INDUSTRIAL AND ENGINEERING CHEiWISTRY
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Vol. 20, No. 10
Dehumidification of Air‘ C . S. Keevil a n d W. K. Lewis DEPARTMENT OF
CHEMICAL
EKGINEERIXG, h’1ASSACHUSETTS
I
T HAS long been known that under special conditions it is possible partially to dehumidify unsaturated air by water-cooling ~ t h o u the t necessity of first bringing the air to its saturation point. Carrier and Busey2 recognized this in the case of pipe coolers. but apparently not in the case of spray dehumidifiers. The phenomena have been discussed on the basis of interfacial diffusion of both heat and vapor through the gas film on the ~ u r f a c e but , ~ the relationships and their significance have not hitherto been doarly appreciated. D i a g r a m m a t i c Representatien of Relationships
I N S T I T U T E OF
TECHXOLOGY, CAMBRIDGE,
M a t h e m a t i c a l Representation
A mathematical statement of the above
Received May 28, 1928. * J. Am. SOC.Mech Eng., 33, 1649 (1911). Walker, Lewis, and McAdams. “Principles of Chemical Engineering,” 438, 442, and 462, McGraw-Hill Book Co , Inc.. 1923. 1
p
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as follows:
Let G = PoundsdrY air Per minute s = humidheatofair =0.24+0.48€€ h = coefficient of sensible heat transfer k‘ = coefficient of vapor diffusion A = area of contact of air and water t = air temperature t, = temperature a t air-water interface H = absolute humidity; pounds water per pound dry air
For the transfer of sensible heat through the air film, we may write Gsdt = ItA
In Figure I let the line LL represent the interface between cold liquid water and a mass of hot humid air. The line MJI is the outer surface of the effective gas film in contact with the water. The point A represents the temperature of the water surface and B that of the outer surface of the gas film. Since the temperature of the main body of the gas will be kept reasonably uniform by convection, the temperature gradient will be represented by some such line as ABE. Let the point D represent the M A I N BODY OF A I R humidity of the main GAS L FILM M body of the air, and c o n s e q u e n t l y also of TEMPERATURE E the outer surface of the gas film. Assume that the temperature A is HUMIDITY below the dew point of the air. The saturation humidity corresponding to A must therefore be lesq than D and FIG I may be represented by the point C. In other L M wordy the air in actual contact with the inter!ace LL cannot poqsibly have the humidity D because it is a t too low a temperature to hold that amount of moisture. Hence thew muqt exist through the gas film a humidity gradient such as CD. Under this gradient water vapor will diffuse from the main body of the air through the film. and because the inner surface is cold. this vapor will condense a t the interface. It should be noted that such condensation in no wise involves the assumption that the main body of the air is saturated. The previous paragraph was based on the assumption that the air was in contact with liquid water. If, however. the air is cooled by a solid surface, such as that of a pipe, the temperature gradiant AB will be set up through the gas film just as effectively as if the cooling medium were water. Since, however, the temperature A is below the dew point of the main body of the air, the air in contact with the surface of the metal cannot possibly retain its original quantity of water, but condensation must occur. This condensation wets the surface of the metal and reduces the problem to that of the previous case.
kfASS.
- t,)
(1)
- Hs)
(2)
(t
For the diffusion of water vapor, GdH = k’A ( H
DiTiding (2) by (1) d- H_ - sk‘ ( H - H , ) dt h i t - t,) sk‘ dt - -dH ( H - H,) It (t - t a )
Assume that H,and t, remain constant and neglect vai iation in the value of s at low humidities. We may then integrate between the limits of H I and H z and ti and t?. wliich gives
It has beeii sh0~1-n~ that h/k’ = s. Therefore, equation (4) reduces to H ti - t , -I-- H , - H2 - H s ti - t,
(3)
This equation gives the history of a mass of air subjected to dehumidification by contact with water of constant surface temperature. It is well known that for unsaturated air in contact with water a t the wet-bulb temperature, the path of the air during cooling and humidification is shown on the ordinary humidity chart (absolute humidity us. temperature) by a straight line joining its initial condition with the wet-bulb temperature. If the water is a t the dew point, the path of the air is a horizontal straight line-i. e., the air cools without change in humidity. The position of saturated air is represented by a point on the saturation curve, and in the past it has usually been assumed that during dehumidification the path followed is along this curve. Equation (5) states that. for the dehumidification of unsaturated air by contact Kith water of constant surface temperature, the path followed by the air is a straight line joining the initial air condition with the saturation point a t the temperature of the surface of the water. More generally, a t low humidities the direction of change in condition of air in contact with water, as shown in the humidity diagram, is always toward the point on the saturation curve corresponding t o the surface water temperature. Experimental
This conclusion is so important and so a t varianve with widely accepted concepts that it was felt that experimental confirmation was essential. 4
Lewis, Tvans. A m . SOL.Mech. Eng., 44, 325 (1922)
I N D UXTRIAL A N D ENGINEERIA7G CHEXIXTRY
October, 1928
Unsaturated air was passed upward through a wetted-wall column, in contact with water below its dew point. The time of contact was brief and sufficient water was used so that the average water temperature was very nearly constant. The initial air condition was determined by first saturating it a t a k n o m temperature, then heating it and taking its temperature just as it entered the column. The exit air temperature was taken just beyond the column. A bend in the exit tubing minimized radiation loss from the thermometer to the cold water, and this tubing was enclosed in a highly evacuated glass jacket, so that the temperature at which the air left the column was obtained with considerable accuracy. For determining the humidity of the exit air a special form of dew-point hygrometer was devised. This
