5

60.000 0.8683 -1

60.000 0.8676 -5

70.000 1.0867 +1

80.000 1.3432 +3

90.000 1.6408 -2

100.000 1.9855 -1

110.000 2.3819 +1

120.000 2.8361 -1

125.000 3.0879 0
Table 6

Fit to vapor pressures of isobutane

4T* = (T-T

c )/Tc

P = 3.6 3 06 MPa''

C

0 = o.n j

A

] = 6.818526+0.006

A" = 22.01824+0.58

A

2 =-10.73853+0.71

A

3 = 6.8431+0.22

P-P

A

1 AT* + A" | AT*| 2-0

+ A

2 (AT*)

2 + A

3

(AT*)

c 3

P c

T f1 xed

c
Impurities in Isobutane, in ppm

Instrument

grade

Research

grade

After Measurements,

representative

Cl aim 99.5% 99.9% minimum

99.98% typical

liquid liquid vapor

nitrogen -10 2000 30

ethane 7000

propane 1000 70 500 300

water (?) 2000

n-butane

(estimated from

claimed overall

impurity)

<5000 <1000 <1000
Table 8

Estimated vapor pressure increase in 10

~ 4

MPa (millibars)

due to 1 % of impurity in isobutane

N 2C

2

H

6

C

3 H 8 n_C4

H 10

300K, P = .3704 MPa

a

-

dewpoint 41 36 23 -14

3

1 cm of liquid 83 64 33 -12

critical density 657 200 50 -10

bubble point 1134 229 51 -10

350K, P = 1.2605 MPa

a dewpoint 166 130 76 -37

3

1 cm of liquid 210 155 114 -35

critical density 1104 385 125 -31

bubble point 2353 473 133 -31

400K* P = 3.193 MPa

a dewpoint 695 426 210 -78

3

1 cm of liquid 719 435 212 -78

critical density 1230 587 242 -75

bubble point 1874 694 259 -73
Table 9

-4

Estimated pressure error, in 10 MPa

(millibars), due to known impurities in our isobutane sample.

30 ppm 300 ppm 1000 ppm

ni trogen propane n-butane

300K dew point 0 1 -1

3

1 cm of liquid 0 1 -1

critical density 2 2 -1

bubble point 3 2 -1

350K dew point 1 2 -4

3

1 cm of liquid 1 3 -4

critical density 3 4 -3

bubble point 7 4 -3

400K dew point 2 6 -8

3

1 cm of liquid 2 6 -8

critical density 4 7 -7

bubble point 6 8 -7
Table 10

Virials of isobutane at 104.444 and 121. Ill °C

3

B, cm /mol

C, cm^/mol

g D, cm /mol

1 04 . 444°C

-378.3436+1

40043.55+3000.

(-5 .66+2.5)xl0

6

121 .111 °C

.344.4418+.

3

36436.58+500.

(-2.01+2. )x!0

5
Table 11

Compressibility factor of isobutane vapor

1 04 . 444°C p, mol /dm

3 Z = PV/RT

0.1 0.96256

0.2 0.92589

0.3 0.88995

0.4 0.85471

0.5 0.82013

0.6 0.78619

0.7 0.75284

121. 111°C 0.1 0.96592

0.2 0.93257

0.3 0.89994

0.4 0.86804

0.5 0.83686

0.6 0.80641

0.7 0.77668

0.8 0.74766

0.9 0.71937

1.0 0.69179

1.1 0.66493

1.2 0.63879

1.3 0.61336
Table 12

Comparisons of vapor pressure

d correlations

T°C Waxman et al.

c f Starling et al

Das et al

e Starling et al

30 .4043 .4078 (0.9) 0.3999 (-1 .1 ) a .3880 (-4.0)

40 .5304 .5350 (0.9) 0.5246 (-1.1) .5093 (-4.0)

50 .6836 .6893 (0.8) 0.6727 (-1.6)

60 .8683 .8740 (0.7) 0.8583 (-1.2)

70 1.0867 1.0926 (0.5) 1.0742 (-1.2)

80 1 . 3432 1.3484 (0.4) 1.3154 (-2.1)

90 1.6408 1.6458 (0.3) 1.6229 (-1.1)

100 1.9855 1.9890 (0.2) 1.9650 (-1.0) 1.9005 (-4.3)

a numbers in parentheses are percent deviation from Waxman et al.

c

k This refers to [SI 977c]

c This work

^Pressure in MPa

eThis refers to [D1973]

p

This refers to a private communication from Starling based on his

use of the equations of [SI 977b]
Tabl e 13

Comparison of correlations of saturated vapor compressibility factors

T°K Star! ing et al

.

Das et al

.

(AZ/Z)100.

