December, 1941
INDUSTRIAL AND ENGINEERING CHEMISTRY
The experimental conditions are set forth which should be observed in order to obtain the greatest possible degree of reproducibility and to permit comparisons of experimental data obtained by different investigators.
Acknowledgment Considerable credit is due to J. M. Hiscott and Carl Pacifico, students in chemical engineering, who carried out most of the experimental work. Nomenclature initial concentration, % ’ solids by weight corresponding C,, to H , C,, = concentration, o/o solids by weight corresponding to H , Ho = initial settling height Hu = final or ultimate settling height =
Su
-
n
= =
CY
1491
exponent which is a function of compressibility constant which is a function of particle size
Literature Cited (1) Akamatu, H., J. SOC.Chem. I d . Japan, 13,456 (1938). (2) Comings, E.W., IND. ENQ.CEEX.,32,663 (1940). (3) Egolf, C. B.,and McCabe, W. L., Trans. Am. Znst. Chem. Engrs., 33,020(1937). (4) Freundlich, H., “Thixotropy”, p. 18, Paris, Hermann & Cie., 1935. ( 5 ) Stern, A. G., U. 5. Bur. Mines, Rept. Investigations 3556 (1941). ( 6 ) Ward, H. T., and Kammermeyer, Karl, IND.ENQ.C H E x . , 32, 622 (1940). (7) Work, L. T.,and Kohler. A. S., Trans. Am. Inst. Chem. Engrs., 36,701 (1940). P R a s E N r E D before t h e Division of Indusrrial and Engineering Chemistry at tho 102nd llceting of tho Arnericnn Chemical Society, Atlnntic City,
N. J.
Hu/Ho
Manganese in Deep Reservoirs EDWARD S . HOPKINS
AND
GEORGE B. MCCALL
Bureau of Water Supply, Department of Public Works, Baltimore, Md.
S
OLUBLE manganese is probably more often present in Data published in 1931 indicated that the seasonal presimpounded raw water supplies than is generally recogence of soluble manganese in waters from deep reservoirs nized. This condition may also be a characteristic of is due to the solution of this element as a bicarbonate. This material is dissolved by the relatively large concenfiltered water when stored in unlined reservoirs. Previous studies by Baylis ( 2 ) advanced the hypothesis tration of carbon dioxide present in these waters. A previous article stated that the manganese seemed to be that the dissolved manganese was leached from the underlying rock and unstripped soils. Weston (IS) stated that the leached from the rock strata underlying the reservoir, and manganese was dissolved by the action of organic and mineral that the continuous deposition of silt on the bottom of acids. An investigation by Hopkins and McCall (7) in 1931 such a reservoir would ultimately overcome this condition. Investigation during the past ten years indicates that indicated that the solution of manganese was caused by anaerobic fermentation of vegetation on the bottom of the unsilting will not overcome this phenomenon. On the contrary, newly deposited muck on the bottom of reservoirs stripped Loch Raven Reservoir, with the liberation of large will continue the trouble for many years in the future, quantities of carbon dioxide as a by-product which dissolved since the sediment contains a large proportion of decomthe manganese from the muck and underlying soil. The posed manganese-bearing vegetation. This is proved by biological activity was accelerated a t temperatures above new data obtained from studies of two reservoirs covering 20’ C. During the autumn “turnover” the water dropped different geological formations. During this ten-year period the manganese on the bottom of a very deep reservoir was practically constant each year, while the shallower reservoir was affected by seasonal “turnover”. The reservoir having seasonal turnover was completely depleted of manganese a t this period, with a subsequent resolution each succeeding year. Since removal of manganese is a coagulation problem in conjunction with water purification plant operation, the isoelectric point of manganese hydroxide has been deterINTERIOR OF MONTEBELLO FILTER PLANT AT BALTIMOR~ mined.
