THE
interest in high pressure research and development is growing a t an accelerated rate. I t is rapidly becoming a n important tool in the ever-expanding scientific field. New processes, applications, equipment, and techniques are appearing from many sources. University, government, commercial, and industrial laboratories are all contributing to the fund of high pressure knowledge. Design and fabrication of the needed equipment have kept pace with the laboratories. For small scale research programs, most of the needed equipment is available commercially “from stock,” and it is also safe, when used u n d e r , the conditions for which it was designed. The papers presented a t the High Pressure Symposium, Division of Industrial and Engineering Chemistry, were
I
representative of the interest and progress in “extreme conditions research.” The general categories were design of high pressure equipment, chemical reactions a t high pressure, safety a t high pressure, and the fundamental subjects of high pressure physics, transport properties, and thermodynamics. The outstanding characteristic of high pressure symposia is the freedom of open discussion that prevails, and the willingness of participants to present papers related to their investigations. John F. Miller Dow Chemical Co. Midland, Mich.
LEON N. VERNON1 and C. M. SLIEPCEVICH University of Oklahoma, Norman, Okla.
Heat Transfer in a High Pressure Reactor A practical design eliminates need for internal cooling or heating coils or external jacketing H E A T TRANSFER and fluid flow were studied in a high pressure reactor, designed for a working pressure of 4000 pounds per square inch at 900’ F. Its unusual feature is the continuous ‘/s-inch radius groove (half-circle in cross section), machined around the liner made of Type 347 stainless steel. The liner was machined to 0.002 inch greater than the maximum bore of the body, to obtain a shrink fit. At each end of the helical groove, ‘/*-inch pipe taps were placed, so that a heat transfer fluid could be passed through the helix. The temperature gradients required to obtain heat transfer are reduced appreciably in the reactor wall, and stresses arising from temperature gradients are decreased. This design permits operating the outer layer of the reactor body a t a lower temperature. Each end of the reactor is sealed by a button-type closure using an 18-8 Flexitallic gasket (Flexitallic Gasket Go., Camden, N. J.). Temperature measurements along the reactor are made by five thermocouples, placed approximately 6 inches apart, and each embedded in a stainless tube ‘/I6 inch in outside diameter.
Pressure Drop in Reactor Helix
The amount of pressure drop through the reactor helix is important, as heat transfer fluids have to be recirculated a t high temperatures. Relatively little work has been done on pressure drop Present address, Continental Oil Co., Ponca City, Okla. 1
through coiled pipe, with no existing correlation for pressure drop in turbulent flow. Friction losses in curved pipe are larger than in straight pipe, because of a secondary flow. The high velocity particles near the flow axis are forced to the outside of the coil by a larger centrifugal force than the slower particles near the wall. The outside particles are then directed back to the inside of the coil along the wall. Increased friction loss is due to the energy supplied to promote this secondary motion. Detra ( 2 ) found that a curved pipe having an elliptical cross section with its major axis parallel to the plane of the curve will have a greater secondary flow velocity than a curved pipe of circular cross section, and, therefore, a greater friction lass. If the major axis is perpendicular to the plane of the curve, the flow loss is less than in a curved pipe of circular cross section. Drew (3) and Prandtl (5) have empirical correlations for calculating the friction factor for laminar flow through coiled pipe. Both methods depend on the Dean number, R e d D j j c . Drew’s correlation consists of a plot of fc/f us. RedD/D,. Drew specifies that if the Fanning friction factor is less than 0.009, the flow is turbulent and the chart should not be used. Prandtl’s equation, fc = f (0.37) (Red/DID,)033, is good for the range 20 < R e d D T o < 1000. These two methods will give two values of the friction factor: A plot of log fc/f us. log R e d / D T , should be a straight line according to Prandtl’s equation, but Drew’s plot on logarithmic paper is not a straight line. Thus, any attempt to calculate a
pressure drop through the coil of the reactor would be largely guesswork; t h e problem is further complicated by the noncircular cross-sectional area of the coil. For taking pressure drop data, tap water was pumped upward through the helix until the temperature and pressure drop were constant. The flow rate and pressure drop across the helix were recorded. The data are plotted in Figure 1 as f us. Reynolds number, where
The length of the helical coil, L, is equal to the number of helical turns multiplied by T times D,,the outside diameter of the liner minus twice the distance from the inside wall to the centroid of the semicircle. As the pipe is noncircular, the equivalent diameter, De, which is 4 times the cross-sectional area of flow divided by the wetted perimeter, is used. Thus: 0.125 0.137 foot
L
=
72 X
T
X 0.137 = 31.0 feet
?r X 0.1252 4x 2 D, = ?r X 0.25
+ 0.25
1 x -12 =
0.01275 foot Reliability of the data is shown by excellent agreement of three methods for measuring pressure drop (Figure 1). VOL. 49, NO. 12
DECEMBER 1957
1945
GASKET 18-8 F L E X I T A L L lC M A I N NUT-ALLOY PART NO. 1 0 - 7 7 7
BODY-16-25-6 ALLOY PART NO 3 0 - 8 0 9 - A
L I N E R 3 4 7 S.S. [PART NO. 3 0 - 8 0 9 - A
7
( 5 ) 1/16 0 D "CONAX
,/-
Design of reactor eliminates need for internal cooling or heating coils or external jacketing
CORP"
THERMoCoUPLES G L A N D RETAINING RING 410 S S
Therefore,
1 -
A plot of 1
u
*:
ax A
1
u- G
-k
us.
