LOW-TEMPERATURE CALORIMETER FOR MEASURING ENTHALPY CHANGES IN GAS MIXTURES UNDER PRESSURE A R T H U R C. J E N K I N S AND OREN E. BERWALDT Research Laboratory, Linde Co., Division of Union Carbide Corp., Tonawanda, A'. Y .
A calorimeter is described which can b e used to measure the heat removed from a gas or gas mixture when it i s cooled from room temperature to a temperature in the range 0' to 195" C. a t any constant pressure from 1 to 100 atm. The refrigerant used to cool the test gas mixture is evaporated in the process. By
-
measuring the test gas flow and the evaporation rate of the refrigerant, and knowing the latent heat of the refrigerant, the enthalpy change in the test gas can b e calculated. The calorimeter was especially designed for use on gas mixtures which are partially liquefied during cooling. Data on such systems were needed for the design of commercial gas-separation processes. Experimental data for air, nitrogen, and nitrogenmethane are compared with literature values; agreement is generally within *370 or better.
Y THE
design of gas separation processes there is a need for
I- data on the enthalpy changes in gas mixtures, particularly in the region of partial condensation. While there are methods for calculating these enthalpy changes from phase equilibrium data and from latent and specific heat data for the pure components, it is desirable to be able to confirm the results experimentally. A search of the literature did not disclose a description of a calorimeter suitable for use with gas mixtures in the partial condensation region. This paper describes a method for the experimental determination of enthalpy changes in gas mixtures cooled from room temperature to temperatures as low as -195" C., a t pressures of 1 to 100 atm. For mixtures in the partial condensation region, the method is believed to be reliable to +3% or better. For gases that are noncondensable under the experimental conditions, the results are believed to be reliable to +1.5%. Principle of Operation
The method used to determine the quantity of heat removed from a gas or gas mixture when it is cooled from one temperature, TI, to a lower temperature, T z ,is as follows: The gas sample is passed a t constant pressure through a copper coil immersed in a refrigerant whose boiling point is Tz. The gas is cooled (and perhaps partially condensed) to T S and, in the process, refrigerant is evaporated. T h e volumes of gas sample and evaporated refrigerant are separately metered. From these volumes and from the known latent heat of the refrigerant, it is possible to determine the enthalpy change that took place during cooling, after making appropriate correction for heat leak, and other minor corrections. Description of Apparatus
The calorimeter with its auxiliary equipment is shown schematically in Figure I . Starting a t "sample inlet," the test gas first passes through a copper coil immersed in a water bath kept a t room temperature to minimize inlet temperature changes during the run, then enters the top of the calorimeter. Gas sample pressure is maintained constant a t the desired value by adjustment of the inlet valve and outlet valve. A . There are pressure gages a t the inlet and outlet, from which
T O VACUUM e PUMPS
_ _
TEST GAS METER
4
INLET VALVE SAMPLE INLET
WATER BATH
NT GAS METER
L
OUTLET PRESSURE GAUGE
VALVE A
Figure 1.
SAMPLE
- OUTLET
Schematic diagram of apparatus
the pressure drop (if any) through the calorimeter can be determined. From the calorimeter the cold gas sample, together with any remaining condensate, passes into a second copper coil in a thermoregulated water bath to bring the test gas back to room temperature before it enters the test gas meter. The evaporated refrigerant passes through another coil in the same water bath and then through the refrigerant gas meter. The calorimeter is shown in Figure 2. Except for the copper coil, the calorimetcr is constructed of stainless steel. The inner container is made from 2'/*-inch o.d., 0.065-inch-wall tubing, 143/,6 inches long. The outer casing is made from 41,/4-inch o.d., 0.120-inch-wall tubing, 17 inches long. Upper and lower heads of the outer casing are inch thick and are arc-welded in place. The space ( 3 / 4 inch wide) between inner and outer vessels is filled with Super Insulation [layers of aluminum foil separated by thin, nonconducting spacing material ( 4 ) ]and is evacuated to 1 X torr or better. The test gas inlet tube is 5/16-inch 0.d. with a 0.032-inch wall; it is enclosed in a n/,-inch o.d.>0.065-inch-wall jacket and is similarly insulated. This inlet-tube jacket requires extremely VOL. 2
NO. 3
JULY
1963
193
-UPPER
HEAD
F I L L I N G PORT
p
INLET THERMOCOUPLE
LEADS
TEST GAS INLETO U T L E T AND R E F R I G E R A N T THERMOCOUPLE L E A D S
VAPOR O U T L E T THERMOCOUPLE L E A D S
TO VACUUM PUMPS
REFRIG VAPOR
1 I ~
b - T O
VACUUM PUMPS
I I
+OUTER
CASING
INLET THERMOCOUPLE-
Leeds and Northrup Type K-3 guarded potentiometer and guarded D-C null detector. Temperatures as measured by us were believed to be accurate to 1 0 . 1' C. The test gas and the evaporated refrigerant pass through water saturators (not shown) before entering the 0.1-cu.-foot American Meter Co. wet-drum meters. Each meter is calibrated a t various flow rates against an American Meter co. 5-cu.-foot meter prover. However, it is more important to know the ratio of the readings of the two meters for the same gas volume than to know the absolute volumetric calibrations. To determine this ratio the meters are connected in series and compared at various flow rates by passing the same volume of nitrogen through both. The ratio, R, of the volumes as shown by the meters are plotted against the rate of flow in cubic feet per 30 minutes. R, which turned out in our work to be constant over the range of flow rates used, can be determined more accurately than the actual volumes can be measured.
