DENSITY OF LIQUID REFRIGERANTS

By

T SHYAMKUMAR

14TH14F

I sem, M Tech Thermal Engineering

CONTENTS Introduction

Methods of measuring density

Literature Review ISH correlation

Rackett equation

Rackett equation by Yamada and Gunn

Spencer and Danner modification of Rackett method(RSD)

Hankinson and Thomson (HT) method(COSTALD)

Reidel method

NM Correlation

Programming

Results

Conclusion

INTRODUCTION

Designing refrigeration cycles require thermodynamic properties of refrigerants, i.e., liquid density, vapour density, enthalpy of vaporization and vapour pressure Liquid density is needed for process simulation and equipment design.

Equations of state (EoS) are used in commercial simulation software for predicting phase behavior and thermodynamic properties.But, equations of state are not accurate enough for a wide range of applications. The popular EoSs such as SRK and PR predict liquid density with an average absolute error of about 8%, much higher than the correlations .

correlations have wider range of applicability and accuracy.

TWO SINKER DENSIMETER

Based on the Archimedes' buoyancy principle.

Both sinkers have the same mass, the same surface area, and the same surface material, but a considerable difference in volume.

Continue...

This sinker support is connected to a commercial analytical balance ( resolution 10 μg) by a thin wire via a magnetic suspension coupling .

“apparent mass difference” Δm* = (mD* − mS*) of the sinkers.

By means of the magnetic suspension coupling, the suspension force is contactlessly transmitted from the pressurized measuring cell to the balance at ambient conditions.

ρ = (Δm* − ΔmVac) / (VS − VD), where ΔmVac= ( mD − mS) corresponds to the very small mass difference of the two sinkers which is accurately determined by weighing in the evacuated measuring cell.

CORIOLIS FLOW METER

Based on coriolis principle.

An exciter causes tube to oscillate constantly

Sensors are located at inlet & outlet

Phase shift during flow is a measure of mass flow rate.

Oscillating frequency is a direct measure of density.

.

LITERATURE REVIEW(a) ISH correlation (Iglesias et al [1])

n=0.5 and β is the scaling exponent having a value between 0.32 and 0.34

= (2.1)

= 0.03 – (2.1.a)

= (1 - ) – 1 -(2.1.b)

=

Rackett equation Rackett(1970),[2] proposed the following correlation

......(Eq 2.2)

is critical compressibility factor.

=

Modified Rackett equation by Yamada and Gunn Yamada and Gunn (1973), [2] proposed

.....(Eq 2.3)

Acentric factor

W represents accentricity or nonsphericity of a molecule.Formonoatomic gases w =0.

For higher hydrocarbon w increases.

=

] - 1

Spencer and Danner modification of Rackett

method

By Kh.Nasrifar et al[3]

Popularly known as RSD equation

.....(Eq 2.4)

ZRA = 0.29056- 0.8775w

= ( )

Hankinson and Thomson (HT) method

By Hankinson et al[4]

.......(Eq 2.5)

a = -1.52816 ; b = 1.43907;c = -0.81446 ; d = 0.190454 ;e = -0.296123 ; f = 0.386914 ;g = -0.0427258 ; h = -0.0480645 ;

is the characteristic volume

( ) = [1- ]

= 1+a +b +c +d

=

Reidel method

Reidel [3] suggested the following correlation

......(Eq 2.6)

is the slope of vapour pressure at critical temperature

= = 1 + 0.85 (1- + (0.53 + 0.2 )

= 1 + 0.85 (1- + (1.6916 + 0.984 )

NM CorrelationKhashayarNasrifar and Mahmood Moshfeghian proposed the following

correlation [5]

d1 = 1.1688d2 = 1.8177d3 = -2.6581d4 = 2.1613δ is the characteristic parameter for each compound.

c1, c2 and c3 are vapour pressure dependent parameters

= [1+ ]

= 1+ + + +

= <1

= >1

Correlation Suitable refrigerants Comments

ISH R22, R123, R134a, R152a, R290, R600,

R600a, R717, R718, R12

Rackett R22, R32, R123, R125, R134a, R152a,

R290, R600, R600a, R717, R718, R1270

R143a, R12

For all

compounds

with Zc > 0.22

Yamada & GunnR22,R32,R123,R125,R134a,R152a,

R290,R600,R600a,R717,R718,R1270

R143a,R12

Spencer& Danner R22,R290,R600,R600a,R717,R718,R1270

Hankinson & Thomson R22, R290, R600, R600a, R717, R718,

R1270

Applicable

when

0.25 < Tr < 0.98

Reidel

R22,R32,R123,R125,R134a,R152a,

R290,R600,R600a,R717,R718,R1270

R143a,R12

NM

R22,R32,R123,R125,R134a,R152a,

R290,R600,R600a,R717,R718,R1270

R143a,R12

PROGRAMMING

Coding language:MATLAB

The program reads input data from excel sheet, calculates saturated liquid densities and percentage deviation from ASHRAE values for temperature ranges specified in ASHRAE data hand book and writes it back to another excel sheet.Average absolute percentage deviation is also calculated.

