Article pubs.acs.org/EF
Soot Oxidation by OH: Theory Development, Model, and Experimental Validation Hossein Ghiassi,† David Lignell,‡ and JoAnn S. Lighty*,† †
Department of Chemical Engineering, University of Utah, 50 South Central Campus Drive, Salt Lake City, Utah 84112, United States ‡ Department of Chemical Engineering, Brigham Young University, Provo, Utah 84602, United States S Supporting Information *
ABSTRACT: Soot oxidation by OH has been represented by an equation developed by Neoh that includes the efficiency of OH radicals to react, the collision efficiency. The focus of this study is the theoretical development of the collision efficiency, enabling a more accurate prediction of soot oxidation where OH is the principle oxidizer. In addition to the traditional parameters, such as OH concentration and temperature, this approach aims to improve the prediction of soot oxidation by considering the fraction of the active area as well as the size of the soot particle and aggregate. The fraction of the active area was correlated with the type of C−H bond on the surface of particles and the concentration of H radicals that causes hydrogen abstraction from C−H bonds to create radical sites. The model was validated using experimental data for various fuels and two burner configurations.
1. INTRODUCTION Soot oxidation and formation are tightly coupled in real combustion systems.1,2 This coupling creates difficulty in isolating oxidation from other processes. Sometimes, fragmentation can also add complexity.3−5 In addition, distinguishing between oxidation by O2 and other oxidizers, such as OH and O, is complex. Soot oxidation by O2 has been studied6−12 with the most widely recognized correlation given by Nagle and StricklandConstable (NSC).13 OH becomes the principle oxidizer14−18 under flame conditions. Fenimore and Jones16 showed that, under slightly fuel-rich conditions, where the O2 concentration was very low, soot oxidation was due to OH radicals. Their observations led to the conclusion that an average of 10% of OH collisions removed carbon atoms from the surface of a soot particle. Neoh et al.15 studied soot oxidation in a two-stage burner, where soot was formed in the first burner and then was oxidized in the secondary burner. A collision efficiency of 0.27 was reported when using an apparent optical diameter for the soot aggregates. Using transmission electron microscopy (TEM) to determine the actual particle size, a collision efficiency of 0.13 was reported. They suggested that the actual value of the OH collision efficiency would be between these two limiting values. Garo et al.19 studied the oxidation of soot in a methane−air laminar diffusion flame by characterizing soot particles using laser light scattering and extinction measurements. Their results showed that soot oxidation required an OH collision efficiency ranging from 0.012 to 0.099. Puri et al.20 also studied soot oxidation with OH radicals in a diffusion flame burning methane, methane/butane, and methane/1-butene in air at atmospheric pressure, using TEM to measure soot particle size distributions. They found the following ranges of collision efficiency for several flames: 0.03−0.12 for methane, 0.044−0.14 for methane/butane, and 0.13−0.65 for methane/1-butene. They concluded that changes in particle reactivity with time might affect the value of collision efficiency. Roth et al.18 studied oxidation of soot particles suspended in different gas mixtures © XXXX American Chemical Society
behind reflected shock waves in the temperature range of 1250− 3500 K. Soot properties during oxidation were determined by a laser system with light extinction. The collision efficiency of soot surface oxidation by OH radicals showed large scatter, ranging from 0.1 to more than 0.3. Haudiquert et al.21 determined the OH collision efficiency of soot oxidation in an ethylene laminar diffusion flame. Laser-induced fluorescence measurements were used for OH determination, and the soot volume fraction was measured by extinction at 531 nm. Collision efficiencies ranged between 0.01 and 0.11. Their results showed that, as the soot volume fraction decreased, collision efficiency decreased. The authors attributed this observation to a reduction in the number of active sites with an increasing extent of oxidation. Kim et al.22 studied soot surface growth and oxidation in acetylene-fueled laminar jet diffusion flames burning in air at pressures of 0.1−1.0 atm. The collision efficiencies of OH for soot surface oxidation showed some degree of scattering at different heights above the burner (HABs), with the minimum of 0.04 and maximum of 0.4 for atmospheric pressure. A number of studies investigated the reactivity of soot particles based on the type and strengths of C−H bonds in the peripheries of polycyclic aromatic hydrocarbon (PAH) molecules,23 the size of particles,24,25 and, more recently, the nanostructure and structural rearrangement of the soot surface.10,26−28 These observations suggest that there are a number of parameters that play a role in soot oxidation. The goal of this study is to formulate the collision efficiency in terms of these parameters to improve the soot oxidation rate in Neoh’s model. Special Issue: In Honor of Professor Brian Haynes on the Occasion of His 65th Birthday Received: September 1, 2016 Revised: November 11, 2016
A
DOI: 10.1021/acs.energyfuels.6b02193 Energy Fuels XXXX, XXX, XXX−XXX
Article
Energy & Fuels
2. THEORY
⎛ mol ⎞ ⎟ = q⎜ ⎝ s ⎠
