110

Vol. 1, No. 2 HVAC&R Research April 1995

INTRODUCTION

Buildup of lubricating oil in refrigeration, air-conditioning and heat pump systems is perhaps the oldestunresolved problem vexing industry. It represents a serious roadblock to accurately modeling these systemsunder actual operating conditions, i.e. with anywhere from negligible oil up to as much as 5% (by mass) oilin the refrigerant charge. Oil also creates considerable uncertainty in the integrity of test results byadversely affecting energy balances, local saturation temperatures implied from pressure measurements,two-phase pressure drops, and also heat-transfer coefficients and equipment performance data derived fromthese tests. To respond to this problem, a new comprehensive method for modeling refrigerant-oil mixtureshas been developed, namely the “Thermodynamic approach,” which can be used as an alternative to thetraditional “Oil contamination approach” in dealing with these mixtures. The new approach not only allowsone to analyze a particular oil's effect on system design and operation but it also provides an improved ther-modynamic method for giving more accuracy when reducing raw experimental test data to heat-transfercoefficients or other design parameters. Hence, this new thermodynamic approach is recommended for usein all new refrigerant-oil heat-transfer studies, and can also be used to reevaluate old test data for improvedresults.

Oil adversely affects the optimal performance of various system components: evaporator, condenser,compressor, expansion device and control valve. The largest effect of oil is on evaporator performance,where it can significantly alter boiling heat-transfer coefficients and reduce the LMTD, lowering the effec-tive refrigeration capacity of the system. Local oil concentrations can become as high as 70 to 80% (bymass) oil in the unevaporated liquid leaving an evaporator, but normally will not exceed 50% (by mass) oilexcept in a very small portion of the evaporator.

Old “Oil Contamination Approach”

Historically, oil has been treated as a contaminant in an otherwise pure refrigerant, similar to moistureand other trace impurities. Thus, pure refrigerant saturation temperatures and properties have been assumedfor determining heat-transfer coefficients and other performance data from raw test data and also in designcorrelations. In essence, the oil concentration has been transformed into an independent contaminationparameter. In practice, this means that during flow boiling experiments and evaporator bench tests with oilpresent, the saturation temperature of the pure refrigerant is utilized to determine the heat-transfer coeffi-

A comprehensive thermodynamic approach for modeling mixtures of refrigerants and lubricating oils ispresented. The new approach includes generalized methods for predicting the following thermodynamicproperties of refrigerant-oil mixtures: bubble point temperatures, local oil concentrations, liquid specificheats and enthalpy changes during evaporation. Using this comprehensive method, heat release (enthalpy)curves are easily generated and also the effect of oil on the LMTD (log mean temperature difference) ofevaporators can be modeled. Importantly, the definition of the boiling heat-transfer coefficient based onthe bubble point temperature is included in the method. This new approach provides the basis for advancesto be made in two-phase refrigeration heat-transfer research and design.

Comprehensive Thermodynamic Approachto Modeling Refrigerant-Lubricating

Oil MixturesJohn R. Thome, D.Phil.

Member ASHRAE

John Thome is a visiting professor at the Laboratory for Industrial Energetics (LENI), Swiss Federal Institute of Technology, Lausanne,Switzerland.

VOLUME 1, NUMBER 2, APRIL 1995 111

cient and LMTD, where Tsat is determined from the vapor pressure curve of the pure refrigerant at the localpressure.

This simple approach is not thermodynamically correct; it ignores the effects of oil on boiling point tem-peratures, specific heats, enthalpies, etc. that, in turn, alter the calculations for energy balances, local boil-ing temperature differences and vapor qualities, log-mean temperature differences, etc. in the datareduction process that is used (1) to determine heat-transfer coefficients and two-phase pressure drops and(2) for the thermal design of evaporators and condensers. In addition, the oil contamination approach pre-cludes introducing the type of oil and its physical properties in the calculations.

Comprehensive Thermodynamic Approach

Superior to the oil contamination approach is one that treats a refrigerant-oil mixture as a zeotropic mix-ture with a temperature glide. This “Thermodynamic Approach” is the subject of this article. The thermo-dynamic approach overcomes the negative aspects of the oil contamination approach mentioned above butrequires methods for determining boiling point temperatures and enthalpy changes of refrigerant-oil mix-tures during their change of phase (evaporation and condensation). The additional complexity is not greatbecause the vapor pressure of oils is approximately one-millionth that of refrigerants and hence its concen-tration in the vapor phase is negligible. Thus the vapor can be assumed to be pure refrigerant.

The negligible quantity of oil entering the vapor phase is verified by the standardized method prescribedfor determining oil concentrations in refrigerant samples in ANSI/ASHRAE Standard 41.4. This standardmethod for measuring oil concentrations by slowly evaporating away the refrigerant from a liquid refriger-ant-oil mixture sample, including use of a vacuum pump and heating the sample to 150°C (302°F), givesthe same concentration as that determined from the masses of the components before mixing, and hence itfollows that only a trace amount of oil is lost to the vapor phase.

Previous work on thermodynamics of refrigerant-oil mixtures reported widely in the literature has cen-tered on individual aspects of the problem (for instance, measurements of solubility curves, viscosity of themixtures, and vapor pressure curves for a refrigerant mixed with a specific grade and type of oil). Thepresent work aims to present a general approach for modeling refrigerant-oil mixtures, in response to thelarge number of new refrigerants and refrigerant blends now becoming available, and the very wide selec-tion of mineral and synthetic oils and viscosity grades now commonly used in industry.

INTRODUCTION TO THE PRINCIPLES OF PHASE EQUILIBRIABefore proceeding, a working knowledge of phase equilibria is required for understanding the thermo-

dynamics of refrigerant-oil mixtures; some elementary background is provided here. For more details onphase equilibria and boiling of mixtures, see Chapter 12 in Collier and Thome (1994), and for a compre-hensive chemical engineering treatment of phase equilibria refer to Smith, Block, and Hickman (1973) orSmith and Van Ness (1987).

