Chemical Kinetics of HC Combustion

Spark Ignition Engine Combustion MAK65E Chemical Kinetics of HC Combustion Prof.Dr. Cem Soruşbay Istanbul Technical University Chemical Kinetics of HC Combustion Introduction Elementary reactions Multi-step Mechanisms Oxidation of Hydrocarbons Oxidation of Carbon Monoxide 1

Introduction The study of the elementary reactions and their rates is a specialized field of physical chemistry called chemical kinetics Overall reaction of a mole of fuel with a mole of an oxidizer to form b moles of products can be expressed by global (overall) reaction mechanism has no physical relevance F + a Oxidizer b Products From experimental measurements the rate at which fuel is consumed can be expressed as, d[ X F ] n k m G ( T) X Fuel X Oxidizer dt where [X i ] is the molar concentration [kmol/m 3 ] in SI, [gmol/cm 3 ] in CGS k G is global rate coefficient strong function of temperature n and m are related to reaction order Introduction In real applications many sequential processes can occur involving many intermediate species example consider global reaction H + O H O elementary reactions, show what happens in a molecular level H + O HO + H H + O OH + O OH + H H O + H H + O + M HO + M H and O collide and react -do not yield water but form intermediate species HO, hydroperoxy radical and a hydogen atom Radicals (or free radicals) are reactive molecules or atoms that have unpaired electrons Collection of elementary reactions to describe overall reaction is called a reaction mechanism

Elementary Reactions Unimolecular reaction single species undergoing a rearrangement (isomerization or decomposition) A B or A B + C d[ A] k dt unimolec A For example, O O + O First order at high pressures, at low pressures reaction rate also depends on concentration of any molecule with which the reacting species may collide d [ A] dt k A M Elementary Reactions Bimolecular reaction A + B C + D d[ A] k dt bimolec A B 3

Elementary Reactions Trimolecular reaction involve three reactant species and correspond to reverse of unimolecular reaction at low pressures A + B + M C + M example, recombination reactions such as H + H + M H + M Third order reactions d[ A] kter A B M dt M is called third body representing any molecule present in the system and it removes some energy released by formation of new chemical bond, preventing the product from immediate dissociation Elementary Reaction Rates reaction rate, d[ A] no of dt collisions A and B molecules unit volume. unit time probability that.. a collision leads to reaction no of kmol of A molecules of A Second term on rhs, can be expressed as a product of two factors energy factor, exp[-e A / R u T] which expresses fraction of collisions that occur with an energy above the treshold level necessary for reaction E A (activation energy) a geometrical (steric) factor, p, that takes into account the geometry of collisions between A and B 4

Elementary Reaction Rates If the temperature range of interest is not too large, bimolecular rate coefficient can be expressed by empirical Arrhenius form, E A k( T) Aexp RuT Here A is a constant called pre-exponential factor or frequency factor, giving collision probability without effect of concentrations (depends on T 1/ ) E is activation energy, energy that the molecule must acquire before it can take part in the reaction three-parameter functional form, E A k( T) AT b exp RuT Multi-step Mechanisms The reaction mechanism - sequence of elementary reactions that lead from reactants to products For example H O reaction mechanism H + O HO + H H + O OH + O OH + H H O + H H + O + M HO + M k f, forward and k b, backward (reverse) rate coefficients 5

Multi-step Mechanisms For example the net rate of production of O is the sum of all individual elementary rates producing and destroying O d[ O] kr1[ HO ][ H ] kr[ OH][ O] kr4[ HO ][ M ] dt k [ H ][ O ] k [ H ][ O ] k [ H ][ O ][ M ] f 1 and for H atoms, f d[ H ] k f 1[ H ][ O ] kr [ OH][ O] k f 3[ OH][ H ] dt k [ HO ][ M ] k [ HO ][ H ] k [ H ][ O ] k r 4 r3 [ H O][ H ] k r1 f 4 f 4 [ H ][ O ][ M ] f H + O HO + H H + O OH + O OH + H HO + H H + O + M HO + M Multi-step Mechanisms Similar expressions can be written for each species in the mechanism which yields a system of first-order O.D.E. describing evolution of the chemical system starting from initial conditions, with d[ X i]( t) f dt i [ Xi](0) [ Xi] 0 [ X ]( t) [ X ]( t)... [ X ]( ) 1 n t The above set of eqns (together with conservation eqns for mass, momentum, energy and state eqns) can be integrated numerically using a computer. 6

