Ind. Eng. Chem. Prod. Res. Dev. 1985, 24, 385-390
385
CATALYST SECTION
Dynamic Behavior of Automotive Catalysts, 4. Impact of Air/Fuel Ratio Excursions during Driving Rlchard K. Herz’+ and Edward J. Shlnouskls phvsical Chemlstry Department, General Motors Research Laboratories, Warren, Michigan 48090
Previous studies of the transient response of three-way automotive catalysts to rapid changes in airlfuel ratio have considered constant speed operation only. The present work analyzes and compares emissions measured over two different three-way catalysts during the warmed-up portion of the Federal test procedure. A computerized relational data base was used to analyze the large amount of data recorded in each test run. The results demonstrate that the large-amplitude, long-duration rich excursions that occur during variable-speed driving have a major impact on CO, hydrocarbon, and NO emissions.
Introduction Most catalytic emission control systems on current automobiles contain a dual-bed converter. The first bed contains a three-way catalyst, and the second bed, which is preceded by an air injection port, contains an oxidizing catalyst. The three-way catalyst converts, to a significant extent, the three controlled exhaust components: CO, hydrocarbons, and NO. However, the oxidation catalyst is required because insufficient conversion of CO and hydrocarbons is obtained over the three-way catalyst during driving. The objective of this work is to develop an understanding of the processes that affect the performance of three-way catalysts during driving. The goal is a single-bed emission control system that is less expensive and less complex than current dual-bed systems. Emission control systems that utilize three-way catalysts contain a control subsystem to maintain the air/fuel ratio (A/F) close to the stoichiometrically balanced ratio. Although the A/F control subsystem in an automobile maintains the time-averaged A/F a t the control point during constant-speed driving, the instantaneous A/F cycles about the control point as a result of the response characteristics of the exhaust sensor (Sell and Chang, 1982). The A/F cycles have an amplitude of about 1A/F unit and frequencies that range from 0.5 to 4 Hz with increasing exhaust flow rate. Several studies have demonstrated that the response characteristics of three-way catalysts are complex. For example, the works by Gandhi et al. (1976), Kaneko et al. (19781, and Schlatter et al. (1983) showed how time-averaged conversions obtained during cycling vary with changes in A/F cycling frequency. Much research has been directed toward identifying the processes that determine the response of catalysts to A/F cycling in the 0.5-4.0-Hz frequency range, including the Present address: Chemical Engineering B-010, University of California a t San Diego, La Jolla, CA 92093. 0196-4321/85/1224-0385$01 .SO10
research described in parts 1-3 of this series (Herz, 1981; Herz et al., 1983; Herz and Sell, 1984). We were surprised to find in part 2 (Herz et al., 1983) that catalysts with very different compositions and A/F step responses performed similarly during A/F cycling at frequencies of 1 Hz and higher. We speculated in the conclusion of part 2 that significant differences between the two catalysts studied might appear during rich A/F excursions associated with rapid acceleration during driving. In order to pursue this thought, we have analyzed the dynamic performance of the two catalysts studied in part 2 during operation on a automobile driven through the EPA urban driving cycle, commonly called the Federal test procedure or “FTP”. Figure 1 presents a plot of the vehicle speed vs. time during the FTP. During the warm-up period, 0-400 s, the performance of a catalyst is determined primarily by the rate at which its temperature increases. In this work we consider only the warmed-up operation of three-way catalysts at times greater than 400 s. During warmed-up operation, the performance of a three-way catalyst is determined primarily by its response to rapid changes in exhaust flow rate and composition and not by the relatively small and slow changes in catalyst temperature that occur. The outstanding feature of Figure 1 is that there are essentially no periods of constant-speed operation during the FTP: urban driving consists primarily of acceleration-deceleration cycles. previous research on the dynamic behavior of automotive catalysts has been confined, however, to constant-speed operation. As we demonstrate below, speed changes introduce large-amplitude, long-duration, A / F excursions. These excursions have a major impact on emissions from single-bed three-way converters and have been ignored in previous studies of the dynamic behavior of automotive catalysts. Experimental Methods The Pt/Pd/Rh/A1203 catalyst and the Pt/Pd/Rh/ Ce/A1203catalyst used’in this work are the same bead-type 0 1985 American Chemical Society
386 Ind. Eng. Chem. Prod. Res. Dev., Vol. 24, No. 3, 1985
500
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Figure 1. Plot of vehicle speed during the Federal test procedure.