REFRIGERANT SPACE INSULATED INLET TUBE J A C K E T
Procedure
INNER CASING
SUPER I N S U L A T I O N SPACE
COPPER COIL REFRIGERANT THERMOCOUPLE OUTLE THERM
STAINLESS STEEL COIL
U 1
TEST GAS OUTLET
Figure 2.
Calorimeter
efficient insulation in order to minimize heat transfer between the incoming test gas and the refrigerant space. As a result of this insulation, the inlet test-gas temperature changes very little as the gas progresses through the inlet tube, and the position of the inlet thermocouple is therefore not critical. Copper-constantan thermocouples for measuring inlet and outlet temperatures and refrigerant and refrigerant-vapor temperatures are made from 30 B & S gage enameled cottoncovered wire and are enclosed in 0.080-inch o.d., 0.010-inchwall stainless steel tubes. The calorimeter was designed with the test gas outlet a t the lower end to help maintain the desired phase equilibrium in the test sample when there is partial condensation. The heat-exchanger coil is made from 10 feet of "/,b-inch 0.d.. 0.030-inch-wall copper tubing. The outside diameter is 2 inches and it has 21 turns. The coil provides enough heat-transfer surface to cool the test gas to the refrigerant temperature. A second coil between the heat-exchanger coil and the outlet is made from 3/16-inch o.d., 0.028-inchwall stainless steel tubing 28 inches long. This second coil. located in the insuiation space, reduces conduction of heat into the refrigerant. A 3/4-inch-diameter port in the top of the calorimeter, through which the liquid refrigerant is poured, is closed with a plug and O-ring seal during operation of the calorimeter. The two external cooling coils (Figure 1) made of '/l-inch o.d., 0.030-inch-wall copper tubing, are silver-soldered to the upper and lower ends of the calorimeter casing. Cold gaseous nitrogen is passed through these coils to keep the outer casing cold and reduce heat leak. A copper cap on the calorimeter head is in contact with the upper external coil. Generally, the calorimeter head is kept a t a constant temperature 6' to 10' C. higher than that of the liquid refrigerant to avoid condensation of refrigerant vapor. Thermocouples are used to measure the inlet and outlet temperatures, liquid refrigerant temperature, outgoing refrigerant-vapor temperature, and surface temperature of the upper head of the calorimeter. Each thermocouple is individually calibrated by comparison with a platinum resistance thermometer calibrated by the National Bureau of Standards. Calibration curves are plotted by the method of Scott (5) to show the deviation of each thermocouple from the values given in standard tables. Thermocouple e.m.f.'s are read Lvith a 194
I & E C PROCESS D E S I G N A N D DEVELOPMENT
First, the Super Insulation space between the inner container and the outer casing (Figure 2) and also the inlet tube jacket torr or lower. The interior of the is evacuated to 1 X calorimeter is then cooled with liquid nitrogen to a temperature near the boiling point of the refrigerant to be used for the particular run. The refrigerant is poured into the calorimeter through a funnel inserted into the filling port in the upper head until the liquid level is 1 to 3 inches from the top, the exact distance depending upon the refrigerant and test gas. If the refrigerant is to be used under pressure-i.e., a t a temperature above its normal boiling point-suitable allowance is made for expansion of the liquid when its temperature rises. The liquid level is measured by means of a thermocouple probe inserted in the filling port. After the liquid space is filled with refrigerant. the filling port is closed. The outside of the calorimeter is then cooled by passing gaseous nitrogen, cooled by passage through a copper coil immersed in liquid nitrogen, through the extcrnal cooling coil (Figure 1). The cold-nitrogen floxv rate is adjusted so that a thermocouple on the