Soot oxidation by OH takes place on active sites on the surface. This is an assumption made in most studies through the collision efficiency. Reactive sites are assumed to be radical sites formed by abstraction of hydrogen atoms from C−H bonds located in the peripheries of PAH molecules on the surface of a particle.23,29 The initial step to determine the area occupied by active sites on the surface of a soot particle is to calculate the diffusive molar flow rate of the oxidizing reactant toward the surface of the particle. It is assumed that active sites are uniformly distributed over the soot particle. If only a few widely separated active sites are located on the surface of a particle, then the diffusive molar flow rate of the oxidizer would be almost linearly proportional to the number of active sites. However, as the number of active sites increases, they start interfering with each other. The particular aspect of the problem is to handle the diffusive interference between individual active sites. The reaction of an active site affects the reaction of neighboring active sites because the concentration of the oxidizing reactant is reduced in its vicinity. Although Monte Carlo modeling has been used to resolve the kinetics of active site oxidation, for example, with O2,30 we approach the problem by offering a solution in two steps. First, obtain the diffusive molar flow rate of an oxidizing reactant toward a sphere-like soot particle of radius R, where the surface is covered entirely with active sites. Second, using the results from the first step, develop a new expression for a sphere-like soot particle covered partially with reactive sites. We begin our analysis using some relevant features of diffusive transport. The steady-state form of Fick’s second law is used for an oxidizing reactant moving toward the surface of a soot particle with a radius R in a flame environment. A complete description of Fick’s second law can be found in Taylor and Krishna’s book.31 The equation is simplified on the basis of several assumptions: steady state, negligible pressure diffusion and thermal diffusion (Soret effect),32 body forces acting equally on all species, the concentration of oxidizers at a certain height above the burner being uniformly distributed, the diffusion coefficient being constant in the vicinity of a soot particle, and convection being negligible (low Reynolds number of ∼10−4). This is illustrated by the following equation:
D∇2 C = 0
at r = R ,
(3)
C = C∞
C=−
C=0
(4) (5)
ϑ1 =
The second boundary condition is based on the assumption that the whole surface of the soot particle is perfectly reactive, and as soon as an oxidizer molecule hits the surface, the reaction happens immediately and its concentration becomes zero. Applying the boundary conditions, the concentration profile becomes ⎛ R⎞ C = C∞⎜1 − ⎟ ⎝ r⎠
∂C ∂r
= k′C|r = R
(9)
r=R
ϑ1 + C∞ r
(10)
The second boundary condition (eq 9) can be used to determine ϑ1. Taking the derivative of eq 10, evaluating this at r = R, and then inserting it into the left-hand side of eq 9 and also evaluating eq 10 at r = R, substituting it into the right-hand side of eq 9 for C|r = R, and finally rearranging for ϑ1 gives
and on the surface of the particle.
at r = R ,
4πR2D
The parameter k′ is the association constant. If k′ = 0, the whole surface is perfectly non-reactive, and if k′ → ∞, the whole surface is perfectly reactive (diffusion-limited case).34 The boundary condition far from the particle remains the same as eq 4. Using this boundary condition (ϑ2 = C∞), eq 3 becomes
(2)
where ϑ1 and ϑ2 are constants of the integration. Two boundary conditions are needed to solve this equation: The oxidizing reactant concentration C at position r, far from the sphere, is maintained at the constant value C∞ at r = ∞ ,
(8)
When nanometer size particles are modeled, it is typical to use a continuum regime expression together with a transition regime correction factor. The parameter ξ in eq 8 is the correction factor introduced to account for non-continuum effects (see Supporting Information). The parameter k in eq 8 is defined as the association constant, and its value determines the extent of diffusion control.34 As discussed, qmax can be reached when a particle is perfectly reactive. In reality, the entire surface is not fully reactive, and reactive sites occupy only a portion of the particle surface. We assume N active sites are randomly distributed on the surface of a spherical particle of radius R. We need to calculate the actual diffusive molar rate of the oxidizer that will ultimately react with these N active sites. The simplest assumption is that the diffusive molar flow rate is proportional to the number of active sites. However, this assumption becomes less satisfying when there is diffusive interference between individual active sites. Thus, the effect of interactions between active sites needs to be considered. This complexity is similar to the classical problem in biology in which ligands bind to a spherical cell containing localized receptors uniformly distributed on its surface. The concept has been widely used to explain the theory of chemisorption.35 A number of solutions to this problem were given in previous studies.34−36 Another solution to this problem can be found by applying a new set of boundary conditions to recalculate the unknowns of eq 2.37 The boundary condition on the surface of the particle can be rewritten by replacing the entirely reactive boundary condition (eq 5) by the partially reactive boundary condition, also called the Robin boundary condition.38
The general solution for eq 2 is
ϑ1 + ϑ2 r
(7)
qmax (mol/s) = ξ 4πRDC∞ = kC∞
For spherical coordinates with diffusion in the r direction, eq 1 becomes
C=−
⎡ ∂C ⎤ D⎢ ⎥ ds ⎣ ∂r ⎦r = R
When we take the derivative of eq 6, evaluate this at r = R, and then use this in eq 7, the diffusive molar flow rate of oxidizing species can be calculated. This is the maximum flow rate (qmax), and it is determined by assuming that the surface of a particle is entirely covered with reactive sites; thus, a particle behaves like a spherical sink. qmax for a particle of radius R is
(1)
1 d ⎛⎜ 2 dC ⎞⎟ r =0 r 2 dr ⎝ dr ⎠
∮
k′C∞ 4πD + k′/R
(11)
Using this expression for ϑ1 in eq 10, the concentration profile is
⎛ k′ C = C∞⎜⎜ − ⎝ 4πD +
(6)
k′ R
⎞ 1 + 1⎟⎟ r ⎠
(12)
To calculate the diffusive molar flow rate of the oxidizer toward a partially reactive surface, we need to take the derivative of eq 7 with respect to r, evaluate this at r = R, then substitute it into eq 12, below, for [∂C/∂r]r = R. Simultaneously applying the correction factor (ξ) and calculating the integral gives the diffusive molar flow rate.
