ABSTRACT
Fuel combustion processes by definition involve chemical reactions that are exothermic and relatively fast� The proper understanding or modeling of such processes needs to define what type and sequence of chemical changes take place and consider their consequent temporal changes in the composition and associated properties of the reactive system� Often, this is no simple task because complex coupled nonlinear differential equations would result with much of the key information about the mode of these reactions, their corresponding properties, and the reactive species may not be sufficiently known� It is only relatively recently, with the continuing increase in the capacity and speed of computing facilities coupled with significant advances made in the solution of complex mathematical systems and continuing progress in the science of chemistry, that much success is achieved in satisfying these objectives� This effort was prompted largely by the need to bring about substantial further improvements to the performance of fuel combustion systems to enhance efficiencies, reduce emissions, and secure greater safety and reliability while burning a wider range of fuels�
Classical thermodynamic consideration of the combustion process, as shown earlier, can yield useful information as to the total ideal amount of energy changes for the reaction and the associated final temperature of the products and their ultimate composition under ideal equilibrium conditions� However, such approaches cannot provide any indication of the rates of processes involved or the transient changes in the properties of the reactive system as it progresses toward the assumed final stage� Such information is of critical importance in practice such as in considering the transfer of energy and extent of associated emissions (Figure 6�1)�
Figure 6�2 shows a typical schematic representation of the temperature rise with time during the course of a combustion reaction process� Initially, due to the low temperature at the commencement of the reaction, there is little noticeable temperature rise for quite some time, which is usually described as the delay time� Often for convenience, this time is assumed to be represented by the time taken to produce either 5% or 10% of the
total temperature rise or of the corresponding energy release� Following this delay period, the temperature begins to increase initially slowly and later much more rapidly as a result of the exponential dependence of the reaction rate and hence the energy release rate on temperature� This rapid acceleration of the combustion reaction rate, as will be discussed later, is associated with the onset of ignition� Toward the end of the combustion process, the rise in the rate begins to slowdown, despite the prevailing high temperature levels due to the depletion of much of the reactants and the buildup of products� Under ideal and adiabatic conditions, the temperature will gradually converge toward the calculated value of the adiabatic flame temperature�
In practice, due to factors such as the inevitable heat loss to the surroundings from the high-temperature reaction zone and some possible incompleteness in the combustion reactions, the associated temperature rise, as shown in Figure 6�3, can be significantly lower than the ideal adiabatic case� Moreover, for the same reacting fuel-air mixture, the temperature rise time development is slowed down very considerably as lower initial temperatures are employed, while preheating speeds up the combustion
reactions very substantially (Figure 6�4)� For sufficiently low initial temperature values, the exponential nature of the dependence of the reaction rate and hence the associated energy release rate on absolute temperature can slowdown the temperature rise� It may even bring it to a virtual halt, thus quenching the combustion process altogether�
A variety of forms of representations may be employed to describe the rate of combustion of fuels� These may include the temporal rate of change of the consumption of the fuel, oxidant, or the appearance of the products� The rate can also be represented by the rates of change in temperature or of the associated energy release by the chemical reaction� These forms of parametric variables are readily interrelated�
Figure 6�5 shows a convenient representation of the course of the combustion process of a homogeneous fuel-air mixture, displaying the variation of the reaction rate and hence the energy release rate with the extent of completion of the reaction� This can be represented in terms of the fraction of the total temperature rise or the relative mass of fuel consumed or the corresponding fraction of the combustion products formed� It is evident that the maximum rate of energy release is encountered well below the peak temperature achieved during combustion� This is a reflection of the associated depletion of the mass of the fuel-air mixture and the buildup of products toward the later stages of the combustion reaction where high temperatures
are involved� Figures 6�6 and 6�7 show schematically the corresponding typical variations in this pattern when the initial mixture temperature and equivalence ratio values are increased�
The property that has the most influence on the overall performance of a combustion system and acceptance of a fuel is the associated combustion reaction rate, which controls key performance parameters such as the flame
speed, its size, energy release rate, and composition of exhaust products (Figure 6�8)� These in turn influence notable characteristics such as the flammability limits, combustion efficiency, and exhaust emissions, among others�
