Analysis of Chemical Reaction Networks

31 Analysis of Chemical Reaction Networks The Dehydrogenation of 1-Propanol on NaOH-Doped γ-Alumina E. KIKUCHI, S. E. WANKE, and I. G. DALLA LANA

Downloaded by CORNELL UNIV on May 18, 2017 | http://pubs.acs.org Publication Date: June 1, 1975 | doi: 10.1021/ba-1974-0133.ch031

Department of Chemical Engineering, University of Alberta, Edmonton, Alberta, Canada The rate behavior of multiple-step reaction systems is difficult to model realistically because of uncertainties in the correctness of the network, its stoichiometry, and the form of appropriate rate expressions. The kinetics of dehydrogenation of 1-propanol raised four alternative networks. The isothermal conversion-space time data were smoothed, differentiated, and decomposed algebrai cally into differential rate data for each step. Rate constants and reaction orders for power-law rate expressions werefittedto each step. A kinetic model was constructed directly, integrated, and compared with experimental results. The models were sorted according to their predictive abilities and agreement with chemical evidence. More statistically significant parameters were then computed for the most acceptable network kinetic model.

I

n 1936 Ipatieff described (I) the gas-phase heterogeneous catalytic reaction of ethanol to acetone and isopropyl alcohol. Later, Komarewsky et al. (2) presented yields from ethanol and other primary alcohols, including 1-propanol, over chromic oxide catalyst. Dalla Lana et al. (3) found diethyl ketone as the main product from when 1-propanol reacted over a NaOH-doped Alundum support containing chromic oxide. Since they encountered all of the species in Reaction 1 but the acid, they interpreted the reaction scheme using IpatiefFs view—i.e., catalytic conversion of primary alcohols to ketones involves two condensation routes from the aldehyde (here propionaldehyde) :

Primary — H alcohol • aldehyde

secondary -CO aldol ——> alcohol

I

2

ketone ester

(1)

• acid +H 0 2

Route II was used by Kagan (4, 5) to interpret the formation of acetone from ethanol in the presence of γ-alumina and A l 0 - F e O - M g O catalysts. In thenview, the ester may also react directly to the corresponding ketone, even in the absence of water vapor. Further work by Komarewsky et al. (6), in which 1-octanol deuterated in the α-position was dehydrogenated over chromic oxide, suggested that the 2

3

410

Hulburt; Chemical Reaction Engineering—II Advances in Chemistry; American Chemical Society: Washington, DC, 1974.


31.

KIKUCHI E T A L .

411

Chemical Reaction Networks

ratio of atomic deuterium to gaseous hydrogen corresponded to route II. More recently, Minachev et al. (7) observed appreciable 4-heptanol during the for mation of dipropyl ketone from 1-butanol over neodymium oxide, corresponding to route I. The relative importance of routes I and II in the dehydrogenation of a primary alcohol is probably determined by the specificity of the catalyst. Although most studies, excepting IpatiefFs, produced only small amounts of the aldol and secondary alcohol intermediates, route I cannot be discounted since small concentrations of these could arise from rapid conversion of these forms to the ketone. Reaction 1 illustrates the complex stoichiometry of a multiple reaction system involving at least six significant species. Until recently, the literature has offered no general basis for interpreting the kinetics of such irreversible systems except when first-order kinetics applies to all steps (8). Thus, quanti tative predictions from empirical rate measurements would probably be re stricted. Further, at higher conversions the 1-propanol system generates (3) many other "unaccountable" high molecular weight products, presumably from the reactive carbonyl compounds. Here, we examine the kinetic behavior of 1-propanol over an NaOH-doped γ-alumina catalyst. The global reaction rates measured for each species should then relate to the overall reaction steps com prising a known or postulated network. To formulate a kinetic model, the observed global integral rate data were first differentiated and then decomposed into single-step rates. These rates were used to model each reaction step by a procedure recently described (9). Lacking a mechanistic basis for developing appropriate rate expressions, power-law rate expressions were used to correlate each set of single step reaction rates. This article develops this approach and describes its usefulness. Experimental Basis Materials. 1-Propanol (Fisher Scientific Co.) was of C P . grade; G C separation revealed only trace impurities. 1-Propanol vapor was diluted with 99.998% argon (Canadian Liquid Air, Ltd.) and used as purchased. The catalyst was prepared by impregnating previously crushed —12+24 mesh Houdry γ-alumina (HS-100S) with an aqueous solution of 3.5N NaOH, allowing the mixture to drain and then to dry overnight at 110°C. Apparatus and Procedures. Global reaction rates for the species in Reac tion 1 were measured by a fixed-bed integral reactor of 96% silica glass, 17 mm id. These species had been previously separated and identified (3). Bed tem peratures were recorded by a traveling axial thermocouple within a 96% silica glass well. Liquid 1-propanol was quantitatively fed to a preheater by a syringe feeder at 0.1033-1.233 ± 1.0% moles/hr. A regulated argon flow was pre heated separately and then mixed with 1-propanol vapor in a final preheating section before entering the reactor. The reactor was immersed in a tempera ture-controlled electrically heated eutectic salt bath. Argon minimized volume changes and was also used as an internal standard in the G C product analysis. A portion of the reaction effluent was condensed in a cold trap at — 60 °C until at least 2 ml was obtained, usually within 5 to 20 min. The combined flow rate of argon plus non-condensed gases, such as H and C O , was then measured using a soap-bubble meter. To determine the concentrations of components in the condensed phase a Carbowax 400 column was used. 1-Butanol was used as an internal standard to obtain production rates of individual components. Calibrations to obtain response factors for the major components were carried out. 2


