Continuous Chromatographic Analysis Using a Pseudo Random Sample Switching Function R a y m o n d Annino' and L. E. Bullock
Comorate Research. The Foxboro
C o m p a n y , Foxboro.
Mass.
The use of correlation techniques in chromatography has been critically examined both in the laboratory and by computer simulation. The origin of a number of previously reported difficulties is established and some basic guidelines are outlined for the effective use of the method in continuous chromatographic analysis.
The normal batch type operation of chromatographs in most process control applications sometimes results in an appreciable delay between the time when a change in cor:iposition occurs in a process stream and the time when ! h ~proper control action is initiated. Some of the reasons for :his delay are easily identified with the lag due to the chromatographic column (retention time) and the length of !he sample lines between the sampling point and the chromatograph. A much more subtle contribution is associated with the time involved in the decision- making pro:.E+..:. In other words, how many samples and subsequent chromatograms are required to establish with confidence i h a t a process deviation from set point has actually OCcurrd? It would appear that a more or less continuous sampling procedure with an updated averaged output could help resolve this problem. Several authors have suggested that a more efficient use of the time required for the development of the chromatogram is possible by using rapid repeated injections of sample so that the fast components can be resolved in the rime interval normally existing between the rapidly eluting components and the slower ones ( I , 2). By judicious choice of !he sampling interval, a more or less continuous output can be obtained (3). With faster sampling rates the rat her complex chromatograms can be handled by Fourier analvsis ( 4 ) or phase modulation techniques (5-8). The most recent proposal for continuous chromatography relies on a computer aided deconvolution of the output (9,
Correlation chromatography is yet another approach to cnnt,inuoiis chromatography and is the subject of this paper. Briefly. the procedure involves switching between two streams (process sample and standard sample) a t the
1
I'resvnt address. D e p a r t m e n t of C h e m i s t r y , Canisius College, 1.Y.1.1208.
command of a pseudo random binary sequence. The properties of this sequence are such that its cross-correlation with the output "summation" chromatographic signal produces what appears to be a normal chromatogram. This signal is called a correlogram and, although quite similar to a normal chromatogram, differs in a number of respects. I t is a composite of much more information and represents, in essence, an averaged chromatogram taken over the time period of the chain code. It displays an increased signal to noise ratio compared to a single impulse chromatogram and is being continuously updated with new information. The application of cross-correlation techniques to produce a continuous chromatogram appears to have been first suggested by Izawa (IO) in a short paper describing some preliminary experimental results. Subsequently, Davies (11) examined its theoretical basis, and Godfrey and Devenish (12) reported on an experimental evaluation of the procedure. A number of disturbing results were noted by the latter authors such as irregularities in the base line leading to decreased signal to noise ratios and a total collapse of the correlogram when changing concentrations of sample constituents. On the basis of these results serious questions were raised regarding the applicability of correlation procedures for continuously monitoring changes in sample concentration. Its use, however, as a method for increasing detector signal-to-noise ratios in trace analysis has not been ruled out (13, 14). The purpose of this paper and our preliminary report (15) is twofold; namely to identify the origin or origins of base-line irregularity leading to decreased S / N in order to establish optimum conditions for the effective use of correlation chromatography, and to demonstrate that under the restraints imposed, application to process control is optimized for chromatographs operating in a differential mode where an accurate continuous measurement of set point deviations is desired.
THEORY A chromatogram represents a convolution of the sample input with the system response function. If the sample input is sufficiently narrow compared to the duration of the output signal, the output is a good measure of the system response. Mathematically, the detector signal, y ( t ) , is expressed as
Huifalo.
