Download Combustion Chemistry

Combustion Chemistry
Hai Wang
University of Southern California
2013 Tsinghua-Princeton Summer School On Combustion
Course Length: 3 hrs/day
July 7 – 12, 2013
Copyright © 2013 by Hai Wang
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This material is not to be sold, reproduced or distributed without prior written permission of the owner, Hai Wang.
Background 1
http://en.wikipedia.org/wiki/File:Bunsen_burner_flame_types_.jpg
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Background 2
• Combustion usually involves the oxidation of a
(hydrocarbon CmHn) fuel to form oxidation
products. Heat is released in the process.
• For complete combustion, the global reaction
in air can be expressed as, e.g.,
– CmHn + (m+n/4) O2 + (79/21)x(m+n/4) N2 
mCO2 + (n/2) H2O + (79/21)x(m+n/4) N2 + Q
• The above equation is balanced on a molar
basis (per mole of the fuel).
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Background 3
• Actual reaction proceeds through a series of
simultaneous elementary reactions resulting
from collision of two species.
• Some of these species are molecules while
others are unstable free-radicals.
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Background 4
• Combustion chemistry involves a study
of elementary reaction processes
–Individually: fundamental reaction kinetics
–collectively: reaction mechanisms and
models
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Background 5
• The end goal is to be able to predict
– Local heat release rate
– Ignition
– Flame propagation and extinction
– Coupled chemistry and fluid mechanics in flames
– Pollutant (e.g., unburned HC, NOx and soot)
formation
– ……
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Background 4
• The lecture series
– Reviews the basic principles of thermodynamics and
statistical mechanics
– Discusses the nature of chain reaction mechanisms
– Present simple theories of elementary chemical
reactions
– Explore the application of combustion chemistry in
combustion studies
– Present several special topics in combustion chemistry
research
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Background 5
• This series of lecture is linked to those given in
the prior years
– 2012 Michael Pilling
• But it emphasizes the very fundamental
knowledge and application of the knowledge
in your work
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Thermodynamics
James Watt
Sati Carnot
James Prescott Joule
Rudolf J. E. Clausius
William Thomson Kelvin J Willard Gibbs
Hermann von Helmholtz
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Thermodynamics
• Describes the driving force of a
chemical process.
• Determines the ideal end state of a
reaction process.
• The very foundation of chemical
kinetics/combustion chemistry.
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The First Law 1
• Energy is conserved:
Q − W = U
For a working fluid in a closed system, the heat (Q) it
receives from the surrounding minus the work (W) it
performs on the surrounding is equal to the change in
its internal energy.
• Q > 0 – receive heat from the surrounding
(endothermic)
Q < 0 – give off heat to the surrounding (exothermic).
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The First Law 2
• The energy in the three forms may be
transformed from one to another without
limits – we know something is wrong here.
• Measured by J, kJ, cal or kcal.
• Internal energy is the total energy of
molecules in the working fluid – a sum of
kinetic and potential energies.
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The First Law 3
• If only boundary work is done (e.g., gas expansion)
under a constant pressure p,
the first law may be re-written as
where V is the volume, and the subscripts “1” and
“2” represent the starting and ending states.
• We define enthalpy as
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Extensive versus Intensive Properties
• Extensive: U, H, Q and W (J); V (cm3)
• Intensive: u, h, q, w (J/mol or cal/mol)
v, p, T (cm3/mol)
• Thermodynamic properties are state functions
• A state is usually defined by two independent
intensive variables – e.g., (p, T), (p, v), (h, T)
etc.
• Equation of state – ideal gas
where Ru is the universal gas constant (8.314
J/mol-K)
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Two More Intensive Properties
• Specific heats:
– Constant volume:
– Constant pressure:
• For an ideal gas, h = h(T), u = u(T) etc
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Second Law and Entropy
• The Kelvin-Planck statement:
It is impossible to construct a device that will operate in
a cycle and produce no effect other than the raising of a
weight and the exchange of heat with a single reservoir.