412

CHEMICAL REACTION ENGINEERING

II

At the maximum feed rate, over 98% 1-propanol could be recovered in a single cold trap during a blank run. Carbon dioxide was determined by vol umetric absorption in a 30% aqueous K O H . Other gaseous products were collected over acidified saturated brine, and samples from this were injected directly into Poropak S or activated charcoal columns via a gas sampling valve. Peak areas were quantitatively related to the argon peak area by previously calibrated concentration peak area relationships. Their production rates could be determined from these analyses and the total gas flow. Although C O and C H could be analyzed, only minor amounts were detected in the gaseous products. The presence of water was checked and was always negligible. Material Balance Calculations. Since the ratio of 1-propanol to argon in both feed and product streams was known, we could calculate the total moles of 1-propanol reacted, independently of product analyses. The individual prod ucts were obtained separately because of the molar correction factors used along with the 1-butanol internal standard. Their stoichiometric equivalents of 1-propanol were then calculated, summed, and compared with the reacted 1-propanol previously calculated. The following notations were adopted:


4

Aj A A A A 2

3

4

5

= = = = =

1-propanol = PrOH propionaldehyde = PrH 3-pentanol = P N η-propyl propionate = PP diethyl ketone = D E K

The yield, Q of component, A was defined by Equation 2, i ?

i9

n. _

m

° l of A j in product moles of Α ι in feed

^\

e s

The fractional conversion of A is given by Equation 3, t

χ = 1 -

(3)

Qi

The reaction time was expressed using the reciprocal space velocity for an integral reactor, τ = W / F , where W and F are weight of catalyst (grams) and feed rate of 1-propanol (moles/hr). Carbon balances were calculated from Equation 4: Carbon accountability (%) = 100 —77— 0

v

it

,

n

.

(TWij

All analyzed products

(4)

where, n = number of carbon atoms in component A^ Hydrogen and oxygen accountabilities were established by similar relationships. {

Results Experimental Studies. Initial studies with 1-propanol over pure γ-alumina showed this catalyst to promote dehydration to dipropyl ether or propylene. When γ-alumina was doped to NaOH content above 8.62 wt % , it catalyzed dehydrogenation but did not promote dehydration of 1-propanol (10). This catalyst was used throughout. The empty reactor showed no catalytic wall influences or homogeneous decomposition of 1-propanol. Isothermal steady-state conversions were obtained at 4 0 0 ° C and 705.1 mm H g for various 1-propanol feed rates. A catalyst charge of 10.08 grams was pretreated by heating overnight at 4 5 0 ° C in an argon stream. The results from seven experiments are reported in Table I. Since some catalyst discoloration occurred, run 1 was repeated (run 7); both runs showed that catalyst activity


31.