1492
INDUSTRIAL AND ENGINEERING CHEMISTRY
-
TABLEI. WEEKLY DATAFROM JUNE TO NOVEMBER, INCLUSIVE, AT No. 1 BRIDGE OF 7-1932iVn p. p. 0.05 0.06 0.04 0.05 0.08 0.07 0.03 0.08 0.13 0.25 0.56 1.14 1.04 1.76 6.40 4.00 5.30 1.78 1.20 0.22 0.12 0.11 0.07
A.
-
Ratio,
con/os 0.5 1.0 0.8 2.5 1.7 1.0 1.7 1.6 1.4 2.6 2.6 2.5 2.7 2.2 5.3 2.1 1.8 1.6 0.6 0.2 0.2 0.2 0.3
Temp., 0
C.
20.5 20.0 20.5 20.0 20.0 21.5 21.0 20.5 21.0 21.0 21.5 19.0 19.0 20.5 17.5 17.5 15.5 15.5 13.5 13.5 11.5 9.5 10.5
7
lln, p. p. m. 0.48 1.20 2.40 2.00 3.52 2.64 2.08 4.24 2.70 4.00 2.64 2.88 4.40 7.20 5.56 4.90 1.20 0.33 0.18
Ratio,
1933 Temp.,
c02/02
2.6 2.6 3.0 2.8 8.9 10.5 6.6 4.2 350.0 300.0 5.7 379.0 6.1 0.0 199.0 11.7 5.7 0.4 0.6
0
C.
23.0 19.5 22.5 25.0 23.0 21.5 23.0 18.5 22.5 18.5 18.5 20.0 16.0 17.5 16.0 13.0 15.5 6.0 3.5
p~ 6.8 6.7 6.9 6.9 6.7 6.7 6.6 6.8 6.5 6.6 6.7 6.3 6.7 -6.0 -6.0 -6.0 -6.0 6.9 6.7
Mn, p. p. m. 0.22 0.19 0.10 0.30 0.16 0.57 0.50 2.22 2.26 4.00 3.20 3.22 3.00 4.00 4.00 5.00 4.68 9.40 6.70 6.00 4.55 0.31 0.30 0.33 0.20 0.10
Ratio
1934 Temp.,
~02/dl 0.9 1.7 i:3 5.7 2.0 4.8 5.7 3.8 3.7 6.9 7.6 6.0 5.4 11.4 7.7 8.2 4.6 2.0 8.8 5.1 0.3 0.3 0.5 0.3 0.3
0
C.
20.0 21.0 22.5 22.0 20.5 20.0 23.0 24.0 22.5 22.0 20.5 22.0 18.0 18.0 18.5 17.5 22.5 17.5 16.0 17.5 15.5 11.0 10.0 10.0 7.5 10.0
THE
PIT 7.4 6.7 6.7 6.6 6.6 6.7 6.6 6.8 6.8 6.9 6.8 6.8 6.8 6.6 6.5 6.9 6.9 6.9 6.3 6.9 6.9 6.9 7.1 7.0 7.0 7.2
.
Vol. 33, No. 12
LOCHRAVENRESERVOIR
- &In,
p. p m 0.19 0.30 1.00 2.20 3.20 3.30 6.70 3.20 3.40
1941 Ratio T,emp., ~02jdn C. 1.1 1.3 3.3 3.6 4.3 4.1 6.7 3.1 3.5
18.0 17.0 19.0 19.5 23.5 21.0 20.0 22.0
p~ 6.8 6.7 6.6 6.8 6.8 6.7 6.8 6.9 6.9
-
to a temperature below 15" C., and the manganese was rapidly diffused throughout the reservoir. This diffusion reduced the manganese concentration each year to the point where it was no longer troublesome. It was also believed by these authors that, with the passage of time, silting would check this phenomenon by covering the manganese-bearing muck and soil with inert material. The completion of the Prettyboy Dam in 1932 created a reservoir holding 20 billion gallons of water and flooding 1500 acres of land. This new reservoir, 130 feet deep a t the dam, presented an opportunity to compare the underlying principles governing the solubility of manganese in a fairly deep reservoir with those in a somewhat shallower one, since the Loch Raven Reservoir utilized in the 1931 study is only 66 feet deep, although it covers 2500 acres of land and impounds 23 billion gallons of water. These two reservoirs cover large areas of land with contributing streams having the same general characteristics. Neither reservoir was stripped of vegetation, but stumps were grubbed before filling. Prettyboy Reservoir overflowed its spillway on August 23, 1933. The area flooded by this reservoir is composed entirely of Wissahickon schist, which does not contain manganous rock; therefore any manganese present in the muck of this reservoir was washed in with the silt or leached from the original plant life. A sampling station mas located in the Prettyboy Reservoir about 5.5 miles below the headwaters, and in the Loch Raven Reservoir about 8 miles below the headwaters. The pools a t these points are not seriously influenced by fluctuations of contributing stream flow, Samples of bottom maters were collected meekly in an apparatus designed for the purpose ( 6 ) .