Phase Equilibrium Diagram

Phase equilibria of binary mixtures are represented on phase diagrams. Figure 1(a) depicts a phase dia-gram for a binary mixture system at constant pressure. Temperature is plotted along the vertical axis; vaporand liquid concentrations are plotted along the horizontal axis. The dew point line represents the dew pointtemperatures of the mixtures Tdew, which is defined as the temperature at which a superheated vapor mix-ture will first begin to condense upon cooling. The bubble point line represents the bubble point tempera-tures of the mixtures Tbub, which is defined as the temperature at which a subcooled mixture will first beginto evaporate upon heating. The equilibrium vapor concentration Y is that which corresponds to the liquidconcentration X at the same temperature.

In Figure 1(a) the saturation temperature of one pure component is on the left vertical axis while that ofthe second component is on the right axis. Evaporation processes ideally move along the bubble point linewhile condensing processes move along the dew point line. For the present situation, a refrigerant-oil mix-ture can be considered as a zeotropic binary mixture where one component is the refrigerant (e.g. R-134a, R-123, ammonia) and the second component is the oil, over the range that these fluids are miscible.

On a phase diagram, the concentrations can be in units of mass fraction (sometimes called weight frac-tion), mole fraction, or volume fraction. The mass fraction of a component is defined as its mass in pounds

112 HVAC&R RESEARCH

or kilograms divided by the total mass of the mixture in pounds or kilograms, respectively, in a particularphase (liquid or vapor).

Figure 1(b) depicts an approximate phase diagram for R-134a mixed with an ester-type lubricating oil at343 kPa (49.7 psia). In this case, the horizontal axis shows the oil concentration in % (by mass) oil. At theleft axis of the diagram the saturation temperature of pure R-134a is 4.4°C (40°F) while at the right axis thedew and bubble point temperatures rise rapidly towards the saturation temperature of the pure oil (notshown), which is in the neighborhood of 350°C (662°F). The bubble point curve is quite flat at low oil con-centrations and starts to rise rapidly at values above 70% (by mass) oil. The dew point curve, which repre-sents the oil concentration in the vapor phase, is not well-known for refrigerant-oil mixtures and was drawnassuming negligible amounts of oil enter the vapor phase at liquid oil concentrations below 70% (by mass).Above this value its concentration is represented by proration towards the pure oil value.

BUBBLE POINT TEMPERATURES OF REFRIGERANT-OIL MIXTURES

An accurate and reliable method for prediction of bubble point temperatures of refrigerant-oil mixturesas a function of oil concentration and pressure is a fundamental building block for the development of thethermodynamic approach with refrigerant-oil mixtures.

Generalized Method

Takaishi and Oguchi (1987) presented an empirical equation for the vapor pressure curve of R-22 mixedwith synthetic alkyl benzene oil over the concentration range from 0 to 70% (by mass) oil (0 to 0.70 massfraction oil) and a temperature span from 10 to 60°C (50 to 140°F). Their empirical vapor pressure equa-tion for predicting the bubble point temperature for a given saturation pressure and oil concentration waspresented as:

(1)

where Psat is the saturation pressure in MPa and Tbub is the bubble point temperature in K. The oil concen-tration in the liquid is given by woil , which is in mass fraction. A(woil ) and B(woil ) were given by the follow-ing expressions:

(2)

TbubA woil( )

Psat( )ln B woil( )–---------------------------------------------=

A woil( ) a0 a1 woil a2 woil3 a3 woil

5 a4 woil7+ + + +=

Figure 1. Phase equilibrium diagram at constant pressure

(b) Approximate diagram for R-134a/oilat 343 kPa (49.7 psia)

(a) Binary mixture

VOLUME 1, NUMBER 2, APRIL 1995 113

(3)

where the values of the empirical constants are:

a0 = −2394.5 b0 = 8.0736a1 = 182.52 b1 = −0.72212a2 = −724.21 b2 = 2.3914a3 = 3868.0 b3 = −13.779a4 = −5268.9 b4 = 17.066

The above method has been generalized by Thome (1992a) for refrigerants other than R-22 and alsotemperatures outside the original range. This was accomplished by replacing the values of a0 and b0, whichare used to model pure R-22, with different values determined for the different refrigerants, such as R-134a. The vapor pressure of oil is very small and hence the effect of the type of oil on the empirical con-stants a1 to a4 and b1 to b4 was found to be small for oil concentrations below 0.50 [50% (by mass) oil] andrelatively minor up to 0.70 [70% (by mass) oil]. Above this the deviations become large. Rather than usingfixed values of a0 and b0 for a particular pure refrigerant, another important improvement is to use an accu-rate pure refrigerant vapor pressure equation to determine the values of a0 and b0 at the design or test pres-sure rather than the simple, less accurate, “Antoine type” of expression used in Equation (1).

Evaluating Equation (1) at 0.55 MPa (5.5 bar or 79.8 psia) provides the values for Table 1, whichdepicts the effect of oil concentration on the bubble point temperature. In addition, the right column showsthe difference between the bubble point temperatures of the mixtures and the saturation temperature of pureR-22 at this pressure.

Importantly, this new generalized method has been verified in Thome (1992a) against vapor pressuredata for the following refrigerant-oil combinations (refer to the Appendix for more information):

R-22/synthetic alkyl benzene oilR-114/synthetic alkyl benzene oilR-113/four types of oil (3GS, 4GS, 5GS, RCO-2)R-134a/synthetic ester oilR-134a/PAG oilR-134a/polyglycol oil

Table 1. Bubble Point Temperatures of R-22/Oil Mixtures at550 kPa (80 psia) Predicted by Equation (1)

Oil Mass Fraction woil Tbub (°C) Tbub − TR-22 (°C)

0.0 3.00 0.00.01 3.01 0.020.02 3.03 0.040.03 3.04 0.050.04 3.06 0.070.05 3.09 0.100.06 3.11 0.120.07 3.13 0.140.08 3.15 0.160.09 3.17 0.180.10 3.19 0.200.20 3.44 0.450.30 3.79 0.800.40 4.31 1.320.50 5.25 2.260.60 7.22 4.230.70 11.53 8.540.80 19.95* 16.96*

B woil( ) b0 b1 woil b2 woil3 b3 woil

5 b4 woil7+ + + +=

114 HVAC&R RESEARCH

Of course, by statistically fitting new constants to Equations (2) and (3) for each specific set of solubilitytest data, more accuracy can be achieved; however, such a specific approach cannot be used as a generalapplication method for any refrigerant and oil combination.

