5438
Ind. Eng. Chem. Res. 2004, 43, 5438-5445
Kinetics of Cracking and Devolatilization during Coking of Athabasca Residues Murray R. Gray,*,† William C. McCaffrey,† Iftikhar Huq,‡ and Tuyet Le† Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB T6G 2G6, and Syncrude Canada Ltd., Edmonton Research Centre, 9421-17th Ave, Edmonton, AB T6N 1H4
The kinetics of cracking, coking, and devolatilization of Athabasca bitumen were investigated by reacting thin films of feed material. Samples of vacuum residue (524 °C+), scrubber bottoms, and residue from a batch fluid coker were reacted in films of thickness 20 µm on strips of Curiepoint alloy. The strips were heated to temperatures of 457, 503, and 530 °C in a nitrogen atmosphere using an induction furnace. After reaction, the remaining unconverted liquid was extracted from the films, the toluene-insoluble residue was weighed, and the condensed vapor and extract liquids were analyzed for microcarbon residue content (MCR) and boiling distribution by simulated distillation. The kinetics of reaction and devolatilization were consistent with a lumped kinetic model that included cracking, coke formation, and vaporization limited by equilibrium ratios and mass transfer. The kinetic model was able to reproduce the experimental data for total extractable and coke yield as a function of time, as well as the yields of residue and gas oil fractions in the vapor product and remaining in the liquid film. Even though the heavy residue fractions had equilibrium ratios of less than 0.01, 10-15 wt % of the feed appeared in the vapor product as 650 °C+ material. MCR content correlated well with the fraction of 650 °C+ material; therefore, the model predictions were consistent with the MCR content of the vapor products. Introduction The kinetics of cracking of the vacuum residue fractions of heavy oil and bitumen have been reported by various investigators. Despite the complexity of these materials, and the wide range of products from freeradical cracking processes, the overall kinetics tend to follow apparent first-order kinetics.1 Many of the reaction schemes and kinetics were studied under hydroconversion conditions, where most of the products remain in the liquid phase and phase behavior has a limited impact on the rates of reaction.2-4 The kinetics of coke formation and cracking from asphaltenes were successfully modeled by Wiehe5 by allowing for phase change within the liquid phase to form coke precursors. This model was successful in representing the changes in kinetics due to different solvents6 and in predicting kinetics from chemical composition data for asphaltenes.7 Wiehe’s5 original model was for an open reactor, where volatiles were removed from the liquid immediately upon their formation from cracking reactions of both the asphaltenes and the maltenes. Cracking processes that operate at temperatures in excess of 500 °C, such as fluid coking, will necessarily give some vaporization of the vacuum residue components (524 °C+), in addition to the gas oil and lighter fractions (524 °C-). For example, Olmstead and Freund8 found that components with boiling points up to approximately 650 °C were subject to cracking and volatilization. The reactors operating in this hightemperature regime usually involve thin liquid films reacting on the surfaces of solid particles which serve as a heat medium;9 therefore, the geometry of the * To whom correspondence may be addressed. Fax: (780) 492-2881. E-mail:
[email protected]. † University of Alberta. ‡ Syncrude Canada Ltd.
reacting liquid phase promotes the transport of highboiling components to the liquid phase. This paper reports the kinetics of cracking of thin films (ca. 20 µm) of vacuum residue based on measurements from a unique Curie-point reactor apparatus. This device provides for rapid heating of the liquid phase to the desired reaction temperature. The gas phase remained much cooler, and a flow of nitrogen gas removed the cracked products from the reactor. These features gave rapid quenching of the cracked products, allowing direct measurement of liquid-phase cracking and devolatilization. Theory The evaporative flux of a component from a liquid surface is governed by the mass transfer coefficient and the concentration driving force.10,11 In the case of evaporation during coking in a thin liquid film, the analysis is complicated by the wide range of boiling points, from cracked products through to vacuum residue components, and a rapid increase in the liquid viscosity with reaction that will reduce the diffusion coefficients.12 For the light components, liquid-side mass transfer was rate limiting for liquid films of thickness 50 µm or greater.13 The less volatile high-boiling components will dominate at the liquid interface; therefore, the transport of these components must be limited by the gas-side film resistance. The present experiments were conducted in thin films of ca. 20 µM, to minimize liquid-side transport resistance; therefore we ignore gradients in the liquid and approximate the interfacial transport as controlled by the gas-side film resistance
Ni′ ) kG′(yi* - yi)
(1)
where kG′ is the gas film mass transfer coefficient on a molar basis, yi* is the gas-phase mole fraction of
10.1021/ie030654r CCC: $27.50 © 2004 American Chemical Society Published on Web 01/30/2004
Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004 5439 Table 1. Properties of Athabasca Residue Materials
property toluene insolubles, wt % MCR, wt % sulfur, wt % nitrogen, wppm density, kg/m3 @ 20 °C boiling fractions, wt % 524 °C524-650 °C 650 °C+
Figure 1. Schematic diagram of lumped reactions and volatilization during coking in a thin film. Reactions are assumed to be first order. Rate constants for reaction are ki, stoichiometric yields are sij, and the mass transfer coefficient is kGa. Equilibrium ratios are Ki.
