1. Material balances (moles)
Maurizio Fermeglia
DIA
Mose.units.it

2. Mole Balances, Conversion & Reactor Sizing
What we expect to cover:
general definitions - homogeneous/heterogeneous reactions, reaction rate.
development of general mole balance and its application to common industrial reactors (batch and continuous)
development of reactor design equations in terms of conversions
application of design equations in reactor sizing

3. Chemical reaction
A detectable number of molecules of one or more species have lost their identity and assumed a new form by a change in the kind or number of atoms in the compound and/or by a change in structure or configuration of these atoms.
Decomposition
Combination
Isomerization
Rate of reaction
How fast a number of moles of one chemical species are being consumed to form another chemical species.

4. Homogeneous & Heterogeneous Reactions
Homogeneous Reactions: reactions that occur in a single phase (gas or liquid)
NO + O 2  NO 2
C 2 H 6  C 2 H 4 + H 2
Can be catalithic
Heterogeneous Reactions: reactions that require the presence of two distinct phases
Coal combustion
SO 2 + 1/2 O 2  SO 3 (for sulphuric acid production)
Reaction types
Decomposition
Combination
Isomerization

5. Reaction Rate (-rA) for Homogeneous Reactions
(-r A ) = rate of consumption of species A
= moles of A consumed per unit volume per unit time
The rate of formation of A is denoted as (r A )
Note: “minus” sign denotes consumption or disappearance
Units of (-r A ) o (r A )
moles (or kilo moles) per unit volume and unit time
mol/l-s or kmol/m3-s

6. Reaction rate (-r A ') for heterogeneous reaction
For a heterogeneous reaction, rate of consumption of species A is denoted as (-r A ')
Units of (-r A ')
Moles per unit time per mass of catalyst
mol/s-g or kmol/hr-kg catalyst

7. Is (-r A ) = dCa/dt ?? Steady state operation = no change with time
C AO C A
10:00 am
12:00 pm
3:00 pm
5:00 pm
Neither C AO nor C A are changing with time  dca /dt = 0  ra=0
… which is impossible.
Ethylene Oxide + water
Ethylene Glycol

8. Reaction Rate - Functional form
Reaction rate is NOT defined by a differential equation but it is defined by an algebraic equation
Reaction rate is
Function of T and concentrations
Is independent from reaction type
Reaction rate is described by a kinetic expression or rate law
an algebraic equation that relates reaction rate to species concentration
(-rA) = [k f (T)] · [f´(Concentrations)]
(-rA)= k · [concentration terms]
e.g. (-r A )= k C A ; (-r A )= k C A 2 or more complex (-r A )= k1 C A / (1 + k2 C A )
Note: a more appropriate description of functionality should be in terms of “activities” rather than concentration.

9. General Mole Balance
Considers chemical species In and OUT of the reactor
Mole balance in terms of chemical species, NOT atomic species
Reaction rate --> number of reacting moles per unit time and volume (r, -r)
Reactor sizing equations are different for types of reactors
IN OUT GEN ACCUMULATION
Ga= generation term
= (ra) V (for homogeneous volume)
Otherwise the integral holds

10. Reactor types Batch reactor Flow reactor Other Reactor Types
Continuous-Stirred Tank Reactor (CSTR)
Plug Flow Reactor (PFR)
Packed Bed Reactor (PBR)
Other Reactor Types
Fluidized Bed Reactor
Trickle Bed Reactor
…..

11. Mole Balance for Batch Reactor
Two different cases:
1. Constant Volume
2. Constant Pressure
If reactor is perfectly mixed

12. Mole Balance for Batch Reactor
Constant Volume (NA = CA V)
Constant Pressure (NA = CA V)

13. Mole Balance for CSTR V V V
Design equation valid with the following hypothesis:
Steady state
Reaction rate constant in space
FAO
X=0 V FA
X=X

14. Example: CSTR
One L/min of liquid containing A and B (C AO = 0.10 mol/l, C BO = 0.01 mol/l) flows into a mixed flow reactor of volume Vr=1.0 L. The materials react in a complex manner for which the stoichiometry is unknown. The outlet stream from the reactor contains of A, B and C at concentrations of C Af = 0.02 mol/l, C Bf =0.03 mol/l and C Cf =0.04 mol/l.
Find the rate of reaction of A, B and C at conditions of the reactor.

