Applications of the Film Concept in Petroleum Refining CARLC. MONRAD,Standard Oil Company (Indiana), Whiting, Ind. Actually, of course, there is no URING the p a s t few During the past f e w years it has become apsharp break between the film years there has been a parent that m a n y supposedly complex problems boundary a n d t h e t u r b u l e n t growing appreciation of in various processes can be correlated by means stream, but the velocity in the the fact that a large number of of the concept of “stagnant” j l m s . film gradually increases f r o m industrial processes, a1t h o u g h Some of the applications of the f i l m theory to zero a t the solid surface until seemingly unrelated, depend on a t length it begins to flow in the properties of thin “stagnant” the petroleum refining industry are reviewed. more or less turbulent fashion. films. In a great many cases I n some cases the application is fairly simpleRecent experiments have shown our information is all too meager, notably heat transfer and friction losses-but that the flow in the film itself is but gradually eve11 t h e m o r e other of the more complex problems still have not altogether linear, but that complex p r o b l e m s a r e b e i n g to be solved. Among these are, particularly, there is probably some flow in solved. the direction of the turbulent Of particular i n t e r e s t a n d deviations *from equilibrium in absorption and stream. However, since the flow value has been the correlation of fractionating towers and evaporation losses f r o m is substantially linear, any transseveral of the unit processes, tankage. port of heat or material from the such as heat t r a n s f e r , f l u i d An equation is developed for evaporation main fluid body to the solid surfriction, and diffusion, so that f r o m large plane surfaces to Jawing gases, based face must take place largely by often a k n o w l e d g e of o n e of c o n d u c t i o n or b y d i f f u s i o n these will permit a t least apon heat transfer and diffusion data obtained by through this film. Because of proximate calculation of t h e several investigators. the erratic movement in the others. I n view of the wide apturbulent stream, either heat or plications of the film concept to very diverse phenomena, the writer here points out some material can be brought ,to the film boundarylargely by the of the possible applications in the petroleum refining industry. mass movement of the fluid itself (so-called convection). Since there is no definite boundary between the film and the The refining of petroleum into its various products involves the separation of the crude by distillation, the thermal de- turbulent stream, i t is not possible to determine the film composition of the heavier constituents into more desirable thickness exactly. Therefore, the term “effective” film products, and finally the treatment of the various fractions thickness has been widely used, which is equivalent to the to produce finished stocks. The design and operation of a thickness that would be necessary if the film were truly stacomplete refinery requires adequate knowledge of practically tionary and the turbulent stream truly turbulent and posall the unit processes of chemical engineering, and the prob- sessing the same velocity throughout. This is very valuable lems to be solved are further complicated by the extreme as an approximation, but such an effective thickness would chemical complexity of the raw material and products as well not be expected to be exactly the same for heat transfer, as the high temperatures and pressures involved in the diffusion, and friction, although they should be of the same various processes. order of magnitude. I n most of the operations of a petroleum refinery the preCORRELATION OF UNITPROCESSES BY FILM THEORY~ dominant factors to be overcome are the resistances of thin films between the various phases. These films tend to retard Reynolds and others have shown that the breakdown of the rate of heat flow and the rate of diffusion from one phase stream-line flow into turbulent flow depends on the properties to another, and are a major factor in determining losses in of the fluid, the character and dimensions of the surfaces in pressure. contact, and the velocity of the fluid. This can be expressed by the relationship dup/p for circular pipes and more generGENERAL CONCEPTS OF THE FILM THEORY ally by mup/p for any conduit where u is the mean fluid The basis of the film theory is that a t the interface of a velocity. At a definite value of this dimensionless Reynolds flowing fluid and a solid surface there is a film of relatively criterion the fluid motion becomes turbulent. The change is stationary fluid. At low velocities the entire body of the not very abrupt, however, and there is a critical region over fluid may be flowing in so-called viscous or stream-line motion which there is a gradual change from stream-line to turbulent and the “film” may be considered to be the entire thickness flow. The value of the lower critical criterion, mup/p varies of the flowing fluid. However, a t higher velocities the nature from 250 to 500 for various conduits when expressed in conof the flow changes so that the main fluid body begins to sistent units. flow in turbulent motion; i. e., the fluid particles travel in all Friction losses in conduits may be correlated by means of directions. However, at the interface between the solid the Fanning equation ; surface and the moving fluid a film of fluid remains in more or less viscous motion and the thickness of this film is determined by the properties of the fluid, the character and shape of the solid surface, and the velocity of the moving fluid. I n where f is a dimensionless friction factor which may be the simplest form one can conceive of this film being abso- correlated by a function of the Reynolds criterion but which lutely stationary with the turbulent fluid moving past the varies somewhat with the roughness and shape of the surface. outer boundary of the film a t constant velocity. I Symbols are in consistent unite unlesa otherwise noted.