Because the molar diffusive flux of the oxidizer is given by Fick’s law (J (mol m−2 s−1) = −D[∂C/∂r]),33 the steady-state molar flow rate, q (mol/s), at the surface at r = R can be determined by integrating the flux over the surface area. B
DOI: 10.1021/acs.energyfuels.6b02193 Energy Fuels XXXX, XXX, XXX−XXX
Article
Energy & Fuels q′ =
∮
⎡ ∂C ⎤ 4πDk′C∞ D⎢ ⎥ ds = ξ k′ ⎣ ∂r ⎦r = R 4πD + R
(13)
To determine k′ as the association constant, active sites are assumed to be hemisphere sites of radius a. The radius of the active site is much smaller than the radius of the main particle, such that its surroundings are locally flat. The diffusive flow rate toward the single active site on the surface of a particle becomes35
q″ = ξ 2πaDC∞ = k″C∞
(14)
In this case, k″ is the association constant of a single active site in the form of a hemisphere located on the surface of a particle and its value is ξ2πaD. Then, it can be concluded that k′ is proportional to the total number of active sites.34
k′ = k″N = ξ 2πaDN
Figure 1. Variation in C−H bonds in PAH molecules with corresponding bond dissociation energies at 298 K and equilibrium constants at T = 1880 K adopted from ref 23. For methylene and methyl groups, the C−H bond dissociation enthalpies for the removal of first and second hydrogens are given. It was assumed that the third hydrogen of a methyl group remained.
(15)
Replacing k′ in eq 15 with this expression gives
q′ = ξ 4πRDC∞
Naξ 2R + Naξ
groups, with the formation of radical sites from ethynyl groups slower than that of methynyl groups. As a result, the population of radical sites strongly depends upon the type of C−H bonds that constitute the surface of the particles. The radical formation by hydrogen loss can be shown in the form of reaction 19, which primarily represents the abstraction process, with A being a PAH molecule on the surface of a soot particle.
(16)
This is the diffusive molar flow rate of the oxidizer toward a particle with N active sites. The maximum possible diffusive molar flow rate of the oxidizing reactant toward the surface of a particle was calculated and given in eq 8, qmax = ξ4πRDC∞. The fraction q′/qmax shows the ratio of the molecular flow to the maximum possible molecular flow. In other words, the fraction of successful collisions to all possible collisions on the surface of the particle, which implies the definition of collision efficiency Γ, is shown by simplifying eq 16.
aNξ Γ= 2R + aNξ
A + H ↔ A* + H 2
In the general molecular case in which the PAH species might have a high molecular weight, more than one hydrogen atom may be lost and the reaction can be extended. The results provided by Chen et al.39 and further analysis by Howard23 showed that the cleavage of an aryl C−H bond in a PAH structure will have negligible energy changes in the remaining C−H bonds. Thus, the enthalpy change is approximately constant for consecutive hydrogen losses. With the assumption that the whole surface of soot particles is covered with C−H bonds, the fraction of hydrogen loss can be taken as representative of the fraction of the active area. While this may not represent all scenarios, the fraction of radicals created by H abstraction of C−H bonds of type i has been formulated by Howard as follows:
(17)
The fraction of the active area is the ratio of the total active surface area to the particle surface area, simply defined as χ = N2πa2/4πR2. Using this definition in eq 17, Γ can be derived in terms of ξ, χ, and R. Γ=
Rξχ Rξχ + a
(19)
(18)
Equation 18 shows that the collision efficiency depends upon the size of an active site (a), soot particle radius (R), and fraction of the active area (χ). The fraction of the active area cannot be directly measured in the lab. However, it is well-known that long exposure to high temperatures may cause dehydrogenation and cross-linking that results in reduced soot reactivity, implying the importance of the presence of C−H bonds. Recently, Edwards et al.29 theoretically explored the elementary reaction pathways of the oxidation of C−H bonds by OH. They showed that OH attack on benzene and a benzene−phenol complex did not produce pathways that lead to substantial CO expulsion. The only promising pathway leading to substantial CO elimination was the OH attack on the radicals. The idea of radical sites as active sites has also been considered in earlier work.23 Hydrogen abstraction (H abstraction) from PAH molecules is considered to be the major process to produce radical sites. H abstraction may occur by several mechanisms, such as addition−elimination, abstraction, displacement, and pyrolysis. However, H abstraction by radicals is the dominant mechanism. Accordingly, the concentration of gas-phase radicals, such as H, OH, and O, becomes important, with H the most important, for two reasons. First, the concentration of H atom is often the highest. Second, its reactivity toward aromatics is substantial; as a result of its small mass, it hits the surface of soot particles with the highest collision frequency compared to other radicals. The formation of active sites through H abstraction couples homoand heterogeneous combustion chemistry. Howard23 showed that the C−H bonds on the surface of soot particles may be present in different structures, including six-membered rings, five-membered rings, and aliphatic groups, as illustrated in Figure 1. Differences between dissociation enthalpies affect the rate of hydrogen loss and, subsequently, radical formation. The calculated equilibrium constants vary significantly from ethynyl groups to methylene
χi =
K i[H]/[H 2] 1 + K i[H]/[H 2]
⎛ ΔGi ⎞ ⎟ K i = exp⎜− ⎝ RT ⎠
(20)
(21)
Table 1. Distribution of C−H Bond Types for Some PAH
C
DOI: 10.1021/acs.energyfuels.6b02193 Energy Fuels XXXX, XXX, XXX−XXX
a
9.109 × 10 17.3
8.204 × 10 19.9
D
5.503 × 10
16.4
1461 1.22 × 10−3 8.08 × 10−4 2.65 × 10−3 5.71 × 10−3
The data are reported versus HAB.