Table I. Run τ, (gm catalyst) (hr) (mole)


X,

Isothermal Kinetic Results

7

1

97.6

97.6

2 65.3

Frational conversion of 1-propanol

0.2064

0.1902

0.1393

1-Propanol Propionaldehyde 3-Pentanol η-Propyl propionate Diethyl ketone Hydrogen Propylene Carbon dioxide

0.7936 0.0531 0.0006 0.0060 0.0251 0.210 0.003 0.025

0.8098 0.0513 0.0006 0.0060 0.0221 0.207 0.003 0.021

0.8607 0.0472 traces 0.0056 0.0185 0.185 0.002 0.021

Material Balances, % carbon hydrogen oxygen

413


KIKUCHI E T A L .

8

4

48.8

32.6

0.1002

5 16.3

6 8.2

0.0865

0.0689

0.0484

0.9135 0.0498 traces 0.0051 0.0083 0.122 traces 0.009

0.9311 0.0306 traces 0.0042 0.0039 0.056 traces 0.005

0.9516 0.0203 traces 0.0023 0.0007 0.036 traces 0.001

Yield, Qi

91.3 93.2 92.8

92.0 94.1 93.9

95.9 97.5 98.0

0.8998 0.0494 traces 0.0052 0.0120 0.143 0 001 0.015 98.6 99.6 100.2

99.0 99.9 100.0

97.8 97.9 98.4

97.8 98.0 97.9

had not changed appreciably. Under our conditions the reactions are essentially irreversible. Table I lists only those products which were previously (3) separated and identified with high certainty. When the Carbowax column was heated to 170°C, the corresponding chromatograms showed many small unidentified peaks at elution times greater than for propyl propionate. With increasing conversions of 1-propanol, these peaks also increased. The material balances in Table I show this increasing discrepancy at fractional conversions greater than 0.1. The unknown products probably formed in side reactions involving highly reactive aldehydes or ketones. With the integral kinetic data from runs 1-6, we postulated a network of apparent reaction steps which could interrelate the compounds and (here) explain the formation of diethyl ketone. Since a network such as Reaction 1 is not generally available from previous studies, alternatives may be validly postulated. The approach of Dalla Lana et al. (9) to such a problem was used to evaluate reaction sequences. Analysis of Experimental Data. The effect of space time on the com position of the product stream is illustrated in Figure 1. Since these plots give integral conversion data, to obtain reaction rates for each species, the Qf-r points were first smoothed and then differentiated. Analytical functions were used to obtain a smooth Q r function subject to: (1) at τ = 0, the compositions were zero for all products and unity for 1-propanol; (2) the smoothing func tions for products could not contain more than one maximum; and (3) the smoothing function had to decrease monotonically for 1-propanol. For each compound, several arbitrary functions were tested; the one which met the above conditions and generated the minimum variance, S (as defined by Equation 5), was taken to be the best, r

2

Ν

Σ S

ΚΟΟκχρ - (QiWdl*

2

N-^P


414


JI

< ~U Φ

φ

vt _ω «*o

c

ε

-

οι A 4

3

4

—> A

5

(7)

—> A 3

Numbers on the arrows refer to each reaction step. These networks relate the species observed but not the unknowns. Although 3-pentanol ( A ) was present in small quantities, model I is not negated since A may have been very reactive. 3

3


31.

KiKucHi ET AL.

415

Chemical Reaction Networfa

The reaction rate of any chemical species, Aj, is r which will always mean a point value for the rate. Since A may take part in several independent steps, the characteristic rates for each jth step will be defined as Rj. Thus, r will include contributions from all Rj which affect the amount of Aj present. To evaluate the contribution from each step to the global rate of produc tion for a given species, the stoichiometry of each step must be evaluated. Except for the formation of diethyl ketone from η-propyl propionate (steps 5 or 3 in models I or II) the network stoichiometry is well defined. Two alterna tive stoichiometries have been proposed: i

i

{

2C H COOC H 2

5

3

2C H COOC H


2

5

3

7

+ H 0 -> C H C O C H 2

2

— C H COC H

7

2

5

2

5

2

+ C0

5

2

5

+ 2C HTOH

(8)

3

+ C H 3

6

+ C H OH 3

(9)

7

Since Reaction 8 requires water, which is absent from the feed and the products, this possibility is eliminated. Reaction 9 is possible, but little propylene was detected and thus did not correspond to the larger amounts of diethyl ketone or C 0 observed. Since propylene may have reacted further, the possibility of either Reaction 9 or 10 was considered for models I and II, 2