catalysts used in part 2. They will be referred to below as catalyst P and catalyst P/Ce, respectively (where P stands for “precious metal” and P/Ce stands for “precious metal with Ce”). A detailed description of the catalysts is given in part 2. Briefly, the loadings of the precious metals and Ce in catalyst P/Ce are typical of those found in fully formulated three-way catalysts, and the precious metal loadings in catalyst P are the same as those in catalyst P/Ce. Except where noted below, all of the data presented were taken during experiments with catalyst P/Ce. The 1982 Buick LeSabre used in this study was equipped with a 4.1-L V6 gasoline-fueled engine. The normal emission control equipment on the vehicle included control of the A/F by a GM Computer Command Control System, an electromechanicalcarburetor, air pump, and a dual-bed catalytic converter. We removed the dual-bed converter and replaced it with a standard GM 160 single-bed converter (pellet-type) filled with 1400 g of the catalyst to be tested. The air pump functioned normally during the warm-up period of the test, injecting air upstream of the converter. Following warm-up, however, the air pump simply discharged into the atmosphere. In summary, the modified emission system functioned in our tests as a single-bed three-way catalyst system. The FTP tests were performed with the automobile mounted on a chassis dynamometer. Two separate sets of exhaust analyzers continuously measured the exhaust composition at the inlet and outlet of the converter. The signals from the exhaust analyzers as well as signals from other instruments (e.g., exhaust sensor, speed, throttle position) were scanned and recorded every 0.5 s during the 31-min duration of the test by a computer. Nineteen readings per scan and 3750 scans were recorded, for a total of 71 250 readings during the entire test. Normally when such a test is performed, only summary numbers such as EPA g/mi are looked at in detail because there is no convenient way to manipulate the massive number of readings taken. In the course of learning about personal computer data-base programs, we realized that a very large data-base program would greatly facilitate detailed analysis of FTP test data. The relational database program REGIS, developed by the Computer Science Department at General Motors Research Laboratories (Joyce and Oliver, 1976), proved to be well suited to the task. The data from each test run were transferred electronically into a table in REGIS,running on an IBM 3081 computer under the TSO operating system. Each row in the table consisted of all of the signal-channel readings recorded in one scan. Each column in the table consisted of all of the scans of a particular channel, with readings in engineering units.
The first operation performed on the data was to shift exhaust concentration columns with respect to each other in order to correct for mismatches introduced during testing as a result of the exhaust analyzers’ different internal time delays and spacing along the tubing leading from the sample taps. The channels were shifted so that plots of the inlet and outlet concentrations of the various exhaust constituents vs. time lined up with changes in throttle position and speed during the early part of the warm-up period, when conversions over a catalyst are negligible. The next operations performed on the data were to calculate (1)A/F from the exhaust composition data, (2) exhaust flow rates from the fuel flow rate and the A/F, (3) emission rates (g s-l) of the exhaust constituents from the constituent concentrations and the exhaust flow rate, and (4) vehicle acceleration from the speed data. Such calculations can be performed interactively in REGIS by using one-line commands that operate on the entire table or by using a set of previously developed command lines collected in a command file. At this stage, a table of FTP data was analyzed by (1) selecting portions of data with logical commands such as “select all scans where the acceleration is greater than 0.0 kph/s and less than 1.0 kph/s and where the A/F is less than 14.5”, (2) running statistical analysis commands on selected portions of data, and (3) plotting selected portions of data on the graphics terminal. The response of the computer was such that commands appeared to be executed instantaneously to an operator analyzing FTP data interactively, even though FTP tables consisted of up to 120 000 entries. Results and Discussion The time scale of the signal variations that are discussed in this work differs substantially from the time scale considered in parts 1-3. In the earlier work, we used fast-response instruments to achieve time resolutions on the order of 0.02 s. Here, exhaust analyzers with characteristic response times on the order of 1s were used, and signals were recorded only every 0.5 s. Thus, the highfrequency (0.5-10 Hz) components of A / F and concentration fluctuations that are present in engine exhaust (Sell et al., 1981) are not seen in the data presented below. In this work we concentrate our analysis on the impact of low-frequency (less than 1 Hz) variations in A/F and exhaust composition. Figure 2 shows clearly the impact of speed changes on A/F control and emissions. The left-hand column of plots are for constant operation at 48 kph (km h-l). The right-hand column is for three acceleration-deceleration cycles during an FTP run, where the speed ranges from 0 to 44 kph. Emission rates (g s-l) of CO and NO (bottom two rows of plots) are very low during constant-speed operation as a result of the good control of A/F (second row) and moderate exhaust flow rate (third row). Substantial “spikes”of CO and NO emission occur during FTP driving because of A/F excursions from the control point and high exhaust flows during acceleration. This comparison shows why the oxidizing bed in a dual-bed converter is needed: to control CO (and hydrocarbon) emissions during acceleration. During the initial portion of a period of acceleration, the average A f F goes rich because of the effect of the extra fuel supplied by the accelerator pump in the carburetor. After a period of rich excursion from the A/F control point, the A / F often swings into a lean excursion as a result of overcorrection by the A/F control system. A somewhat erratic pattern of A / F during variable-speed driving re-
Ind. Eng. Chem. Prod. Res. Dev., Vol. 24, No. 3, 1985 387
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Time(s) Figure 2. Comparison of A/F ratio control, exhaust flow rate, and CO and NO emission rates from the converter (left) during constant-speed driving and (right) during a selected segment of an FTP test, both with catalyst P.