upper head sho\vs a temperature approximately 10' C. above the refrigerant temperature. M'hen the refrigerant is to be used a t a temperature higher than its normal boiling point. gaseous nitrogen or helium is passed temporarily through the calorimeter in a reverse direction in order to warm the refrigerant liquid from the bottom, until the desired refrigerant vapor pressure is reached ; this reverse gas flow is then stopped and the pressure is maintained by adjusting outlet valve I3 (Figure 1 ) . After the heat-leak measurement, test-gas flow through the calorimeter is started and adjusted to the desired pressure and flow rate by means of the inlet valve and outlet valve, A . Fifteen minutes or more is required for equilibrium to be reached before the actual run is started. (It is necessary to wait until the gas inlet temperature reaches room temperature; this takes a few minutes because, without gas flow, the inlet tube is chilled by the precooling and by heat conduction to the liquid refrigerant. However, the insulated jacket around the inlet line permits the incoming gas to reach room temperature.) When the inlet temperature becomes stabilized, measurement of gas and refrigerant flow rates is started, using two stopwatches. one for each meter. The run is continued for 30 minutes. During this time, the follotving temperatures are recorded a t 5-minute intervals: test-gas temperature a t inlet thermocouple (Figure 2), test-gas temperature a t outlet thermocouple, refrigerant-liquid temperature, refrigerant-vapor temperature at outlet, and temperature of calorimeter top.
Evaluation of Heat Leak. This should be done before and after every run; it requires more time than the run itself. It is carried out by measuring the rate of evaporation of the refrigerant due to heat leak after the rate becomes almost constant. During the time constant heat leak is approached, the external calorimeter temperature is kept constant a t some temperature about 10' C. above the liquid refrigerant temperature. In practice, the heat leak is plotted as rate of
evaporation of refrigerant us. refrigerant liquid level. When the curve thus plotted levels out, the test-gas flow is started and a calorimeter run is begun. When the run is over, the testgas flow is shut off, and plotting of rates of evaporation of the refrigerant is continued. The refrigerant liquid level is computed from the following: original liquid level, volume of evaporated liquid, densities of the liquid and gas under the conditions of the test, and internal dimensions of the calorimeter. The heat leak is always smaller after a run than before, because the level of the liquid refrigerant is lower. The average heat leak during the actual run is determined from the plot. I n this plot. the section between the start and end of the run is hypothetical, since the more rapid boiling off of the refrigerant probably changed the heat leak by a n unknown amount. However, reliable results were obtained by simply averaging the heat leaks before and after the run. Since the heat leak was only a relatively small part of the total heat input, some uncertainty was permissible. In addirion to the heat-leak correction, a correction has to be applied for the change in vapor space in the calorimeter. As liquid refrigerant is boiled off, its place is taken by vapor which remains in the calorimeter and is not measured by the wetdrum meter. This correction is computed from the refrigerant flow rate, F. and from the ratio Vl/Vt, where Vl is the specific volume (reciprocal of the density) of the liquid refrigerant and V , is the specific volume of h e saturated refrigerant vapor, both a t the temperature and pressure of the test. The corrected refrigerant flow rate, F,, is: F I
=
F[V,/(VL -
(1)
Vl)l
The vapor-space correction is not applied to heat leak flow rates because it is not significant at very low flow rates.