+
A1
ih3A8
1
(1 0,011 Tav.)$.8 should yield a straight line. If the line is extrapolated to
\
36"APPROX
0 A LENGTH
LTHRUST W A S H E R - ALLOY
STEEL
P A R T NO. 1 0 - 7 0 4 ~ ~ U T T OCOVER N 347 PART
WORKING P R E S S U R E - 4 0 0 0 P S . I . @ 9 0 0 O F .
s.s
NO. 3 0 - 8 0 9 - D
H Y D R O S T A T I C T E S T P R E S S U R E - 6 0 0 0 P.S.I. @ 7 Z ° F .
The friction factor for a circular pipe using the equivalent diameter was calculated by both Prandtl's and Drew's methods (Figure 1). The data agree very well with Prandtl's equation, especially for Reynolds numbers greater than 500. If the equivalent diameter calculated above were arbitrarily reduced by 1/3, the data would agree very closely with Drew's correlation. However, there seems to be no justification for arbitrarily defining an equivalent diameter a t this point, as data on only one helical coil were obtained. Practically, the friction loss in the helix should be reasonably close to that of a coil of circular cross section. Although the cross section is roughly similar to that of a curved pipe having an elliptical cross section and oriented with its major axis perpendicular to the plane of the curve, where a lower friction loss would be expected, a t the corners where the half-circle meets the flat side a larger friction loss would naturally be expected. These two factors might balance each other. Heat Transfer in Reactor Coil
Even less ~7orkhas been done on heat transfer than on fluid flow in coiled pipes. Jeschke ( 4 ) found that for
turbulent flow of air in coils the heat transfer coefficient in long straight pipes should be multiplied by [ I f 3.50/0,]. Heat transfer in the reactor coil is further complicated by the shape of the system, which does not lend itself to an analytical solution by known methods. As the wall temperature of the coil is not constant a t all points on the circular side, A T across the inside film will vary, and the film coefficient for the helix cannot be determined experimentally. For design purposes experimental values of the inside film coefficient times an area, h3A3, would be of more value than the film coefficient itself. Values of h3A3 were determined experimentally by Wilson's method ( 3 ) . Steam was passed through the reactor and partially condensed by water in the coils. Only the water rate was varied. 'I\Tilson's method was then used to calculate h3A3 for the inside of the coil by assuming that the condensing coefficient and the resistance due to the wall were constant and that the inside film coefficient is a function only of the velocity and average temperature of the water. The Dittus-Boelter equation for water between 40" and 220" F. becomes
1
IO
A
AP MEASURED BY PRESSURE GAUGE P R A N D T L ~ EQUATION FOR COILED
-x-
DREW'S CORRELATION FOR COILED
Figure 1. Moody friction factor plot for reactor coil
I .o
LL
IQ
0.I
b .o I
10
100 REYNOLDS
1946
1000
10,000
NUMBER =
INDUSTRIAL AND ENGINEERING CHEMISTRY
100,000
Figure 2. Temperature profile around coil
+
1
(1 0,011 7-",8. = 0, 1/U a t this point is equal to C1, resistance due to the wall pl;s the condensing coefficient (the coefficient inside the coil is assumed to be infinite at infinite velocity). As the slope of the line is equal to CZ, h3A3 is now available as a function of temperature and velocity. Assuming a constant temperature around the half-circle, the temperature profile was found by relaxation methods to be similar to that shown in Figure 2. I t is believed that h3A3 measured experimentally corresponds to using A T = Ti - T,. Thus neither is As a measurable area, nor is ha a true film coefficient, as some conduction through the wall occurs before T, is reached, except a t the mid-point of the circles. Low pressure steam (1 to 3 pounds per square inch gage) was passed downward through the reactor while water was pumped upward through the helical coil. Terminal temperatures were rneasured by calibrated thermometers graduated to 0.1 F. Flow rates of water were measured by weight; of steam, from heat balances. The validity of using a heat balance was established by several runs in which the inlet and outlet conditions of the steam were determined by calorimetry and the mass flow by total condensation of steam outside the reactor. Heat losses from the uninsulated reactor were negligible. In the runs from which heat transfer data were obtained, the flow rates were so adjusted that steam did not completely condense nor cooling water vaporize. The cooling water through the helical coil was in turbulent
L.
