Batch Reactors

Batch Reactors Batch processes are suggested forproduction rates of less than 1,000,000 lb per year and orproducts that are seasonal, have short lifetimes in themarket or very low reaction rates or multi-product plants. Ina batch reactor rates are less important, the time required tocomplete an operation is usually all you need. Partly for thisreason the kinetics of fine chemical and pharmaceuticalprocesses are rarely known. Batch reactors are the mostversatile reactors, they can be used for almost anything.Other benfits are even if recycles are used it is usuallystored in a holding tank so inert buildups are more easilytaken care of after the reaction is over. Batch processes aremore likely used for comlplex organic molecules, thissometimes makes safety an issue in the form of runawayreactions because the molecules may be less themallystable. Batch reactors are not time efficient, the reactorworks on 'triggers' like when the reactor is full it triggers theheat or cooling required for the reaction stage. The onlytime dependent part of the batch reactor is the reaction time,and that is determined by the engineer for its most costefficient product vs time.

Batch Derivation

General Mole Balance on System Volume V

No inflow or outflow-

Assumptions

Well mixed

The design equations for a batch process are asfollows:

An example procedure follows :

A 200-dm3 constant-volume batch reactor ispressurized to 20 atm with a mixture of 75% Aand 25% inert. The gas-phase reaction is carriedout isothermally at 227 C.

V = 200-dm3

P = 20 atmT = 227 C

a. Assuming that the ideal gas law is valid,how many moles of A are in the reactorinitially? What is the initial concentrationof A?

b. If the reaction is first order:

Calculate the time necessary to consume99% of A.

c. If the reaction is second order:

Calculate the time to consume 80% of A.Also calculate the pressure in the reactorat this time if the temperature is 127 C.

Answer:

• How many moles of A are in the reactor initially? What is the initialconcentration of A?

If we assume ideal gas behavior, then calculating the moles of A initiallypresent in the reactor is quite simple. We insert our variables into theideal gas equation:

Knowing the mole fraction of A (yAo) is 75%, we multiply the totalnumber of moles (NTo) by the yA:

The initial concentration of A (CAo) is just the moles of A divided by thevolume:

• Time (t) for a 1st order reaction to consume 99% of A.

With both 1st and 2nd order reactions, we will begin with the molebalance:

There is no flow in or out of our system, and we will assume that there isno spatial variation in the reaction rate. We are left with:

Knowing the moles per volume (NA/V) is concentration (CA), we thendefine the reaction rate as a function of concentration:

First Order Reaction

This is the point where the solutions for the different reaction ordersdiverge.

Our first order rate law is:

We insert this relation into our mole balance:

and integrate:

Knowing CA=0.01 CAo and our rate constant (k=0.1 min-1), we can solvefor the time of the reaction:

• Time for 2nd order reaction to consume 80% of A and final pressure(P) at T = 127 C.

Second Order Reaction

Our second order rate law is:

We insert this relation into our mole balance:

and integrate:

We can solve for the time in terms of our rate constant (k = 0.7) and ourinitial concentration (CAo):

To determine the pressure of the reactor following this reaction, we willagain use the ideal gas law. First, we determine the number of moles inthe reactor:

Now, we calculate the new pressure using the ideal gas law: