MIXED SOLVENT EXTRACTION Batch-Extraction Stoichiometric Computations' T. G . HUNTER The University of Birmingham, England
I T H I N recent years considerable development has taken place in the use of mixed solvents for solvent extraction operations, particularly in the refining of mineral oils. I n mixed solvent processes the two or more solvents employed are mutually soluble under the operating conditions, and the mixed solvent is therefore a single homogeneous liquid phase. A mixed solvent of two components is commonly usdd, in which one solvent component is only partially miscible with the stock mixture being treated under the prevailing operating conditions, while the other solvent component is completely miscible with both the fbst solvent component and the stock mixture under the operating conditions. A good example of this important case is the benzenesulfur dioxide process as normally operated for refining lubricating oils. The separation of a binary mixture by solvent extraction and the refining of a mineral oil with a solvent a t constant temperature have been extensively studied and described by means of phase equilibrium relationships (6-8). These investigations have now been extended to the study of mixed solvent extraction processes, and the present paper deals with the stoichiometric computations involved in the simple separation of a binary mixture by batch extraction with a mixed solvent consisting of two components.
Four-Component System The simplest example of such a mixed solvent extraction process, corresponding to the important case quoted above, consists of the separation of a mixture of two mutually miscible liquids, A and B, by treatment with a solvent consisting of a mixture of two mutually miscible liquids, XI and&. I n the latter mixture liauid SI, the principal solvent, is partially miscible with B and completely miscible with A,
Hunter, and Nash (9, 4) employing acetone, acetic acid, chloroform, and water a t 25" C. for the four components. Using this system it was empirically established that the two equilibrium curves in the ternary systems ABSl and BSISz define the heterogeneous region on two sides of the tetrahedron in Figure 1. The frustum formed by connecting these curves by sloping straight lines in planes of section perpendicular to both the base BSlS2and the edge BX1of the tetrahedron defines the complete heterogeneous region. A plane passing through any tie line in the ternary system ABSl and the opposite apex Sz will intersect a second plane passing through any tie line of the ternary system BSl& and the opposite apex A to give a quaternary tie line, the two terminal points of which lie on the surface of the frustum. I n Figure 1 the plane P&S2which passes through tie line CD in the ternary system ABSl, intersects plane AIL, which passes through tie line J K in the ternary system BSISz,in the line RT. A quaternary tie line is situated on line RT and has its terminal points X and Y on the surface of the frustum. The existence of a frustum-shaped equilibrium surface and tie line planes has been demonstrated (4) for a single quaternary system containing only one pair of partially miscible components-viz., the system acetone-acetic acid-chloroform-water. Confirmation from equilibrium studies of other quaternary systems containing one pair of partially miscible components is necessary, however, before this can be established as a rigid generalization for such systems. Since it is felt that cases giving rise to such equilibrium relations will be common a n d since, moreover, it h a s b e e n shown that such phase behavior describes M an oil-binarv P --;-;'-\ mixed solvent sys*-x- - - tem (X), computay . : . tions applied to
saw 'A ==--
6 -=---= z while liquidor82, auxiliary secthe 8 tf rhus i st um-s c a s eh aof p e da ondary solvent, is equilibrium surwholly miscible face have been inwith liquids A , B, vestigated. and S1. st It has been in FIGURE 1. GENERALIZED PHASE DIA- FIGURE 2. FORMATION OF MIXTURE N shown (9) that, such a four-comwith proper planGRAM FOR FOUR-COMPONENT SYSTEM BY ADDINGSOLVENT S TO MIXTURE M, ponent system of HAVINQONE IMMISCIBLE PAIR O F AND SEPARATION INTO PHASES O F ning, three batch five completely COMPONENTS, BSI COMPOSITION X AND Y treatments of a miscible liquid stock mixture pairs and one imwith a solvent will miscible liquid pair, existing as two liquid phases a t consuffice for setting up a three-component phase diagram. If stant temperature and pressure, was studied by Brancker, the existence of the frustum-shaped equilibrium surface and tie line planes of Figure 1 is eventually established as a gen1 The first paper in this seriee appeared in July, 1941 (a). 963 \
INDUSTRIAL AND ENGINEERING CHEMISTRY
964 A
Vol. 34, No. 8
6 enable the system BSISz to be plotted. Tie line data for these two ternary systems may be extended by interpolation using any of the methods described by Brancker, Hunter, and Nash (3)and Bachman (1). Experiments 7 to 10 enable the rule for the position of the quaternary tie lines to be proved. In actually setting up Figures 10 (a) and (b) only experiments 1 to 6 are required since it has been established that quaternary tie lines can be derived from the ternary tie line data.
B a t c h Extraction Sf
Consider a mixture of A and B which is to be separated by batch extraction with the binary solvent mixture S, consisting of the two mutually miscible solvents 8,and 8,. Let the equilibrium between the four components A, B, SI, and Sz be represented by the frustum in Figure 1. Suppose the composition of thk mixture of A and B to be treated is given by point M in Figure 2. Let the ratio by weight of mixed solvent S to mixture M be R M ,and the ratio of solvent S1to solvent Sfin the mived solvent S be Rs.
