Experimental Evaluation of Digital Algorithms for Antireset Windup Jawahar Khandheria and William L. Luyben’ Department of Chemical Engineering, Lehigh University, Bethlehem, Pennsylvania 180 15
Several algorithms for preventing reset windup in digital computer control loops were experimentally evaluated. A PDP 11/40 minicomputer was used to control a 24-tray, 8-in. i.d. distillation column. Results showed that all of the methods proposed in the literature performed poorly under certain conditions. A new algorithm was developed that overcame all the problems of the previous methods.
Introduction The problem of reset windup has been recognized for many years in analog controllers. Reset windup occurs in controllers with reset or integral action when the controller is unable, for some period of time, to drive the controlled variable back to its set point. Typically, this occurs because the manipulative variable is temporarily unable to respond to changes in the controller output signal. A common example is a batch process where, during the discharge, charging, and heat-up portions of the cycle, the controller output is not permitted to drive the control valve. For example, an electrical interlock keeps a solenoid valve open, which vents off the air to an air-to-open control valve until the proper part of the cycle is reached. During the interlock period, the controller will continue to see an error and will continue to integrate its output signal up or down, if it is left on “automatic”, until it reaches one end of the control-signal range. Continuous processes also can have reset windup problems during periods of abnormal operation. If a pump goes down for a short period, if steam pressure drops in a supply header, or if a block valve is shut in the line, the controller will temporarily be unable to maintain the set point. The increasing use of “override” or “selective” control systems (Buckley, 1968; Shinskey, 1967) has increased the occurrence of reset windup problems since the manipulative variable can be controlled by one of several different controllers a t different times. The controllers that are not in use will windup if they have integral action. The reset-windup problem can be prevented by switching the controller into manual when a windup condition occurs and then switching the controller back into automatic a t the right time. This requires constant operator attention and may increase safety risks. The first cure proposed was the “batch controller”, a pneumatic controller that had a switch which vented the reset bellows of the controller when the error signal exceeded some set limit. This prevented saturation of the controller, but the transition from automatic to manual and back again was not humpless. A more satisfactory solution for analog controllers is “external reset feedback” (Buckley, 1968; Shinskey, 1967) which has been used for a number of years. Figure 1A illustrates how a conventional pneumatic controller achieves integral action by feeding the controller output signal (CO) back into the reset chamber of the controller through a restriction. If the air pressure in the reset chamber is PRJthe controller output is
co = K,(SP - P ) + P R
(1)
where SP is the set point signal and P is the process measurement signal. K , is the controller gain. Because of the 278
Ind. Eng. Chem., Process Des. Dev., Vol. 15,No. 2, 1976
restriction and the volume of the reset chamber, PR is related to CO by the dynamic relationship
Combining eq 1 and 2 gives
(3) where E is the error ( S P - P ) . This is the transfer function of a conventional proportional-integral controller, Basically, a positive feedback loop, with a gain of unity, is used to achieve integration and reduce the error to zero a t steady state. Suppose now the control valve can be “overriden” or taken over by another signal through the low selector ( L S ) , shown in Figure 1B. If the signal to the control valve ( V )is fed back to the reset chamber instead of feeding back the controller output signal (CO), the equation for the controller is
When the control valve is not overridden, V is equal to CO, and the controller will integrate. When the control valve is overridden, V is equal to the override signal, and there is no positive feedback and no integration. The transfer from override to conventional control is bumpless. Figure 1C illustrates how two external reset feedback loops can be used to prevent windup in a two-controller cascade system. The secondary loop is a flow controller, whose set point comes from the output of the primary temperature controller. Notice that the flow signal ( F ) is fed back to the reset chamber of the primary temperature controller. Neither controller will windup during override periods. External reset feedback can be used in either pneumatic or electronic analog controllers (Shunta, 1974). I t should be emphasized that the commonly used strategy of simply limiting the controller output signal (at full range or at some suppressed range) will not eliminate reset windup as the term is used in this paper. Some people define reset windup as permitting the controller to become completely saturated a t pressures (or voltages) far above or below the normal range. This is a very severe windup. But even if the controller only winds up to the limits of a certain range, it is still wound up and will result in an overshoot when it comes on control. The above point is equally valid for digital computer controllers. Several process control software vendors claim to offer control algorithms with reset-windup protection. What they really provide is controller output limiting. This does not prevent reset windup.