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consisted of a thin-walled, water-cooled copper tube, nickelplated and polished, surrounded by a glass tube. The air passed through the annular space continuously. Provision was made to vary the temperature of the water to cause appearance and disappearance of a fog on the polished surface of the metal. Since both air and water flowed a t a considerable velocity, and since the heat necessary to dissipate the fog was supplied from the water within the tube, the objections to the use of the ordinary Regnault hygrometer do not apply and the temperature indicated by the water thermometer may, without appreciable error, be taken as the temperature of the outside of the tube. Runs were made with entering air at substantially constant temperature and humidity and the extent of cooling and dehumidifying was progressively increased by increasing the wetted area in each successive run of the series. The experimental points,6 two for each run, are shown in Figure 11. The group to the right represents entrance and that nearer the saturation curve, exit air conditions. The average water temperature is shown as t, on the saturation curve. There was no way to determine the temperature of the water surface, but the average water temperature rose less than 1O F. during its flow down the column, and it is believed that in these runs the surface temperature cannot be far above this average. Another series of runs, shown in Figure 111,was made with constant wetted area, but with different initial conditions. These plots show that the path of the air is undoubtedly toward the water condition. If the straight line connecting the experimental points is extended, the intersection with the saturation curve is in some cases above the point which represents the water condition. In other cases, where the initial air is nearly saturated, the extended line does not intersect the saturation curve. The surface temperature of the water of necessity rises during the dehumidification process. I n these experiments it was only possible to measure the average temperature of the water, not the true surface temperature. Therefore, Original data from thesis presented to the faculty of the Massachusetts Institute of Technology in partial fulfilment of the requirements for the degree of master of science, by C. S. Keevil, June, 1927.
1059
the average water temperature does not properly determine the point on the saturation curve toward which, according to equation ( 5 ) , the air proceeds during the dehumidification process. The true surface temperature is somewhat higher than this average. Inspection of Figures I1 and I11 shows that in all cases in which the initial temperature was high the straight line joining initial and final conditions tends to hit the saturation curve above the average temperature of the cooling water, thus confirming the conclusion just given. However, in runs in which the initial temperature was lower and particularly in those cases where the initial air is nearly saturated, the continuation of the straight line connecting the initial and final states not only falls below the point on the saturation curve corresponding to the average water temperature, but would never hit the saturation curve a t all. However, in all experimental runs in which this effect was a t all marked, a straight line connecting the initial air condition with a point on the saturation curve corresponding to the average water temperature would cut and cross the saturation curve between these two points. Hence, if the air in the process of dehumidification actually followed this line, the air in the interior portion of the film next to the water surface would of necessity be supersaturated. Since this air in the film is subjected to this condition continuously, condensation in the film is to be expected. This Condensation, releasing as it does latent heat which must be conducted through the remainder of the gas film, lessens thereby the heat-conducting capacity of this film for sensible heat. Therefore, the air leaves the apparatus a t a higher temperature than would correspond to the straight line connecting the initial air condition with t,, as is shown by the experimental results in these cases. This phenomenon is a complicated one and is being subjected to further study. One of the most vitally important consequences of these results has already been mentioned elsewhere6-namely, that in the condensation of water from unsaturated air the heat of condensation is evolved, not out in the main body of the air, but a t the interface between the air and the water layer on the cooling surface. Therefore, this latent heat does not 025
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travel by the process of heat conduction through the gas film. I n many cases this gas film is the controlling factor in the final resistance to heat transmission. I n the past the conductivity of such films has usually been computed on the assumption that all the heat, both latent and sensible, travels through the films. It has never been possible to reduce the experimental results obtained under such conditions to orderly analysis. This new point of view makes it possible to attack the problem from a different and more promising angle. Limitations of Application
Attention should be called to the fact that the derivations here given assume conditions of low humidity-i. e., low ratio 6
Lewia, Chem. Met. En&, 84,736 (1927)a
INDUSTRIAL AND ENGINEERING CHEMISTRY
1060
of condensable vapor to non-condensable gas. Furthermore, the experimental results of Figures I1 and I11 are limited to such cases. At high humidities, while the same principles apply, computation methods become more involved. Further work is being done in this laboratory to include
Vol. 20, No. 10
cases where the initial humidity is much higher and where liquids other than water are employed, special attention being devoted to the concomitant problem of heat transmission and to securing more precise data than were possible in these preliminary experiments.
