Post on 12-Nov-2021
CHEE 321: Chemical Reaction Engineering
Module 1: Mole Balances, Conversion & Reactor Sizing(Chapters 1 & 2, Fogler)
Module 1: Mole Balances, Conversion & Reactor Sizing
• Topics to be covered:– Basic elements of reactor design, terminology/notation
– Development of general mole balance equation with reaction
– Key characteristics and mole balance equations for common industrial reactors (batch, CSTR, PFR, PBR)
– Reactor design for single-reaction systems• Definition of conversion• Levenspiel Plots
Basic Elements of Reactor Design• Reactor design usually involves the following:
– Knowledge of nature of reaction • Catalytic or Non-Catalytic• Homogeneous or Heterogeneous• Reversible or Irreversible
– Selection of operating conditions• Temperature, Pressure, Concentrations• Type of catalyst (if applicable)• Flow rates
– Selection of reactor type for a given application– Estimation of reactor volume required to process given amount
(moles or molar rate) of raw material to desired amount of products• How fast the reaction occurs (reaction rates) dictates how large the
reactor volume will be
Our approach to reactor design• Operation of most reactors are relatively complex
– Temperature is not uniform and/or constant– Multiple reactions can occur– Flow patterns are complex
• To gain an insight into basic concepts relevant to reactor design, we will first consider simplified and/or ideal reactor systems.
• Design of isothermal reactors involves solution of MOLE BALANCE equation only– In some cases, pressure drop must also be calculated
• Let us first familiarize ourselves with some common terminology and notation that we will be using throughout the course
Monomer Feed
Initiator
Feed
- A multi-zone Autoclave is a vertical cylindricalvessel with large L/D of 10-20. The reactionmixture is intensely mixed by a stirrer shaft.
- Reactor is divided into separated reaction zones.
- Reactor (and each zone) is considered as well-mixed CSTR in perfect mixing model approach.
- Imperfect mixing of initiator feed can occur dueto very fast initiator decomposition rate, despiteintense agitation
Ethylene Low Density Polyethylene
Reversible and Irreversible Reactions
Irreversible Reactions: Reactions that proceed uni-directionally under the conditions of interest
Reversible Reactions: Reactions that proceed in both forward and reverse directions under conditions of interest.
SO2 + 0.5 O2 ⇄ SO3
CH4 + 2O2 CO2+2H2O
H2S⇄ H2 + 1/xSx
Thermodynamics tells us that all reactions are reversible.However, in many cases the reactor is operated such that therate of the reverse reaction can be considered negligible.
Homogeneous Reactions: reactions that occur in a single-phase (gas or liquid)NOx formationNO (g) + 0.5 O2 (g) ↔ NO2 (g)Ethylene ProductionC2H6 (g) ↔ C2H4 (g) + H2 (g)
Heterogeneous Reactions: reactions that require the presence of two distinct phases
Coal combustionC (s) + O2 (g) ↔ CO2 (g)
SO3(for sulphuric acid production) SO2 (g) + 1/2 O2 (g) ↔ SO3 (g) Vanadium catalyst (s)
Homogeneous & Heterogeneous Reactions
Material Balances: It all starts from here!
Rate of INPUT – Rate of OUTPUT + Rate of GENERATION – Rate of CONSUMPTION
= Rate of ACCUMULATION
Input RateOutput Rate
Note: Rates refer to molar rates (moles per unit time).
Before we get into the details of the mole balance equation, we must introduce definition for reaction rate as well as associated notation.
System with Rxn: use mole balances
(– rA) = rate of consumption of species A (A is a reactant)= moles of A consumed per unit volume per unit time
(rA) = rate of formation of species A (A is a product)
Units of (rA) or (– rA)• moles per unit volume per unit time• mol/L-s or kmol/m3-s
Notation: Reaction Rate for Homogeneous Reactions
A + B C
D A
Notation: Reaction Rate for Heterogeneous Reactions
For a heterogeneous reaction, rate of consumption of species A is denoted as (-rA')
Heterogeneous reactions of interest are primarily catalytic in nature. Consequently, the rates are defined in term of mass of catalyst present
Units of (-rA')•mol per unit time per mass of catalyst•mol/(g cat)-s or kmol/(kg cat)-h
Reaction Rate and Rate LawReaction Rate• Rate of reaction of a chemical species will depend on the local conditions
(concentration, temperature) in a chemical reactor
Rate Law• Rate law is an algebraic equation (constitutive relationship) that relates reaction
rate to species concentrations.• Rate law is independent of reactor type
(-rA) = k ·[concentration terms]
e.g. (-rA) = k CA or (-rA) = k CA2
where, k is the rate coefficient [k=f(T)]
Note: a more appropriate description of functionality should be in terms of “activities” rather than concentration.