0.48
0.46 6.7
6.9
7.3
1463 1.47 × 10−3 1.12 × 10−3 3.09 × 10−3 7.01 × 10−3
8.32 × 10
0.44
3.41 × 10 7.3
1.40 × 10
1470 1.60 × 10−3 1.25 × 10−3 3.26 × 10−3 7.59 × 10−3
−3
1472 1.66 × 10
−3
0.42
−3
0.40
−3
7.7 1.588 × 10
−3
4.046 × 10
−3
1.252 × 10
−2
12.1
9.0
9.4
1452 1.647 × 10−3 1.323 × 10−3 3.339 × 10−3 7.910 × 10−3 1474 1.534 × 10−3 1.189 × 10−3 3.174 × 10−3 7.300 × 10−3
9.5
1460 1.660 × 10−3 1.484 × 10−3 3.489 × 10−3 8.809 × 10−3
1468 1.585 × 10−3 1.624 × 10−3 3.660 × 10−3 1.012 × 10−2 10.3
1476 1.406 × 10
−3
1484 7.351 × 10−4 1.180 × 10−3 5.054 × 10−3 1.777 × 10−2 13.1
1.034 × 10
1475 1.62 × 10−3 1.57 × 10−3 3.56 × 10−3 9.39 × 10−3
8.948 × 10
0.38
1494 3.777 × 10
1487 1.320 × 10−4 4.449 × 10−4 6.808 × 10−3 2.882 × 10−2 14.4
18.4
−2
1482 1.53 × 10−3 1.64 × 10−3 3.81 × 10−3 1.11 × 10−2 10.6
2.25 × 10
−2
0.36
5.86 × 10
−6
1491 2.515 × 10−5 7.646 × 10−5 8.639 × 10−3 4.277 × 10−2 15.4
8.21 × 10
−6
1488 1.13 × 10−3 1.44 × 10−3 4.44 × 10−3 1.46 × 10−2 16.5
−2
1493 3.21 × 10
−3
0.34
−4
0.32
−4
1492 4.143 × 10−7 9.994 × 10−7 1.195 × 10−2 6.471 × 10−2 17.0
1.626 × 10
1484 5.92 × 10−5 1.98 × 10−4 7.74 × 10−3 3.58 × 10−2 19.9
5.664 × 10
0.30
1499 3.262 × 10 1508 4.543 × 10−8 1.087 × 10−7 1.347 × 10−2 7.212 × 10−2 17.8
26.0
−2
1504 1.01 × 10−5 2.66 × 10−5 9.50 × 10−3 4.92 × 10−2 22.4
6.87 × 10
−2
0.28
1.27 × 10
−9
1507 1.077 × 10−8 2.249 × 10−8 1.490 × 10−2 7.772 × 10−2 18.3
3.23 × 10
−9
1506 1.29 × 10−6 3.00 × 10−6 1.12 × 10−2 6.02 × 10−2 23.7
−2
1496 1.30 × 10
−2
0.26
−7
0.24
−7
1506 1.102 × 10−9 1.623 × 10−9 1.753 × 10−2 8.533 × 10−2 17.3
2.093 × 10
1521 2.66 × 10−8 6.17 × 10−8 1.42 × 10−2 7.50 × 10−2 27.7
3.741 × 10
0.22
1507 3.907 × 10 1506 3.777 × 10−10 4.779 × 10−10 1.873 × 10−2 8.783 × 10−2 17.7
24.8
−2
1512 6.43 × 10−9 1.26 × 10−8 1.56 × 10−2 8.00 × 10−2 29.6
8.67 × 10
−2
0.20
1.81 × 10
−11
1509 1.256 × 10−10 1.363 × 10−10 1.987 × 10−2 8.971 × 10−2 17.1
8.60 × 10
−11
1525 1.95 × 10−9 3.15 × 10−9 1.69 × 10−2 8.38 × 10−2 25.8
−2
1530 6.31 × 10
−2
0.18
−10
0.16
−10
1520 1.099 × 10−11 1.164 × 10−11 2.193 × 10−2 9.211 × 10−2 19.1
1526 2.01 × 10−10 2.30 × 10−10 1.93 × 10−2 8.89 × 10−2 26.3
20.9
0.14
9.326 × 10
1523 2.619 × 10−12 6.803 × 10−12 2.286 × 10−2 9.283 × 10−2 19.8
2.359 × 10
1529 6.33 × 10−11 6.18 × 10−11 2.04 × 10−2 9.05 × 10−2 25.7
7.983 × 10
0.12
1448 5.891 × 10 1497 1.348 × 10−12 6.909 × 10−12 2.319 × 10−2 9.304 × 10−2 19.0
27.7
−2
1545 1.93 × 10−11 1.81 × 10−11 2.14 × 10−2 9.17 × 10−2 27.9
9.30 × 10
−2
0.10
2.31 × 10
−12
1494 9.685 × 10−13 7.446 × 10−12 2.339 × 10−2 9.315 × 10−2 20.2
6.75 × 10
−13
1530 5.29 × 10−12 7.73 × 10−12 2.24 × 10−2 9.25 × 10−2 31.2
−2
1488 1.46 × 10
−2
0.08
−12
0.06
−12
1390 2.097 × 10−13 8.521 × 10−12 2.379 × 10−2 9.337 × 10−2 22.8
1476 8.47 × 10−13 7.62 × 10−12 2.35 × 10−2 9.32 × 10−2 31.0
0.04
H2 (atm)
O2 (atm)
7.237 × 10
−11
1.863 × 10
−2
1.325 × 10
−1
1.075 × 10
−7
1.388 × 10
−2
1.264 × 10
−1
1.127 × 10
−4
5.116 × 10
−3
9.922 × 10
−2
3.225 × 10
−4
7.521 × 10
−4
7.704 × 10
−2
1.201 × 10
−4
3.253 × 10
−4
7.272 × 10
−2
1511 1.182 × 10−3 4.255 × 10−5 1.716 × 10−4 7.191 × 10−2
1510 1.254 × 10−3 5.472 × 10−5 2.010 × 10−4 7.202 × 10−2
1513 1.318 × 10−3 7.090 × 10−5 2.358 × 10−4 7.217 × 10−2