X-Ray Methods Used in Determining Structure of Cellulose Fibers’ Organomolecular Investigations 0. L. Sponsler UNIVERSITY OF CALIFORNIA AT Los ANGELES, CALIFORNIA
A
S a result of x-ray diffraction studies of plant fibers, three hydroxyl groups produces the destruction of the fibrous carried on during the past few years, a conception of nature of the material; and the substitution of larger groups, cellulose has been obtained in which glucose residues such as acetyl, tends to weaken the fiber, as such, even when are pictured as occurring in long chains in the fiber wall. This three groups or less are involved. chain structure, proposed by Sponsler2and Sponsler and Dore13 A considerable amount of work is still to be done, along the has been verified lately by hleyer and Mark4 by somewhat lines suggested above, in the correlation of x-ray data with t h o s e from chemical and different x-ray methods, but physical reactions. It is for a complete agreement in all that reason that the followdetails has not yet been The very fine capillary tube-like character of the fibers ing discussion is presented reached. T h e present introduces several complicating features into the of several methods used in status of these investigainvestigations of their molecular structure by x-ray x-ray work w i t h fibers, tions is briefly summarized methods. A n approximately parallel arrangement which are somewhat differhere. They show (1) that a of the fibers into a block which can be turned as desired ent from those used with space lattice with structural with respect to the x-ray beam gives control of the crystals or crystal powders. units of 84-glucose residues atomic planes in the fibers to a limited extent. When In general, x-ray work exists in the wall; (2) that the beam passes lengthwise through the fibers, the block with fibers i n v o l v e s t h e these residues are attached resembles a mass of crystal powder; when at right same fundamental methods by glucosidal linkages into angles to the fibers the block resembles in its reflections and principles as with ordilong chains; and (3) that the a single large orthorhombic crystal: but when at any nary crystalline materials,6 chains are parallel to one other position, on account of the cylindrical construcbut there are a few unusual another and extend lengthtion of the individual fiber, it resembles a block concomplications when working wise of the fiber. Those taining a few large crystals so oriented that their with fibers t h a t a r e d u e features of the fiber wall are b axes are parallel but otherwise in random arrangeprimarily to the characterisfairly well established, but ment. tics of the individual fiber, other points need verificathat is. to its shaDe and tion. The distance between flexibility, and to t i e way the chains and the orientation of the glucose residues in the chain, as well as the orienta- in which it is formed in the plant. I n addition, the irregularity in the shape of the constituent structural units tends tion of the chains themselves, are still in question. In the fiber wall the glucose residues, acting as links to introduce further complications into the interpretation of of the chain, are held together through oxygen bridges by the x-ray diffraction patterns. The discussion may become somewhat clearer if we recall primary valence forces; while the chains are held to one another laterally by either secondary valence forces or by some kind very briefly the principles involved in x-ray diffraction. of residual force fields which produce cohesion. The primary When a beam of x-rays is directed on to a natural face of a valence forces, being much stronger than the other, give the crystal a t a suitable very small glancing angle, the effect is fiber different properties longitudinally from those laterally. somewhat as though it were split into two beams-a strong Qualitatively, at least, that construction is in agreement one which continues through the crystal in a straight line, with such physical properties of the fiber as tensile strength, and a weaker one which is diffracted a t an angle equal to the glancing angle. This effect is produced only when a swelling phenomena, and thermal expansion-properties which have different values for the longitudinal and lateral definite relation is established between the wave length, directions. This chain structure is also consistent with cer- the glancing angle, and the distance between the atomic tain chemical properties, such as those involving the formation planes, of which there must be a considerable number lying of substitution products of cellulose, at least to the extent parallel to the crystal face and separated from one another to which ester formation may occur before the fiber structure by equal distances. The diffracted beam does not come from is destroyed, for example, the esterification of more than a single atomic layer, but is an additive composite of many weak beams, each from one of the parallel layers. The 1 Received March 27,1928. Presented before the Division of Cellulose actual production of this resultant beam depends upon the Chemistry at the 75th Meeting of the American Chemical Society, St. Louis, conditions just mentioned; the intensity of the beam, Mo., April 16 t o 19, 1928. 2
J. Gca. Physiol., 9,221 (1925); 677 (1926). Vol. I V , p. 174 (1926). B w . , 61,593 (1928).
a Colloid Symposium Monograph, 4
6
1924.
Bragg, W. H., and W. L., “X-Rays and Crystal Structure;” tondon,