Lock Raven Reservoir Table I presents analyses of weekly samples taken over the period from June to Xovember a t KO. 1 bridge about 2 miles above Loch Raven Dam. The water a t this point is 66 feet deep. There is a constant increase in manganese during the period when the water is above 20" C., with a sudden decrease a t the autumn turnover. This occurred when the temperature fell below 15" C. During the turnover period, fresh surface water diluted the manganese and carbon dioxide and greatly increased the oxygen concentration. This increase in oxygen concentration checked the biological activity and also precipitated a portion of the manganese as the hydrated oxide. The data in Table I disclose that the carbon dioxide con-
centration must be twice that of the oxygen, or there must be a carbon dioxide-oxygen ratio of a t least 2 before manganese will be dissolved and retained in solution. This is not surprising, since the previous study (7) disclosed that the solubility of the manganese was in direct ratio to the concentration of carbon dioxide, when the temperature had been higher than 20' C. for a t least 60 days. It is evident from this relatively high temperature that biological action is necessary to produce a high carbon dioxide-oxygen ratio. Additional evidence is that this phenomenon occurs under similar conditions each year and is probably due to enzymic action.
Prettyboy Reservoir Conditions in the Prettyboy Reservoir, which is 130 feet deep (Table 11),are quite different from those in the shallower Loch Raven Reservoir. The samples from this reservoir were taken a t the dam. During its filling in 1933 the pH value of the water vias quite high; it reached a maximum of 9.0, indicating that alkalinity was leached from the face of the dam. During this period the soluble manganese varied directly with the stream flow, and since the concentration was relatively high, it was present either as a sulfate or as a soil acid salt. However, in 1934 the carbon dioxide-oxygen ratio stabilized after 35 days of temperature above 20" C. a t a high value, and there have been instances of total depletion of oxygen. This increased carbon dioxide concentration, as the end product of biological action, raised the manganese content t o a maximum of 25 p. p. m. S o yearly turnover has taken place in this reservoir since the temperature has also stabilized a t about 12" C. The manganese concentration has continuously averaged 18 p. p. m. each year, indicating that biological action has not taken place. With yearly turnover, the stabilized conditions in this reservoir would vanish, and characteristics comparable to those of the shallower Loch Raven Reservoir would be presented. The pH of the Loch Raven Reservoir has continuously been slightly under neutrality, averaging 6.8. This condition suggests the existence of organic acids as an additional decomposition by-product, since the buffer action of dissolved bicarbonates would tend to increase the pH value if only carbon dioxide wcrc the contributing factor. This is confirmed by the average pH value of 7 . 3 in Prettyboy Reservoir since stabilization occurred. When variations in these data were noted, the figures mere carefully checked with stream flow records, and in every instance low values were caused by a greatly increased flow for those individual days.
INDUSTRIAL AND ENGINEERING CHEMISTRY
December, 1941
1493
L
TABLE 11. WEEKLY DATAFROM JUNE TO NOVEMBER, INCLUSIVE, AT PRETTYBOY DAM 1933
c
Mn Ratio Temp., p . p . h. COe/ds O C.
