J. Phys. Chem. 1993,97, 3319-3323
3319
Frequency Response Method for Study of Kinetic Details of a Heterogeneous Catalytic Reaction of Gases. 2. A Methanol Conversion to Olefins Yusuke Yasuda' and Kaon Nomura Faculty of Science, Toyama University, Toyama 930, Japan Received: November 2. 1992
To confirm the ability of the new method, a complex reaction such as methanol conversion to olefins over HZSM-5 catalysts was investigated. The frequency response (FR) data of each component were obtained over a range of angular frequency w from 5 to 50 rad/min. According to the theoretical treatment in paper 1, the FR spectra were analyzed; as many as 15 elementary reaction steps included in the reaction were considered and 15 "complex" rate constants, {N,,,/- id,,,/), with respect to the transformation of 1 to m component at an elementary step were determined by a computer simulation. The results were discussed on the basis of the characteristic functions derived in paper 1; it is shown that the functions are valid to construct the network of the elementary steps. It is concluded that the merits of the present method would be enhanced in a complex reaction because (i) any assumptions with respect to the reaction mechanism, the reaction order, the ratelimiting step, and so on are not required in this method and (ii) kinetic data can be accumulated as well in order to obtain more reliable rate constants by scanning w over a wider range.
1. Introduction The methanol conversion to olefins and gasoline is industrially important and has been intensely studied.' The reaction pathway can be represented as follows:2
[2CH,OH a (CH3),0
-
+ H,O]
-
C2-4 olefins (paraffins aromatics) (1) The mechanism of the reaction, particularly as concerns the formation of the first C-C bond has been the subject of much controversy.3 The high complexityof the reaction system containing a variety of species has prevented rigorous kinetic study in spite of great practical importance. To obtain a kinetic description, many assumptions based on a kinetic model are usually needede4 Recently, frequency response (FR) method has been applied to a reaction of H2 C3H6 C3Hs over Pt/A1203 catalysts.5 It seems of interest to apply the new method to complex reaction, because (i) the previously derived rate equation R(P,P) has not been established yet and (ii) the network of elementary steps in eq 1 are under discussion.
+
-
+
2. Experimental Section The apparatus and procedure was decribed previ~usly.~ HZSM-5 powders (binder free) weresupplied by Prof. T. Yashima of Tokyo Institute of Technology. They were a bit compressed and crushed into small pieces; 0.5 of the catalysts were placed in the reactor. They were evaluated at 673 K and kept at 593 K during the FR measurements. Methanol vapor involving 10%of Ar (as the referencestandard) was continuously fed to the reactor through a needle valve. A steady state was attained after 1&20 min and then the FR measurements were carried out. The gas space Y was varied sinusoidally with an angular frequency w:
Y(t) =
V(1 - u cos ut)
(2) where Pwas about 1 dm3 and u was 7.4 X 10-2. The induced partial pressure variation of various components was expressed well by
p,(t) = PI(1
03 6 k
+ pI cos(wt + cp,))
(3) and followed by a mass spectrometer, where PIdenotes the partial 0022-3654/93/2097-33 19$04.00/0
Benzene Toluene
65 (Pa)
HI
Figure 1. Partial pressuresof the starting material, CHIOH, and products at the steady state before the FR measurements were carried out.
pressure at a steady state; p~is the relative amplitude; c p ~is the phase difference. 3. Results
The value of {&I are compared in Figure 1. They were evaluated from calibrationcurvesdetermined by their peak heights of mass spectra: m/r = 26 for CtH4, 31 (CHjOH), 40 (Ar), 42 (C3Hf.1, 46 ((CH3)20), 56 (C4Hd. Changes inpl and cp/ are plotted as functions of log w in Figure 2a,b, respectively. The dash-dotted curves represent the most probablevalues for Ar in consideation of the theoretical expression given by6 Ar
eiQAr
= iwu/ ( u + iw)
(4)
where u = 9.0 min-' (5) was adopted. It seems of interest that (i) cp of CHIOH was larger than that of Ar over the whole range of w scanned and (ii) cp's of olefins were smaller than that of Ar or on the opposite side of CH3OH, while (iii) that of (CHJ20, which is well-known to be the intermediate product, crossed the dash-dotted line of Ar. Although the partial pressure of C3H6was significantly larger than those of other olefins, the results in Figure 2a,b were in the order of carbon numbers. The fact suggests that C2H4 is the first C-C bond formation. To remove apparent changes in pI and due to the apparatus,
0 1993 American Chemical Society
Yasuda and Nomura
3320 The Journal of Physical Chemistry, Vol. 97, No. 13, 1993 1
L
J.
