Oil concentration variation for bottled refrigerant/oil mixtures during extraction

ORIGINAL

Oil concentration variation for bottled refrigerant/oil mixturesduring extraction

Vipin Yadav

Received: 1 January 2010 / Accepted: 8 July 2011 / Published online: 24 July 2011

� Springer-Verlag 2011

Abstract In order to cut down setup cost for maintaining

a constant concentration of oil in refrigerant/oil mixtures

during experimentation, a bottle filled with a refrigerant/oil

mixture having a predetermined oil concentration occurs as

a suitable option. An attempt has been made to find the

limits of variation in oil concentration during the extraction

process so that the above technique can be suitably

employed. Cases for oil with specific gravity in the range

0.80–1.00 and three refrigerants, viz., CO2, R290 and

R134a are analysed. A sharp rise in oil concentration is

revealed toward the end of the extraction process. It is

proposed that oil concentration variation can be con-

strained by supplying the lowest residual/left mass fraction

(LMF) value (or the maximum extractable mixture weight)

along with other specifications for the refrigerant/oil mix-

ture. A correlation is obtained to determine oil concentra-

tion during various stages of the extraction process.

List of symbols

c Oil concentration

Dc Change in concentration

Cp Specific heat, kJkg-1K-1

D Bottle diameter, m_E Energy flow rate, W

H Height/level, m

h Heat transfer coefficient, Wm-2K-1

k Wall thermal conductivity, Wm-1K-1

_m Rate of mass extraction, kgs-1

M Mass left inside the bottle, kg

R Thermal resistance, KW-1

_q000 Heat energy entering per unit volume of the

bottle, Wm-3

t Time, s

tw Wall thickness, m

Dt Time step, s

T Temperature, K

V Bottle volume, m3

LMF Left mass fraction

M.F.R. Mass flow rate, kgs-1

a Refrigerant vapor-to-liquid density factor,

defined by Eq. 19

b Refrigerant vapor-to-oil density factor, defined

by Eq. 19

f Refrigerant specific heat factor, defined by

Eq. 16

l Ratio of left mass to initial mass at the process

end, defined by Eq. 24

n Refrigerant specific heat factor, defined by

Eq. 16

q Density, kgm-3

r Factor defined by Eq. 16, m6J-1

/ Factor defined by Eq. 19

x Thermophysical property factor for refrigerant,

m3kg-1K-1, defined by Eq. 16

G Function representing dependence of rate of

change in temperature upon rate of

concentration change, K, defined by Eq. 28

G Function defined by Eq. 24

P� Dimensionless variable appearing in Eq. 25

C � Defined in Eq. 25

C Defined in Eq. 28

hfg Enthalpy of vaporization, kJ kg-1

s Oil specific gravity

r Fraction of liquid volume inside bottle

V. Yadav (&)

Department of Mechanical Engineering, Rajiv Gandhi Institute

of Petroleum Technology, Raebareli, Uttar Pradesh 229 316,

India

e-mail: [email protected]

123

Heat Mass Transfer (2012) 48:191–203

DOI 10.1007/s00231-011-0869-6

De Bottle outside diameter, m

He Bottle outside height, m

hl Liquid mixture heat transfer coefficient

ha Air side heat transfer coefficient

hv Vapor side heat transfer coefficient

P Pressure, Pa

Subscripts

0 Initial value

a Air

b Bottle

e Ambient

f Final value

fg Vaporization

i Inside the bottle

l liquid

max Maximum value

o Oil

r Liquid refrigerant

s Starting value

sat Saturation

T Total

v Refrigerant vapor

1 Introduction

Bottles of liquefied gas having a desired concentration of a

refrigerant/oil (lubricant) mixture possess great potential

for heat transfer experimentation targeted for performance

improvement in refrigeration and air-conditioning systems.

The literature [1–12] reveals a considerable amount of

research for in-depth understanding of heat transfer prop-

erties for boiling refrigerant/oil mixture under diverse

geometrical and thermophysical conditions. Various

methods have been developed for measuring the concen-

tration of a flowing oil-refrigerant mixture, viz., using a

bypass viscometer [13], a vibrating U-tube densitometer

[14], refractive index [15], visualization techniques [16],

and acoustic velocity sensors [17]. Overall measurement

accuracy and cost of instrumentation for concentration

measurement is highly dependent on the underlying mea-

surement principle and subsequent methodology followed

for signal interpretation from the sensors. The overall

exercise may be quite expensive. However, situations may

occur when costly instrumentation can be avoided and

simple analytical techniques can be used to estimate oil

concentration in a flowing mixture.

The present work is based upon the concept of using a

refrigerant/oil mixture directly from a bottle having a

known concentration of oil. Unfortunately, there is no

information available in the literature on the impact that the

extraction process and various thermophysical parameters

can have upon the actual concentration of the remaining

mixture in the bottle. The problem is intensified by the

possibility of having various mixtures which use different

refrigerants and lubricants. Furthermore, careful review of

the literature and the information available about concen-

tration measurement devices shows that oil concentration

measurement at low temperature is a challenge [18–20],

particularly due to degradation in response characteristics

or malfunctioning of piezoelectric and semiconductor

based sensors.

This paper presents a transient analysis for variation in

oil concentration of a refrigerant/oil mixture during its

extraction from a rigid bottle. Isothermal, adiabatic and

non-adiabatic conditions are analyzed for the liquid–vapor

system in order to identify and quantify the effect of

thermophysical parameters upon the oil concentration.

Cases are considered for oil with specific gravity in the

range 0.80–1.00 and three refrigerants, viz., CO2, R290 and

R134a having liquid phase density in the range

400–1,300 kgm-3 and vapor phase density in the range

10–200 kgm-3. The mixture is assumed to be homoge-

neous and at a uniform bulk temperature during the entire

process. The numerical solution technique implemented

using the EES code [21] takes into account the effect of

temperature and associated variation in pressure upon the

mixture component properties. Based upon certain input

parameters, such as bottle size (or volume), initial tem-

perature and initial oil concentration, the proposed analysis

can be used to evaluate the concentration and temperature

at any instant during the extraction process. An approxi-

mate analytical solution has also been developed for esti-

mating the oil concentration in the mixture during

extraction under isothermal conditions.

