THE MEASUREMENT AND PREDICTION OF THE DENSITIES OF THE TERNARY MIXTURE

HEXANE + HEXADECANE + n-PROPYL ALCOHOL

PETER RICE* Department of Chemical Engmeering, Loughborough University, Loughborough, England

and

A. S. TEJA School of Chemical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, U.S.A.

(Received 20 July l!Xl; accepted 3 May 1982)

Abstract-The densities of mixtures of hexane, hexadecane and n-propyl alcohol were measured at 298.15 and 323.15-K using a IO ml pyconometer. The results were correlated using a multifluid corresponding states principle based on using all pore components as reference fluids. For the prediction of the densities of ternary mixtures, only the binary interaction coefficients found for the three binary mixtuies are required.

INTRODUCTION

Recently we have proposed a “multifluid” corresponding states’ model for the prediction of the densities of fluid mixtures [l]. In the model, all pure liquid components are used as reference fluids. This is an extension of a two fluid model previously proposed by us [2-4]. To test the multifluid model, we used the measurements of densities of simulated LNG mixtures, the components are “similar” and the multifluid model did not show any significant improvement over the two fluid model.

To demonstrate the advantages of the multifluid model we present some measurements of the densities of the ternary mixture hexane, hexadecane and n-propyl alco- hol. Our measurements were used for comparison with values predicted by the multifluid model.

Multifluid model The multifluid model consists of a series of two

reference fluid interpolations. Thus a two fluid expansion is carried out using components I and 2 say to obtain a pseudo component “12”. This is then used with com- ponent 3 to obtain a pseudo component “123” and so on such that for compression factor 2 we get:-

z ,~...“=z”-w~~~...II__~~ EkZ,,...,~II (1) ”

where (L),*. .” is defined by eqn (2) and

The reduced orthobaric density pn is a function of the reduced temperature r, only, so that given this function we may calculate the orthobaric density of mixtures using eqns (2)-(4). For mixtures, the critical properties in eqns (2)-(4) are replaced by pseudo critical properties which are defined as

V‘.“, = 7 E: x,xjv,-;, (6)

in the van der Waals model. We must assign values to the cross parameters TCij and VCii-

As in [l] we write

r,,, Vri, = ( T,ii V,,,T,, V,,)“’ (7)

where where vii is a binary interaction coefficient which must be obtained from experiment. No additional information

(2) is required to calculate the properties of ternary and higher mixtures.

In particular for the saturated density at a given P, and Tn we write Application

The liquid densities of the pure components are

.z,~...“=Z~ WI2 .” - W” Z” z,,...-, represented as functions of reduced temperature by an

pnfi2. n Pn. PR, PR12..“ml 1 (3) W,2...n I-0”

equation of the type

*Author to whom correspondence should be addressed.

CES Vol. 37. No. I,--P

PH = a + b(1 - Tn)‘” (9)

1675

1676 P. RICE and A. S. TEJA

Table 1. Constants in equation pn = Q + b(1 - TR)“’ The choice of equation is one of convenience and ac- curacy. A more complicated equation will give greater accuracy but will require more data to fit.

he-s o&22 W&W The values for the constants a and b in eqn (9) are heludecan. - 1.76371tl 5.962oG given in Table I for hexane, hexadecane and n-propyl

n-PmPYl rlCOhOl - 0.354601 alcohol. The pure component critical constants used

.t.zW236.2 were those reported in [6].

Table Z(a). Hexane-hexadeiane

i-::; 6:mO 5.5%0 5.W? b695 4.3558 LO74 3.tM2 3.593 3.39’1

7.551 6.762 6.144 5.573 5;1t5 4.772 4.3?5 4. cm5 3. w5 3.594 3.390

7.551 6.739 6.Od2 5.539 5.w2 1.694

iit 0.2 0.3 a4 0.5 0.602 0.7 0.d 0.9 1.0

Cl 323. 0.1 0.2 0.3 0.4 a49Y 0.582 0.699 0.8 0.9 1.0

q5 7.275 6.M 5.659 5.342

7.273 6.521 5.903 5.m 4.947 4.573 4.296 3.959 3.7a 3.481 3.2d3

4.902 4.5% L-271

_~. 3.693 3.476 3.2d3

f 00397 .00158 .ocQw+ em616

7.558 7.907 8.309

7.552 7.916

“,:% 0.301 0.739 0.4 9.2!+9 0.502 9.653 0.6 IO. 2% 0.7 lO.833 0.8 t*.7a 0.904 12.Jtx) ‘(.O 13.364