• Entropy
where (Q)int rev is the heat a working fluid receives
during an infinitesimal, reversible process.
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Entropy
• A measure of molecular randomness
• Ssolid < Sliquid < Sgas
• For closed system, a spontaneous process
(from 1 to 2) must have S2 – S1 ≥ 0
• That is, randomness always increase (a desk
never cleans itself, cloths never fold
themselves etc).
• S increases as T , but decreases with p
• The third law: S = 0 at 0 K.
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S(T,P)
• Apply the first law to a reversible constant T,P
(piston) process
Ideal gas law
S(T,P)
Standard-state entropy (1 atm)
Po is the standard pressure of 1 atm
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Three forms of enthalpy
•
•
•
•
Sensible – heating/cooling
Latent – melting, evaporation/condensation
Reaction – due to chemical composition change
Enthalpy of formation
– the heat released from producing 1 mole of a substance
from its elements at a constant temperature T
– the enthalpy of formation is zero for the reference
elements: graphite C(S), hydrogen H2, oxygen (O2),
nitrogen (N2), and chlorine (Cl2).
– C(S) + O2  CO2 + Q (= 393.522 kJ @298 K),
hf,298K = 393.522 kJ/mol of CO2
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Enthalpy of formation
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Enthalpy of formation varies with T
Generalize to
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Total Enthalpy
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Enthalpy of Reaction/Combustion
• Standard enthalpy of combustion
– Heat released from complete combustion of 1
mole of a fuel
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Enthalpy of Reaction/Combustion
For a generalized combustion reaction
The heat of combustion is
For a generalized chemical reaction
The heat (enthalpy) of reaction is
DH r ,T
ìï
üï
= DH r ,298 + í å n i ' éëh (T ) - h (298)ùû - å n i éëh (T ) - h (298)ùû ý
i'
i
ïî prod.
react.
ï
25þ
Chemical Equilibrium
• Compare
The first reaction gives greater heat release, but
the second reaction produces more entropy.
So, how does the reaction know when to stop?
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Chemical Equilibrium
Gibbs free energy defines the compromise
Equilibrium is found when dG/dε = 0
Equilibrium Constant
• Quantify equilibrium
• Consider the generic reaction
• Keep in mind that during an equilibration
process, reactants/products co-exist
where ni and ni’ are the number of moles of the
ith reactant and i’th product, respectively
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Equilibrium Constant
• For equilibrium at constant T & P, we have
• Mass conservation requires
Cannot be zero
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Standard Gibbs Free Energy
é
æP
g i (T , P ) = h f (T ) - Tsi (T ) = h f (T ) - T ê si ( T ) - R u ln ç
èP
ë
æPö
= h f (T ) - Tsi (T ) + R uT ln ç ÷
èP ø
Standard Gibbs free energy (T, po = 1 atm)
and then,
öù
÷ø ú
û
Back to Equilibrium Constant
Gibbs free energy of reaction
Rearrange to give
or the equlibrium constant
Note Kp is a function of temperature only
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Equilibrium Constant
The equilibrium constant may also be defined by concentrations
where
Note Kc can be a function of pressure
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About Equilibrium Constant
• Kp is a function of temperature only
• Forward/backward equilibrium constant
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About Equilibrium Constant
• Alternatively, for
• The larger the equilibrium constant, the
greater the completion of a reaction
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About Equilibrium Constant
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Adiabatic Flame Temperature
Reactants
(P, T0)
Adiabatic Reactor
(P)
Products
(P, Tad)
Adiabaticity gives
Let T0 = 298 K
i.e., heat of combustion is used entirely to raise the
temperature of the products
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Adiabatic Flame Temperature
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Adiabatic Flame Temperature
Effect of Pressure
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Equilibrium Composition
Effect of Pressure
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Thermochemical Properties
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Thermochemical Properties
The NASA Polynomials
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Thermochemical Properties
• Alex Burcat’s compilation (Elke Goos)
http://garfield.chem.elte.hu/Burcat/burcat.html
• Active tables (Ruscic)
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