1518 1.371 × 10−3 9.220 × 10−5 2.768 × 10−4 7.239 × 10−2
1515 1.410 × 10
−3
1527 1.416 × 10−3 1.571 × 10−4 3.838 × 10−4 7.322 × 10−2
1529 1.380 × 10−3 2.058 × 10−4 4.592 × 10−4 7.401 × 10−2
1525 1.327 × 10−3 2.631 × 10−4 5.679 × 10−4 7.521 × 10−2
1526 1.221 × 10
−3
1532 1.046 × 10−3 3.662 × 10−4 1.105 × 10−3 7.982 × 10−2
1537 8.000 × 10−4 3.643 × 10−4 1.786 × 10−3 8.398 × 10−2
1537 4.764 × 10−4 2.732 × 10−4 3.034 × 10−3 9.012 × 10−2
1541 1.717 × 10
−4
1546 4.608 × 10−5 3.497 × 10−5 7.383 × 10−3 1.083 × 10−1
1547 7.708 × 10−6 7.068 × 10−6 9.646 × 10−3 1.160 × 10−1
1558 7.689 × 10−7 1.024 × 10−6 1.182 × 10−2 1.220 × 10−1
1564 5.167 × 10
−8
1565 1.612 × 10−9 4.909 × 10−9 1.578 × 10−2 1.294 × 10−1
1571 1.176 × 10−9 3.584 × 10−9 1.638 × 10−2 1.301 × 10−1
1563 7.402 × 10−10 2.259 × 10−9 1.699 × 10−2 1.309 × 10−1
1544 3.044 × 10−10 9.330 × 10−10 1.760 × 10−2 1.316 × 10−1
1509 2.218 × 10
−11
1432 8.311 × 10−13 2.291 × 10−12 2.035 × 10−2 1.336 × 10−1
1295 5.633 × 10−13 2.044 × 10−12 2.196 × 10−2 1.344 × 10−1
1164 4.623 × 10−13 3.034 × 10−12 2.291 × 10−2 1.212 × 10−1
H (atm)
ethylene ⌀1 = 1.98, ⌀overall = 0.9, and v (cm/s) = 3.77
O2 (atm) D (nm) T (K) OH (atm)
1265 7.694 × 10−13 2.921 × 10−11 2.455 × 10−2 9.369 × 10−2 19.7
H2 (atm)
1393 2.31 × 10−13 8.49 × 10−12 2.38 × 10−2 9.34 × 10−2 29.5
H (atm)
0.02
O2 (atm) D (nm) T (K) OH (atm) 1072 7.694 × 10−13 2.192 × 10−11 1.459 × 10−2 9.563 × 10−2 19.4
H2 (atm)
1004 7.69 × 10−13 2.92 × 10−11 2.46 × 10−2 9.37 × 10−2 30.9
H (atm)
60% n-butanol/40% n-dodecane ⌀1 = 2.2, ⌀overall = 1.1, and v (cm/s) = 3.5
0.00
HAB (cm) T (K) OH (atm)
30% n-butanol/70% n-dodecane ⌀1 = 2.2, ⌀overall = 1.1, and v (cm/s) = 3.5
Table 2. Experimental Data Sets from the Second Flame of the Two-Stage Burnera
12.4
13.1
14.6
16.2
18.2
21.8
22.9
26.2
29.7
30.3
35.3
42.2
43.5
47.4
48.4
48.8
49.2
49.6
49.9
49.6
50.1
50.1
49.9
50.1
50.4
D (nm)
Energy & Fuels Article
DOI: 10.1021/acs.energyfuels.6b02193 Energy Fuels XXXX, XXX, XXX−XXX
Article
Energy & Fuels
Figure 2. H/H2 (a), H (b), average mobility diameter (c), and collision efficiency values calculated by eq 18 (d) for n-butanol/n-dodecane and ethylene flames as a function of height above burner (HAB). where Ki is the equilibrium constant for reaction 19 for the present case of the C−H bond of type i. Equation 20 may not be applicable under all conditions, for example, when there is more than one C−H bond of the type being considered per molecule.23 Ki can be obtained following the procedure given by Howard. The enthalpy difference between A and A* at 298 K can be computed from the bond dissociation energy given in Figure 1 as well as the enthalpy of H and H2. The corresponding value at flame temperatures can be computed by adding the enthalpy of reaction calculated at 298 K to the integrated heat capacity data. For the entropy difference between A and A*, the rotational and translational contributions are negligible and the vibrational and spin contributions can be taken into account.23 When more than one type of C−H bond is present, the above equilibrium distributions are determined independently for each bond type.