2 Modelling and analysis

Consider a rigid bottle (Fig. 1) of volume, V, containing a

mixture of liquid refrigerant and oil (lubricant) of known

concentration (c) at a saturation pressure corresponding to

the temperature of the refrigerant. Following are the basic

assumptions:

1. mixture is homogeneous and at a uniform bulk

temperature;

2. instantaneous values for concentration and temperature

of the liquid drawn from the bottle are the same as

those of the mixture remaining in the bottle;

3. oil is completely miscible and non-volatile;

4. the heat exchange between the bottle and the sur-

roundings is taken as a surface phenomenon;

5. conduction and convection are the only modes of heat

transfer;

192 Heat Mass Transfer (2012) 48:191–203

123

6. at any instant during the extraction process, the bottle’s

wall is at a uniform temperature; and,

7. for small oil concentration value, the equilibrium

pressure inside the bottle remains unaffected by the

presence of oil.

2.1 Isothermal mixture

For the isothermal state, the thermophysical properties

influenced by temperature remain constant. Liquid-to-

vapor phase change is necessary to maintain constant vapor

pressure inside the bottle. Let Mr and Mo be the mass of the

refrigerant and oil components, respectively, in the mixture

at any instant during the extraction process. Then oil

concentration (by weight) in the liquid mixture is

c ¼ Mass of oil Moð ÞMass of liquid refrigerant Mrð Þ þMass of oil Moð Þ

ð1Þ

Total initial mass of the mixture (Ms), final (or residual)

mass remaining (Mf) and left mass fraction (LMF) are

given as

Ms ¼1

qo

� 1

qr

� �c0 þ

1

qr

� ��1

V; Mf ¼ qvV ;

LMF ¼ M �Mf

Ms �Mf

ð2Þ

where, c0 is initial concentration of oil in the mixture;

qo, qr and qv are the densities of oil, liquid refrigerant

and vapor respectively and M is the mass remaining

inside the bottle at any particular instant during

extraction.

Consider that, as a result of extraction of liquid mass,

DM, from the bottle, DMr and DMo are the corresponding

changes in the mass of liquid refrigerant and oil, respec-

tively. The resulting change in oil concentration, Dc, and

the change in mixture volume, DV, are given by the rela-

tionships as below

cþ Dc ¼ Mo � DMo

Mr � DMrð Þ þ Mo � DMoð Þ

DV ¼ DMr

qr

þ DMo

qo

þ DMv

qv

9>>=>>;

ð3Þ

Note that the decrease in the mass of the mixture results

in an increase in the mass of vapor. Since the bottle is

assumed to be rigid, we have DV = 0, therefore,

DMv ¼ �qv

DMr

qr

þ DMo

qo

� �; DMr ¼ 1� cð ÞDM � DMv;

DMo ¼ cDM ð4Þ

Now, small changes in Mr and Mo can be expressed as

(see Appendix 1)

DMr ¼ 1� 1� qv

qo

� �c

� �1� qv

qr

� ��1

DM

DMv ¼qv

qr

1� 1� qr

qo

� �c

� �1� qv

qr

� ��1" #

DM

9>>>>=>>>>;

ð5Þ

From Eqs. 3, 4 and 5, we get the following expression

for the change in concentration, Dc, of remaining mixture

in the bottle (see Appendix 2)

Dc ¼1� 1� qr

qo

� �c

n o1� qr

qv

� ��1DM

M�Mvð Þ

1� 1þ 1� 1� qr

qo

� �c

n o1� qr

qv

� ��1�

DMM�Mvð Þ

c

ð6Þ

For infinitesimal DM and under the condition when

sufficient amount of liquid mixture is still in the bottle i.e.

M �Mvð Þ

Mf [ 1, we can apply the limiting case

1þ 1� 1� qr

qo

� �c

� �1� qr

qv

� ��1" #

DM

M �Mvð Þ\1

So Eq. 6 can be written as

Dc

DM¼ 1� 1� qr

qo

� �c

� �1� qr

qv

� ��1c

M �Mvð7Þ

For the limit DM ? 0, Eqs. 5 and 7 provide the

following set of coupled differential equations

Fig. 1 Schematic of the refrigerant/oil mixture inside the rigid bottle

Heat Mass Transfer (2012) 48:191–203 193

123

dc

dM¼ 1þ qr

qo

� 1

� �c

� �1� qr

qv

� ��1c

M �Mv

dMv

dM¼ 1þ qr

qo

� 1

� �c

� �qr

qv

� 1

� ��1

9>>>=>>>;

ð8Þ

Note that in the above equation, under isothermal

condition, c, M and Mv are variables. In order to evaluate

the change in oil concentration during the extraction process,

the equations in the set (8) need to be solved simultaneously.

2.1.1 Approximate analytical solution

From equation set (8) we get (refer Appendix 3)

dc

dðM �MvÞ¼

1þ qr

qo� 1

� �c

n o1� qr

qv

� ��1

1þ 1þ qr

qo� 1

� �c

n o1� qr

qv

� ��1� c

M �Mv

ð9Þ

Integrating Eq. 9 we get

c

c0

� � 2�qrqv

� �1þ qr

qo� 1

� �c0

1þ qr

qo� 1

� �c

0@

1A

1�qrqvð Þ

¼ M �Mv

Ms

� �¼ LMF

ð10Þ

(Appendix 4) for qr & qp, above relation can be written as

c ¼ c0ðLMFÞ 2�qrqv

� ��1

ð11Þ

2.2 Mixture under non-isothermal state

Let us consider _q000 as heat energy entering per unit volume

of the bottle. The energy balance for the heat entering the

system (bottle) and used in liquid to vapor phase change for

the refrigerant is

VoqoCp; o þ VrqrCp; r þ V � Vo � Vrð ÞqvCp; v

� dT

dt

¼ hfgqv

d

dtV � Vo � Vrð Þ þ _q000V ð12Þ

where, Vo, Vr, are the volume of oil and liquid refrigerant;

Cp; o Cp; r Cp; v are specific heat values for oil, liquid

refrigerant and vapor; hfg is heat of vaporization of liquid

refrigerant.