D
1087
I N D U S T R I A L A N D E N G I N E E R I N G C H E hI I S T 11 Y
1088
Reynolds (16) first suggested an analogy between fluid friction and heat transfer, and later Stanton (18) and others applied this suggestion to heating and cooling a turbulent fluid in smooth tubes, leading to the expression: where u
h = f2
= av.
fluid velocity
Prandtl (15) later pointed out that the above correlation is correct only when the value c p / k for the fluid was unity. This is substantially correct for most gases. h more exact relationship was derived by Prandtl to be:
{ cup where
= %l
ratio of velocity at film-core interface t o av. fluid velocity
On the basis of studies of velocity gradients this value was shown later to be approximately 5.9 G(3, 7). For example, if air a t 60" F. and atmospheric pressure is flowing through a 1-inch i. d. tube a t a velocity of 10 feet per second, the following results are obtained for €he computed heat-transfer rate: From correlation of heat transfer data:
1. h=
0 . 0 1 4 5 ~(up)".* dO.2
- 0.0145 X
0.238 X (10 X 3600 X 0.076)o.8 / 1 \os2 =
\G)
3.2 B. t. u./sq.
2. From Revnolds' eauation: h =
f
'-z
= 0.0014
[ -
cup f = 0.0014
+ 0.125
ft.1' F./hr.
(+37
+ 0.125
=
0.0087
h - 0'0087 X 0.238 X 3600 X 10 X 0.076 = 2.8 B. t. u./sq. 2
ft./' F./hr.
3. From Prandtl's equation:
2 urn
h = 1
- 0.55 +
I.t' A~
=
ueight of vapor transferred per unit time and a w , ~
m
=
main stream properties
For flow in tubes,
cilp
= 5.940.0087 = 0.55
2.8 0.238 X 0.0672 X 0.00018 X 3600 0.55 0.0135 > = 3.2
(
The correlation in the case of liquids is not very satisfactory, particularly when cp/k is very high. Colburn (5) has discussed this point in some detail. Although the correlation between heat transfer and fluid friction is not exact a t present, the results are sufficiently good to permit a rough estimate of one of these factors from the knowledge of the other. Of particular importance to the design engineer, perhaps, is the fact that there is a direct relationship between heat transmission and fluid friction, but that other sources of pressure loss (i. e., contraction and expansion) are not directly related to heat transfer. Several attempts have been made to correlate mass transfer (diffusion) with fluid friction. Of these perhaps the most valuable is the theoretical development by Colburn (3) for dehumidification, This correlation was based on similar concepts to those used by Prandtl for heat transfer and is given (in consistent units) by the following equation:
Vol. 26, No. 10
-
3 -
MuPmUm
Ap
Po/Mm+
This equation has been applied to condensation of vapors in admixture with noncondensable gases ( 3 , 1 1 ) and to evaporation from a thin liquid layer to flowing gases ( 1 , 7 ) . Although subject t o considerable inaccuracy because of our present lack of knowledge of the properties of thin films, this correlation has led to a much better understanding of the mechanism of diffusion. Colburn's and Kirkbride's data were found to agree substantially with the proposed equation, but Gilliland's results show that the computed diffusion rate is about 30 per cent low. Since very little is known about the effects of concentration gradients on the velocity gradients in thin films, a deviation of this magnitude is not surprising. Recently Colburn (5) has suggested a method for correlating heat transfer, fluid friction, and mass transfer in variou.; conduits, and eventually we may hope to be able to correlate these and other unit processes more exactly. APPLICATIOXS TO PETROLEUM REFINING HEATTRANSFER. By far the most important operations in petroleum refining are those involving the transfer of heat from one fluid to another, either by direct contact or through a solid separating wall. Problems of the latter type involve the determination of the resistance to heat flow from one fluid to the solid surface, resistance of the separating wall, and the resistance between the wall and the second fluid. These resistances can be computed separately and the net effect determined in a manner similar to resistances in electricity. A large amount of data has been obtained for varying conditions and correlated by means of theoretical equations or by dimensional analysis. These equations may be generally summarized as follows:
Nu = function of Pr and Gr (2) Forced convection: Turbulent flow: Nu = function of Re, Pr, and ( L , / L 2 ) Viscous flow: Nu = function of Pe(L1/L2) (3) Condensation of pure vapors (film viscous) : p2k3gr h = function of I_. pLL At (4) Condensation of vapors by diffusion through noncondensable gas: See Colburn equation above (5) Conduction: h = k/x (6) Radiation: Involves radiation from solid surfaces, hot gases, and particles, but is independent of film re(1) Natural convection:
sistances
All of the above methods of heat transfer are involved in petroleum refining. The first finds applications to heat pick-up or loss from tanks and equipment to the air, the second to heat exchangers and pipe stills, the third and fourth to the condensation of distilled products, the fifth to losses from insulated equipment and through tube walls, and the last to heat transfer to storage tanks from the sun and from hot furnace gases and walls t o tubes in pipe stills. In reviewing our present knowledge of the above general types of heat transfer it appears that present data are reasonably adequate except for the following cases: (1) Effects of baffling in heat exchangers. (2) Heat transfer t o boiling and/or decomposing fluids particularly at high values of Re. In fact, even in the design of pipe stills the liquid coefficient often must be based on an extrapolation of data at lower values of Re. Fortunately this is not usually vital as the resistance on the gas side is predominant. (3) Condensation of vapors when film of condensate is no longer entirely viscous but is either turbulent or condensation is
October, 1934
INDUSTRIAL AND EKGINEERING
dropwise. Some work has been doneonthisproblem (4,1B, 13,14), but the present results are hardly satisfactory for design purposes. (4) Effectsof fouling of tubes on the heat transfer coefficients. ( 5 ) Heat transfer t o large plane surfaces.