sampling line were carried out. R was given as the soot particle diameter divided by 2, and a, the radius of an active site (nm), was assumed to be 0.18 nm. Finally, the active surface area was calculated by eq 20. To determine the fraction of the active area, the types of C−H bond for the soot in each flame need to be known. Identifying the variation in C−H bonds is complex as a result of the complicated structure of soot. Cain et al.41 showed that, at lower heights above the burner in a co-flow diffusion flame, pericondensed PAHs were major components in soot particles. At higher heights, particles were enriched with aliphatic components as they grew in mass and size. Although their results did not show what types of C−H bonds are the majority, they revealed a possibility of having a broad range of surface groups, from simple aryl type to complicated aliphatic groups, depending upon where soot was sampled in the flame. In addition, as shown in Figure 1, the equilibrium constant of C−H bond dissociation may vary drastically. The variations in the flame temperature also affect the equilibrium constant. To simplify the calculation and avoid complexities, Ki was calculated in Cantera based on the ABF kinetic model42 for the reaction A4−H + H = A4− + H2 at the flame temperatures reported in Table 1. The Ki values ranged from 3.5 to 3.7 compared to the values reported by Howard, which were 2.99 and 5.1 for aryl types 2 and 3, respectively, at 1880 K. Aryl bonds, types 2 and 3, are the dominant form of C−H bonds in the structure of graphene-like structures. Table 1 illustrates the molecular structure and distribution of hydrogen atoms according to C−H type bonds for four common forms of PAH: pyrene, antrathrene, corenene, and ovalene. Even if an aliphatic group is placed on the edge of a carbon plane (i.e., a methyl group in Figure 1), after removal of this group, the remaining C−H bonds are in the form of aryl types. Considering aryl types 2 and 3 to be the
3. CALCULATION OF THE COLLISION EFFICIENCY Neoh’s rate40 is the most widely used correlation used to determine the soot oxidation with OH, where W
⎛ g ⎞ 2 POH ⎜ ⎟ = 1.29 × 10 Γ 2 ⎝ cm s ⎠ T
(22)
Γ is the collision efficiency and Neoh used a constant value of 0.13. In our case, collision efficiency is calculated from eq 18. First, ξ was determined from the equations shown in the Supporting Information, given the soot particle diameter. The soot particle diameter was found using the particle size distributions and the resulting average mobility diameter. Particle size distributions (PSDs) were measured with a scanning mobility particle sizer capable of measuring particles in the range of 3−135 nm. High dilution ratios (∼4000−5000) were used to minimize particle losses and coagulation in the sampling system; corrections for diffusion loss and coagulation along the E
DOI: 10.1021/acs.energyfuels.6b02193 Energy Fuels XXXX, XXX, XXX−XXX
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Figure 3. (a and c) Oxidation rates of NSC and Neoh with constant collision efficiency and variable collision efficiency determined by eq 18. Plots b and d are the comparisons between experimental rates and the NSC + Neoh (both constant and variable collision efficiency) rates.
dominant form of C−H bond in the structure of soot particles to simplify the Ki calculation seems to be a strong assumption. The fraction of the active area was calculated on the basis of Ki and H/H2 according to eq 20. The data from the first three flames were taken from our previous studies4,26 using a two-stage burner. The last flame was adopted from the data published by Guo,43 using the ternary flame system comprised of a co-flowing propylene/air diffusion flame, followed by a hydrogen ring flame.43 The two-stage burner was initially proposed by Sarofim and Neoh44 and then has been developed by our group over time.2,45−47 This experimental apparatus isolates the oxidation from the formation process, and thus, investigation of the oxidation process becomes easier. In the two-stage burner, soot is generated in the first stage under a fuel-rich premixed flame. The formed soot is successively sent together with flue gas and excess air to the secondary burner, in which soot is oxidized. The soot from two liquid fuel mixtures composed of 30:70 and 60:40 (mol %) n-butanol/n-dodecane and one gas fuel (ethylene) was tested. Ethylene was used because it is a common fuel in flame studies. Oxygenated fuels were used because the nanostructures have been found to be different and our studies have focused on different nanostructures and these effects on soot reactivity. All experimental data, including gas species, PSDs, and temperature profiles were measured above the secondary burner.
The details of the experimental methods and measurements for n-butanol/n-dodecane fuel mixtures26 and the ethylene flame4 are provided in the given references. For the sake of convenience, the data are reported in Table 2. The table also includes the flame conditions studied, namely, the initial and overall equivalence ratio and the velocity of the unburned gases in the bottom burner at standard conditions. The burner setup and conditions have been previously described in detail.4,26 The concentration of O2 is included to take into account the role of O2 during the oxidation process.