The mass of refrigerant vapour, Mv, can also be given as

V � Vo � Vrð Þqv ¼ M � Voqo � Vrqr ð13Þ

From Eqs. 12 and 13 we get

Cp; v M þ Voqo

Cp; o

Cp;v� 1

� �þ Vrqr

Cp; r

Cp;v� 1

� �� dT

dt

¼ �hfgqv

d

dtVo þ Vrð Þ þ _q000V ð14Þ

or

x M þ Voqofþ Vrqrnf g dT

dt¼ � d

dtVo þ Vrð Þ þ r _q000

ð15Þ

where,

f ¼ Cp; o

Cp; v� 1; n ¼ Cp; r

Cp; v� 1; x ¼ Cp; v

hfgqv

; and

r ¼ V

hfgqv

ð16Þ

The quantities Vo and Vr can also be related as

Vo ¼cqrVr

qo 1� cð Þ *c ¼ Voqo

Voqo þ Vrqr

� ð17Þ

Equations 13 and 17 gives

Vr ¼M � Vqv

qr � qvð Þ þ qo � qvð Þ c1�c

� � qr

qo

� � ð18Þ

We now introduce following new parameters

/ ¼ c

1� c; a ¼ 1� qv

qr

and b ¼ 1� qv

qo

ð19Þ

Differentiating of Eq. 18 both sides with respect to t

dVr

dt¼ 1

qr aþ b/ð ÞdM

dt

�M �Mf

� �b

qr aþ b/ð Þ2d/dt

dc

dt¼ 1

/þ 1ð Þ2d/dt

; Mf ¼ Vqv

" #

ð20Þ

Differentiating of Eq. 17 both sides with respect to t and

using Eq. 20 we get

dVo

dt¼ /

qo aþ b/ð ÞdM

dt

þM �Mf

� �a

qo aþ b/ð Þ2d/dt*

dVo

dt¼ qr

qo

Vrd/dtþ /

dVr

dt

� ��

ð21Þ

Substituting values from Eq. 20 and 21 in Eq. 15

followed we get

xM

M �Mfþ nþ /fð Þ

aþ /bð Þ

� dT

dt¼ 1

aþ /bð Þ2bqr

� aqo

� �d/dt

� 1

aþ /bð Þ1

qr

þ /qo

� �� 1

M �Mf

dM

dtþ r _q000

M �Mf

ð22Þ

Equation 22 can be written as

Eð/Þ dT

dt¼ P�ð/Þ d/

dt� C�ð/Þ dM

dtþ K�ð/Þ _q000 ð23Þ

where,


123

Eð/Þ ¼ x 1þ lGð/Þ þ nþ /faþ /b

� ; l ¼ Mf

Ms �Mfand

G /ð Þ ¼ Ms �Mf

M �Mf

ð24Þ

P�ð/Þ ¼ 1

aþ /bð Þ2bqr

� aqo

� �;

C �ð/Þ ¼ 1

aþ /bð Þ1

qr

þ /qo

� �� 1

M �Mf

ð25Þ

K�ð/Þ ¼ rGð/ÞMs �Mf

� � ð26Þ

Equation 23 can further be expressed as

dT

dt¼ Pð/Þ d/

dt� Cð/Þ dM

dtþ Kð/Þ _q000 ð27Þ

Where,

PðuÞ ¼ P�ðuÞEðuÞ ; C ¼ C�ð/Þ

Eð/Þ and KðuÞ ¼ K�ðuÞEðuÞ

ð28Þ

Desired solution can be obtained by integrating Eq. 27.

Note that Eq. 22 inter-relates the change in temperature

with the change in concentration and the change in the

mass of system. At this stage, the solution can be obtained

by performing numerical integration of Eq. 22. Another

possible way to obtain the solution is by representing terms

consisting mass in the concentration terms as

M ¼ Mf þ Ms �Mf

� �Gð/Þf g�1 ð29Þ

G(u) is a continuous function of u for u(c) [ 0 in the

range 0\c� 1. G(u) is associated with the solution

corresponding to Eq. 8.

Volumetric heat input can be obtained as [see Appendix 6]

_q000 ¼ Te � Tið ÞV

X4

i¼1

1

Ri

" #: ð30Þ

3 Results and discussion

The presented results are based on the finite difference

methodology implemented using Engineering Equation

Solver (EES Version-V7.695-3D) to obtain the solutions to

the derived equations (6, 10 and 11; also see Appendix 7).

The initial and test conditions used as basic input param-

eters are given in Table 1. Analysis is used for generating

concentration and temperature data for three refrigerants

viz. CO2, R290 and R134a with three miscible oil types

with specific gravity in the range 0.80–1.00. The selection

of these refrigerants, oil specific gravity and physical

details of the bottle are based upon the literature [22–24]

and commercial information sources (Tables 2 and 3). The

specific heat for the lubricating oils for given values of

specific gravity is evaluated following Liley and Gambill

[25]

Cp; o ¼ 4:186 0:388þ 0:00045 1:8T þ 32ð Þ½ �=s1=2n o

ð31Þ

where the unit of liquid specific heat Cp,o is kJ/kg�C, oil

temperature, T, is �C (valid for the range -18 \ T \ 204�C),

and s is the liquid specific gravity at 15.6�C (60�F) valid for

0.75 \ s \ 0.96.