Another important point is that regardless of the inlet oil concentration before the expansion device (nor-mally in range from 0 to 5% (by mass) oil), 90% or more of the evaporator will always have local concen-trations less than 50% (by mass) oil [this is evident from evaluation of Equation (5) presented in the nextsection for the complete range of local vapor qualities]. Consequently, the method given by Equations (1),(2), and (3) is proposed for general use in research and industry.

HEAT RELEASE (ENTHALPY) CURVES FOR EVAPORATIONOF REFRIGERANT-OIL MIXTURES

During evaporation of a refrigerant-oil mixture inside a direct expansion evaporator, the local bubblepoint temperature increases as the concentration of the oil in the liquid phase becomes richer along the tubeduring the evaporation of refrigerant into the vapor phase. Similar observations may be made up throughthe tube bundle of a flooded-type evaporator, on passage through a compact plate-type evaporator or in afalling film evaporator. In order to determine the local liquid composition at some point in the evaporator,a heat release (enthalpy) curve must first be prepared. This curve allows one to determine how much heat isrequired to evaporate a mixture from some starting condition up to the desired local condition.

Local Vapor Quality

The local vapor quality x is that defined by the total mass of vapor (all refrigerant in the present case)divided by the total mass of fluid (refrigerant plus oil). This is the correct thermodynamic definition ofvapor quality. It is not appropriate to define the vapor quality as the mass of refrigerant vapor divided bythe total mass of refrigerant when reporting test data (which is normally denoted in previous literature asxR ) because this only perpetuates the confusion created by the oil contamination approach.

Heat Release (Enthalpy) Curve

The literature refers to the change in enthalpy of a mixture during evaporation or condensation by vari-ous names—condensation curve, heat release curve, evaporation curve, cooling curve, and enthalpy curve.The term “evaporation curve” is easily confused with “boiling curve” used in pool boiling research; thusthis name should be avoided. The most commonly used name is heat release curve, even though for boil-ing, heat is actually added to the mixture, not released. For this reason, this terminology will be used here.

The local change in enthalpy dH of a mixture during evaporation is comprised of three contributions:

1. Latent heat to the fraction of liquid vaporized (dx );

2. Sensible heat to the fraction of fluid in the liquid phase (1− x ) heated to a higher bubble point tempera-ture;

3. Sensible heat to the fraction of fluid in the vapor phase (x ) heated to a higher bubble point temperature.

In mathematical terms this is:

(4)

where

x = local vapor qualityhLV = latent heat of vaporization of the refrigerant(cp)L = specific heat of the liquid refrigerant-oil mixture(cp)V = specific heat of the pure refrigerant vapor

The values of (cp)L and (cp)V are a function of the local oil concentration and bubble point temperature

* Extrapolated value.

Table 1. Bubble Point Temperatures of R-22/Oil Mixtures at550 kPa (80 psia) Predicted by Equation (1)

Oil Mass Fraction woil Tbub (°C) Tbub − TR-22 (°C)

dH hLV dx 1 x–( )dTbub cp( )L

dTbub cp( )V

+ +=

VOLUME 1, NUMBER 2, APRIL 1995 115

while hLV is a function of only the bubble point temperature. Equation (4) reduces to the latent heat for apure refrigerant.

A heat release curve is not actually determined as a curve, but instead as a series of points at a set inter-val of temperature or vapor quality indicating the amount of heat absorbed by the fluid per unit mass. Inother words, dH is in J/kg or Btu/lb, relative to its inlet state together with the bubble point temperature andvapor qualities that correspond to these points. At the inlet no heat has yet been added so the heat absorbedis zero. Figure 2, adapted from Collier and Thome (1994), graphically depicts a heat release curve for anevaporating zeotropic mixture. Temperature is plotted on the y-axis while the heat absorbed is plotted onthe x-axis. The vapor quality is shown at intervals along the curve. The bubble point temperatures corre-sponding to points on the curve are read off the y-axis.

Local Oil Concentrations

Preparation of a heat release curve (and determination of local thermodynamic and transport properties)requires knowledge of the local oil concentration. The liquid phase concentration of oil circulating in arefrigeration system is a function of its location in the system. Thus, to unequivocally define this concentra-tion, a point is chosen where all the circulating fluid is in the liquid phase, which occurs in the refrigerantline between the condenser and the expansion device. The oil concentration at this location will be definedas winlet. After the expansion device the local vapor quality will range from 0.10 to 0.30 and the oil concen-tration in the liquid phase will have increased. Along the evaporator the oil concentration continues to riseas the refrigerant evaporates into the vapor phase.

From a conservation of the mass of the two components, and assuming no oil enters the vapor phase, thefollowing expression relates the local oil concentration wlocal to the local vapor quality x and the inlet oilconcentration winlet :

(5)

For a pure refrigerant without any oil, wlocal is always equal to zero. Because the oil is essentially non-volatile, the maximum exit vapor quality that can be achieved in refrigeration, air-conditioning and heatpump systems is (1−winlet ). This is an important limiting point because in designing a system with, forexample, 3% (by mass) oil, the exit vapor quality from the evaporator has to be less than 0.97. Equation (5)is based on complete flow of the mixture through the system, i.e. no local oil holdup in the heat-transfer

Figure 1. Heat release curve for a zeotropic mixture

wlocal winlet 1 x–( )⁄=

116 HVAC&R RESEARCH

tubes.

Procedures for Preparation of Heat Release Curve

The following procedure is used for preparation of a heat release curve at a fixed, isobaric pressure:

1. Select the desired pressure Psat and inlet oil concentration before the expansion valve, winlet.2. Determine two pure refrigerant saturation temperatures at pressures just above and below Psat with an

accurate equation-of-state of the user's choice for determining the vapor pressure curve.3. Use these two sets of values for Tbub and Psat to solve for a0 and b0 in Equation (1) with woil set to zero.

The solution is straightforward with two equations and two unknowns.4. Use the new values of a0 and b0 in place of a0 = −2394.5 and b0 = 8.0736, respectively. All the other

values of a1 to a4 and b1 to b4 remain the same as in the original correlation since they only refer to theeffect of the oil on Tbub.

5. Select the vapor quality range for the heat release curve, i.e. set the inlet vapor quality, the exit vaporquality [always less than the value of (1− winlet )], and the number of design intervals; i.e. if an evapora-tor is divided into ten heat-transfer zones for design then 11 points are needed in the heat release curve.