FIGURE3. COMPOSITIONOF SOL- FIGURE4. GRAPHIC CONVERSIOX VENT-FREE AND EXTRACTFROM FOUR-COMPONENT JfIXTURE x"AND y" ARAFFINATE S DERIVED GR.4PHIC.kLLY TO THREE-COMPONENT MIXTCRE N FROM
x
AND
Y
eralization for quaternary systems containing one pair of partially miscible components, then six properly chosen batch treatments will suffice for setting up the three-dimensional diagram. For example, only the two ternary diagrams ABS, and BS,S2 need be set up in order to define the
TABLE I.
COMPOSITION OF THE
QUATERSARY S Y S T E M ACETONE (A)--CHLOROFORM IX
7 -
Expt. No. 1 2 3 4 5 6 7 8 9 10
A 6.0 34.0 50.0
..
..
6:5 36.7 21.6 18.0
Initial Mixture-B Si 44.0 60.0 33.0 33.0 30.0 20.0 50.0 40.0 40.0 36.5 41.0 22.0 43.5 28.4 21.7 25.6 32.8 36.3 30.0 20.0
WEIGHTPERCEKT
.s 2
.. .. 1o:o
23.5 37.0 19.6 16.0 9.3 32.0
A 3.0 22.1 44.5
.. ..
4:6 24.4 11.2 13.6
system ABSISzof Figure 1, provided the shape of the frustum and existence of tie line planes is of the type illustrated in this figure. In a quaternary system containing one pair of partially miscible components where the frustum shape and the tie line planes are as in Figure 1, but where this fact is unknown, a total of ten properly chosen batch treatments are necessary to provide sufficient data for setting up the diagram. [It was previously shown (4) that lines such as UZV (Figure 7) are straight for the system acetone-chloroformwater-acetic acid. If this is found not to be true for other quaternary systems, it will be necessary to obtain many more data to establish the degree of curvature of these lines.] The data given in Table I are the results from ten batch treatments in the system acetone-chloroform-water-acetic acid at 25" C. and are sufficient to completely characterize the phase equilibrium relations. When set up in a threedimensional diagram, they result in a drawing similar to Figure 1, where A , B, SI, and Szrepresent acetone, chloroform, water, and acetic acid, respectively. Exact quantitative plots of the systems acetone-chloroform-water and acetic acid-chloroform-water set up from these data are shown in Figure 10 (a)and (b). An orthogonal projection of the complete quaternary system onto the acetic acid-chloroformwater base set up from these data is also shown in Figure 10 (b). The three batch treatments in experiments 1 to 3 are sufficient t o set up the ternary system ABS, ; experiments 4 to
BTop Layers1 1.0 1.8 4.5 1.1 2.6 12.4 3.1 6.9 1.8 19.1
96.0 70.1 51.0 81.5 63.3 38.1 59.5 44.5 71.7 28.3
s 2
.. ..
17.4 34.1 49.5 32.8 24.2 15.3 39.0
(B)-IvIT.4TER
--
(Si)-ACETIC
ACID (s,)
Bottom Layer-------
.4
B
SI
SI
9.0 42.5 57.0
90.0 55.0 38.0 95.0 87.8 74.4 76.8 30.8 63.5 42.5
1.0 2.5 8.0 0.9 1.4 3.0 1.8 13.7 1.6 10.6
..
..
.. ii:s
44.3 31.6 22.8
.. ..
4.1 10.8 22.6 9.6 11.2 3.3 24.1
Mixed solvent S is added to solution M in the batch extraction process. The composition of the complex resulting from this operation must be on the straight line MS in Figure 2. If this complex is denoted by point N , then the ratio M N / N S must equal RAM. The complex hr falls within the area bounded by the frustum and must therefore separate into two ooexisting liquid phases, whose compositions will be given by the terminal points X and Y of the quaternary tie line passing through N . In order to ascertain the results from this batch extraction operation, it is required to locate point N and the quaternary tie line XY passing through it. Since the required quaternary tie line XY must be located from the intersection of two ternary tie line planes, obtained from a knowledge of the tie lines in the ternary systems ABS1, and BS,S2,it is convenient to consider the formation of the complex N in the following way: Instead of adding mixed solvent S directly to mixture M , consider the addition to be made in two steps. First, to mixture iM the single solvent SIis added in the correct ratio R1 which will be such that
The composition of the complex resulting from this step must lie on the straight line iMS, in Figure 2 . If the composition of this complex is denoted by point 0, then the ratio
INDUSTRIAL A N D ENGINEERING CHEMISTRY
August, 1942
iMO/OS1 must equal R1. Complex 0 falls within the area bounded by the binodial curve and must therefore separate into two ternary phases, whose compositions can be ascertained from the ternary tie line CD passing through point 0. Secondly, to complex 0, solvent S2is added in correct amount to give the required ratio, R M ,of binary solvent to mixture. The complex resulting from this second step must be N . That is, instead of adding double solvent S directly to mixture M to get complex N , single solvent 81 has been added to mixture M , and to the intermediate complex 0 so formed, the second solvent Sz has been added, giving complex N in two steps. The composition of the complex resulting from this second step must lie on straight line OSz, and the ratio ON/NSzmust equal the ratio of solvent 8s to complex 0. Complex 0, from which complex N has been obtained by the addition of solvent SZ, lies on the ternary tie line CD, and therefore both 0 and N must lie in plane PQ& which passes through ternary tie line CD. T&t is, complex N lies in a plane passing through a tie line in the ternary system ABSl. In order to locate the tie line passing through N , the intersection of the ternary tie line plane PQSzwith a plane passing through a tie line in the second ternary system BSlSz must be found. It is now simply a matter of locating the tie line J K (Figure 3) in the ternary system BSlS2such that the plane A I L passing through it will intersect plane PQS2 in a straight line RT which passes through N . The required quaternary tie line must be on RT and must be the line X Y in Figure 3 where RT is cut by the quaternary equilibrium curve CED lying on plane PQSZ. Curve CED, called here a “quaternaiy equilibrium curve”, is the intersection of the frustum and piane PQSz. From Figure 4 it is seen that complex N lies in plane AIL. Further, if from complex N component A is completely removed, there must result a new complex N’ which also lies in plane AIL. This new complex N’, consisting only of B , S1, and Sz, must be situated on the base plane BS1S2,and