PRESSURE DROP. The film theory has led to the development of adequate equations for computing friction losses for a large number of cases. The total loss in pressure involves not only this friction loss but also losses due to expansion and contraction, static head, etc. At the present time it cannot be said that an accurate method is available for predicting pressure drops in cracking coils since the pressure-volumetemoerature relation.. -z ships a t h i g h p r e s s u r e s a r e n o t very well known, and the rate of cracking depends both on time of contact and temperature. THERRL4L DECO~V- $ POSITIOX. The cracking of p e t r o l e u m fractions involves the u s e of high temperadide Elevation t u r es and pressures, and a knowledge of the true cracking rate 6eet;on on A-A. is v e r y d e s i r a b l e . The reaction r a t e doubles for approximately a 25" F. rise in temperature and also depends on the time of contact, which in turn is fixed by the pressure-volume-temperature relationships. The latter may be estimated only roughly a t present owing to large deviations from perfect gas laws as well as the complex nature of the materials handled. It is often necessary to transfer cracking data from a laboratory apparatus to full-sized plant equipment. Since cracking rates are determined not only by the character of the stock but also by the time-temperature relationships, it is obviously necessary to determine these relationships in the small-scale equipment. In this laboratory a large amount of experimental work has been done in coils immersed in molten lead. The over-all temperature and pressure changes and cracking rates can, of course, be readily obtained, but the pressure and temperature curves must be computed in order to obtain the specific reaction rate. This has been done by a trial and error method, calculating the heat transfer by natural convection from molten lead to the tube wall, and forced convection inside the tube. The pressure-length curve and temperature-length curve can then be constructed so that the total effects check the over-all average observed, and the instantaneous points are in accord with the heattransfer calculations. The deposition of coke in cracking tubes and drums is the most general cause of a shutdown of equipment. The maximum heat input to the tubes is limited by the tendency to coke, a t a point often considerably below limitations set by the properties of the tube material. Since this coke has a low thermal conductivity, it offers high resistance to heat flow which, if counterbalanced by increased furnace temperatures, results in the accumulation of more coke. The exact mechanism of coke formation is a t present unknown, but a possible explanation is that the cracking rate in the film becomes high enough above the average to permit deposition. Owing to the relatively slight motion from the film into the main body, it may be that cracking in the film goes much farther toward completion (i. e., gas and coke), and the products do not diffuse rapidly enough into the main stream. This mechanism would also explain why coke tends t o build ~
~
2
CHEMISTRY
1089
up rapidly after it is first formed a t one spot and why high velocities tend to reduce coke formation. The rough surface produced would make the film thicker and diffusion less rapid. An alternative possible explanation is that the surface boils dry in spots, similar to the phenomena observed in evaporators, and a small amount of residual coke is built up each time this occurs. FRACTIONATION AND ABSORPTION.I n the design of fractionating or absorption columns two general methods have been tried. The most generally used method is based on the concept of equilibrium plates, which assumes that the vapor leavine each d a t e is in equilibrium with the liquid. T h e $ n u m b e r of equilib6 'a f rium plates is then 9 w P divided by the "plate 2 efficiency" to obtain 9 the number of actual plates to be used. This efficiency is obtained from informat i o n o n similar colTYPICAL REFINERY u m n s O r SEPARATOR B~~ guessed. Because of the fact that, in general, efficiencies run from 0.4 to nearly 1.0, this method has been quite valuable, particularly since flexibility is usually desired and extra plates are not very expensive. The second method of design is based on the diffusion rates of one or more components. It is obvious that the plate efficiency is merely a measure of the deviation from equilibrium, which in turn is determined by the rate of diffusion from the contacting vapor to the liquid on the plate. Recently Carey (2) has developed an equation for mixtures indicating that the plate efficiency is given by the relationship: - c1 -
-
s
%
~
=
l
-
e
~
where C = function of diffusivity d = av. diam. of gas bubbles L = effective depth of liquid through which the bubble rises In the petroleum industry the number of components to be handled is limitless. Even in an absorption tower the inlet gas contains all the paraffin hydrocarbons from methane to hexane, as well as unsaturated compounds. The plate efficiency for each of the components is undoubtedly different, but few if any data have been obtained on this subject. It would appear that in the future the diffusion theory could be used to predict the relative efficiencies, since the film thickness, bubble size, velocity effects, etc., are identical for all components. Deviations from the perfect gas laws must be allowed for, however, and fugacities substituted for pressures when operating a t high pressures. If we consider a simple case, the absorption of a gas composed largely of methane but containing small and equal molecular percentages of ethane, propane, butane, and pentane, and assume that the perfect gas laws hold, the relative deviations from equilibrium may be qualitatively calculated. The equation for diffusion of each substance through the film is given by W