6. Calculate the local oil concentrations corresponding to the local vapor qualities using Equation (5), i.e.determine wlocal for each of the eleven vapor quality points above.

7. Calculate the local bubble point temperatures corresponding to the local vapor qualities and local oilconcentrations using Equations (1), (2), and (3) with woil set equal to wlocal at each point.

8. Calculate the values of hLV and (cp)V at these bubble point temperatures using methods for pure refriger-ants. Determine the liquid specific heats of the refrigerant-oil mixtures (cp)V for each point based on thelocal values of wlocal and Tbub (using the method described in the next section).

9. Determine the heat absorbed by the refrigerant-oil fluid in each interval, dH, and then add these toobtain the total heat absorbed per unit mass of fluid from inlet to outlet.

The heat release curve preparation is now complete and the following values required for thermal designof an evaporator are known for each local vapor quality x : wlocal, Tbub, and dH. (Note that the abovemethod ignores heats of mixing, which are normally small and typically not available for refrigerant-oilmixtures, but these could be included when available.)

LIQUID SPECIFIC HEATS OF LUBRICATING OILS ANDREFRIGERANT-OIL MIXTURES

Liquid Specific Heat of Lubricating Oils

Liquid specific heats of lubricating oils are not normally cited by manufacturers; hence a general corre-lating equation is required for their estimation. Thome (1992b) recommended the following equation forlubricating oils as a function of specific gravity:

(6)

where the liquid specific heat [(cp)L]oil is in kJ/(kg·K), the temperature of the oil T is in °C (valid for −18°C< T < 204°C) and s is the specific gravity of the liquid at 15.6°C (valid for 0.75 < s < 1.05). The expressionis an adaptation of the equation for crude oil cuts in Smith, Block, and Hickman (1973) to lubricating oils.Manufacturers usually provide the density or specific gravity of lubricating oils at 60°F (15.6°C), whichfacilitates the use of Equation (6). This correlation compares well with the tabular values for engine oilcited in Incropera and DeWitt (1981) which have maximum deviations of −2% to +7%, which is sufficientfor present purposes because the sensible heat contribution is small (but not negligible) compared to thelatent heat term in Equation (4).

Liquid Specific Heat of Refrigerant-Oil Mixtures

For preparation of a heat release curve, the liquid specific heat of the refrigerant-oil mixture is required

cp( )L

[ ]oil

4.186 0.388 0.00045 1.8T 32+( )+

s --------------------------------------------------------------------=

VOLUME 1, NUMBER 2, APRIL 1995 117

at each local vapor quality as a function of oil concentration wlocal and bubble point temperature Tbub.Working in the units of kJ/(kg·K) (Btu/lb·°F), a linear mixing law based on mass fractions of oil gives theliquid specific heats of these mixtures as:

(7)

The above equation is evaluated with the refrigerant and oil properties at the local bubble point temper-ature of the mixture. Because heats of mixing data are not available and because the values for the oil andrefrigerant are often within 10 to 30% of one another while the value for the oil is accurate to about ±10%,the linear mixing law approach is appropriate here.

Heat Release Curve for R-134a/Oil Mixture

A common design temperature for evaporators is 4.4°C (40°F). For pure R-134a this temperature corre-sponds to a saturation pressure of 343 kPa (49.8 psia). Table 2 lists the heat release curve for an R-134a/ester oil mixture with an inlet concentration of 3% (by mass) oil for an evaporator covering the vapor qual-ity range from 0.15 to 0.95. The oil has a density of 971 kg/m3 at 15.6°C. The first column is the localvapor quality at intervals along the evaporator, Tbub and wlocal are given in the next two columns, and thetotal heat absorbed relative to the inlet is shown in the fourth column. The contributions of latent heat andsensible heating of the liquid and vapor are given in the last two columns, respectively. As can be seen, therise in the bubble point temperature and oil concentration in the liquid is sharpest at high vapor qualities.The contribution of sensible heat becomes important at high vapor qualities because its effect is directlydependent on the rise in Tbub.

DEFINITION OF BOILING HEAT-TRANSFER COEFFICIENT FORREFRIGERANT-OIL MIXTURES

Definitions of boiling heat-transfer coefficients

Application of the thermodynamic approach to heat transfer requires a corresponding change to the def-inition of the boiling heat-transfer coefficient. The pool boiling heat-transfer coefficient h for pure refriger-ants is defined as:

(8)

Table 2. Heat Release Curve for R-134a/Oil Mixture

LocalVapor Quality

BubblePt. Temp. (°C)

Oil Concentration (% by mass)

Total Heat Absorbed(kJ/kg)

LatentHeat

(kJ/kg)

SensibleHeat

(kJ/kg)0.150 4.509 3.53 0.00 0.00 0.000.230 4.516 3.90 15.64 15.63 0.010.310 4.525 4.35 31.28 31.26 0.020.390 4.536 4.92 46.92 46.89 0.030.470 4.550 5.66 62.56 62.51 0.050.550 4.570 6.67 78.20 78.13 0.070.630 4.598 8.11 93.85 93.75 0.100.710 4.643 10.34 109.52 109.37 0.150.790 4.729 14.29 125.23 124.99 0.240.870 4.954 23.08 141.05 140.59 0.460.950 8.289 60.00 159.76 156.07 3.69

Saturation temperature of pure refrigerant = 4.4°CIsobaric pressure for heat release curve = 343.1 kPaInlet oil concentration specified = 3.00% (by mass)Oil density at reference temperature = 971.0 kg/m3

Reference temperature for oil = 15.6°C

cp( )L

woil cp( )L

[ ]oil

1 woil–( ) cp( )L

[ ]ref

+=

h q Tw Tsat–( )⁄=

118 HVAC&R RESEARCH

where

q = heat flux (Q/A)Tw = heated wall temperatureTsat = saturation temperature of the pure liquidQ = heat flowing through the heated area A

For flow boiling this definition refers to the local heat-transfer coefficient at a specific local vapor qual-ity, local heat flux, local wall temperature and local saturation temperature. Experimentally, Tsat is nor-mally determined from the vapor pressure curve of the pure fluid and the measured pressure.

For refrigerant-oil mixtures, the pool boiling heat-transfer coefficient h is defined as:

(9)

where

q = heat flux (Q/A)Tw = heated wall temperatureTbub = bubble point temperature of the bulk liquidQ = heat flowing through the heated area A

In flow boiling, Equation (9) refers to the local heat-transfer coefficient at a specific local vapor quality,local heat flux, local wall temperature, and local bubble point temperature.