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Figure 1. A , Conventional analog controller; B, external reset feedback; C, cascade system. Digital Algorithms A cascade supervisory computer control loop occurs when the analog primary temperature controller in Figure 1C is replaced by a digital computer. The analog flow controller is proportional-integral with external reset feedback of the valve signal V t o prevent windup. T h e normal proportional-integral control algorithm is CO,=Bias+K,[E,tP T ~ n Ej]
(5)
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where CO, and E , are controller output and error signals a t the n t h sampling period ( T s ) The . bias signal is the original controller output when the controller is placed on automatic with zero error and zero summation of errors. Writing eq 5 for the n t h and ( n - 1)th sampling times and subtracting the two gives r
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If the control valve is overridden, the temperature controller will windup because the error E , does not go to zero. There are several more or less obvious methods for avoiding reset windup in digital algorithms. As discussed below and demonstrated experimentally, none of these “obvious” methods performs well under all conditions. (1) Controller O u t p u t Limiting. As discussed for analog controllers, this reduces windup but does not eliminate it. (2) Detecting a n O v e r r i d e f r o m the E r r o r i n the Computer Control Loop. The error E , is monitored and, if it exceeds some set value, it is assumed that an override has occurred. A number of different strategies can then be implemented. The controller output CO or the integral term could be frozen a t their present values until a smaller error tells the computer to begin integrating again (Fertig and Ross, 1967). Another approach is to automatically throw the controller on “manual” and continually back calculate the bias value from the actual flow signal and the temperature signal. When the controller goes back onto automatic the transfer will be bumpless. This method can run into difficulties under certain conditions. Suppose a large load disturbance hits the process or a large set point change is made. A large temperature
error will occur, and the algorithm may take the incorrect action of turning off the controller. The process will never recover without operator intervention. (3) Detecting a n Override f r o m t h e E r r o r i n t h e Flow Controller. This would appear to be a good approach since it avoids problems when a large temperature error occurs. However, as will be shown experimentally later, it can run into problems when load or set point changes are made during an override period. Cox and Shunta (1973) discussed the problems of reset windup in digital control systems with analog overrides. They suggested use of a digital equivalent of analog external reset feedback, which they called the “tracking algorithm”. The tracking algorithm uses the same strategy as used in analog controllers. If the actual flow signal F , a t the n t h sampling period is used in eq 6 instead of CO,-1, the result is the tracking algorithm (see Figure 2).
Con= F ,
+ K, [E,
- E,-l
+9 E, ] TI
(7)
When the computer temperature loop is in normal operation, the value of F , will be CO,-1 since the analog flow control loop is usually fast enough t o bring the flow to the flow set point in one sampling period T , of the temperature controller (a T , of 0.5 min was used in most of the experiments reported here). Thus in normal operation, eq 6 and 7 are identical. However, when an override occurs, F , will be the actual flow signal, not COn-l, and no windup will occur. The same algorithm could be used in a DDC loop if the control valve signal were fed back into the computer. Cox and Shunta (1973) investigated the tracking algorithm by digital simulation studies. No experimental verification on real processes or using a real control computer was presented. The objective of our study was to experimentally evaluate the tracking and other algorithms, and to develop improved antireset-windup algorithms if necessary. E x p e r i m e n t a l Equipment The process under computer control was a 24-tray, 8-in. i.d. distillation column separating methanol and water a t atmospheric pressure. Pneumatic analog controllers were used to hold reflux flow, reflux drum level, and base level constant. The cascade computer control system is shown in Figure 3. Tray-four temperature was measured by a filled-bulb pneumatic temperature transmitter with a 60-120 “C range. Steam flow rate to the reboiler was measured by an orifice plate/differential pressure transmitter and controlled by a pneumatic analog proportional-integral conInd. Eng. Chem., Process Des. Dev., Vol. 15, No. 2, 1976
279
manually to drop the base level. The lower three psi of the base level transmitter range was used to pinch the steam valve through the gain four relay and low selector. The digital computer control loop was tuned by experimentally determining the process open loop transfer function between tray-four temperature and steam flow rate by pulse and step testing
The digital proportional-integral controller was
Including the zero-order hold H ( s ) in the loop, the closed loop characteristic equation of the sampled-data system with a sampling period T , = 0.5 min was
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l + K c ( z (Z - 0.951) The reset time T I was set equal to 1min, reducing eq 10 to
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Figure 3. Experimental setup.
