776
INDUSTRIAL AND ENGINEERING CHEMISTRY NOMENCLATURE
A
= cross-sectional area of capillary, sq. om.
constant in Equation 2 ” = diameter of capillary, cm. = length of capillary, em. = distance from entrance of capillary that grease travels in time t , cm. m = constant depending on the rate of softening of grease with time when flowing P = pressure, dynes/sq. cm. = 69,000 p , where p is pressure in lb./sq. in. rate of flow, ml./sec. Q = radius of capillary, cm. R = s = value of the expression 4Q/nR8, termed rate of shear, reciprocal see. t = time, see. of entranceYo capillary, sec. time tl = t 2 = time of discharge from capillary, see. t , = residence time in capillary, sec. t,”. = time a t which in the equation q = clm is equal to ?la,.. as calculated by Equation 4 v = volume of capillary, ml. v = velocity, cm./sec. x = ratio t., It, 9 = ipparint Gscosity, poises 7lm = apparent viscosity, calculated by either Equation 1 or 4, C
D L I
qav.
Vol. 41, No. 4
from data talcrn only with 8.O.D. standard caoillaries. poises = apparent viscody, calculated by Equation 1 or 4 using any capillary, poises LITERATURE CITED
(1) Arveson, M. H., IND. ENG.CHEM.,24, 71 (1932) ; 26, 628 (1934). Pathevg, J. B., and Zimmev, (2) Beerbower, A., Rproule, L. W.. J. C., Inst. Spokesman, 6, No. 8, 9 (1942); No. 10, 11 (1943). (3) Blott, J. F. T., and Samuel, D. L., IND.ENG.CIIEX., 32, 08 (1940). ‘(4) Brunstrum, L. C., Adania, E. W.,arid Ziegler, E. E., Znst. Spokesman, 9, No 3 , 4 (1946). (5) Hersey, M. D., and Zimmer, J. C., J . A p p l i e d Phys., 8, 359 (1937). (6) McLennan, L. K.,and Smith, G. H., A.S.T.M. Bull., 152, 123 (1948). (7) &looney, M., J . Rheol., 2, 210 (1931). (8) Roehner, T.G., and Robinson, R. C., Znst. h’pokesman, 10, No. 12 (1947). -., (9) Sproule, L. W.,Zbid., 8, No. 11, 12 (1945). (10) Tollenaar, D., and Bolthof, H., IND. ERG.CHmr., 38,851 (1946) (11) Zimmer, J. C.,lnst. Spokesman, 7,No. 12; 8, No. 1 (1944). (12) Zimmer, J. C., andPatberg, J. B., Ibid., 9, No. 5 (1945).
.-
RECEIVED January 26, 1948.
Power Savings in Process
Refrigeration FREDERICK CARRI 25 Arkwright Road, London, N.W.3, England
A distinctionis drawn
between the requirements of cold storage or space refrigeration duties, and of duties occurring in the chemical process industries. Analysis of the performance of different refrigeration cycles suggests the use of a variation of the vapor compression cycle, on which calculated data are presented.
EFRIGERATION systems are required to perform duties vrhich may be divided into two main classes. The f i s t type of duty consists of the transference of heat from a constant low temperature to a constant high temperature; in the second type of duty, such as occurs in cooling a liquid of finite specific heat, the heat is removed at a varying temperature, and may also be required to be delivered at a varying temperature. The first type of duty occurs in cold storage applications (space refrigeration); the second type occurs frequently in the chemical process industries (process refrigeration).
source a t a higher temperature than itself; in this process i t boils and more vapors are evolved. Compression of the vapors from the chiller by the. compressor, E, and delivery to the condenser complete the cycle. This cycle performs a space refrigeration duty; the heat is absorbed a t the constant boiling temperature of the liquid in the chiller, and is delivered at the constant condensing temperature of the vapor in the condenser. If such a cycle could be operated under thermodynamically reversible conditions, the relation between heat and work quantities would be given by Equation 1.
I -
t
F=+
I
SPACE REFRIGERATION
Space refrigeration duties are conveniently and efficiently performed by systems in which heat removal is effected by means of a boiling liquid refrigerant; the vapor compression system is the most widely used of these. Figure 1 is a diagrammatic flowsheet of such a system.
