🔥Advanced Combustion Technologies Unit 2 – Chemical Kinetics in Combustion

Fundamentals of Chemical Kinetics

• Chemical kinetics studies the rates of chemical reactions and the factors that influence them
• Reaction rate measures the speed at which reactants are consumed or products are formed per unit time
• Stoichiometry determines the quantitative relationships between reactants and products in a balanced chemical equation
• Collision theory states that reactions occur when reactant molecules collide with sufficient energy (activation energy) and proper orientation
• Transition state theory describes the formation of an unstable intermediate species called the activated complex during the reaction
  • The activated complex is a high-energy state that exists briefly at the top of the energy barrier between reactants and products
  • The rate of a reaction depends on the concentration of the activated complex
• Molecularity refers to the number of reactant molecules that participate in an elementary reaction step
  • Unimolecular reactions involve a single reactant molecule (isomerization, decomposition)
  • Bimolecular reactions involve the collision of two reactant molecules (most common in combustion)

Reaction Rates and Rate Laws

• Reaction rate is defined as the change in concentration of a reactant or product per unit time
• Rate law expresses the relationship between the reaction rate and the concentrations of reactants
  • For a general reaction aA + bB → products, the rate law is: Rate = k[A]^m[B]^n
  • k is the rate constant, [A] and [B] are reactant concentrations, and m and n are the reaction orders
• Reaction order determines how the concentration of a reactant affects the reaction rate
  • Zero-order reactions have rates independent of reactant concentrations
  • First-order reactions have rates directly proportional to the concentration of one reactant
  • Second-order reactions have rates proportional to the square of the concentration of one reactant or the product of the concentrations of two reactants
• Integrated rate laws describe the concentration of reactants or products as a function of time
  • For a first-order reaction: ln[A]_t = -kt + ln[A]_0, where [A]_t is the concentration at time t, and [A]_0 is the initial concentration
• Half-life (t_1/2) is the time required for the reactant concentration to decrease by half in a first-order reaction
  • t_1/2 = ln(2) / k, where k is the rate constant

Temperature Dependence and Activation Energy

• Temperature significantly affects reaction rates in combustion processes
• Arrhenius equation describes the relationship between the rate constant (k) and temperature (T): k = A * e^(-E_a / RT)
  • A is the pre-exponential factor, E_a is the activation energy, and R is the universal gas constant
• Activation energy (E_a) is the minimum energy required for reactants to form the activated complex and proceed to products
  • Higher activation energies result in slower reaction rates
  • Catalysts lower the activation energy by providing an alternative reaction pathway
• Collision frequency increases with temperature, leading to more frequent collisions between reactant molecules
• Maxwell-Boltzmann distribution describes the distribution of molecular energies at a given temperature
  • As temperature increases, a larger fraction of molecules possess energy greater than the activation energy, increasing the reaction rate
• Van't Hoff equation relates the change in equilibrium constant (K) with temperature: dlnK / d(1/T) = -ΔH° / R
  • ΔH° is the standard enthalpy of reaction, and R is the universal gas constant
• Temperature can also affect the selectivity of competing reaction pathways in combustion, favoring the formation of certain products over others

Reaction Mechanisms in Combustion

• Reaction mechanisms describe the step-by-step sequence of elementary reactions that lead from reactants to products
• Elementary reactions are the individual steps in a reaction mechanism, each with its own rate law and molecularity
• Initiation steps generate reactive species (radicals) that propagate the reaction chain
  • Example: CH4 + O2 → CH3• + HO2•
• Propagation steps involve the reaction of radicals with stable molecules, producing new radicals and maintaining the chain reaction
  • Example: CH3• + O2 → CH2O + OH•
• Termination steps consume radicals, leading to the formation of stable products and the end of the chain reaction
  • Example: CH3• + CH3• → C2H6
• Rate-determining step is the slowest step in a reaction mechanism, controlling the overall rate of the reaction
• Steady-state approximation assumes that the concentration of reactive intermediates remains constant during the majority of the reaction
  • This allows the derivation of a rate law expression based on the rate-determining step
• Potential energy diagrams illustrate the energy changes along the reaction coordinate, showing the activation energies and relative stabilities of reactants, intermediates, and products

Combustion Chain Reactions

• Chain reactions are a key feature of combustion processes, involving the production and consumption of highly reactive species (radicals)
• Radical species have unpaired electrons, making them highly reactive and short-lived
  • Examples: H•, O•, OH•, CH3•, HO2•
• Chain initiation produces radicals from stable molecules, often through thermal decomposition or reaction with another radical
  • Example: H2 + M → H• + H• + M, where M is a third body that absorbs excess energy
• Chain propagation involves the reaction of radicals with stable molecules, generating new radicals and maintaining the chain
  • Example: H• + O2 → OH• + O•; O• + H2 → OH• + H•
• Chain branching reactions produce more radicals than they consume, accelerating the overall reaction rate
  • Example: H• + O2 → OH• + O•; O• + H2 → OH• + H•
• Chain termination occurs when radicals are consumed through recombination or disproportionation reactions, forming stable products
  • Example: H• + OH• + M → H2O + M
• Chain length is the average number of propagation steps occurring before termination, influencing the overall reaction rate and heat release
• Ignition delay is the time between the start of a combustion reaction and the rapid increase in temperature and pressure associated with ignition
  • Determined by the balance between chain initiation, propagation, and termination reactions