Effects on Experimental Data

In all (or nearly all) published flow boiling heat-transfer tests to date for refrigerant-oil mixtures, thedefinition given by Equation (8) has been used where Tsat was determined from a vapor pressure curve forthe pure refrigerant. Using the correct definition given by Equation (9) and the fact that Tbub > Tsat (e.g.,consider values of Tbub in Table 2 where Tsat = 4.4°C (40°F) for pure R-134a), all of the published datashould actually have smaller boiling wall superheats than those reported by a value of (Tbub − Tsat ); andthus the correct heat-transfer coefficients will be larger than those reported at the heat fluxes cited.

For example, at a typical heat flux of 10 kW/m2 (3170 Btu/h·ft2·°F), for a plain copper tube the reportedlocal heat-transfer coefficient would be in the range of 2500 W/(m2·K) (440 Btu/h·ft2·°F), such that thewall superheat (Tw − Tsat ) is 4.0 K (7.2°F). If (Tbub − Tsat ) is equal to 0.2 K (0.36°F), then the correct heat-transfer coefficient will actually be 5.3% higher, i.e. [10000/(4.0 − 0.2) = 2632 W/(m2 ·K) (463.5 Btu/h·ft2·°F)]. For the widely-used microfin type of copper tubes, the reported flow boiling heat-transfer coef-ficient will be approximately twice that of the plain tube, or 5000 W/(m2 ·K) (880.6 Btu/h·ft2 ·°F), givingan apparent wall superheat of 2.0 K (3.6°F) and a correct value of 1.8 K (3.24°F). The correct heat-transfercoefficient will then be 5556 W/(m2 ·K) (978.4 Btu/h·ft2 ·°F) or 11.1% larger. With large local oil concen-trations, which occur at high local vapor qualities in these tubes, the effect is much more dramatic. Forinstance, evaluating the effect of using (Tw − Tsat ) equal to 0.5 K (0.9°F) in the above example, the correctheat-transfer coefficients for the plain and microfinned tubes will be higher by 14.3% and 33.3%, respec-tively. Hence, applying the thermodynamic approach in future tests (or reevaluating prior data) provides asubstantial improvement in the accuracy and the integrity of experimental test data.

Another important aspect to consider is the manner in which published refrigerant-oil flow boiling datahave been presented to date. All local coefficients are cited for the nominal inlet oil concentration winlet,say 1, 2 or 5% (by mass) oil. Using Equation (5), it can be seen that the local oil concentration wlocalincreases as a function of the inlet oil concentration and the local vapor quality. Thus, comparing localheat-transfer coefficients at a local vapor quality of 0.50 really means a comparison of data at local oil con-centrations wlocal at 2, 4 and 10% (by mass) rather for winlet values of 1, 2 and 5% (by mass); similarly at avapor quality of 0.80 the comparison is for wlocal of 5, 10 and 25% (by mass) oil in the liquid phase, respec-tively. As a consequence, in the future it would be helpful if refrigerant-oil flow boiling data were pre-sented showing the local oil concentration in addition to the nominal value at the tube inlet.

HEAT EXCHANGER DESIGN APPROACH FORREFRIGERANT-OIL MIXTURES

The thermodynamic approach for modeling refrigerant-oil mixtures was developed with the objective ofkeeping it simple enough for engineering practice while not sacrificing on accuracy. The implications of its

h q Tw Tbub–( )⁄=

VOLUME 1, NUMBER 2, APRIL 1995 119

use and improvements for design of refrigeration system evaporators are discussed in the following sec-tions.

Heat Exchanger Design by Zone

Modern, computerized thermal design methods subdivide a heat exchanger into five to ten zones wherelocal heat-transfer coefficients are determined for each zone individually. In each zone j a mean overallheat-transfer coefficient (Uo )j is determined for the evaporating fluid and the heating fluid. Since two-phaseheat-transfer and pressure drop correlations are functions of vapor quality, it is convenient to divide anevaporator into zones by equal steps in local vapor quality. For each zone, the following equation applies:

(10)

where the subscript j refers to the particular zone, Qj is the heat duty of that zone in W (or Btu/h), (Uo )j isthe overall heat-transfer coefficient for the zone in W/(m2 ·K) (or Btu/h·ft2·°F), (Ao )j is the heat-transfersurface area required for the zone in m2 (ft2), Fj is the crossflow correction factor to the log-mean tempera-ture difference (Fj = 1.0 for pure counterflow or pure cocurrent flow or when one fluid is isothermal), and(LMTD)j is the log-mean temperature difference for the zone in K (or °F) determined from its standardequation with the four terminal temperatures of the zone.

As an example of how the thermal design process proceeds, refer to Table 2, where each heat-transferzone will be defined by one step in vapor quality. Thus consider here the first zone ( j = 1) with a vaporquality change from 0.15 to 0.23. The bubble point temperatures at the inlet and outlet of the zone are4.509°C and 4.516°C. The heat absorbed by the refrigerant-oil mixture is 15.64 kJ/kg in this zone. Thethermal heat duty of this zone Q1 is then determined by multiplying 15.640 kJ/kg by the mass flow rate ofthe refrigerant-oil mixture in kg/s to obtain the duty in watts. The design outlet temperature of the chilledwater is normally 45°F (7.2°C) for ARI standard conditions. Thus, the water's outlet temperature in thiszone is assumed to be 7.2°C for counter-current flow. Using the flow rate of the chilled water and its spe-cific heat together with the zone's heat duty Q1, the inlet temperature of the chilled water in this zone is cal-culated. Now the four terminal temperatures of the zone are known and (LMTD)1 can be calculated (andthe crossflow correction factor F1 too). Fixing the number of tubes and assuming a length for the zone suchthat (Ao )1 is obtained, the heat flux is determined for the zone. The chilled water heat-transfer coefficient iscalculated based on the bundle geometry and water flow rate. The boiling-side heat-transfer coefficient isthen determined for the zone; it is normally determined at both the inlet and outlet vapor qualities of thezone, 0.15 and 0.23 for the present example, and then the average coefficient is determined from these twovalues. Now (Uo )1 for the zone can be calculated. The calculation iterates with assumption of a new valueof (Ao)1 until the heat duty predicted by the right-hand side of Equation (10) matches the heat duty of thezone Q1.

