Graphical Methods’ in Rayon Manufacture Characteristic g r a p h i c a 1 methods for the control of solutions in rayon manufacture are illustrated. Application of graphical methods to solution control, production, and operating problems in rayon manufacture is presented.
CONTROL OF FACTORY SOLUTIONS JOSEPH H . KOFFOLT AND J A M E S R . WITHROW
T
HE factory control of solutions within very narrow limits is an important chemical engineering problem in many industries. Even apparently insignificant variations of concentrations sometimes bring about marked variations in the properties of the products. This is especially true in the manufacture of rayon by the viscose process. The mere chemical correctness of the solutions is not enough. The color, luster, feel, and strength of the finished yarn depend also on the accurate and uniform control of solutions in the process a t all times, in the face of constant changes in composition, concentration, and other factors due to both the chemical reactions and engineering dperations taking place. With several variables, obviously the computations for “butting-up” (or strengthening) such solutions from stocks which themselves vary from day to day, are not only time consuming but also a fertile source of error, which is financially disastrous to plant operation. Factory-solution control problems in rayon manufacture involving from three to twenty variables have been simplified by the use of graphical methods and especially nomographic charts. Examples of nomographic charts given in this paper are typical of charts used by the authors in large rayon plants for solution control work. Over one hundred such charts were used. The following characteristic types of charts are presented in this paper: 1. A simple typical three-variable chart used for computation of amount of acid required to butt-up the sour bath in the bleach-
ing of rayon yarn. 2. A chart used for the computation of water and sodium hydroxide to be added to a sodium hydroxide-sodium sulfide desulfurizing solution when the concentration of sodium sulfide is above the prescribed operating strength. 3. A comprehensive chart used in solution control work in which the addition of one of the components affects the concentration of another, such as the effect of alkalinity of sodium sulfide solutions on caustic concentration of a desulfurizing solution. 4. A complex spin-bath solution chart involving four components in solution, such as sulfuric acid, zinc sulfate, glucose, and sodium sulfate, where change of solution due to addition of sulfuric acid is involved.
--
1 Full-soale prints of the nomographs described here may be obtained at cost from the,authors.
The Ohio State University, Columbus, Ohio
Factory-Solution Control Problem Analytical research has placed us in the position that almost anyone can be taught routine control analysis. To teach elementary or high school and even many university graduates what to do after the analysis is another problem. Even in the event that one has a t his command a welltrained and organized technical staff, the chance that error will creep into calculations is ever present, whether these calculations be made by the slide rule, logarithms, or otherwise. Then, too, the time factor is an important consideration in production work. Both the personal eguation in the calculations and the time factor can now be eliminated by the use of graphical methods of computation for the control of these solutions. Computations in solution control work involving two variables can be plotted easily on ordinary coordinate paper. In work involving three variables, a family of curves can be plotted; in some cases this can be simplified by the use of logarithmic coordinate paper or of hexagonal charts. Construction of such charts is time consuming, and interpolation is sometimes difficult. When there are more than three variables, a differenttype of chart has to be used. For this work none is so rapidly constructed and easily read as the nomographic (or alignment) type of chart. APPLICATIONOF AT^^^^^^^^^. The fundamental principle involved in the construction of nomographic charts consists in the representation of an equation of three variables by means of three scales in such a manner that a straight line intersects each scale a t values satisfying the equation. There is no limit to the number of variables that can be plotted on such charts. It has been the writers’ experience that absolute chemical control in the manufacture of rayon can be entrusted to men without a technical education or with only subgrade-school training when use is made of such charts; the expense of hiring univFrsity graduates for this important work can thus be reduced. CONSTRUCTION OF NOMOGRAPHS. Methods of construction of these nomographs are not given here, as they are covered adequately in the numerous books on graphical methods such as those by Lipka (4), Hewes and Seward (8), and Davis and Genereaux ( I ) . 923
924
VOL. 30, NO. 8
INDUSTRIAL AND ENGINEERING CHEMISTRY
following equation. Any change in volume caused by solution effects of sulfuric acid in water was assumed to be negligible for this particular case. A method for taking this into consideration is presented later in the paper. L = 0.426 D(6.55 - T ) (1) where L = 65.7' BB. HgSOd to be added, liters T = strength of acid in tank, grams/100 cc. solution D = depth of acid solution of strength T in the tank, inches 0.426 = a constant dependent upon Rize of tank (18.42 gallons/inch), strength of concentrated butting-up acid (170 grams HzSO4/100cc. solution), convergion factor from gallons to liters, and strength finally desired
TYPICALPROBLEM.Suppose the sulfuric acid stocksolution tank as made up contained 40 inches of acid solution consisting of 6.00 grams of sulfuric acid per 100 cc. Ifit it be required to calculate the amount of 65.7' RB. acid that mu8t be added to bring the strength to 6.55 grams per 100 cc. of solution. Figure 1 is the nomograph for Equation 1 and is a simple type I1 (log-scale) chart as given by Lipka (7). Procedure for solution of the problem was as follows: Courtesy, Industrial R a y o n Corporation
STEEPING PRESS The first step in the viscose process is the steeping of pulp with about 18 per cent sodium hydroxide solution to form alkali cellulose. Uniform impregnation of pulp with sodium hydroxide is essential. Excess sodium hydroxide solution and so-called hemicellulose formed are removed from the steeped pulp by hydraulic pressure.