sults. In addition to the increase in emissions caused by A/F excursions, emissions also increase with exhaust flow rate. This is because higher exhaust flows result in both (1) higher feed rates of exhaust constituents to the converter (even at constant concentration) and (2) lower residence times of the constituents in the converter. The detailed patterns of A/F excursions measured here are unique to the vehicle used in our tests, of course. Vehicles with more sophisticated A/F control systems, such as those that utilize inlet air measurement, feedforward control components, and port fuel injection, will achieve closer control of A/Fduring acceleration, deceleration, and other engine load changes. However, all vehicles utilizing current technology will show A/F excursions to some extent during speed and load changes; thus, the qualitative findings of this work are generally valid. Figure 3 is a histogram summarizing the control of A/F during the warmed-up portion of the FTP for the vehicle used. The A/F control point for this vehicle was 14.7, somewhat lean of the stoichiometrically balanced ratio of 14.6. The control point chosen by system designers depends on the relative extents of control of CO, NO, and hydrocarbons required for a particular engine-vehicIeconverter combination. We have chosen to define the range of A/F from 14.5 to 14.9 (14.7 f 0.2) as the control range for this system. Thus,the control system is defined to be in a fuel-rich A/F excursion when the A/F is less than 14.5 and in a fuel-lean excursion when the A / F is greater than 14.9. The results and conclusions of this work are not sensitive to the exact A/F values chosen in these definitions. Although the pattern of A/F vs. time during variablespeed driving is somewhat erratic and does not show an exact correlation with acceleration, our statement in part 2 that rich excursions are associated with acceleration is shown to be statistically valid in Figure 4, in which the percents of time that the system is in rich and lean A/F excursions are plotted vs. acceleration. Deceleration
4
2
0
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4
Acceleration (kp h/s) Figure 4. Percent of time at the indicated acceleration that the A/F is in a rich or lean excursion. Negative values of acceleration refer to vehicle deceleration.