0.91 8.53 9.60 6.40 5.44 6.40 5.44 10.50 10.56 5.76 4.16 4.97 6.40 18.50 5.00 4.16 7.68
0.0 0.0
0.0
0.0
0.0 0.0
0.8 2.2 3.2 4.2 5.5 3.9 4.6 2.7 6.1 4.3 2.1
21.6 19.0 19.5 18.5 19.5 20.5 20.0 20.5 17.5 18.5 18.5 17.5 17.0 16.0 15.0 10.0 6.5
Mn pH
p. p.
1934
k.
0.80 1.34 5.00 1.17 1.30 3.51 3.21 3.08 7.68 6.16 10.64 13.28 7.04 14.40 7.04 18.18 15.00 25.00 20.00 19.00 17.00 18.20 17.00
Ratio
COe/ds 0.8 0.8
...
1.2 0.2 1.3 0.9 1.9 2.7 1.6 7.9 12.6 12.2 16.1 140.3 68.3 68.3 104.2 73.0 189.0 258.5 177.5 144.0
T:mz.,
7
PH
17.5 15.0 17.0 25.0 22.5 15.5 20.5 20.0 25.0 20.0
16.5 13.6 15.0 15.5 16.5 16.5 12.5 12.0 11.0 9.5 8.5 8.5 9.5
6.5 6.6 7.3 6.5 6.7 6.9 6.9 7.2 7.2 7.7 7.1 6.9 6.9 7.4 7.3 7.0 7.1 7.3 7.3 7.4 7.5 7.4 7.5
1935 Ratio Temp., COa/da C. 18.00 11.5 64.7 18.30 107.0 13.5 16.60 39.2 13.5 15.5 4.80 40.0 26.70 13.0 154.0 20.00 14.5 131.0 16.80 15.0 88.0 11.5 21.60 44.9 19.20 63.6 11.0 15.87 165.0 20.00 63.0 li:5 21.40 73.7 11.5 20.00 156.0 10.5 17.50 52.7 9.5 20.00 92.6 8.5
r
-
Mn, p. P. m.
pH
7.6 7.5 7.4 7.4 7.5 7.5 7.4 7.6 7.5 7.1 7.4 7.3 7.2 7.4 6.4
1941 Ratio Temp., COe/ds C. 14.80 171.8 11.0 13.80 12.0 71.0 14.40 12.0 0.0 20,oo 235.0 14.5 12.00 13.5 54.9 13.50 13.0 105.0 7h.3 43.00 14.0 17.00 13.5 0.0 15.50 12.0 181.8 16.00 0.0 12.0 16.00 0.0
Mn, P. P. m.
..
DH 7.3 7.3 7.3 6.9 7.3 7.2 73 7.3 7.3 7.3 7.3
Theoretical Considerations
LOCHRAVENRESERVOIR (above)
AND
PRETTYBOY RESERVOIR (below)
Decomposing plant life is a prolific source of manganese, since it is now known that this element is an important constituent of plant growth and is found in all vegetation (1). The organic acids and large quantities of carbon dioxide present with decomposition will break the manganeseoxygen complex found in plant life and produce a soluble manganese salt. Soluble manganese sulfate directly leached from soils and plants will also be present. Harden in 1919 (4) described the disintegration and solution of iron soil compounds by the action of carbon dioxide and organic acids. His concept is that these compounds are produced by the decay of organic matter due to bacterial action and also by the breakdown of inorganic material by chemical agencies which owe their origin to bacterial action. He believes that the enzymic action produced by all green plants, many molds, and a few bacteria is responsible for the production of large quantities of carbon dioxide as the end products of -organic decomposition. He further stated that nearly all ferrous compounds, especially ferrous carbonate, are readily acted upon by carbonic acid, are taken in solution as the bicarbonate, and are carried as such as long as the water contains an excess of carbon dioxide in solution. Purcell (9)indicated that organic deoomposition will cause ferric and manganic salts to give up oxygen and be reduced to ferrous and manganous compounds. These salts will finally be precipitated by oxidation. This was confirmed by Weber (11). Tillmans’ study (IO) supported this theory, since he indicated that the manganous salts are precipitated by oxygen and are subsequently slowly oxidized by the dissolved oxygen in the whter to those of a higher valence. Beijerinck (a), on the other hand, showed that bacteria and fungi are capable of transposing manganous carbonate to manganic salts. It is obvious, therefore, that the type of com-
Vol. 33, No. 12
INDUSTRIAL AND ENGINEERING CHEMISTRY
1494
#
TABLE111. MANGANESE STABILIZATION IN RESERVOIRS 1930 1931 June 0.19 0.28 July 0.34 0.46 Aug. 4.72 1.08 Sept. 1.13 Oct. 2.09 Nov. 0.60 a Prettyboy filling, water over
.. ..