(11) A root locus plot of the system in the z-plane was made and a K , of 1 was chosen to give a damping coefficient of 0.33. The 0.5-min sampling period was selected by calculating the value of gain that gave a 0.33 damping coefficient for various sampling periods and finding where a reduction in T , produced little or no increase in the gain K,.
troller. The full-scale range of the flow transmitter was 4.2 lb/min of 7 5 psig steam. The 3-15 psig pneumatic temperature and flow signals were converted to 0-10 V dc signals in potentiometric P/V transducers. These voltage signals were fed into the computer through a DEC (Digital Equipment Corporation) AD 01 analog-to-digital converter. The 0-10 V dc output signal from the computer (from a DEC AA 11 digital-to-analog converter and hold) was transduced into a 3-15 psig pneumatic signal in a PIV transducer and fed into the set point input of the pneumatic steam flow controller. The minicomputer used in these studies was a DEC P D P 11/40 equipped with 16K core memory, moving-head disk (RK 11 with 1.2 million words), 30 cps Decwriter, 300 cpm card reader, high-speed papertape reader and punch, 32 analog inputs and four analog outputs..RSXllB was used as the real time executive. All control, scanning, and operator interfacing programs were written in FORTRAN IV and input from cards. The time required to read in a typical 100-card program, compile, assemble, link, load, and begin real-time execution of two real-time tasks was about 5 min. Figure 3 is a sketch of the computer and the interfacing equipment. A flexible input/output interface was constructed which converted 15 pneumatic and 10 thermocouple inputs into 0-10 V dc signals. Any of the pressure or voltage signals could be displayed or recorded on a sixchannel recorder. Voltage output signals from the computer could also be displayed or recorded. A pneumatic switch was used to transfer control from analog temperature control to computer temperature control (Khandheria, 1975). The override on the steam valve used in these experiments was low base level. Normally, bottoms product flow held base level. But to cause an override on the steam valve, the control valve on the bottoms product was opened
Experimental Results Figure 4 gives experimental results for a computer control loop in which controller output limiting a t 80% of scale was used. The drop in base level overrides the steam flow a t about t = 7.5 min. Base level ( B L ) controls steam flow until t = 23 min. During this time the temperature controller output (the steam flow controller set point) winds up to the 80% limit because the actual tray-four temperature is below the temperature set point. As the override drops out of the picture, the steam flow shoots all the way up to the limit. A fast temperature response occurs, but a temperature overshoot of 8% (4.8 OC) occurs a t t = 30 min. T o make it easier to see the data, the steam flow signal ( F ) was displaced from the steam set point signal (CO) in all the figures except in Figure 11. Figure 5 gives results for an algorithm in which the integral term in eq 5 was frozen whenever a difference (AF)was detected between the steam flow controller set point and the actual steam flow signal. This difference was used to detect when the control valve was overridden. Thus the error in the flow controller is used, not the error in the temperature controller. Because of noise in the flow signal, the difference AF cannot be set too small. A AF of 2.5% of scale was used in Figure 5 . A typical noisy flow signal in a plant might require a AF of 5 or 1oo/o of scale. The larger ilF must be made, the more the controller will windup before it is frozen. Note that the proportional term was still active; only the integral was frozen. The temperature overshoot was reduced to 3% (1.8 "C).This algorithm was better than simple controller output limiting, but it performed worse as the noise level in the flow signal increased. Figures 6 and 7 show results using an algorithm in which the controller output was frozen, and integration stopped whenever a difference AF was detected between flow and flow set point. A A F of 2.5% of scale was used in Figure 6. There was very little temperature overshoot. Figure 7 illus-
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Ind. Eng. Chem., Process Des. Dev., Vol. 15,No. 2, 1976
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Figure 5. Integral term frozen. trates what would occur in a noisy system. Random noise of f 5 % of scale was added to the actual flow sigwl. A AF of 8% was used, Some windup occurred and there was more temperature overshoot. The results above show that the “freeze” algorithm is better than controller output limiting, but it exhibits partial windup which gives progressively worse control as signal noise increases. T h e freeze algorithm also can run into problems when a load disturbance or temperature set point change is made during an override period. The temperature controller will not be unfrozen (put back on automatic) until the actual steam flow is close to the frozen temperature controller output. But this may correspond to more steam than is needed to attain the desired set point. T h u s a large temperature error may be experienced before the
TIME I M I N I
Figure 7. Controller output freeze with noise in the steam flow signal. temperature controller is unfrozen. The actual temperature could even go above the temperature set point, but the controller would stay frozen until the steam flow comes up to the frozen controller outut signal. Figure 8 illustrates the problem. A large temperature set point change was made a t t = 23.5 min, during the override period. The set point was below the actual temperature a t that point in time, but the temperature controller did nothing. Its controller output CO stayed frozen until the steam flow came up to the steam set point. At that point the temperature controller became active, but the temperature was even further away from the set point. Figure 9 gives experimental results using t h e tracking algorithm. No windup occurs. However, the recovery from Ind. Eng. Chern., Process Des. Dev., Vol. 15, No. 2, 1976