Kinetics of Fuel Oxidation

• Fuel oxidation is the primary process in combustion, involving the reaction of a fuel (hydrocarbons, hydrogen, or other species) with an oxidizer (typically oxygen)
• Hydrogen oxidation is a simple yet important reaction in combustion: 2H2 + O2 → 2H2O
  • Involves chain reactions with H•, O•, and OH• radicals
  • Highly sensitive to temperature and pressure conditions
• Methane oxidation is a key reaction in natural gas combustion: CH4 + 2O2 → CO2 + 2H2O
  • Involves a complex series of elementary reactions, including abstraction, addition, and dissociation steps
  • Produces intermediate species like CH3•, CH2O, and CO
• Higher hydrocarbon oxidation (e.g., propane, butane) involves even more complex reaction mechanisms
  • Includes the formation and oxidation of smaller hydrocarbon fragments (C2, C3 species)
  • Can lead to the formation of polycyclic aromatic hydrocarbons (PAHs) and soot under fuel-rich conditions
• Partial oxidation occurs when the fuel is not completely oxidized to CO2 and H2O, leading to the formation of CO, H2, and other products
  • Important in fuel reforming and synthesis gas production
• Negative temperature coefficient (NTC) behavior is observed in some hydrocarbon oxidation reactions, where the reaction rate decreases with increasing temperature over a certain range
  • Caused by a shift in the balance between chain-branching and chain-terminating reactions
  • Has implications for engine knock and autoignition in internal combustion engines

Modeling Combustion Kinetics

• Combustion kinetic models are used to predict the rates of chemical reactions and the formation of products in combustion processes
• Detailed kinetic mechanisms include a large number of elementary reactions and species, aiming to capture the full complexity of combustion chemistry
  • Example: GRI-Mech for methane combustion includes 53 species and 325 reactions
  • Requires significant computational resources for solving the coupled differential equations
• Reduced kinetic mechanisms are derived from detailed mechanisms by removing less important species and reactions, while maintaining the essential features of the chemistry
  • Aim to reduce computational cost while preserving accuracy
  • Example: 4-step reduced mechanism for methane oxidation
• Global reaction mechanisms lump multiple elementary steps into a single overall reaction with an empirical rate law
  • Greatly simplify the kinetic description but may not capture all the important features of the chemistry
  • Example: 1-step global reaction for methane oxidation: CH4 + 2O2 → CO2 + 2H2O
• Sensitivity analysis assesses the importance of individual reactions or species on the overall combustion process
  • Helps identify the rate-limiting steps and the most influential reactions for optimization or reduction
• Uncertainty quantification evaluates the impact of uncertainties in kinetic parameters (rate constants, thermochemical data) on the model predictions
  • Uses techniques like Monte Carlo sampling or polynomial chaos expansions
• Validation of combustion kinetic models involves comparing the model predictions with experimental data from well-characterized systems (laminar flames, shock tubes, flow reactors)
  • Assesses the accuracy and reliability of the kinetic mechanism for different operating conditions and fuel compositions

Applications in Advanced Combustion Systems

• Advanced combustion systems aim to improve efficiency, reduce emissions, and expand the fuel flexibility of combustion processes
• Low-temperature combustion (LTC) strategies, such as homogeneous charge compression ignition (HCCI) and reactivity-controlled compression ignition (RCCI), rely on the autoignition of fuel-air mixtures
  • Kinetic understanding is crucial for predicting ignition timing, heat release rate, and emissions formation
  • Requires detailed kinetic models that capture the low-temperature oxidation chemistry of fuels
• Turbulent combustion modeling couples the chemical kinetics with the turbulent flow field in practical combustion devices (engines, gas turbines, furnaces)
  • Approaches like flamelet models, conditional moment closure (CMC), and probability density function (PDF) methods incorporate kinetic information into the turbulence modeling framework
• Pollutant formation and control, such as nitrogen oxides (NOx) and soot, depend on the kinetics of specific reaction pathways
  • Thermal NOx formation is governed by the Zeldovich mechanism, which is highly sensitive to temperature
  • Prompt NOx formation involves the reaction of hydrocarbon radicals with nitrogen, and is more important in fuel-rich conditions
  • Soot formation involves the growth and coagulation of polycyclic aromatic hydrocarbons (PAHs), and is influenced by the fuel composition and local mixture stoichiometry
• Alternative fuel combustion, such as biofuels, syngas, and hydrogen-enriched fuels, requires kinetic models that capture the specific oxidation pathways and interactions of these fuels with conventional hydrocarbons
  • Kinetic understanding helps optimize fuel blends and operating conditions for improved performance and emissions
• Combustion-based power generation, such as gas turbines and reciprocating engines, relies on kinetic control of the combustion process for efficient and clean operation
  • Kinetic models inform the design and optimization of combustion chambers, fuel injection systems, and emission control strategies
• Fire safety and hazard analysis utilize combustion kinetics to predict the ignition, spread, and suppression of fires in various scenarios (buildings, transportation, wildland)
  • Kinetic models help evaluate the effectiveness of fire retardants, suppressants, and ventilation strategies