I n this work of solution control computation it was found that all charts could be constructed according t o the first three types discussed by Lipka (4). However, the presentation of Lipka's type I11 chart was modified to take into consideration possible positive and negative values; Lipka does not appear to cover this phase. It was also found that many of the simpler and more widely used charts could be constructed by men on routine control testing, whose education did not usually extend beyond the second year of high school but who had fair drafting ability. This was done by summing up the basic mathematical principles of nomography into simple rules.
Joined 40 (D scale, corresponding to depth of solution in tank) and 6.00 (Tscale, corresponding to strength of acid in tank) with a straight line; then the number of liters of 65.7" BB. acid to be added to bring the strength to 6.55 grams per 100 cc. of solution was read directly from the L scale and was noted to be 9.3 liters. Although the computations involved in Equation 1 are simple, experience in a rayon plant, where over fifty such or similar solutions had to be controlled, showed that a nomo-
L
T
D
Nomograph for Butting-up Acid Used as Sour after Bleaching A simple but widely used, typical, three-variable solution control chart is illustrated in Figure 1. This chart was used for computing the amount of 65.7' BB. sulfuric acid required to butt-up the sour bath in the bleaching of rayon yarn. For example, it was found by analysis and calculation that the strength of acid required to butt-up the sour bath after bleaching 120 pounds of rayon yarn with sodium hypochlorite solution was one bucket (11 liters) of solution, made up of 6.55 grams of sulfuric acid per 100 cc. In the make-up of this acid many things happened. Theoretically, all that should be necessary would be to add a definite amount of 65.7" BB. acid (170 grams of sulfuric acid per 100 cc. of solution) to a definite amount of water. But in plant operation, the process did not always run normally. For example, the solution-preparation man often forgot to shut off the water valve and obtained too much water in the tank, or the water valve,leaked, or carboys of acid did not always contain the same amount of acid; occasionally the acid was not as high as 65.7' BB. in strength. If the acid as originally made was found not to be of the desired strength, then the amount of 65.7' BB. acid to be added to butt-up stock acid to bring the strength to 6.55 grams per 100 cc. of solution could be computed from the
FIGVRE1. CHARTFOR BUTT-UPOF ACIDSOLUTIONS
+
Key for use: T D = L Butt-up equation: L = 0.4260(6.55
- T)
graph such as Figure 1 was a great aid; it saved time, and errors in computations were reduced almost to zero. It also gave the solution-preparations man a feeling of the "imminency of error,' in make-up and butt-up of solutions. He could see a t a glance the effect of adding too little or too much acid and therefore took more pains with his work. The technical director thus had less cause for complaint.
925
AUGUST, 1938
Special Nomograph for Control of Desulfurizing Solutions
A special type of chart used for computing the amount of water and concentrated sodium hydroxide solution of varying strength to be added to a sodium hydroxidesodium sulfide desulfurizing solution when the concentration of sodium sulfide was above the prescribed s t r e n g t h is i l l u s trated in Figure 2. This chart was used in cases where the resulting strength of sodium sulfide in the desulfurizing BUTT- UP Equations Key FOPU s e solution tank was D+ Do,x So I: D o t so= D+ too high (as a re2: DL + c. -- c a 933 D+ - 2.33Doc. sult, for example, of 3:D,+C = P L= 0.0~2 6 mistakes made by 4: P+ 6 s L t h e solution-preparation man). It FIGURE 2. CHART FOR BUTT-UP OF SODIUM SULFIDE SOLUTION was also used to the c o m 1) u t e amount of stock sodium hydroxide solution required in the 100 cc. of solution. Let it be required to compute the amount of water and the units of butting-up sodium hydroxide solumake-up of fresh desulfurizing solutions. Data and variables pertaining to this solution control tion (concentration, 21.55 grams per 100 cc.) to be added so that the resulting solution will contain 1.00 gram sodium problem were as follows: sulfide and 0.40 gram sodium hydroxide per 100 cc. of soluK = tank constant = 28 gallons/inch of solution tion. Do, D, = initial and final depth of solution in tank; maximum Equations 2 and 3 have the forms of Lipka's type I and working depth = 50 inches so, si = initial (varied from 1.00 to 1.20 grams NazS/lOO cc.) type I11 equations and stationary scales ( 5 ) . Graphical and desired final