2C H COOC H 2

5

3

7

— C H COC H 2

5

2

+ C0

5

2

+ unknowns

(10)

On this basis, four alternative networks must be tested with the smoothed rate data: Model Model Model Model

la: step 5 described by Equation 9 l b : step 5 described by Equation 10 Ha: step 3 described by Equation 9 l i b : step 3 described by Equation 10

The procedure used to decompose the global rates into characteristic reac tion rates for single steps—i.e., (r , r , . . .) transformed to (Ri, R , · · ·)— will be illustrated for model la. Differential material balances for model la within an isothermal volume element are: t

r r r

"-1 2

=

3 4

2

0 -1 1 02 0

1 0 0 0

2

0 0 -1 0 1

0 -1 0 1

02

1 02 0 -1 1 2

~

R2 Rz Ri

which must be solved for [Rj] using the known values of [ r j . lb, Ha, and l i b lead to:

(11)

Thus, models

Model lb 9 1

Ai —* A

èA

3

r and rz r

2

~-l

ο

^ J A .

y

2

=

4

2A 4

0 -1

1 0 0 0

_^5_

\

0 0

0 0 -1 0 1

0 -1 0 1 02

0 0 0 -1 2

Ί

Ri' R2 Rz R,

(12)

J

Model Ha (JA) + ΙΑ,

r rz 2

_r _ 5

"-1

=

1 0 0 0

0 -1 0 1 02

1 0 0 -1 1 2

0 0 1 0 -1


R2 «4

(13)

416


II

Model l i b 0 0 0

0

1

2

3

T

4

— > A —» |A —» 1A —• 1Ar 2

4

5

2

3 3

r _r _

-1

1

=

0

0 0 0

4

5

1 02

Ί

0 0

2

1 0

-1 1 2

"β Γ R Rz RA

-1

_

„

Each contains one linearly dependent equation. Eliminating one of the r equations arbitrarily from each set removes this degeneracy. We eliminated r from Equations 11 and 12 and r from Equations 13 and 14. In the latter two cases, one may then readily solve for the unknown R in terms of In the former two cases, a solution is still not possible because the reduced coefficient matrix is only of rank 3, but four Rj are unknown. This difficulty can be overcome by introducing another independent condition. This was achieved by independently estimating the parameters for a kinetic model postulated for one (or more) of the unknown Rj. We restricted the choice of rate functions to simple power-law relationships. Using this approach for model la, the following combination of steps provided a convenient additional inde pendent condition for solving Equations 11, x

5

3


i

ri + r + i r 2

- - R - |β

4

2

= - k C " - \kzC ™ 2

4

n

2

(15)

2

To solve Equations 12, the condition used was, r,+r = 2

- R - RA « - k C 2

2

nn

2

-

n24

fc C 4

(16)

2

Using the smoothed differentiate functions for Q

b

and the corresponding,

Ci = 8.44 (ΙΟ" ) Qi, moles/liter

(17)

3

where 8.44 (10~ ) is the concentration of A in the feed, numerical values of their derivatives were calculated for values of τ to obtain 3

1

η =

f

(18)

Equation 17 approximates C closely since the volume changes from reaction were small because of low fractional conversions and dilution of 1-propanol with argon. Using smoothed points ( ( ^ , τ , η ) , the parameters, fcj and n were determined by a nonlinear parameter estimation based upon a steepest descent technique. Equations 15 and 16 were estimated: {

ijt

ri + r + | r 2

= 8.65(10- )(7 · 3

4

2

0

336

- 2.79(10 )C 3

178 2

(19)

and, η + r = - 17.7CV- - 2.21(10 )CV2

40

3

82

(20)

Equations 19 and 20, in principle, can then be used to generate values of R and/or R and thus solve matrix Equations 11 and 12. At this stage, smoothed characteristic rate data are available for each step in any if the four networks. A power-law rate expression may be fitted 2

4

Ri = /byCVij to each reaction step.

(21)

The appropriate fitted Rj can be substituted into the


31.

KiKucHi E T AL. Table III.