J . L Power, Pittsburgh Conference on Anal. Chem. and Appl. Spectroscopy. Cleveland. Ohio. March 1-6. 1970. H R Murdock. J r . , Anal. Chem.. 42. 687 (1970). D MacNaughton. J r . . and L. B. Rogers, Anal. Chem.. 43, 822 (1971I C N Reilley. G. P. Hildebrand. and J. W. Ashley, Anal. Chem.. 34, 1;98 (19621 D. E. Carter, Belg. Patent 616,066 to Monsanto Co., Oct. 5. 1962: U S Patent 3.236.092 Feb. 22, 1966. D. E. Carter and Y . L. Esterson. Ind. Eng. Chern.. Fundam., 9 . 661 119701. S. Hiratsuka and A. lchikawa. Bull. Chem. SOC. Jap.. 40, 2303 (19671 D. Obst. J Chromatogr , 32. 8 (19681 H Clough. T . C Gibb. and A. 8. Littlewood, Chromatographia. 5, 351 (1972)
110) K . Izawa. K. Furuta. T. Fujiwara, and N. Suyama. Ind. Chirn. Belge, 32, 223 (1967). (11) W . A. T. Davies. Instrum. Pract.. 2 2 , 213 (1968). (12) K. R . Godfreyand M. Devenish. Meas. Contr., 2, 228 (1969). (13) G. C. Moss, P. J. Kipping. and K. R. Godfrey, "Application of Statistical Correlation Techniques and Pseudo Binary Sequences to Trace Chromatographic Analysis," presented at the Ninth International Symposium on Chromatography. Montreux, Switzerland, Oct. 9-13, 1072. (14) H . C. Smit. Chromatographia, 3 , 515 (1970) (15) R. Annino and L. E. Bullock. "Continuous Chromatography Using Pseudo Random Inputs." presented at the Ninth International Symposium on Chromatography, Montreux, Switzerland, Oct. 9-13. 1972, proceedings to be published. A N A L Y T I C A L C H E M I S T R Y , VOL. 45, NO. 7 , J U N E 1973
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VENT
4 4
DETECTOR
I
UTAH SPEAKER MAGNET AND CORE
/
Figure 2. Snapshot correlogram of propane ( A ) Standard gas = 100% helium: Sample stream = 0.2% ethane, 0.8% propane, 99.0% helium. PRBS = 127 units of 0.6 sec each (for a total 76.2 sec code length). (B) A n example of correlatlon noise experienced
Figure 1. Stream switching valve assembly (Courtesy Institute of Petroleum)
y ( t ) = Jmh(h)ci(t- A) dX Z h(t)
(1)
where h(X) is the impulse response to a narrow sample input, 6 ( t ) applied X units earlier. If one uses a pseudo random binary sequence (PRBS) as a sampling function, its convolution with the resulting detector output yields a cross correlation funct-ion (15) which is described by an equation very similar to Equation 1. $*)(T)
= [h(X)G(t
- A) dX
Z h(~)
( 2)
Thus the correlogram which is a plot of + x y ( ~ ) us T looks very much like the common y ( t ) us. t plot describing a normal impulse chromatogram. An estimate of the cross correlation function + J T ) of the signals x ( t ) and y ( t ) is given by &.,(T)
=
1 T TJ x ( t - ~ ) y ( tdt )
(3)
where a time function y ( t ) is multiplied by the delayed replica of x ( t ) , subsequently integrated, and averaged over the period T. It is evaluated from the digital approximation of the form
(4) k=l
In practice an array of signal values is memorized from the present time to N A t in the past, where NAt is the length of the code. The signal is sampled every A t seconds and the new value is placed in the array while the oldest value is dropped. Thus the recalculated correlogram represents a new averaged set of data the oldest of which is, a t the maximum, one chain code out of date. 1222
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early in the research
It is important to note that if an input concentration change occurs, it is only a t a maximum of one chain code period after the signal appears a t the detector that the nature and extent of the perturbation can be exactly correlated. The import of this restriction is examined in detail in the next section.