concentration (1.00 gram Na2S/ solution of the problem is shown by the dash-line construc100 cc.) of NazSin solution tion in Figure q. The steps in the graphical procedure were co, c/ = initial (varied from 0.20 to 0.60 grams NaOH/100 cc.) as follows: and desired final concentration of NaOH in solution B = concentration of butting-up NaOH solution (varied (1) Joined 40 (DOscale) and 1.2 (sa scale) with a straight line, from 10 to 22 grams NaOH/100 cc.) and marked its point of intersection 48 on the D, scale, This L = amount of butting-up NaOH to be added from stock point represents the depth of solution in the tank after water tank which was calibrated so that one unit on scale and sodium hydroxide solution have been added. attached to sight glass was equal to 1 liter (2) Joined 40 (Do' scale) and 0.30 (co scale) with a straight line, and marked its point of intersection c on the C scale. The amounts of sodium hydroxide solution and water to be (3) Joined 48 (0, scale) with c (C scale), and marked its added to the desulfurizing solution tank to bring it to the depoint of intersection p on the P scale. sired strength of 1.00 gram of sodium sulfide and 0.40 gram (4) Joined p ( P scale) with 21.5 ( B scale), and marked its of sodium hydroxide per 100 cc. of solution were computed from point of intersection 35.5 on the L scale. This point re resents the units of sodium hydroxide solution to be added from tEe stock the following equations, derived from material balances: tank and was noted to be 35.5 units. Therefore add 35.5 units of sodium hydroxide from stock tank, and add water to a depth of 48 inches. = fink depth of solution in tank after addition of water In addition to the typical example just illustrated, Figure and NaOH solution 2 was used in many desulfurizing solution control computation problems. Some examples follow: L = 0.933Dl - 2.33CoDo (3) 0.022B BATCHDESULFURIZING. I n the desulfurization of rayon = units of NaOH solution to be added from stock tank waste and skeins by the batch tank method, the depth of to maintain a concentration of 0.40 gram NaOH/ solution in the tank was kept a t a constant level. By modi100 cc. at a final depth of Dfinches fying or changing the order of steps of the graphical solution, TYPICAL PROBLEM. The desulfurizing solution tank as Figure 2 was used for these two special cases. The Dl scale made up contained 40 inches of solution containing 1.2 (which represented the depth to be maintained) was joined grams sodium sulfide and 0.30 gram sodium hydroxide per with the SO scale, and the point of intersection was noted on
.
INDUSTRIAL AND ENGINEERING CHEMISTRY
926
(Right) SPOOL-SPINNING MACHIKE SPOOLVACUUMWASH Box
AND
After being blended, aged, and filtered, the viscose is. converted into endless filaments of rayon by either the spool-spinning or the pot-spinning method. The cellulose is regenerated and converted into rayon by the reaction of viscose and the spin-bath solution. The acid and salts in the rayon spools are removed by washing in vacuum wash boxes.
Courtesy, I n d u s t r i a l
Rayon
Corporation
VOL. 30, NO. 8
AUGUST, 1938
INDUSTRIAL AND ENGINEERING CHEMISTRY
the Doscale. The point of intersection on the Doscale represented the depth to which the tank had to be drained, or the depth of solution in the tank before water or sodium hydroxide solution was added. The steps in the graphical solution from this point on were the same as discussed above in the solution of the typical illustration. MAKE-UP OF DESULFURIZING BATH. In the make-up of a desulfurizing solution to 1.00 gram sodium sulfide per 100 cc., the alkalinity of the resulting solution was found to be 0.25 gram sodium hydroxide per 100 cc. of solution. It was therefore necessary to add stock sodium hydroxide solution to bring it up to 0.40 gram sodium hydroxide per 100 cc. Figure 2 was used to determine the amount of sodium hydroxide solution to be added by following the graphical procedure steps 2, 3, and 4 (omitting step 1) given for the typical problem. I n this case 01represented the inches of solution in the tank at final make-up. Figure 2 showed that the concentration of both sodium hydroxide and sodium sulfide could be above the desired strength. The amount of water required to bring the sodium sulfide to the desired strength may or may not be sufficient to bring the sodium hydroxide concentration below or just to 0.40 gram sodium hydroxide per 100 cc. of solution. I n the latter case Equations 2 and 3 were not applicable. By the algebraic method of calculation, this was found out only after tedious computations, This information was obtained a t once and with very little effort by the graphical method.
