I
M. E. FINDLEY Engineering Experiment Station, Auburn University, Auburn, Ala.
Concentration Control
by Electrochemical Methods
Use of APPROXIMATE titration simplifies the control loop
I,
THE APPLICATION of automatic process control to chemical processes, one of the most frequent problems encountered is the lack of suitable automatic composition measuring instruments. Measurements of physical properties are frequently used as indications of chemical compositions, but in many cases this proves to be unsatisfactory, because the physical properties are too dependent on other factors. Thus means are needed which are more exclusively dependent on the component to be measured. Electrochemical measurements, such its p H and oxidation-reduction potentials, are measurements which depend almost exclusively on composition and for which instruments are available. Electrode potentials, being proportional to the logarithm of concentration, are relatively insensitive to small changes in concentration (7, 2 ) . For example, 0.02 p H corresponds to a 501, change in strong acid concentration. However, potentials are widely used to indicate end points of titrations, including continuous titration control systems as shown in Figure 1 ( 3 ) . Such system contain two interdependent control loops and more sources of difficulty than the usual simple control loop. One method of simplifying such a system would be to
Control of solutions amenable to electrochemical measurement through pH or redox potential can be readily effected by
b Proportionately adding an offsetting solution b Measuring the small residual difference between
the expected resultant composition and the actual composition of the mixture by potential
Using this signal, which is a sensitive measure of the difference, for
control
This system can be applied to many problems in routine onstream process control meter sample and titrating streams a t constant rates according to the desired concentration and use the potential to determine whether the concentration were high or low and control, accordingly as shown in Figure 2. However, such approximately titrated potentials would be extremely nonlinear with concentration, and very difficult to “read” in terms of concentration, as shown by the calculated curve A in Figure 3 . The neutralizing solution in Figure 2 could contain a component which would produce buffering compounds at the end point, such as a weak acid and its basic salt.
In this case, the p H would depend on the resultant amounts of weak acid and its salt which in turn would vary only with sample concentration. Over a range of concentration directly proportional to the amount of buffer, the p H would vary more gradually and linearly with sample concentration. The same considerations should apply for oxidizing or reducing reactions using an oxidationreduction buffer. This study covers some investigations on the feasibility of using buffered approximately titrated sample potentials as measurements of concentrations.
H
NEUTRALIZING
H
SOLUTION
NEUTRALlZlNG SOLUTION J CONTROLLED,
I
ROCESS
I
I
CONCN. REC. CONTROLLER
CONCN CONTROL MEANS REC. CONTROLLER Figure 1. This type of automatic titration system, available commercially (3), contains two interdependent control loops
Figure 2. This proposed control system, with constant speed ratio metering pumps, will give satisfactory results for some concentrations if the end point is properly buffered VOL. 53, NO. 6
JUNE 1961
471
Figure 3. The variation of NaOH sample pH after constant acid addition shows how the end point can be buffered to provide an accurate measure of concentration b y PH
Measurement of Concentrations of a Single Strong Base
Samples were made up containing 35 grams per liter 3 ~ 1 0 % NaOH to be measured by approximate neutralization with a standard solution of H2SO4, with acetic acid to produce a buffered end point. The neutralizing solution contained HzS04 equivalent to 95y0 of the average amount of NaOH when mixed 5 to 1 by volume with sample. The acetic acid was equivalent to 10% of the same amount. On mixing sample and solution in the above proportions, a solution containing NazS04,sodium acetate, and acetic acid resulted within *5yc of average sample concentration. The ratio of acetic acid and sodium acetate determined the resultant pH. Five samples were neutralized and the pH determined to obtain a calibration curve. Various samples were then checked in the same way, including three samples made up and checked a month later. A Zeromatic meter standardized at p H 7 was used. The results showed an accurate and fairly linear pH-concentration relationship over a A570 range of concentration. The same principles would apply in measuring a strong acid conceiitration, and results should be similar. In the case of weak acids and bases, the buffer should be effective in a pH range where the samplc would be completely neutralized. If not, the sample might form a buffer itself, which would prevent significant p H changes. To increase the range of measurable concentration, an increased amount of buffer could be used, but errors of pH measurement converted to concentration wouId be increased proportionally. In order to double the range of the tests made, 90%
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HzS04 and 207, acetic acid equivalents would be used. Doubling the concentration scale in Figure 3 would indicate expected results. In this case, the deviations from the curve of the tests-not including calibration-were determined. The averageactual-indicated-was - 0.25Yc. The square root of the mean of squared deviations was 0.26$& of average concentration. Thus approximately 95y0 of the time the error would be less than 0.5270. This was approximately the reliability of the procedure. Since continuous metering errors would be about 1%, these would dominate the accuracy of both the titration system, Figure 1, and the approximate titration system, Figure 2. Metering might be less critical in Figure 2, since only a constant ratio is required.