270 .9512 .9386 1.3

280 . 9375 .9228 1.6

300 .9035 .8842 2.2

320 .8597 .8360 2.8

340 .8046 .7767 3.6

360 .7350 .7032 4.5

380 .6436 .6074 6.0

390 .5839 .5441 7.3

400 .5043 .4564 10.5

406 .4308 .3657 17.8

408 .3846 .3069 25.3
Table 14

Compari sons of second virial coefficients

1 04. 444°C 121 .111°C

This work -378.34 -344.44

Connolly -374.0 -341 .1

Das et al

-393.9 -353.4

Starling et al. [SI 977b] -368.1 -335.6
Table 15

Comparison of the compressibility factor predicted by

Starl ing et al . and the data of Waxman and Davis

for T = 104.44°C

P (atm) ^Starling ^Waxman % De

1 . . 98802 .98768 .03

2. .97582 .97513 .07

3. .96339 .96233 .11

4. . 95072 .94927 .15

5. .93779 .93593 .20

6. .92458 .92227 .25

7. .91108 .90828 .31

8. .89725 .89392 .37

9. .88307 .87916 .44

10. . 86851 .86396 .53

11 . .85353 .84825 .62

12. .83810 .83198 .74

13. .82215 .81508 .87

14. . 80563 .79745 1.03

15. .78847 .77897 1.22

16. .77058 .75949 1.46

17. .75184 .73878 1.77

21. .66461 .63502* 4.66

* extrapolated value
Figure Captions

Figure 1

Figure 2

Figure 3

Figure 4

. Fit of Linear Model scaled equation to critical -region isotherms

of Beattie et al . [B1949],

. Fit of Linear Model scaled equation to critical -region isotherms

of Beattie et al . [B1 949,1 950].

. Intercomparisons of vapor pressure data in the literature.

Base line is scaled equation fitted to our vapor pressures.

. Intercomparisons of the PVT measurements of Sage et al

[Ml 940, SI 938], Connolly [Cl 962] and the results of this

work. The base line is based on calculations using the

virials of Table 10.

V
AP,

(10

MPa)

Fi gure 1

.

4

2

0

•2

-4

10

—1 1 I 1 1

—

1 millibar

o

•

,4 • A

• o

-p

1

1

—

• 408.14 K

o •0

A

A A £

A

1 #

o o

A

* A —

— a 408.15K o -

o 408.20K

—

-

v ; A

•

•

• •

•

•

• •

• A

13 ^ millibar A — • 408.30K

a 423.15 K

—

|

1 1 1 1

-10

2.5 3.0 3.5 4.0 4.5

DENSITY, mol/dm'
0

0

6

4

2

0

2

6

4

2

0

-2

-4

-6

Figure 2.

T

• 407.75K

a 407.85K

o 407.95K

]

0.01 bar

* « t

O o o

A •

A

• 408. 00K

a 408.03K

a 408. 05K

1 millibar

2

O

o

A

o

•

I 1 millibar - ^

A

• • • i # O

•

• —

— • • A «& A —

• 408.10 K o

* a % o 0 1 A A.

a 408.12K

o

o —

o 408.13 K A aA •

1 ! 1 1 2.5 3.0 3.5 4.0 4.5

DENSITY, mol/dm 3
Figure 3.

CM

CO

CO

«- CM

BdlAJ 'd

I

T,C


U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

4. TITLE AND SUBTITLE

1. PUBLICATION OR 2. Performing Organ. Report No. 3. Publication Date REPORT NO.

IR 79-1715 9/19/81

The Equation of State of Isobutane: An Interim Assessment

5. AUTHOR(S)

Meyer Waxman, Harry A. Davis, J. M. H. Level t Senders, Max Klein

6. PERFORMING ORGANIZATION (If joint or other than NSS. see instructions) 7. Con tract/ Grant No. national bureau of standards

DEPARTMENT OF COMMERCE 8. Type of Report & Period Covered

WASHINGTON, D.C. 20234

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

10.

SUPPLEMENTARY NOTES

| 1 Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11.

ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here)

New and very accurate measurements of the vapor pressure and two PVT isotherms

of isobutane below critical are presented. The vapor pressure data have been

correlated to within parts per 10,000 using a scaled vapor pressure equation.

The Beattie data in the critical region has been correlated using a scaling law

approach. This required a shift in the critical temperature of 0.3 K from that

published by Beattie. The significance of this shift in an overall correlation

is not yet clear. The two PV isotherms are compared with literature data and the

results of Sage and Lacy shown to be inaccurate. Those of Connolly appear to be

sufficiently accurate for including in future correlations. Two correlations

of Starling et al . and that of Das et al . are intercompared and are compared with

these new results. As might be expected, these correlations, being based on inaccurate data, are not of sufficient accuracy for use as representations of the

properties of isobutane. A program is presented for the completion of a correlation of the properties of isobutane to engineering accuracy.

12.

KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolon s) Critical region; density; equation of state; geothermal; isobutane; thermodynamic;

vapor pressure.

13.

AVAILABILITY

| ."j Unl imited

| 1 For Official Distribution. Do Not Release to NTIS

| | Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402.

| P/f Order From National Technical Information Service (NTIS), Springfield, VA. 22161

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