965
I n Figure 4 point N’ is located on line BS such that the ratio BN’IN‘S = Rz. The tie line passing through N’ is the desired ternary tie line J K . The composition of the solvent-free raffmate and extract resulting from a batch extraction process can conveniently be ascertained by considering the removal of solvents S1 and S2from raffinate X and extract Y in two steps. The composition of the complexes resulting from the removal of solvent Sz must be given by points X‘ and Y‘ (Figure 3) obtained by joining point Sz to points X and Y and producing lines SzX and S2Y to intersect plane ABSl in X‘ and Y’, respectively. The compositions of the solvent-free raffinate and extract must be given by points X” and Y’‘ where lines &X’ and Sly’ produced intersect side A B of the tetrahedron.
Orthogonal Projection It is inconvenient to calculate batch extraction results by such constructions using a solid model, and computations are best carried out on a projection of the solid figure. The projection usually found most convenknt is the orthogonal projection onto the base BS& illustrated in Figure 5 . The orthogonal projection may be visualized by considering curve CED in Figure 3 as being constructed of wire and illuminated by plane-parallel light which is projected from above apex A and which falls on plane BSISz a t right angles. The shadow of curve CED on plane BSISzis then the orthogonal projection and is designated CoEoDo (Figure 5). (The superscript O is used to designate points in orthogonal projection except where the small letters m, n, 2, y, z , etc., are used.) The most convenient way of making this projection is to calculate the position the points to be projected would occupy on the base triangle BSISIand then plot the calculated positions. If the position of any point within the tetrahedron is defined by weight percentages a, b, sl, s2 of the four comrespectively, then the position of ponents A , B , SI, and Sz,
SI
B
FIGURE5. ORTHOGONAL PROJECTION ON BASE BSiSz
hence tie line J K must pass through N ’ . The complex represented by point N’ may also be produced by mixing binary solvent S with pure component B in the correct ratio Rz, which will be such that
where b = weight yo of component B in mixture M
FIGURE6. ORTHOGONALPROJECTIOX AOIL PLANE AIL
OF
the projection of such a point onto base triangle BSISs can be defined by the distances of the projected point from the three sides of the base triangle, which distances are weight percentages of B , SI, and 82. If these distances are b’, si, and si, respectively, then the relation between a, b, sl, sz, and b’, si, and si can, from geometrical considerations, be shown to be: b’
=
b
+ (a/3);
S;
SI
+ (~/3);
S:
=
SZ
+ ( ~ / 3 ). .. . .
(1)
INDUSTRIAL AND ENGINEERING CHEMISTRY
966
These equations enable the position of the projected point to be calculated and subsequently plotted on BS,Sz. The orthogonal projection m on plane BSISzof point 144 representing the composition of the mixture to be extracted lies on the line AOB of Figure 5. The orthogonal projection 0" of complex 0 is located graphically on line mS1 from the the relation mOO/O"S1 = R1. Alternatively the composition of complex 0 may be calculated arithmetically from a knowledge of the composition of mixture 144 and the ratio R1,and the orthogonal projection 0" on BSl& plotted. The tie line in the ternary system ABS, (Figure 2) which passes through 0 is drawn-namely, CD. Producing CD to intersect lines AB and ASl in P and Q, respectively, and joining P and Q t o Sz gives the ternary tie line plane PQSZ. This plane is shown in projection as P0Q0S2in Figures 5 and 6. The line 0x2 (Figure 2 ) , on which the required complex N lies, is obtained in projection (Figure 5) by joining points 0" and Sz. As Figure 2 shows, the complex N also lies on line M S and is actually the intersection of MS and OS2. Point S on SlS2 is easily located such that SSJSS1 = S1/& = Rs, and mX is drawn (Figure 5). The orthogonal projection n of the required complex N is the point of intersection of mS and O"Sz. Alternatively, the composition of complex N may be calculated arithmetically from a knowledge of M , R M ,and Rs, and its orthogonal projection n plotted. Tie line XY passing through N lies on the line of intersection of the two planes PQS2 and AIL. This line of intersection, RT, has now to be located. Complex N is situated in plane AIL. If from complex N component A is removed, complex N' of Figure 4, free from A , is obtained. This complex N' must be on tie line J K . Therefore if complex N' can be located, tie line J K passing through it may be easily drawn. Since the composition of complex N in terms of A , B, Sl, and S2 is known, the composition of complex N' in terms of B, S1, and S2 is easily calculated arithmetically, and point N' plotted in triangle BS1S2. (Since, as previously pointed out in connection with Figure 4,point N' is situated on line BS such that BN'IN'S = R z ,an alternative method is t o plot point S,draw line BS, and divide it in the correct ratio; or to join point A" to point n in Figure 6 and produce
A
Vol. 34, No. 8
and T (R" and T oin projection), and by joining these points the line of intersection RT (or ROT") of the two tie line planes is located.