The combustion of fuel-air mixtures does not proceed via a single-step reaction where the reactants are converted directly to products� Instead, fuel combustion involves many simultaneous reaction steps where numerous transient species are generated and consumed in the course of the oxidation reaction� Among these elementary reaction steps, each has different reacting species and reaction rates� The net effect of these reactions while converting the reactants to products is to establish the key parameters of the combustion process, such as the rates of fuel and oxygen consumption, the energy release rate, and the production rates of the different reacting species, both transient unstable and those stable, which appear eventually in the exhaust gas�
Historically, a simplifying and very approximate approach to the prediction of the chemical processes of the combustion of a fuel was to consider the reaction rate on an overall global basis involving only the fuel and oxygen, while ignoring all details of the changing reaction activity of the mixture and the numerous transient and eventual product species� The results of corresponding experimental observations can then be employed to produce an optimized fitted relationship for an apparent assumed single-step overall reaction for the observed conversion rate of the fuel and air to products by combustion� The relevant fitted key kinetic data in this simplistic approach, such as the activation energy, order of the reaction, and reaction rate constants, are obtained through a best fit of the observed experimental data available�
Such a formulation for the oxidation of common fuels such as methane is described as the global reaction rate and traditionally represented as follows:
d CH
n
t k n n n e
= [ ] −d E RT/ (6�1)
where [n] is the molar concentrations, often for simplicity referred erroneously to those values of the initial mixture rather than the transient values, and k, a, b, c, and E are constants for that specific reaction� However, the actual combustion reaction activity strictly cannot be represented universally sufficiently reliable by such a relatively simplistic formulation, and these constants can vary very widely depending on the conditions under which the experimental data were obtained� For common diluents with methane, including carbon dioxide, the index c of Equation 6�1 tends to be generally much smaller than unity� Thus, the reaction rate under isothermal conditions will be little affected by the diluent addition (Figure 6�9)� It is the energy released by the reaction and the consequent temperature rise with time that will be affected very significantly by the increased presence of the diluents in the mixture� These factors are mainly responsible for bringing about the substantial reduction normally observed in the oxidation rates in combustion processes involving fuels containing diluents such as under constant pressure or volume conditions� Similarly, this is also reflected in the slow reaction rate activity of lean fuel-air mixtures, where the excess air lowers the resulting temperature and reduces the reactivity of such mixtures�
The temporal progress of the reaction and the associated kinetic ignition delay time are primarily dictated by the time required to build a sufficient pool of the highly reactive transient unstable species known as radicals, for example, OH, H, O, and HO2� The carbon in the fuel gets oxidized initially through a number of steps to carbon monoxide that does not react with the available oxygen to produce carbon dioxide very significantly during the course of the reaction until much of the hydrocarbon molecules are depleted sufficiently� Accordingly, the typical chain reaction of the oxidation of methane in air in which the carbon in the fuel, for example, goes sequentially as shown in the following equation to the ultimate final product of carbon dioxide via formaldehyde and carbon monoxide:
→→ →→ →→ →→ →→CH CH CH O HCO CO CO4 3 2 2
By employing a fairly comprehensive detailed representative scheme for the possible important elementary reaction steps in the oxidation of fuel paths such as that for the simple fuel hydrogen, as listed in Figure 6�10, the course of the oxidation reactions can be followed computationally right to the ultimate end product� This can be done for a wide range of values of initial composition, temperature, and pressure right from the initial state of reactants to eventual products� Each of the reaction rate constants for the various steps listed is known as follows:
−AT E RTBexp( / )
where A, B, and E are constants and R is the universal gas constant� The exponential dependence of the reaction rates on absolute temperature accelerates
them very rapidly as the temperature increases� The higher the value of the activation energy constant of the reaction step, E, the slower will be the rates for any temperature�
The time needed to complete the combustion process and approach nearequilibrium conditions will be reduced very appreciably with high temperatures� The concentrations of the products, eventually if sufficient time is provided, will be essentially those expected at the very high final temperatures reached�
Extensively detailed and comprehensive information can be obtained about the chemical processes in the combustion of common more complex fuels, for example n-heptane� Such kinetic modeling shows that the increased presence of a diluent such as carbon dioxide with the fuel reduces expectedly the reaction rates for the same operating conditions� It would extend the time
needed before the acceleration of the reaction rate and the onset of ignition as well as the time needed to complete the combustion to achieve essentially near-equilibrium conditions� During the course of the reaction, the concentrations of various species change very significantly before approaching their expected eventual equilibrium concentration values� This is far more representative and produces a more realistic simulation than those approaches based on the simplistic form of Equation 6�1�
