832
Ind. Eng. Chem. Res. 2011, 50, 832–842
Temperature Excursions in Diesel Particulate Filters: Response to Shift to Idle K. Chen† and D. Luss* Department of Chemical and Biomolecular Engineering, UniVersity of Houston, Houston, Texas 77204, United States
Diesel particulate filter (DPF) is the most efficient method for particulate matter (PM) emissions removal. The accumulated PM is removed by periodic controlled combustion. In some cases, the regeneration leads to excessive local temperature excursions that may melt and destruct the ceramic filter. The cause of this DPF melting is still an open question. The temperature rise under stationary (constant) operation is not sufficiently high to explain these destructive events. Numerical simulations were conducted for cases in which the regeneration occurred by a moving temperature front. A shift to idle increases the oxygen concentration and decreases the exhaust gases flow rate and temperature. The simulations revealed that the transient temperature response to a rapid change from normal driving to idle is higher than those attained under stationary operation under either the initial or the final operating conditions. The magnitude of the transient temperature rise depends on when the change in the driving mode occurred relative to the time at which a moving temperature front formed. An early change may reverse the direction of the moving temperature front from that following a later change. The response to the rapid increase in the feed oxygen concentration and decreased flow rate is faster than that to the decrease in the feed temperature. However, a rapid feed temperature decrease may eventually decrease the temperature of the moving front and cause in some cases incomplete local PM regeneration. The temperature rise following a step-change of the feed conditions is higher than that when the same change occurs by a ramp. The shorter is the period of the ramp change, the higher is the transient temperature rise. Introduction Currently, diesel particulate filter (DPF) is the most efficient device for removal of engine particulate matter (PM) emissions. It consists of thousands of square parallel channels, with the opposite ends of adjacent channels being plugged. The exhaust gas in the square inlet channels flows through the porous walls to the surrounding four outlet channels. More than 95% of the PM accumulates in the inlet channels. A schematic of a diesel particulate filter and the flow in the DPF channels is shown in Figure 1.1,2 The collected PM has to be removed by either continuous or periodic combustion. Experience has shown that in some cases the regeneration leads to high local temperature excursions that may melt the ceramic filter and destruct it. Avoiding this unexpected melting is the most demanding technological challenge in the operation of the DPF. The cause of this unexpected destructive melting is still an open question. Following the pioneering papers by Bissett,3,4 many theoretical and experimental studies determined the maximum temperature rise during DPF regeneration under stationary (constant) feed conditions. They revealed that the peak temperature rise under realistic stationary feed conditions was not sufficiently high to melt the Cordierite filter (melting temperature ∼1250 °C).5-15 The literature reports several cases of counterintuitive temperature rise during the dynamic operation of chemical reactors. For example, a rapid decrease of the feed temperature to a packed bed or monolith reactor leads to a transient temperature exceeding the maximum obtained under stationary operation with the initial higher feed temperature.16-25 This is referred to as the wrong-way behavior. Knowledge of this effect suggested that the temperature excursions that cause DPF melting may be a dynamic response to a rapid change of the * To whom correspondence should be addressed. E-mail:
[email protected]. † Current address: School of Earth Science and Environmental Engineering, Southwest Jiao Tong University, China.
driving mode such as a shift to idle operation, which increases the oxygen concentration and decreases the feed filtration velocity and temperature.26-29 Our recent experiments confirmed the conjecture that a sudden change in the feed conditions can lead to a temperature exceeding the maximum that can be obtained under stationary operation.30,31 We conducted simulations to determine the maximum temperature rise in response to various perturbations and to gain insight about the interaction among several simultaneous sudden changes. While the dynamic response to a shift to idle is affected by the initial DPF temperature profile, all the simulations reported here are for a case in which the initial DPF temperature
Figure 1. Schematic of (a) a diesel particulate filter and (b) the flow in DPF channels. Reprinted with permission. Copyright 2000 Corning Inc.