(negative values of acceleration) results in lean excursions while positive acceleration results in rich excursions. The figure clearly shows that good control of A/F is achieved only at constant speed (a zero value of acceleration). Note that the detailed shape of the plot in Figure 4 is specific to the FTP test. Better control of A/F would be achieved in a less erratic driving schedule in which periods of acceleration and deceleration are held for longer times, thus allowing the A/F system to achieve control. Emission rates are also greatly affected by the variation of exhaust flow rate with acceleration. Figure 5 is a plot of the average flow rate obtained in each range of acceleration vs. acceleration. Exhaust flow rate increases by about a factor of 4 over the range of acceleration in the FTP. Since both rich excursions and high exhaust flow rates are associated with acceleration and since both lean excursions and low exhaust flow rates are associated with deceleration, exhaust flow rates, on the average, increase with decreasing (richer) A/F. The combination of Figures 4 and 5 strongly suggests that periods of acceleration contribute significantly to
388
Ind. Eng. Chem. Prod. Res. Dev., Vol. 24, No. 3, 1985
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Acceleration (kph/s) Figure 5. Variation in average exhaust flow rate with acceleration. Table I. A/F Control and Emissions during Warmed-up Portion of FTP control, rich 14.5 5 lean excursion, A/F 5 excursion, AIF < 14.5 14.9 A/F > 14.9 % of total time 14 76 10 % of total flow 20 73 7 % of total co 48 39 2 % of total HC 56 41 4 % of total NO 34 64 2
emissions during the FTP. The rich excursions associated with acceleration will reduce conversion of NO as well as CO and hydrocarbons by shifting the A/F away from the range of optimal conversion. The increased exhaust flow associated with acceleration will increase the rate of emission of NO, CO, and hydrocarbons from the engine and will decrease the residence of exhaust in the converter. The main function of the second bed of a dual-bed converter, then, is to control CO and hydrocarbon emissions during acceleration. Table I shows how strongly rich excursions of the time-averaged A/F contribute to emissions. The first row of the table shows the percent of the total time during the warmed-up portion of the FTP that the A/F is in a rich excursion, in the control range, and in a lean excursion. A substantial portion of time (76%) is spent with the A/F in the control range. The second row shows the percent of the total exhaust flow that occurs in the three A/F ranges. A comparison of the time and flow data reflects the fact that flow rates, on the average, are higher at richer A/F’s. Note that large percentages of the CO and hydrocarbon (HC) emissions occur during rich excursions, even though only a small fraction (14%) of the operating time is spent in a rich excursion. Not surprisingly, lean excursions contribute very little to CO and hydrocarbon emission. We were somewhat surprised, however, by the data for NO. Rich excursions are responsible for a significant portion (34%) of NO emission, whereas lean excursions account for a negligible portion (2%). Conventional thinking might predict that lean excursions result in significant NO emission because NO conversions are measured to be low at lean A/F’s in tests performed at constant A / F settings or with 1-Hz cycling of A / F settings. We first discuss NO emission during rich excursions and
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Time(seconds) Figure 6. Plot showing the characteristic time scale of rich A/F excursions (A/F < 14.5). The horizontal lines marking the rich excursions at 780 s are located at A/F = 14.5.
then, below, discuss NO emission during lean excursions. There are three reasons for our fiiding of significant NO emission during rich excursions in variable-speed driving: (1)the rate of NO emission from the engine increased as a result of both the increased exhaust flow rate and increased NO concentration that occurred during periods of acceleration and associated rich excursion; (2) the residence time of exhaust in the converter decreased during periods of acceleration and associated rich excursion; (3) NO conversion is low over catalysts at very rich A/F’s because of inhibition of surface reactions by CO and hydrocarbons, even though the exhaust is very reducing. Figure 6 is a plot of A/F vs. time during one segment of an FTP test. This figure serves to remind us that conditions vary erratically during the FTP and that the results shown in Figures 3-5 and Table I are statistical summaries. More importantly, Figure 6 shows that the time scale of the rich A/F excursions we are considering is on the order of several seconds. The time-averaged A/F that is plotted deviates below the rich control range limit of 14.5 for several seconds at a time, and A/F levels as low as 14 are frequently reached. We also performed Fourier transform power spectrum analysis on the FTP A/F data in order to determine whether characteristic frequencies could be assigned to the A / F fluctuations induced by perturbations associated with variable-speed driving. The results of this analysis were not conclusive when the entire warmed-up portion of the FTP was analyzed. However, analysis of sections of this data did show peaks in the power spectra at about 0.1-0.2 Hz, depending on the section analyzed, in good agreement with our conclusion from Figure 6 that the large-amplitude A / F excursions have characteristic periods of several seconds. Because of the relatively slow responses of the conventional exhaust analyzers used, the A/F’s that are plotted in Figure 6 are running averages which do not show the high-frequency (ca. 1-10 Hz) components present. The exhaust sensor on the vehicle, however, did respond fast enough to reflect the high-frequency components associated with the control system limit cycle. Although the sensor signal was recorded only every 0.5 s, the recording occurred randomly with respect to cycling of the sensor signal, and thus we are able to make a statistical analysis of the sensor signal records.