Comprehensive Nomograph for Control of Desulfurizing Solutions An interesting but confusing problem in solution control work was one in which the addition of one component, due to hydrolysis, affected the c o n c e n t r a t i o n of the other. Such was the case, for instance, with concentrated sodium sulfide solutions which had a ratio of sodium sulfide to sodium hydroxide Of4tO1. If sodium sulfide was added t o the desulfurizing bath, it would change the sodium hydroxide concentration. If the latter was a t the desired concentration, this addition of sodium sulfide solution would make it therefore necessary t o add water and also additional concentrated sodium sulfide to compensate for the water added. Data and variables pertaining to this solution control problem were the same as for previous problems with the following exceptions: SO = initial concentration of Na2S(varied from 0.55 to 1.00 gram NazS per 100 cc.) N = concentration of butting-up NazS solution (varied from 8 to 20 grams NazS
P
The amounts of water, sodium hydroxide, and sodium sulfide solution to be added to the desulfurizing tank to bring it to the desired strength of 1.00 gram sodium sulfide and 0.40 gram sodium hydroxide per 100 cc. of solution were computed from the following equations, derived from material balances :
If G was positive, water and additional stock sodium sulfide solution were added to compensate for the excess sodium hydroxide in solution; then H
=
2 . 8 G = increase in depth after Na28
solution and water were added
(5)
If G was negative, sodium hydroxide solution was added to bring the strength to 0.40 gram of sodium hydroxide per 100 cc. Therefore, L
=
45.3 G / P
(6)
Units of stock sodium sulfide to be added from stock tank were computed by the following equation:
M
=
17.8
[
(7)
N - 1
If G was negative, no water had to be added and the effect of dilution by addition of sodium hydroxide solution was assumed to be negligible, in which case the term 2.8 G / N is zero.
per 100 cc.)
=
M =
H
927
=
+G =
concentration of butting-up NaOH solution (varied from 10 to 23 grams NaOH per 100 cc.) amount of NalS solution to be added from stock tank which was calibrated so that 1inch of solution in desulfurizing tank was equal to 17.8 units on the scale attached t o the sight glass of the tank increase in depth in desulfurizing tank after M units of NazS solution and water have been added excess or deficiency, in pounds of NaOH, after stock NazS solution has been added to bring the strength from so to 1 gram of NaaS per 100 cc.
Courtesy, H . W . Butterworth S: Sons
BATTERY OF POT-SPINNING MACHINES The parallel oblique white lines (Zejt) are rayon filaments as they leave the spin bath. The filaments are carried up to a roller (godet wheel) from where they are fed to the spinning pot, which revolves at a high rate of speed and'twists the filaments to form thread and rayon cake.
INDUSTRIAL AND ENGINEERING CHEMISTRY
928
J
M
B‘
VOL. 30, NO. 8
+
/
I
t
K e y FOPUse I! 2!
of
Chart
Do
3 1
t Sa - T T + N - B 6 + N’ = J
4;
Do’
+
c,
=
=
-
P
+C
-c
or8
2G
!I
If G is positive 6e G +N“ 8‘ 7a: B B’= M If G i s negative 6b: -G + p L 7 b : (Oaf 8’)i B = M
i
I H
-C
0::
-
FOR BUTT-UPOF SODIUM SULFIDE SOLUTIONS FIGURE 3. CHART
TYPICAL PROBLEMS. Consider the following illustrations : Inches of solution in tank Strength of concd. NazS stock soln., grams/100 cc. Strength of concd. NaOH stock soln., grams/100 cc. Strength NazS in desulfurizing tank, grams/100 cc. Strength NaOH in desulfurizing tank, grams/100 cc.
Case I 25 16
22.64 0 75 0 43
Case I1 25 1.16 22.64 0.75 0.27
The problem is to compute for case I and case I1 the units of sodium sulfide and of sodium hydroxide solution and the inches of water to be added so that the resulting solution will contain 1.00 gram sodium sulfide and 0.40 gram sodium hydroxide per 100 cc. of solution. Equations 4,5 , 6, and 7 have the forms of combined type I and type I11 equations and stationary scales (6). The possible positive and negative values of G obtained by solving Equation 4 did not appear to be covered by Lipka or others. Nomographic treatment of the problem is illustrated in Figure 3 by scales Do‘,DO’’, co, * C , and * G. The points C, and G, on the horizontal line of Figure 3 represent the amount of sodium hydroxide sufficient to maintain a concentration of 0.40 gram sodium hydroxide per 100 cc. of solution. All values above these points on scales C and G represent pounds of sodium hydroxide in excess, and all values below these points on the same scales represent a deficiency of sodium hydroxide. The resultant of a particu-
lar value on J (pounds of sodium hydroxide added with sodium sulfide in bringing up the strength from so to 1.00 gram sodium sulfide per 100 cc. of solution) and a particular value on scale A C will be either positive or negative, depending upon conditions existing in the tank before buttingUP * Case 1. Solution of the problem for case I is shown by dash-line construction on Figure 3. The steps in the graphical procedure were as follows: (I) Joined 25,(Doscale) and 0.75 (so scale) with a straight line, and marked its point of intersection t on the T scale. (2) Joined t (2’ scde) and 16 ( N scale) with a straight line, and marked its point of intersection b on the B scale. (3) Joined b ( B scale) and 16 (N‘ scale) with a straight line, and marked its point of intersection j on the J scale. (4) Jpined 25,(Do’ scale) and 0.43 (cg scale), and marked its point of intersection +c on the +C scale. (5) Joined + c (+C scale) and j ( J scale), and marked its point of intersection 15.83 inches on the +G scale. (6) Joined 15.83 ( + G scale) and 16 (N” scale), and marked the point of intersection b’ (B’ scale). ( 7 ) Joined b’ (B’ scale) and b ( B scale) with a straight line, and marked its point of intersection 25 on the M scale.