,.
Loch Raven, No. 1 Bridge, 1932 1933 1934 1937 0.06 0.20 0.06 1:iQ 0.86 0:95 0.12 2.90 3.23 1.92 2.18 3.05 4.42 3.38 3.07 5.51 5.39 2.48 0.13 0.57 0.30 0.08 spillway September 23, 1933.
66 Feet 1938
1939
2:SO 3.63 4.50 0.82
1:i6 2.41 2.69 0.58
..
pound remaining in solution is more or less directly controlled by the specimen of organism creating the phenomenon. As shown by the following data, manganese in the bottom water of Prettyboy Reservoir and, it may also be assumed, of Loch Raven Reservoir is in the form of manganous bicarbonate and is held in solution by the presence of carbon dioxide: As Collected 7.3 13.6 62.0 0.0 15.2 28.0 4.5 Clear
PH Alkalinity, p. p. m. CO1, p. p. m. Dissolved oxygen, p. p. m. Mn, p. p. m. Fe, p. p. m. 0.01 N KMnOd. cc. Appearance
Aiter 48 Hr. in Atmosphere 7.0 8.0 23.0 6.0 11.4 0.05 2.0 Opalescent
The permanganate titration of the newly collected sample is equivalent to 25.1 p. p. m. of iron and indicates that all of the iron present is in the ferrous state. This titration also shows the manganese to be present in the manganous state, since none of it is oxidized by a double oxidation reaction. The corresponding titration upon the opalescent colloidal atrate from the settled sample gave a value of 10.99 p. p. m. as hydrated manganese. This equals the 11.4 p. p. m. of manganese as determined by the persulfate method. The precipitated manganese is equivalent to 9.0 p. p. m. of calcium carbonate, and the precipitated iron to 51 p. p. m., making a total of 60 p. p. m. compared to a loss of 56 p. p. m. as shown by the differences in alkalinity titration. These results confirm the fact that the manganese and iron are held in solution by carbon dioxide as the bicarbonate, since the alkalinity is due to this salt. It is further confirmed by the fact that the manganous bicarbonate in the absence of air is not further oxidized by permanganate. This is to be expected, since it does not contain an unstable ion. Manganous sulfate also is not oxidized by permanganate in the presence of air. Table I11 shows that the reservoirs have become stabilized in relation to manganese content; it proves definitely that purification procedu’res for the removal of this element during the period from July to November will be required for many years in the future, since concentrations above 0.1 p. p. m. are detrimental to a water supply. This fact is confirmed by the data in Table IV taken from plant operating records showing daily peaks each year above 1.0 p. p. m. Conditions presented in this table frequently TABLEIV.
Year 1924 1025 1926 1927 1928 1929 1930 1981 1932
MANGANESE (P. P. M.) IN RAWWATERAT MONTEBELLO FILTERS
Peak Day 1.67 1.11 1.43 1.10 0.50 0.86 0.92 1.33 1.00
Daily Av. for Peak Month 0.67 0.65 0.78 0.52 0.32 0.54 0.69 0.93 0.53
Av. per Day (Aug.Nov., Inolusive) 0.45 0.44 0.49 0.32 0.19 0.33 0.45 0.56 0.27
Daily Av. Year 1933 1934 1935 1936 1937 1938 1939 1940
Peak Day 1.10 1.25 1.80 1.16 1.57 1.30 1.05 1.33
for
Peak Month 0.61 0.78 1.09 0.79 0.73 0.74 0.82 0.84
Av. per Day (Aug.Nov., Inclusive) 0.48 0.52 0.65 0.47 0.40 0.46 0.44 0.44
..
