Fonn THTCXENERS ( RACKGROUND) WASHING CYANIDE PU1.P COUNTERCURRENTLY A T A
GOLDMILL Courle.sy
The Dorr Co.: Inc.
COUNTERCURRENT LEACHING Graphical Determination of Required Number of Units E.T. ARMSTRONG'
AND
KARL KAMMERMEYER
A graphical method for determining the required number of units in a countercurrent leaching system is described. It is believed that this is somewhat more accurate than any of the available methods, since it takes into account the effect of adsorption of the solute by the solid from which it is leached and the effect of incomplete mixing of the solution retained by the solid with the main portion of the solution. The method is easily understood and easily applied.
Drexel Institute of Technology, Philadelphia. Penna.
'
m H E calculation of the proper number of unite in il countercurrent extraction process by present methods can be made easily \There the following conditions are met: The wash liquid is completely and uniformly mixed with the solution adhering to the surface of the solid; the solid exerts no selective absorbing action on the solute but is completely inert; and the solution does not become saturated with the solute. Elgin (+$),Ravenscroft (S), and Tsao (10) have presented methods for solving the problem graphically, but the application of these methods is rather tedious. Elgin's method is probably the most comprehensive as i t can also be applied in the case where the third condition is not met. If the additional condition is met, that the weight of the solution leaving with the inert solid is constant, the most convenient method of calculation is by an analytical solution as presented by Badger and McCabe ( I ) , Baker ( 2 ) , or Wawley (6),or a semigraphical method as presented by Donald (3) or Sanders (9) The present paper gives a giaphical method of solution in which none of these limitation& apply except the third. The method is easily applied but requires the determination of experimental data. Xlethods
presented by Elgin ( 4 ) , Ravenscroft (8), and Tsao (IO) also require experimental data; while those given by Badger ( 1 ) Baker ( 2 ) , Donald ( 3 ) , Griffin ( 6 ) , Hawley ( B ) , and Sanders ( 9 ) require that experimental facts be expressed or at least itpproximated by bome simple algebraic expression. As a consequence, these latter methods may be less accurate.
I
I
Present address, Foater Wheeler Corporation, New York, N 1 ' .
Required Experimental Data For applying the present method, the following data are iequired: the weight of solution and weight of solute retained by the inert solids as a function of the concentration of the
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.
INDUSTRIAL AND ENGINEERING CHEMISTRY
October, 1942
supernatant liquid. Both of these relations may be determined by a single scries of experiments, carried out as follows: The solvent is added to the inert solid containing the solute; the mixture is agitated for a period of time which approximates the anticipated plant practice and is transferred to a graduated cylinder. The volume of the mixture is noted, and after the solid has settled to a height determined by operating factors, the volume of the sediment is observed. From this volume, the volume of the inert solid is subtracted to find the volume of solution retained. A portion of the supernatant liquid is withdrawn and analyzed for solute content. The concentration of the supernatant liquid multiplied by its total volume gives the amount of solute in the total supernatant liquid. By difference, the weight of solute retained by the solid is obtained. A fresh quantity of solvent is added to the sediment, and the procedure is repeated to obtain data for a lower concentration. The experiments may be carried out gravimetrically instead of volumetrically. I n any event, the results should be converted to a weight basis. Laboratory conditions must be carefully chosen so that the holdup of the solid sediment is identical both in quantity and in composition with that to be obtained in plant practice.
Derivation of Equations If the entire extraction system of Figure 1 is considered as a unit, the following quantities must be known or are to be determined: &, JVt, 4,&, wd, xd,W d , 6d, X,, wf,and sr. The relations between these quantities are: By definition, Sf = W/Xf S d = WdXd
(1)
(2)
Sa
= .fI(xm)
COUNTERCURRENT WASHING AT A M A ~ N E S I U M OXIDE
P L A N TO F W E S T V A C O C H L O R I N EP R O D U C T S C0hlPAh.Y
Courtesy, Ths Dwr Campanu, Im.