Ind. Eng. Chem. Prod. Res. Dev., Vol. 24, No. 3, 1985 389
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Figure 7 summarizes such an analysis and shows the frequency that the instantaneous A/F, as indicated by the sensor signal, switched to the “opposite side” of the stoichiometric point during excursions of the time-averaged A/F from the stoichiometric point. During rich excursions of the average A/F below values of 14, there are no highfrequency lean excursions of the instantaneous A/F. Such lean excursions, if they were to occur, would enhance CO and hydrocarbon conversion by allowing “storage” of oxidants and reactivation of the water-gas shift activity of Rh (Herz and Sell, 1984). The performance of a three-way catalyst is often evaluated by plotting time-averaged conversions measured at a series of average A/F’s during cycling of the A/F setting. Such a plot typically shows relatively high CO and hydrocarbon conversions a t lean A/F’s, with these conversions decreasing a t richer A/F’s. NO conversions will typically be relatively high slightly rich of the stoichiometric point, somewhat lower at richer A/F’s, and very low on the lean side of the stoichiometricpoint. Figure 8 shows a similar type of plot that statistically summarizes conversions obtained over catalyst P/Ce during the warmedup portion of an FTP test. (The erratic variation of the hydrocarbon conversion line at rich A/F’s was only seen
Figure 9. Comparison of the CO conversion performance of catalyste P and P/Ce during the warmed-up portion of the FTP shown vs. average A/F.
in this test run and is not statistically significant; fewer data points become available for averaging with greater deviation from the A/F control point of 14.7.) The striking difference between Figure 8 and a standard catalyst evaluation plot is that the time-averaged conversion of NO remains high at lean A/Fs. This somewhat surprising difference is primarily a result of the fact that the time-averaged A/F remains lean for only short periods (ca. 1-3 s) during the FTP test, rather than for the relatively long periods (ca. minutes) used to achieve constant levels of time-averaged conversions in catalyst evaluation testa. NO conversion over a three-way catalyst can remain high for the initial periods of lean excursions (Shulman et al., 1982), presumably because NO can participate in the oxidation of the metals in the catalyst. A secondary contributing factor to the difference between Figure 8 and typical catalyst evaluation plots is the fact that exhaust flows are relatively low at lean A/F’s during the FTP, whereas exhaust flow rates are held constant across the range of A/F’s in catalyst evaluation tests. We now return to the two catalysts compared in part 2. There, the oxygen storage capacity added by the Ce in catalyst P/Ce resulted in dramatically enhanced CO conversion following lean-to-rich step changes. However, the CO conversion performance of catalysts P and P/Ce differed only slightly during A/F cycling. Figure 9 compares the average CO conversions obtained over the two catalysts during FTP testing. The performance of catalyst P was only slightly worse than the performance of catalyst P/Ce near the stoichiometric point and at lean A/F’s, in reasonably good agreement with the relative performances of the two catalysts during cycled A/F tests. However, the superior step-response performance of catalyst P/Ce did come into play in the FTP during very rich A/F excursions (A/F < 14). The superior performance of catalyst P/Ce results primarily from the capacity of Ce compounds for storing oxygen and making it available for oxidation of CO during rich excursions.
Conclusions Large-amplitude, long-duration rich A/F excursions are associated with vehicle acceleration during urban driving and have a major impact on CO, NO, and hydrocarbon emissions from three-way catalyst beds. Two three-way catalysts, one containing the base metal Ce and one lacking Ce, performed similarly during rapid sensor-induced cy-
Ind. Eng. Chem. Prod. Res. Dev. 1985, 24, 390-393
390
cling about the A/F control point. However, the performances of the two catalysta differed significantly during rich excursions of the average A/F from the control point. In view of these results we conclude that (1)relatively large-amplitude, low-frequency (with respect to sensorinduced cycling) components of A/F fluctuations must be considered in future studies of the dynamic behavior of automotive catalysts, (2) reductions in emission levels should be especially sensitive to future improvements in A/F control, and (3) the complex nonlinear nature of A/F fluctuation and catalyst response during variable-speed driving mandates close collaboration between researchers studying engines, A/F control, and catalysts. Acknowledgment We thank S. J. Westfall and W. K. Haverdink of the GMR Engine Research Department and V. K. Breault of the GMR Instrumentation Department for assistance with the experiments and data analysis. Registry No. CO, 630-08-0; NO, 10102-43-9; Pt, 7440-06-4;