J.
7
1
I
t
1
0.7
1.3 log ( o h a d min-'1
1
1.6
where the bar and the subscript s mean the value at the steady state. The values of NTm/ and Lim/ are expected to be positive; n corresponds to the reaction order but I is a new kind of rate constant. According to eq 8, we may have the following equations applied to the data analysis:
60
B'&
ApM
1 - 1 = +-(NM
+
- iwL,) (N,, 0, iwLM,)p,eiAm (NM2- iuLM2)p2eiAM) (14)
+
-6Ot
I
I
1 1.3 . log ( o/rad mi n-'I Figure 2. FR data on (a, top) Pk and (b, bottom)
0.7
pk of the major the results components in Figure 1 versus the angular frequency w. (0) of CHJOH; ( 0 )thoseof (CH3)20; (0)those of C2H4;( 0 )those of CjH,; ( 0 )those of CdHs. The dash-dotted curves represent the most probable results for Ar added to the starting material as the reference standard.
P//PAr
Aq/E q/ - VAr
+
p,,,eiA@" - 1 = - -1S ( - ( N ~ - i w ~ , )+ (N,, e m
+
iwLmM)pdiAPM(N,, - iwL,,)pDeiAVD]; m = 2 , 3 , 4
(16)
we introduce PI and A ~ defined I by
p/
PDeiApD - 1 = y 1{ - ( N , - ioL,) (NDM0, iwLD,)p#iA'"M (ND2- iwLD2)p2eiAM) (1 5 )
+
1
1.6
(6)
It is convenient to plot these data by polar coordinate as demonstrated in Figure 3a. To make comparison easier, seven equally spaced points of log w were used in the data analysis, which are indicated by the arrows in Figure 2a,b: 1 = 5.6, 2 = 7.9,3 = 11.2,4 = 15.8,s = 22.4,6 = 31.6,and7 = 44.7radfmin. The polar plots of other components are shown in Figures 4a-7a.
4. Data Analysis The following abbreviations will be used below: M for CH3OH, D for (CH3)20, 2 for C2H4, 3 for C3H6, and 4 for C4Hs. The material balance with respect to a starting material m may be described by
The left-hand side gives the change in the amount of molecules contained in the reactor (that of adspecies on and within the catalysts was neglected in this work because of the high reaction temperature); J,,, denotes the flux of the injection through a needle valve; a,'P,(f) gives the overflow rate through a variable-leak va1ve;R-,(t) and R+,(t) denote thedisappearance and appearance rates of m component, respectively. Substituting V ( t ) and P m ( f )in eqs 2 and 3 into eq 7, we can
In eqs 14-16, two approximations have been introduced: (1) Equation 8 is exact if m component is directly produced from 1 in a singlestep. However, for instance,CH3OH could not directly be produced from C2H4. (2) Only CHSOH,(CH3)2O, and C2H4 are regarded as the source materials in eqs 14 and 15; the term ofP2* was neglected in eq 16 in order to save time for the computer simulation. Consequently,each equation containssix parameters. The six parameters were determinedso that the empirical results on the left hand side may be reprocued well by the equation on a trial and error basis, wherebyP,eiA*lon the right-hand side was replaced by the experimental results in Figures 3a-Sa. Since each equation is described in the complex notation, two equations concerning the real and imaginary parts are derived from one equation. Therefore, inserting the FR data obtained at seven different w's, we have fourteen simultaneous equations involving six parameters. The calculated results are plotted with solid circles in Figures 3a-7a; the contributions of the three terms on the right hand side to the calculated result are individually shown in Figures 3b-7b. It is demonstrated in Figure 3b that the calculated result (number 6, for instance) of the solid arrow was derived from the vector sum of the dashed arrows; the open squares of M represent contributions of the first term in eq 14, the half-solid squares of MD represent those of the second term, and the open circles of M2 represent those of the third term. Similar plots for other components are shown in Figures 4b-7b. Theagreement between the experimental and theoretical results would be satisfactory, compared with the experimental errors. Thecoupleof parameters, N,,,//min-' and L,,,,, concluded are summarized in Figure 8. It should be emphasized that both appearance (the plot above
Heterogeneous Catalytic Reaction of Gases. 2.
