Conversion and Reactor Sizing

Lec 5 week 6

Definition of Conversionfor the following reaction

• The reaction can be arranged as follows:

• Now we ask such questions as "How can we quantify how far the above reaction proceeds to the right?" or “How many moles of C are formed for every mole A consumed?

• A convenient way to answer these questions is to define a parameter called conversion.

• The conversion XA is the number of moles of A that have reacted per mole of A fed to the system.

Batch Reactor Design Equations in terms of conversion

• In most batch reactors. the longer a reactant stays in the reactor, the more the reactant is converted to product until either equilibrium is reached or the reactant is exhausted, Consequently. in batch systems the conversion X is a function of the time the reactants spend in the reactor.

• If NAO is the number of moles of A initially in the reactor then the total number of moles of A that have reacted after a time t is [NA0 *X]

Batch Reactor Design Equations in terms of conversion

• the mole balance on species A for a batch system is given by the following equation:

• reactant A is disappearing: therefore, we multiply both sides of Equation by -1 then

Batch Reactor Design Equations in terms of conversion

• For batch reactors. we are interested in determining how long to leave the reactants in the reactor to achieve a certain conversion X. To determine this length of time, we write the mole balance. Equation in terms of conversion.

NA=NA0(1-XA)• by differentiating the above equation with

respect to time, remembering that NAo is the number of moles of A initially present and is therefore a constant with respect to time.

dt

dXN

dt

dNA

A0

Batch Reactor Design Equations in terms of conversion

To determine the time to achieve a specified conversion X

This equation is now integrated with the limits that the reaction begins attime equal zero where there is no conversion initially (i.e., t = 0, X = 0).

Design Equations for Flow Reactors

• For a batch reactor. we saw that conversion increases with time spent in the reactor. For continuous-flow systems, this time usually increases with reactor volume. E.g. the bigger /longer the reactor, the more time it will take the reactants to flow completely through the reactor and thus, the more time to react.

• The conversion X is a Function of reactor volume V.

• If FA0 is the molar flow rate of species A fed to a system operated at steady state. The molar rate at which species A is reacting within the entire system will be FA0X.

Design Equations for Flow Reactors

Design Equations for Flow Reactors

• For liquid systems, CA0, is commonly given in terms of molarities, for example,CAO = 2 moll/dm3.

• For gas systems, CAo can be calculated from the entering temperature and pressure using the Ideal gas law.

Design Equations for Flow Reactors

Example(1 )

• A gas of pure A at 830 kPa (8.2 atm) enters a reactor with a volumetric flow rate,v0 of 2 dm3/s. at 500 K. Calculate the entering concentration of A, CA0, and the entering molar flow rate. FAo.

solution

• For flow reactors (CSTR)

For gas phase reactor.

Tubular Flow Reactor (PFR)

For a flow system, FA has previously been given in terms of the entering molar flow rare FA0 and the conversion X

By differentiate

Substitute in the 1st equation to give the differential form of the design equation for a plug-flow reactor (PFR):

We now separate the variables and integrate with the limits V = 0 when X = 0 to obtain the plug-flow reactor volume necessary to achieve a specified conversion X:

Packed-Bed Reactor

Example• Consider the liquid phase reaction which we will write symbolically as

– A B• The first order (-rA = k CA) reaction is carried out in a tubular reactor in

which the volumetric flow rate, v, Is constant i.e. v =v0. • (a) Derive an equation relating the reactor volume to the, entering and

exiting concentrations of A the rate constant k, and the volumetric flow rate v.

• (b) Determine the reactor volume necessary to reduce the exiting concentration to 10% of the entering concentration when the volumetric flow rate is I0(dm3/min) and the specific reaction rate, k. is 0.23 min-1 .

Solution