flow for the heat transfer experiments. Quantities derived from the data obtained during the first series of runs are plotted in Figure 3, as the middle line. I t was believed that filmwise condensation was occurring; however, the extremely low value of the intercept a t infinite velocity indicated dropwise condensation. The reactor top was removed immediately after a run and drops were observed on most of the inside, probably as a result of a film of oil left after the machining of the reactor. By scrubbing the reactor bore with steel wool, the oil film was removed and drops no longer appeared. More runs supplied data for plotting the top line of Figure 3. The slope of this line is considerably different from that of the first line, as the over-all coefficient is more sensitive to changes in water velocity for filmwise than for dropwise condensation. T o induce dropwise condensation once more, a thin film of oleic acid was rubbed on the reactor wall. Drops formed immediately when water was poured through the reactor. Experimental runs gave the data plotted as the bottom line of Figure 3. The slope is the same as before-but the intercept is slightly less. Most reported values of dropwise condensation coefficients for steam range from 10,000 to 15,000, although coefficients as high as 75,000 are listed (3). The coefficient for the runs with oleic acid as a promoter was conservatively assumed to be 10,000, as the rather low steam velocity through the reactor would not suggest an extremely high coefficient. By using a value of 10,000 an average wall thickness of about 0.15 inch is calculated: i Ax,,. -U1 _-- hi1 + Ak A2
1 0.736 Ax,,. 0.00138 = 10,000 + 9.0 X 0.80
0.00138 Ax,,.
-
0.00010 = 0.1022 Ax,,,
= 0.0125 foot = 0.150 inch
The average wall thickness lies between 0.125 and 0.25 but closer to the former (Figure 2 ) . Therefore the calculated value of 0.15 seems reasonable. Coefficient h,, even if off by loo%, does not change the average wall thickness appreciably; therefore the assumption that hl is a constant is justified. I n Figure 3, the slope of the bottom line is 0.00620,giving the relationship ha& = (119.0) (1 3. 0.011 T&,,)UO.S. Experimental values of h3A3 are from 650 to 1600 B.t.u. per hour (" F.). Corresponding heat transfer rates are 12,050 to 30,100 B.t.u. per hour. Experimental values of h3A3 are plotted against water velocity in Figure 4; also values of the water film coefficient: h
4000.
3000
-
2000
-
I
U
.:." &
-
;$ ;L + mz =
1000-
OO
I!O
2jo
,Io
410
,io
,Io
,Io
VOL. 49, NO. 12
J.0
slo
10.
DECEMBER 1957
1947
300
TEMPERATURE, O F 340 360
320
380
400
----I
I-z
L P A C K E D BE0
PACKED BED 1/4 I N C H A L U M I N A
INCH S T E E L SPHERES
EMPTY TUBE A-HEATING A I R 0-COOLING AIR
a W
>
/
0
c/’D IT T U S - B 0 E LT E R
A
+ I 400
E M P T Y - TUBE--HEATING
G=I
PACKED BED - A L U M I N A
G=I
X PACKED BED - S T E E L
420
440 460 T E M P E R A T U R E , OF,
EQUATION
Figure 6.