Chemical Reaction Networks Estimates of Kinetic Parameters for Model l b 0.273 17.7 1.72 (10 ) 2.21 (10 ) 9.19 (10 )

Ri β β

2

= = n 4 = n = W45 -

n n

n

3

3

Ri

2 2

3

3

β*


417

2 3

10

1.00 1.40 1.22 1.82 3.25

differential material balance equations, such as Equation 11, allowing simul taneous integration. The experimental points may be compared with these predictions from the integrated network power-law kinetic model. Since none of the above models included step(s) for formation of unknowns, Rj values were calculated using smoothed data at τ = 0-45, the region of good material balances. Normally, 19 points were used at equidistant Δ τ of 2.5. Model la was rejected because k was negative. Table III summarizes the parameters estimates for model lb, and Table IV for models Ha and l i b . Model la predicted that n should be negative, —1.21. Since this step follows monomolecular stoichiometry, a negative exponent predicts an anomalous rate be havior, and model H a was also rejected. Models l a and H a were rejected because of inconsistencies between estimated parameters and implied chemical behavior. While this reasoning is valid, error in the manipulated and smoothed data cannot be discounted. 2

n

Figure 1 compares the predictions with results for components A , A , A , 2

3

4

and A using the network power-law rate expressions for models l b and l i b . 5

The agreement is satisfactory up to τ = 45; at higher τ , and thus higher conTable IV.

Estimates of Kinetic Parameters for Models H a and l i b

Rji

Ri

Model Ha

R2

ki

n

2

-1.21 7.15(10" )

4

1.00 0.273

2 3

kz

2.70(10 ) 4

R 4

nz

n 4

k

A

2.10 3.18(10 )

6

lib

n

k

u

R 3 A

5

1.89

2.08

1.74(10 ) 2.11

9.55(10 ) 1.91

1.58(10 )

4.38(10 )

5

5

4

2.31

5

versions of 1-propanol, model lb does not correlate the yields for A , and model l i b fails for A and A . 1-Propanol yields are not shown since both models predict satisfactory but identical results. The addition of reaction steps to these networks to account for unknowns should result in better agreement at τ > 45. Examination of Figure 1 suggests that a reaction of the type, 5

3

5

6 Αδ — > unknown products

(22)

should force model lb to predict a smaller yield of A , and model l i b to predict a smaller yield of A . When l b is adjusted by adding step 6, we obtain model Ic, in which all the characteristic rates except R , are identical to those in l b . R was calculated from the material balance for A —i.e., 5

3

6

6

5

ββ = # 3 + TzRb — 7*5


(23)

418


The values of r were obtained from the smoothed data for τ < 100. a power-law function to R yields 5

Π

Fitting

6

#

6

= fc C 6

n56

5

= 158.8C5

(24)

143

Model Ic was numerically integrated, and the predicted Q -T plot was compared with the experimentally determined points. Before commenting on the results, the modification to model l i b , leading to model lie, is developed. To improve model l i b , the production of unknowns from A should be considered. This leads to 5

5

Model He: 1 2 j 3 j 4 A — > A —• ^A — > ^A — > A Downloaded by CORNELL UNIV on May 18, 2017 | http://pubs.acs.org Publication Date: June 1, 1975 | doi: 10.1021/ba-1974-0133.ch031

t

2

4

5

(25)

u

which now includes the formation of A within the unknown products, A . Since Q was always small, especially relative to the total unknowns at τ > 45, this simplification is justified. The essential differences between Ic and lie remain: formation of A from A as a parallel route to A or formation of A from A via a network involving only consecutive reaction steps. Model lie is identical to l i b if A is replaced by A (Equation 14). Values of R were calculated using 3

u

3

3

2

5

3

5

3

u

4

Ri « \Rz - r

(26)

5

r being evaluated from the smoothed function for A resulting power-law equation for R is: 5