4. RESULTS AND DISCUSSION The collision efficiency given in eq 18 depends upon the particle size and the H/H2 ratio through Xi defined in eq 20. Figure 2 shows plots of the collision efficiency, H concentration, H/H2 concentration ratio, and particle diameter. The HAB axis has been shifted by 0.1 cm for the ethylene flame and 0.06 cm for the 30:70 n-butanol/n-dodecane flame, so that the HAB of the peak efficiency coincides for all three flames. The fraction of active surface depends upon the H/H2 concentration; therefore, initially, the collision efficiency is almost zero because the H concentration is nearly zero, resulting in a negligible fraction of the active surface area. The peak efficiency coincides very closely with the peak in the H/H2 concentration profile for all three flames. However, the large difference in F
DOI: 10.1021/acs.energyfuels.6b02193 Energy Fuels XXXX, XXX, XXX−XXX
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Figure 4. NSC and Neoh (with both constant and variable collision efficiency) rates for the (a) ethylene flame and (b) overall oxidation rates (O2 + OH).
the values of the collision efficiencies for the three flames is dominated by variations in the particle size rather than variations in the H/H2 ratio, which are shown to be fairly close, as a function of HAB. It is worth noting that fragmentation can also affect the collision efficiency values as a result of potential significant changes in the average particle size. The ethylene flame discussed here, the base-case flame in a previous publication,4 exhibited slight fragmentation but not enough to affect the trend of D32, evidenced in Figure 2c. In addition, our TEM analysis confirmed that aggregates are mainly in the form of spheroidal type rather than fractal type. Please note that the equivalence ratios used in the given flames were slightly sooting and the maximum particle mobility diameters were less than 130 nm, meaning that the number density of aggregates was relatively small. In other conditions previously studied,6 when the maximum particle mobility diameter was around 600 nm, fractal-type aggregates were observed. Furthermore, D32 was used to represent the average particle diameter. For example, in the ethylene flame, the maximum particle diameter was around 130 nm, whereas D32 was around 40 nm. The collision efficiency calculated at each height above the burner was used in Neoh’s model to calculate soot oxidation. Results for the two n-butanol/n-dodecane fuels are shown in panels a and c of Figure 3. These two figures compare the variable collision efficiencies to the constant collision efficiency of 0.13. The contribution of O2 was evaluated with the NSC rate and is also shown in the figure. O2 did not notably contribute to the rate at a higher flame elevation where OH was formed.2 Despite the minor effect of O2 in the OH region, the NSC results were added to Neoh’s results to determine the overall oxidation rates (O2 + OH), as illustrated in panels b and d of Figure 3. The results are shown along with the experimental data, where the PSDs were integrated to provide measures of the area and mass concentration, as reported in our previous work.48 Oxidation rates were found to be relatively low close to the burner surface, where OH was not being formed and reaction by O2 was dominant. Rates increased with increasing the distance from the burner (HAB > 2.5 mm) until reaching the maximum, consistent with the maximum OH concentration.
To further compare the O2 and OH oxidation rates, the heightintegrated rates were computed. For the 30% n-butanol mixture, the fraction of the total (integrated) oxidation as a result of OH is 76 and 72% for the constant and variable collision efficiency models, respectively. For the 60% n-butanol mixture, the fraction of the total (integrated) oxidation as a result of OH is 73 and 60% for the constant and variable collision efficiency models, respectively. Despite having a similar temperature and gas-phase environment, each fuel mixture had a different oxidation rate.26 The maximum experimental oxidation rate was found to be 0.0012 g cm−2 s−1 for 30% n-butanol and 0.0004 g cm−2 s−1 for the 60% n-butanol fuel mixture, almost 3 times lower. Clearly, the changes in the oxidation rate are a result of the changes in the collision efficiency, which, in this case, was driven by changes in the particle size. For the two flames shown in Figure 3, the use of a variable collision efficiency model gives oxidation rates in better agreement with the experimental data (both qualitatively and quantitatively). Both models tend to overpredict the rates late in the flame. This is the result of overprediction of H and OH radicals obtained in the detailed kinetic modeling. To test the applicability of the given approach to a different fuel, an ethylene flame was used. The methodology to calculate the experimental rate was similar to what was used for n-butanol/n-dodecane mixtures. The results of NSC and Neoh models are depicted in Figure 4a. The NSC model predicts the oxidation rate in the pre-flame zone, where the O2 concentration is high. At higher elevation, where OH is formed and O2 is low, the NSC rate decreases. The fraction of the total (integrated) oxidation as a result of OH is 65 and 87% for the constant and variable collision efficiency models, respectively. The addition of NSC to the Neoh model is given in Figure 4b and is compared to the experimental rate. The variable collision efficiency model predicts experimental data somewhat better than the constant collision efficiency model. The variable model does appear to more closely follow the trend in the data, notably capturing the peak more accurately. The data published by Sunderland’s group43 was used to explore the model on non-premixed flames. In their work, soot oxidation was examined by using a ternary flame system.49 G
DOI: 10.1021/acs.energyfuels.6b02193 Energy Fuels XXXX, XXX, XXX−XXX
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Figure 5. (a) Calculated NSC and Neoh (with both constant and variable collision efficiency) rates and (b) comparison between the overall oxidation rate (NSC + Neoh) and experimental measurements.43