1940 0.60 0.71 2.78 0:50
..
1941 0.25 2.13 4.15
.... ..
1933 O.9la 8.53 6.66 7.85 9.99 5.61
Prettyboy, 130 Feet 1934 1935 1940 2.08 18.00 , 2.78 18.30 8.16 10.20 9.60 10.44 21.17 20.00 18.92 14.17 15.00 18.40 19.98 22.00
.....
1941 14.34 22.12 16.12
... .... ..
occur in storage reservoirs, more or less unknown to the o p erating personnel.
Isoelectric Point The isoelectric point for hydrated manganous oxides is a t a pH value of 9.8 (Table V). Table V actually shows the maximum precipitation value; yet sulfates were absent at pH values greater than 9.8, and it is therefore obvious that this hydrogen-ion concentration is also the isoelectric point since only hydrated manganese oxides were present. If i t were other than the isoelectric point, sulfates would have been absorbed in the precipitate since the hydrated oxides were prcduced from a manganous sulfate solution by the action of sodium hydrbxide (8). This fact is of importance to water supplies having well sources without turbidity. It indicates that removal of manganese by purification processes using alkali to secure a pH value of 9.3 is a practical method for removal of this element from this type of supply. This waa confirmed by Hoover (6) who did not experience any trouble from soluble manganese in lime softening plants.
TABLE V. MAXIMUM PRECIPITATION OF MANQANESE (0.0001 M CONCENTRATION) PH 7.0 8.0 8.8 8.9 9.0 9.2 9.3 9.4 9.6 9.8 10.6 11.0 11.6 11.9 12.3
Residual Mn Mu./l. .. 6.49 5.49 5.49 3.00 1.90 1.00 0.28 0.11 0.03 0.00 0.00 0.00 0.00 0.00 0.00
-Precipitated
MOA. 0.00 0.00 0.00 2.49 3.59 4.49 5.21 5.38 6.46 6.49 5.49 5.49 5.49 5.49 5.49
MnMoles 0.0000 0.0000 0.0000 0.000045 0.000065 O.OO0081 0.000094 0.000098 0,000099 0.000100 0.000100 0.000100 0.000100 0.000100 0.000100
Per cent
0.0 0.0
0.0 45.4 65.4 81.7 94.9 98.0 99.4 100.0 100 I O 100.0 100.0 100.0 100.0
L
I n making this study the precipitated hydrated oxide was obtained by mechanically agitating a liter sample contained in a beaker exposed to the air for 15 minutes a t 100 r. p. m. and then allowing the sample to stand quiescent for an additional 15 minutes. The precipitate obtained in this manner had the following composition: pH = 9.2 3Mn(OH)1.Mn02.16Mn0 9.4 3Mn(OH)z.2MnOn.15Mn0 9.8 3Mn(OH)p.3Mn02.14Mn0 2Mn(OH)r.3MnOz.15Mn0 11.O 12.0 3MnOe.17Mn0 These precipitates vary slightly in composition with increased pH value. It is believed that by selective surfaceadsorption oxidation processes the precipitate will ultimately be converted into a mixture of manganous oxide and manganese dioxide in accordance with Weiser’s investigation (12).
