December 1949
INDUSTRIAL AND ENGINEERING CHEMISTRY
mole fraction of component in vapor in equilibrium with liquid of composition L = length of column M = coefficient as defined in Equations 17a, b, and c N = number of transfer units R = refluxratio s' = reboilratio E(z, 4 ) = function as defined by Expression 7 LY = relative volatility 4 = parameter defined by Equation 6 Subscripts 1, 2, 3!, etc., are used to identify a component. Superscripts, as ' and , are used to denote the values of a component, at different points in the column. y* =
LITERATURE CITED s
ip
(1) Chilton, T.H.,and Colburn, A. P., IND. ENG.CEEM.,27,255-60 (1935).
2847
(2) Colburn, A.P.,Ibid., 33,45%67 (1941). (3) Dodge, B. F.,and Huffman, J. R., Ibid., 29, 1434-6 (1937). (4) Hausen, H.,"Der Chemie-Ingenieur," Vol. I, Part 111, Leiprig, Akad. Verlags., 1933. (5) Murphree, E. V.,IND. ENG.CHEM.,17, 960-4 (1925). (6) Thormann, K.,"Destillieren und Rektifizieren," Leipzig, Spamer, 1928. (7) Underwood, A. J. V., Chem. Eng. Progress, 44, 603-14 (1948). (8) Underwood, A. J. V . , J . Inst. Petroleum, 29, 147-56 (1943). (9)Ibid., 30,225-42(1944). (10)Ibid., 31,111-18 (1945). (11) Ibid., 32,598-613 (1946). (12)Ibid., pp. 614-26. RECEIVEDApril 1 , 1949.
Viscosity of Pulping Waste Liquors KENNETH A. KOBE' AND EDWARD J. McCORMACK2 University of Washington, Seattle, Wash.
In the wood pulp industry the sulfite, sulfate, or soda process may be used for the pulping process to give a cellulose fiber. In the alkaline processes it is usual practice to concentrate the liquor and burn it to recover the soda base. I n the sulfite process it is becoming necessary to carry out some processing prior to disposal. For all of these waste liquors a knowledge of their viscosities is necessary for calculations involving pumping costs, pressure drop in fluid flow, heat transfer coefficients, and cost of concentrating the liquor. Because the viscosity of the waste liquor is largely due to the dissolved sugars and colloidal lignin molecule it was hoped that some general relation might exist among these three liquors so that the viscosity of a l l could be represented by one set of curves with an accuracy sufficient for most engineering calculations, as was previously found to be the case with the specific heats of these liquors (2,3).
s
w
v
ULFITE waste liquor, sulfate black liquor, and soda black liquor were obtained from pulp mills of the state. The sulfite waste liquor was from the pulping of western hemlock a t the Soundview Pulp Company, Everett, Wash. The sulfate black liquor was from the pulping of western hemlock with a small amount of Douglas fir a t the St. Regis Kraft Company, Tacoma, Wash. The soda black liquor was from the pulping of cottonwood with some hemlock a t the Everett Pulp and Paper Company, Everett, Wash. The liquor was taken directly from the digester. Before use the liquor was strained to remove any fibers or particles that might clog the capillary of the viscometer. Part of each sample was evaporated to approximately three quarters, one half, and one quarter of its original volume, This evaporation was conducted on the stream plate at approximately 80" C. by allowing 1 liter of the liquor to evaporate, portions being removed a t each of the three desired concentrations, Each time care was taken to decant the liquor from any objectionable solid matter that might be present due to surface film formation. Total solids was determined on each sample by pipetting a 5-ml. sample onto 10 grams of sand in an evaporating dish. The sample was placed on a steam plate for 24 hours and in an oven a t 105" C. for another 24 hours, An Ostwald viscometer was calibrated against glycerol-water 1 Present address, Department of Chemical Engineering, University of Texas, Austin, Tex. 9 Deceased.