MDPAn
If z were the same for all constituents and p,t substantially equal to P: WIAsM = C D A p
1090
INDUSTRIAL AND ENGINEERISG CHEhIISTRY
However, Colburn and Gilliland and Sherwood have shown that 2 is not exactly the same for all materials. Assuming Gilliland’s data inside tubes to apply :
Vol. 26, No. 10
Evaporation in tankage is due to two major sourcespumping and breathing. If a n empty tank is being filled with a volatile product such as gasoline, the air in the tank is expelled as the gsqoline comes in. At the surface of the gasoline W/AOM = CDOS6Ap in contact with the air, there will be a tendency of the liquid The value of D mill decrease in going from ethane to pentane to vaporize and to saturate the air, in the vapor space. However, the rate of evaporation will depend on the diffusion of gasoline vapor through a stagnant layer of air to the vapor s p a c e a b o v e . T h e thickness of this stagnant layer will depend on the natural or forced convection currents i n t h e v a p o r space, which in turn will be controlled by other factors as noted below. The second source of evaporation in tankage, so-called breathing, is due to daily and seasonal changes in the temperature of the surroundings. During the daytime the hot sun beats down on the tank and tends to heat the liquid as well as the vapor above it. As the temperature of the vapor riqes, it expands and p a s e s out through openings in the tank roof, carrying out air and gasoline vapor. As the hiin goes down, the tank cools and the vapors contract, drawing in air from the outside. This daily fluctuation in t e m p e r a t u r e t h u s causes an appreciable loss of maMODERNCOMBINATION CRACKING UNIT, SHOWINGDISTILLATION COLUMNS ABOVE, terial. HEATEXCHANGERS BELOW.AND FURNACE AT RIGHT There are several ways by means of w h i c h s u c h losses can be miniaccording to Gilliland’s (6) equation (units in the metric sys- mized. One method is to connect the vapor outlet to a flexible bag, which will expand and contract with fluctuations in tem-centimeters, seconds, grams, O C., atmospheres), temperature. A second method is to use a floating roof, which is sealed a t the sides and floats above the liquid so that there is practically no vapor present. Other methods are to use heavy insulation or a coating of low emissivity on where the subscripts denote the two vapors interdiffusing. the tank to minimize heat pick-up, or to connect all the vapor D0sb6will not be very different for these various materials, howlines to a gas absorption or compressor plant. ever, and essentially the diffusion rate of each will depend on A method has been devised in this laboratory to measure the difference in its partial pressure in the gas phase and a t these losses accurately (19). Since the evaporation is simple the liquid interface. If we assume that the liquid diffusion batch distillation, a determination of the vapor pressure of the rate is very rapid, the interface will have essentially the same gasoline before and after storage permits ready calculation of partial pressure as the main liquid body, Under these the loss sustained. In some cases the losses are great enough conditions, since the original partial pressures in the gas to be measured adequately by gages, but this method is not phase are the same, and a t equilibrium the partial pressures very accurate in general. in the liquid and gas phases will be the same but different for An understanding of the mechanisms involved in the losses each component, it is obvious that the deviations from equi- of volatile components is of considerable value in deciding on librium will be greatest for pentane and least for ethane. the proper steps to be taken. Radiation from the sun is of the Under more general conditions where the percentagec of order of magnitude of 350 to 400 B. t. u. per square foot per the entering gases are widely different, the problem becomes hour when a t its peak. During the daytime the sun radiates difficult, since p,/ will vary from gas to gas and with time of to the tank surface. The tank partially absorbs the sun’s contact, and A p will vary with the relative amounts ah- radiation, depending on its emissivity, and radiates back to sorbed. In general one would expect that the component- the atmosphere, depending on the temperature it finally possessing the highest vapor pressure will have the lowebt attains; it picks up or loses heat to the atmosphere by conmolecular weight and highest diffusivity and therefore more vection and traiwmits heat to the liquid and vapor by natural moles will diffuse per unit difference in partial pressure. or forced convection. The tank roof and part of the sides However, the percentage approach to equilibrium may not radiate to the liquid surface, and the liquid surface loses heat always be greater for the more volatile component, as thiq by evaporation of the liquid and picks up from or loses heat depends on the average Ap as well as pQ/. to the liquid body below and the vapor above by natural The major losses of material in petroleum convection. The rate of evaporation is controlled by the EVAPORATIOK. refining are due to evaporation and drainage of oil. Evapora- general diffusion law: tion takes place not only by leaks from processing equipment W MDPAp but also from tankage, separating devices, and loading El== facilities.