(3)
fdXd
(4)
By a material balance for the solutions,
+
Wf
Wf
= Wa
+
Wd
By a material balance for the solute, & 8f = s d f 8 d
+
(5 )
( 6)
Thus there are six equations involving eleven quantities, so that if the equations are to be determinate, five of these quantities must be fixed. Care must be exercised in fixing these quantities so as not to have equations which are incompatible. The following conditions must be fulfilled simultaneously: First, in any one stream entering or leaving the system, except the outgoing sludge, not more than two quantities may be fixed. Secondly, not more than one of the three quantities in Equations 3 and 4 may be fixed. Thirdly, not more than three quantities may be fixed in Equation 5 or 0. These considerations apply to any of the present available methods. After the five quantities have been fixed, they are to be used in Equations 1 to 6. A plot of experimental data is required to solve Equation 3 or 4,but in general a complete solution of the six equations is not necessary since only the following quantities are needed for the application of the method: xd, Xf,(Wd - w,) which is equal to (W/ - wd), and (A% - si) which is equal to (8, - S d ) . A material balance for the solutions taken over the first 7t units is:
Wn+1 = Wd - Wf
+
Wn
A material balance for the solute over the same units is:
From the experimental data, wd
3.
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Therefore,
( 7)
INDUSTRIAL A N D ENGINEERING CHEMISTRY
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FIQTJRE
S'd
1. COUNTERCURREST LEACHING SYSTEN
=
Vol. 34, No. 10
0.0
+ 0.800
- 0.012 = 0.788
From Equation 2 : Mid
The quantities ( S d - SJ) and (Wd - W J ) are constants for the system and are determined by the terminal conditions; s,, and w,,are lrnown functions of X, (determined by experiment) Therefore, from Equation 9 the value of X,+ may be determined, and then the equation reapplied t o the (n 1) unit.
= 0 788/0.1 = 7 88
Therefore Equation 9 becomes: Xn,,
=
+ sn +
0.788 - 0.800 7.88 - 1.50
~
+
Graphical Procedure The procedure for the determination of the number of units is as follows: For various values of X, the corresponding values of X n + are calculated from Equation 9. A plot of X,+ as ordinate against Xnas abscissa is prepared as shown in Figure 2, which also includes the line for the equation: Xn = Xn+,
The number of units is obtained by proceeding froni point on the X, axis vertically to the curve of X,us. X,+ 1, then horizontally from the point of intersection to the diagonal line. From this intersection another vertical line is drawn to the curve, and subsequent steps are completed until the value of X,+ corresponds to Xf. The total number of vertical lines is then equal t o the required number of unitr. X d
- 0.0120 6 38
+
zli,
+ Sn
The first three coluninb of Table I give the experimentally determined data (room temperature). The fourth column gives values calculated from Equation 10. The experimental data were obtained by settling to ultimate height. However, it should be noted that the height to which settling is to be carried out need not be the ultimate height; but it should approximate the height attained in plant practice, which may hare to be estimated as it depends on the thickener design. The use of a thickening curve as described by Work and Kohler (12) and Ksmmermeyer (7) will permit making the neressary estimate.
Illustration Sodium hydroxide is to be made by reacting sodium car' bonate with lime to form sodium hydroxide and calcium car-
bonate. The hydroxide is to be washed from the calcium carbonate in a continuous countercurrent decantation system. I The slurry entering the system contains 1.50 pounds of solu' tion per pound of calcium carbonate. The amount of sodium hydroxide in this slurry is equivalent to the amount of cal' cium carbonate. The overflow solution from the first thickener (the most concentrated) is to contain 10 per cent by weight of sodium hydroxide. The slurry from the last ,thickener is to contain not more than 1.5 per cent of the sodium hydroxide entering the system. Fresh water is added in the last thickener. Find the number of units required, basing the calculation on the assumption that plant practice Rill give amounts and composition of holdup corresponding with the table of data. I
TABLEI. EXPERIMENTAL AND CALCULATED DATA Xll
UJn
8%
FIGURE2.
GRAPHICALDETERMIXATION
OF
KUMBEK
OF
TTUITG
I n Figure 2, X,+ is plotted against X,. Starting at the point where X, = Xd = 0.10, a vertical line is drawn to the curve. From the point of intersection, a, a horizontal line is drawn to the diagonal line, intersecting at b. From point b a
October, 1942
INDUSTRIAL AND ENGINEERING CHEMISTRY
vertical line is drawn to the curve and the process repeated. The vertical line from point c intersects the X , axis before reaching the curve so that the next horizontal line would lie below X,+ = X/ = 0.0. The required number of units is therefore 4.