A refrigerant vapor-for instance, ammonia-is delivered under pressure to a condenser, A , in which i t is condensed, and heat is removed by cooling water. The condensed liquid is accumulated in a receiver, B, from which i t is allowed to expand through a valve, C, into a chiller D. The receiver liquid being saturated, expansion is accompanied by partial vaporization and a fall of temperature. The cold liquid remaining in the chiller may then be employed as a refrigerant, absorbing heat from a 1
Present address, Polymer Corporation, Sainia, Ontario, Canada.
HEAT-
Figure 1. Diagrammatic Flow Sheet of Vapor Compression System
April 1949
INDUSTRIAL AND ENGINEERING CHEMISTRY
I n the practical application of this system, however, apart from .increases in work requirements due to mechanical imperfection of the compressor, losses occur owing to the inherently irreversible. Joule-Thomson expansion a t valve C. The work quantity as given by Equation 1 may therefore be regarded as a theoretical standard only. The application of the cycle t o a given space refrigeration duty is also accompanied by irreversible effects due to the necessity of establishing finite temperature differences to .maintain heat flow into the boiling liquid refrigerant and out of the condensing refrigerant vapors. However, these differences may be made infinitesimal by the use of infinite heat transfer surfaces; and therefore do not present a thermodynamic obstacle to efficiency such as occurs in the valve expansion of the refrigerant liquid.
777
able; however, systems reproducing the temperatlure conditions of Figure 3 are in use and have been suggested. A well known example of this type of cycle is the air refrigeration system represented by the Allen dense air system and by the refrigeration system employed in the Claude and Heylandt air liquefiers. In this system the operating medium is a permanent gas-for instance, air-which is compressed and then cooled by cooling water. The cooled high pressure air is expanded through an expansion engine which is coupled to the'compressor. The cold low pressure air exhausted from the expansion engine is used as the refrigerating medium before returning to the suction side of the compressor and thereby cgmpleting the cycle.
VAPOUR
T
PROCESS REFRIGERATION
Vapor compression systems are applied t o process refrigeration duties. Consider a case where a liquid stream of constant specific heat is to be cooled, being passed through a coil in contact with the boiling liquid refrigerant, and where the condenser coolant is also a liquid of constant specific heat, and is passed through a coil in the condenser. Figure 2 illustrates heat and temDerature conditions in this case.- The abscissa represents heat- transferred as a fraction of the total heat transferred in the unit considered; thus the abscissa range of the chiller and condenser temperature curves is the same, although more heat is removed in the condenser than is absorbed in the chiller. Losses due t o mechanical inefficiency, isenthalpic expansion, and irreversible heat transfer occur, as in the application of the vapor compression cycle t o space refrigeration duties. Provision of infinite heat transfer surfaces, however, will not reduce irreversibility of heat transfer to an infinitesimal amount-for instance, in the chiller, infinite surface will reduce only the terminal temperature a t the cold end t o zero; heat transferred in cooling the liquid stream t o its outlet temperature is still transferred a t finite temperature differences, and is therefore irreversible and results in power losses. A similar condition occurs in the condenser. The application of a simple vapor compression cycle to a process refrigeration duty therefore suffers from two inherently irreversible effects: isenthalpic expansion and finite temperature differences for heat transfer even with infinite surfaces. Inherent irreversibility of heat transfer in a process refrigeration duty could be avoided by a system having the temperatureheat transferred characteristics shown in Figure 3. Such characteristics would be produced by the use of an infinite number of vapor compression cycles each absorbing an elementary heat quantity, d H , a t varying temperature t and delivering it a t varying temperature T. If such a system could be operated reversibly, the relationship between heat and work quantities and temperatures could be obtained by rewriting Equation 1 in a differential form
dW=dH-
T - t
t
and integrating between the appropriate limits with regard t o the fact that T and t may be written as functions of H . For the case considered, where both chilled liquid and condenser coolant are liquids of constant specific heat, the integrated equation, arranged in a form similar to that of Equation 1, is