EXPERIMENTAL Laboratory Correlation Experiments. A simple chromatograph was constructed using the cylindrical slide valve shown in Figure 1 to switch between a helium diluted process sample (“ON” or +1 position) and a helium diluted standard sample (“OFF” or -1 position). Depending on the position of the sample valve (+1 or - l ) , either the helium diluted process stream or the standard gas stream entered the column. The valve was driven by the voice coil of a 15-in. Utah speaker of frequency response 1212,000 cycles on command from the PRBS generator. Analysis and reference columns were 6-ft X 0.085-in. i.d. and filled with 80-100 mesh Chromosorb P coated with 20% w/w bis(2-ethoxyethyl) sebacate. A thermal conductivity detector (Gow-Mac JDC-470) was used to generate the output signal to the correlator. Because of its increased flexibility, a research computer was used to generate the PRBS switching function and to correlate it with the chromatographic detector output. Obviously a commercially available correlator or one specially designed for the problem could have been used. The cross correlation function was generated and displayed on a CRT and updated five times per second. The CRT was limited to 256 points which could span any portion of the code down t o 0.2 sec. The correlogram shown in Figure 2A is of a ethane/propane/helium mixture. Since only the propane peak was of interest, the correlation was calculated only over this time interval. The full 256 points lie between these time limits and the area displayed in the lower left-hand corner of the display represents the updated area above a line joining the two cursors positioned a t 52.9 and 60.3 sec. Provisions were made to effect gradual changes in component concentrations in the process stream and to monitor its overall thermal conductivity for comparison with the continuously recorded chromatographic area obtained from the correlogram. This
Figure 3. C o n t i n u o u s m o n i t o r i n g of c h a n g e s i n t h e p r o p a n e c o n c e n t r a t i o n of a s a m p l e s t r e a m ( A ) Continuous recording of the process stream thermal conductivity. (B) Simultaneous recording of propane area obtained from correlogram. (C) Correlogram snapshots. Numbers correspond to the time points indicated in ( A ) . Sample stream nominally 0.07% propane, 0.03% ethane, 99.9% helium. Standard stream = 100% helium (Courtesy Institute of Petroleum)
A N A L Y T I C A L C H E M I S T R Y , VOL. 45, N O . 7, J U N E 1973
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t
I
30.3%
--
lil -O.m
+ j . 3
c
m . 0
150.0
m.0
4M.o
TIME x IO-' V
1.-
OUTPUT
Figure 4. VRSP Output IBM 1620 plots of VRSP showing input sampling function x j t ) . detector output y ( t ) . and final correlogram output
is illustrated in Figure 3, where in the region labeled 1 to 2 the sample stream is being varied by the addition of a more concentrated propane-ethane stream of the same relative composition as the original. In the region 2 to 5, the ratio of ethane to propane is being changed by the addition of propane t o the sample stream and in the region 5 to 7, the sample stream is being diluted with helium. The maximum propane concentration attained is indicated by correlogram 5 as a deviation of 0.03% from the original set point concentration of propane. Computer Simulation. Initially, in order to expose and study possible subtleties of the cross-correlation procedure as distinct from possible chromatographic complications, a fairly simple program describing a linear system was constructed. It consisted of a selectable PRBS input and a variable system response function which allowed a modification of the output from square wave to Gaussian. The correlogram produced by cross-correlating input and output along with the input and output waveform was plotted on a IBM 1620 Plotter. A typical output from this Variable Response Simulation Program (VRSP) is shown in Figure 4. It is what would be expected as correlogram output from a chromatograph operating in its linear nonideal range. Options were also built into the program so t h a t an input concentration change could be effected at any time and the correlograms produced at any time after this perturbation could also be outputted. Whereas the VRSP model was not derived from any fundamental chromatographic relationships, the so-called "real" correlation chromatography simulation program (CCSP) was based on the physical model of the chromatographic processor which had been previously found to adequately describe finite concentration chromatography 116). The program was modified so that a predetermined PRBS input function controlled a simulated stream switching valve. The synthesized detector output was cross correlated with the PRBS input to give the final correlogram output. A t this point, the correlogram peaks could he analyzed by an internal peak parameter subroutine and the retention time, peak areas and heights, peak asymmetry, etc. made available as output for further analysis. Alternately or in addition, the correlation function could be outputted for plotting and analysis by the peak parameter subroutine included in the plot program. Options were made available to either vary the sample concentration linearly a t any desired rate or to change it in