For this particular case, 25 units of sodium sulfide from stock tank and water must be added so that the increase in depth of solution in the tank is 15.83 inches (total final
AUGUST, 1938
INDUSTRIAL AND ENGINEERING CHEMISTRY
depth of solution in tank after butting-up = 40.83 inches), and that the resulting strength of solution will be 1.00 gram s d i u m sulfide and 0.40 gram sodium hydroxide per 100 cc. of solution. Case I I . The first three steps of the graphical solution for case I1 were the same as for case I and are shown by the same dash-line construction on Figure 3. The other steps in the graphical solution are shown by dash-dot construction. They were as follows: (4) Joined 25 (Do" scale) and 0.27 (CO scale), and marked its point of intersection - c on the -C scale. (5) Joined - c ( - C scale) and j ( J scale), and marked its point of intersection -g on the -G scale. (6) . Joined -g (-G scale) and 22.64 (P scale), and marked its point of intersection 8.6 units on the L scale. (7) Joined 0 of the B' scale (since it has been shown that 2.8 G / N = 0, and therefore B' = 2.8 G / N = 0) and b of the B scale, and marked its point of intersection 7.5 on the M scale.
For this particular case, 7.5 units of sodium sulfide from stock tank and 8.6 units of sodium hydroxide solution have to be added to 25 inches of desulfurizing solution (consisting of 0.75 gram sodium sulfide and 0.27 gram sodium hydroxide), so that the resulting strength of solution will be 1.00 gram sodium sulfide and 0.40 gram sodium hydroxide per 100 cc. of solution. ALGEBRAIC us. GRAPHICAL METHOD. The time required for computation of the typical problems shown in cases I and I1 by the algebraic and graphical methods was determined by stop watch tests. It was found that the average time for the average solution-preparation man to compute the results arithmetically was about 20 minutes. This time was cut down to 8 minutes when a slide rule was used, down to 3 minutes by a calculating machine, and down to 40 seconds when the nomograph was used. It was also found that the solution-preparation man would rather use the rule-of-thumb method, which was usually 100 per cent off, than to calculate. He was very receptive to the nomographic method. The computations involved a t higher initial concentrations of sodium hydroxide were cumbersome and time consuming by the algebraic method, and were more or less cutand-try in procedure. For example, if the sodium hydroxide concentration of case I was 0.56 instead of 0.43
929
gram sodium hydroxide per 100 cc., and other conditions of the problem were unchanged, calculations indicated that the increase in depth after concentrated sodium sulfide and water had been added was 27 inches. Since the tank had a maximum working depth of 50 inches, a cut-sndtry calculation had to be made to determine how much solution had to be drained or pumped from the tank so that the resulting desired strength was obtained after butting-up. Such calculations sometimes took as much as one hour by the algebraic method, but Iess than 3 minutes by the nomographic method. '
Nomograph for Control of Spin-Bath Solutions Another comprehensive butting-up problem related to the control of spin-bath solutions in viscose-rayon pot spinning. This problem involved the control of four components in solution, such as sulfuric acid, zinc sulfate, glucose, and sodium sulfate. At the same time "nonadditive" changes in volume of sulfuric acid and the spin-bath solution were taken into account, since it is well known, for example, that if 100 cc. of 66" BB. sulfuric acid are mixed with 100 cc. of water, the resulting volume is not 200 cc. but 188 cc. Data for this problem were as follows: Component His04 ZnSOd NrtiSOa Glucose
Find Initial Concn. Desired Conon. G r a m s per io0 cc. 8.t = 10.3 so = 0-10 3 2, = 1.0 20 = 0- 1 .oo nf = 15.0 no = 0-15 0 go = 0- 7.00 g, = 7 . 0 0
