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Ind. Eng. Chem. Res. 1996, 35, 2-13
KINETICS, CATALYSIS, AND REACTION ENGINEERING Modeling Catalytic Regeneration of Wall-Flow Particulate Filters Grigorios C. Koltsakis and Anastasios M. Stamatelos* Laboratory of Applied Thermodynamics, Aristotle University Thessaloniki, 540 06 Thessaloniki, Greece
The problem of initiating and controlling the regeneration of diesel particulate filters is the major obstacle in the wide application of trap systems in diesel-powered vehicles. The most promising solution approaches to this problem, in terms of minimization of system cost and of additional fuel consumption, are based on the use of catalysts to lower soot ignition temperatures. Various mechanisms have been invoked so far to explain and model catalytic filter regeneration. However, a significant gap is still observed between experimental findings and modeling predictions. This paper presents an attempt to shorten this gap, starting from the special case of fuel additive assisted trap regeneration. The mechanism proposed is based on a dynamic oxygen storage/release model of the metal oxides accumulated in the trap and is applicable to most types of fuel additives. The mechanism was embodied in an existing zero-dimensional regeneration model. The results of simple, full scale experiments are employed in the process of model development and evaluation. Dimensional analysis is used for the evaluation of the parameters affecting the evolution of catalytic regeneration in a concise form. Methods of the comparative assessment of different fuel additives, based on the theory presented, are discussed. Finally, the application of the mathematical model in the design of regeneration control systems is illustrated in a real-world filter failure scenario. Introduction The interest in diesel engine exhaust aftertreatment systems is expected to grow in view of the stricter US and European emission legislation amendments planned for the near future. The wall-flow particulate filter is today the most efficient device for reducing diesel soot emissions, attaining filtration efficiencies of the order of 90% at nominal operation conditions (Johnson et al., 1994). Soot trapping is especially important in the case of worn-out diesel engines with poorly controlled fuel combustion. Specific application problems, basically related to filter durability, have limited the use of particulate traps mainly on city buses, some delivery trucks, and fork-lift trucks. Intensive research is aimed at developing trap systems suitable for a wider application to commercial vehicles or passenger cars. The particulate trap concept has focused research and development activities around the world, and a variety of systems is offered by various manufacturers (Hoepke, 1989; Stamatelos, 1991; Pattas et al., 1992; McKinnon, 1994; Rao and Cicanek, 1994). Any trap oxidizer system is based on a durable temperature resistant filtersthe trapswhich removes particulate matter from the exhaust before it is emitted to the atmosphere. The accumulated particulate raises trap backpressuresthe pressure difference across the trap which is necessary to force the exhaust through it. The typical backpressure level depends on the filter type and increases as the trap becomes loaded with particulate. High backpressure is undesirable, since it increases fuel consumption and reduces available power. It is necessary to clean the trap periodically by burning off (oxidizing) the * To whom correspondence should be addressed. Telephone: +30-31-996066. FAX: +30-31-996019. E-mail: stam@ vergina.eng.auth.gr.
0888-5885/96/2635-0002$12.00/0
collected particulate. This process is known as regeneration (Weaver, 1983). Under the conditions met in diesel exhaust systems regarding exhaust flow rate and oxygen content, soot ignition is observed above 550 °C without catalytic aids. However, reliable and complete filter soot combustion requires inlet temperatures above 600 °C. Exhaust temperatures of that order are observed only at high load operation of the diesel engine. They are scarcely attained in the driving cycles of the official tests (e.g., ECE-EUDC, FTP-75, etc.). Thus, special regeneration techniques are employed that fall into two broad categories: (1) thermal regeneration by use of engine measures or by the supply of external energy; (2) catalytic regeneration (catalytically coated filter or fuel doping). In the first category, a significant fuel consumption penalty must be foreseen to supply the additional energy required for regular thermal regeneration during city driving. Catalytic regeneration, on the other hand, is based on the use of catalysts to effect the onset of regeneration at significantly lower temperatures. The catalyst may impregnate the porous ceramic wall or be used as a fuel additive, which is emitted and accumulated in the filter together with the particulate. The use of catalysts is critical to the design of a successful trap system, because it overcomes both problems mentioned above: namely that of mininizing backpressure levels and that of sustaining regeneration at low temperatures (Montierth, 1984; Wiedemann et al., 1983; Wiedemann and Neumann, 1985; Lepperhoff et al., 1995; Pattas et al., 1990, 1992). Catalytic regeneration is a very complex phenomenon which only recently is starting to be understood in depth (Lepperhoff et al., 1995). As a matter of fact, the specialized literature does not yet contain a comprehensive model of the catalytic regeneration process. The © 1996 American Chemical Society
Ind. Eng. Chem. Res., Vol. 35, No. 1, 1996 3
Figure 1. Simplified mechanisms of soot and additive deposition and combustion in diesel particulate traps, catalyzed or assisted by the use of additives mixed in the fuel or in the exhaust stream (Lox et al., 1991).