component i in equilibrium with the liquid surface concentration, and yi is the gas-phase mole fraction at the gas interface. Further, when the vapor phase is swept by an inert gas, the vapor-phase concentration of the reacting species will be negligible and we obtain
Ni′ ) kG′yi*
(2)
(3)
The value of this relationship is that the equilibrium ratio can be calculated at the reaction temperature using an equation of state, such as Peng-Robinson. In the cracking of vacuum residue, the changes in molecular weight with reaction and the difficulty in measuring molecular weight of high-boiling components make the determination of molar concentrations difficult. A convenient approximation, therefore, is a restatement of eq 3 in an approximate form on a weight basis
Ni ) kGKiwi
vacuum residue
pilot coker product residue
2.4 24.6 5.8 8365 1102
1.8 27.8 5.7 7206 1086.8
0.03
30 37 33
10 40 50
15 60 25
1060
was made up of five lumped species: heavy residue (lump 1, 650 °C+), light residue (lump 2, 524-650 °C), gas oil (lump 3, 343-524 °C), distillates (lump 4, 343 °C-), and coke precursors and coke. Coke was defined as toluene-insoluble material. The distillates were assumed to be evolved as soon as they were formed (K4 ) ∞), because of measured concentrations of components in this boiling range in the extracts from the liquid films. The equilibrium ratios for the other lumps were calculated using the Peng-Robinson equation of state (HYSYS, Hyprotech Ltd, Calgary, AB). The system of kinetic equations was as follows for the components in the liquid film
dw1/dt ) -k1w1 - k1cw1 - kGaK1w1
(5)
dw2/dt ) k1s12w1 - k2w2 - k2cw2 - kGaK2w2 (6) dw3/dt ) k1s13w1 + k2s23w2 - kGaK3w3
(7)
dwcp/dt ) k1cw1 + k2cw2 - kcwcp
(8)
dwc/dt ) kcwcp
(9)
while the equations for the components in the vapor product were as follows
From the definition of the equilibrium ratio, Ki
yi* ) Kixi
fluid coker scrubber bottoms
(4)
This equation represents the driving force for transport to the flowing inert vapor phase as the mass of a lumped component i. The kinetics of coke formation have been successfully modeled on the basis of phase separation of reacted asphaltenes following an induction time.5,6 When cracking vacuum residue at over 500 °C, the induction time will be at most a few seconds in duration due to the high rates of reaction and the rapid loss of liquid components. In this reaction regime, boiling point of residue components is more significant than solubility in n-pentane. Consequently, the reaction scheme illustrated in Figure 1 was adopted for modeling the kinetics of vacuum residue conversion in thin films. The reacting mixture
dw1P/dt ) kGaK1w1
(10)
dw2P/dt ) kGaK2w2
(11)
dw3P/dt ) kGaK3w3
(12)
dw4P/dt ) k1s14w1 + k2s24w2
(13)
The mass transfer coefficients in the liquid phase for the heavy residue (lump 1), light residue (lump 2), and the gas oil (lump 3) were assumed to be approximately equal. Given the uncertainty of the molecular size of the lumped species, particularly the residue components, the mass transfer coefficients for each lump were not corrected for differences in diffusion coefficients. The differences in volatility were reflected by the equilibrium ratios. Analytical solutions for the system of equations are given in the Appendix. Experimental Section Fluid coker scrubber bottoms, Athabasca vacuum residuum (+524 °C), and coker product residue were supplied by Syncrude Canada Ltd. The properties of the feed materials are presented in Table 1. The scrubber bottoms were obtained from a commercial fluid coker at Fort McMurray, AB, and contain a mixture of unreacted Athabasca vacuum residue and condensed
5440 Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004
Figure 2. Schematic diagram of apparatus.