It can be noted that the initiation time for fuel oxidation reaction occupies a relatively substantial part of the reaction time, because much of the early part of the ignition delay time is associated with relatively low initial temperature levels with very low concentrations of the active radicals needed to accelerate the reaction� The dominant role played by the changing mixture temperature is evident throughout, as shown in Figure 6�8, for the adiabatic oxidation of stoichiometric methane and air� It is also evident that interrupting the full course of the sequence of combustion reactions suddenly, such as through quenching some intermediate products, make them survive to the exhaust stage� For example, higher concentrations of carbon monoxide and lower concentrations of carbon dioxide than expected can appear in the final products over the whole range of concentrations of the fuel in the mixture� This is of much importance in relation to the reduction of exhaust emissions components in practical combustion systems� It reflects on the important roles played by the resulting temperature, time, and the initial composition of the reactive mixture�
The time needed for self-ignition of a homogeneous fuel-air mixture is usually logarithmically dependent on temperature� Accordingly, high temperatures are needed to effect rapid reaction to ignition and completion of fuel conversion within the available residence time in a combustor� Moreover, the time needed for ignition under isothermal conditions when they can be maintained is essentially linearly related to the equivalence ratio for lean mixtures� This time increases rapidly as leaner mixtures or increased diluents are involved�
Through a fairly comprehensive representative kinetic scheme for the oxidation of a fuel such as methane or hydrogen, the course of the oxidation reactions can be followed readily entirely computationally over a wide range of values of initial composition temperature and pressure� Figure 6�10 shows as an example of a listing of the numerous main significant reaction steps that make up the relatively simple reaction mechanism for the oxidation of hydrogen in air� Similarly, Figure 6�11 shows a schematic representation of some aspects of the complex path of converting methane to its final oxidation products during a combustion oxidation process� Many intermediate products and radicals are produced and consumed, including the possible formation of C2 and C3 compounds in small concentrations, especially with rich fuel mixtures� Figure 6�12 shows a listing of some of the main reaction steps in the oxidation of methane�
1� In an experiment, it was found that an increase in temperature of a reactive system by 50 degrees from 800 K doubled the overall reaction rate� Derive an expression for the effective activation energy of the overall reaction rate�
Answer: The rate of the given overall oxidation reaction, RR, may be assumed to
vary with temperature according to the following relationship:
where E is the effective activation energy� It was found that an increase in temperature from 800 K to 850 K increased
the value of the rate by a factor of 2, that is
2RR RR ln(RR /RR ) ln 2 0�5 ln (850/8
=
= = 00) (1/850 1/800) 0�03031 / /13600
E R
− −
+
E R
E R
/
/ =
= 9015K
2� A stoichiometric mixture contains the theoretical amount of air that will permit combustion of the fuel� However, in practice, there is no assurance that simply by providing the correct fuel to air ratio, combustion will be initiated or completed� Very briefly outline the reasons for this behavior� Indicate some of the measures that may be taken to ensure more complete combustion�
Answer: There are many possible contributory factors� These may include having too
low temperature and pressure, excessive heat loss, insufficient time for reaction, insufficient ignition energy provided, presence of too much diluent, excessive turbulence, fuel and air not thoroughly mixed, and so on� Corresponding remedial action can address such factors and correct them accordingly�
Figure 6�13 shows as an example of the calculated maximum temperature and maximum concentrations of some radicals and other species during the combustion of heated methane-air mixtures, as a function of the equivalence ratio� (The variation in scale needs to be noted�)
Much effort is normally expended in trying to achieve reliable modeling of the performance of fuel combustion systems� This is prompted largely by the need to effect active control and optimization of the variables influencing the
combustion process and achieve improvements to combustion and energy release utilization efficiencies�
For numerous combustion devices that are of much economic significance, such as furnaces, engines, and reactors, the following options for modeling considerations are usually available:
1� Thermodynamic equilibrium conditions may be assumed to apply throughout such that the products and energy release rates and associated properties are functions of the prevailing conditions and independent of time� This, as was indicated earlier, is an idealized condition that is not necessarily approached normally in most practical processes�
2� The conversion of fuel-air mixture to known products (e�g�, CO2 and H2O) is assumed to be complete and invariant, releasing the heating value of the fuel irrespective of the local operating conditions� For example,
= ×Q t M td /d HV d /df
where HV is the heating value of the fuel and dMf/dt is the rate of mass of fuel change with time representing the overall reaction rate� Again this very convenient representation is approximate, limited in its applicability, and does not provide any sufficiently realistic