K = tank constant = 120 gallons per inch DO,Dj = initial and final depth of solution in tank (varied from 20 to 40 inches) Vo,V, = initial and final volumeof solution in tank, gallons S, G, 2,N = pounds of H&04 (66" B6., 93.19% by weight). glucose (as 70% reducible sugar), ZnSOr (as 36% XnSOa.5Hg0), and NazSOI (as salt cake, 93% NalS04),respectively, to be added to bring the solution from initial concentrations at depth Do to final concentrations at depth 0,
The amount of sulfuric acid, glucose, zinc sulfate, and sodium sulfate to be added (in pounds) to the spin-bath solution to raise the concentration from SO, 9 3 , 20, and no to sf,
Courtesy, Industrial R a y o n Corporation
CORNEROF DYEHOUSE, SHOWING Two TUBSFOR BLEACHING AND DYEING RAYONFABRIC
INDUSTRIAL AND ENGINEERING CHEMISTRY
930
VOL. 30, NO. 8
Since the change in volume is due to butting-up spin-bath solution from an initial concentration (so) to a final and c o n s t a n t c o n c e n t r a t i o n of 10.30 ( s f ) g r a m s of s u l f u r i c a c i d p e r 100 cc. of solution, is therefore a function of so, the values of which are given in Table I. The values in columns 1 and 2 were taken from tables by W. C . Ferguson and H. P. Talbot given by Sullivan (8). The values in the other columns were computed. Table I shows that the variation of with so for this particular problem is very small, and therefore an = 0.0492 was average value of justifiable; the maximum error introduced by making this assumption was less than 0.3 per cent. This was well within the accuracy of reading the depth of solution in the spin-bath tank and other variables. Substituting the value of 0.0492 for in Equation 14:
[;I,
[SI
[SI
[g]
Dj = 1.047 (1
Courtesy, I n d u s t r i a l R a y o n Corporation
WASHING AND DESULFURIZING RAYON ON SPINSPOOLS Sulfur and its compounds are removed from the rayon by treatment with alkaline sodium or ammonium sulfide.
- 0.0043 SO)DO
Equations 8, 9, 10, and 11 can be written in the final usable forms:
x = 10.7 Do [10.78(1 - 0.0043So)
- Sol
(15)
G = 14.2Do [7.33(1 - O.OO43So) - no1 (16)
gj,
5 , and nf grams per 100 cc. may be computed from the
following equations if Dj is known, or if the change in depth due to the addition of sulfuric acid is negligible, in which case Do= Dl (simplest case):
s = O*OB3 G =
z =
I2O (Dfsf 0.93
O'OB3
10.7(10.3D, - Doso) (8)
I2O (Df@- Dogo) = 14.2(7.00D, 0.70 120 (Dfzf -
O'OB3
= 16.7(1.00 0,
- Doga) - Dgo)
(9) (10)
ZnS04 X 0.96 ZnS04.5Hz0 0,083 X 120 (Din/ - Dono) N = 0.93
[$I
since
+
[s] S
S = 0.089 K (10.3 Dj - DOSO)
Equation 12 can be written thus: Do (1
Df
- 0.089 so
(1 - 0.917
TABLE I. CHANGEIN VOLUMEOF 66" B6, SULFURIC ACID ADDEDIN BUTTING-UP SPIN-BATHSOLUTIONS TO 9.66 PER CENT SULFURIC ACIDBY WEIGHTO 66O BB. &SO4
10.7 (15 0, - Dono) (11)
However, since B, is not known in practically all cases and was not an additive function of original volume of spinbath solution and added sulfuric acid, Equations 8, 9, 10, and 11were modified as outlined below. Let be the change in volume of the spin-bath solution, in gallons per pound of 66" BB. sulfuric acid added. The volume of solution in the tank after adding sulfuric acid is then : KD/ = KDo
A sample of spin-bath solution was TYPICAL PROBLEM. titrated and was found to contain 8.00 grams sulfuric acid, 5.00 grams glucose, 0.50 gram zinc sulfate, and 10 grams
(12)
Q
t o Buttup to
9 . 6 6 % Vol. after Change Change Butting- in Vol., in Vol., AS UP AV AV/A&' Lb. Gal. Gal. Gal./Lb. 0.04811 7.827 0.347 7.213 0.04849 0.315 6.496 7.795 0.04857 0.278 7.759 5.739 0.04898 0.243 4.979 7.724 0.04903 0.205 7,685 4.185 0.04936 0.167 7.647 3.386 0.04924 0.126 2.563 7.606 0.04960 0.086 1.734 7.566 0.0499 0.044 7.523 0.877 Average 0 . 0 4 9 2
HsSOa,
9.66 per cent HzSOa by weight = 10.3 grams per 100 cc. of solution.