281
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Figure 8. Controller output freeze with 8 " C temperature set point change during the override period. 60
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Figure 9. Ideal tracking algorithm. the override is quite slow, taking about 15 min to reach the temperature set point. This slow recovery occurs because the reset action must integrate the steam flow set point up from the low level it dropped to during the override period. Thus the tracking algorithm may give slow recovery in processes with moderate to large reset constants. A reset time of 1 min was used in our studies. Since reset times of five to 30 min are not a t all unusual in many chemical engineering processes, it appears t h a t use of the tracking algorithm may be limited. Two other difficulties were also uncovered with the tracking algorithm. The first is the propagation of noise in the flow signal. Equation 7 shows that any noise in the flow F , will appear immediately in the temperature controller output. If filtering is possible, this problem would not be serious. But if the noise frequency is not significantly higher than the natural frequency of the process, filtering would be limited. Note that this noise problem is present 282
Ind. Eng. Chem., Process
Des. Dev., Vol. 15, No. 2, 1976
during normal operation as well as during override periods. Figure 10 illustrates how control performance deteriorates when noise is introduced during normal control. Another problem encountered with the tracking algorithm was a sensitivity to zero adjustments and drift in the D/A and A/D converters and in the analog flow controller. This can be seen by examining eq 7. Any errors or zero shift anywhere in the loop between the digital number the computer calculates as its output signal and the digital number that it sees as the actual steam flow will mean that the system will come to a steady state where the F , and CO, terms are not the same. Since E, and E,-1 will be the same a t steady state, eq 7 can be rearranged t o give the steadystate error or offset that must exist in the computer temperature controller.
An interesting observation is that this steady-state error gets bigger as the sampling period is reduced (smaller Ts). Figure 11 gives experimental verification of this offset. As the sampling period is reduced from 1.0 to 0.5 to 0.25 min, the tray-four temperature offset increases. For T I = 1, K , = 1, and T s = 1, a 5% error in (CO, - F,) will give a 5%
Table I. Real-Time Fortran IV Program Using Modified Freeze Algorithm c . ....
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.... G2
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Figure 13. Steam valve overrides.
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0
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Figure 12. Modified freeze algorithm with 8 O C temperature set point change during the override period. error in temperature (or 3 "C for the 60 O C temperature transmitter span). Unlike the freeze algorithm, the tracking algorithm, however, can handle the set point and load disturbances occurring during the override period. New Algorithm
Evaluation of the limiting, freeze, and tracking algo-
rithms revealed that all of these methods perform poorly under certain conditions. Limiting the controller output permits the controller to windup too far. Using tracking has the opposite effect of letting the controller output drop too low. Freezing the controller output when an override is detected (by checking the error in the flow controller) worked very well since it kept the output about where it should be. However, the freeze algorithm did not handle load and set point changes well. If this problem could be overcome, the freeze algorithm would be quite effective. The new algorithm proposed is a modified freeze algorithm which is basically a combination of the old batch controller and external reset feedback. Both the error in the flow controller (CO - F ) and the error in the temperature controller ( E ) are used to detect both override conditions and load and set point changes. Table I gives a listing of the FORTRAN IV program used for this modified freeze. The temperature controller is initially frozen whenever there is a significant difference between the controller output CO, and the actual steam flow signal F,. T h e temperature controller output is frozen for one sampling period (by setting IWAIT = 1).Thereafter the sign of the temperature controller error E , is also checked during the override. If this error ever goes negative, the temperature is above the set point and the temperature controller is put back onto automatic. I t is automatically balanced at that Ind. Eng. Chem., Process Des. Dev., Vol. 15, No. 2, 1976
283
D I S 7 ILLATE
GI L O W L E V E L C L O S E S R E C L U X VALVE G 2 H l G V L E V E L OPEYS R E F L L X VALVE
proach will take care of any load or set point changes occurring during the override period. Whenever low base level controls the steam flow, Ef = Con-]- F , will be positive and Et = Tq set - T4 will also be positive. Therefore, the product EfX Et should be pgsitive. Whenever high base level controls the steam flow, Ef and Et both will be negative; therefore, the product EfX Et should be again positive. Thus, during an override, the temperature controller output is frozen as long as the product of errors is positive. Now consider a control system in which increase in the manipulated variable results in the decrease in the control variable. Such a control system is shown in Figure 15. Any increase in the reflux flow will result in the decrease in the control tray temperature. Whenever a negative error occurs in the reflux flow controller, a positive error should occur in the temperature controller and vice versa. Therefore, for this case whenever the sign of the product Ef X Et is positive, the temperature controller is put back on automatic (unfrozen) so that it can handle any load or set point changes occurring during the override period.