I N D U S T R I A L ,4?J D E N G I r\; E E R I S G C H E 31 I ST R Y
October, 1934
x will be determined largely by natural convection currents set up because of heat transfer in the vapor space, and Ap will vary with the temperature of the evaporating surface and the partial pressure of vapor in the space above. Although the above mechanism is very complicated, it may be possible in the future to calculate what losses should be expected by making a complete heat balance in the above manner. All of the individual items can be calculated a t least approximately by themselves, but no attempt has been made, apparently, to combine them in this manner. Obviously the easiest method is to determine the losses directly, but it is difficult to apply data obtained on one stock to the evaporation of another, or even to the same stock in different localities. It is interesting to note that the volume of material lost in a simple tank is nearly the same whether the tank is nearly full or nearly empty. This would be difficult to explain if the vapor space were always saturated with vapors but appears quite reasonable when diffusion rates are considered. With a large vapor space Ap average will be greater than when the tank is nearly full, and the rate of evaporation will be considerably greater but not proportional to the increased vapor space. More vapor and air will be expelled each day as the temperature fluctuates, but the expulsion will not be proportional to the vapor space volume and the vapor saturation will be less, Apparently the net effects of these various factors nearly counterbalance. I n every refinery there are sources of leakage to the sewer system due to leaky pumps, lines, and tanks, as well as to withdrawal of water-oil emulsions from treating operations. This oil may run from 1 to 5 per cent of the crude run a t the refinery. It is obTiouqly desirable to recover the oil, both from the economic standpoint as well as to keep from polluting the water unduly. The water is generally run into separating boxes, which act as large settling basins, in which the water flow is very slow and the oil is able to rise to the top, from which it is skimmed off and reprocessed. The oil lost in the effluent from the separators is easily determined by a steam distillation and extraction, but it is more difficult to determine the possible losses by evaporation. A large amount of work has been done on determining the evaporation of water from large surfaces. Perhaps the best data are those by Hinchley and Himus (8) who propose: W/AO = (0.0063 0.00084u)Ap where W / A e = water evaporated, lb./hr./ sq. ft. Ap = difference between vapor pressure of water at the surface and in the air, mm. Hg u = linear velocityof air, ft./sec.
Hine's equation when converted to Hinchley's units is equivalent to : TY/As
= MAp(0.000072
For water, therefore, V W/Ae
W
=
Hg wind velocity, miles/hr.
W
+ 0.00088~)Ap
MDPAp =
RTp,/r
where x varies with air velocity a4 well as the expreysion p / p D . Since Ap is generally small, and if 5 varies as ( p D / p ) o44 ( 7 ) TThen the properties are taken in the main gas stream, a simplified form of the exact equation might be TY/AO = constant X M D o J 6 ( u p ) o . 8 A p
Very approximately, D varies as the square root of the inolecular weight, and the above equation becomes for liquids of low vapor pressure evaporating in air a t ordinary pressures and temperatures : W/As
=
0.00030M0~'S~0~8 Ap
This equation checks the data by Hinchley and Hine satisfactorily and may be used for rough approximations as follows. Example. = 10,000 sq. ft., separator comArea pletely covered with oil Wind = 10 ft./sec. Surface = 100" F. (vapor pressure, 5 mm.) Mol. weight of material evapd. = 100 Oil loss per day = 10,000 X 24 X 0.00030 X 100°,i5 X X t = 70,000 lb. or about 10,000 gal.