high-boiling components from the cracking of Athabasca bitumen. The pilot coker product was obtained from a fluid-coker pilot reactor at Syncrude Research, with Athabasca residue feed undergoing coking reactions at 520-540 °C. The total liquid from condensing the vapor product from the pilot was distilled by the ASTM D1160 method to obtain the vacuum residue fraction. These three vacuum residue materials gave a range of concentrations of the 650 °C+ fraction. Methylene chloride (Fisher Scientific) and prepurified nitrogen (Matheson) were used as received. The basic design of the reactor followed Gray et al.,13 except that the vacuum residue material was coated onto strips of Ni/Fe alloy (Ametek Special Metals, Wallingford, CT) with Curie-point temperatures in the range of 457-530 °C, following Soundararajan.14 A simplified schematic of the reactor system is presented in Figure 2. The reactor consisted of inductively heated strips of Curie-point alloy (25 cm × 2 cm × 0.04 cm), each coated with residue to give a film area of 46 cm2. Gold plating was used to passivate the surface of the nickel/iron alloy strips prior to experiments. Up to six strips were held in ceramic holders to form an annulus within a Pyrex glass cylinder capped with stainless steel flanges.Both the alloy strips and the glass tube were held within the induction coil (Ameritherm Inc., induction furnace model XP-30). The Curie-point temperatures of the alloys were verified using fine-gauge thermocouples that were spotwelded to the metal surface. Nitrogen sweep gas was introduced at one end of the glass tube through a sintered metal diffuser and exited the opposite end through a conical section. The gas flow rates used for the experiments were between 11 and 13 L/min, which corresponded to a sweep gas residence time of approximately 3 s. Condensable reaction products were
collected using a liquid nitrogen cooled trap. To remove aerosols, the trap was filled with glass wool. Thin films of vacuum residue material were created by dissolving the feed in methylene chloride and then spraying the solution onto the strips. The strips were dried overnight and reweighed to determine the amount of vacuum residue. Mean film thickness was 20.0 ( 1.5 µm in all experiments, calculated as volume of residue divided by the area coated. Prior to reaction, the alloy strips were placed in their ceramic holders and then inserted into the glass tube. The entire system was sealed and purged with nitrogen (10.2-10.5 L/min) for 0.5 h. The induction heater was then turned on, and the strips were brought to reaction temperature for 5-240 s. At the end of this time, the alloy strips were cooled by injecting liquid carbon dioxide into the glass tube. The combination of induction heating and rapid quench minimized the time for heating from 400 °C to reaction temperature and cooling the vacuum residue to 1 and 2 s, respectively. Reaction rates were insignificant below 400 °C. Additional experimental details are provided by Soundarajan.14 Extractable vacuum residue was recovered from the strips by sonicating in methylene chloride, filtering the solution through a 0.3 µm filter (Millipore Ltd., Mississauga, ON), and evaporating the solvent. Coke yield was determined gravimetrically from the weight of solids remaining on the alloy strips after sonication plus the weight of solids from the filter. Coke yields are reported on a solids-free basis by subtracting the solids in the initial feed material (Table 1). The condensed vapor product was recovered by washing the reactor, cold trap, and connecting tubes with methylene chloride and then evaporating the solvent. Extract and condensed vapor samples were analyzed by high-temperature simulated distillation, using the
Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004 5441
Figure 3. Yields of toluene-extractable liquid (Extract) and toluene-insoluble solids (Coke) from cracking of scrubber bottoms at 503 °C. Where included, the error bars show plus and minus 1 standard deviation from three repeat experiments. The curves are from the kinetic model with parameters from Table 3 for the scrubber bottoms.
