Conversion and Reactor Sizing

Lec 4 week 4

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 how far the above reaction proceeds to the rightthe above reaction proceeds to the right?" or “How many moles How many moles of C are formed for every mole A consumed?of C are formed for every mole A consumed?

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

• 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 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:

• To write the mole balance Equation in terms of conversion. We use

NA=NA0(1-XA)

Vrdt

dNA

A

Batch Reactor Design Equations in terms of conversion

• 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).

conversion increases with time spent in the reactor.

Design Equations for CSTR

• 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 CSTR

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