Measurement of Concentrartions of Mixed Ncs&Oa and N a O H
I n order to measure both NaZC03 and NaOH in the same solution, the NaOH and one half the Na2C03 could be
099
LO1
NORMALITY
1.03
neutralized to a pH of about 8, and additional acid could be used to neutralize the NazCO3 completely a t a pH of about 4. The same neutralizing solution could be used if it contained a buffering agent at each pH. A buffering acid solution was made up containing about 0.4M H3PO4, 0.44iM phenol, and 0.35M acetic acid, which gave an almost linear pH ts. 7 0 neutralized curve. The amount of buffering acid solution to use for a given neutralization could be calculated based on the range of concentration to be covered, the corresponding p H range desired, and the buffering acid neutralization curve. To simulate such a control system, 11 samples of NazCO3. NaOH solutions were made up containing from 0.722 to 0.797N NaOH, and from 0.538 to 0.5941V SazC03. A 25-ml. volume of neutralizing solution containing HC1 and buffering acids was used to neutralize approximately a 5-ml. sample to the pH 8 end point and the pH was determined. An additional 14.1 ml. of the same neutralizing mixture was then added to neutralize approximately the remaining Sa2C03, and the p H of around 4 was then read. From these two pH values, the amount of NazCO3 and NaOH could be estimated. In order to obtain reproducible results in the pH 8 range, it was necessary to take the reading immediately after mixing the neutralization solution and the sample due to a tendency for the p H to drift. This was not necessary a t p H values of about 4. Four samples were used to draw calibration curves for each end point. -4 number of samples were then run in a similar manner. These data are shown in Figures 4 and 5. From the calibration curves and the data, the deviations indicated by p H for concentrations of half the NaZCO3and all the WaOH were determined. The square root of the average squared deviation was found to be about 0 . 6 7 ~of the average concentration. Thus 9570 of the time this value should be within about 1.2y' of the true concentration. A similar root mean square of deviations of total Na&03 and NaOH concentrations was found to be 0.570 of average indicating probable errors of about
*I%.
1.05
1.07
1.09
OF NOOH t V2 N o ~ C OIN~ SAMPLE
Figure 4. The p H of a NaOH and NaZC03 sample neutralized with constant acid and buffered to a pH of 8 may b e used as a measure of NaOH and '/2 of the Na2C03
INDUSTRIAL AND ENGINEERING CHEMISTRY
CONCENTRATION CONTROL BY ELECTROCHEMISTRY Table I. The Actual, Measured, and Calculated Concentrations of N a O H and Na2C03 Using Figures 2 and 3 Demonstrate the Results Which Could Be Obtained on Separate Determination of Two Such Components Measured Normalities from pH Calculated Normalities from Measured Values Actual Normalities NaOH & NaOH Narc03 */z NatCOa Total base NaOH NazCOs 0.722
0.538 0.538 0.566 0.566 0.594 0.594
0.997 0.992 1.008 1.008 1.019 1.027
1.257 1.257 1.291 1.287 1.323 1.324
0.737 0.727 0.725 0.729 0.715 0.730
0.520 0.530 0.566 0.558 0.608 0.594
0.747
0.538 0.594 0.594
1.017 1.055 1.049
1.282 1.350 1.348
0.752 0.760 0.750
0.530 0.590 0.598
0.771
0.538 0.538 0.566 0.594
1.052 1.043 1.064 1.077
1.317 1.317 1.349 1.373
0.787 0.769 0.779 0.781
0.530 0.548 0.570 0.592
0.797
0.538 0.566
1.070 1.087 1.081
1.345 1.373 1.365
0.795 0.801 0.797
0.550 0.572 0.568
0.797
0.594
1.088
1.391,
0.785
0.606
From the above values, indicated NaOH concentrations and NazCOs concentrations were calculated (Table I). These values, obtained by subtracting two experimental results, differing by 25 to 30700,were not so accurate as the results as measured because of accumulation and amplification of errors. For the case of NaOH, the results indicated a likely deviation of about =t2.26% of average, and for Na2C03, =!z 3.170 would be the expected deviation. I n a continuous system these accuracies would be worse owing to metering errors. The most obvious method of improving the accuracy would be to draw better calibration curves, by taking more points or obtaining prior knowledge of the shape of the curve. Either of these methods might be feasible for an industrial controller.