The Journal of Physical Chemistry, Vol. 97, No. 13, 1993 3321
0.5t
xo'
0.5
0'
0.5;11
-iy m
-iy
I $0.5
.
I
0.5
I x
I
D
L-0.5 Figure 3. (a, top) Polar plots of p,,, A ~ Mwith ) respect to CHIOH. (0) Those derived from the FR data in Figure 2; ( 0 )those calculated from q 14 containing six parameters by a computer simulation on a trial and error basis. (b, bottom) Contribution of the three terms on the righthand side in q 14 to the calculated result; the vector sum of the dashed three arrows corresponding to the three terms gives the calculated result of the solid arrow. The number indicates a definite w shown by the arrow in Figure 2a or 2b. ( 0 )The contribution of the first term representing thedisappearancerateofCH,OH;( 0 )that ofthesecond term representing the appearance rate of CHIOH from (CH&O; (0)that of the third term of the appearance rate of CH3OH from C2H4. Calculated results from thecharacteristic functionsyl*(.) toexplain the resultsof O'sandy**(O) to explain those of 0's.
the x axis) and disappearance (the plot below the x axis) rates occurring simultaneously could be separated by the data analysis. 5. Mscussion
According to the theoretical treatment, wemay have thegeneral expression based on the material balance:
where these characteristic functions are defined by
y,(rml)* =
a
(a
+ io
+ N m )+ io( 1 - Lm)
Figure 4. (a, top) Polar plots of ($0, Atp,) with respect to (CH3)20. (0) Those derived from the FR data in figure 2; ( 0 )those calculated from eq 15. (b,bottom)Contributionofthethreetermsineq I5 tothecalculated result. (m) Calculated result from 7 1 ' to explain 0's. Notation is that of Figure 3.
y2(rml;klk)* =
(a
a + io + N m )+ io(1 -L,)
N & / k - iwL&lk Nrml - io&m/ (20) (a+N,)+io(l-LI)(a+ Nk)+iw(l-Lk)
The terms in the first bracket in eq 17stem from thedisappearance rate of R-, and those in the second bracket, from the appearance rate of R+, in eq 7. The first function yo* arises from the pressure dependence of R,, (..,;P,,P,;...), because it contains the parameter of N,,,. The second one yI is concerned with the elementary step of I m derived from R,,( ...; ...). The third one y2* is concerned with the sequential process of k 1 m, because it contains N,,/N*/k. Since the semiempirical results in Figures 3b-7b are ascribed to a definite component, they could be interpreted by the theoretical function(s). 5.1. Rate of Self-Decay. The first terms in eqs 14-16 agree with-yo(-mm)* or +yo(+mm)* and represented by a semicircle, of which two parameters, N, and L,, are summarized in Table I: ( I ) CHjOH Since the results in Figure 3b were below the x axis, they may be explained by -yo(-MM)* of disappearance rate and we have
--
-
N-,,/min-l = 7.2 L-,, = 0.45 (21) (2) Olefins:Since the results in Figures 5b-7b were above the x-axis, they may be explained by yo(+mm)* of autocatalytic reaction, and we have N+,,/min-' = 1.6
L,?, = 0.19
(22)
N+,,/min-' = 1.2
L+,, = 0.23
(23)
= -0.1 L+,, = 0.19 (24) (3) (CHJJ20: Although the results in Figure 4b were below the x axis, the origin was outside the semicircle. It is impossible N+,,/min-'
3322 The Journal of Physical Chemistry, Vol. 97, No. 13, 1993
Yasuda and Nomura
0.5
I
0.5
0' X
.