s, B
FIGURE7. SECTIONHGh THROUGH FRUSTUM PERPENDICULAR TO PLANE ABS,
As explained in connection with Figure 3, terminal points X and Y of the quaternary tie line are obtained from the intersection of line RT with the quaternary equilibrium curve CED which is actually the curve of intersection of plane PQS2 with the frustum. It is now necessary, therefore, to plot the projection C"E"D" of curve CED on base BSiSz. A perpendicular section through the tetrahedron on the line Hh of Figure 6 is shown as the triangular plane HGh in Figure 7 . Line Hh is a t right angles to the edge BS1. This plane of section intersects the equilibrium curve in the ternary system ABSl a t U and intersects the equilibrium curve in the ternary system BSIS, a t V; straight line UV is the intersection of this plane with the frustum. This perpendicular
A
FIGURE8. COXSTRUCTIONAL DIAGRAMS FOR LOCATING POINT2
to cut line BS in point N' since line A N when produced intersects BX in N'.) I n Figure 6 the tie line J K passing through N' in the ternary system BSISzwas drawn and proin points I and L. By duced to intersect lines BS2 and SISz joining I and L to A (Figure 3), the ternary tie line plane A I L is obtained (A'IL in projection, Figure 6). The two ternary tie line planes A I L and PQS, intersect a t points R
plane HGh also intersects the tie line plane PQS2 in the straight line WZg. Lines UV and Wg intersect at 2 which is a point on the quaternary equilibrium curve CED.
Location of Point Z The length of any selected line H h on which a perpendicular section through the tetrahedron is taken, together with the
August, 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 CH E M I S T R Y
FIGURD 9. ORTHOGONAL PROJECTION OF A PORTION OF LINE CED ON PLRNEBS1&
length H V may be measured directly from the base projection shown in Figure 6. A line of the correct length, Hh, is drawn and point V located on it in Figure 8 (c). From Figure 6 the ratio AoGo/GoSIwhich equals AG/GS1 may be measured, and the position of point G located on triangle ABSl as in Figure 8 (a). Since the position of H is known, line GH can be drawn on ABSl normal to BS1, and point U , the intersection of GH with the equilibrium curve in the ternary system ABSl, is obtained as the length H U . The tie line plane PQS2 passes through the known tie line CD in the ternary system ABS,. This tie line, CD, may be drawn as in Figure 8 (a), and point W located. Triangle ASlS2is now drawn separately, as in Figure 8 (b), and point G on ASl marked. The position of h on S1S2is known from the base projection on BSISz of Figure 6 and may also be marked. Line Gh is now drawn. The position of Q on A S I , ascertained from triangle ABSl of Figure 8 (a), is located and line QS2 drawn. The intersection of Gh and
967
&S2 gives point g. The lengths of Gh and HG may now be measured, and the triangular plane of section HGh completely set up as in Figure 8 (c). Lengths HW and H U from Figure 8 ( a ) and length hg from Figure 8 (b) enable points U , W , and g to be marked on triangular section HGh of Figure 8 (c). UV and Wg may now be drawn in Figure 8 (c), and their intersection gives Z, the required point on quaternary equilibrium curve CDE. (This graphic constructiqn depends upon points UZV being on a straight line, which may not always be true.) Point z, the orthogonal projection of Z onto the base BS,S2, lies on Hh. Point z is easily located and, by means of length Hz, transferred to the base projection as in Figure 9. Similar perpendicular sections through the tetrahedron on lines such as Hlhl and Hzh2wil) give other points such as z1 and z2; when joined, these points give the projected quaternary equilibrium curve C"EoDo. The intersection of this curve with RT gives projections x and y of the two points X and Y, representing the composition of the required two coexisting phases. I n Figure 9 lines S2x and Szywhen produced cut line Pogo in x f and y'. Lines Slx'and Sly' when produced cut line A"B in XI' and y". Points x', y', XI', andg" are the orthogonal projections of X ' , Y'and X" and Y" of Figure 3. If only the composition of the solvent-free extract and raffinate are required, and the actual percentage of the two solvents S1 and Sz in the extract and raffinate is not desired, then the ratio A / B in the solvent-free extract is given by the ratio of the lengths of lines By" and Ay", and percentages of A and B can be calculated accordingly. Similarly the percentages of A and B in the solvent-free raffinate may be calculated from the ratio BZ"/AZ". Alternatively the percentages of A and B may be calculated from the coordinates of point x" or the point y" on the base plane projection. If b', s;, and s; are the coordinates of such a point on the base plane projection, then the weight per cent a of component A may be calculated by any of the equations: a = 3 4 , or a =
35:,
or a =
3(100
- h')
2
.....
ACETONE
A
FIGURE10. QUANTITATIVE DIAGRAMS FOR SYSTEM CHLOROFORM-ACETONE-ACETIC ACID-WATER
(2)
968
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
If. however. the comDosition of t h e 'two coexisting liqiid phases represented by points X and Y of Figure 2 is required in terms of the four components, this has to be obtained from a knowledge of the coordinates of points x and y of Figure 9, which are the projections of X and Y on base BSIS2,and from a knowledge of plane P&S2in which the quaternary tie line is situated. Points x" and y" in Figure 9 are the orthogonal projections of points Y" and Y" of Figure 3, and from x" and y" the ratio A / B in the phases whose compositions are represented by points X and Y is readily ascertainable as explained above. If b', si, and s; are the Coordinates of point x, and if a, b, sl, and s2 are the coordinates of point X and also the weight percentages of the components A , B, SI, and Sz, then from point x" the ratio a/b = Bx"/Ax". Since b', si, s;, and the ratio a/b are all known, the values of a, b, SI, and sz may be calculated by the following relations :
TABLE11. COMPLETE CALCULATIOXS Operation Step 1
Point
Coordinates of Point, %
m
b' = 81.46; s ; = 9.26; s i = 9.26 b' = 52.7; s i = 41.3; : 5 = 6.0
00
C"
83.0; si = 9 2 ; 7.8 b' = 4; s: = 93; s: = 3
b'
5:
D" Step 2
Step 3
S
s:
n
b'
N'
b'
J K Step 4
RO TO
H h
Step ;(a)
v
Line
Length of Line, Cm.
Remarks
...
. ..
Calcd."; Figs 2 8: 5
..,
.. .
...
...
Located graphically, may be calcd.*; Figs. 2825
I
Projected tie line through 0 ' ; Fig. 5
=
= 58.5; s: = 42.2; s ; s: = 24.8
= =
41.5 33.0;
...
...
Figs. 2 & 5 Located graphically, m a y be calcd.c; Figs. 2 & 5
...
...
43.6; s ; = 33.0; 23.4
...
.. .
b' = 86.6; s i = 2.0; = 11.4 b' = 3.0; s i = 63.0; s ; = 34.0
... ...
... . ..
...
line through 1TieFigs. 3 &6
... ...
...
) Intersection of planes [ PQS? and AIL
"*
j(
=
SA
Located graphically, m a y be calcd.d; Figs. 4 & 6
=
77.0; si = 7 . 2 ; 15.8 b' = 2 . 0 ; s ; = 63.0; si = 35.0 b'
=
5 :
=
b' = 23.0; s ; = 77.0 s i = 53.5; si = 46.5 b' = 4.4; s ; = 58.0; s; = 37.6
...
...
...
Hh HV
10 3 8.3
b'
=
s:
The necessary computations may be conveniently summarized in six steps. These operations are carried out using the orthogonal projection on the base BSISz (Figures 5, 6, and 9).
15.4; 5: = 69.2; = 15.4 46.2; s1 = 53.8
G
a =
U
a = 38.7; b = 3.7: s 1 = 57.6 a = 11.6; b = 17.2; SI = 71.2 a = 4 . 5 ; s1 = 5 3 . 5 ; s2 = 42.0 b' = 6.0; s ; = 60.0; sh = 34.0
W Q z
...
N';
(Fig. 3) or planes PoQoSz (Fig. 6) and AOIL
..... ..... ..... )
GO
b b' - ( a / 3 ) ; SI S: - ( ~ / 3 ) ;~2 si - ( a / 3 ) ;a / b = Bx"/Ax". . . . . (3)
Computations STEP 1. LOCATION OF TIE LINE COD" OR CD. Plot m, the orthogonal projection of the treated mixture, and join mS1. On mS1locate 0" such that mO "/O "SI= ?I, Draw tie line COD" through 0 . Alternatively, calculate 0 from a knowledge f: M , S , and ratio R1; then plot 0 , the orthogonal projection of 0, and draw
Vol. 34, No. 8
1
"'
GH
10.2
1
HU
8.6
'i
HW
2.6
Gs Gh HZ
10 6 11 8 7.5
Position of G i n triangle ABSI located graphically from ratio A o G o / G o S ~ ; may be calcd.e; Figs. 6, 7, &- 8
Fig. 8
f
-
a Mixture AM is 27.870 A , 72.2Y0 B. Point m, the orthogonal projection of M on BSl& (Fig. 5 ) , is calculated by Equation 1 t o have t h e following coordinates: b' = 72.2 (27.8/3) = 81.46; s: 0 (27.8/3) = 9.26; s ; = 0 9.26 = 9.26. Complex 0 is obtained b y mixing 1 part b y weight of M with the Si present in 0.93 part b y weight of mixed solvent S (Fig. 2 ) . Therefore 0 = 0 . 