TYPICAL PETROLEUM DISTILLATIOPI COLUMS M ITH PROVISION FOR W-ITHDRAM ING SIDE STRE.4hIS
AT
18 and
(0.0013
KO
Sherwood ( I ? ) recommends the use of a more general equation with the same units : w / A e = 0.021 A ~ ( u ~ ) o . ~
+
=
=
+ 0.000049~)
which is slightly below Hinchley's equation, particularly a t low velocities. With Colburn's and Gilliland's results as a bask, one would expect that the diffusion coefficient should enter tlie equation and that the more exact equation would be,
+
Hine (3) has studied the evaporation of chlorobenzene, m-xylene, nitrobenzene, and toluene from a pan 60 cm. in diameter in a wind tunnel and proposes for his apparatus: Gram moles/hr. = Ap(0.l 0.lV) where Ap = vapor pressure of liquid, mm.
1091
SEVERALPOINTS
The accuracy of the above equation has not get been checked in actual practice except by extrapolation of data obtained in small pans under similar conditions and by material balances on oil into and out of a separator. Data on small pans are not very desirable, as side effects are quite large and evaporation is accelerated. However, it is extremely important that such s e p a r a t i n g devices be watched carefully, and every effort made to keep oil of high vapor pressure from entering the sewer systems, or if this is impossible it might actually be advantageous to put a stock of low vapor pressure into the separator to reduce the average vapor pressure. It may be of some interest a t this point to compare the effective film thickness due to diffusion and that due to heat transfer for air flowing above a liquid surface. The best available equation for heat transfer is based on data by Jurges (IO): h = 0.50u0.78above u = 16 (where u is in ft./sec.) 0.99 0 . 2 1 below ~ u = 16 Assuming u = 10 ft ./set., h = 3.1 R. t. ti./ sq. ft./" F./hr.
h
=
+
At 60' F., k
=
0.0135 a n d x
=
0.0135/
3.1 = 0.00435 ft. or 0.133 cm.
INDUSTRIAL AND ENGINEERING CHEMISTRY
1092
Using Sherwood’s equation for water: W/AO = 0.021 (10 X 0.076)0.sAp
0.0168 lb./hr./sq. ft./mm. gram/sec./sq. cm./mm. 18 X 1 X 0.26 X 1 W RTp,fr0 82.07 X 288 X =
= 2.28 X M P D Ap x=-=
=
0.116 cm.
This would appear to be an excellent check since Gilliland’s data on inside tubes show that for water the heat-transfer “effective thickness” is 10 to 15 per cent greater than the diffusion thickness, and the heat transfer data by Jurges on a small plate (0.5 meter square) are not strictly applicable to large bodies where the length is infinite. For gases other than air, very little is known about the heat-transfer coefficients. However, since h for flow inside tubes is proportional to the specific heat, a rough estimation can be made by assuming z proportional to k/c. The following equation, based on the Sherwood equation for water diffusion into air, is therefore proposed tentatively for diffusion of any vapor from a large plane surface to any gas flowing in turbulent motion above it:
Thus a stationary thermocouple in a gas stream that is hotter than the surroundings will not measure the gas temperature but will show a temperature determined by the balancing of heat absorbed by it from the gas and heat radiated by it to the surroundings. The true temperature may be calculated approximately but it is much more desirable to use a velocity thermocouple in which the gas is sucked very rapidly past the thermocouple junction, and radiation to the surroundings is minimized. In a similar way a large number of laboratory workers have not fully appreciated the fact that a temperature taken in the gas stream in an electric furnace does not represent the true temperature. In this case it is more difficult actually to measure the true temperature since often the product cannot be removed through a velocity couple. The corrosion of furnace tubes a t high temperatures may be partially due to erosion effects caused by very high velocities. It has been noted that the outlet end corrodes very much more rapidly than the inlet or the middle of a tube. The erosion effect on the steel itself cannot be a very important factor, but the erosion of protective films due to increased turbulence may be the cause of increased corrosion a t this point.
W - MPDAp - RTp,f2
xi where x =
30k
o,44
(in consistent English units)
Applying this equation to the previous example we obtain : x =
30 X 0.0135 = 0.00380 feet 0.238 X (36,000 X 0.076)0.8 X (0.60)0.44 = 0.116 cm.
The application of the equation to evaporation in sewers is more complicated. The average composition of the material evaporating must be determined or estimated as this will, in general, be different from the material in the separator. From this the average moIecular weight can be determined, the diffusivity calculated by Gilliland’s equation above, and the expression p / p D evaluated. The rest of the calculation is reasonably straightforward since the physical properties of the evaporating material can be readily determined or estimated. When more adequate data are available on heat transfer and diffusion to gases flowing over large plane areas, this equation will undoubtedly be modified somewhat. Such an equation can be applied to a large number of processes such as the following: (1) Drying of flat surfaces with surface evaporation controlling. ( 2 ) Evaporation of water from large bodies such as lakes. (3) Evaporation in oil separators. (4) Solar evaporation of salt solutions.