a random fashion. Detector noise could also be simulated and added to the detector signal. Thus it was possible with this model to repeat all of the laboratory experiments with a degree of control not available in the laboratory. For example, Figure 5 illustrates the results from one experiment to determine the uncertainty in correlogram peak height measurements cs. the rate of change of concentration. The initial composition of the sample stream was 31% component 2 and 69% of component 3. This sample was diluted tenfold with component 1 (comparable to helium in the laboratory) before being compared to the standard gas. Between the time 5100 and 20,000, component 2 varied in a linear manner to 30.3% and component 3 was similarly changed from 69.0 to 69.7%. The direction of change was (16) R . A n n i n o , J . Franko. and H . Kelier. Anal. Chem., 4 3 , 107 ( 1 9 7 1 ) . 1224
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A N A L Y T I C A L CHEMISTRY, VOL. 45, N O . 7, J U N E 1973
TIME x Figure 5. Computer simulation IBM 1620 plot of CCSP peak height output (indicated by crosses X ) at various times after a continuous rate of change of input concentration has been initiated (shown by dashed lines). Standard gas: 90% component 1 ( k = 0 ) . 3.0% component 2 ( k = 0 . 7 5 ) . 7 . 0 % component 3 ( k = 3 . 0 ) . Sample stream: initial composition after a tenfold dilution with component 1 to 3.10% component 2 and 6.9% component 3
then altered so that at time 30,000 component 2 reached 30.6% and component 3 reached 69.4%. Thereafter the concentrations were not changed.
RESULTS AND DISCUSSION The correlogram snapshot shown in Figure 2B is typical of our initial experiments with correlation chromatography. The base-line irregularities are what we later termed correlation noise and were unacceptable in our work. The thrust of this research was to identify and explain the source or sources of this noise. To this end, two major areas were identified and are discussed in this section. ORIGIN OF BASE-LINE INSTABILITY Instability Due to Method of Correlogram Construction. The construction of a correlogram plays an important part of any discussion regarding base-line irregularities. The procedure can best be explained by reference to Figure 6. In this example (which may be considered as one option of the VRSP program), it has been assumed that the chromatograph has not modified the input, x ( t ) , but only delayed it in time. The experiment has been in operation for some time and an array of output, y ( t ) , values has been stored from time = now to time = 7 units in the past. The input, x ( t ) , is a pseudo random binary sequence of seven units, and two code periods of seven units each have been stored (from time = now to time = 14 units in the past). Assume that when the sample switch is in the + position, process sample is entering the column and that in the -position, standard sample is en-
+xy~el-l/7(+l - I -I -I +I - I + 1 ] = - 1 / 7
0
/ 1
1 2
1 3
! 4
I 5
i 6
1 7
T (DELAY TIME I
+xY(4)-1/7(tl +I + I + I + I ti + I ! = I
Figure 6. Construction of Correlograms I Calculation and plot of correlation function,
( T ) in
real time = now
value was entered into the data array. Examine the correlograms that were calculated a t now 2 and a t various times after the abrupt change (see Figure 7 ) . Base-line irregularities occurred because the new data, when averaged with the old, did not lead to cancellation a t all time shifts. Note that it is not until one chain code later (after the change appears at the detector) that the change is fully correlated. However, the peak height does on the average follow the change. Thus there is a problem of base-line instability caused by sample concentration changes which is basically related to the correlation calculation procedure and not a t all to any chromatographic problems. What are the implications of these results in terms of using the method to monitor continuously a change in process stream composition? Obviously the procedure offers no advantage over single impulse techniques in situations where large concentration changes are expected. A gross example of the above behavior is illustrated by the work of Godfrey et al. (12) when they reduced the concentration of one of their components to zero. The large baseline perturbations which occurred indicated the total collapse of the correlogram and it was not restored until one chain code later. Therefore, the accuracy with which one can monitor continuous changes will depend on the rate a t which the change takes place. The greater the rate of change, the smaller the S / N and the more uncertain is the peak height or area measurement. A graphic illustration is provided by the laboratory results summarized in Figure 3. Note that as the rate of change of concentration increased so did the uncertainty of the continuously updated area measurement recorded in Figure 3B. Also, an inspection of the various snapshot correlograms shown in this figure will verify the fact that S / N decreases when concentration is changing. Similar results are obtained by computer simulation using the CCSP model (see Figure 5 ) . Only for gradual input changes with respect to the length of the chain code is an accurate profile of the composition variation obtained.