2 7 8 part A 0.722 part B (0.585 X 0.93) part SI 18% A 35.3% SI 4- 46.7% B. Point 0' is the orthogonal projection of 0, and its coordinates must (18/3) = 52.7; si = 0 (18/3) = 6.0. b e s ; = 35.3 f (18/3) = 41.3; b' = 46.7 Complex N is obtained b y mixing 1 part b y weight of M with 0.93 part b y weight of S (Fig. 2 ) ; or in terms of orthogonal projections, n is obtained by mixing 1 p a r t b y weight of m with 0.93 part b y weight of S (Fig. 5). T h e coordinates of point n must be: b' = 81.46/1.93 = 42.2; s ; = (9.26 0.93 X 58.5)/1.93 = 33.0; si = (9.26 0.93 X 41.5)/1.93 = 24.8. Complex N' is obtained b y mixing t h e weight of B present i n 1 part of M with 0.93 part b y weight of S (Fig. 6). T h e coordinates of point N' must be: b' = 72.2/(0.93 0.722) = 72.2/1.652 = 43.6; si = (5S.5 X 0.93)/1.652 = 33.0; s i = (41.5 X 0.93)/1.662 = 23.4. T h e coordinates of t h e orthogonal projection, G o , of point G are: b' = 15.4; si = 69.2; si = 15.4. G lies on line ASi, and its coordinates (in terms of A and Si) can be calculated irom Equation 1. I n this
+
+
+
+
+
+
+
+
-+
+
COD". STEP 2. LOCATIOK OF POINTn. Plot S,join mX; join OOSZ, aFd the intersection of O'SZ and mS gives n. Alternatively, calculate the composition of complex N from knowledge of M , S , and ratio E M ; then plot n. STEP 3 . LOCATION OF TIE LINE J K . C a l c u l a t e t h e composition of complex N ' from knowledge of N . Plot N',and draw tie and line J K through it. Alternatively, join BS, then join A produce it to cut BS in N ' . OF INTERSECTION ROT" OR CT' OF TIE STEP 4. LOCATION LINEPLAXES.Draw Po& by extending tie line COD ; complete plane P0QoS2. Draw I L by extending tie line J K , and complete plane A OIL. Draw R " T o , the intersection of planes Po&"SZ and A OIL. STEP 5. LOCATIOX OF QUATERNARY EQUILIBRIUM CURVE C " E " D " OR CED. Locate point z on orthogonal projection C "E" D oof quaternary equilibrium curve C E D by taking a perpendicular cross section through tetrahedron on line H h at right angles to edge BSl. Draw and measure Hh. Locate point V at intersection of H h and ternary equilibrium curve for the system O n ,
-
+
BS1Sz. Measure H V . Locate G o at intersection of A "SIand Hh. Measure ratio A "G0/GoS1. Construct separate ternary diagram for system ABSI, Figure 8 ( a ) . In triangle ABS, plot H on BS1; locate G on AS,from measured ratio AG/GS1; draw and measure GH. Then locate U , the intersection of the ternary equilibrium curve and GH, and measure H U . Finally draw tie line C D and produce it to intersect sides AB and AS1 in P and Q; locate W , the interseetion of C D and G H , and measure H W . Construct separate triangle AS&, Figure 8 ( b ) , and mark points G, &, and h on edges AS1 and S,SZ, respectively. Join Gh and QSZ, and locate g at their intersection. Measure Gh and Gg. Construct triangle HGh, Figure 8 ( c ) ,from the previously ascertained lengths H h , HG, and Gh. On side GH set off points U and W from the previously measured lengths H W and H U ; on side Gh measure
August, 1942
INDUSTRIAL AND ENGINEERING CHEMISTRY
Coordinates of Point, %
Operation
Point
Step 5(b)
Hi hi VI
b'
GO,
b'
Ql
n
Ul
a
Wl
a
81
a = 19.7;
b' b'
-
81.0; 8 ; = 19.0 = 62.3; s i 37.7 = 67.4; s i = 5.0; 8: = 27.6 = 74.6; s i 12.7; s: = 12.7 = 38.1; b = 61.9 = 33.7; b = 64.3; =
s1 = 2.0 = 22.5; b = 69.7; s1 = 7.8
b = 62.0;
18.3 72.6; s;
sz = 21
b' =
HZ hz
Va
4
Remarks
...
...
.....
Hthi HiVi
8.3 6.1
.....
...
...
..
GIHI H i UI
8.4 7.5
HI WI
5.0
GIQI Gihi Hizi
4.7 9.7 3.7
.....
0
.... ..... h
.....
.....
= 17.2
s:
Step 5 ( c )
= 10.2;
Line
si
b' = 82.4; = 17.6 b' = 64.5; s: = 35.5 b' = 69.2; s i = 4.5; = 26.5 b' = 76.4; si = 11.8; 8; = 11.8 a = 35.4; b = 64.6 a = 31.4; b 66.7; s, = 1.9 a = 22.8; b = 70.8; SI = 6.4 a = 20.4: b = 64.6;
si
Hzhz Hz Vz
7.8
6.8
..... .....
...
...
.....
GzHz Hz Uz
7.8 7.0
...
...
point X which represent the com osition of mixture x in terms of B, Si, and Sa. The composition of mixture Y may be obtained in a similar manner.
1,
TABLE11. COMPLETE CALCULATIONS (Cont'd) Length of Line. Cm.
969
.....