external reference method, and for microcarbon residue (MCR) by Syncrude Canada. Previous studies showed that the reactor system gave an overall material balance on the feed vacuum residue of over 95%.13 The gas products were not analyzed due to their low yields and the extreme dilution by the nitrogen sweep gas, which gave concentrations at or below the detectable limits by gas chromatrography with flame ionization detection. 13 Results and Discussion The experimental method gave excellent repeatability, with yields of extractables to (1 wt % or better and yield of coke (0.7 wt % or better. As illustrated in Figure 3, the yield of extractable material from the liquid film dropped to negligible levels after 60 s at 503 °C, with a corresponding rise in the yield of coke (toluene-insoluble material). All yields are reported on a solids-free basis, by subtracting the toluene-insoluble material present in the starting feed. The experimental data from the reactions of the scrubber bottoms were used to estimate parameters for the kinetic model. The model gave too many adjustable parameters; therefore, the following assumptions were used to reduce the number of adjustable parameters: (a) All rate constants follow the Arrhenius relationship with temperature [ki ) Ai exp(-Eai/(RT))]. (b) The cracking reactions and the coke-forming reactions had different activation energies, but these energies were the same for the two residue lumps (fractions 1 and 2). Consequently, for cracking Ea1 ) Ea2, and for coking Eac1 ) Eac2. The resulting model had 12 adjustable parameters, because two stoichiometric coefficients (s14 and s34) were determined by material balance (∑j)14sij ) 1). The sum of squared residuals was minimized to estimate the best set of parameters n
SSR )
∑ j)1
[
]
wj - wj,pred σj
2
(14)
where wi and wi,pred are experimental values and predicted values for mass fraction of extractables, toluene-insoluble coke, and mass fractions of boiling fractions (fractions 2 and 3) in the extractables and in the vapor products at all temperatures. The Solver routine of Microsoft Excel was used to perform the
Figure 4. Evolution of cracked products in the liquid film and in the condensed vapor product with time from scrubber bottoms at 503 °C. Data points are mean values from three experiments, and curves are from the kinetic model with parameters from Table 3 for the scrubber bottoms. Vapor ) condensed vapor product; Extr ) toluene-soluble fraction extracted from the liquid film. Table 2. Mean Equilibrium Ratios for Boiling Fractions T ) 457 °C
T ) 503 °C
T ) 530 °C
2.134 0.0402 0.00121
3.136 0.0994 0.00531
4.216 0.1719 0.0106
fraction 3,343-524 °C fraction 2, 524-650 °C fraction 1, 650 °C+
Table 3. Kinetic Parameters Estimated from Data for Scrubber Bottoms (subscripts follow Figure 1) kGa, s-1 s12 s13 s23 Ea1, kcal/mol log A1 log A2
5.63 0.344 0.656 0 52.0 12.82 0.432
Ea1c, kcal/mol log A1c log A2c Eac, kcal/mol log Ac
22.2 4.40 0 51.0 19.88
calculations. The equilibrium ratios for each lump were determined from HYSYS using the weighted sum of the calculated Ki values for the pseudocomponents in each boiling fraction. The optimal set of parameters, estimated from the data for scrubber bottoms only, is listed in Table 3. The value of SSR was relatively insensitive to the activation energy of cracking (Ea1) over a wide range of (15 kcal/ mol. Consequently, the value was set at 52 kcal/mol (218 kJ/mol) following typical values for cracking of heavy hydrocarbons.8 The minimum value of the sum of squared residuals (SSR) was 2997. Given the number of parameters that were estimated from a limited data set, the specific values of the parameters would have broad confidence intervals. The lowest confidence is for the values of the stoichiometric ratios (sij), because values of zero are not consistent with the extremely broad product distributions from cracking reactions. Consequently, we recommend that the parameters be considered as giving qualitative predictions, but not necessarily global optimum values with physical significance. The comparison of the model to the experimental data, therefore, is useful as a test of the structure of the model, rather than specific parameter values. The model gave satisfactory agreement with data for the boiling fractions in the vapor product and in the extractables remaining on the strip (Figure 4), except the 343-524 °C fraction in the extractables. This fraction was predicted to evolve much more rapidly than that observed experimentally, which may reflect liquidphase mass transfer resistances for this fraction. The amount of extractable material in the liquid film did
5442 Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004
Figure 5. Yield of extractable liquid from cracking of scrubber bottoms at 457 °C (4), 503 °C (0), and 530 °C (O). The curves are from the kinetic model, using the parameters of Table 3. Figure 7. Yield of heavy residue fraction (C1; 650 °C+) in the condensed vapor product with time, as a fraction of the feed. Data at 503 and 530 °C are mean values of three experiments, and the error bars show the standard deviation. The curves are values from the kinetic model, using the parameters of Table 3.