10.1021/ie101844r 2011 American Chemical Society Published on Web 12/17/2010
Ind. Eng. Chem. Res., Vol. 50, No. 2, 2011
was uniform. In almost all the simulations, the initial assumed DPF temperature of 700 K was lower than the PM ignition temperature. The only exceptions are the cases shown in Figures 7b and 11. When the combustion occurs by a moving temperature front, the peak temperature is higher than that when the combustion occurs all over the surface. All the simulations, unless otherwise stated, were of cases in which the initial feed gas temperature was sufficiently high to locally ignite the PM and form a moving temperature front. Mathematical Model We describe a single DPF channel by a one-dimensional model that assumes that a soot layer of thickness w is deposited uniformly on the four walls of the square inlet channels and all the channels in a DPF exhibit the same behavior. The model dose not account for wall heat losses, for potential radial temperature gradients, and potential flow maldistribution among the channels. Simulations predicted that the temperature in the thin soot and filter layer were essentially uniform at any axial (z) location in the channel.32 Because of the small thickness of the soot deposit, we ignored the change in flow area in the inlet channel upon combustion of the PM. The mass, momentum, energy, and oxygen mass balances of the exhaust gas in the inlet (i ) 1) and outlet channel (i ) 2) were: ∂(d2i FiVi) ) (-1)i4dFwVw ∂z
(1)
∂pi ∂ + (FiVi2) ) -R1µ(Ti)Vi /d2 ∂z ∂z
(2)
∂T1 4 ) h1(Ts - T1) ∂z d
(3a)
Cpg(T1)F1V1
∂T2 ) (4/d)[h2 + Cpg(T2)FwVw](Ts - T2) Cpg(T2)F2V2 ∂z
(3b) d
∂ (V y ) ) -4Vwy1 + 4k1(y-w - y1) ∂z 1 1
(4a)
∂ (V y ) ) -4Vwy2 + 4k2(yws - y2) ∂x 2 2
(4b)
d
where the value of R1 in eq 2 was assumed to be 28, y-w was the oxygen concentration at the interface between the inlet channel and soot layer surface, and yws was the oxygen concentration at the interface between the outlet channel and the filter surface. Both inlet (k1) and outlet (k2) channels’ oxygen mass transfer coefficients were assumed to be equal to 0.16 m/s. The pressure difference across the soot layer and ceramic wall satisfied the Darcy law:33,34 µ(T)Vw µ(T)Vw p1 - p2 ) ws + w ks kp
(5)
The ideal gas law was used to calculate the incoming gas density. Because the pressure changes were very small, we calculated the gas density under atmospheric pressure. The other gas properties were calculated using the empirical relations reported in the Bissett paper.3 The soot permeability was determined by the Pulkrabek and Ibele predictions.35 Bissett and Shadman4 showed that the length scale over which the gas temperature in the PM layer reached the solid temperature was
833
several orders of magnitude smaller than the typical PM layer thickness. Thus, we assumed that the gas and solid temperatures normal to the flow direction were equal in the PM layer. The energy balance of the solid phase was ∂ (F wC (T )T + FswsCps(Ts)Ts) ) ∂t p pp s s -h1(Ts - T1) - h2(Ts - T2) + ∆H × Rsoot
( )
(6)
∂2Ts ∂ ∂Ts +λp w + λsws 2 + CpgVwFw(T1 - Ts) ∂z ∂z ∂z where the effective PM and filter conductivity accounted for the contributions of both the gas and solid, that is: λp ) ελgas + (1 - ε)λsoot λs ) ελgas + (1 - ε)λwall
(7)
The soot deposit thermal conductivity (λp) was calculated to be 0.831 W/(m · K), and the ceramic filter thermal conductivity (λs) was calculated to be 0.9 W/(m · K). The heat transfer coefficients h1 and h2 were assumed to be equal and were determined by the Shah and London (1978) prediction.36 For all the simulations, except when otherwise stated, we assumed that h1 ) h2 ) 160 W/(m2 · K). The corresponding channel entrance and exit boundary conditions were T1 ) Tinlet ;υ1 ) υinlet ;T2 ) Ts ;υ2 ) 0;
∂Ts )0 ∂z
y1 ) yinlet ;y2 ) yinlet ;at z ) 0 υ1 ) 0;P2 ) Patm ;
∂Ts ) 0;at z ) L ∂z
(8) (9)
The upstream inlet channel pressure was initially guessed. The set of differential eqs 1-5 and the corresponding boundary conditions were solved by adjusting the entrance pressure until the outlet pressure was equal to the atmosphere and the inlet velocity equal to the specified value. The axial filter temperature was assumed to be initially constant: Ts(0, z) ) Tini
(10)
After the soot ignited locally and a temperature front formed, the feed operating conditions (T1, υ1, y1) were step-changed to a new set of operating conditions (Tnew, υnew, ynew) at a specified time t. The oxygen mole fractions in the PM and filter were computed by ∂y ∂ ∂y - Da ) spkox(Ts)y ∂x ∂x ∂x ∂ys ∂ ∂ys Vw - Da )0 ∂x ∂x ∂x
Vw
( )
( )
(11)
The dispersion coefficient in the porous media was calculated by the empirical relation proposed by Yan (1996)37 and Delgado (2007):38 Da ) εDm + 0.5dpµ
(12)
where u was the gas filtration velocity, ε was porous media porosity, and dp was the diameter of PM particles that was assumed to be 1 µm.
834
Ind. Eng. Chem. Res., Vol. 50, No. 2, 2011
The corresponding boundary conditions were at z ) 0 Vwy-w
∂y - Da ∂x
|
) Vwy1 - k1(y-w - y1)
(13)
x)-w
at z ) L -Da
Table 1. Geometry and Thermophysical Properties of the DPF and Soot Deposit Used in the Simulations
∂y ∂x
|
) k2(yws - y2)
ws
(14)
The mass transfer coefficient ki for the inlet and outlet channels was computed by the relation: ki )
Sh × D di
(15)
The Hayes and Kolaczkowski equation39,40 was used to determine the Sherwood number for the laminar flow in the square channels.