MISCELLANEOUS. There is a large number of miscellaneous applications of the film theory in petroleum technology. Among these may be mentioned the acid or solvent treating of oils. In the first case there is a chemical reaction occurring with subsequent diffusion of reaction products. However, the method of contacting is rather crude, consisting of turning the stock over with direct steam or air. The second is purely a diffusional process, limited a t equilibrium by the partition coefficients of the various components. The burning of fuels in furnaces is to a considerable extent a diffusional process as shown by several authors recently. True temperature measurements in gas streams may be obtained by using the principles suggested by the film theory.
Vol. 26, No. 10
A C c D d
E j
F
= =
= = = = = = = =
g h k =
L,L,,L,
=
m = M =
P = Ap =
1
’ ! i ! r =
t = At = T = u =
V = W = x = p = /L
=
p = 0 =
Nu Pe
Pr
= =
=
NOMENCLATURE (Consistent English Units) area, sq. ft. constant sp. heat, B. t.u./lb./’ F. diffusion coefficient, sq. ft./hr. diameter, ft. late efficiency Lction factor frictional resistance per unit area, lb./hr./hr./ft. acceleration of gravity, ft./hr./hr. heat transfer coefficient, B.t.u./sq. ft./’ F./hr. thermal conductivity, B. t. u./ft./’ F./hr. length factors, ft. area of cross section hydraulic radius ft. wetted perimeter mol. weight, lb. pressure (total), lb./sq. ft. pressure gradient, lb./sq. ft. log mean pressure of inert gas in film, lb./sq. ft. gas constant, lb. ft./‘ R. latent !eat, B. t. u./lb. temp., F. temp, gradient, ’ F. abs. temp., 460 F. = R. linear velocity, ft./hr. molal vol. of liquid at atm. B. P., cu. ft. mass, lb. film thickness, ft. density, lb./cu. ft. viscosity, lb./hr./ft. expansion coefficient, 11” R. time, hr. Nusselt group, hL/k Peclet group, Lupc/k Prandtl group, c @ / k Reynolds group, L u p / p Grashof group, Lap2,9Atg/p2
),
(
+
O
Re = Gr = Subscripts: rn = average B = film boundary f = mean a m I) = vapor
LITERATURE CITED (1) Arnold, Physics, 4, 255 (1933). (2) Carey, Chemical Engineer’s Handbook, p. 1189, McGraw-Hill Book Co., New York, 1933. (3) Colburn, IND.EKG. CHEM.,22, 967 (1930). (4) Ibid., 26, 432 (1934). (5) Colburn, Trans. Am. Inst. Chern. Engrs., 29, 174 (1933). (6) Gilliland, IND.ENQ.CHEM.,26, 681 (1934). (7) Gilliland and Sherwood, Ibid., 26, 516 (1934).
October, 1934 (8)
INDUSTRIAL AND ENGINEERING CHEMISTRY
Hinchley and Himus, Trans. Inst. Chem. Engrs. (London), 2,
57 (1924). (91 Hine. Phvs. Rev.. 24. 79 (1924). (10) Jurges, Beih. Gesundh. In;., 19 (1924). (11) Kirkbride, IND. ENG.CHEM., 25, 1324 (1933). (12) Ibid.. 26, 425 (1934). (13) Kirschbaum and Kranz, Chem. Fabrik, 7, 176 (1934). (14) Monrad and Badger, IND. ENG.CHEM.,22, 1103 (1930). (15) Prandtl, Physik. Z . , 11, 1072 (1910). (16) Reynolds, Proc. Jlanchestw Lit.Phil. SOC.,14, 7 (1875). \-,
I~
-
1093
Engineer’s Handbook, p. 1222, McGrawHill Book Co., New York, 1933. (18) Stanton, Brit. Advisory Comm. Xironautics, Rept. & .)fern., (17) Sherwood, Chemical
94 (1913). (19) Stauffer, Roberts, and Whitman, 2, 88 (1930).
IND. ENG.CHEar., Anal. Ed.,
RECEIVED July 30, 1934. Presented as part of the Symposium on Diffusional Processes before the Division of Industrial and Engineering Chemlatry a t the 88th AIeetmg of the Amerlcan Chemical Society, Cleveland, Ohio, September 10 t o 14, 1934.