9.i39 9.774

m.340 to.977 11.6& =.507 13.359

0 0.126 0. 209 0.3 0.41, 0.516 0.6 0.792 0.9 3.0

323.15 ?Z 71947 8.311 d.835 9.347 9.825

qq.057 1?‘.9% 12 8M

7.272 7.720 &c&t

7.272 7.694 7.999 a.363 8.852 9.37% 9.83*

11.072 r%.9+6 32.817

tl.421 n.g2n 9.459 9.924

*%.I53 r1.966 12.837

A.&D. Y.&D.

.0070

.m46 .w34 .ol,o

The measurement and prediction of the densities of the ternary mixture hexaoe + henadecane + n-propyl alcohol

Table 2(c). Hexadecane-n-propyl alcohol

1677

0 29*.1s 3.391 0.0992 3.656 0.15 3.813 0.196 3.981 0.247 4.148 Cl. 3 4.355 cl. 315 4.411 0.5 5.411 0.65 5.57, 0.715 7.263 0.9 IO.289 1.0 13.364

0 323.15 3.284 0.1 3.543 0.177 3.773 0.3 ‘.LlZ cl.4 4. ,754 0.5 S.:15 0.6 5.907 0.7 6.822 0. SC1 8.106 0.9 9.809 1.0 12.E20

A.0 NAKJ

3.390 3.707 3.889 4.069 4.281 4.524 4.597 5.694 6.967 7.683

10.67‘ 13.359

3.283 3.591 3.863 4_.376 4.883 5.499 6.262 7.231 8.518

10.252 12.817

.032

.059

3.390 3.665 3.823 3.978 4.164 4.377 4.441 5.411 6.570 7.245

10.279 13.359

3.283 3.549 3.783 4.226 4.667 5.209 S.894 6.791 S.0‘1

.9.847 12.817

.0028

. 0080

c 0 1, 0 0 1 0.2 0.6

29d.15 7.558 3.390

‘:-2: 5:a23 L.&X3 7.i79 5.4X

7.552 3.390

13.359 7.995 6.050 4.699 7.lp3 5.537

7.552 3.390

13.359 7.665 5.8% 4.590 7.179 5.416

0.6 0.2~ 0.2 6.554 6.6% 0.e 0.f cl.* 6.VV5 7.070 ;:Zf

1 0 0 323. q5 7.275 7.273 7.273 0 1 0 3). 283 3.2n3 3.283 0 0 %2.820 12.816 I Z.dlh 0.2 0.2

k6 7.388 7.696 7.36i

0.2 0.L 0.4 5.530 5.767 5.533 0.2 0.6 b419 4..545 4.4211 0.418 0.164 %x3 6.919 7.323 6.913 0.408 0.394 0.198 5.2ja 5.3% 0.6 0.2 0.2 6.2997 6.b17 ‘H’Z 0.8 at 0.1 6.798 6.q81, 61757

- .maa .co178 MAD *ok46 .00595

EXPERIMENTAL Measurements were made for all the binaries as well as Measurements of densities were made at 25°C and for the ternary mixtures.

50°C using 10 ml pycnometer. The experimental details are explained in [5]. RESULTS AND DISCUSSION

The chemicals were supplied by B.D.H. Ltd. as Results for the measured orthobaric densities of the research quality and used without further purification. three binary mixtures are shown in Tables 2(a), (b) and We estimate the accuracy of the density and composition (c) with nij = 1 and with nii = optimum value. measurements to be 0.05% and 0.001% respectively. The results for the ternary mixture is shown in Table 3

I678 P. Rrr~ and A. S. TEIA

again with q,i = 1 for all mixtures and with vi, = optimum

value for each binary pair. The overall average absolute deviation for the three

binary mixtures was found to be 0.0026 (54 points) while for the ternary mixture it was 0.0018 with the binary interaction coefficient set to its optimum value. If the binary interaction coefficient was set to 1 the correspond- ing values would be 0.0143 and 0.0188 respectively.

Using the two fluid model with hexane and hexadecane as reference fluids the average absolute deviation for the ternary mixture is 0.0112 with a binary interaction coefficient of 1.015. If the binary interaction coefficient was set equal to 1 the average absolute deviation is 0.0301.