is one for air, with liquid argon as the refrigerant. Data recorded during the 30-minute run are given in Table I. T h e enthalpy change, AH,is computed by use of the following heat balance equation: AH
R[K(AH,
+ 1.8 C,
AT)
- F2(AHv f 1.8 C p A T ' ) ]
Fa
(2)
Substituting in Equation 2 the data from Table I and values for the latent heat of argon and specific heat of argon vapor
(3):
+
1.8 X 5.0 X 7.0) 0.195 (2802 1.8 X 5 X 10.3)]/3.432 = 1.022 X 8856 ______ = 2637 B.t.u.Ab.-mole 3.432
AH = 1.022 [13.290 (2802
+
While Equation 2 is not rigorous, it is adequate for engineering purposes. Refrigerants
Table I1 lists some of the refrigerants which can be used in the calorimeter and the temperature ranges over which they can be used. Operation of the calorimeter is somewhat easier when a refrigerant is used a t its normal boiling point. However, refrigerants were used a t pressures above l atm. when it was desired to extend their useful temperature range. Satisfactory data must, of course, be available for rhe latent heat, liquid and vapor densities, and specific heats of the vapor. Certain precautions are necessary when using flammable refrigerants, such as methane. I n our work, the calorimeter was installed in a ventilated hood so that refrigerant vapors released during the filling operation, as well as gases leaving the wet-drum meters, would be carried airay safely.
Calculation of Results
The method of computing the enthalpy change in the gas sample from its flow rate and the flow rate of evaporated refrigerant is straightforward. The procedure can be illustrated by using a typical run as an example. The run chosen
Table 1.
Experimental Data for a Typical Run for Air
.4v. temp., O C.. inlet air Outlet air Outgoing refrigerant vapor Liquid refrigerant Calorimeter top Test gas pressure, atm. Refrigerant vapor pressure, atm. Flow rate of refrigerant, cu. ft. evaporated in 30 min. Corrected for vapor space Flow rate of test gas, cu. ft. in 30 min.
22.6 -184.5 -177.1 -184.3 -175.8 1.1 1.1
3.275 3.290 3.432
Heat Leak Data Outgoing refrigerant vapor temp., ' C. -174.0 Liquid refrigerant temp., C. -184.3 Rate, .Meter Liquid Level, Cu. Ft./ Reading, Inches from 30 Min. Cu. Ft. TOP Before run 0.340 0.0 2.74 0.289 0.4 2.92 0.261 0.75 3.10 After run 0.155 6.07 5.93 0.151 6.85 6.40 Evaporation rate of argon due to heat leak, cu. ft./30 min., 0.195.
Table II.
Calorimeter Refrigerants Normal AjProximate B.P., c'seful Range,
c.
Rpfrigerant
Isobutane Dichlorodifluoromethane Chlorodifluoromethane Propane Chlorotrifluoromethane Ethane Ethylene Methane Argon Nitrogen
-102 - 29 8 - 40 8 - 42 1 - 81 3 - 88 6 -103 7 -161 5 -185 9 -195 8
c.
-1OtoO - 29 to 0 - 40 to 0 - 42 to - 30 - 80 to - 45 - 88 to - 33 -104to - 88 -161 to -113 -185 to -160 -195 to -185
Performance
Table I11 gives the experimental values obtained for air and for nitrogen under various conditions of temperature and pressure. Values are compared with data obtained with the help of the Claitor-Crawford equation of state (2). The with two of the 15 runs differing average difference is 1.3yo0, from the calculated values by about 47,. These 'TWO runs appear to be in error for some reason lvhich could not be determined. If they are discarded, the remaining runs agree on the average within lyc. Differences are about evenly divided between plus and m.inus. S o n e of the data in Table I11 is in the condensation range. Table IV gives experimental data for a nitrogen-methane mixture a t 300 p.s.i.a. \-slues are compared Lvith data calculated by Bloomer, Eakin, Ellington, and Gami ( 7 ) . Six VOL. 2
NO. 3 J U L Y 1 9 6 3
195
Test Gas
Air
Nitrogen
Test Gas Press., P.S. I.A. 29 5 29.4 29.5 15.9 15.7 15.5 15.4
15.9 15.7 15.7 147.4 147.5 174.5 29.2 29.5 147.0 147.0 147.0 44.1 44.1 44.1
Table 111. Enthalpy . . Data for Air and Nitrogen Refrigerant Inlet Ouilet Press., Temp., Temp., Refrigerant P.S. I.A . O O CClzFz 26.7 - 29.1 15.1 CClPFz 15.0 24.2 - 29.3 CClqFq 15 0 27 ..8 - 29 3 Argon’ 23.3 -ilo.o 60.3 Argon 23.4 -172.9 48.2 Argon 48,2 20.0 -172.9 Argon 45.6 20.8 -173.6 Argon 16.9 22.6 -184.5 Argon 23.2 -184.5 16.9 Argon 16.8 20.4 -184.6
c.
~
~~
c.