few attempts presented so far mainly rely upon a phenomenological modification of the apparent activation energy of soot combustion in existing thermal (noncatalytic) regeneration models. A unified approach that supports modeling of catalytic fuel additive assisted regeneration in a novel way is described in this paper. This approach is based on modeling the metal oxide transient oxygen storage and release. Because of the fact that the modeling problem is complicated and significant difficulties exist in exploiting laboratory results in the estimation of kinetic parameters, a special engineering approach is adopted. The approach comprises two equally important parts, namely, the mathematical formulation of the model and the development of a specific tuning methodology for the estimation of critical model parameters. As regards the mathematical formulation, a zerodimensional approach is selected at this stage. Despite its simplicity, such an approach has proven quite effective in our past investigations with thermal regeneration in a multitude of applications. Even this zerodimensional approach becomes complicated by the introduction of a reaction scheme pertaining to our approach concerning the catalytic activity. Thus, a specific mathematical handling is applied in order to minimize the additional independent variables introduced. The resulting mathematical model comprises a set of three differential equations instead of two for the case of noncatalytic regeneration. The second part of the work presented deals with model tuning to represent the behavior of real-world catalytic regeneration systems. This part also presents examples of how the model results are used to explain and even predict experience with some commonly used fuel additives. Furthermore, a number of ways to test the validity of our approach and to get independent estimates of the oxidation and reduction rate constants and activation energies are suggested. Catalytic Regeneration As mentioned above, in the absence of catalysts, soot ignition is observed at temperatures above 550 °C, depending on the exhaust flow rate and the available oxygen. Soot ignition at lower temperature often produces partial combustion of a soot deposit, leaving behind a less reactive carbon. Soot can differ consider-
ably in its reactivity according to the degree of graphitization after partial oxidation and the amount of hydrogen retained. Several investigations have addressed the H/C ratio in diesel soot deposits (Hare and Bradow, 1979; Funkenbusch et al., 1979). The use of some catalytic fuel additives, such as Cu, Fe, Ce, and Mn, results in regeneration temperatures as low as 350 °C (Pattas and Michalopoulou, 1992; Konstandopoulos 1987; Johnson et al., 1994; Wiedemann et al., 1983), although stochastic regenerations may be observed even down to 200 °C under favorable engine and trap operating conditions (Lepperhoff et al., 1995). The use of catalytic fuel additives presents also some minor secondary effects, such as incomplete filter cleaning, as it weakens the necessary temperature increase (thermal runaway) to achieve reliable combustion, or filter backpressure increase due to the retaining of fuel additive ash after regeneration. Figure 1 presents simplified mechanisms of soot and additive deposition and combustion in diesel particulate traps, catalyzed or assisted by the use of additives mixed in the fuel or in the exhaust stream (Lox et al., 1991). The process of catalytic regeneration may be divided in four stages, just like the normal (thermal) regeneration. The first stage involves the preheating of the ceramic. A slow oxidation of soot is observed in the second stage. When exhaust conditions are favorable, this is followed by a fast oxidation stage (third stage), which is controlled by the rate of oxygen transport in the reaction front. Finally, the fourth stage comprises the cooling of the ceramic after completion or freezing of the oxidation process. The main influence of the catalyst is observed during the second stage of regeneration. There exist two major hypotheses for the explanation of the catalytic activity of the fuel additives (McKee, 1981): the electrontransport theory and the oxygen-transport theory. According to the first theory electron exchange among additive and carbon atoms results in a weakening of the carbon bonds in the boundaries of carbon matrix. Thus, reaction with oxygen is enhanced. According to the second theory, which is the basis of our approach, the additive stores and exchanges oxygen atoms with the surrounding carbon and gas. Stochastic regenerations may be observed at even lower temperatures (Lepperhoff et al., 1995; Wiedemann
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Ind. Eng. Chem. Res., Vol. 35, No. 1, 1996
Figure 2. Comparison of computed (three-stage model) and measured thermogravimetric analysis results on a soot sample collected at part-load operation with Fe fuel additive.