Steps 5 and 6 are the two most laborious operations but are not so lengthy as appears from the descriptions; once the sequence of construction has been understood, the actual performance is simple and comparatively rapid. With a little practice it becomes easy to select positions for the necessary cross sections to get point x , for example, with only two points such as z1 and z2, one on each side of line RT.
Example
The procedure is best illustrated by means of a n example: A mix.... UZ ture, consisting of 27.8 per cent by weight of acetone and 72.2 per 5.05 ..... Hz Wz wz cent of chloroform, is to be batchh extracted a t 25' C. in a single stage 3.8 Gzgz 82 sz = 15.0 9.05 ..... Gzhn with a mixed solvent. The com3.4 b' = 74.5; si = 10.0; Hzzz ..... zz position of the mixed solvent is s: = 15.5 58.5 per cent by weight of water and 41.5 per cent of acetic acid. b' = 6.0; s; = 60.0; Step 6 ( a ) 2/ s: = 34.0 The ratio of the weight of mixed By"/Aoy" b' 7 57.6; s: = 21.2; Fig. 9 YN solvent to the weight of treated 8, 21.2 = 1.75 mixture is to be 0.93. Assuming Y ... ... Calad.i a = 6.6; b = 3.8; equilibrium is reached in the single8% = 57.8; s1 = 31.8 stage batch operation, what will be 5 ... X b' 73.3; si = 10.0; ... Step 6(b) the composition of the two resultSA = 16.7 ing phases? The equilibrium data b' = 84.0; si = 8.0; Bx"/A"x" 2" ..... at 25" C. given in Table I are = 0.303 s: = 8.0 X ... Calcd. as for Y in ... a = 20.2; b 66.5; available, and it is known that the SI 3.3; 82 = 10.0 ... note i ... system belongs to the general type illustrated in Figure 1. case, since b' = 0 t. ( 4 3 ) ; s: = 0 + (a/3); and si = SI + (a/3), then a = 3b' or 3.3: and SI = s: - b' To conform with the desigor si - 8:. Therefore, a = 3 X 15.4 = 46.2; 81 = 69.2 - 15.4 = 53.8. nations previously employed, let f In this instance the cross section selected has been such that the resulting point z on the orthogonal acetone be denoted by A , chloroprojection of the quaternary equilibrium curve has fallen on line R T ; therefore point x is also the projected quaternary tie line point y (Fig. 9) used in step 6. form by B, water by 81, and 0 The aross sections through Hihi and Hzhz are now on the opposite side of the tetrahedron to the cross acetic acid by SZ. A quantitaaection through H h of step 5; therefore points G I and Gz are situated on line AB. The position of GI tive plot on ternary coordinates and Gz on A B may be caloulated as for U on A B described in note e. of the AB& data is shown in Since cross sections Hlhl, etc., are now on the opposite side of the tetrahedron, points 01, etc., lie in Figure 10 (a). A similar plot of triangle AB&. The relations given in Equation 3 enable Y to be calculated from II and the ratio Bg"/AOg"as folthe BX& data is given in Figure lows: a/& 1.75; b = 6 - (a/3); SI = 60 - (a/3); s i = 34 - (a/3). Thereforea = 6.6; b = 3.8; 10 (b), and the ABSl data are SI = 57.8; sz = 31.8. orthogonally projected so t h a t i The cross seotions selected have been suoh as t o give points z i and zz straddling line R T . Point x Figure 10 (b) is also the orthogois then obtained as the intersection of the line joining 11 and zz with line R T . nal projection of the equilibrium 'frustum onto the base B S I X ~ . The actual diagrams used in the calculations were drawn on _ . off Gg t o locate point g; and on side H h locate V from the known triangular coordinate paper; each side of the paper emlength H V . lh"lines uy and wg which intersect at 2. Draw ployed is 10 inches long, divided into ten l-inch parts, and a line through 2 perpendicular to H h and intersecting it at 2. Measure Hz, and hence mark off point z on base projection each of these ten parts is again subdivided into ten 0.1-inch BSIS2. parts. By taking other cross sections through the tetrahedron on lines H1hl, Haha, etc., locate enough additional points 21, 22, etc., to deThe calculations are shown in 'I. The fine curve C"E"D" near its intersections with line ROT". various points used in carrying out each step or located by STEP6. LOCATION OF POINTS X AND Y. Read off the eomeans of it are listed, as well as their coordinates, if on the ordinates of intersections z and Y of curve C"E"D" with lin,e If, however, base triangle BS1&, in terms of b', si, and 5;. ROT". Draw line Xpz, and produce t o intersect line Po&"in z the point referred to should lie on any of the other three Draw slz!, and produce to intersect in z,,. Measure Bz,; triangles or inside the tetrahedron, its coordinates are given and A0x" and obtain their ratio. From a knowledge of this with the notation a, b, sl, and 52. Where the measurement ratio and dhe coordinates of point x, calculate the coordinates of GZ
-
...
-
1..
1 . .