(
)
di Sh ) 3.66 1 + 0.095 Pe L
0.45
(16)
The soot oxidation reaction was C + RO2 f 2(R - 0.5)CO2 + 2(1 - R)CO
(17)
where R was the oxidation reaction index. Reported R values for PM combustion were between 0.55 and 0.9 (Koltsakis and Stamatelos).41 We assumed that R ) 0.75. The corresponding heat release was ∆H ) 2(R - 0.5)∆HCO2 + 2(1 - R)∆HCO
(18)
The soot layer reaction rate was Rsoot )
w spkox(Ts)Fgy
∫
0
dx
(19)
( )
(20)
Mg
kox(Tw) ) k0Ts exp -
E RTs
The reported apparent activation energy E was in the range of 80 000-160 000 J/mol (Koltsakis and Stamatelos).41 Our simulations were conducted with a value of 150 000 J/mol. The specific area of soot deposit layer sp was assumed to be 5.5 × 105 cm-1, and the collision frequency factor was assumed as 6.0 m/s · K.41 The transient soot thickness during the regeneration satisfied the relation: Fp
dw ) -McRsoot dt
(21)
We assumed that a uniform soot layer was deposited on the surface. w(0, z) ) wini
(22)
Numerical simulations were conducted for a DPF with a uniform initial PM layer thickness of wini and initial temperature of Tini. The set of differential eqs 1-5 and the corresponding boundary conditions were solved by a shooting method. The solution of the system equations determined the axial variations of the channel flow, pressure, and gas temperature. These results were used to adjust the gas properties to the computed gas temperature. The transient
filter material DPF length channel width filter thickness bulk density of filter permeability of clean filter porosity of filter mean pore size of clean porous wall bulk density of soot deposit permeability of soot deposit porosity of soot deposit
Cordierite 150 mm 1.0 mm 0.40 mm 1400 kg/m3 1 × 10-12 m2 60% 25 µm 160 kg/m3 1 × 10-14 m2 60%
differential eq 6 was then solved by an implicit finite difference method in space using 40 grid points in the axial direction. An implicit solution in time with a time step of 0.1 s was used to avoid numerical instabilities. The oxygen flux through the PM layer was computed by an implicit finite difference method, which led to tridiagonal algebraic equations. Because of the soot consumption and shrinkage, the soot layer was redivided into 20 elements of equal mass at every time step. The solution of the tridiagonal system determined the oxygen concentration inside the soot layer and filter wall. The concentration of the first and the last element was used to calculate the oxygen flux from the inlet to outlet channel. This calculation was repeated until reaching the channel exit. Response to Rapid Feed Perturbations. Numerical simulations were conducted to determine the impact of simultaneous rapid changes of several input variables on the magnitude of temperature excursions during the soot regeneration. All the simulations were conducted for a single DPF channel with a cross section area of 1 × 10-6 m2 and 0.15 m long. The total surface area for this channel was 0.6 × 10-3 m2. The properties of the DPF used in the simulations are reported in Table. 1. Almost all simulations, except when otherwise stated, were conducted for a uniform soot loading of 10 g/L, which corresponded to a layer thickness of about 120 µm. In all the simulations, unless otherwise stated, the initial DPF temperature and feed temperature were 700 and 923 K, respectively. The initial oxygen feed concentration was 7.5 vol %, and the superficial filtration velocity (flow rate per unit inlet channel surface area) was 5 cm3/(cm2 · s), which were typical exhaust gas conditions under normal driving conditions. The simulations revealed that the maximum transient temperature rise depended on the location of the temperature front when the feed step-change occurred. Hence, the step-changes in all the simulations, except when otherwise stated, were done when the temperature front moved to the same position (x/L ) 0.5). An initial set of simulations determined the soot combustion behavior under relatively low feed temperature of 823 K (which is lower than the soot ignition temperature of about 873 K) and an initial DPF temperature of 700 K. The simulations of the transient soot profiles (Figure 2b) revealed that the soot was combusted almost at the same rate all over the surface. The soot combustion rate was rather slow due to the low feed temperature, and it was completely consumed in about 1800 s. This is more than an order of magnitude longer than when the combustion proceeds by a propagating front. The maximum corresponding temperature rise over that of the feed was rather small, less than 30 K (Figure 2a). Simulations, not shown here, revealed that a decrease in the filtration velocity increased the DPF temperature due to the decrease in the heat removal efficiency. However, the maximum temperature rise attained
Ind. Eng. Chem. Res., Vol. 50, No. 2, 2011
835
Figure 2. (a) Temporal axial temperature profiles during homogeneous PM regeneration with relatively low feed temperature of 823 K; and (b) corresponding temporal deposited PM profiles.
Figure 4. Impact of the filtration velocity on the peak temperature at stationary feed conditions of O2 ) 7.5 vol % and (a) Tini ) 700 K, (b) Tini ) 923 K.
Figure 3. (a) Temporal axial temperature profiles during PM regeneration with a high feed temperature of 923 K; and (b) corresponding temporal deposited PM profiles.
under this homogeneous combustion for filtration velocity of 0.83 cm3/(cm2 · s) was too low (