+
AK
0
-7, ~
1
2
3
4
5
6
7
7 [DELAY)
Figure 7. Construction of Correlograms I I The state of the correlation function at various times after an abrupt concentration change
tering the column. At time = now, a decision has been made to calculate a correlogram. This is accomplished by multiplying each output value with the corresponding input, summing the results over the period of the code, and dividing by the period (in this case 7). This yields one point on the correlogram $ x y ( 0 ) = -I/+ a t T = 0. The input is then shifted one unit (T = 1) and the calculation re= -I,$ a t T = 1. The process is repeatpeated to give $xv(l) ed until the total correlogram is generated. As indicated in the experimental section a new correlogram is calculated every 50 msec. Assume that a t time = now -3 in the past the concentration of process sample has changed. However, since a t this time the sample switch was in the standard sample position, no change in column composition occurred. At time = now - 2 the new process stream sample entered the column. This change first appeared a t the detector four time units later a t time = now + 2. The new y ( t )
ANALYTICAL C H E M I S T R Y , VOL. 45, NO. 7, J U N E 1973
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ATTIME 2500
I
I
\
1 1 =?wp&&-
SAMPLE 0.90 0.031 0.069
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Figure 8. Computer simulation
/
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CCSP correlogram output illustrating the appearance of correlatlon noise due to large concentration differences between the standard sample stream (100% component 1, k = 0) and the process streams A (90% component 1, 10% component 2) and B (99% component 1,1% component
2)
Sample Averaging. Another possible advantage to employing correlation techniques is that random variations in sample concentrations are averaged in the correlogram and thus reduced in importance. These sample variations may occur because of an improper sampling point in the process stream or because of various hardware problems such as leaky sample valves, etc. In light of the previous discussion with regard to base-line irregularities, the correlation technique is not expected to resolve difficulties which cause large concentration fluctuations. However, some improvement should be observed, especially with smaller sample variations. Two experiments were run using CCSP. In one case, the 63 unit PRBS commanded a simulated stream switch mode of operation and in the other case, the injection of a discrete amount of sample of much smaller width than the switch code unit was initiated at each code interval when sample was called for. A 2% random concentration variation was impressed on the sample input a t a frequency such that each discrete injection contained a different sample concentration. Thus, when using the discrete mode of injection the correlogram area represents the averaged value of 32 injections and one would expect the 2% input variation to be decreased by The peak width, however, spanned approximately 12 samples of noise (which were summed in the area). Thus the variance of the sum was increased by 12 times. Therefore the expected standard deviation of the peak was (2%)(dTZJ/(d\/32) = 1.23%. The experimental value was 1.24%which in view of the decreased S / N of the correlograms is in excellent agreement with the predicted value. When using the stream switching mode of operation in the identical experiment, 20 different concentrations are averaged per code unit every time the switch is in the sample position. This increased averaging should and did result in an answer which was ~ ' 2 6 times better or 1.24,' \/m = 0.28%us. the 0.22%found by experiment. Instability Due to Nonlinear Behavior. The mathematical description of the detector response as given by Equation 1 assumes that the chromatograph operates as a linear system. If this were the case, the chromatogram obtained by injecting a narrow plug of concentrated sample would be exactly the same (except for area) as that ob-
m.