5
s4 9,
3 I
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1
II
II
1.26 1.30 1.34 1.38 142 TOTAL BASIC NORMALITY OF SAMPLE
Figure 5. The pH of a N a O H and N a 2 C 0 3 sample neutralized with constant acid and buffered to a pH of 4 may be used as a measure of total base
In this case, the measured concentrations varied by approximately the same percentages as a metering pump, and for high accuracy a titrating system might be preferable in some cases. In control of both NaOH and Na2C03 concentrations separately, the p H corresponding to NaOH and l / 2 N a 2 C 0 3could be used to manipulate NaOH concentration, and the p H corresponding to total base could be used to manipulate the Na2C03 concentration. When the proper control points were reached, the concentrations would be close to that desired. In this system, it would be necessary to make certain calculations automatically or manually in order to determine individual concentrations from the recordings of pH. Measurement of Sodium Hypochlorite
For determining oxidizing or reducing components, similar methods should be applicable, providing equilibrium is attainable in a reasonable time, the reaction is consistent, and the electrodes are not fouled. An attempt was made to determine the concentration of nitric acid in the presence of sulfuric acid, using SnClz as a reducjng agent and ferrous and ferric ions as buffers. However, the results were not consistent, probably because of more than one reaction taking place. An attempt was made to determine the concentration of sodium hypochlorite solutions (Chlorox) using the same solutions. This was more successful. A platinum electrode was used with a calomel reference electrode, and it was found necessary to clean the platinum
electrode at least once every 24 hours. After mixing the solutions, a 5-minute heating in a water bath at 50' C. was used to ensure equilibrium. The reducing solution, which was kept under nitrogen after makeup, was approximately 0.11N in SnC12, 0.0125Nin FeCI3, with a large excess of HCl, and 25 ml. were used for the tests. These do not quite correspond, but the SnCl2 solution was not analyzed and these amounts gave satisfactory results. Four tests were run to obtain the calibration curve, and 18 tests were made to determine how well the concentration could be measured. I n this case, the root mean square of the deviations from the curve was 0.44% of average indicating measurements would probably be within +0.9% of actual concentration. These results are plotted in Figure 6. Although more sources of error were encountered, it does appear likely that for certain components approximately titrated and buffered oxidation-reduction potentials may be used to measure concentrations with accuracies in the same range as continuous titration systems.
Continuous Control
Since the above tests were carried out in batch by simulation with pipets and beakers, other important variables might affect the accuracy when under continuous measurement, metering, and control. For this reason, such a control system was needed continuously, and a system such as shown in Figure 2 was set u p for this purpose. The process consisted of simple dilution of approximately 0.4N Na2C03 solution with tap water. Both the Na2C03 solution and the water were flowing from 10-gallon drums placed horizontally, and the water flow was controlled by means of an electric motoroperated control valve. The Na2C03 solution flowed through a hose clamp set to give an approximately 45-minute run. The diluted solution flowed through a gallon jug to the drain. A sigma motor pump metered both a sample of the diluted stream, from the jug and the neutralizing solution through rubber tubes to a short piece of glass tubing where the solutions mixed and flowed to a piece of rubber hose placed horizontally and cut to allow insertion of p H electrodes. A Beckman Zeromatic p H meter was used as an amplifier and the potentiometer connections were connected to a Leeds & Northrup Speedomax H, 3-mode, recording controlling, potentiometer. This controller operated the control valve on the water line. I n an industrial application, the sigma motor pump, the p H meter, and the electrode cell system could not be utilized as they were designed for laboraVOL. 53, NO. 6
JUNE 1961
473
550
Table II. Analyses of Samples during Continuous Control Runs Indicate a Reasonably Constant Concentration Can Be Maintained
530 c v)
3
510
Sample
0
3i ,
Normality t o Phenolphthalein-End Point Run 1 Run 2
1 2 3
490
e
4
si
5 6
k6 4 7 0
7 8 9 10
a
0.132 0.133 0.134 0.132 0.132 0.135 0.134 0.133 0.134 0.135
0.1276 0,1248 0.1260 0.1270 0.1274 0.1270 0.1274 0.1271 0,1270 0.1271
450
430 0.46
047 0.40 0.49 0.50 0.51 NORMALITY OF HYPOCHLORITE SAMPLE
052