(3) The system visualized in arriving a t Equation 3, in which an infinite number of compressors is required, is obviously unrealiz-
BOILING LIQUID
HEAT TRANSFER-RLD
. . . _
Figure 2. Heat Transferred vs. Temperature in Ammonia System Applied to Process Refrigeration Duty
The general impression that this cycle is thermodynamically inefficient is based on its application to space refrigeration duties, for which its characteristics are unsuitable. Comparison of its performance with an ammonia cycle for a process refrigeration duty shows the air cycle in a more favorable light. The duty considered is to cool a liquid of constant specific heat from 55" to -30" F. Cooling water is-available a t 65" F. and may be heated to 100" F. The calculated performances of the two cycles are tabulated in Table I. In the calculations on which Table I is based the air was considered t o be a perfect gas with a specific heat ratio of 1.4. The temperatures and pressures tabulated for the air cycle are those for a compressor and expansion engine of 1 0 0 ~ oefficiency. Under these conditions the net theoretical work for,the aic cycle represents a 39% saving over that for the ammonia cycle. The net actual work tabulated is calculated for air and ammonia compressor efficiencies of 8570 of isentropic, and expander efficiency of 75% of isentropic, with an actual tehperature drop in the expander of 85% of the thepretical. These conditions are the same as those suggested in a similar calculation on an air cydle ( I ) . The severe effect of expander and compressor imperfection on the air cycle is due to the fact that the net work is a difference between two relatively large quantities, the work required by the compressor and the work recovered from the expander. The
INDUSTRIAL AND ENGINEERING CHEMISTRY
778
operation of the efficiency factors is to increase the work required and t o reduce the work recovered; even the relatively high efficiencies assumed increase the net actual work vary considerably as compared with the net theoretical work.
d
L
;TEMP
I / /
I
/ i.2
-
HEAT TKAN5FERRED
,_
J
Figure 3. Heat Transferred os. Temperature in System Avoiding Inherent Irreversibility
Quite apart from questions of power consumption, however, the air cycle has disadvantages which make it unsuitable for general application. The low specific heat of the operating medium calls for a compressor of excessively large displacement, and the low rate of heat transfer to the operating medium requires large heat transfer surfaces. Even if it were possible by increasing the efficiency of the machines t o reduce its power consumption below that of a vapor compression cycle applied to the same duty, these disadvantages would rule out its use in the average process iefrigeration duty. I t s use in air liquefaction is due to the special advantages it enjoys in the production of very low temperatures. Furthermore, the disadvantage of low heat transfer rates is not so serious when a low film rate is unavoidable on the
TABLE I. CALCULATED PDRFOR~IANCES Teniperature conditions in air cooler condenser, F. H o t medium Water Differences Log h1.T.D. Teomgerature conditions in chiller,
Air Cycle
Ammonia Cycle
lig 70 100 c 6 3 79 o 26.8
105 105 100 c- 6.7 8 43 20.8
-
E .
Fluid stream Refrigerant Differences Log M.T.D. Corngrossor suction pressure, b / sq. inch abs. Compressor discharge pressure Ib./sq. inch abu. S e t work, B.t.u./lOG I3.t.u. absorhed in chillrr Theoretical Actual
55, -30 3 5 4 - -50 20 20 20
55, -32
-30 -32 87 2 32.5
13,14
13.14
32.2
239.7
282,000
460,000 575,000
1.330,OOO
Vol. 41, No. 4
side of the air being cooled; and the duty performed by the expalision engioe cycle in a Heylandt air liquefier is an extreme example of a process refrigeration duty, consisting of the cooling of an air m e a m from atmospheric temperature to -200” F. ( 9 ) . A second refrigeration cycle of this type is that suggested by hlaiuri ( 2 ) . This is an absorption refrigeration system in which heat is absorbed over a range of temperature by using a refrigerant liquid evaporating into an inert gas a t increasing partial pressures; this is likely to be handicapped by low rates of heat transfer from the fluid to be cooled to the evaporating refrigerant, as heat transfer here will be by convection, the vaporization of the refrigerant being unaccompanied by the bubble formation which assists heat transfer to boiling liquids, From consideration of the ammonia cycle, the air cycle, and the diffusional vaporization cycle, i t is possible to state the qualities which would be desirable in an ideal system for process refrigeration.