Two plots for each refrigerant:

Density vs temperature

%error vs temperature

ERROR ESTIMATION

Percentage deviation from ASHRAE values,

δ =(ρs –ρexp)*100 .... (Eq 7)

Average absolute percentage deviation = 1/N*Σ|δ|..(Eq8)

Where N is the number of data points .

RESULTScalculated densities

Refrigerant ISH Rackett Yamada

& Gunn

RSD HT Reidel NM Best

correlation

R22 0.281556 1.442423 1.2503372 1.52110 0.33468 0.29246 0.25362 NM

R32 2.289975 3.49270887 2.91578 0.7023 NM

R123 1.049479 1.049479 0.3235613 0.68225 0.37057 Yamada

& Gunn

R125 2.3816 0.80894612 0.43202 0.56296 Reidel

R134a 1.225932 1.225932 1.21537009 1.09272 0.40607 NM

R152a 0.65903 0.65903 3.44362871 2.90145 0.52618 NM

R290 0.371952 0.618689 0.363586 0.3766 0.1066 0.49043 0.29022 HT

R600 0.374877 0.691794 0.45620980 0.3777 0.3487 0.58189 0.25245 NM

R600a 0.484182 3.240646 2.36065152 0.5651 0.0735 2.16849 0.75051 HT

R717 0.55532 1.184232 4.15963261 1.2214 0.9787 3.39811 0.8985 ISH

R718 6.659881 4.832748 4.70070317 3.1206 23.835 4.57693 RSD

R1270 1.552219 1.13710968 0.6716 0.3774 3.26391 0.6126 HT

R143a 2.530843 1.580401291 1.36151 1.78446 Reidel

R12 2.3492844 2.3492844 1.20655272 1.476334 0.89878 NM

Average absolute percentage deviations

CONCLUSIONS

NM correlation has been found the best the for prediction of saturated liquid densities for R22, R32, R134a, R152a, R600 and R12 with a maximum AAPD of 0.89878 % for R12

Equation predicted by Hankinson and Thomson.et al is best suited for R290, R600a and R1270

Reidel’s correlation can be applied to R143a and R125

Modified Rackett equation by Yamada and Gunn and Spencer and Danner gives fairly accurate results for R123 and R718 respectively.

ISH correlation is best suited for R717 with AAPD of 0.555%.

REFERENCES[1] Gustavo A Iglesias-Silva,Kennath.R.Hall,”A saturated liquid density

equation for refrigerants”,Fluid Phase Equilib 131(1997) 97-105

[2]The properties of Gases and Liquids, Fifth Edition, Bruce E poling, John MPrausnitz John P O’Conell , McGraw Hill, ’Rackett equation’(145-146)

[3]Khashayar Nasrifar, Mahmood Moshfeghian, ”Evaluation of saturated liquid density prediction methods for pure methods”, Fluid phase Equilib158-160(1999),437-445

[4]Risdon W Hankinson, George H Thomson, AIChE Journal (vol25, no4)(1979), 653-663

[5]Khashayar Nasrifar, Mahmood Moshfeghian, “A saturated liquid density equation in conjunction with the Predictive-Soave–Redlich – Kwongequation of state for pure refrigerants and LNG multi component systems”, Fluid phase Equilib 153(1998),231-242

[6]Kh.Nasrifar,Sh.Ayatollahi,M.Moshfeghian,”An extended saturated liquid density equation”,Fluid phase Equilib166 (1999),163-181

[7]Kh.Nasrifar,Sh.Ayatollahi,M.Moshfeghian,”Generalised saturated liquid density prediction method for pure compounds and multi-component mixtures”,Fluid phase Equilib168(2000),71-90

[8]”Refrigerants-Physical properties”, http://www.EngineeringToolBox.com

[9] “Liquid density by volume translated method-Part1”,http://www.jmcampbell.com/tip-of-the-month/2011/03/liquid-density-by-volume-translated-method-%e2%80%93-part-1-pure-compound/

[10]“Liquid density by volume translated method-Part2”,http://www.jmcampbell.com/tip-of-the-month/2011/07/liquid-density-by-volume-translated-method-%e2%80%93-part-2-recent-development/