Literature Cited Gandhi, H. S.;Piken, A. G.; Shelef, M.; Delosh, R. G. "Laboratory Evaluation of Three-way Catalysts"; Society of Automotive Engineers: Warrendale, PA. 1976: No. 760201. Hem, R. K. Ind. Eng. Chem. Rcd. Res. Dev. 1981, 20, 451. Herz, R. K.; Klela, J. B.; Sell, J. A. Ind. Eng. Chem. Prod. Res. Dev 1983, 22,387. Herz, R. K.; Sell, J. A. J. Catal., in press. Joyce, J. D.;Oliver, N. N. Roc. AFIPS Natl. Comp. Conf. 1976, 45, 839. Kaneko, Y.; Kobayashi, H.; Komagome, R.; Hirako, H.; Nakayama, 0. "Effect of Air-Fuel Ratio Modulation on Conversion Efficiency of Three-way Catalysts"; Society of Automotive Engineers: Warrendale, PA, 1978; No. 780607. Sell, J. A.; Herz, R. K.; Perry, E. C. "Time Resolved Measurements of Carbon Monoxide in the Exhaust of a Computer Command Controlled Engine"; Society of Automotlve Englneers: Warrendale, PA, 1981; No. 810276. Sell, J. A.; Chang, M.-F. "ClosedLoop Control of an Engine's Carbon-MonoxMe Emissions Using an Infrared Diode Laser"; Society of Automotive Englneers: Warrendale, PA, 1982; No. 820388. Schlatter, J. C.; Sinkevitch, R. M.; Mitchell, P. J. Ind. Eng. Chem. Prcd. Res. Dev. 1983, 22, 51. Shulman, M. A.; Hamburg, D. R.; Throop, M. J. "Comparison of Measured and Predicted Three-way Catalyst Conversion Efficiencies under Dynamic Air-Fuel Ratio Conditions"; Soclety of Automotive Engineers: Warrendale, PA, 1982, No. 820276.
Receiued for review December 10, 1984 Accepted April 22, 1985
Pd, 7440-05-3; Rh, 7440-16-6; Ce, 7440-45-1.
General Economic Evaluation of the Use of Quaternary Ammonium Salts as Catalysts in Industrial Applications Beno Zaidman, Yoel Sasson;
and Rony Neumann
Casali Institute of Applied Chernlstty, School of Applied Science and Technology, The Hebrew University of Jerusalem, Jerusalem 9 1904, Israel
The use of quaternary ammonium salts (Quats) as phase-transfer catalysts is analyzed from a technological and economic point of view. The limiting price for Quats is determined by establishing a qualitative relationship between technical parameters and economic factors. Specific examples show that the present price of Quats limits their commercial use to the area of highpriced commodities and specialty chemicals. Quats may be used in commodity manufacture provided they are produced on a larger scale. A simulation of such a large-scale production of a representative Quat (tetrabutylammonium bromide) has been made and its consequences are discussed.
In the last decade or so, a new synthesis technique termed phase-transfer catalysis (PTC) has been developed and applied to a large variety of organic reactions. In these reactions, anionic nucleophiles are extracted from a solid or liquid water phase into an organic phase containing a substrate that reacts with the extracted anion. These reactions are performed most popularly by using quaternary ammonium salts, Quats, as catalysts. As examples of these reactions one can cite aliphatic nucleophilic substitutions (eq l),eliminations, dichlorocarbene reactions, cyci
I
CH2CN
I
and many others. There are several excellent books that review the phase-transfer literature in great detail: Dehmlow and Dehmlow (1980);Starks and Liotta (1978). A general flow sheet of a phase-transfer reaction and the subsequent separation of reaction mixture and recycle of catalyst is presented in Figure 1. In this paper we define the areas where industrial application of phase-transfer catalysis by Quats is possible. 0196-4321/85/1224-0390$01.50/0
This evaluation is a general one and cannot eliminate the necessity for a detailed analysis of each specific process. Therefore, the scope of this work is to establish a preliminary connection between various technological parameters of phase-transfer catalysis, specifically those related to utilization of Quats, and possible economic consequences. We would like to furnish a tool that will permit initial screening of technological parameters from an economic point of view. Determination of Limiting Price The first step in our work is to establish a quantitative relationship between technical parameters and economic factors. The amount of catalyst, Q1, needed to obtain a ton of product by phase-transfer catalysis is defined in eq 2a, where MWQ = molecular weight of Quat, MWP =
Q1 = MWQ X MWP-'
X
MR
(24
molecular weight of product, and MR = mole ratio Quat/product. If recovery of the catalyst is possible, then we have a corrected equation taking into account catalyst recovery (eq 2b). Q2
= MWQ X MWP-I X MR X QR-I
0 1985 American
Chemical Society
(2b)