-
-
-
-
. . I
0
970
I N D U S T R I A L A N D. E N G IN E E R I N G C H E M I S T R Y
of a line is a necessary part of the operational step, the line and its length are given. These data enable the complete calculation t o be followed in detail on any triangular coordinate paper. All calculations were made on a lO-idch slide rule, and measurements were taken t o the nearest millimeter. The operation described in the example quoted was carried through experimentally, and comparison between actual and calculated results are shown below: Phase Upper layer (point Y ) Actual Calculated Lower layer (point X ) Actual Calculated
--Compn., A
B
weight yo-
s2
3.5 3.8
57.4 57.8
31.6 31.8
20.3 20.2
67.3
2.8
9.6 10.0
3.3
a
solved in less than 3 hours. Three to four days are required to carry out the operation experimentally. A previous publication (3) showed that similar equilibrium relations apply to an oil-binary mixed solvent system, and computations in such a system will be the same as those described here with some slight modifications. Such modified calculations for an oil-single solvent system compared to those for a three-component system have already been discussed (6, 6, 7).
Literature Cited
si
7.5 6.6
66.5
voi. 34, NO.
The time taken in carrying out these computations is not excessive. The above example, for instance, was completely
(1) Bachman, IND. ENG.CHEM.,-4h.i~. ED., 12, 38 (1940). (2) Brancker, Hunter, and Nash, IND.ENG.CHEM.,33, 8 8 0 (1941). (3) Brancker, Hunter, and Nash. IND.ENG.CHEM.,ANAL.ED., 12, 35 (1940). (4) Brancker, Hunter, and Nash, J . Phus. Chem., 44, 683 (1940). (5) Hunter, in “The Science of Petroleum”, Vol. 111, p. 1818, Oxford Univ. Press, 1938. (6) Hunter and Nash, IND.ENG.CHEM.,27, 8 3 6 (1935). (7) Hunter and Nash, J. Inst. PetToleum Tech., 22, 4 9 (1936). (8) Hunter and Nash, J . SOC.Chem. Ind.,51, 285T (1932). (9) Kurtz, IND.ENG.CHEM., 27, 8 4 6 (1935).
Chemical Treatment of Trade Waste LAUNDRY WASTES FOSTER D E E S N E L L AND J. MITCHELL FAIN Foster D. Snell, Inc., Brooklyn, N. Y.
P
ROPOSED treatments for laundry wastes fall broadly into two types, bacterial and chemical. M‘hile bacterial methods are considered the most economical in operating costs, detailed operating procedures are involved and experience with the methods is limited. Difficulties due to alkalinity of the waste could arise. Eldridge (a) estimates the biological oxygen demand (B. 0. D.) of laundry waste a t 400 to 1000 parts per million and recommends an intermittent biological filter a t 1 gallon per square foot per hour. Costs are estimated by analogy t o milk-plant wastes where it would appear that excavation and materials such as concrete, pumps, piping, stone, housing, etc., would average about $100 per thousand gallons, plus $500. Thus a plant to treat 75,000 gallons daily would cost $8000. The cost of operation is small in terms of electricity, but substantial expense in terms of repairs and supervision may be entailed. * Such a plant produces no sludge. Chemical methods for treating laundry wastes have somewhat wider application. References in the technical literature are relatively few, with considerable disagreement among them as to recommended procedures. This is not surprising in view of the diversity of operations in different plants, varying from family laundry in some to industrial overalls in others. Sakers and Zimmerman (6) found the best treatment to be 1200 p. p. m. of lime and 280 p. p. m. of ferrous sulfate, at a cost of 12.3 cents per thousand gallons. After the This is the seventh paper in this series. The first appeared in A m . the third paper was not published. The others were printed in INDUBTRIAL AND ENGINEERINQ CHEMISTRY as follows: 19, 237 (1927); PO, 240 (1928); 21, 210 (1929); 16,580 (1934). 1
D y e s h f Repti-,, 16, 54 (1927);
waste was sedimented in tanks, the upper layer flowed through a baffled ditch t o a cinder bed to catch any escaping floc. The sludge from the settling was passed t o a drying bed and, on a dry basis, contained 2.6 per cent of grease and 1 per cent of combined nitrogen. Improvements in the treated waste over the raw waste were as follows: turbidity 92.9 per cent, color 64.4, total solids 65.5, suspended solids 96.7, and oxygen consumed 89.3. Daniels (3) adjusted laundry waste with sulfuric acid to pH 2.6 for lime treatment or to pH 7.0 for aluminum sulfate treatment. After settling, the clear supernatant liquor was run off. The settled sludge was dried on beds. Alum treatment after sulfuric acid addition was found cheaper than lime treatment. Tabular data by Pohl (6) s h o w lime to be the poorest coagulant and aluminum sulfate the best. Kline (4) in a report of studies on four laundries found that results varied considerably in each laundry from one part of the day to another. He quotes an average B. 0. D. of 183 p. p. m. and suspended matter of 252 p. p. m., as similar to values for domestic sewage. The oxygen-consumed figure of 196 p. p. m. is higher than the normal for domestic sewage. Boyer (1) found pH adjustment t o 6.4-6.6 with sulfuric acid desirable before treatment. After such adjustment it was necessary to use 240 p. p. m. of ferric sulfate, 160p. p. m. of ferric chloride, or 200 p. p. m. of aluminum sulfate. The B. 0.D. was reduced by 85-90 per cent; 4 per cent by volume of wet sludge resulted. The laundry whose waste disposal problem is the subject of this paper is situated on a n arm of the sea on the south shore of Long Island. A maximum of 75,000 gallons of waste
