Environ. Sci. Technol. 1999, 33, 3978-3992
Mechanisms of Particulate Matter Formation in Spark-Ignition Engines. 3. Model of PM Formation DAVID KAYES* AND SIMONE HOCHGREB Massachusetts Institute of Technology, 77 Massachusetts Avenue, Room 31-167, Cambridge, Massachusetts 02139
A combined experimental and modeling effort was performed in order to understand how particulate matter (PM) is formed in spark-ignition (SI) internal combustion engines. Application of the model allows quantification of the amount of PM nucleated at sites of burning liquid fuel (either droplets or pools) and in homogeneous gasphase chemical reactions. Moreover, it quantifies PM growth by condensation and absorption/adsorption of hydrocarbon (HC) vapors as well as PM reduction by oxidation both in the cylinder and in the exhaust pipe. Model parameters, fit by comparison to experimental data, show the strong dependence of PM formation on the presence of liquid fuel in the cylinder and HCs in the exhaust, temperatures in the intake port and cylinder, air/fuel ratio, and propensity of the fuel molecule to break down into soot precursors. PM emissions calculated by the 13-parameter model compare to 84 experimental data sets with an R 2 correlation coefficient of 0.81, demonstrating good correlation. The effects of individual engine, fuel, and dilution parameters on modeled PM emissions are discussed, elucidating the mechanisms causing experimentally measured trends in PM emissions as a function of the respective parameters.
Introduction The first two papers in this series (1, 2) detailed the significance of spark-ignition (SI) engines to the total urban particulate matter (PM) emissions and demonstrated that liquid fuel in the combustion chamber, combustion temperatures, and fuel type have critical roles in PM formation, while the lubricating oil and catalytic converter do not. During these experiments, PM number and mass concentrations as well as size distributions were measured in the diluted exhaust of modern 4-cylinder, port fuel injected (PFI) SI engines coupled to dynamometers and operated at a variety of steadystate conditions. Measurements of PM were made downstream of a dilution tunnel using a scanning mobility particle sizer (SMPS) from TSI Inc. Complete details of the experimental apparatus and methodology are described in the previous papers, as are more details of the experimental results (1, 2). The present paper details a model of PM formation based upon factors found to dominate (such as liquid fuel, air/fuel ratio, and combustion temperatures) but neglecting less important factors (such as the contribution of lubricating oil). Because the catalytic converter was not found to eliminate a statistically significant amount of PM (2), it is considered a less important factor in PM emissions; consequently, the present model quantifies only “engineout” particle emissions (i.e., emissions without catalytic aftertreatment). * Corresponding author phone: (617)253-3358; fax: (617)253-9453; e-mail:
[email protected]. 3978
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The aforementioned experimental results suggest the probable mechanisms of PM formation; the following is a discussion of previous research regarding these mechanisms. While experimental evidence in (1, 2) suggests that liquid fuel in the cylinder is associated with increased exhaust PM, recent research by Witze and Green corroborates the effect that liquid fuel in the cylinder can have on the formation of PM (3). In-cylinder visualization during cold starts indicates that pools of liquid fuel may be ignited by the flame passage, resulting in sooty flames. Although Witze and Green’s measurements were made at cold start conditions, the occurrence of sooty pool fires had a relatively slight dependence on coolant temperature; thus, the mechanism of soot production via liquid fuel combustion observed during the warmup may also occur in steady-state warm engine operation. PM production from in-cylinder liquid fuel is presumably associated with the following processes: (a) ignition of liquid fuel, whether in the form of droplets or pools on cylinder walls, and (b) subsequent locally fuel-rich diffusion burning. Liquid fuel can ignite when surrounding temperatures are high enough, either during flame passage or in the postflame regions, provided enough oxygen remains in the burned gas (i.e., the mixture is sufficiently lean) (4). For instance, Witze and Green observed sooty pool fires in SI engines after flame passage when oxygen concentration is low relative to that in the unburned gas, but temperatures are high (3). The model that follows assumes therefore that the formation of PM via liquid fuel combustion is related to the amount of in-cylinder liquid fuel and the likelihood that that fuel and any available oxygen will ignite into a diffusion flame. Likelihood of ignition is based upon conditions for spray ignition developed by Law (5). In addition to particles formed by heterogeneous-phase combustion, particles may also be formed by homogeneousor gas-phase combustion, in particular under rich conditions. According to the Edelman expression, which models soot formation in well-stirred toluene combustion and is discussed in the Model section of the present paper, the rate of homogeneous-phase soot production is approximately proportional to the square of HC concentration (6). However, experimentally measured PM concentrations are higher at both rich and lean conditions than at stoichiometric (1, 2), suggesting that homogeneous-phase combustion does not influence PM emissions alone. Both homogeneous- and heterogeneous-phase combustion are examined in the Model section. Once particles nucleate, they can undergo growth and/or diminution. HC vapors can bond either physically or chemically to the surface of the particles and thereby increase the particle size and mass. Plee and MacDonald (7) have used the Langmuir (8) adsorption concept to treat physical and chemical bonding in the case of diesel exhaust, although it is only strictly valid where the vapor present does not overwhelm the amount of adsorption sites available on particulate surfaces. Thus, the accepted model of growth is valid only on the condition that the layer of HC adsorbate be of molecular width, a condition that may not be true for either diesel or SI engine exhaust. For instance, chemical analysis of PM from SI engines indicates that 38-75% of the PM mass comes from organic carbon as opposed to 4-37% from the soot or elemental carbon that makes up the nucleus (9), requiring the layer of adsorbed material on the particles of the size found in SI engine exhaust (10) to be on the order of 100 molecular diameters thick, i.e., vapor has to stick to 10.1021/es981101o CCC: $18.00