G2
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Conclusion
Figure 15. Reflux valve overrides.
point by setting bias equal to the actual steam flow F , so that the transfer is bumpless. Figure 12 shows the effectiveness of this modified freeze algorithm for a set point change during the override period. The set point is changed a t t = 18 min. The controller output is immediately dropped to the actual steam flow value, and temperature control is resumed.
New Algorithm and Various Override Systems The modified freeze algorithm discussed earlier is quite general in its application. Several more complex override systems are considered below and a general criterion for “freezing” is developed. The basic strategy is to detect an override from an error in the secondary controller and to detect a load or a set point change, occurring during the override, from an error in the primary controller. I t should be emphasized here that the control systems discussed herein are cascade type control systems, where the primary controller is a computer while the secondary controller is an analog controller with external reset feedback. Consider the control system shown in Figure 13. In this case we have two kinds of overrides. When the base level is too low, it pinches the steam valve; and when the base level is too high, the steam valve is opened. Apparently, the approach shown in modified freeze algorithm may not work in this case, because whenever high base level controls the steam flow, the error in the temperature controller will be negative, and according to the algorithm the temperature controller will be unfrozen even when it is not needed. This problem, however, can be handled very easily as shown in Figure 14. The relationship between the manipulated variable and the control variable is such that whenever a negative error occurs in manipulated variable, it results in a negative error in the control variable, and a positive flow controller error results in a positive temperature controller error. Unlike the previous approach of checking the sign of the error in the temperature controller, the sign of the product of the flow controller error and the temperature controller is checked. Whenever the sign of this product is negative, the temperature controller is unfrozen. This ap284
Ind. Eng. Chern., Process Des. Dev., Vol. 15, No. 2, 1976
An improved digital computer control algorithm that prevents reset windup has been developed and experimentally tested.
Nomenclature AC = air to close valve A 0 = air toopenvalve BL, = base level signal CO = temperature controller output signal CO, = temperature controller output signal a t n t h instant CO,-1 = temperature controller output signal a t ( n - 1) instant = finite difference equation approximating a continuous PI algorithm E = error signal E f = flow controller error E, = error in the temperature controller a t n t h instant E , - ] = error in the temperature controller at ( n - 1) instant Et = temperature controller error F = actual steam flow signal F , = actual steam flow signal a t n t h instant FB = feedbacksignal FC = flow controller FT = flow transmitter GI,Gz = gain four relays G M = process open loop transfer function ( T J F ) H(,)= zero-order hold K , = temperature controller gain LC = level controller LT = level transmitter P = process measurement signal PR = air pressure in the reset chamber s = Laplace transform variable SP = set point signal t = time,min T4 = tray-four temperature, “C T 4set = tray-four temperature set point, “C T I = temperature controller reset time, midrepeat T , = sampling time, min T C = temperature controller TT = temperature transmitter V = signal to the control valve z = z-transform variable
Literature Cited Buckiey, P. S., hstrum. Tech., 51 (Aug 1968). Cox, R. K.,Shunta, J. P., Chern. Eng. Prog., 69, 56 (1973). Fertig, H. S., Ross, C. W., paper presented at 22nd Annual iSA Conference, Chicago, Ili., Sept 1967. Khandheria, J., Ph.D. Thesis, Lehigh University, Bethlehem, Pa., 1975.
Sninskey, F. G., “Process Control Systems”, McGraw-Hili. New York, N.Y., 1967. Shunta, J. P., paper presented at Lehigh University, course on Distillation Control, 1974.