We’ll learn more about rate laws in Modules 2 and 4.
General Mole Balance Equation (GMBE)
Rate of INPUT – Rate of OUTPUT + Rate of GENERATION/CONSUMPTION = Rate of ACCUMULATION
System volume VFA0
FA
GA = (rate of generation of A) · V
dtdN AFA0 =GA+FA−
General mole balance equation is the foundation of reactor design.
If A is consumed, add a –ve sign
All terms with units of mol/s
V
Ar dV ′= ∫Need to integrate over reactor volume, as reaction conditions (T, CA ) may vary with position
Common Reactor Types
• Batch Reactor
• Flow Reactors– Continuous-Stirred Tank Reactor (CSTR)– Plug Flow Reactor (PFR)– Packed Bed Reactor (PBR)
• Other Reactor Types– Semibatch Reactors– Fluidized Bed Reactor, Trickle Bed Reactor, Membrane
Reactor, …
Batch Reactor
Key Characteristics• No inflow or outflow of material• Unsteady-state operation (by definition)• Mainly used to produce low-volume high-value
products (e.g., pharmaceuticals)• Often used for product development• Mainly (not exclusively) used for liquid-phase
reactions• Charging (filling/heating the reactor) and clean-
out (emptying and cleaning) times can be large
For an ideal batch reactor, we assume no spatial variation of concentration or temperature. i.e.; lumped parameter system (well-mixed)
General Mole Balance for an Batch Reactor
If well-mixed (no temperature or concentration gradients in reactor):
differential form integral form
Input = Output = 0
0
;
at 0
AA
A A
dN r Vdt
N N t
=
= = 0
A
A
NA
AN
dNtr V
′= ∫
VA
AdN r dVdt
′= ∫
Class exercise: Derive concentration vs. t profiles for A and B for A B with rB=-rA=kCAfor a well-mixed constant-volume isothermal batch reactor. At t=0, CA=CA0 and CB=0
Continuous Stirred Tank Reactor (CSTR)
• Can be used in series• Mainly used for liquid phase
reaction, high-volume products• Suitable for viscous liquids
Picture Source: http://www-micrbiol.sci.kun.nl/galleries/two.html
FA0
FA
For an ideal CSTR, we assume no spatial variation of concentration or temperature. i.e.; lumped parameter system (well-mixed)
0
VA
A A AdN F F r dVdt
′= − + ∫
0A
A A AdN F F r Vdt
= − +
For an ideal CSTR operating at steady-state (no time variation of flows, concentrations, temperature) 0 0A A AF F r V− + =
General Mole Balance for Ideal CSTR at Steady-State
FA0=v0CA0
Class exercise: Derive expressions for concentration of A and B for A B with rB=-rA=kCA for a well-mixed steady-state CSTR with inlet concentrations CA=CA0 and CB=0, assuming no density change.
CSTRs are also known as “back-mix” reactors, as concentrations in the outlet stream are the same as concentrations in the reactor (a consequence of being well-mixed)
FA=vCANA=VCA
v0, v= volumetric flowrates (L/min, m3/s) of inlet and exit; if at steady-state and constant density, v0 = v
Average residence or space time of fluid in vessel based on inlet conditions τ = V/v0
Class Problem
Calculating Reaction Rate in a CSTR1.0 L/min of liquid containing A and B (CA0=0.10 mol/L, CB0=0.01 mol/L) flow into a mixed flow reactor of volume 1.0 L. The materials in the reactor interact (react) in a complex manner for which the stoichiometry is unknown.
The outlet stream from the reactor contains A, B and C at concentrations of CA= 0.02 mol/L, CB=0.03 mol/L and CC=0.04 mol/L.
Find the rate of reactions of A, B and C at conditions of the reactor.