I I I1000 I
I .o 100 AIR
M A S S VELOCITY,
LB/HR-FT2
Values of G ranged from 900 to 2000 Ib./(hr.)(sq. ft.). U , the over-all coefficient based on the area of the reactor bore, is essentially equal to hi, because the air film resistance is many times larger than the other two resistances combined (Figure 5). The experimental values of U for the empty tube are exceptionally high, since U should be nearly the same as hl, determined by the Dittus-Boelter equation. It is believed that the over-all coefficient is high because of increased turbulence a t the entrance caused by expansion of the air from the ‘/g-inch inlet to the I1/4-inch reactor bore. Colburn (7) reports coefficients 7070 high when air expands from a 1-inch pipe to a 3-inch empty tube. The temperature profile along the reactor supports this theory of increased turbulence a t the entrance. In Figure 6, for the empty tube the temperature changes over G O o F. for both heating and cooling in the first 3 inches of the reactor. For the packed bed this change is much less, because of the calming effect of the bed. Because of the poor insulation at the bottom of the reactor, the temperature of the exit air was approximately 15’ F. lower than the temperature measured by the last thermocouple in the reactor; this last was used as the exit temperature. Over-all coefficients were then based only on the area down to thermocouple 5. The reactor was packed with 3/16inch steel balls and with ‘/pinch alumina balls. Air was heated as before, from 400’ to 500” F. The over-all coefficients are close to those reported in the literature for these two packings. The temperature profile down the length of the bed is given in Figure 6 for one run with each packing. Heat transferred ranged from 100 to 300 B.t.u. per hour. Conclusion For a coil of half-circular cross section
1 948
I I I Ill//
I
G=1030.
&Sz
I
480
500
Temperature pro-
all thermal coefficients with air mass velocity
the friction factor for laminar flow can be predicted reasonably well by Prandtl’s equation, using the equivalent diameter. Heat transfer coefficients inside the helix are relatively high. Over-all heat transfer coefficients between steam and water were from 335 to 540 B.t.u./ (hr.) (sq. ft.) ( O F.), with corresponding heat transfer rates of 11,000 to 30,000 B.t.u. per hour. Because of the unusual shape of the system, it is suggested that A3 be taken as the total area of the circuIar part of the coil, and ha as one third to one half that calculated from the product of the Dittus-Boelter equation and the factor [I 3.5 O,/D,l. Rates of heat transfer in the empty reactor are very high when increased turbulence is caused by expansion of gas from a small hole to the reactor bore. The reactor design is practical, because heat transfer rate is high, and the pressure drop through the helix is not excessive, it is equally satisfactory for exothermic or endothermic reaction, it obviates the need for internal heating or cooling coils or external jacketing, and stresses arising from temperature gradients across the reactor wall are substantiallv reduced.
+
AP
= pressure drop, pounds per sq.
Re
= Reynolds number DG/,u, dimen-
foot sionless
Tay = average water temperature beTi
T,
U
= =
=
= Ax,,. =
u
p
,u
= =
tween inlet and outlet conditions, O F. temperature of fluid inside helical coil, O F. helix wall temperature a t midpoint of half-circle, ’ F. over-all heat transfer coefficient, B.t.u./(hr.) (sq. ft.) ( ’F.) velocity, feet per second average wall thickness between reactor bore and helical coil, feet density, pounds per cu. foot viscosity, lb./(hr.)(ft.)
Acknowledgment
The authors deeply appreciate the financial support and technical assistance of Autoclave Engineers in providing a graduate student fellowship and in donating the reactor to the university for these studies. 0. K. Crosser contributed many worth-while suggestions. literature Cited (1) Colburn, A. P., IND.ENG. CHEW23,
910-13 (1931).
Nomenclature
A C,
D D, De f
f, g,
G h
k
INDUSTRIAL AND ENGINEERING CHEMISTRY
area of heat transfer, square feet specific heat, B.t.u./(lb.) (” F.) inside diameter, feet = diameter of helical coil, feet = equivalent diameter, feet = friction factor for straight pipe, dimensionless = friction factor for coiled pipe, dimensionless = conversion factor, dimensionless = mass velocity, lb./(hr.) (sq. ft.) = coefficient of heat transfer. B.t.u./(hr.)(sq. ft.)(” F.) = thermal conductivity, B.t.u./ (hr.) (ft.) ( F.)
= = =
( 2 ) Detra, R. W., “Secondary Flow in
Curved Pipes,” Comm. Aerodyn. Inst. ETH, Zurich, No. 20 (1935). ( 3 ) McAdams, W. H., “Heat Transmission,’’ 3rd ed., McGraw-Hill, New York, 1954. (4) Perry, J. H., “Chemical Engineers’ Handbook,” 3rd ed., McGraw-Hill, New York, 1950. (5) Prandtl, L., “Essentials of Fluid Dynamics,” Blackie & Son, London, 1949.
RECEIVED for review April 8, 1957 ACCEPTEDOctober 14, 1957
Division of Industrial and Engineering Chemistry, High Pressure Symposium, 131st Meeting, ACS, Miami, Fla., April 1957.