solutions over the range of temperatures and viscosities found in the waste liquors (6). The viscometer was placed in a small thermostat, the temperature of which could be varied from 0 " to 100"C. at approximately 20" intervals. It was not possible to cover the entire temperature range with the most concentrated samples because the liquor would not flow through the capillary a t the lower temperatures. Even the unconcentrated solution possessed a certain amount of gel-like properties below 20" C. The specific gravity of each sample was determined by means of a hydrometer graduated to 0.002 unit. The experimental values of density and viscosity for the various concentrations of solids over the temperature range used are recorded in Tables I, 11, and 111. Various methods of plotting were attempted to produce a straight line for viscosity and temperature, such as the reciprocal of viscosity against temperature ( O K.) or reciprocal of temperature, or the logarithm of viscosity against the logarithm of temperature. All of these methods gave a certain amount of curvature in the lines a t lower temperatures. An Othmer plot (6) of the logarithm of the viscosity of the waste liquor plotted against, the logarithm of the viscosity of water a t the same temperature
TABLE I. VISCOSITY OF SULFITE WASTELIQUOR Total
Solids, %
Temp.,
11.2
0.2 20.8 38.6 62.8 65.8 74.8 81.0 96.8
c.
Density arams/cb. 1.065 1.057 1.049 1.041 1.040 1.036 1.033 1.027
Viscosity,
CP. 3.072 1.620 1.083 0.712 0.673 0.605 0.657 0.468
15.0
26.6
0.3 20.0 42.8 60.4 77.7 94.8
1.133
1:ii4 1.103 1,094 1.083
9.36 4.200 2.462 1.672 1.249 0.988
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Vol. 41, No. 12
INDUSTRIAL AND ENGINEERING CHEMISTRY 100 -
T
80-
f
60 ---
--
w --__ 8
v
2 116
2 1:
I
5
40.-
a:
5
-- 3
__
% P
-4
w
0 -3
w
20.- w
110
z >
::2 -- 1.5 --
5 1; TEMPERATURE
- ‘C
IO-.
Figure 1. Viscosity-Temperature Relations for Sulfite, Sulfate, and Soda Waste Liquors of Various Concentrations of Total Solids
TABLE 11. VISCOSITYOF SVLFATE BLACKLIQUOR 70
Temp.,
c.
Density,
Grams/Cc.
22.8
0.4 19,8 4.51 61.9 81.8 97.2
1.145 1 134 1,119 1.108 1 097 1,088
47.8
97.0 79.2 86.4
1.248 1.257 1.254
TABLE Total Solids,
% 12.4
15.1
24.1
111.
VISCOSITY O F
Temp.,
c.
0.3 19.7 39.9 59,3 87.9 80.9 96.0 0.3 22.0 40.0 60.8 80.3 94.8 0.3 20.4 44.0 61.2 72.4 Y5.Q
52.5
96.1
80.0
Viscosity, CI-’.
6.76 3 47 1 R38 i ,346 0 991 0 824
6,54 11.22 9.30
SoD.4 BLACKLIQUOR
Density, Grams/Cc. 1.087 1,077 1,066 1.055 1,010 1.044 1.036 1,092
Visvosivttl
CP. 3,215 1.765 1.11s 0.780 0.632 0.582 0,492
1 ,082
1 ,074 1 ,064 1,055 1,047 1.159
1 .l i s
1,130 1.119 1.112 1.098
1.275 1,285
7.78 3,74 2.032 1.430
1.202
0.853 10.93 20,06
produced straight lines for both absolute and kinematic viscosities. The A.S.T.M. standard viscosity-temperature chart for liquid petroleum products ( 1 ) is useful as it produces straight lines for the kinematic viscosity plotted against temperature. The lines are different for each concentration of solids in the waste liquor, but these lines converge to a common pole point.
1.0
g:j
0.50 OA 5
0-
Total Bolids,
15
-- 10
0
30.-
25
-- 20