Plug Flow Reactor (PFR)
Key Characteristics• Generally a long cylindrical pipe with no moving parts (tubular reactor)• Suitable for fast reactions (good heat removal), mainly used for gas phase
systems• Concentrations vary along the length of the tube (axial direction)
0
VA
A A AdN F F r dVdt
′= − + ∫
For an ideal PFR, we assume: - constant flowrate - no variation of fluid velocity or species concentration in radial direction
We also generally assume reactor is operating at steady-state: i.e.; no variation in properties with time at any position along reactor length
General Mole Balance for Ideal PFR at Steady-State
Infinitesimally small control volume
ΔV A V VF
+ΔA VF
0A A AV V VF F r V
+Δ− + Δ =At steady state:
0
;
at 0
AA
A A
dF rdVF F V
=
= =
differential form
integral form
0
A
A
FA
AF
dFVr′
= ∫
Class exercise: Derive concentration profiles for A and B for A B with rB=-rA=kCA for a isothermal PFR at steady-state, assuming constant volumetric flowrate. At the reactor inlet, CA=CA0 and CB=0
Packed Bed Reactor (PBR)
FA0 FA
Key Characteristics• Can be thought of as PFR packed with solid particles, usually
some sort of catalyst material.• Mainly used for gas phase catalytic reaction although examples for
liquid-phase reaction are also known.• Pressure drop across the packed bed is an important consideration.• This is the reactor type used in your integrated design project.
Mole Balance for PBR
FA0 FA
Let W = Weight of the packing
Making the same assumptions as for a PFR:- no variation of fluid velocity or species concentration in radial direction- operating at steady-state
integral form
0
A
A
FA
AF
dFWr′
=′∫
0
;
at 0
AA
A A
dF rdWF F W
′=
= =
differential form
Same as PFR, but with rate (r ) specified per mass of catalyst (instead of per unit volume) and using catalyst wt (W) instead of V as the coordinate
Summary - Design Equations of Ideal Reactors
DifferentialEquation
AlgebraicEquation
IntegralEquation Remarks
Vrdt
dNj
j )(=0( )
j
j
Nj
jN
dNt
r V′
= ∫Conc. changes with time but is uniform within the reactor. Reaction rate varies with time.
Batch(well-mixed)
CSTR(well-mixed at steady-state)
0
( )j j
j
F FV
r−
=−
Conc. inside reactor is uniform. (rj) is constant. Exit conc = conc inside reactor.
PFR(steady-state flow; well-mixed radially)
jj r
dVdF
=
0( )
j
j
Fj
jF
dFV
r′
= ∫Concentration and hence reaction rates vary spatially (with length).
Human Body as a System of Reactors
MouthStomach
Small IntestineLarge
Intestine
What reactor type can we represent the various body parts with?
Food
• We can often approximate behaviour of complex reactor systems by considering combinations of these basic reactor types (batch, PFR, CSTR)
• Next step (Fogler Ch 2): Formulate design equations in terms of conversionApply to reactor sizing
Feed
Recycle from
the next zone
CSTR segment
Plug flow
segment
Recycle to
previous zone
Each reaction zone is considered as a CSTR section followed by a plug flow section. The plug flow is considered as a series of CSTR’s in series due to complex mathematical difficulties. Recycle streams show the effects of imperfect mixing.
Chan ,W., Gloor, P. E., & Hamielec, A. E., AIChE J. 39, 111 (19xx).
Marini, L., Georgakis, C., AIChE J. 30, 401 (1984).
Each reaction zone is considered as a set of interconnected three CSTR’s. Recycle flow models the effect of imperfect mixing in initiator injection point and backmixing in the reaction space. The model parameters are based on geometrical and flow dynamic of the industrial system.
