Isothermal Temperature Report

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Journal Article Report 2012

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NAME: Sandra Enn Bahinting STUDENT #: 2012-79306COURSE: MS CHE PROFESSOR: Dr. Richard Chu

Journal Title: Isothermal Temperatures for Reversible Reactions

Statement of the Problem:

The optimum temperature progression maximizes the production rate for a given reactor. It

may be an isothermal or varying temperature conditions; in time for a batch, plug flow and back mix

reactors. However, this may not be the case when considering the type of reaction such as the

exothermic reversible reaction.

The optimum temperature for this kind of reaction is being investigated over a wide range of

kinetic parameters. Furthermore, it compromises the kinetic and thermodynamic factors to maximize

the final conversion for a given reaction time. Thus, the paper establishes the best approach to

determine rapidly the optimal temperature and equilibrium conversion for some commonly

encountered homogeneous reversible exothermic reactions.

Brief Background

It follows that at any composition for a given type of reactor, the optimum temperature

progression is the temperature, which the rate is at maximum. Thus, for an irreversible reaction, the

optimal temperature is the highest allowable where highest rate occurs as determined by physical

factors such as reactor material of construction, selectivity and decomposition of the product. Similarly,

for endothermic, reversible reactions, a rise in temperature increases both the equilibrium conversion

and the rate of reaction. Thus, the highest allowable temperature should be use.

For exothermic reversible reactions, the case is different. The increase in temperature results in

a speeds up of the rate of forward reaction but a decrease in the equilibrium conversion. Thus, the

optimal temperature has to be a compromised of these kinetic and thermodynamic factors to attain

rationally high reaction rates and yet large conversions.


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Materials and Method

A. Development of GraphsConsider the first-order reversible reaction involving chemical species and :

Eqn. [1]

where A is the reactant, S is the desired product to be maximized, and are the forward and

backward reaction rate constants.

For a given constant-volume batch reactor, the rate of disappearance of A may be expressed by:

Eqn. [2]

where is the rate of disappearance ofA, and is the concentration ofA and S, respectively; and t

is time.

For such reaction, the temperature-dependent term, the reaction rate constant, is practically be

well represented by Arrhenius law. The variation in rate with temperature is expressed as follow:

Eqn. [3]

Eqn. [4]

where and , are called the frequency or pre-exponential factor of forward and reverse reaction,

E1 and E2 are the respective activation energies of the forward and reverse reaction, R is the gas

constant, and Tis absolute temperature.

As suggested by Millman and Katz, the following equations define dimensionless parameters:

Eqn. [5]

Eqn.[6]

Eqn.[7]

kf

kr


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Eqn. [8]

Eqn. [9]

where is the reaction time, is fractional conversion of A and is the initial concentration of A.

Substituting Eq. (3) to (9) into Eq. 1 yields the following dimensionless form of the rate

expression:

Eqn. [10]

Integrating the equation above from initial conversion to final conversion, and tfrom 0

to 1, yields:

] Eqn. [11]

A search technique on a digital computer was use to maximize the equation above. Two graphs

were obtained after maximizing in Eq. (11) with respect to T11 for different values ofa and B11, with

for this reaction. Furthermore, a series of graphs were made for other reaction mechanism

having a similar development above considering also its dimensionless parameters.

B. Using the GraphsTwo approached used to solve for the optimal isothermal temperature using these graphs (Fig. 1

and 2);

1. Specify desired conversion. The value of B may be obtained using the conversion vs.dimensionless parameter B by stating the conversion desired. From B and kinetic

parameters, the reaction time tf is then calculated using the definition of B in Table 1. From

the dimensionless temperature T vs B plot, T can be obtained and actual temperature is

calculated using the definition in Table 1.

2. Specify reaction time. Using the definition in Table 1, B11 is then calculated. Obtained thevalue of T from Tvs. B plot. The actual temperature is computed using the definition of T

from Table 1.The value for optimal conversion is obtained from the conversion of A vs. B

plot.


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Summary and Results

The development of the graphs started from a simplest form of exothermic reversible reaction,

which carried out in a constant-volume batch reactor as shown in Eq. (1). The rate of A was expressed in

its disappearance form in Eq. (2) and the rate constant was expressed in the usual Arrhenius form to

have a variation in rate with temperature in Eq. (3).

Moreover, Millman and Katz, in which these were substituted in Eq. (2) to yield a dimensionless

form of the rate expression as shown in Eq. (10), suggested some dimensionless parameters equations.

Furthermore, integration and simplification for the equation was made to derive Eq. (11). The equation

was maximize using a search technique on a digital computer.

The figures below was the result for maximizing in Eq. (11) for different values ofa and B11,

with . Figure 1 shows the plot ofT11vs. B11 , where T11is obtained after calculating the value of

and B11 . The optimal temperature is calculated using Eq. (7). On the other hand, Figure 2 shows the

optimal conversion , obtained by operating at the corresponding optimal temperature.

Figure 1. TEMPERATURE is in a dimensional form


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Figure 2. FRACTIONAL conversion of reactant A

The preceding analysis above assume a batch reactor, however this may also be applied to plug-

flow reactor provided that the changes in volume accompanying the reaction are small and t as

residence time must be interpreted. A series of graphs are developed for other exothermic reversible

reaction mechanisms having a similar development shown above to be able to rapidly determine the

optimal temperature as well as its conversion, taking into consideration the dimensionless parameters

for the given reaction mechanism which is summarized in Table 1.

Table 1:Reaction Mechanisms and Their Corresponding Dimensionless Parameters

REACTIONS

Dimensionless Parameters

B T

A P

A + B P + S

A + B P


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Principal Conclusions

The optimal isothermal temperatures for reversible exothermic reactions is obtained and

investigated over a broad range of kinetic parameters. A compromise between kinetic and

thermodynamic dynamic factors to maximize the final conversions at a given reaction time for a batch

and plug-flow reactors operation is accomplished by computer optimization technique. This yields a

series of graph not just for a first-order reversible reaction but also for many homogeneous reversible

exothermic reactions. Thus, the developments of these graphs enable to rapidly determine the optimal

temperature and equilibrium conversion for this type of reaction.

Critique

The article presented well the statement of the problem through the brief review of the topic. In

which it was very concise, significant, and direct to the main point details. The purpose was clearly and

concisely stated, easy for the reader to understand and it definitely agreed with the title. The

presentation of the methods was stated in a systematic and simplified manner, which the reader can

easily follow. The equations were expressed correctly and relating each equation to another in an

organize and logical approach. The findings were reported objectively especially the graphs on how to

use it properly. However, the graphs have a limitation considering the values for , so estimation should

be made. The example problem given in the article had well clarified and explained further the function

of the equations as well as the principle of the graphs. The table was well organized and easy also to

comprehend.

Thus, the article had fully met the purpose or the objective of the study. The answer to the

problem was attained efficiently through the findings, which was logically stated. The article may not

detail the derivations of some equations nevertheless; its to erase confusion for the reader. The article,

as a whole, may be brief but it was a really an interesting and definitely a significant one.

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