Diffusion of Vapors through Gas Films T. K. SHERWOOD AND E. R. GILLILAND, Massachusetts Institute of Technology, Cambridge, Mass.
D
IFFUSION plays a tremendously i m p 0 r t a n t
gas flow past the liquid or solid phase, it seems probable that there exists a thin layer of gas moving in stream-line or viscous motion over the surface of Ithe other phase, and that the flow breaks suddenly into turbulent motion beyond t h e outer boundary of this viscous layer. If this is the nature of the film, it seems probable that the thickness of the laminar layer fluctuates rapidly and to a considerable degree, owing to the turbulent motion of the main gas current. The experimental evidence apparently does not exclude the possibility, however, of a continuous gradation in turbulence from the surface of the solid or liquid phase through the film to the main body of the gas stream. I n the turbulent gas stream the movement of vapor through the gas is mainly by the mechanism of turbulent mixing or eddy diffusion. Eddy diffusion is very rapid, but the distances involved are much greater than in the relatively stagnant film so that it is possible for the eddy diffusional resistance to be as great or greater than the resistance to molecular diffusion offered by the laminar film. The total resistance to diffusion of the gas film may be considered to be the sum of the resistance of the turbulent layer to eddy diffusion and the resistance of the laminar layer to molecular diffusion. The two diffusional mechanisms are quite different in nature. Since the nature of the film is not fully understood, the attack on the problem of diffusion through gas f 3 m s must necessarily be empirical. This empiricism may be veiled by the introduction of the theoretical equations for diffusion in stagnant gases, but appears in the treatment of the “effective film thickness” involved in using this method of approach to the problem. For example, the Stefan equation for the steady-state diffusion of one gas through a layer of a second stagnant gas is :
The nature of a gas f i l m is discussed briefly and the application of the Stefan-Maxwtdl equation to diffusion in gas films is explained. The results of experiments on rates of vaporization of various liquids into air are reviewed, and rules are given for estimating the diffusion rate of a vapor through a gas film, on the basis qf data on the diffusion rate f o r another uapor. Numerical examples illustrate the necessary culculations. Derivations of algebraic equations connecting the absorption coeficient Kca with the height of packing equivalent to one theoretical plate (H. E. T. P . ) are given, and the use of the latter concept in the design of packed towers .for absorption is discouraged.
role in industrial processes because the capacity and consequently the fixed charges on many types of i n d u s t r i a l equipment are determined by the rate of diffusion of heat or of material f r o m o n e p h a s e t o a n o t h e r . Diffusion in gas films is one of the most important technical problems which confronts the chemical engineer. The rate of interaction of a gas with a l i q u i d o r solid m a y be governed by the rate of a slow chemical reaction, or by the slowness of diffusion t h r o ugh the liquid phase. In many -of the most i m p o r t a n t of s u c h operations, however, the rate a t which the operation proceeds is determined by the slowness of diffusion in the gas phase. This condition may be summarized by the statement that “diffusion through the gas film is controlling.” Such is the case in the absorption by liquids of soluble gases from mixtures with an inert gas; in adsorption of gases by solid adsorbents; in the air-drying of wet solids; in vaporization of water or other liquids into air, as in humidification; in condensation of vapors from mixtures with noncondensable gases, as in dehumidification; in the evaporation of solvents, as in drying of lacquers; and in the combustion of solids a t high temperatures. In interphase reaction, the distribution of diffusional resistance in the gas phase depends mainly on the velocity characteristics of this phase. For the case of a quiescent gas phase, as in a bubble rising through a deep liquid layer, the diffusional resistance is constant throughout. If the gas phase is in laminar flow, the diffusional resistance is still constant at all points, but the progressively lower mass velocity of the gas as the interface is approached causes a very different distribution of the diffusing substance from that which would be encountered with a stagnant gas. In the case of turbulent flow a large resistance to diffusion in the gas phase is encountered in a narrow region adjacent to the iquid or solid phase. This fact has been well understood for a number of years, as evidenced by the widespread use of the phrase “gas film.” The physical nature of this film is, however, not well known, although it appears certain that it is not the simple layer of perfectly stagnant gas which affords such a convenient, although erroneous, mental picture of the reason for the concentration of the diffusional resistance near the phase boundary. Under conditions of appreciable
where N A
diffusion rate per unit interfacial area, gram moles/ (sec.)(sq. cm.). D = diffusivity of system, sq. cm./sec. P = total pressure, atm. R = gas constant: (cc.)(atm.)/(gram mole)(’ K.). T = abs. temp., K. z = thickness of stagnant gas layer, cm. k~ = film coefficient, grams/(sec.)(sq. cm.) (atm.). =