Multi-step Mechanisms Stiff system equations one or more variables change rapidly while others change very slowly time scales of radical reactions (very fast) are much different than reactions involving stable species Reduction of chemical reactions assumed steady state reactions expressed in form of algebraic equations instead of time dependent Steady-State Approximations Highly reactive intermediate species (radicals) are formed in many chemical systems of interest to combustion These can be simplified by appliying steady-state approximation to reactive intermediate species, radicals After rapid initial buildup in concentration, radicals are destroyed as rapid as they are formed then forming the intermediate species is slow, destroying them is with fast reactions - as a result their concentrations are small Zeldovich mechanism is a good example 7

Steady-State Approximations Consider Zeldovich mechanism, O + N (k1) NO + N slow, hence rate limiting N + O (k) NO + O extremely fast hence net production of N atoms, d[ N] k dt [O][ N ] 1 k ][N][O ] This approaches zero, and 0 k1[ O][ N] k[ N] StedyState[ O ] k1[ O][ N] [ N] StedyState k [ O ] Steady-State Approximations Time rate of change of [N] ss can be obtained by differentiating the above eqn (as it rapidly adjusts), d[ N] StedyState dt d dt k 1[ O][ N] k [ O ] 8

Temperature Dependence of Rate Coefficients Rate coefficients depend strongly on temperature in a nonlineer way Arrhenius law E A k( T) AT b exp RuT Pressure Dependence of Rate Coefficients Consider a three-step mechanism, A + M ka A* + M activation A* + M ka A + M deactivation A* ku P Products unimolecular reaction Energy is added to the molecule by collision with other molecules M for the excitation of molecular vibrations. Then excited molecule may decompose into Products or it can deactivate through a collision Lindemann mechanism 9

Lindemann Mechanism d[p]/dt = k u [A*] d[a*]/dt = k a [A][M] - k -a [A*][M] - k u [A*] where A* is high internal energy (energised) molecule assuming concentration of A* is in steady state, d[a*]/dt = 0 [A*] = k a [A][M] / k -a [M] + k u d[p]/dt = k u k a [A][M] / k -a [M] + k u Lindemann Mechanism In low pressure range concentration of collision partner M is small, k a [M] << k u d[p]/dt = k a [A] [M] reaction is proportional to concentration of A and M because activation is slow at low pressures (rate limiting) In high pressure range M has large concentration, k -a [M] >> k u d[p]/dt = k u k a [A] / k -a = k [A] Reaction rate does not depend on concentration of M (high collision), decomposition of activated molecule A* is rate-limiting 10

Reaction Mechanisms Chain Reactions involve production of a radical species that subsequently react to produce another radical. This radical in turn reacts to produce another radical It continues until formation of a stable species from two radicals break the chain example A + B AB global reaction chain initiating reaction chain propagating reactions chain terminating reaction A + M (k1) A + A + M A + B (k) AB + B B + A (k3) AB + A A + B + M (k4) AB + M Reaction Mechanisms In early stages conc of product AB is small, A and B are also small thus reverse reaction can be neglected d[a ]/dt = -k 1 [A ][M] k 3 [A ][B] d[b ]/dt = -k [B ][A] d[ab]/dt = k [A] [B ] + k 3 [B][A ] + k 4 [A][B][M] A + M (k1) A + A + M A + B (k) AB + B B + A (k3) AB + A A + B + M (k4) AB + M For radicals A and B, steady state approximation k 1 [A ][M] k [A][B ] + k 3 [B][A ] - k 4 [A][B][M] = 0 k [A] [B ] - k 3 [B][A ] - k 4 [A][B][M] = 0 [A] and [B] obtained from ss d[a ]/dt, d[b ]/dt, d[ab]/dt calculated from initial concentrations 11

