Application of Analog Techniques in Studying the Kinetics of the Reaction of Phenol Alcohol Formation
Abstract Generated abstract
This paper examines the alkaline oxymethylation of phenol with formaldehyde and evaluates a proposed reaction mechanism by comparing experimental kinetic data with analog computer modeling. Assuming mass action kinetics, the authors formulate a system of differential equations for phenol, formaldehyde, and substituted phenol alcohol intermediates and products, then implement the system on an MN-7M analog computer using experimentally determined rate constants. Simulations for several initial phenol, formaldehyde, and caustic soda ratios at 30 degrees Celsius reproduce reported experimental behavior within the stated accuracy of the analog device and indicate that formaldehyde-deficient systems are dominated by mononuclear mono- and disubstituted phenols. The work presents the kinetic equation system as a basis for further mathematical description of phenol alcohol production.
Full Text
Application of Analog Techniques in Studying the Kinetics of the Reaction of Phenol Alcohol Formation
P. A. Andriyanov, V. G. Martynenko
(Presented by the Scientific-Methodological Seminar of the Faculty of Chemical Technology)
The validity of the hypothesis [1] concerning the mechanism of the reaction of alkaline oxymethylation of phenol with formaldehyde can be checked by comparing the experimental data [2] with the results of studying the reaction kinetics on an analog computer.
Assuming that the reaction obeys the law of mass action, we compose a system of kinetic equations:
\[ \begin{aligned} \frac{dx_1}{dt} &= -x_8 \cdot x_1 (k_1+k_2);\\[4pt] \frac{dx_2}{dt} &= x_8 (k_1x_1-k_3x_2);\\[4pt] \frac{dx_3}{dt} &= x_8[k_2x_1-x_3(k_4+k_5)];\\[4pt] \frac{dx_4}{dt} &= x_8(k_3\cdot x_2+k_4\cdot x_3-k_6\cdot x_4);\\[4pt] \frac{dx_5}{dt} &= x_8(k_5\cdot x_3-k_7\cdot x_5);\\[4pt] \frac{dx_6}{dt} &= x_8(k_6\cdot x_4+k_7\cdot x_5)-2k_8\cdot x_6;\\[4pt] \frac{dx_7}{dt} &= k_8\cdot x_6;\\[4pt] \frac{dx_8}{dt} &= -x_8\cdot x_1(k_1+k_2)-x_8(k_3\cdot x_2+k_4\cdot x_3+{}\\ &\qquad {}+k_5\cdot x_3+k_6\cdot x_4+k_7\cdot x_5)+k_8\cdot x_6; \end{aligned} \tag{1} \]
where, at
\[ t=0;\qquad x_1=x_{10};\qquad x_8=x_{80};\qquad x_2=x_3=x_4=x_5=x_6=x_7=0. \]
Here \(x_1,\ldots,x_8\) are, respectively, the concentrations of phenol, para-hydroxybenzyl alcohol, saligenin, 2,4-dimethylolphenol, 2,6-dimethylolphenol; 2,4,6-trimethylolphenol; 3,3′,5,5′-tetramethylol-4,4′-dihydroxydiphenylmethane; and formaldehyde.
\(k_1,\ldots,k_8\) are the rate constants of the elementary stages of the reaction, found experimentally [2].
To solve system (1) using an analog device, it is necessary to carry out several preparatory operations [3]:
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Construct a structural scheme for connecting the solving elements, corresponding to the specified conditions.
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Choose scales for representing the variables and time.
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Calculate the parameters of the model from the coefficients of the original equations and the selected scale values.
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Determine the initial conditions of the model in those physical quantities which, in the analog computer, represent the original variables of the problem.
The block diagram for solving system (1) on the MN-7M machine is shown in Fig. 1.
Fig. 1. Diagram for setting up the system of equations (1) on the machine.
The output quantities of integrating amplifiers 1—7, 15 are the concentrations of the reaction components at any specified instant of time. B1—B8 are multiplication blocks, in which the nonlinearities present in the right-hand sides of the equations of system (1) are implemented. Amplifiers 8—14 are intended for carrying out the operations of addition and subtraction of variables. By changing the initial conditions on amplifiers 1 and 15, one can quantitatively trace the influence of different ratios of the initial components (formaldehyde : phenol) on the rate of formation and disappearance of the individual substituted phenols. In the present work the kinetics of the alkaline oxymethylation of phenol was studied at the ratio phenol : formaldehyde : caustic soda = 1:3:1; 1:2:1; 1:1:1 and 1:3:0.625 (in moles) and at a temperature \(T = 30^\circ\mathrm{C}\).
Figure 2 presents kinetic curves that make it possible to judge the appearance and disappearance of various phenol alcohols with time. In reproducing the experiment [2] on the model (Fig. 2, a), satisfactory agreement was achieved for the rates of the elementary stages
Fig. 2. Dependence of the rate of formation of phenol alcohols on the duration of the reaction at the following component ratios:
a) 1:3:1; b) 1:1:1.
The designations correspond to: 1—phenol, 2—para-hydroxybenzyl alcohol, 3—saligenin, 4—2,4-dimethylolphenol, 5—2,6-dimethylolphenol, 6—2,4,6-trimethylolphenol, 7—3,3′,5,5′-tetramethylol-4,4′-dihydroxydiphenylmethane.
of the process. The error in the calculations does not exceed that permissible for an MN-7M type analog computer, taken to be within 7–10% [4].
The study of the reaction kinetics with a deficiency of formaldehyde (Fig. 2, b) agrees with the conclusions of [5] that, in such systems at \(T = 30^\circ\mathrm{C}\), the predominant components of the mixture are mononuclear mono- and disubstituted phenols.
Conclusions
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With a certain amount of experimental data on the reaction, further study of the kinetics should expediently be carried out using computing techniques.
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The system of kinetic equations (1) can serve as the basis for work on compiling a mathematical description of the process of obtaining phenol alcohols.
LITERATURE
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- M. G. Slinko. In: Modeling and Optimization of Catalytic Processes, Izd-vo “Nauka”, 14 (1965).
- R. Dijkstra, J. De Jong, M. F. Lammers, Recueil Trav. Chim. 81, 3, 285–296 (1962).