The thermal design process then passes onto the next zone ( j = 2) and the procedure is repeated. The heatabsorbed in the second zone is (31.28 − 15.64) = 15.64 kJ/kg, the inlet and outlet vapor qualities are 0.23and 0.31, and the inlet and outlet bubble point temperatures are 4.516°C and 4.525°C, respectively. Afteranalyzing all the individual zones, the size of the evaporator is known from summation of the tube lengthsfor each zone.

Physical Properties

Besides the heat release curve, the thermodynamic and physical properties of a refrigerant-oil mixtureare required for thermal design. These properties are determined at the vapor quality values correspondingto the heat release curve. The liquid phase properties must be estimated for each local vapor quality usingthe local oil concentration and the local bubble point temperature. The liquid phase properties required aredensity, viscosity, specific heat, thermal conductivity and surface tension. The vapor phase properties arefor the pure refrigerant since no oil is present in the vapor. The vapor physical properties usually requiredare density, viscosity, specific heat, thermal conductivity and latent heat. These are evaluated at the localbubble point temperature at each vapor quality.

Effect of Pressure Drop

Qj Uo( )j

Ao( )jFj LMTD( )j=

120 HVAC&R RESEARCH

During thermal design of an evaporator the effect of two-phase pressure drop on the local boiling pointtemperature should be taken into account to increase the accuracy of the calculations. Thus, one has severaloptions: (1) calculate the heat release curve values stepwise with the local pressure, the latter obtained froma stepwise calculation of the two-phase pressure drop, (2) prepare two heat release curves, one at the inletpressure and another at or near the outlet pressure, and interpolate between them using the calculated localpressure from a stepwise calculation of the two-phase pressure drop, or (3) prepare only one heat releasecurve at the mean pressure between the inlet and outlet of the evaporator.

Exit Conditions

Within an evaporator it is not thermodynamically correct to refer to superheating of the refrigerant whenoil is present because the rise is that of the local bubble point temperature along the equilibrium bubblepoint curve, not superheating of the fluid. The word superheat implies that all of the liquid has been evapo-rated and become superheated vapor.

The temperature difference between the chilled water and the refrigerant at the exit of the evaporator isnormally small; for chilled water entering at 12.8°C (55°F) and refrigerant evaporating at 4.4°C (40°F), thetemperature difference is only 8.3 K (15°F) at the exit. Thus the rise in the bubble point temperatureseverely limits the fraction of refrigerant that can actually be evaporated.

Log-Mean Temperature Difference and Heat Duty

Figure 3 depicts a plot of the bubble point temperatures versus enthalpy change for the values in Table 2.For comparison purposes, pure R-134a evaporating at the same pressure (Tsat = 4.4°C or 40°F) is alsoshown with an exit superheat equal to the final bubble point temperature of the mixture of 8.29°C(14.92°F). Inlet and outlet chilled water temperatures of 12.8°C (55°F) and 7.2°C (45°F) are assumed andits temperature-enthalpy profile is shown on the diagram. The graphical comparison is indicative of theeffect oil has on the LMTD of an evaporator, in this case neglecting the effects of two-phase pressure dropon Tbub and Tsat . The effective LMTD determined by dividing the evaporator into 10 zones is about 6%lower for the 3% (by mass) oil mixture. Thus, use of the thermodynamic approach yields a significantimprovement in accuracy in evaluating LMTDs during thermal design of an evaporator and eventual benchtests.

In a performance test an exit temperature equal to the exit bubble point temperature of 8.29°C (14.92°F)in Figure 3 might be measured. Using the old oil contamination approach, one would have presumed therefrigerant was completely evaporated and superheated by 3.85°C (6.92°F), which gives an enthalpychange of 169.60 kJ/kg (73.07 Btu/lb) rather than the actual value of 159.76 kJ/kg (68.83 Btu/lb) for therefrigerant-oil mixture. In that case the heat duty obtained by multiplying the enthalpy change by the mea-sured refrigerant flow rate would be too high, by 100 (169.6 − 159.76)/159.76 = 6.2%, and seriously affectthe accuracy of the test results plus any conclusions drawn from them. Thus, the new thermodynamicapproach provides significant improvement in the integrity of heat balances in evaporator performance

VOLUME 1, NUMBER 2, APRIL 1995 121

tests.

Effect of Oil on Boiling Heat-Transfer Coefficients

Experiments have shown that boiling coefficients can be significantly increased or decreased by thepresence of oil depending on the local conditions, albeit based on test data reduced using the oil contamina-tion approach.

REFRIGERATION SYSTEM CONTROLS AND OIL PROBLEMS

Refrigeration equipment controls based on pure refrigerant operating cycles are well developed and pro-vide relatively trouble-free operation. Yet precise control is impeded by oil buildup over time in the refrig-erant charge. The thermodynamic approach has important implications for the improved design of thesecontrol systems (and thus increased energy efficiency). For example, in small systems the sensing device ofthe control system is often a thermostatic valve, which is comprised of a tubular-type element filled withpure refrigerant and placed in the refrigerant exhaust flow of the evaporator. This element is then con-nected via a small diameter tube to a spring- loaded bellows that regulates the movement of the needle inthe expansion valve. The internal pressure increases when the element is heated by the exhaust flow andvice-versa when it is cooled. The movement of the needle caused by this pressure change regulates therestriction in the expansion valve and hence the pressure drop across it, which in turn sets the saturationpressure, temperature and vapor quality after the valve for the refrigerant entering the evaporator and henceregulates refrigeration capacity.

The evaporator exhaust temperature is equal to the exit bubble point temperature when oil is present (i.e.8.29°C in Figure 3). Thus, the temperature difference sensed by the thermostatic valve is equal to the exitbubble point temperature minus the saturation temperature of the pure refrigerant inside the element (i.e.4.4°C), not the implied “superheat.” As the oil concentration increases in the refrigerant charge over time,

Figure 2. Temperature-enthalpy (LMTD) diagram forpure R-134a and an R-134a/oil mixture

122 HVAC&R RESEARCH

the exhaust bubble point temperature tends to rise further. This causes the thermostatic valve to errone-ously “think” that the exit superheat has increased, such that the increased temperature difference acts onthe needle in the expansion valve to increase refrigerant flow and thermal capacity.