3.1 Effect of factor x

One of the interesting aspects of analysis is that it is pos-

sible to predict the combined effect of vapor specific heat,

enthalpy of vaporization and specific volume [through the

factor x as defined by Eq. 16] upon variation of mixture

concentration. The results in Fig. 2 show the effect of xupon final concentration of the mixture. For the entire

range of oil sp gravity and all of the refrigerants under

consideration, the range of x is 1.0 9 10-4–3.2 9 10-4.

Initially, increase in x from 1.2 9 10-4 to 2.0 9 10-4

resulted in gradual increase in concentration however, the

slope of the curve decreased with increase in oil density;

and further increase in x in the range 2.0 9 10-4–

3.2 9 10-4 resulted in gradual drop in c. Evidently, the

maximum change in concentration has been found for the

case of CO2 for least value of initial oil concentration.

3.2 Effect of factor G

The factor G [as given by Eq. 28] signifies variation in

mixture temperature per unit change in the oil concentration

under adiabatic conditions. The overall range of G is -7 9

103 to -2 9 102 for various cases under investigation.

Table 1 Details of input parameters

Input parameters Value/range

Air to wall outside heat transfer coefficient (ha) 5.0 W m-2 K-1

Liquid to wall heat transfer coefficient (hl) 20.0 W m-2 K-1

Inside vapour to wall heat transfer

coefficient (hv)

3.0 W m-2 K-1

Bottle material Steel

Bottle body material density (qb) 7,900 kg m-3

Bottle body thermal conductivity (Kb) 20.0 W m-1 K-1

Bottle body specific heat (Cp, b) 0.477 kJ kg-1 K-1

Ambient temperature (Te) 20.0�C

Initial internal temperature (Ti) 20.0�C

Initial oil concentration range (c0) 0.0–0.20

Internal pressure (Pi) Psat at Ti


123

Under adiabatic conditions, G\ 0 signifies a reduction in

the temperature of the mixture as the mass is drawn out.

Figure 3 shows the variations in G due to the change in

LMF for different oil specific gravity values and refriger-

ants. In general, G increases with a decrease in left mixture

mass, M. The maximum variation in G can be observed for

the lowest value of initiation concentration, i.e., c0 = 0.02.

The effect of oil specific gravity upon G is more significant

in the region LMF B 0.4 (when the bottle is about to be

emptied).

3.3 Change in concentration due to mixture extraction

Under isothermal condition, the pressure inside the bottle is

assumed constant and is equal to the saturation pressure of

the refrigerant component of the mixture at considered

temperature; consequently, density of liquid mixture and

vapour can be considered constant during the extraction

process. It can be observed from Fig. 4 that increase in

concentration, c, is near linear towards initial stage of the

extraction process; however, the nature of trend turns

exponential towards end phase. At particular LMF value,

magnitude of variation in concentration is largely deter-

mined by the refrigerant component of the mixture. For

CO2/oil mixture, the change in oil concentration is highest;

about 50% change in concentration occurs when 4/5th of

the bottle is emptied. Described trends pertain to oil spe-

cific gravity = 0.90 and c0 = 0.05. It can be observed as

the bottle is 3/5th emptied; the change in concentration is

near 25, 3.5 and 2% for the cases of CO2, R290 and R134a

respectively (for small sized bottle). Under adiabatic con-

dition, concentration patterns for all mixtures deviate from

Table 2 Detailed specification of oils used for selecting oil specific gravity

Oil Sp. g. (at 15�C) Type ISO grade Refrigerants Manufacturer

158 RF ISO 100 0.835 Polyalhpaolefin (PAO) 100 Ammonia, CO2, R 11 Schaeffer

Conco refrigerant oil ISO 46 0.862 Paraffinic 46 Ammonia, CO2 ConcoPhillips

Chevron ammonia refrigerant oil 0.867 Naphthenic 68 Ammonia, R 22, R 502 Chevron

Conco refrigerant oil ISO 68 0.868 Paraffinic 68 Ammonia, CO2 ConcoPhillips

BVA ALKYL 150 0.87 Alkylbenzene 150 R 22, R 124 Atlantic chemicals

RENISO S 68 0.872 Synthetic alkylbenzol 68 Ammonia FUCHS

RENISO SP 46 0.874 Synthetic alkylbenzol 46 R 22, R 401 FUCHS

CITGO NORTH STAR ISO 32 0.896 Naphthenic 32 Ammonia, CO2 CITGO

Capella WF 68 0.91 Naphthenic 68 Ammonia, CO2, R 12 Chevron

CITGO NORTH STAR ISO 54 0.914 Naphthenic 54 Ammonia, CO2 CITGO

Phillps 66 baltic oil 0.927 Naphthenic 68 Ammonia, CO2, R 22 ConcoPhillips

SUNISO SL-10S 0.928 Polyol ester 10 R 134, R 404a, R 410a SUNISO

SOLEST 220 0.955 Polyol ester 220 R 134a Atlantic Chemicals

SUNISO SL-32S 0.956 Polyol ester 32 R 134, R 404a SUNISO

SUNICE T-68 0.960 Polyol ester 68 R 407c, R 410a, R 404a SUNISO

SOLEST LT 32 0.965 Polyol ester 32 R 23, R 508b, R 404a Atlantic Chemicals

Emkarate RL 68H 0.977 Polyol ester 68 R 404a Nu-Calgon

RENISO C 85 E 1.004 Synthetic EO 85 R 744 FUCHS

Capella HFC 55 1.01 Synthetic polyol ester 55 R 134a Chevron

XADO 1.064 Synthetic PAG ester 100 Ammonia 76 lubricants company

Table 3 Details of physical dimensions of bottle

Size/

specification

Physical dimensions (in m)

Height

(H)

Ext. diameter

(De)

Wall thickness

(t)

Small 0.337 0.084 0.005

Medium 1.183 0.187 0.010

Large 1.473 0.270 0.016

Fig. 2 Variation in mixture concentration due to change in factor xfor different initial concentration values for various refrigerants