Figure 6. Yields of extractable liquid and coke from cracking of scrubber bottoms at 457 °C, 503 °C, and 530 °C. The curves are from the kinetic model, using the parameters of Table 3.
not follow first-order kinetics. As illustrated in Figure 5, an initial nonlinear period was followed by a loglinear decrease with time. This behavior was consistent with the kinetic model, which showed initial rapid devolatilization followed by cracking. The fit of the model to the data for extractables was not as satisfactory at 457 °C (Figure 6), where the model tended to overpredict the remaining extractable material in the liquid film. Good agreement was obtained for the yields of extractables and coke at 530 °C, except at the shortest reaction time of 5 s (Figure 6).Consistent with the fit to the extractables at 457 °C, the only significant mismatch between the data for the yields of the 343-524 and 524-650 °C fractions and the model was at 457 °C (data not shown). This mismatch indicated that these products were formed more slowly than those indicated by the Arrhenius dependence in the model, possibly due to the assumption that the reactions of the two residue fractions had the same activation energies. The most significant discrepancy between the model and the experimental data was in the yield of coke as a function of temperature (Figure 6). The experimental data for the scrubber bottoms (Figure 6) and vacuum residue (data not shown) showed that the yield of coke
after time g60 s was less sensitive to reaction temperature than that predicted by the model. This discrepancy was insensitive to the model parameters, even though the activation energy for coke formation was independent of cracking. The kinetic model suggested that coke yield would decrease with higher reaction temperatures, due to enhanced devolatilization. The heavy residue fraction (C1 ) 650 °C+) was allowed to vaporize according to the model and the equilibrium ratios given in Table 2. The experimental yields of heavy residue in the vapor product are illustrated in Figure 7, along with the predictions of the model. The experimental data for heavy residue had more error than the other measurements due to variability in the data from simulated distillation, as indicated by the error bars (Figure 7). The yield of this heavy material in the overhead product was significant, but its evolution in the vapor product was insensitive to temperature. The data suggest that the evolution of the heavy residue was rapid during the first 20 s, whereas the model gave a slower rate of evolution. The final yields of the heavy residue in the vapor product were in good agreement between the experiments and the model, in the range of 10-15 wt %. Prediction of Conversion of Vacuum Residue and Coker Product Residue. The best test of any kinetic model is the prediction of experiments that were not used to estimate the parameters. The yields of extractables and coke were estimated for two other feeds, using the data in Table 1 and the parameters in Tables 2 and 3. The experimental data and the model predictions at 503 °C are shown in Figure 8 for Athabasca vacuum residue and pilot coker product. The predicted and actual values for the pilot coker product are illustrated in Figure 9 for 457, 503, and 530 °C. The model and the data for extractable liquid from the pilot coker residue were in agreement. The coke formed more slowly from this feed at 503 and 457 °C than predicted by the model, exhibiting a lag time of ca. 15 s at 457 °C. Conversely, the evolution of the 650 °C+ fraction was faster than predicted, especially at 457 °C. The structure of the kinetic model, with the inclusion of a coke precursor, does allow for a lag time in the formation of coke. The mismatch in the model for the pilot coker
Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004 5443
Figure 10. Yield of heavy residue fraction (C1; 650 °C+) in the vapor product from pilot coker product with time, as a fraction of the feed. Curves are predicted values from the kinetic model, using the parameters of Table 3, fitted for scrubber bottoms only. Table 4. Kinetic Parameters Estimated from Data for All Feeds (subscripts follow Figure 1)
Figure 8. Yields of extractable liquid and coke from cracking of three residue feeds (scrubber bottoms, Athabasca vacuum residue (data of Soundararajan14), and pilot coker product) at 503 °C. The curves are predictions from the kinetic model, using the parameters of Table 3, fitted for scrubber bottoms only.