I
- 0.5t
- iy
-iy
0'5t
2D
I
I
X
I
-0.51 Figure 5. (a, top) Polar plots of ($2, Acp2) with respect to ClH4. (0) Those derived from the FR data in Figure 2; ( 0 )those calculated from eq 16. (b,bottom)Contributionofthethreetermsineq 16tothecalculated result. (8)Calculated results from TI*. Notation is that in Figure 3.
-0.51 Figure 6. (a, top) Polar plots of ( p 3 , Acp3) with respect to C3H6. (0) Those derived from the FR data in Figure 2; ( 0 )those calculated from eq 16. (b,bottom)Contributionofthethreetermsineq16 tothecalculated result. (m) Calculated results from TI*. Notation is that in Figure 3.
therefore to describe them by a single yo*. However, it would be possible if two yo's are used, that is q o ( - D D ) * + yo(+DD)*. The parameters are interpreted in this case by
N-,, - N,,
= 12.9 min-'
L-,, - L,,, = -0.19
(25) It is worth noting that every Nand L are expected to be positive because of the causality. 5.2. Rate of Direct-Transformation. The contributions of the second terms in eqs 14-15 and the third term in eq 16 appear to correspond to yI *: (I) CH30H Since the results in Figure 3b were above the x axis, -yl(+MD) of appearance rate is assigned, which contains six parameters. Inserting
+
N,/min-' = 7.2, L, = 0.45; N+,,/min-'
- 0.5t
= 3.8,
L+MD= 0.13; N,/min-' = 12.9, L , = -0.19 (26) (which are given in Figure 8) into the function, we have the results shown by the solid squares in Figure 3b. The considerable agreement with the empirical results support the assumption that the transformation of (CH3)zO to CHIOH occurs in a single step.
(2) Other components: In the same way as CH3OH, the values of +TI* can be calculated using six parameters in Figure 8.The results are shown by the solid squares in Figures 4b-7b. The agreement between the semiempirical and theoretical results were not satisfactory. However, since they were similar in shape, the transformation of (CH&O could be regarded as a single step. The values of L,o ( m = 2, 3, 4) were very small, which suggests that the phase lag in the course of the transformation is very small and propagation of the pressure variation of (CH3)20 to the appearance rates of the olefins are very fast. 5.3. Transformationvia IntermediateProduct. For the results in Figures 3 b 7 b which crossed the x axis it is impossible to be
*
-i y
0.5
,
-0.5
4D
7m
'
D D
m' -X
0.5
I Figure 7. (a, top) Polar plots of ( p d , Av,,) with respect to CsH4. (0) Those derived from the FR data in Figure 2; ( 0 )those calculated from eq 16. (b,bottom)Contributionofthethreetermsineq 16tothecalculated result. (m) Calculated results from T I * . Notation is that in Figure 3.
described by 71.. Therefore, y2* is assumed. (I) CHjOH: If the transformation of C2H4to C H 3 0 H occurred via (CH&O, it would be described by y2(+MD:-
Heterogeneous Catalytic Reaction of Gases. 2.