123

linearity in the slightly later stage of the extraction process

when compared to isothermal case; also, magnitude for the

change in concentration is reduced. For instance, for CO2/

oil mixture at LMF = 0.2, concentration change is near

50% for isothermal case while near 30% for adiabatic

condition. Similarly, the change in concentration is found

to be near 16 and 12% for R290/oil and R134a/oil mixtures

respectively; note that the corresponding values for iso-

thermal case were near 20 and 15% respectively. Inter-

estingly, the trends for the CO2/oil mixture cases exhibit

Fig. 3 Dependence of factor G upon left mass ratio and different initial concentration values for different refrigerant oil mixtures

Fig. 4 Dependence of oil

concentration upon left mass

ratio for different refrigerant oil

mixtures for c0 = 0.05, oil

specific gravity = 0.9


123

exponential increase in concentration towards the second

half of the extraction process; similar trends also occur for

R290/oil and R134a/oil cases, however, only when the

extraction process is near completion. Non-adiabatic case-

1, case-2 and case-3 stands for small, medium and large

size bottles respectively (as defined in Table 3) at mass

flow rate of 0.01 kgs-1. On an average, for same LMF

value, the observed concentration change for large bottle is

nearly 1% lower as compared to small bottle. For the other

cases of refrigerant/oil mixtures the effect is not significant.

The effect of oil specific gravity upon concentration can

be observed from Fig. 5a where the representative trends are

presented for CO2/oil mixture. Reduction in the specific

gravity of oil from 0.90 to 0.80 resulted in about 0.5%

increase in concentration value; increase in the specific

gravity from 0.90 to 1.00 led to near 0.5% decrease in

c. Trends are identical for R290/oil and R134a/oil; however,

deviation in concentration is proportional to the magnitude

of overall change in the concentration.

For isothermal case, it can be observed that for a par-

ticular value of LMF, as oil specific gravity reduces from

0.90 to 0.80, concentration increases nearly by 0.3%.

Similarly near 0.3% decrease is observed in concentration

as the oil specific gravity increases from 0.90 to 1.00.

Effect of initial concentration upon the magnitude of the

change in concentration during the extraction process can

be observed from Fig. 5b. As the value for c0 reduced from

0.05 to 0.02, the resulting increase in the concentration is

by 0.2%; and as c0 increased from 0.05 to 0.20, about 1%

reduction in occurred. In general, the effect of variation in

oil specific gravity and c0 upon c is negligible near the start

of the extraction process however; its effect is dominating

towards the end. Representative trends in variation pattern

for the concentration of CO2/oil mixture under non-adia-

batic condition with three different mass flow rates along

with corresponding data for isothermal and adiabatic cases

are shown in Fig. 5c for comparison purpose. Apparently

there is no deviation in concentration for R290/oil and

R134a/oil mixture due to variation in mass flow rate. As far

as the size of the bottle is concerned, influence is found

significant only for CO2/oil mixture.

3.4 Temperature variation patterns

Variation of temperature inside the small sized bottle

during different stages of the extraction process is shown in

Fig. 6a; information is presented for individual cases of oil

mixtures with CO2, R290 and R134a, c0 = 0.05, specific

gravity = 0.90 and Ti = 20�C. Maximum temperature

drop is found to occur for CO2/oil mixture for which final

temperature approaches near 2�C towards the end of the

extraction process; corresponding values for R290 and

R134a are near to 6�C and 10�C respectively. The effect of

mass flow rate or extraction rate upon the temperature

inside the bottle for the cases of CO2/oil mixture is shown

in Fig. 6b. The trends of variation in temperature for

mixture under non-adiabatic condition are significantly

different from adiabatic condition, in former case the

curves representing the variation of temperature with LMF

exhibit pattern with downward concavity however, in this

case similar curves exhibit concavity upwards pattern.

Also, as compared to the previous case, the extent of

Fig. 5 For mixture under isothermal condition a effect of oil specific

gravity on concentration for CO2/oil mixture with c0 = 0.20, b effect

of initial concentration for the same case with oil specific

gravity = 1.0, c effect of extraction rate on oil concentration for

CO2/oil mixture under non-adiabatic condition with c0 = 0.05, oil

specific gravity = 0.90


123

variation in the temperature is subtle; for CO2/oil mixture,

temperature is found to be lowered by near 2�C towards the

end of the extraction process for mass flow rate value of

0.100 kg/s (under adiabatic condition corresponding

decrease is near 18�C). Variation pattern in temperature for

the CO2/oil mixture for mass flow rate value of 0.010 kg/s

is shown in Fig. 6c; towards the end of the extraction

process, the temperatures of mixture in small and large

bottles differ nearly by 1.5�C.

3.5 Discussion on approximate analytical solution

Trends for the difference in the analytical solutions due to

Eq. 10 and the numerical solutions of Eq. 6 for different

refrigerant/oil mixtures at c0 = 0.2 and oil specific grav-

ity = 1.0 are presented in Fig. 7. For the case of R134a/oil

and R290/oil mixtures the deviation between two solutions

is within 10% as long as the left mass fraction values do not

fall beyond 0.2. Furthermore, for the case of CO2/oil

mixture the deviation between two solutions is below 18%

as long as the left mass fraction values do not fall beyond

0.2. For individual mixtures with lesser oil concentration

values (i.e. c0 \ 0.2), the deviation is found only lesser.