(13)
[%I)
[SI)
Initial HzSO4 Wt. of Initial Concn. 1 Cu. Ft. Vol. % by wt. Lb. Gal. 62.37 7.48 0.00 7.48 1.02 62.80 7.48 63.24 2.08 7.48 3.13 63.69 7.48 4.21 64.14 7.48 5,28 64.60, 7.48 6.37 65.06 7.48 7.48 65.53 7.48 8.55 66.01
(14)
sodium sulfate per 100 cc. of solution. The depth of solution in the tank was 40 inches, Let i t be required to compute the pounds of chemicals to be added so that the resulting solution will contain 10.3 grams of 66" BB. sulfuric acid, 7 grams glucose, 1 gram zinc sulfate, and 15 grams sodium sulfate per 100 cc. of solution.
AUGUST, 1938
INDUSTRIAL AND ENGINEERING CHEMISTRY
scale marked "lbs. HzS04 and NanSOl to Be Added" and was found to be 2220 pounds.
Equations 15, 16, 17, and 18 have the forms of type I and type I11 equations and stationary scales (6); in addition they contain the factor [1.047 (1 - 0.0043 so)] which is a function of the initial concentration (SO) of sulfuric acid in the spin-bath solution.
[SI
Since an average value of can be taken without aff scting seriously the accuracy of computations, the factor [1.047 (1.0 - 0.0043 SO)] is a straight-line function of so. The SO scale was graduated by the method given for stationary scales ( 5 ) . If an average value of could not have
[s]
been assumed, the value of the factor could have been determined by means of a curve and two perpendicular scales as covered by Lipka (6) or by Hewes and Seward ( 3 ) . For this particular problem, though not for any butting-up problem, only one curve would be required. The chart illustrated by Hewes and Seward required a family of curves. The data given for the spin-bath butt-up problem represents all possible variations of the solutions when they are below t h e p r e s c r i b e d strength. Under normal operating conditions when there was trouble in maintaining the desired concentration, the variance was usually never more than 2.00 grams per 100 cc. for the sulfuric acid, sodium sulfate, and glucose, and F 0.50 gram for the zinc sulfate. The variance in the volume of spin bath was hardly more than 5 inches of d e p t h in t h e t a n k . With these conditions and for this limiting case, a chart similar to that illustrated in Figure 4 would give a very high degree of accuracy, as it would permit smaller limits on the F scale. Graphical solution by the nomograph for t h e t y p i c a l problem is shown in Figure 4 by fullline coiistruction for sulfuric acid, dash-line construction for glucose, dot-dash construction for zinc sulfate, and dot-line construction for sodium sulfate. The steps in the graphical procedure for sodium sulfate, for example, were as follows: (1) Joined 8.00 (so scale) and Na2S04(a point on the C scale), and marked its point of intersection n on the B scale. ( 2 ) Joined point n ( B scale) and 10 (0 scale), and marked its point of intersection en on the E scale. (3) Joined point e,, (E scale) and 40 ( D scale), and marked its point of intersection on the F scale. The amouni of sodium sulfate to be added was read from the
93 1
A similar procedure was followed for sulfuric acid, glucose, and zinc sulfate as indicated on Figure 4. Thus, 2220 pounds sodium sulfate, 330 pounds zinc sulfate, 1190 pounds glucose, and 1025 pounds sulfuric acid had to be added to bring the components in the spin bath to the desired strength. Scale Representation The orthodox method for scale representation by vertical or oblique lines with graduations as a series of short perpendicular lines is illustrated in Figure 5. This representation was used when the writers first introduced graphical methods in a rayon plant for solution control work and other problems concerned with plant operation and production They seemed to be confusing to the average worker. By adopting the block outline form of scale representation as illustrated in Figures 1, 2, 3, 4, and 6, the charts seemed much clearer to him. The average worker seemed to be able to visualize the
Key For Use 0) (2)
s+C=B B+O=E
cs) E + D = F
FIGERE 4.
SPIN-BATH Bwrr-u~CHART
INDUSTRIAL AND ENGINEERING CHEMISTRY
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Key-For Use J.hl+I-l4. A + 6 $
depth in the tank and the units of solution to add, and Figure 6 seemed to bring out more sharply the scale graduations. As a result, the time for making graphical computations was decreased. For this reason the block outline form of scale representation was used in this paper. Figures 5 and 6 are both given to show the two methods of scale representation. They are identical in every other respect. Figure 6 was used for calculating the amount of water and 20 per cent sodium hydroxide to be added to a batch of cellulose xanthate in the dissolvers to produce viscose containing 5 per cent sodium hydroxide and 8 per cent cellulose by weight. The original batch varied from 500 to 600 pounds.