Figure 9. Yields of extractable liquid and coke from cracking of pilot coker product at 457, 503, and 530 °C. The curves are predictions from the kinetic model, using the parameters of Table 3, fitted for scrubber bottoms only.
product could be due to altered composition within the residue fractions due to its prior passage through a coker. The differences between the feeds were 2-fold. First, they differed in the amounts of the boiling fractions, with Athabasca vacuum residue richest in 650 °C+ fraction and the coker product leanest in this fraction. Second, they differed in their reaction history, with Athabasca vacuum residue containing all unreacted
kGa, s-1 s12 s13 s23 Ea1, kcal/mol log A1 log A2
3.80 0.242 0.416 0 52.0 13.08 0.432
Ea1c, kcal/mol log A1c log A2c Eac, kcal/mol log Ac
31.75 7.102 0 51.0 19.88
material and the coker product entirely comprised of material that had passed through the reactor. The data of Figures 8-10 show that the fit of the model to data from these other feeds was as good as that for the scrubber bottoms. From these figures, we can conclude that the structure of the kinetic model is consistent with the behavior of residue materials reacting in a thin film, except for the yield of coke as a function of temperature (Figures 6 and 9). The data of Figures 8-10 also show that the differences between the three feeds can be modeled from the boiling curves. Although there are undoubtedly chemical differences between these feeds, the differences in reactivity were adequately represented on the basis of the boiling curve of the feed material. Any changes in the kinetics due to detailed chemistry were much less significant. Parameters from Data for Three Feeds. The data for extractables and coke yield from the other two feeds (Vacuum residue and batch coker product residue) were added to the optimization calculation. The resulting parameters are listed in Table 4. These results illustrate that the values of the mass transfer coefficient (kGa) and the stoichiometric constants (sij) are most sensitive to the data set, along with the values for log A. These estimates could be improved by reacting narrow fractions of the residues, perhaps prepared by short-path distillation, to better distinguish the relative yields of the various fractions from cracking reactions. Microcarbon Residue Carbon Content of Reacted Samples. The analysis of condensed vapor products from these experiments showed significant MCR content. The MCR content gave an excellent correlation with the fraction of 650 °C+ fraction in the samples, as illustrated in Figure 11. The correlation was not improved by adding the fraction of 524-650 °C material. These results are consistent, therefore, with coke formation primarily from the highest boiling fractions.
5444 Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004
of extent of conversion and extend the model to improve the prediction of the composition and transport with time. Variable mass transfer with time as coking proceeds would also give better agreement with the evolution of 650 °C+ fraction with time (Figures 7 and 10) and could account for the insensitivity of the coke yield to temperature. More complex polymerization kinetics in the liquid phase could also be used to better describe the observed coke yields at 457 °C. A lumped model that included compositional data, such as aromaticity, could reconcile the differences between the pilot coker product and the other feeds (i.e., coking kinetics in Figure 9). Conclusions Figure 11. Correlation of microcarbon residue content (MCR) with amount of 650 °C+ fraction (Data from extractables and vapor product from all three feeds reacted at 457, 503, and 530 °C.)
A model for cracking and devolatilization of bitumen residues was developed, including the role of vaporliquid equilibrium, mass transfer, and reaction kinetics. Data from the cracking of scrubber bottoms in thin films (20-25 µm) at 457-530 °C were used to estimate the parameters, then the yields from unreacted vacuum residue and a pilot coker product residue were predicted. The model structure was appropriate to represent the reaction-devolatilization process. The differences in kinetics and yields between the three feeds were primarily due to differences in the initial boiling distributions, so that chemical differences from their different reaction histories were a secondary factor. The MCR content of condensed vapor products and extractable liquids correlated with the fraction of 650 °C+ fraction. Nomenclature
Figure 12. Predicted microcarbon residue (MCR) content versus experimental values from reaction experiments at 503 °C with scrubber bottoms. Predictions were from the amount of heavy residue fraction (650 °C+) in condensed vapor product and extractable samples from the kinetic model and the correlation of Figure 9.
The kinetic model allows for volatilization even of very heavy material; therefore, we can use the kinetic model to predict the MCR content of vapor products and extractable liquids as a function of time. This type of prediction is illustrated in Figure 12 for scrubber bottoms. The agreement between predicted and actual MCR content in the vapor product (