15. Solution VR = 1.0 L vf = ?? CAO = 0.10 mol/L Basic Design Equation
CBO = 0.01 mol/L
CCO = 0.00 mol/L
Basic Design Equation
(-rj) = [Fjo - Fjf]/[VR]
Approach
Fj = Cj x v (molar flow rate)
vf = vi = v
conc. inside reactor = conc. in exit
(-rj) = [Cjo-Cjf] [v]/ [VR]
(-rA) = [ ] [1]/[1] = mol/min
(-rB) = [ ] [1]/[1] = – 0.02 mol/min
(-rC) = [ ] [1]/[1] = – 0.04 mol/min
VR = 1.0 L
vi = 1.0 L/min
vf = ??
CAF = 0.02 mol/L
CBF = 0.03 mol/L
CCF = 0.04 mol/L

16. Mole Balance for a PFR Differential Form Integral Form
Design equation valid with the following hypothesis:
Steady state
Reaction rate constant in space
Note: conversion depends from VOLUME only (and not from shape)
Differential Form
Integral Form

17. PFR: derivation Mole balance for a generic volume V Steady state
The derivative

18. Summary - Design Equations of Ideal Reactors
Differential
Equation
Algebraic
Integral
Remarks
Conc. changes with time but is uniform within the reactor. Reaction rate varies with time.
Batch
CSTR
Conc. inside reactor is uniform. (rj) is constant.
Exit conc = conc inside reactor.
PFR
Concentration and hence reaction rates vary spatially.

19. Exercise: PFR reactor sizing
Reaction A  B cis-2-butene  trans-2-butene
PFR
First order reaction: -ra= kCa
Constant volumetric flow rate v=v0
Determine
A qualitative graph with the concentration profile as a function of V
The equation giving the reactor’s volume as a function of inlet and outlet concentrations, constant k and volumetric flow rate v.
The volume needed to reduce the concentration of A at 10% of the inlet one.
Assume v= 10 liters /min and k = 0.23 min-1

20. PFR reactor sizing: solution
A qualitative graph with the concentration profile
Ca0 Ca V

21. PFR reactor sizing: solution
Design equation for a PFR:
For a first order kinetic:
Volumetric flow rate v0 is constant:
Substituiting rA:
BC: V=0 for CA=CA0
With numbers …

22. Reactor Characteristics
Batch Reactor
mainly used for small scale operation
suitable for slow reactions
mainly used for liquid-phase reaction
charge-in/clean-up times can be large
CSTR
steady state operation; used in series
good mixing leads to uniform concentration and temperature
mainly used for liquid phase reaction
suitable for viscous liquids
PFR
suitable for fast reaction
gas phase reaction
temperature control is difficult
there are no moving parts

23. Mole balance for Packet Bed Reactor - PBR
Considers INLET and OUTLET species in the control volume
Mole balance
Rate law --> number of reacting moles for unity of time and volume (r, -r)
Different sizing equations for different reactor types
-r’A specific rate law for mass of catalyst
IN OUT GEN ACCUMULATION
Ga= generation term
= r’ W
mole balance in terms of mass of catalyst W

24. PBR: derivation Mass balance in terms of W Steady state
Differentiation with respect to W

25. Mole balance for Packed Bed ReactorW
Integral form
Differential form

26. Industrial reactors

27. Hydrogenation reactors

28. Industrial reactors: liquid phase
Batch
Used for low scale productions, good for high value product (pharma, bio,…)
Difficult temperature control
High conversions
High cost of labor, complex operation
Semi Batch
Like batch but with a better temperature control
Good for minimizing secondary reactions
Used for two-phase reactions (bubbles)

29. Industrial reactors: liquid phase
CSTR
Characterized by a strong mixing
Used in series or in parallel
Conversion is the lowest among flux reactors
Easy to reuse old reactors (flexibility)

30. Industrial reactors: gas phase
PFR
Easy maintenance
High conversion (the highest among flux reactors)
Difficult temperature control
Parallel pipes
Cost (and construction) is similar to heat exchangers
PBR (fixed bed)
Similar to PFR, contains solid phase
Catalytic reactions
Fluidized bed
Similar to CSTR (good mixing an temperature control)
Must be modelled with specific equations
Used for high productions

31. Industrial reactors
Fixed bed
Fluidized bed

32. Industrial reactors
Slurry reactor

33. Reforming reactors (BP)

34. Reactor modelling in process simulators
Demo on the use of:
Aspen +
PRO II
COCO - COFE