1. Mole balance for chemical reaction engineering (Design Equations for reactors) Lec 3 week 3

2. The General Mole Balance Equation To perform a mole balance on any system, the system boundaries must first be specified. The volume enclosed by these boundaries is referred to as the system volume.

3. where N j, represents the number of moles of species j in the system at time t.

4. The rate of generation of species j is expressed as The product of the reaction term and can be written in more familiar terms, G A = r A V V is volume of the system. Note that the units for this relation are consistent: If G A (and hence r A ) varies with position in the system volume, we can take this into account by evaluating this term at several locations. Then  G A1 = r A1  V 1,

5. Summing the reactions over the entire volume yields: As (that is, as we decrease the size of these cubes and increase their number) then which gives we now replace G in equation (1) to get :

6. From this general mole balance equation we can develop the design equations for the various types of industrial reactors: batch, semi-batch. and continuous- flow.

7. Types of Reactors Batch – No flow of material in or out of reactor – Changes with time Fed- Batch (semi batch) – Either an inflow or an outflow of material but not both – Changes with time Continuous – Flow in and out of reactor – Continuous Stirred Tank Reactor (CSTR) – Plug Flow Reactor (PFR) – Steady State Operation ( no change with time)

8. General Mole Balance in terms of number of moles

9. Batch reactor mole balance Generalized Design Equation for Reactors No flow into or out of the reactor, then, F A = F A0 = 0 Good mixing, constant volume

10. Batch Reactor

12. Fed Batch Reactor Reactor Design Equation No outflow F A = 0 Good Mixing r A dV term out of the integral

13. CSTR General Reactor Design Equation Assume Steady State Well Mixed Soor Continuous Stirred Tank Reactor

14. CSTR

15. Tubular Reactor (Plug Flow Reactor) (PFR) Tubular Reactor Pipe through which fluid flows and reacts. Poor mixing Difficult to control temperature variations. An advantage is the simplicity of construction

16. PFR Design Equation Design Equation Examine a small volume element (  V) with length  y and the same radius as the entire pipe. If the element is small, then spatial variations in r A are negligible, and Flow of A into Element Flow of A out of Element Assumption of “good mixing” applies only to the small volume element

17. If volume element is very small, then assume steady state with no changes in the concentration of A. Simplify design equation to: r A is a function of position y, down the length of the pipe and reactant concentration take the limit where the size of a volume element becomes infinitesimally small This is the Design Equation for a PFR

18. take the limit where the size of a volume element becomes infinitesimally small or because  y A = V, This is the Design Equation for a PFR Bioapplications - Sometimes hollow fiber reactor analysis is simplified to a PFR

19. Plug Flow Reactor Mole Balance PFR: The integral form is: This is the volume necessary to reduce the entering molar flow rate (mol/s) from F A0 to the exit molar flow rate of F A.

20. Packed Bed Reactor PBR The integral form to find the catalyst weight is:

21. Reactor Mole Balance Summary