Conversion and Reactor Sizing Lec 4 week 4

Definition of Conversion for the following reaction The reaction can be arranged as follows: how far the above reaction proceeds to the rightHow many moles of C are formed for every mole A consumed? 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? conversion A convenient way to answer these questions is to define a parameter called conversion. The conversion X A 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 N AO 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 [N A0 *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 N A =N A0 (1-X A )

Batch Reactor Design Equations in terms of conversion by differentiating the above equation with respect to time, remembering that N Ao is the number of moles of A initially present and is therefore a constant with respect to time.

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 at time 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 F A0 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 F A0 X.

Design Equations for CSTR

Tubular Flow Reactor (PFR) For a flow system, F A has previously been given in terms of the entering molar flow rare F A0 and the conversion X By differentiate Substitute in the 1 st 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 – AB The first order (-r A = k C A ) reaction is carried out in a tubular reactor in which the volumetric flow rate, v, Is constant i.e. v =v 0. (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(dm 3 /min) and the specific reaction rate, k. is 0.23 min -1.

Solution