V3
V2
V1
Flow from previous zone
Flow of initiator and side feed
Recycle
flow
Compartments model
Segments model
Approaches in modeling imperfect mixing in LDPE Autoclave Reactors
Monomer Feed
Initiator
Feed
Conversion (X) [Single Reaction System]
• Quantification of how far a reaction has progressed
Batch Reactors
0
0
mols of species- reactedmols of species- fedj
j j
j
jXj
F FF
=
−=
Continuous (or Flow) Reactors
0
0
mols of species- reactedmols of initial species- j
j j
j
jXj
N NN
=
−=
A + B C + D
A + B C + D
a b c db c da a a
→
→
• Defined in terms of limiting reactant
Reactants Products
Assume “A” is our limiting reactant
Design Equation in Terms of Conversion(limiting reactant A)
IDEAL DIFFERENTIAL ALGEBRAIC INTEGRAL REACTOR FORM FORM FORM
0 ( )AA A
dXN r Vdt
= − 00
AXA
AA
dXt Nr V′
=−∫
0 ( )AA A
dXF rdV
= − 00
AXA
AA
dXV Fr′
=−∫
CSTR
PFR
0 ( )( )A A
A
F XVr
=−
BATCH
These equations can be used to size reactors required to achieve a desired conversion for a single-reaction system
Levenspiel Plots (Fogler, Ch 2.4-2.5)
Octave Levenspielconsidered to be one of the founders of Chemical Reaction Engineering
Basic idea: use plot of vs. X to calculate V
0
0
PFRXA
PFRA
FV dXr
=−∫
X
)(0
A
A
rF−
][])(
[ 0CSTR
A
ACSTR X
rFV ×−
=
Plug Flow Reactor (PFR)
Continuous Stirred Tank Reactor (CSTR)
)(0
A
A
rF−
XEvaluated at X=XCSTR
XPFR
XCSTR
)(0
A
A
rF−
Class Problem
The following reaction is to be carried out isothermally in a continuous flow reactor operating at steady-state:
A → B
Compare the volumes of CSTR and PFR that are necessary to consume 90% of A (i.e. CA=0.1 CA0). The entering molar and volumetric flow rates are 5 mol/h and 0.5 L/h, respectively. The reaction rate for the reaction follows a first-order rate law:
(-rA) = kCA where, k=0.0001 s-1
For same conversion, is the CSTR volume always higher than PFR volume ?
FA0-rA
X
For most cases yes, provided that rA decreases as X increases.
See Fogler Section 2.4 (Ex. 2-2 to 2-4) for using Levenspiel plots to size reactors (PFR vs. CSTR)
The real power of Levenspiel plots is for reactor networks (reactor in series)
PFR in Series
X
FA0-rA
Let us compare two scenarios
(i) Single reactor achieving X3(ii) 3 reactors in series achieving X3
• How is the total volume of 3reactors in series related to single reactor ??
FA0
X=0FA1
X=X1
FA2
X=X2 FA3; X=X3
CSTR in Series
FA0
X=0 FA1
X=X1FA2
X=X2FA3; X=X3
FA0-rA
XWe can model a PFR as a series of
“n” equal volume CSTRs
Compare volume for the following 2 cases
(i) A single reactor achieving X3(ii) 3 reactors in series achieving X3
How is the total volume of 3 reactors in series related to single reactor ??
See Fogler 2.5.1
If you could replace one of the CSTRs with a PFR, which one would you choose to minimize the total volume of the reactor system
Closing Thoughts on Levenspiel Plots
• Levenspiel Plots are useful means to illustrate the difference between PFR and CSTR behavior– If the rate law is given in terms of conversion (-rA) = f(X) or can be
generated/derived by intermediate calculations, one can size PFR, CSTRs, and batch reactors.
– PFR can be modeled as many CSTR in series (strategy used in UNISIM design software)
• Levenspiel plots are seldom used to design ‘real world’ reactors– Restrictive conditions: no secondary side streams, single reaction– Can only be used for scale-up if reaction conditions are kept identical: i.e.;
(-rA) varies with conversion identically in the full-size reactors as in the lab
Class ProblemThe following aqueous-phase reaction is carried out isothermally in both a laboratory-scale reactor and an industrial-scale continuous stirred tank reactor:
A → B The reaction rate follows a first-order rate law:
(-rA) = kCA where, k=0.1 min-1 at 50 oC
The operating conditions of the reactors are provided below
Industrial CSTR Lab CSTR
Feed concentration 10%A in solution 2% A in solution
Reactor volume 3600 L 63 mL
Volumetric flow rate 40 L/min 0.7 mL/min
The two reactors, vastly different in scale, and with different feed concentrationsyield similar conversion. Why?
Time is of the Essence
• The extent of conversion of reactants in a chemical reactor is related to the time the chemical species spend in the reactor.
• Remember the definition: Average residence or space timeof fluid in vessel is τ = V/v0– Space time is often used as a scaling parameter in reactor design
• Residence time is chosen to achieve desired conversion (different for PFR and CSTR!), and can vary from a few seconds to several hours, depending on the rate of reaction – See Fogler Table 2.5
Reaction Rates of Some Known Systems
Slow reaction Fast Reaction(requires large residence time) (short residence time)