Representative trends for deviation in concentration

values for analytical solutions due to Eq. 10 from its

numerical solution at c0 = 0.2, oil specific gravity = 0.8

for CO2/oil mixture are shown in Fig. 8a; corresponding

data for cases of R290/oil and R134a/oil mixtures are

presented in Fig. 8b. In general, the analytical solution due

to Eq. 10 for 0:1� LMF� 1 were found to be with

in ± 10% agreement with the corresponding numerical

results; however, disagreement increased up to ± 5.0% for

the case of analytical solution due to Eq. 11. The analytical

solution due to Eq. 11 provided better results

(within ± 0.2% agreement) for R290/oil and R134a/oil

mixtures. The existence of band (instead of line) for Eq. 11

Fig. 6 Variation of mixture temperature with LMF a under adiabatic

condition for CO2/oil, R290/oil and R134a/oil mixtures, c0 = 0.05

and oil specific gravity = 0.90, b for mixture under non-adiabatic

condition effect of extraction rate on temperature for CO2/oil mixture,

c0 = 0.05, oil specific gravity = 0.9; and c for CO2/oil mixture under

non-adiabatic condition, c0 = 0.05, oil specific gravity = 0.90,

Ti = 20�C, for different bottle sizes

Fig. 7 Deviation in analytical solutions due to Eq. 10 from the

numerical solutions of Eq. 6 for different refrigerant/oil mixtures at

c0 = 0.2 and oil specific gravity = 1.0


123

in Fig. 8b is due to magnification of plot area to the level of

numerical inaccuracy.

4 Conclusions

The model for evaluating oil concentration for refrigerant/

oil mixture extracted out of a rigid bottle has been pre-

sented. Extreme limits of variation in oil concentration are

identified for the cases of various mixtures under near

practical conditions. Among the cases under investigation,

maximum variation in concentration is found to occur for

CO2/oil mixture, where the concentration increase was as

much as by 150% towards the end of the extraction pro-

cess; corresponding values for R290/oil and R134a/oil

mixtures were near 20%. Interestingly, reduction in the

temperature under adiabatic condition resulted in increase

in the concentration change (by near 20%) for CO2/oil

mixture; however, the influence was lesser for other mix-

tures. Trends in the variation of temperature and concen-

tration under various flow rates, different sizes of bottle are

also presented. As regards the practical utility of the

information presented; it is possible to determine the extent

to which the bottle mixture be extracted so that the varia-

tion in concentration remains within the desired limits. For

example if the concentration change is intended to be

within 10% of initial value (at the start of extraction) for

CO2/oil mixture bottles it would be advisable to extract

only 30% of initial mixture mass (i.e. LMF C 0.7); how-

ever for other two mixtures up to 90% of the initial mixture

mass can be extracted (i.e. LMF C 0.1). The analytical

solution has been developed after introducing some

approximation. Predicted concentration values out of

approximate analytical solution are within 10% of

numerical results for R134a/oil and R290/oil mixtures;

corresponding deviation is less than 20% in case CO2/oil

mixture.

Substantiation of results in the current work using

experimental data is one possible scope for future research.

Appendix 1

From Eq. 4 we have

DMr ¼ 1� cð ÞDM � DMv

¼ 1� cð ÞDM þ qv DMr=qr þ DMo=qoð Þ ð32Þ

DMr 1� qv=qrð Þ ¼ 1� 1� qv=qoð Þc½ �DM*DMo ¼ cDM½ � ð33Þ

From Eqs. 4 and 32 we have

DMv ¼qv

qr

1� 1� qv=qoð Þc1� qv=qrð Þ

� �þ qvc=qo

� DM

¼ 1� 1� qr=qoð Þcf gqv=qr

1� qv=qrð Þ DM ð34Þ

Appendix 2

From Eq. 3 we get

cþ Dc ¼ Mo � DMo

Mr þMoð Þ � DMr þ DMoð Þ ð35Þ

Using Eq. 4, we get

cþ Dc ¼ 1� DMo=Moð Þ1� DMr þ DMoð Þ= Mr þMoð Þf g

Mo

Mr þMoð Þð36Þ

Fig. 8 Deviation in

concentration values for

analytical solution due to

Eqs. 10 and 11 from the

numerical solution at c0 = 0.2

and oil specific gravity = 1.0 a

for CO2/oil mixture b for R290/

oil and R134a/oil mixtures


123

cþ Dc

c¼ 1� cDM=Moð Þ

1� DMr þ DMoð Þ= M �Mvð Þf g*Mr þMo ¼ M �Mv½ � ð37Þ

1þ Dc

c¼ 1� DM= M �Mvð Þ

1� DM � DMvð Þ= M �Mvð Þ�*Mo ¼ c Mr þMoð Þ ¼ c M �Mvð Þ; DMr þ DMo

¼ D Mr þMoð Þ ¼ D M �Mvð Þ�

Dc

c¼

1� 1� qr

qo

� �c

n o1� qr

qv

� ��1DM

M�Mvð Þ

1� 1þ 1� 1� qr

qo

� �c

n o1� qr

qv

� ��1�

DMM�Mvð Þ

ð38Þ

[using Eq. 5].