5

for τ
45 may be ques tioned on the basis that the material accountabilities in this range of τ are inaccurate. The accountabilities at lower τ values are good since it was shown experimentally that the condensation efficiency in the product collection cold trap increased from ' 98% to almost 100% when τ went from 8.2 to 48.8. This explains the < 100% accountabilities obtained where formation of un knowns is small. At τ > 45, the condensation efficiency is — 100%, and thus, the decreasing accountabilities relate to the increasing extent of unknown products being formed, not to the lack of reliability of chemical analyses for known products. Models Ic and lie agree with the experimental results equally well. While model Ic is more general in that 3-pentanol formation is treated more realisti cally; being a closed network it required additional independent information (via nonlinear parameter estimation) with consequent computational difficulties before the network rates could be decomposed into single-step rates. On the other hand, model lie provided a simpler basis for calculating single-step rates but subject to negligible formation of 3-pentanol. In addition, the orders of reaction obtained for each step in model lie approximate those expected from the law of mass action—i.e., 1.0 and 2—whereas the order of reaction for step 5 in model Ic was more suspect, being 3.25. The agreement between observed and measured yields demonstrates the adequacy of the smoothing technique since the rate of formation of unknowns, r , was obtained from material balances. Further experimental validation was tried with η-propyl propionate as feed. The results were nullified because the formation of many unknowns (probably polymeric) caused the catalyst to deactivate rapidly. These experiments presumably failed to duplicate the microscopic reaction conditions at the catalyst surface. Other experiments at higher conversions and with mixed feeds should be used to test (or extend) the models for extrapolated predictions. In estimating values of multiple parameters for nonlinear models, others may prefer a statistical basis for multiresponse analysis (12). For example, model lie could be examined by simultaneously estimating all of the power-law parameters (eight) in the differential equations for network 25, from the original experimental data (seven sets of integral responses). This is difficult, w

u


31.

KIKUCHI E T A L .

Table V .

421


Comparison of Rate Constants Obtained by Various Parameter Estimation Methods for Model He Rate Constants


Method of estimating rate constants Network decomposition Simultaneous, using experimental concentrations Simultaneous, using smoothed concentrations

ki 0.273

k 2.70(10 )

kz 1.58(10 )

ki 14.6

0.274

2.51(10 )

1.56(10 )

11.4

0.273

2.67(10 )

1.58(10 )

11.5

2

4

4

4

5

6

5

and attempts proved to be computationally indecisive. As a compromise, rate constants were calculated for model lie by simultaneous parameter estimation, assuming the orders of reaction to be those in Table IV. Table V gives rate constants from experimental and smoothed data (seven and 12 points) and contrasts them with those from the decomposition approach. The computational difficulties and the comparison in Table V vindicate our view that the decomposition method and the use of single-step power-law rate expressions provide a direct route for kinetic modeling. The simultaneous estimation of rate constants and orders of reactions for networks containing more than eight steps may be possible but certainly not easier. Also, one can interject physical and chemical insights into the modeling—e.g., selecting smoothing functions, testing different forms of global or intrinsic rate expres sions. The statistically sound methods for simultaneous parameter estimation are limited when integral rate data cannot be treated easily or when few experi mental data are available. With the decomposition method, however, valid models may be rejected prematurely. The combination of using the simple decomposition method and power-law expressions to relate the observed physicochemical data to a valid chemical network and its kinetic model and then obtaining statistically sound parameter estimates should provide an adequate basis for network modeling.

Literature Cited 1. Ipatieff, V. N., "Catalytic Reactions at High Pressures and Temperatures," pp. 411-451, MacMillan, New York, 1936. 2. Komarewsky, V. I., Coley, J. R.,J.Amer. Chem. Soc. (1941) 63, 700, 3269. 3. Dalla Lana, I. G., Vasudeva, K., Robinson, D. B.,J.Catalysis (1966) 6, 100. 4. Kagan, M. J., Rossinskaya, Y., Cherntsov, S. M., Zh. Obschch. Khim. (1932) 3, 244. 5. Kagan, M. J., Sobolew, I. Α., Lubarsky, G. D., Chem. Ber. (1935) 68, 1140. 6. Komarewsky, V. I., Coley, J. R., Advan. Catalysis (1956) 8, 207. 7. Minachev, M., Loginov, G. Α., Markov, Μ. Α., Kin. i Kat. (1966) 7, 904. 8. Wei, J., Prater, D.C.,Advan. Catalysis (1962) 8, 581. 9. Dalla Lana, I.G.,Myint, Α., Wanke, S. E., Can. J. Chem. Eng. (1973) 51, 578. 10. Chuang, T., Dalla Lana, I.G.,J.Chem.Soc.,Far. Trans. I. (1972) 68, 773. 11. Wanke, S. E., M.Sc. Thesis, University of Alberta, 1966. 12. Box, G. E. P., Draper, N. R., Biometrika (1965) 52, 355. RECEIVED January 2, 1974.


Analysis of Chemical Reaction Networks

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