In simple terms, existing controllers have a problem telling the difference between (1) a change in therequested refrigeration duty of the system indicated by a temperature change of the setpoint thermistor and(2) a change in oil concentration in the refrigerant charge. Thus, new improved control schemes requiremeasurement of a parameter related to the oil concentration, together with new control logic that appropri-ately models the oil's effect on refrigeration capacity.

CONCLUSIONSA new, comprehensive thermodynamic approach for modeling mixtures of refrigerants and lubricating

oils has been presented. The model includes generalized methods for predicting the following thermody-namic properties of refrigerant-oil mixtures: bubble point temperatures, local oil concentrations, liquid spe-cific heats and enthalpy changes during evaporation. Using this method, heat release (enthalpy) curves areeasily generated, and the effect of oil on the LMTD of evaporators can be modeled. The boiling heat-trans-fer coefficient has been redefined for refrigerant-oil mixtures, based on the bubble point temperature ratherthan on the saturation temperature of the pure refrigerant. The thermodynamic approach enables advancesto be made in two-phase refrigeration heat-transfer research and design by including in the analysis thetype of oil and the effects of its physical properties.

NOMENCLATUREA empirical constantA surface area(Ao)j outside surface area of zone ja0 (a1, a2, a3, a4) empirical constantsB empirical constantb0 (b1, b2, b3, b4) empirical constants(cp)L specific heat of liquid(cp)V specific heat of vaporFj cross-flow correction factor of zone jh heat-transfer coefficienthLV latent heat of vaporizationH enthalpy(LMTD)jlog-mean temperature difference of zone jPsat saturation pressureQ heat dutyq heat fluxs specific gravity of liquidT temperatureTbub bubble point temperatureTsat saturation temperatureTw wall temperature(Uo)j outside overall heat-transfer coefficient of zone jX liquid concentrationx vapor qualitywinlet oil inlet concentrationwlocal local oil concentrationwoil oil concentrationY vapor concentration

ACKNOWLEDGEMENTSThe present study is part of ASHRAE Research Project 800-RP titled, “Heat-Transfer And Pressure

Drop In The Dryout Region Of Intube Evaporation With Refrigerant/Lubricant Mixtures,” sponsored bythe technical committee TC 1.3. The Swiss Federal Office of Energy (OFEN) has also provided key fund-ing for this study.

VOLUME 1, NUMBER 2, APRIL 1995 123

REFERENCESCollier, J.G., and J.R. Thome. 1994. Convective boiling and condensation, 3rd Ed. Oxford, England: Oxford University

Press.Hesse, U., and H. Kruse. 1988. Prediction of the behavior of oil refrigerant mixtures. In Status of CFCs—Refrigeration

Systems and Refrigerant Properties, IIR, Commissions B1, B2, E1 and E2, Purdue University 2: 101-109.Incropera, F.P., and D.P. DeWitt. 1981. Fundamentals of heat transfer, p. 780. New York: John Wiley.Jensen, M.K. 1987. Rensselaer Polytechnic Institute, Troy, New York (Private communication).Liley, P.E., and W.R. Gambill. 1973. Physical and chemical data. In Chemical Engineering Handbook, 5th ed. Chapter

3, pp. 3-226 - 3-250. Perry and Chilton, eds. New York: McGraw-Hill.Shao, W., H. Kraft, and E. Granryd. 1992. A simple experimental investigation of saturated vapor pressure for HFC-

134a-oil mixtures. Int. J. Refrig. 16 (6): 357-361.Smith, B.D., B. Block, and C.D. Hickman. 1973. Distillation. In Chemical Engineers’ Handbook, pp. 13-4 to 13-14.

New York: McGraw-Hill.Smith, J.M., and H.C.Van Ness. 1987. Introduction to chemical engineering thermodynamics, 4th Edition. New York:

McGraw-Hill.Takaishi, Y., and K. Oguchi. 1987. Measurements of vapor pressures of R-22/oil solutions. In Proceedings of the XVII-

Ith International Congress of Refrigeration, Vienna, Volume B: 217-222.Thome, J.R. 1992a. Prediction of vapor pressures of refrigerant-oil mixtures. Internal Report, LENI Laboratory, Swiss

Federal Institute of Technology, Lausanne, Switzerland (Dec. 16).Thome, J.R. 1992b. Thermodynamic and Transport Properties of Lubricating Oils. EPFL, Lausanne, LENI Report

(December 21). Lausanne, Switzerland: LENI (Laboratory for Industrial Energetics), Swiss Federal Institute ofTechnology.

APPENDIXNumerous comparisons were made of Equations (1), (2), and (3) to measured vapor pressure/tempera-

ture data for refrigerant-oil mixtures (and also with Equation (1) rearranged to predict Psat for a given Tbubwhen data were presented at isotherms). A selection of these are shown in Tables 3 through 6, which dem-onstrate that the accuracy of the present method for oil concentrations of woil < 0.50 is very good, similar tothat of predictions of independent vapor pressure data for pure refrigerants with a general type of vaporpressure equation. The level of accuracy is less from 0.50 < woil < 0.70, while for woil > 0.70 the accuracyis poor as the type of oil becomes more important.

Hesse and Kruse (1988) measured vapor pressure curves for R-22, R-114 and their binary mixturestogether with an unspecified synthetic alkyl benzene lubricating oil. Tables 3 and 4 show a comparisonwith some of their R-22/oil and R-114/oil data, respectively, at the temperature of 60°C. The values of a0and b0 for R-114 were determined by fitting Equation (1) to the pure refrigerant vapor pressures at 0 and60°C (so that a0 = −2849.839 and b0 = 7.99403). For oil mass concentrations up to 0.50, the generalized

method works well.Jensen (1987) measured saturation temperatures

and pressures of R-113 and 4 different types oflubricating oils (identified as 3GS, 4GS, 5GS andRCO-2) at ambient atmospheric pressure. Oil con-centrations of 0, 0.02, 0.05 and 0.10 were tested. Asshown in Table 5, his data compare very well with

those predicted using a0 = −3384.388 and b0 =8.251246 obtained from fitting Equation (1) to val-ues of the vapor pressure for pure R-113. The aver-age error for the pure R-113 values is 0.33°C whilefor the R-113/oil mixtures the average error isslightly larger, 0.37 K.