Appendix 3

From Eq. 8

dMv

dM¼ 1þ qr

qo

� 1

� �c

� �qr

qv

� 1

� ��1

ð39Þ

)dM

dðM �MvÞ¼ 1� 1þ qr

qo

� 1

� �c

� �qr

qv

� 1

� ��1" #�1

ð40Þ

Again from Eq. 8

dc

dM¼ 1þ qr

qo

� 1

� �c

� �1� qr

qv

� ��1c

M �Mv

dc

dM

dM

dðM �MvÞ¼ dc

dðM �MvÞ

¼1þ qr

qo� 1

� �c

n o1� qr

qv

� ��1

1þ 1þ qr

qo� 1

� �c

n o1� qr

qv

� ��1� c

M �Mv

ð41Þ

Appendix 4

1

c

1þ 1þ qr

qo� 1

� �c

n o1� qr

qv

� ��1�

dc

1þ qr

qo� 1

� �c

n o1� qr

qv

� ��1

¼ 1

cþ 1

1� qr

qv

� ��1

c 1þ qr

qo� 1

� �c

n o0B@

1CAdc

¼ dðM �MvÞM �Mv

1

cþ 1� qr

qv

� �1

c�

qr

qo� 1

� �

1þ qr

qo� 1

� �c

n o0@

1A

24

35dc

¼ dðM �MvÞM �Mv

ð42Þ

Integrating both sides of Eq. 42

ln cþ 1� qr

qv

� �ln c� ln 1þ qr

qo

� 1

� �c

� �� c

c0

¼ ln ðM �MvÞ½ �M�Mv

Ms

ð43Þ

ln cc

1þ qr

qo� 1

� �c

n o0@

1A

1�qrqv

� �2664

3775

c

c0

¼ ln ðM �MvÞ½ �M�Mv

Ms

ð44Þ

c

c0

� � 2�qrqv

� �1þ qr

qo� 1

� �c0

1þ qr

qo� 1

� �c

0@

1A

1�qrqvð Þ

¼ M �Mv

Ms

� �ð45Þ

At LMF = 1, Mv = 0 and LMF = 0, Mv = Mf

Assuming Mv varying linearly with LMF, we can write

Mv ¼ 1� LMFð ÞMf

therefore,

M �Mv

Ms¼ 1�Mf

Ms

� �LMF þMf

MsLMF ¼ LMF

Now the Eq. 45 can be written as

c

c0

� � 2�qrqv

� �1þ qr

qo� 1

� �c0

1þ qr

qo� 1

� �c

0@

1A

1�qrqvð Þ

¼ LMF

*M �Mv � LMF:Ms½ �

ð46Þ

Appendix 5

x M þM �Mf

� �aþ /bð Þ /fþ

M �Mf

� �aþ /bð Þ n

� dT

dt

¼ �

/qo aþ /bð Þ

dM

dtþ

M �Mf

� �a

qo aþ /bð Þ2d/dt

" #þ

1

qr aþ /bð ÞdM

dt�

M �Mf

� �b

qr aþ /bð Þ2d/dt

" #

8>>>>><>>>>>:

9>>>>>=>>>>>;þ r _q000


123

x M þM �Mf

� �aþ /bð Þ /fþ

M �Mf

� �aþ /bð Þ n

� dT

dt

¼ �

1

aþ /bð Þ1

qr

þ /qo

� �� dM

dt

� þ

M �Mf

� �aþ /bð Þ2

aqo

� bqr

� �d/dt

" #8>>>><>>>>:

9>>>>=>>>>;þ r _q000 ð47Þ

Dividing both sides by M �Mf

� �

xM

M �Mfþ nþ /fð Þ

aþ /bð Þ

� dT

dt¼ 1

aþ /bð Þ2bqr

� aqo

� �d/dt

� 1

aþ /bð Þ1

qr

þ /qo

� �� 1

M �Mf

dM

dtþ r _q000

M �Mfð48Þ

Appendix 6

As the heat transfer coefficient for liquid phase is much

higher than that for vapor phase, the quantity of heat

exchanged between the contents inside the bottle and

ambient is essentially dependent on the proportions of

inside bottle surfaces that are in contact with the liquid

and vapor phases. At any instant for a cylindrical bottle

the fractional liquid volume inside, r, can be evaluated

as.

r ¼ Hl= Hl þ Hvð Þ ¼ Mr=qr þMo=qoð Þ=V ð49Þ

where, Hl and Hv are the height of liquid and vapor

sections in the bottle. The total resistance from ambient to

the liquid mixture via cylindrical surface of bottle (R1),

total resistance from the ambient to the liquid mixture via

bottle base assuming it flat and circular (R2), total

resistance from ambient to the refrigerant vapor via

cylindrical surface of bottle (R3), and total resistance

from the ambient to the refrigerant vapor via bottle top

assuming it flat and circular (R4) are

R1 ¼ pDerHð Þ�1�De=hl De � 2twð Þ

þDe ln De= De � 2twð Þf g=2k þ 1=ha�

R2 ¼ 4 pD2e

� ��11= hl þ hað Þ þ tw=k½ �

R3 ¼ pDe 1� rð ÞHg�1

�De=he De � 2twð Þ

þDe ln De= De � 2twð Þf g=2k þ 1=ha�

R4 ¼ 4 pD2e

� ��11= hv þ hað Þ þ tw=k½ �

9>>>>>>>>>>=>>>>>>>>>>;

ð50Þ

where, H, De and tw are the height, external diameter and

wall thickness of the bottle; inside and outside temperature

be Ti and Te respectively. Also, hl, hvap and ha are heat

transfer coefficient for inside liquid-wall interface, inside

vapor-wall interface and outside air-wall interface,

respectively. Note that the thermal resistances R1 and R3

are dependent upon the level of liquid mixture (r). In case

the heat transfer coefficient values for pure refrigerant (hr)

and oil (ho) are known, the heat transfer coefficient for the

liquid mixture (hl) can be evaluated as

hl ¼ hr þ cho ð51Þ

Note that role of r in evaluation of R1 and R3 turns them

into dynamic variable.

Appendix 7

Important steps involved in numerical solution are briefed

below.

1. The value for number of LMF intervals, N, is set and

initial mass of contents inside the bottle (Ms) and

DM is evaluated for chosen set of refrigerant/oil

mixture and bottle size combination.

2. Subsequent values of M during extraction process are

evaluated taking M0 ¼ Ms (at i = 1). Initial value (at

i = 0) for concentration, co is taken as co and M0r and

M0o are determined using Eqs. 4 and 5. Expressions for

evaluating Miþ1r , Miþ1

o and Miþ1v will appear like

Miþ1r ¼ Mi

r � DMf ciþ1; qir; q

iv

� �Miþ1

o ¼ Mio þ ciþ1DM

Miþ1v ¼ Mi

v þ DM:f ciþ1; qir; q

iv

� �

9>=>; ð52Þ

3. For the isothermal case, changed oil concentration ciþ1

is simply obtained by Eq. 6 using Miþ1;Miþ1v ; ci; qi

r; qio

and qiv whereby qi

r; qio and qi

v are taken fixed.