BUTT- UP Equations A - 0.0.5(0.625G-N)6 W-O.I256G-(A+O)
I. O + G - M 2. ij'+N = H
A
T
5 T+M-W
MI
_-
VOL. 30, NO. 8
+ 0
-a .-C
.F
0
Other Uses of Graphical Methods
k 6 0 0
l i
K e y For Use I:
E+G = M
2:6'+N- H 3:M+H-A 4: A + 6'-T
BUTT-UP Equations A = 0.05(0.625G-N)5) W-0.125 6 G -( A + O )
% T + M= W
0
~r
A '
N
__/---
BUTT-UPCHARTS FIGURES 5 A N D 6. ALKALICELLULOSE
-
0'
Many other uses for graphical methods of computation were found in connection with the work in rayon manufacture; most of them involved charts of the nomographic type. Some specific examples follow: OPERATING SCHEDULES.In the bleach and washing department, which worked 24 hours per day, the department superviser had the responsibility of operating the department a t a fixed minimum labor cost per pound of yarn processed. There were over fifteen operations in this particular department, such as washing, stoving, stripping, waste bleaching, drying, etc. Suppose the production of the plant a t a given time varied from 1000 to 2500 pounds per day. The operating schedule of the department had to be flexible to maintain this cost. It was further complicated by the fact that if production did not keep in pace with the reeling a n d i n s p e c t i o n department, equipment would be tied up and thus affect t h e production schedules in other departments. This setup made it necessary for the superviser to work late in the evening to calculate the changes i n t h e o p e r a t i n g schedules. A series of equations for these schedules were developed to maintain the necessary production and, a t the same time, the fixed minimum labor cost. A nomographic chart,
AUGUST, 1938
INDUSTRIAL AND ENGINEERING CHEMISTRY
similar to the solution control charts presented in thi:: paper, was drawn. With this chart the foreman, and even the average worker, could determine the operating schedule, no matter how wide the variation in production. It gave such information as the time for turning steam on and off the dryer; the time for stripping; the time for a crew to work on the dryers, whizzers, and waste bleach; the number of men to be borrowed from a particular shift to work overtime; and the lunch hour for the various workers. It even took into consideration changes in the operating schedule due to breakdown of a particular piece of equipment. MAX-HOURS OF WORK. Nomographs were also constructed for use by the foreman to compute the man-hours of work done by his shift, i n units of time required per pound of yarn processed for each operation. It gave him a check on what he was producing and acted as a “watchdog” for the department superviser. Nomographs were used in the FINISHINQ DEPARTMENT. finishing department for rapid computation of the value to the company in dollars and cents of the work turned out by the inspectors. Those inspectors with ratings that consistently deviated from the average were subject to closer scrutiny by the forewoman.
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Acknowledgment The authors wish to acknowledge the courtesy and kindness of Hayden B. Kline, of the Industrial Rayon Corporation, and William F. Hennessy, of the Rayon Division, H. W. Butterworth & Sons Company, in furnishing the photographs used in this paper,
Literature Cited (1) Davis, D. S., and Genereaux, R. P., in Chemical Engineers’ Handbook, pp. 261-0, New York, McGraw-Hill Book Co., 1934. (2) Hewes, L. I., and Seward, H. L., “Design of Diagrams for Engi-
neering Formulas and the Theory of Nomography,” New York, McGraw-Hill Book Co., 1923. (3) Ibid., p. 87. (4) Lipka, J., “Graphical and Mechanical Computation,” New York, John Wiley & Sons, 1918. (5) Ibid., pp. 5 and 114.
( 6 ) Ibid., p. 20. (7) Ibid., p. 47. (8) Sullivan, Sulphuric Acid Handbook, p. 54, New York, McGraw-Hill Book Co., 1918.
RECEIVED April 13, 1938. Presented before the meeting of the American Institute of Chemical Engineers, White Sulphur Springs, W. Va., May 9 to 11, 1938.
ALCHYMIST By Thomas Wijck (1617-1677)
A list of Reproductions Nos. 1 t o 60 appeared in our issue of January, 1936, page 129. the list of Nos. 61 t o 7i appeared in January 1937 page 74; NOS. 73 to’84 a d lieted in January 1938 page 70, where also is showd Np., 85 and details for obtaining photographic copies of the originals. No. 86 appear? on page 145, February issue‘ No. 87, page 269, March’ issue; No. 88, page 427, April issue. No. 89. Daze 500. Mav ’issue:
ied in black and white only.
No. 92 in the Berolzheimer series of Alchemical and Historical Reproductions is the least somber of the numerous paintings of this famous Dutch painter, seven of which have previously been included in the series, with another on hand to be presented later. Attention is called to the resemblance of some of the equipment t o that in the painting by a n unknown artist shown last month, also t o the fact that the alchemist is obviously the same man as the one depicted in No. 5 in the series.
Here the alchemist has three assistants a t work, while he himself is directing the activities of two ef them, instead of being shown reading, as in the others by Wijck. The original painting is located in the Gemaeldegallerie in Karlsruhe, Germany. D. D. Berolzheimer 50 East 41st Street New York. N. Y.