1. The absorption of heat by the refrigerant should be accompanied by a rise of temperature-that is, enthalpy should be a function of temperature, and generally should be a linear function. 2. The effective specific heat of the refrigerant should be high. 3. Mechanism of heat transfer should be such as to give high heat transfer rates. 4. The use of an expansion engine should be avoided, as this makes the efficiency of the cycle too much dependent on mechanical factors. 5 . Inherently irreversible processes should be avoided; the thermodynamic efficiency of the cycle relative to its reversible analog should be a t least as high as in the ordinary vapor compression cycle. The air cycle fulfills only the first of these conditions; the diffusional vaporization cycle the first, second, and possibly the fifth. A material which fulfills conditions 1, 2, and 3 is a mixture of niutually soluble volatile liquids; for there is a temperature range (condition I ) over which the mixture boils (condition 3), and the large latent heat of the constituents is absorbed over the relatively short temperabure range from bubble point to dew point. This refrigerant would be used in an ordinary vapor compression cycle, except that provision would have to be made for countercurrent flow in the heat exchangers. In condition 5 no expansion engine is used, but the expansion of the saturated liquid refrigerant leaving the condenser is irreversible, as in the case of the ordinary vapor compression cycle. If the liquid refrigerant were precooled before expansion t o its bubble point temperature at the pressure after expansion, no vaporization would occur in the valve and the entropy increase would be negligible. An attempt to reduce the losses in the ammonia cycle by precooling the liquid refrigerant would be unsuccessful, for the only coolant available is the ammonia itself, boiling a t the chiller pressure; a heat balance shows that the vapor quantity evolved in the precooler would be exactly the same as that evolved during the valve expansion. I n fact, the irreversibility has simply been transferred from the valve to the precooler. I t is, however, a characteristic of the mixture refrigerant that it reduces the irreversibility of heat exchange when employed to cool liquids of substantially constant specific heat; and use of a counterflow refrigerant precooler using boiling refrigerant ns coolant might be expected to reduce thc total entropy increase associated with the valve expansion. 4 possible source of losses occurs in the mixture refrigerant cycle which is not present in the ordinary vapor compression cycle. An irreversible change takes place if the vapors evolved at wide1,v different temperatures are allowed t o mix. Such irreversible mixing: is a characteristic of the differential, or “open” mode of vaporization in which vapors are removed from contact with the boiling liquid as they are evolved. I n “closed” or equilibrium vaporization, in which the liquid and
INDUSTRIAL A N D ENGINEERING CHEMISTRY
April 1949
779
The mixture chosen had the following composition :
t
I
Figure 4.
Diagrammatic Flow Sheet of Mixed Refrigerant System
vapor are kept in equilibrium during the whole period of phase change, such irreversibility does not occur. I n the process refrigeration cycle on which calculated data are presented the refrigerant mixture used is a mutual solution of ethane, propane, and butane. Enthalpy data for these hydrocarbons are taken from the nomogram presented by Scheibel and Jenny (4). Phase equilibrium calculations were made using the vapor pressure of the pure compounds and assuming ideal solution. This procedure gives a higher ratio of condenser t o chiller pressure than the use of either extrapolated K data or su'oh experimental data as are available, and is therefore chosen as giving a high power consumption.