~
CCl?F? CCIFI CClFI CH4 CH4 CH4 CH4 CHI Ar Ar C2H6
15.0 15.7 15.4 93.5 91.4 15.0 15.0 32.5 26.5 26.5 70.6
-
25.2 25.6 29.0 27.2 28.1 22.8 21.3 21.6 25.4 24.7 23.2
29.3 80.2 - 80.6 -133.0 -133.5 -159.8 -160.7 -150.8 -180.0 -179.7 - 53.9
AH, B.t.u./Lb. Mole Exptl. Calcd.
706.2 641 5 709 7 2423 2452 2440 241 9 2637 2629 2620 680.7 1333 1392 2026 1954 2387 2395 2266 2672 2681 965
698.3 670.6 716 6. 2433 2470 2428 2449 2617 2624 2589 693.9 1337 1406 2021 2037 2445 2441 2283 2643 2632 970
Expt1.-Calcd. X 700 Exptl. fl.l -4.5 -I
~~
Av.
n
-0.4 -0.7 +0.5 -1.2 $0.8 -I-0.2 +1.2 -1.9 -0.3 -1 .o 4-0.2 -4.2 -2.4 -1.9 -0.7 $1.1 +1.9 -0.5 1.3%
Enthalpy Data for a 79.9 Mole % CH4-21.1 Mole % Nz Mixture at 300 P.S.I.A. Rqirigerant Inlet Temp., Outlet Temp., AH, B.t.u./Lb. Mole Expt1.-Lit. X 700 Press., P.S. I. A . a . a Exptl. Lit. value Exptl. 15.5 22.4 -102.7 2010 2080 -3.5 231.4 26.0 -113.3 2528 2520 $0.3 151 . O 20.3 -123.1 4374 4250 f2.8 151 .O 21.9 -123.2 4082 4290 -5.1 151 . O 20.6 -123.3 4304 4290 $0.3 150.0 22.9 -123.4 4361 4340 $0.5 93.8 26.9 -132.9 5045 4940 $2.1 23.7 -133.0 5009 93.8 4890 $2.4 Av. 2.170
Table IV. Refrigerant
c.
of the eight points in Table IV are in the region of partial condensation of the nitrogen-methane mixture. The calorimeter described has been used successfully for a number of special gas mixtures in the range of partial condensation. The data given in this paper were selected because they could be compared with other data t o illustrate the accuracy which can be expected. Nomenclature
C,
= heat capacity a t constant pressure. B.t.u.:lb.-mole-
F FI F?
=
F3
=
= =
AH = AHb =
R
=
AT = AT’ =
196
O F. flow rate, cu. ft. per 30 minutes corrected flow rate (see Equation 1) flow rate of refrigerant corresponding to the heat leak, cu. ft. per 30 minutes flow rate of test gas, cu. ft. per 30 minutes change in enthalpy, B.t.u./lb.-mole heat of vaporization of refrigerant, B.t.u./lb.-mole wet-drum correction factor, equal to ratio of readings on two gas meters for same gas flow difference in temperature of refrigerant vapor at outlet and temperature of liquid during run, O C. same as 4T, but during heat-leak measurement
I&EC PROCESS DESIGN A N D DEVELOPMENT
c.
Acknowledgment
The basic principle of the calorimeter was used by L. I. Dana and one of us (A.C.J.) several years ago to measure “cooling curves” for natural gas; these were not published. C. R. Baker helped to design the present version of the calorimeter, and P. S.O’Seill derived the heat balance equation and made many helpful suggestions. The Engineering Laboratory of Linde Co. prepared the temperature-enthalpy charts for air and for nitrogen from which the calculated values in Table I11 were taken. literature Cited (1) Bloomer, 0. T., Eakin, B. E., Ellington, R. T., Gami, D. C . , Inst. Gas Technol., Res. Bull. 21 (1955). (2) Claitor, L. C., Crawford, D. B., Trans. Am. SOC. Mech. Engrs. 71, 885 (1949). (3) Din. F.. “Thermodvnamic Functions of Gases.” Vol. 2. Butterworth’s, London,‘1956. (4) Matsch, L. C., “Advances in Multilayer Insulations,” in “Advances in Cryogenic Engineering,” K. D. Timmerhaus, ed., Vol. 7, pp. 413-18, Plenum Press, New York, 1962. (5) Scott, R. B., J . Res. .\‘at/. Bur. Std. 25, 459 (1940). RECEIVED for review September 13, 1962 ACCFPTEDMarch 8, 1963 \
,