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ANALYTICAL C H E M I S T R Y , VOL. 45, NO. 7 , J U N E 1973
I K=0.75
Figure 9. Computer simulation CCSP correlogram output illustrating the absence of significant correlation noise in finite concentration chromatography
tained from a very dilute sample. In other words the larger chromatogram could be represented as the summation of a number of smaller ones of exactly the same shape. Practically speaking this is not the case. Peaks are apt to become more asymmetric as the sample concentration is increased. Therefore the deconvolution which occurs in the cross correlation operation is not accurate. Some degree of correlation occurs a t various points along the chain thus contributing to an erratic and irregular base line. It should be emphasized at this point that this difficulty is not peculiar to the correlation procedure of deconvolution but to all methods which assume a linear system approach. Contributors to Nonlinear Behavior. Sample Profile. The linear system approach assumes an extremely narrow sample plug so that its width does not contribute greatly to the peak shape. The correlogram of propane shown in Figure 2 does not represent a particularly fast analysis. The standard deviation of the peak is about 2 sec. A sample plug width of 0.2-0.5 sec is necessary so as not to appreciably affect the peak shape. This defines the width of the unit code. If an injection procedure is desired, its width should be very much smaller (perhaps % to lho) than this unit code width. This implies an extremely fast and accurate (in terms of sample quantity) sample switch, perhaps like the one reported by Cram and his students (17). Alternately the sample can be prediluted with carrier gas and the sample valve then becomes a stream switching valve which is required to switch in its fastest mode a t 0.5 sec. This is the alternative we adopted. (17) T .
H. Glenn and S. P. Cram, J. Chromatogr. Sci., 8, 46
(1970),
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Plot of concentration difference between sample and standard streams of varioub composition. Open symbols refer to component 2 ( k = 0.751, halfshaded symbols refer to component 3 ( k = 3 ) , and full-shaded symbols refer to component 4 ( k = 7 ) ; concentrations are shown as mole fraction (75). Courtesv Institute of Petroleum
Nonlinearities i n Finite Concentration Chromatography. Simple derivations of chromatographic theory assume a constant partition coefficient. In practice, however, the partition coefficient varies with the concentration of sample and thus leads to a nonlinear system. In order to approximate linear behavior, it is usually recommended that one work in dilute solution where the partition coefficient is fairly constant. Actually, linear behavior can be obtained at any concentration if one works in a comparison or deviation mode provided that the composition of the two streams is not too different. Another advantage to working in the region of small differences in process sample and standard sample concentrations is that the nonlinearities which are the result of the several other physical effects accompanying operation a t finite solute concentration are also minimized (See ref. (16) for a discussion of this effect in differential chromatography and for a bibliography of previous references to this problem). These nonlinearities form an integral part of the physical chromatographic model used in CCSP. Thus although a linear isotherm is assumed, base-line irregularities are observed (see Figure 8) as the system departs from the dilute solution region. However, if the two streams do not differ radically, even quite concentrated samples can be analyzed with good S / N . (see Figure 9). Similar results are obtained in the laboratory where analysis of process stream samples of 20% organic/80% helium by comparison with standard samples of 20.270 organic/79.8% helium produced correlograms comparable to Figure 2A (15). Quantitative Relationships. For the reasons discussed in the previous section, the S / N decreases markedly if too large a concentration difference is encountered between process sample and standard sample. While this may limit laboratory applications, it presents no real problem
in terms of process control applications. In fact, a measurement is normally required a t or about a set point. It is precisely under these conditions, where little or no difference exists between the process stream and the standard sample, that correlation chromatography is the most sensitive and yields accurate results. The potentially high sensitivity of the method for measuring deviations of a process stream composition from that of a standard is illustrated in Figure 10. The process samples have been diluted with component 1 (comparable to helium in the laboratory) before comparison with the standard sample. The deviations shown are on this diluted~stream. Notice that these are absolute values. Assuming accurate dilutions, deviations at the 99% level can be determined with the same absolute accuracy as those a t the 1% level. Operation of the system at or close to set point also minimizes the other problems associated with multicomponent chromatography (16). CONCLUSION Conditions have been outlined for the operation of a correlation chromatograph with excellent S/N. In these circumstances, it appears that this form of continuous chromatography is ideally suited to process control applications where accurate measurements of small deviations in the process stream composition are desired. ACKNOWLEDGMENT The authors would like to acknowledge the valuable contribution of W. E. Earle, who developed the real time computer and corresponding laboratory correlation programs. Received for review November 22, 1972. Accepted January 31, 1973. ANALYTICAL C H E M I S T R Y , VOL. 45, NO. 7, J U N E 1973
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