Figure 3. Approximate ranges in which the particulate trap regenerates on its own (Wiedemann et al., 1984).
et al., 1983). This phenomenon is aided by the presence of part of the volatile hydrocarbon fraction of the soot adsorbed on the particulate (this part is completely gasified and desorbed at temperatures above 300 °C). In this case, the regeneration initiates in specific channels, where the local soot loading and temperatures are favorable. The associated heat release, apart from the soot, gasifies and ignites the volatile hydrocarbons, thus enhancing the propagation of the reaction. These unpredictable, low-temperature regenerations may also be “ignited” by hot particles originating from engine deposits formed by the additive (Lepperhoff et al., 1995). The above-described mechanisms are not occurring with catalytic coatings on wall-flow filters, where there is no microscale contact among carbon and catlyst particles (Figure 1). This explains why coatings have not proven effective in lowering regeneration temperatures. It is well-known that even under the most favorable conditions, such as a low exhaust flow rate, high oxygen content, and low trap loading, less than 100 °C decrease in ignition temperatures is attained. By the use of fuel additives, continuous regeneration conditions may be set on the filter during city driving, if the additive concentration is high enough and sufficient oxygen is present at the exhaust. However, the catalytic regeneration shows very special characteristics that have presented difficult-to-solve problems to the researchers. Trap loading must be safely kept at low levels, in order to prevent the random occurrence of very high temperatures inside the trap. Experience from the application of catalytic fuel additives has shown that the reaction may lead to temperatures as high as that observed with uncontrolled regeneration without catalytic aid, although initial temperature levels are significantly lower. The process of catalytic regeneration has been extensively studied during the past decade. Continuing efforts to explain and predict the outcome of catalytic regeneration by means of chemical kinetics experiments are reported in the literature. A number of researchers tried the application of single or multiple stage reaction kinetics for catalytic soot oxidation (Figure 2) (Hoffmann and Ma, 1990; Hoffmann et al., 1991; Wiedemann et al., 1989; Simon and Stark, 1985; Frohne et al., 1989). These attempts mainly rely upon a phenomenological modification of the apparent activation energy of soot combustion in existing thermal (noncatalytic) regeneration models. The results were strongly dependent on the reaction environment, indicating that a more fundamental approach was necessary. A significant step toward a unified approach able to explain catalytic regeneration was done by Pattas and
Michalopoulou (1992). The authors used a simplified mechanism for soot oxidation by atomic oxygen released by the catalyst oxides. This approach could not, however, sustain a model of catalytic regeneration, due to the lack of a kinetics submodel for oxygen release. However, it could support steady-state calculations of regeneration limits in the engine map with different catalytic additive concentrations in the fuel. This could give some hints to the explanation of the specific behavior of the catalytic regeneration by use of fuel additives, summarized below. (i) Regeneration characteristics vary widely in the engine map (Wiedeman et al., 1985). As an example, Figure 3 shows a temperature map for a four-cylinder diesel engine (Wiedemann et al., 1984). The shaded areas represent the ranges in which the particulate trap may regenerate on its own without externally induced lightoff. Just as with catalyst-coated traps, selfregeneration may occur at temperatures in excess of 400 °C. In contrast to such traps, the additive/ceramic trap system also self-regenerates at exhaust gas temperatures less than 250 °C. The wide range between these two temperatures is characterized by exhaust gas temperatures above 250 °C and oxygen concentrations from 8 to 14%. (ii) A set of exhaustive series of experiments conducted by Lepperhoff et al. (1995) shows a strong effect of trap loading on lower regeneration temperature limit, when fuel additive is present in the soot layer. (iii) The strong effect of additive concentration in soot (affected by a combination of engine-out soot emissions and additive concentration in fuel) has been extensively studied by Pattas and Michalopoulou (1992) based on the huge data acquired by