The ternary flame system consists of a co-flowing propylene/air diffusion flame to produce a steady soot column flowed by a hydrogen ring flame to oxidize them. The flow of propylene (2.1 mg/s) was surrounded by co-flowing air (1.18 g/s) in a co-flow burner. The propylene flame exhibited a steady luminous length of 50 mm and emitted soot in a vertical column. The secondary flame was a ring burner positioned 80 mm above the co-flow burner and on the same axis. Hydrogen (1.48 mg/s) was delivered to the ring burner and assisted burning formed in the co-flow burner. The secondary flame was lean, and radical concentrations, OH and H, were determined using complete equilibrium. The OH partial pressure was in the range from 10−4 to 10−3 bar, and H partial pressure was between 10−8 and 10−5 bar. The details of the experimental data can be found in refs 43. K was calculated as for the previous flames. In this case, using eq 18 resulted in a peak collision efficiency of 0.13 (HAB = 1.25 cm), which was the same value as Neoh’s collision efficiency (0.13); therefore, using the variable collision efficiency approach resulted in the same predicted peak. In contrast to the premixed flame in the two-stage burner, in addition to OH, the contribution of O2 was significant to the overall oxidation rate. The results given in Figure 5a show the NSC and Neoh predictions of the soot oxidation rate. As shown, NSC starts with a maximum value of around 0.0004 g cm−2 s−1. The Neoh models (variable collision and constant collision) also show peaks in the same region as NSC, consistent with the observed peak for the OH, H, and temperature profiles reported in their work. The fraction of the total (integrated) oxidation as a result of OH in this flame is only 35 and 8% for the constant and variable collision efficiency models, respectively. The addition of NSC to the Neoh model is plotted in Figure 5b. Two regions can be specified: (i) the region between 1 and 2 cm, where O2 and OH are highest and the overall oxidation rate is consequently at a maximum, and (ii) a postflame zone, where the oxidation is slower. In the second region, considering that the variation in the collision efficiency values improves the model prediction. The ratio of H/H2 in these flames was almost 50 times lower than that in the flames discussed earlier. With reference to eq 20, this difference in the concentration ratio resulted in active area fractions that were 1−2 orders of magnitude smaller than the flames from
the premixed burner. In addition, the fraction of active area calculation was more sensitive to Ki as a result of the reduction in H/H2, unlike the previously discussed premixed burner flames. This sensitivity was also higher than the particle size in these studies compared to the premixed burner flames, which showed more sensitivity to the particle size.
5. CONCLUSION The results from the current study provide expressions to bridge the gap between particle reactivity and oxidation rate. Results showed that the fraction of the active area should be considered in the determination of the collision efficiency. The fraction of the active surface area was determined from the equilibrium formation of the aryl C−H bond according to the C−H + H = C* + H2 reaction and the H/H2 concentration ratio. For premixed studies, the changes in collision efficiency were dominated by the particle size, because the H/H2 concentrations were nearly identical. However, for the case of a propylene/air diffusion flame, where H/H2 was orders of magnitude lower, the results were more sensitive to the chosen value of Ki, a function of the temperature. In this case, the particle size was also not a factor. The oxidation rate was determined under two scenarios: (i) constant collision efficiency (0.13) and (ii) variable collision efficiency values determined by eq 18. In all cases where OH oxidation was significant, the variation in collision efficiency was able to differentiate between different soot oxidation rates, yielding improved predictions. The main equations to represent the oxidation model are Neoh’s model W
⎛ g ⎞ 2 POH ⎜ ⎟ = 1.29 × 10 Γ ⎝ cm 2 s ⎠ T
collision efficiency Γ=
Rξχ Rξχ + a
fraction of the active area χi = H
K i[H]/[H 2] 1 + K i[H]/[H 2] DOI: 10.1021/acs.energyfuels.6b02193 Energy Fuels XXXX, XXX, XXX−XXX
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equilibrium constant
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⎛ ΔGi ⎞ ⎟ K i = exp⎜ − ⎝ RT ⎠
REFERENCES
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.energyfuels.6b02193. Knudsen correction (PDF)
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Article
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
JoAnn S. Lighty: 0000-0002-1552-0098 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This material is based on work supported by the National Science Foundation (NSF) under Grant 1133480 while Dr. Lighty served at the NSF. Any opinions, findings, and conclusions expressed in this publication are those of the authors and do not necessarily reflect the views of the NSF.
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NOMENCLATURE a = radius of an active site (nm), assumed to be 0.18 nm C = concentration of the oxidizer reactant at any point Ci = concentration of any oxidizing species i in the vicinity of a particle C∞ = concentration of the oxidizer reactant at infinity COH = concentration of the OH radical (mol/cm3) D = diffusion coefficient (cm2/s) k = association constant for a fully reactive particle k′ = association constant for a partially reactive particle k″ = association constant of a single active site Kn = Knudsen number l = non-continuum correction factor mi = mass of carbon removed from the surface per mole of oxidizing species i MWi = molecular weight of species i qmax = maximum possible diffusive molar flow rate of oxidizing reactants (mol/s) q = diffusive molar flow rate of oxidizing reactants (mol/s) q′ = diffusive molar flow rate of oxidizing reactants toward a partially reactive particle (mol/s) q″ = diffusive molar flow rate toward the single-hemisphere active site R = radius of a soot particle (nm) R = universal gas constant r = any distance from the surface of a particle
Greek Symbols
Γ = collision efficiency ξ = correction term for non-continuum transport based on the Knudsen number χ = fraction of the active area ϑ1 = first constant of the integration ϑ2 = second constant of the integration I
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J
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