Receiued /or reuiew June 11,1975 Accepted October 14,1975
High Voltage Pulsing of a Laboratory Aluminum Electrolysis Cell Constance F. Acton,’ Paul C. Nordlne, and Daniel E. Rosner* Department of Engineeringand Applied Science-Chemical Engineering Section, Yale University, New Haven, Connecticut 06520
A small laboratory aluminum electrolysis cell has been fabricated in an attempt to reproduce experimentally the reported observation that short duration, high voltage pulses applied to a conventional aluminum electrolysis cell can significantly increase the energy efficiency for subsequent aluminum extraction (Diller, 1966) over present practice. First, we investigated current-voltage relationships associated with the electrolysis of fused cryolite-alumina melts in the absence of pulsing. Results obtained were in agreement with those reported by other investigators using similar laboratory cell designs. Then, high voltage pulsing was imposed upon the electrolysis circuit in attempts to achieve the previously reported activation. We observed no effect of kilovolt pulsing on the (post-pulse) conductivity behavior of the cryolite-alumina melt over the parameter range specified herein. Unfortunately, we can presently offer no satisfactory explanation for the differences between these and earlier results (Diller, 1966) based on available documentation.
1. Introduction
tion from A1203(s),the bauxite ore, impure Al(OHI3, is first refined to pure A1203(s) powder by the Bayer Process. I t is then dissolved in molten cryolite, Na3AlF6, containing various additives a t about 1250 K. When a potential of 5-7 V is applied across the cell aluminum metal is plated out, forming a liquid pool on the cathode that can be tapped off periodically. Some 6-8 kWh/lb of Al(1) are now required to extract aluminum from alumina using this conventional Hall process. 1.2. Electrolysis Following High Voltage Pulsing. Diller (1966, 1969, 1974) has described a method which according t o his experiments, would cut the electrical energy requirement for aluminum production by a factor of about 2. The main idea is to use high voltage pulses to “activate” cryolite. Two different effects of pulsing are described in the 1966 patent. The “mobility effect” is reported t o occur when a pulse having a peak voltage of 1 kV in the bath is superimposed codirectionally upon the electrolysis voltage a t Ih-s intervals. The most effective pulse width is reported to be about 1 p s . This relatively low voltage pulse is supposed to enhance the electrical conductivity of the melt. T h e second effect, called the “crystal effect”, is reportedly produced by a 3-5-kV pulse (fired and measured a t the anode) which has a 1-10-ps (or more) pulse width. From 1 to 20 pulses may be fired in a 5-s interval but 6 pulsed5 s is stated to be the optimum firing rate. This effect was named for its presumed ability to cause ionic dissociation and
“crystal breakdown” in the cryolite melt. A claim of 1003000% increase in current density a t fixed voltage is made by Diller (1969). For the crystal effect to occur, the low (dc) voltage reportedly does not need to be superimposed with the high voltage pulse(s). 1.3. Purpose of the Present Investigation. Following systematic improvements in the energy efficiency for A1 production by the Hall process during the period 19201950, recent gains have been more modest, with the present requirement of 6-8 kWh/lb Al(1) being far greater than the thermochemical minimum values discussed in Section 2. Since increased costs of electrical energy and raw materials are now stimulating activity on alternative techniques of aluminum production (see, e.g., Peacey and Davenport, 1974), it is interesting to inquire if the above-mentioned scheme of high-voltage electrolyte pulsing is capable of “rescuing” the Hall Process from its competitors. While one can set useful model-free thermochemicar bounds on the electrical energy requirements for A1 production via electrolysis (see Section 2 ) , many important details of conventional aluminum electrolysis (e.g., melt constitution, mechanisms of ion transport, and anode polarization, etc.) remain incompletely understood. Since the possible effects of high voltage electrolyte pulsing are even less transparent, and the experiments on which the above-mentioned patent claims are based have to our knowledge never been independently reproduced in another laboratory, we decided that such independent experiments would be both a necessary and timely prelude to any further developments along these lines.
T o whom inquiries concerning this paper should be directed a t Olin Corporation, Metals Research Laboratories, New Haven, Conn. 06540.
2. Thermodynamic Considerations The laws of thermodynamics set firm limits on the minimum energy required to obtain Al(1) from A120&), regard-
1.1. Conventional Aluminum Electrolysis (Hall Process). In traditional aluminum electrolysis for Al(1) extrac-
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