One observes that the multifluid model predicts to the same accuracy with qij = 1 as the two fluid model does with vii = optimum value. With vii = 1 in the multifluid model no experimental data are required. However, if experimental data are available to determine the opti- mum value of binary interaction coefficient then the prediction can be further improved, in our case by factor of 10.

w,,=((0.2x0.2%)+(0.2x0.742))/0.4=0.519

w,>~=(0.2x0.296)+(0.2~0.742)+(0.6~0.624)=0.582

V,-,? = ((0.37”‘+0.Y5”‘)1.003)‘+8 = 0.621

V,,, = ((0.37”‘+0.2185”‘)1.0@4)‘t8 = 0.291

Vc2> - ((0.95”’ + 0.2185”‘)1.026) + 8 = 0.538

v,, = vc,23 = X,’ v,, + x,2 VCL + x,2 v,, + 2x,x, v,,, +2x,&Vcll+2x,&Vc,,

= (0.2* x 0.37) + (0.2’ x 0.95) + (O.62 x 0.2185)

t (2 X 0.04 X 0.61) t (2 X 0.12 X 0.291) + (2 x 0.12 x 0.538) = 0.3801

(T,V,),,=(r,,V,,T,zVr,) “* = 357.6

( TrVc),3 = (T,, I’,-, Tc3 V,,)“’ = 148.4

(TrVc.h = (‘G, V,.,Tc, Vc-4 “’ = 282.6

~~,V,~,=~~cVc~I?I=~,2TcIVcI+~*z~c2Vcz+~~~~c3Vc3 +ZX,&(TcVc),z

We have shown how the effects of components which exhibit specific interaction can be incorporated in the prediction by using all pure components as reference fluids in the multifluid model.

+~X,X,(~,V,),,+~X~~~(TCVC)Z,

=(0.04~507.4~.37)+(0.04~707x.95)+(0.36x536.2x.2185)

+ (2 X 0.04 X 357.6) + (2 X 0.12 X 148.4) + (2 X 0.12 X 282.6) = 209.03

NOTATION LI, b constants in eqn (9)

p pressure T thermodynamic temperature V molar volume x mole fraction

T - T CM - Cl21 = e = 209.03/0.3801

= 549.93

Z compression factor

Greek symbols q binary interaction coefficient w acentric factor ( = In P,,p, (at TH = 0.7) - I) p density

T, = $$ = 0.5876

. : (I ~ T&“) = 0.745

eR = LI + b(l - T,)“’

Subscriprs c critical n component n

i, j components i, j R reduced

eR, = .832722 + 9.02597 x 0.745 = 1.557 kg mollm’.

Similarly

eR1 = 2.819kg mol/m’

eH1 = 13.003 kg mollm’.

REFERENCES Fist interpolation using n-hexane and n-hexadecane as reference fluids.

[I] Teja A. S. and Rice P., Chem. Engng Sci. 1981 36 1. [2] Teja A. S., A.I.Ch.E.J. 1980 26 337. [3] Teja A. S. and Sandier S. I., A.I.Cb.E.J. 1980 26 341. [4] Teja A. S., Sandier S. I. and Pate1 N. C., C&m. Engng J. 1981

21 21. [5] Rice P. and Teja A. S., J. Chem. Engng Data 1976 21 193. [6] Reid R. C., Prausnitz J. M. and Sherwood T. K., The Proper-

ties of Gases nnd Liquids, 3rd Edn. McGraw Hill, New York 1977.

APPENDIX

Demonstration of the method for the mixture 0.2h n-hexane 0.2 n-hexadecane 0.6 n-propyl alcohol at 323.15”K, for which the measured density was 7.388 kg mol/m”, using a hand calcuhtor.

z=$xz.i$x,

(&),,=&+z[*-&.J =&

+ (0~19-0.742) [~_~~,o.,887. 0 2% 0.742 7.557 x 0.37 2.819 x 0.95

Second interpolation using n-propyl alcohol as fhe third reference fluid and pseudo fluid 12

(z&=&+zz [G&&l

= l3.~;.2,85+:::;;-::; [o~0887-13.00!-~~,2185]

= 0.0889

Z,,,=(0.2~0.26)+(0.2x0.226)+(0.6x0.253)=0.249 eRII, = o.38~‘~~,0889 = 7.366 kg mollm’.

The computer program value was 7.361