Reaction Mechanisms Chain-branching Reactions involve formation of two radical species from a reaction that consumes only one reaction. Example O + H O OH + OH Concentration of radical species build up rapidly rapid formation of products The rate of chain initiation step does not control overall reaction rate rates of radical reactions dominate. Chain branching reactions are responsible for a flame being self-propagating H + O O + OH a very important reaction laminar flame speeds are critically dependent on the rate of this reaction Reaction Mechanisms Chain-propagating Reactions have same number of radicals on both the reactant side and the product side OH + H H + HO Chain-termination (Chain-breaking) Reactions consume radicals H + OH + M HO have normally no temperature dependence, which is reflected in zero value of activation energy 1

Hydrocarbons Low temperature mechanism There is clear distinction between types of reactions that dominate overall combustion process as temperature rise from 850 K to beyond 100 K Much of low temp chemistry of HCs is governed by size and structure of carbon backbone. It is generally accepted that initial attack on saturated HCs involve abstraction of hydrogen atom to give alkyl radical and hydroperoxy radical C n H n+ + O C n H n+1 + HO Hydrocarbons In methane, CH 4 + O CH 3 + HO HO radical may attack methane CH 4 + HO CH 3 + H O or undergo a radical recombination reaction such as HO + HO H O + O or CH 3 O + HO CH 3 OOH + O The methyl radical CH3 plays important role in overall process CH3 + O + M CH3O + M 13

Hydrocarbons High temperature mechanism Free radical chain initiation processes are not normally predominant in control of events Consider the possibilities, C n H n+ + O C n H n+1 + HO, k I = 10 14 exp{-500/t} oxidation of fuel by hydrogen abstraction may yield a hydroperoxy radical (HO ) and an alkyl radical (C n H n+1 ) in which carbon backbone of the alkane remains intact C n H n+ C j H j+1 + C m H m+1, k II = 5x10 16 exp{-400/t} By contrast unimolecular decomposition of fuel may yield two new alkyl radicals as a result carbon backbone of the alkyl is severed Hydrocarbons Temperature has greatest effect on which reaction will dominate, but oxygen concentration is also important oxidation route predominate at temperatures below 1000 K and carbon backbone structure of fuel remain intact 14

Engine Fuels - Classification Liquid hydrocarbons C H n m Engine fuels are mainly mixtures of hydrocarbons, with bonds between carbon atoms and between hydrogen and carbon atoms. During combustion these bonds are broken and new bonds are formed with oxygen atoms, accompanied by the release of chemical energy. Principal products are carbon dioxide and water vapour. Fuels also contain small amounts of O, N, S, HO Alkanes Alkanes or Paraffins can in general be represented by C H n n all the carbon bonds are single bonds they are saturated high number of H atoms, high heat content and low density (60 770 kg/m 3 ) The carbon atoms can be arranged as a straight chain or as branched chain compounds. 15

Alkanes Straight chain group (normal paraffins) shorter the chain, stronger the bond not suitable for SI engines high tendancy for autoignition according to the value of n in the formula, they are in gaseous (1 to 4), liquid (5 to 15) or solid (>16) state. Branched chain compounds (isoparaffins) when four or more C atoms are in a chain molecule it is possible to form isomers they have the same chemical formula but different structures, which often leads to very different chemical properties. example : iso-octane C 8 H 18..4 trimethyl pentane Naphthenes Also called cycloparaffins C H n n saturated hydrocarbons which are arranged in a circle have stable structure and low tendancy to autoignite compared to alkanes (normal paraffins) can be used both in SI-engines and CI-engines low heat content and high density (740 790 kg / m 3 ) 16