4. For the adiabatic condition mixture temperature is

evaluated using Eq. 12 (with _q000 ¼ 0) in the following

form (taking temperature of bottle contents at i = 1 as

T0 ¼ Te),

Tiþ1 ¼ Ti þhfg

qiv

qir

1� 1� qir

qo

� �c

n o1� qi

v

qir

� ��1�

DM

Miþ1o Ci

p; o þMiþ1r Cp; r þMiþ1

v Cp; v

n o

ð53Þ

Now based upon new temperature value, values for

qir; q

io and qi

v are updated and used for getting changed

oil concentration ciþ1.

5. For non-adiabatic condition, riþ1 is evaluated using

Miþ1r , Miþ1

o , and qir in Eq. 49. The value for Riþ1

eq is


123

then evaluated using riþ1 and employing Eq. 30,

followed by evaluation of temperature employing the

relation:

Tiþ1 ¼ Ti

þhfg

qiv

qir

1� 1� qir

qo

� �c

n o1� qi

v

qir

� ��1�

DMþ _q000V DM_m

Miþ1o Ci

p;oþMiþ1r Cp; r þMiþ1

v Cp; v

n o

*Dt ¼ DM= _m½ �ð54Þ

where, _m is the mass flow rate for the mixture. Now the

values for qir; q

io and qi

v are updated and used for getting

changed oil concentration ciþ1.

References

1. Cho K, Tae SJ (2001) Condensation heat transfer for R-22 and

R-407C refrigerant-oil mixtures in a microfin tube with a U-bend.

Int J Heat Mass Transf 44:2043–2051

2. Eckels SJ, Doerr TM, Pate MB (1998) A comparison of the heat

transfer and pressure drop performance of R134a-lubricant mix-

tures in different diameter smooth tubes and micro-fin tubes.

ASHRAE Trans 104:376–386

3. Hambraeus K (1995) Heat transfer of oil-contaminated HFC134a

in a horizontal evaporator. Int J Refrig 18:87–99

4. Memory SB, Sugiyama DC, Marto PJ (1995) Nucleate pool

boiling of R-114 and R- 114-oil mixtures from smooth and

enhanced surfaces-I Single tubes. Int J Heat Mass Transf

38:1347–1361

5. Memory SB, Sugiyama DC, Marto PJ (1995) Nucleate pool

boiling of R-114 and R- 114-oil mixtures from smooth and

enhanced surfaces-II Tube bundles. Int J Heat Mass Transf

38:1363–1376

6. Grebner JJ, Crawford RR (1993) Effects of lubricant on evapo-

rator capacity for systems using mixtures of R-12/mineral oil and

R-134a/synthetic oil. ASHRAE Trans 99:380–386

7. Webb RL, McQuade WF (1993) Pool boiling of R-11 and R-123

oil-refrigerant mixtures on plain and enhanced tube geometries.


8. McMullan JT, Hewitt NJ, Masson AJ, Murphy NE (1992)

Influence of oil viscosity and refrigerant quality on evaporator

performance. Int J Energy Res 16:567–581

9. Bell KI, Hewitt GF (1987) Nucleate pool boiling of refrigerant/oil

mixtures. Exp Heat Transf 1:71–86

10. Tichy JA, Macken NA, Duval WMB (1985) An experimental

investigation of heat transfer in forced-convection-condensation

of oil-refrigerant mixtures. ASHRAE Trans 91:297–308

11. Hahne E, Noworyta A (1984) Calculation of heat transfer coef-

ficients for nucleate boiling in binary mixtures of refrigerant-oil.

Int Commun Heat Mass Transf 11:417–427

12. Jensen MK, Jackman DL (1984) Prediction of nucleate pool

boiling heat transfer coefficients of refrigerant-oil mixtures.

J Heat Transf 106:184–190

13. Baustian JJ, Pate MB, Bergles AE (1998) Measuring the con-

centration of a flowing oil-refrigerant mixture with a bypass

viscometer. ASHRAE Trans 94(2):588–601

14. Baustian JJ, Pate MB, Bergles AE (1988) Measuring the con-

centration of a flowing oil-refrigerant mixture with a vibrating

U-tube densimeter. ASHRAE Trans 94(2):571–587

15. Fukuta M, Yanagisawa T, Miyamura S, Ogi Y (2004) Concen-

tration measurement of refrigerant/refrigerant oil mixture by

refractive index. Int J Refrig 27:346–352

16. Motta SFY, Parise JAR, Braga SL (2002) A visual study of

R-404A/oil flow through adiabatic capillary tubes. Int J Refrig

25:586–596

17. Andrade EN, Skowron E, Goldschmidt VW, Groll EA (1999) Oil

concentration in liquid refrigerants: in situ measurement. Int J

Refrig 22:499–508

18. ABB automation products, Germany, 2000, ‘‘Document number:

D184S021U02’’. [WWW] http://www.abb.com/automation

19. Sensotech, Barleben 2005 Liquisonic: ultrasonic analyser for

liquids, 07/2005 02_01_29.doc’’. [WWW] http://www.Senso

Tech.com

20. FLEXIM, Berlin, Document number: GSPIOXSV2-1EN. [WWW]

http://www.flexim.com

21. Klein S, Alvarado F (1995) Engineering equation solver, F-chart

software. Middleton, WI, USA

22. Baustian JJ, Pate MB, Bergles AE (1986) Properties of oil-

refrigerant liquid mixtures with applications to oil concentration

measurement: Part I- Thermophysical and transport properties.


23. Lebreton JM, Vuillame L, Morvan E, Lottin O (2001) Oil con-

centration measurement in saturated liquid refrigerant flowing

inside a refrigeration machine. Int J Appl Thermodyn 4:53–60

24. ASHRAE handbook-2006 refrigeration (2006) The American

Society of Heating, Refrigeration and Air-Conditioning Engi-

neers, Atlanta

25. Liley PE, Gambill WR (1973) Chemical engineers handbook.

McGraw-Hill, New York, p. 98


123

http://www.abb.com/automation

http://www.SensoTech.com

http://www.SensoTech.com

http://www.flexim.com

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