Conclusions Silting of a reservoir will not remove soluble manganese since the deposited vegetation is manganese bearing. Reservoirs that are slowly silting will have troublesome concentra-
INDUSTRIAL AND ENGINEERING CHEMISTRY
December, 1941
1495
Literature Cited
(2) Baylis, J. R.,J.A m . Water Works AS800., 12,213 (1924). (3) Beijerinck, M.W., Zentr. Biochem. Biophys., 16,277 (1914). (4) Harden, E. C.,U. S. Geol. Survey, Professional Paper 113, 46-7 (1919). (6) Hoover. C. P., J . A m . Water Works hsOC., 23,1282 (1931). (6) Hopkins, E.S., Eng. News-Record, 100,870 (1928). (7) Hopkins, E. S.,and McCall, G. B., IND.ENQ.CHIOM., 24, 106 (1932). (8) Hopkins, E.S.,and Whitmore, E.R., Ibid., 22, 79 (1930). (9) Purcell, L.T.,J . A m . Water Works Assoc.. 31, 1776 (1939). (10) Tillmans, J., Hirsch, P., and Haffner, F., Gus- a. Wasserfach, 70, 26 (1927); 71,481 (1928). (11) Weber, O.,Chem-Zto., 51, 794 (1927). (12) Weiser, H.B.,“Hydrous Oxides”, p. 294, New York, McGrawHill Book Co., 1926. (13) Weston, R. S.,and Griffin, A. E., J. New En& Water work8 Assoc., 47, 40 (1933).
(1) Am. SOC.of Agronomy, “Hunger Signs in Cropa”, Waahington, D.C.,1941.
PRESENTED before the Division of Water, Sewage, and Sanitation Chemistry at the 102nd Meeting of the Amerioan Chemical Society, Atlantic City, N. J.
tions of soluble manganese each autumn, and with the turnover this manganese will be diffused through the water, ridding them of the trouble until the warm weather period of the following year. If reservoirs are of sufficient depth to preclude a turnover, it is believed that the manganese will remain constant for a long time. This situation is believed to be true regardless of whether the reservoir has been previously stripped or not. The data in this paper depict conditions on the bottom of all deep reservoirs that have flooded large areas of vegetation, and show that purification processes for the removal of manganese are a necessity for all supplies obtaining water from this type of storage.
Mean Temperature Difference in
Multipass Exchangers Correction Factors with Shell Fluid Unmixed KARL A. GARDNE Mean temperature difference correction factors are presented for heat exchangers where the shell fluid is not mixed. These factors are shown to be higher than those for exchangers with the shell fluid completely mixed for the same temperature conditions. The limits within which the true correction factors may vary due to an unknown degree of mixing are thus defined by Nagle’s curves (lower limit) and the author’s (upper limit). Conditions are discussed under which it may be desirable to design a heat exchanger deliberately to prevent mixing of the shell fluid.
ORRECTION factors for the mean temperature difference in multipass heat exchangers may be derived on the basis of either of two assumptions: The shell fluid is completely mixed over any cross section; or the shell fluid does not mix at all. I n deriving his correction factors, Nagle (6) considered both assumptions and, concluding that the former was probably the more accurate, proceeded on that basis. Subsequent work of Underwood (Y), Fischer @), and Gardner (4) was predicated upon this same assumption.
C
The Griscom-Russell Company, New York, N. Y.
It is not my intention t o question the validity of the assumption of perfect mixing in baffled heat exchanger shells. However, it appears that the possibilities of baffling systems deliberately designed to discourage mixing have received little attention, and i t seems desirable t o investigate the results obtained under such conditions. Correction factors derived on this basis, when compared with Nagle’s, will show the limits within which the true correction factors may lie, and will provide a quantitative indication of the relative merits of the two types of flow. Equations for MTD in Multipass Exchangers with Shell Fluid Unmixed Equations are derived for correction factors by which the logarithmic temperature difference may be multiplied t o obtain the true mean temperature difference in multipass heat exchangers with the shell fluid unmixed. The basic a s s u m p tions are: 1. The over-all heat transfer coefficient, U,is constant throughout the exchan er. 2. The rate of flow o? each fluid is constant. 3. The specific heat of each fluid is constant. 4. There is no condensation of vapor or boiling of liquid in part of the exchanger. 5. Heat 13sses are negligible. 6. There is equal heat transfer surface in each pass. 7. There is equal rate of flow of the shell fluid around each tube pass. 8. The equal streams of shell fluid are independent, and no heat is. transferred between them by mixing or any other mechanism.