Nomenclature S,s = pounds of solute in clear liquid and sediment, respectively, per ound of inert solid in sediment W ,w = pounds of sogtion (solute plus solvent) in clear liquid and in sediment, respectively, per pound of inert solid in sediment X = concentration of clear solution, pounds of solute per pound of solution Subscripts d = streams delivered by the system f = streams fed to the system m = last unit in the system (the least concentrated) n = number of unit, counting from more concentrated end 1,2,etc. = number of unit from which the stream is leaving
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Literature Cited (1) Badger and McCabe, “Principles of Chemical Engineering”, pp. 423-34, New York, McGraw-Hill Book Co., 1936. (2) Baker, E. M., Chem. & Met. Eng., 42, 669-71 (1935); Trans. Am. Inst. Chem. Engrs., 32, 62-72 (1936). (3) Donald, M. B., Trans. Inst. Chem 4ngrs. (London), 15,77-109 (1937). (4) Elbgn, J. C., Trans. Am. Inst. Chem. Engrs., 32,451-71 (1936). (5) Griffin, C.W.,IND.ENG.CHQM., ANAL.ED.,6,40-1 (1934). 9, 866-71 (1917); 12, 492-6 (6) Hawley, L. F.,IND.ENG.CHHIM., (1920). (7) Xammermeyer, Karl, Ibid., 33,1484-91 (1941). (8) Ravenscroft, E.A.,Ibid., 28,851-5 (1936). (9) Sanders, M. T., Chem. & Met. Eng., 39, 161-2 (1932). (10) Tsao, Yu Teh, J. Chem. Eng. China, 4,164-8 (1937). (11) Work, L. T., and Kohler, A.. S.,Trans. Am. Inst. Chem. Engrs., 36, 701 (1940). , PREBENTBD before the Division of Industrial and Engineering Chemistry a t the 104th Meeting of the AMHRICAN CHEMICAL Socmm, Buffalo, N. Y.
Surface Tension-Viscosity Nomograph for Organic Liquids D. S . DAVIS Wayne University, Detroit, Mich.
F
OR thirty-two organic compounds Buehler (I) drev attention to an important relation between surface tension and viscosity:
+
1% (log 9) 2.9 I/P where y = surface tension, dynes/cm. Q = viscosity, millipoises, at same temperature as 7 I = viscosity-constitutional constant P = parachor E
’*I
The table lists compound numbers and values of I / P (1,4) for the organic liquids in question. No. 15 6 17 3 10 11 7 16 17 13 5
”I
17 13 4
20
/
_I K)
/----
20 12
I/P 1.226 1.195 1.253 1.186 1.205 1 208 1: 198 1.243 1.253 1.217 1,192 1.253 1.217 1.190 1.303 1.212
Compound Acetate, ethyl Acetate, methyl Acetate, propyl Acetone Benzene Benzene ethyl Bromide: ethyl Bromide, isobutyl Bromide, isopro yl Bromide, propyf Bromobenzene Chloride, isobutyl Chloride, propyl Chlorobenzene Decane Ether, ethyl
No. 12 18 17 10 1 14 14 12 10 2 19 9 8 11 15 13
I/P 1.212 1.286 1.253 1.205 1 103 1:222 1.222 1.212 1.206 1.172 1.280 1.202 1.201 1.208 1.226 1.217
Compound Formate, ethyl Heptane Hevane Iodide ethyl Iodide’ methyl Iodide: prppyl Ketone diethyl Ketone: methyl ethyl Naphthalene Nitrobenzene Octane Tolune m-Toluene m-Xylene o-Xylene p-Xylene
The use of the nomograph, constructed to solve the equation conveniently and accurately, is illustrated as follows: What is the surface tension of ethyl iodide a t 16’ C. when its viscosity is 6.2 millipoises (3) at this temperature? The compound number for ethyl iodide, read from the table, is 10. Connect 6.2 on the 7 scale with 10 on the compound number scale and produce the line to the y scale where the surface tension is read as 29.1 dynes per em. The experimental value reported in the International Critical Tables (2) is 29.9.
Literature Cited (1) Buehler, C.A.,J.Phys. Chem., 42,1207 (1938). (2) International Critical Tables, Vol. IV, p. 436, New York, McGraw-Hill Book Co., 1028. (3) Perry, J. H.,Chemioal Engineers’ Handbook, 2nd ed., p. 794, New York, McGraw-Hill Book Co., 1941. (4) Soudera, Mott, Jr., J . Am. Chem.Soc., 60,154 (1938).