information about the key features of the combustion process such as the transient composition and final products of combustion�
3� The conversion of the reacting fuel-air mixture is considered to proceed with time at varying rates, producing continuing changes in composition and varying energy release rates� This is the most realistic representation of the progress of the combustion process via its multichain reactions�
To model the reaction rate and associated temporal variations in the properties of the reacting system and hence the energy release rate, recourse to a single-or a few-step reaction representations is inadequate for modeling key details of the changes to the combustion system� Comprehensive chemical kinetic schemes are needed such as that shown for hydrogen oxidation in Figure 6�9� Often, these schemes require consideration of a very large number of reaction steps with knowledge of their corresponding kinetic data� Some reduction in the length and details of the kinetic schemes may be prudent to consider, particularly for applications involving a relatively narrow range of changes in operating variables and where high accuracy and a need for detailed information are not required� Specialized schemes have become increasingly available in recent years for most fuels depending on the corresponding ranges of temperature, pressure, equivalence ratio and diluents present, and their concentrations� Of course, validation of predicted results with an experiment is always needed�
A single reaction jth step in the many-reaction steps sequence may be represented as follows:
aA bB cC dD+ ↔ +
The net reaction rate for such a step, RRj, will be the result of a change due to the rate of the forward direction (RRjf) less than the rate of production by the backward reaction (RRj b):
RR RR RRf bj j j= –
where
and
where K, C, d, dj, and E are specific constants for each reaction step� It is to be noted that at equilibrium, for any reaction step, j, the forward
rate must be equal to the corresponding backward rate, which leads to the following:
K ( ) ( ) e ( ) ( )f –
D d dC C T K C C Tj j j/ = e b− E RTj /
This produces the definition of the equilibrium constant on a concentration basis, Kceq, as follows:
Kc C C C C
K T e C
( ) ( ) /( ) ( )= ⋅ ⋅ ⋅
= ⋅ ⋅ − jf RT
with the following relationship:
E E Hb f-=
where ΔH is the enthalpy change for the reaction� For example, the formation of oxide of nitrogen, NO, may be considered for
simplicity to be due to the net outcome of the following two simultaneous reactions:
N O NO N2 + ↔ + (6�2)
O N NO O2 + ↔ + (6�3)
Then the rate of production of NO will be given by the following:
= − + − C
t R R R R
d d
On this basis, it can be seen that the change in the concentration of any species taking part will be dependent in a complex manner on all the reaction steps of the combustion process and the associated prevailing concentrations during the course of the reaction�
Examples of some of the chemical reaction processes employed in various stages of the processing and utilization of fuels include mainly the following:
• Oxidation is the process of stripping electrons off the fuel molecule� • Reduction is the process of adding electrons to the fuel molecules� • Hydrogenation involves the increased concentration of hydrogen in
the fuel� Often this is made in the presence of suitable catalysts to target the desired products�
• Dehydrogenation reactions relate to those that remove some hydrogen from the fuel molecules, usually with the aid of catalysts to produce suitable unsaturated compounds�
• Cracking is the process of breaking up large molecules into simpler fragment species� These processes usually take place at high temperatures in the absence of air, while catalytic cracking usually takes place at correspondingly lower temperatures in the presence of catalysts�
• Pyrolysis is the thermal cracking of fuel molecules when heated in the absence of air�
• Isomerization is the process of production of isomers from compounds with the same mass and elements but having different arrangements of atoms making up the material�
• Cyclization is the production of cyclic compounds from other hydrocarbons�
• Alkylation is the production of alkyls from other compounds� • Polymerization is the process of combining two or more molecules to
form a single large molecule� • Chlorination is the process of adding chlorine to the fuel molecule�
Chemical changes in the wide variety of processes involving fuels are usually made through controlling suitably the variations in the following key parameters:
• Type and composition of reactants • Concentrations of the reactant mixture • Temperature • Time allowed for the reaction, often described as “Residence Time” • Pressure • Supply or removal of heat • The presence of suitable catalysts
1� The peak temperature measured in practice within the combustion zone of a fuel-consuming device is usually found to be less than that predicted according to the assumption of homogeneous adiabatic thermodynamic equilibrium combustion� List five major factors that would contribute to such a difference in temperature�
2� For an exothermic single-step reaction indicate whether the activation energy for the backward reaction should be numerically (a)
greater than, (b) less than, or (c) equal to the corresponding value for the forward reaction�
3� Explain why the maximum burning rate of a homogeneous fuel-air mixture is not reached at the maximum attained temperature�
4� Briefly explain why fuel-lean homogeneous fuel-air mixtures produce lower energy release rates than corresponding mixtures prepared in stoichiometric proportions�
5� Explain what an ignition delay is� Why does it occur? How is it measured in relation to combustible fuel-air mixtures?