The Journal of Physical Chemistry, Vol. 97, No. 13, 1993 3323 TABLE 111: Parameters N,,,, and L,,,!for the Rate of Transformation via Intermediate Product and Characteristic Functions Assinned m M D 2 3 4 I 2 2 M M M N,,,//min I L,,/ charact function
-0.8 0.55
-0.9 -0.72
-10.0
-7.9
0.48
0.48
+yz*
-yz*
-7,. -Y ?*
-YI*
-72*
-5.7 0.53 -71' -Y?*
(2) (CHJ20:The results of 0 2 crossing the x axis seem to be described by -72(-D1;+12)*. Unfortunately, we have no experimental endorsement with respect to the intermediate product 1. However, since the four parameters NO,LO,N z , and L2 have been determined, only six parameters remain unsettled; it would not be impossible to determine them by a computer simulation if the FR spectrum was reliable. (3)Olefins:The results of mM in Figures 5b-7b were strange in form because they did not turn around the origin and therefore it is impossible to describe them by y2*. However, it is found that the linear combination of
U 10.1, -0.19 I
Figure 8. Parameters [Nlmin I, L] determined by the computer simulation with which the calculated results in Figures 3a-7a have been derived. Abbreviations: DME denotes (CH3)20; Cz2-,C3?-,and C42are CzH4, C,H6, and C4H8, respectively.
TABLE I: Parameters N,,, and L,,, for the Rate of Decay and the Characteristic Function(s) Assigned m M D 2 3 4 N,,/min- I L", charact function
7.2
12.9
-1.6
0.45 -Yo*
-0.19
-0.19
-1.2 -0.23
0.1 -0.19
-yo* +YO*
+yo*
+yo*
+yo*
TABLE II: Parameters N,I and L,,,, for the Rate of Direct Tnnsformation of I to m Component and the Characteristic Function Assigned m M D 2 3 4 I D M D D D 0.13
-2.0 0.72
9.7 -0.05
14.6 -0.10
14.9 -0.02
+yI*
+yI*
+yI*
+yI*
+yI*
N,,,/lmin I
3.8
L,,I/
charact. function
D2)* of which ten parameters (given in Figure 8) are
= 7.2, L , = 0.45; N+,,/min-'
= 3.8, L+,D = 0.13; ND/min-' = 12.9, LD = -0.19;
N,/min-'
N-,,/min-'
= 0.9, L-D2= 0.72; N2/min-' = -1.6, L2 = -0.19 (27)
The calculated results are shown by the half solid circles in Figure 3b. The disagreement with the experimental results suggests that (CH,)20 is not the intermediate product.
-TI(-mM)* - y2(-ml;+lM)* (28) would be valid to reproduce them. The results are given in Table 111. Unfortunately, among the S/N ratios of the mass spectra, that of Ar was the worst. If we had more reliable data, improvement of the parameters for y I* in Figures 4b-7b would be possible by making use of eq 36 in paper 1. 6. Conclusions
As many as 30 rate constants summarized in Figure 8 or in Tables 1-111 have been determined from the FR data in Figure 2a,b. It should be emphasized that since o is variable in the FR method, many simultaneous equations based on the material balance can be derived to determine the various parameters. Each elementary reaction rate may be characterized by a couple of the parameters, N and L (see Figure 8). The FR spectrum of the transformation shown in Figures 3b-7b have been explained by the characteristic function(s) yi* as shown in Tables 1-111, which would contribute toconstruct the networkof the elementary steps; if the value of L / N at a step of j i, ( L / N i j ,agreed with ( L / N ) k , at I k step, the two steps would be coupled with each other. The kinetic details thus obtained would evidently effective to compare differently prepared catalysts and could contribute to improve them. The role of the new rate constant L would also be interesting.
-
-
References and Notes ( I ) Chang, C. D. Carol. Reu.-Sci. Eng. 1983, 25, I . ( 2 ) Chang, C. D. Carol. Reu.-Sci. Eng. 1984, 26, 323. (3) Hutchings, G . J.; Hunter, R. Cutal. Today, 1990, 6, 279. (4) Sedran, U.; Mahay, A.;de Lasa, H. I. Chem. Eng. J . 1990,45, 33. ( 5 ) Yasuda, Y . J. Phys. Chem. 1989, 93, 7185. (6) Yasuda. Y. J. Phys. Chem.. preceding article in this issue.