the Athens pilot experiment (Pattas et al., 1990). (iv) Stochastic three-dimensional evolution of regeneration inside the filter was early observed by Wiedemann et al. (1983) by placing a number of thermocouples inside a trap with fuel additive assisted regeneration (v) The strong influence of oxygen availability was mentioned by Koberstein et al. (1983) for the case of catalytically coated traps and and confirmed later for fuel additives by Wiedemann et al. (1984, 1989) and Pattas and Michalopoulou (1992). (vi) There are significant differences in activity of different additives. A multitude of additives have been tested by a number of researchers and companies since 1982 (Wiedemann et al., 1985; Simon and Stark, 1985; Rao et al., 1985; Lepperhoff et al., 1995). The results significantly varied with engine operation mode, engine emissions, and fuel additive concentration. Only very
Ind. Eng. Chem. Res., Vol. 35, No. 1, 1996 5
recently, Lepperhoff et al. (1995) presented a valid methodology for screening different types of additives that is discussed in a following section. (vii) There are also significant differences in CO production during regeneration with different additives. New Approach to the Modeling of Catalytic Regeneration As discussed above, a large number of catalytic regeneration theories have already been presented in the literature regarding both coated filters and use of fuel additives. It still seems, however, that we lack a theory applicable to a wide range of additives and applications. Such a theory would support a computer code for modeling catalytic regeneration that could be useful for the sake of optimization of catalyst-aided trap systems. The new approach presented here refers to regeneration by use of catalytic fuel additives. It is based on the consideration of soot oxidation by the catalyst oxides inside the soot layer, as a triggering process for the ignition of the remaining soot. It is well-known that the commonly used metal additives for promoting filter regeneration form more than one type of oxides corresponding to the possible valent states they can assume. We can, therefore, distinguish between the metal being in “higher” or “lower” oxidation state. The fuel additive participates in the combustion process, leaves the combustion chamber, and accumulates in the filter together with the emitted soot. Typical filtration efficiencies for additives in the trap are usually over 95% (Lepperhoff et al., 1995). We can assume that during this process each metal additive molecule is bonded with a number of soot constituents, such as carbon and hydrocarbon molecules. By reaching the filter the metal additive is actually in its higher oxidation state. Provided that the filter temperature reaches a sufficiently high value the metal oxide in the deposit layer releases an oxygen atom to react with soot and assumes its “lower” oxidation state. The reduced oxides produced in this way may react at the same time with the oxygen contained in the flowing exhaust gas. This continuing oxidation/reduction process, which takes place at significantly lower temperatures than unaided soot oxidation, results in the reaction of soot with oxygen from the exhaust gas via the fuel additive, which acts as a catalyst itself. The starting point for the development of the new mathematical model of the process is a zerodimensional thermal regeneration model recently published by the authors (Koltsakis and Stamatelos, 1995), which was based on the classical Bissett and Shadman (1985) approach. The catalytic regeneration model presented here includes important features allowing it to successfully model catalytic activity with the appropriate number of additional degrees of freedom, despite its zero-dimensional nature. The basic features of the model are outlined below: The exhaust gas is considered to flow through two layers: the particle deposit containing the fuel additive, which shrinks uniformly with time during regeneration, and the porous ceramic channel wall (Figure 4). This simplifying model construction employs a single spatial variable x, whereas all variations in the direction perpendicular to x are neglected. The uniform soot deposition assumed over the monolith channels is expected since the combined flow resistance of the porous wall and soot deposit is typically much greater than the flow resistance of the open monolith channels. The assumption of equal exhaust gas temperature
Figure 4. Model geometry for a section of the filtration area of a wall-flow monolithic trap loaded with soot and fuel additive.
