Fonn THTCXENERS ( RACKGROUND)

WASHING CYANIDE

GOLD MILL

PU1.P COUNTER- CURRENTLY AT A

Courle.sy The Dorr Co.: Inc.

COUNTERCURRENT LEACHING Graphical Required

E. T. ARMSTRONG' AND KARL KAMMERMEYER Drexel Institute of Technology, Philadelphia. Penna.

m H E calculation of the proper number of unite

Determination of Number of Units

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) I The present paper gives a giaphi- cal method of solution in which none of these limitation& apply except the third. The method is easily applied but re- quires the determination of experimental data. Xlethods

I Present address, Foater Wheeler Corporation, New York, N 1'.

A graphical method for determining the re- quired 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.

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.

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

1228

. October, 1942 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 M I S T R Y 1229

supernatant liquid. Both of these relations may be deter- mined 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 approxi- mates 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 super- natant 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. In 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, Wd, 6d, X,, wf, and sr. The relations between these quantities are:

Sa 3. fdXd (4) By a material balance for the solutions,

Wf + Wf = Wa + Wd ( 5)

By a material balance for the solute,

& + 8f = s d f 8d ( 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 incom- patible. The following conditions must be fulfilled simul- taneously: First, in any one stream entering or leaving the system, except the outgoing sludge, not more than two quan- tities 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 re- quired 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

By definition,

Sf = W/Xf S d = WdXd

From the experimental data, wd = . fI(xm)

units is: Wn+1 = Wd - Wf + W n ( 7)

(1)

(2) A material balance for the solute over the same units is:

(3) Therefore,

COUNTERCURRENT W A S H I N G AT A M A ~ N E S I U M OXIDE P L A N T O F W E S T V A C O C H L O R I N E PRODUCTS

C0hlPAh.Y

Courtesy, Ths Dwr Campanu, Im.

1230 INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY Vol. 34, No. 10

FIQTJRE 1. COUNTERCURREST LEACHING SYSTEN

The quantities ( S d - SJ) and (Wd - WJ) are constants for the system and are determined by the terminal conditions; s,, and w,, are lrnown functions of X, (determined by experi- ment) ~ Therefore, from Equation 9 the value of X, + may be determined, and then the equation reapplied t o the (n + 1) unit.

Graphical Procedure

The procedure for the determination of the number of units is as follows: For various values of X, the corresponding values of Xn+ are calculated from Equation 9. A plot of X, + as ordinate against Xn as 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 X d 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 to the required number of unitr.

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 thick- ener (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 TABLE I. EXPERIMENTAL AND CALCULATED DATA

Xll UJn 8%

S'd = 0 .0 + 0.800 - 0.012 = 0.788

From Equation 2 :

M i d = 0 788/0.1 = 7 88

Therefore Equation 9 becomes:

0.788 - 0.800 + sn 7 . 8 8 - 1 . 5 0 + zli, Xn,, =

- - 0.0120 + Sn - 6 38 +

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 ulti- mate 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.

FIGURE 2. GRAPHICAL DETERMIXATION 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 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 M I S T R Y

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,+ The required number of units is therefore 4.

Nomenclature S, s = pounds of solute in clear liquid and sediment, respec-

tively, 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

= X/ = 0.0.

1231

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). (6) Hawley, L. F., IND. ENG. CHHIM., 9, 866-71 (1917); 12, 492-6

(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).

(1920).

(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.

’*I ”I

Surface Tension-Viscosity Nomograph for Organic Liquids

20

D. S . DAVIS Wayne University, Detroit, Mich.

_I K)

/---- /

OR thirty-two organic compounds Buehler (I) drev F attention to an important relation between surface tension and viscosity:

E 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

The table lists compound numbers and values of I / P (1, 4) for the organic liquids in question. No. I / P Compound No. I / P Compound 15 1.226 Acetate, ethyl 12 1.212 Formate, ethyl

17 1.253 Acetate, propyl

10 1.205 Benzene 1 1 103 Iodide’ methyl 11 1 208 Benzene ethyl 14 1:222 Iodide: prppyl

16 1.243 Bromide, isobutyl 12 1.212 Ketone: methyl ethyl 17 1.253 Bromide, isopro yl 10 1.206 Naphthalene 13 1.217 Bromide, propyf 2 1.172 Nitrobenzene 5 1,192 Bromobenzene 19 1.280 Octane 17 1.253 Chloride, isobutyl 9 1.202 Tolune 13 1.217 Chloride, propyl 8 1.201 m-Toluene 4 1.190 Chlorobenzene 11 1.208 m-Xylene 20 1.303 Decane 15 1.226 o-Xylene 12 1.212 Ether, ethyl 13 1.217 p-Xylene

6 1.195 Acetate, methyl 18 1.286 Heptane

3 1.186 Acetone

7 1: 198 Bromide: ethyl 14 1.222 Ketone diethyl

17 1.253 Hevane 10 1.205 Iodide ethyl

The use of the nomograph, constructed to solve the equa- tion 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 com- pound 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,

(3) Perry, J. H., Chemioal Engineers’ Handbook, 2nd ed., p. 794,

(4) Soudera, Mott, Jr., J . Am. Chem. Soc., 60, 154 (1938).

McGraw-Hill Book Co., 1028.

New York, McGraw-Hill Book Co., 1941.