Alkenes Also called olefins mono-olefins C H n n or dio-olefins C H n n have the same C-to-H ratio and the same general formula as naphthenes, their behavior and characteristics are entirely different they are straight or branch chain compounds with one or more double bond. The position of the double bond is indicated by the number of first C atom to which it is attached, ie, CH=CH.CH.CH.CH3 called pentene-1 CH3.CH=CH3 called butene- olefinic compounds are easily oxidized, have poor oxidation stability can be used in SI-engines, obtained by cracking of large molecules low heat content and density in the range 60 80 kg / m 3 Aromatics Aromatic hydrocarbons are so called because of their aromatic odor C H n n6 they are based on a six-membered ring having three conjugated double bonds aromatic rings can be fused together to give polynuclear aromatics, PAN, also called polycyclic aromatic hydrocarbons, PAH simplest member is benzene C H 6 6 can be used in SI-engines, to increase the resistance to knock not suitable for CI-engines due to low cetene number low heat content and high density in the range 800 850 kg / m 3 17

Aliphatic Hydrocarbons Alicyclic and Aromatic Hydrocarbons 18

Oxygenic Hydrocarbons Composition of Engine Fuels 19

Typical Boiling Curves for Gasoline and Diesel Octane Numbers Properties of Engine Fuels 0

Hydrocarbon Oxidation Process Diagram of Hydrocarbon Oxidation Process 1

Diagram of Hydrocarbon Oxidation Process Reaction diagram of alkanes both at low and high T : h abstraction from HC molecule Low Temp : R OOH formed will break down to smaller HC by oxidation and dehydration important in engine combustion Diagram of Hydrocarbon Oxidation Process High Temp : one alkane and alkyl radical formed from larger alkyl radical - produced by H abstraction

Hydrocarbon Oxidation Process To estimate T and concentration at flame front - partial equilibrium assumption due to high T Mechanism of Alkane Oxidation High temperature combustion of methane and ethane main propagating free radicals are H, O, OH, HO, CH 3 Key features are, *Mechanism of two step primary fuels are linked at interplay between CH 3 and C H 5 or C H 4 *Formaldehyde, CH O and formyl radicals, CHO are the main partially oxygenated products of C 1 and C hydrocarbon fragments Decomposition of CHO can be source of H by CHO + M CO + H + M But competitive oxidation also a major source of HO at all temps CHO + O CO + HO *Carbon monoxide, CO is end product of virtually all chain sequences 3

Oxidation of Carbon Monoxide From practical point of view it is difficult to free CO from all traces of hydrogenous material there are often traces of CH 4 in CO (in ppm) Oxidation of hydrogen or methane involve OH and HO radicals, thus if small quantities of H or CH 4 present, chain propagation and branching in CO oxidation is promoted by, CO + HO CO + OH propagation CO + OH CO + H propagation followed by H + O OH + O branching or H + O + M HO + M propagation followed by CO + O + M CO + M termination Also supplementary branching step, O + CH 4 CH 3 + OH Oxidation of Higher Paraffins C n H n+, higher paraffins n > Oxidation of paraffins can be characterized by three sequential processes *Fuel molecule attacked by O and H atoms, breaks down primarily forming olefins and hydrogen hydrogen oxidizes to water, if oxygen is available *Unsturated olefins further oxidize to CO and H essentially all of H is converted to water *CO burns out by CO + OH CO + H nearly all heat release associated with overall combustion process occurs in this step 4

Reaction Kinetics in Engine Simulation Reaction Rate Parameters Westbrook and Dryer 5

Consumption Times for an iso-octane/air System Constant global consumption times for iso-octane/air system as a function of pressure and temperature - constant pressure and temperature calculations Normalized Fuel and Total HC Mass Profiles 1450 K, atmospheric pressure in an iso-octane/air system; 1000 ppm isooctane, 9% CO, 14% HO, 4.5% CO, % H, 1% O 6