Table 3. Predicted Vapor Pressures of R-114/Oil MixturesMeasured by Hesse and Kruse (1988)

woil (by mass) (Psat )exp (MPa) (Psat)calc (MPa) % error0.10 0.5765 0.561 −2.70.30 0.551 0.5424 −1.60.50 0.498 0.5075 +2.0

0.70 0.357 0.4193 +17.5

Table 3. Predicted Vapor Pressures of R-114/Oil MixturesMeasured by Hesse and Kruse (1988)

woil (by mass) (Psat )exp (MPa) (Psat)calc (MPa) % error

124 HVAC&R RESEARCH

Table 4. Comparison to Measured Bubble Point Temperatures ofR-113/Oil Mixtures from Jensen (1987)

Oil Type woil (by mass) (Psat)exp (MPa) (Tbub)exp (°C) (Tbub)calc (°C) Error (°C)None 0.0 0.09980 47.0 47.47 +0.473GS 0.02 0.10051 47.8 47.78 −0.023GS 0.05 0.10016 47.8 47.81 +0.013GS 0.10 0.09861 48.6 47.56 −1.04

None 0.0 0.09820 46.6 46.97 +0.374GS 0.02 0.09820 47.0 47.07 +0.074GS 0.05 0.09820 47.6 47.21 −0.394GS 0.10 0.09833 48.6 47.48 −1.12

None 0.0 0.09733 46.5 46.71 +0.215GS 0.02 0.10027 47.5 47.71 +0.215GS 0.05 0.10027 48.2 47.85 −0.355GS 0.10 0.10027 48.2 48.07 −0.13

RCO-2 0.02 0.09887 46.8 47.28 +0.48RCO-2 0.05 0.09887 47.5 47.62 +0.12RCO-2 0.10 0.09887 48.6 48.05 −0.55

Table 5. Predicted Bubble Point Temperatures of R-134a/EXP-0275Oil Mixture Data of Shao, Kraft and Granryd (1992)

woil(by mass)

(Psat)exp (MPa) (Tbub)exp(°C)

(Tbub)calc(°C)

Error(°C)

Tsat ofR-134a (°C)

Rise inTbub (°C)

0.05 0.127 −20.0 −21.28 −1.28 −21.28 0.000.05 0.197 −10.0 −10.43 −0.43 −10.47 0.050.05 0.291 0.0 0.04 +0.04 0.04 0.080.05 0.414 10.0 10.23 +0.23 10.11 0.120.05 0.571 20.0 20.22 +0.22 20.06 0.160.05 0.767 30.0 30.03 +0.03 29.82 0.210.05 1.014 40.0 39.93 −0.07 39.68 0.25

0.11 0.125 −20.0 −21.65 −1.65 −21.66 0.010.11 0.196 −10.0 −10.51 −0.51 −10.60 0.090.11 0.290 0.0 0.04 +0.04 −0.14 0.180.11 0.411 10.0 10.16 +0.16 9.90 0.260.11 0.568 20.0 20.25 +0.25 19.89 0.360.11 0.763 30.0 30.10 +0.10 29.64 0.460.11 1.010 40.0 40.09 +0.09 39.53 0.56

0.398 0.124 −20.0 −20.44 −0.44 −21.85 1.410.398 0.193 −10.0 −9.25 +0.75 −10.99 1.740.398 0.283 0.0 1.26 +1.26 −0.82 2.080.398 0.401 10.0 11.58 +1.58 9.16 2.420.398 0.551 20.0 21.69 +1.69 18.92 2.770.398 0.742 30.0 31.85 +1.85 28.69 3.150.398 0.972 40.0 41.67 +1.67 38.14 3.53

0.67 0.113 −20.0 −20.11 −0.11 −24.01 3.900.67 0.169 −10.0 −9.70 +0.30 −14.35 4.650.67 0.244 0.0 0.57 +0.57 −4.85 5.420.67 0.341 10.0 10.66 +0.66 4.43 6.230.67 0.462 20.0 20.48 +0.48 13.43 7.05

Table 3. Predicted Vapor Pressures of R-22/Oil MixturesMeasured by Hesse and Kruse (1988)

woil (by mass) (Psat )exp (MPa) (Psat)calc (MPa) % error0.20 2.350 2.345 −0.20.30 2.310 2.304 −0.30.50 2.175 2.156 −0.90.70 1.590 1.781 +12.00.80 1.177 1.506 +28.0

125 HVAC&R RESEARCH

Shao, Kraft and Granryd (1992) measured vapor pressure curves for R-134a/oil and R12/oil mixtures.Table 6 shows a comparison of Equation (1) to the tabular data presented in their article for four differentR-134a/oil concentrations over a wide range of temperature (for a synthetic ester-based oil designated asEXP-0275). Their woil = 0.88 data are not shown because the errors are very large since 0.88 is greater thanthe limit of 0.70 of Equation (1). The accuracies were cited to be 0.3 K and 0.1% for their measured valuesof temperature and pressure. Examination of Table 6 shows quite accurate prediction of the bubble pointtemperatures with an average error of 0.63 K; for Tbub = 273.15 K this represents an error of 0.23%. Themaximum error is +1.85 K, which represents an error of 0.61% in the bubble point temperature of 303.15K. The values of a0 and b0 were determined from saturation temperatures of −10 and 30°C (a0 = −2685.141and b0 = 8.597401).

The two columns to the right in Table 6 show the saturation temperature of pure R-134a calculated usingEquation (1) and the increase in the saturation temperature of the R-134a/oil mixture relative to that of pureR-134a. The rise in Tbub with increasing pressure for a fixed oil concentration is clearly demonstrated. (Theaccuracy of the predictions in Table 6 could be improved by calculating different values of a0 and b0 foreach temperature (−20, −10, 0, 10, 20, 30 and 40°C)] as recommended by the method.

0.67 0.605 30.0 29.78 −0.22 21.92 7.870.67 0.778 40.0 39.01 −0.99 30.31 8.70

Table 5. Predicted Bubble Point Temperatures of R-134a/EXP-0275Oil Mixture Data of Shao, Kraft and Granryd (1992)

woil(by mass)

(Psat)exp (MPa) (Tbub)exp(°C)

(Tbub)calc(°C)

Error(°C)

Tsat ofR-134a (°C)

Rise inTbub (°C)