Figure 6. The potential o f a sodium hypochlorite sample reduced with a constant amount of SnCI2 in the Presence of Fe ions gives a measure of hypochlorite concentration
tory use. However, similar purpose equipment for industrial use is available from several sources with equivalent or better accuracies. The p H meter had no automatic temperature compensation which would be desirable in an industrial application. The neutralizing solution contained HCl and buffering acids similar to that used in measuring h-aOH and N a 2 C 0 3 concentrations. The flows were about equal and the concentration was such that a 0.25N Na2COs solution would be approximately one half neutralized a t p H 8. The metering ratio varied somewhat between runs and therefore no specific concentration could be expected without calibration for each run, for which there was insufficient time. However, the ability of the system to hold the concentration constant for a 30-minute period was determined. The important dynamic elements of the system were a 4minute time constant of the jug and a dead time of about 1 minute for the sampling lines and electrode cell. The control settings were established by trial and error and were a proportional band of 160, a reset rate of 0.3 repeats per minute, and a rate time of 2 minutes. The ratio of pH change to controller output was not determined. Preliminary runs indicated the necessity for good mixing ahead of the electrode cell to prevent erratic measurements. The results of two runs are shown in Table 11. These are concentrations obtained by analysis on 10 samples taken at about 3-minute intervals during each run after the set point was reached. The analyses were titrations with standard acid to the phenolphthalein end point. The p H record-
474
ings are shown below. The standard deviation of the analytical results for the two runs were 0.9% of the average concentration for the first and 0.770 for the second. This indicates that this control system is capable of maintaining a concentration within 1.1.4 to 1.8% of average for at least a 30-minute period. These deviations were due not only to measuring errors, but also to flow metering errors and deviations from the set point which in turn were partially caused by continuously changing heads in the water and Na2C08 tanks. In addition, it is possible that some temperature changes occurred during the run. Discussion The methods discussed above would be applicable primarily where a simple titration without elaborate pretreatments may be used as an analysis of the desired components. This would include, as demonstrated in this investigation, analysis of single strong or weak acids or
bases; a combination of a strong and a weak base or acid, if two different end points exist; and oxidation or reducing compounds such as sodium hypochlorite, where a single nonfouling reaction goes to completion. The methods used would also require the absence of appreciable amounts of components having a buffering effect in the range of the end point. However, neutral salts should have little or no effect. Where pretreatments are required, such as in back titration procedures, it might be possible to utilize an approximate titration in the final step, but the sources of error would be greater and the errors might be magnified. The major advantage of the approximate titration system over the titration system would be the simplification of the control system, and the fact that the results would be dependent on fewer mechanical and control components. In any case, where the dead time due to sample flow could be reduced appreciably by using less complicated and critical pumping, the approximate titration system would be more advantageous. In the use of continuous titration systems, the inner control loop-controlling the p H or potential by manipulating titraring solution flow-would be subject to the same variations mentioned for approximate titrations. Thus, even with the continuous titration system, it might be advisable to use a buffering component if excess variations are a problem.
91%B!:
literature Cited ( 1 ) Kolthoff, M., Laitinen, H. A., “pH
45
-
TIME RUN I
0
45
t
0
7
TIME RUN 2
Records from continuous control runs indicate how pH of neutralized and buffered sample can b e controlled
INDUSTRIAL AND ENGINEERING CHEMISTRY
and Electro Titrations,” 2nd ed., Wiley, New York: 1952. ( 2 ) Potter, E. C., “Electrochemistry,” Cleaver-Hume Press Ltd., London, 1956. ( 3 ) Siggia, Sidney, “Continuous Analysis of Chemical Process Systems,” Wiley, New York, 1959. RECEIVED for review August 15, 1960 ACCEPTED February 6, 1961
This article contains results of Project CH.E.-3, sponsored by the Auburn University Engineering Experiment Station, June 1959 to June 1960.