1999 American Chemical Society Published on Web 10/14/1999
previously adsorbed or absorbed vapor. Moreover, although Plee and MacDonald do not rigorously model absorption, they and MacDonald et al. estimate that as much as about 35% of their diesel-derived particle mass is extractable (or adsorbed/absorbed) material (7, 11, 12), which would require a layer of adsorbed/absorbed material on diesel PM as large as 50 molecular diameters thick. Rather, adsorption may account for the first layer of trapped vapors, after which vapor absorption on previously adsorbed material dominates the particle growth. Their calculation that such a large fraction of mass comes from so-called “adsorbed” material suggests that their model may inadvertently account for absorption as well as adsorption. Nonetheless, to be strictly accurate, the present model expands the Langmuir adsorption concept to include the possibility of absorptionswhen HC vapors stick to the vapor already adhering to particle surfaces. Oxidation causes particles to diminish in size, but to date, there has been no model specific to the oxidation of PM generated by SI engines. Although the widely used Nagle and Strickland-Constable model of soot oxidation (13) is applicable to soot over a broad range of temperatures (14), its applicability to SI engine-derived particles is questionable because they consist of as little as 4% soot by mass (9). The present model uses a general expression based on the variables used in the Nagle and Strickland-Constable model: an Arrhenius expression with values of the parameters such as the activation energy calculated by comparison to experimental data, as will be discussed shortly. The objectives of the present work are to formulate a model of PM emissions and to compare it to experimentally measured PM concentrations with the purpose of understanding which are the important mechanisms in the PM emission process. The model incorporates the two types of nucleation (homogeneous- and heterogeneous-phase reactions), the three growth mechanisms (condensation, adsorption, and absorption), and oxidation. All submodels are based upon models of soot formation, growth, and oxidation found in the literature and summarized above.
Experimental Conditions Following presentation of the model is a comparison of its calculations to PM emissions measured in a matrix of tests, which is described in refs 1 and 2) and is centered about the baseline operating conditions of 2000 rpm, 4 × 105 dyn/cm2 (0.4 bar absolute) intake manifold air pressure (IMAP), fuel/ air equivalence ratio of φ ) 1.0 (stoichiometric), closed valve fuel injection, minimum spark advance for maximum brake torque (MBT), 87 °C coolant and oil temperatures, no exhaust gas recirculation (EGR), and an exhaust dilution ratio, Λ (defined as the ratio of mass flow rates of diluted exhaust to undiluted exhaust), of 15:1. The baseline fuel is indolene, a research gasoline with low sulfur content. Comparison is made between model results and 84 experimental conditions presented in the preceeding papers in this series (1, 2), all conditions except for the experiments to measure the effect of lubricating oil and the catalytic converter: the present model is not capable of explaining particle dynamics within the catalyst nor does it attempt to explain the effect of oil composition on PM formation, as indicated in the Introduction. The model relies upon some inputs regarding the geometry of the engine used [in particular, for use in an engine-simulation program to calculate peak cylinder temperature and pressure (15)]; parameters used in the present research are those of the Ford Zetec engine described in ref 1. The geometry of the Saturn engine, also used for experimental measurements, is quite similar: both are 1.92.0 L, PFI, SI engines with 4-valves per cylinder, pent-roof chambers, and compression ratios of 9.5-9.6.
Model A physically based model has been formulated to characterize mechanisms leading to measured PM emissionsshomogeneous and heterogeneous nucleation mechanisms (plus other nucleation mechanisms that are negligible by comparison, as will be discussed), oxidation, and growth via condensation, adsorption, and absorption. The model takes into account only particulate mass due to the complexity of modeling the effects of coagulation on PM number concentration and size. The basic structure of the model is the following. The total measured PM mass concentration is the mass of PM nucleated via the homogeneous and heterogeneous mechanisms minus the mass oxidized both in the cylinder and in the port plus the mass added by the condensation, adsorption, and absorption mechanisms (all expressed per unit volume). The upcoming section describes each part of the model and derives a formula for the PM nucleated, oxidized, or added in each submodel; afterward, coefficients involved in the model are evaluated by comparison to experimental data. Nucleation. Homogeneous (Gas-Phase) Nucleation Mechanism. Experiments using a well-stirred spherical combustor suggest the so-called Edelman expression for soot formation during toluene combustion (6):
(
)
d[See] Ta,gp ) AeeT a[HC]b[O2]c exp dt T
(1)
where d[See]/dt is the rate of change of soot mass concentration due to formation (in g cm-3 s-1), with subscript ee referring to the Edelman expression; Aee ) 4.7 × 1014 (cgs units); T is the gas temperature (in K); [HC] is the hydrocarbon concentration (in mol/cm3); [O2] is the oxygen concentration (in mol/cm3); Ta,gp is the activation temperature ) 16 110 K; a ) -1.94; b ) 1.81; and c ) -0.50. The use of an expression derived for a well-stirred reactor in the context of the premixed homogeneous-phase combustion within the SI engine cylinder does not necessitate that the model be modified to account for the difference between the engine and reactor geometries. However, differences in fuel types necessitate modifications to the expression. The Edelman expression was derived for prevaporized toluene combustion in air, while the present model concerns combustion of a variety of fuels. Hence, to apply Edelman expression, the present model assumes that only precursors of sootsaromatic species and acetylenesformed by partial oxidation of fuel can nucleate particles, even if the fuel is toluene (when the fuel is toluene, this alteration results in