TABLB 11. COMPARISON OF MIXTURE AND AMMONIACYCLES Mixture
Ammonia
55 + -30 85 c -48 18 2o 17
55 + -80 -32 -32 87 2 22.6
157 -+ 70 100 + 65 57 5 21i3
108 108 100 c 65 8 43
Temperature conditions in chiller,
-Fluid . stream
o w
Refrigerant Differences Corrected M.T.D. Temperature conditions in aondenser, a F. Vapors Water Differences Log M.T.D. Enthalpies, B.t.u./!b. mole Vapor from ohiller Liquid from condenser Differenoe Lb. moles circulated per 108 B.t.u. Suation diaplacement of compressor, cu. ft. of low preasure gas per 106 B.t.u. Chiller pressure, lb./s inch abs. Condenser pressure, &./sa. inch ebs. Compression ratio Net theoretical work, B.t.u./lOa B.t.u. abaorbed in chiller Astual work Comparison
20.8
12,630 6,250 6,380 186.5
10,200 2 800 7:400 135.0
20,800 40
45,900 13.14
241 6.02
239.7 18.22
526,000 408,000 71
460,000 676.000 100
Mole % 36.96 32.04
CzHe CsHs Cd%a
31.00
At a chiller pressure of 40 pqunds per square inch absolute the bubble point is -50" F. and the dew point is 35 " F. Calculation of the temperature-enthalpy curve between these temperatures shows a slight curvature; temperature for any given enthalpy is higher than the straight line joining the two terminal points. The high pressure liquid refrigerant is assumed to be precooled to -40" F., so that the effective boiling range of the refrigerant in the chiller is from -48" F., 2" F. above the bubble point, to 35" F., the dew point. The effective mean temperature difference for heat transfer in the chiller, corrected for the curvature of the enthalpy-temperature line of the refrigerant, is 17" F. The condenser pressure chosen is 241 pounds per square inch absolute. At this pressure the dew point of the refrigerant is 157" F. and the bubble point 70" F. The log mean temperature difference is 21.4" F.; the actual mean temperature difference will be slightly higher, owing to the curvature of the enthalpytemperature line, but this correction was not calculated. The high dew point of the vapor with the water outlet temperature of 100O F. indicates thermodynamic losses; a similar irreversibility of heat transfer occurs a t the hot end of the refrigerant precooler, where there is a temperature difference of 35" F. Improvements in this cycle should be possible at these points. A tabular comparison of the mixture cycle and the ammonia cycle is shown in Table 11, and Figure 4 is a diagrammatic flow sheet indicating the method of precooling the liquid refrigerant. A further comparison is made in Table I11 of the relations between the work quantities calculated and the theoretical minima as given.
TABLE 111. COMPARISON Theoretical minimum work of cooling Theoretical minimum work to operate cycle Work t o operate cycle with 100% compressor efficiency
OF W O R H
QUANTITIES
Mixture
"8
248,000
100
248,000
100
266,000
107
327,000
132
326,000
131
460,000
186
The theoretical minimum work of cooling was calculated from Equation 3, allowing the appropriate temperature differences in the chiller and, condenser: It is clear that this cycle is well suited to the duty, and that further improvements will have t o come from more efficient operation of the cycle. Returning to Table 11, it will be seen that the low compression ratio, together with the high suction pressure, gives the mixture refrigerant a considerable advantage in compressor suction volume; the possibility of varying the refrigerant composition t o suit any given duty will ensure that this advantage is available for any duty, and is not restricted t o particular temperatures. The pressure conditions for the ammonia cycle were chosen t o give as nearly as possible the same mean temperature difference for heat transfer in the comparable heat exchange units, so that equal surfaces for heat transfer would be required for the two systems and their power consumptions may fairly be compared. The mixture cycle requires the additional surface of the refrigerant precooler, but this has been neglected; first because both transfer rate and mean temperature difference are high, and secondly because this unit can be incorporated in the chiller so that the additional cost of the precooler is negligible. Although a simple ammonia cycle would never in practice be applied to such a duty, the comparison is presented t o show that a cycle of a similar degree of elaboration is capable of securing savings in capital and power costs. Elaborations of the mixture
180
INDUSTRIAL AND ENGINEERING CHEMISTRY
cycle analogous t’o the use of st’age compression for the ammonia cycle are possible; these are directed towards reducing the inherently irreversible effects whose presence is indicated by the 22% difference between the theoretical minimum work required to operate the cycle, and the work to operate the cycle with 100% compressor efficiency. The use of mixed refrigerants is not new; many attempts to apply them t o space refrigerat.ion duties have been made with little success. The mixed refrigerant has some of those characteristics of the air cycle which make it unsuitable for space refrigeration duties, and its use for process refrigeration without refrigerant precooling would also be unsuccessful. There is also the tradit’ional objection that owing to differential rates of leakage, make-up of refrigerant losses presents difficulties. This would certainly be true in space refrigeration; but on a process plant where a higher grade of technical skill is available, the difficulty should not be serious. The system as described has not been practically operated; it was the author’s intention to restrict, this paper t,o an analysis of possible methods of improving the thermodynamic efficiencies of refrigeration cycles applied to process refrigeration duties. The pract,ical possibilities of the mixture cycle with refrigera.nt precooling are, however, briefly surveyed. Application of this system mill offer the greatest’ advanta.gc where cold recovery is not used. For example, in a solventtreating plant where & liquid is treated with a solvent at a sufficiently low temperature to cause t’he separation of two liquid phases, it is usual to perform the major cooling of t,he charge and solvent by heat’exchange with the cold liquids leaving the treating vessels. Under these circumstances the duty of the external refrigerant is to cool the entering liquids through a relatively short t,cmperature range, equal to the terminal temperature difference a t the cold ends of the exchangers; this duty approximates the space refrigeration type and is efficiently performed by the usual vapor compression system. I n cases where a number of products leave a t low temperatures cold recovery may become uneconomic, and a process refrigeration system becomes applicable; similarly it is applicable when the product of a process is required a t a low temperature, as in gas liquefaction.
Pore-Size
Vol. 41, No. 4
Difficulties in application may be principally expected at three points: ( I ) in securing countercurrent flow of refrigerant and fluid to be cooled, and (2) in maintaining equilibrium vaporization. I n a multicomponent mixture equilibrium vaporization in this context does not imply that phase equilibrium should subsist; the requirement is only that the liquid and vapor phases coexisting should be at the same temperature; this is possible even if the compositions of the phases are not in equilibrium. Such temperature equilibrium is more easily attainable than full phase equilibrium. Finally, the heat transfer rate to the refrigerant will drop off as vaporization approachea completion and the mechanism of heat transfer approximates forced convection to a gas. The solution of these difficulties is, however, a function of equipment design and does not fall nithin the scope of the present theoretical anal)-sis of the problems of process refrigeration. NOR.IENCL4TURE
H
= heat removed in chiller, B.t.u. T = high level ternperatuie to which heat is delivered, a ab?. T3 = higher tenipeiature when heat is delivered over a tcmperature rang?, abs. T I = lower tempeiakure when heat i> delivered over a tcmprratiire range, abs. TV = work required, B.t.u. t = low level temperature from vhich heat is absorbed, abs. f2 = lovrer temperature when heat is absorbed over a temperature range, ’ abs. tl = higher temperature when heat is absorbed over a tcmpc~iah r e range, abs. A T = Tz - Ti O
at
= tl
-
t2
LITERATURE CITED
(1) Dodge, B. F., ”Chemical Engineering Thermodynamics,” New York, McGraw-Hill Book Co., 1944. (2) Maiuri, G., Brit. Patent 462,981 (1929). (3) Ruhemann, M., “Separation of Gaqes,” London, Oxford University Press, 1945. (4) Scheihel and Jenny, IND. EKG.CHEW,37, 990 (1945). Received July 22, 10471
istribution in Materials
row
APPLICATION OF HIGH PRESSURE MERCURY POROSIMETER TO CRACKING CATALY STS L. C. DRAKE Socony-Vacuum Laboratories, Paulsboro, N . J .
ASHBURN ( 9 )in 1921 was the first to suggest the use of pressured mercury in determining the pore-size distribution of porous solids. The relation developed by him may be stated in the following form: 0 D = -4u Pcos -
where D is the diameter of the pore just enterable by mercury of surface tension u, under pressure P , and at a contact angle e with the material being tested. Independent measurements of the contact angle of mercury with several oxides have indicated
values in the vicinity of 1.10’ C. ( 6 ) . Table I shows the rclation between the applied pressure and the diameter of pores enterable by mercury, calculated by means of the Washburn equation. Henderson, Ridgway, and Ross (3) were the first to publish experimental data obtained by pressuring mercury-covered fuller’s earth and bauxite samples from 30 to 900 pounds per square inch. Their data were reported in connection with other work and appeared t o be very limited. Ritter and Drake ( 6 ) developed apparatus and methods for meas2ring the penetration of mercury into pores down t o 200 A. in diameter, at 10,000 pounds per square inch pressure,