entering the deposit layer over the monolith channels is realistic for sufficiently high exhaust flow rates related to the monolith volume, considering that the conductive heat transfer between the channel gas and the monolith walls is negligible compared to convective transport in the channels. This has been also proven experimentally by Lepperhoff and Kroon (1984). Typical diesel particulate consists mainly of a carbonaceous core (soot formed during combustion), adsorbed compounds such as unburnt and partially oxygenated hydrocarbons, sulfates (due to the oxidation of the sulfur contained in the fuel), and metal oxides (Huehn and Sauerteig, 1989). Several works in the area (Johnson et al., 1994) have shown that carbon monoxide is provident in the reaction products. Instead of assuming complete carbon oxidation, the following reaction is considered:
C + RO2 f 2(R - 0.5)CO2 + 2(1 - R)CO
(1)
where R is an index of the completeness of the reaction taking values from 0.5 to 1. The parameter R should, however, be estimated beforehand by means of exhaust gas analysis. Typical values reported in the literature range between 0.8 and 0.9 (Koltsakis and Stamatelos, 1995; Aoki et al., 1993). Mass exchange between exhaust gas flow and reactants or products is negligible compared to the exhaust flow itself. The conservation of mass for the exhaust gas can then be expressed as
ρv )
F(t) A
(2)
Assuming that reaction 1 is first order in O2 and that diffusion is negligible compared to convection the oxygen balance equation is
∂ (ρvy) ) -sjkjρyR ∂x
j ) 1, 2
(3)
where subscript j identifies regions 1 and 2. Since there is no reaction in region 2 (porous wall), k2 ) 0. The coefficient k1 for region 1 is calculated from the following rate expression:
k1 ) kTe-E/RT
(4)
For the apparent activation energy E appearing in eq 4 several values have been proposed ranging from 80.000 to 160.000 J/mol (Pattas and Michalopoulou, 1992; Bissett and Shadman, 1985; Pauli et al., 1984; Hoffmann and Ma, 1990). Experimental evidence (Lepperhoff and Kroon, 1984; Pattas et al., 1995; Pattas and Michalopoulou, 1992) implies that a value of 150.000 J/mol satisfactorily represents regeneration reaction
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Ind. Eng. Chem. Res., Vol. 35, No. 1, 1996
behavior. Having adopted a value for the apparent activation energy, the factor k can be accordingly tuned to obtain good agreement between calculations and measurements. Such a procedure is described in the following sections. Assuming that the gas temperature equals that of the solid phase very near the entrance region of the deposit layer and considering negligible heat losses to the surroundings, the heat conservation equation can be formulated as below
ρjCpj
(
)
( )
∆H ∂ ∂T ∂T ∂T ) sj k ρy + λ - ρvCpg ∂t MR j ∂x j ∂x ∂x j ) 1, 2 (5)
∆H indicates a combined reaction enthalpy resulting from the complete and incomplete oxidation of carbon, which is linked to R according to the relation:
∆H ) 2(R - 0.5)∆H(i) + 2(1 - R)∆H(ii)
(6)
The rate of shrinkage of the deposit layer is proportional to the rate of oxygen consumption and inversely proportional to oxidation efficiency index R:
ρ1
1 dw Mc F(t) ) [y(x)0) - y(x)-w)] dt MR A R
(7)
h 1 ∂T )F h (T h -T h i) ∂xj for xj ) w j s: ∂T h ∂xj
(8)
w(t)0) ) wb
(9)
The boundary conditions at x ) -w are
y ) yi(t)
(10)
∂T ) ρvCpg[T - Ti(t)] λ1 ∂x
(11)
where F(t), yi(t), and Ti(t) are the known conditions of the exhaust gas. At x ) ws:
∂T )0 ∂x
(12)
Using the dimensionless variables given in the Nomenclature, the system can be written as follows:
for -w j < xj < w j s, xj * 0: F h
C h pj
∂T h ∂th
)
∂y ) ∂x
h )yR -k h j(T T h
j ) 1, 2
( )
∂T h ∂T h h )y ∆ hH hk h j(T 1 ∂ -F h λhj + ∂xj ∂xj T h ∂xj dw j dth
(13)
j ) 1, 2
T h ) T0 + T1 + 2T2 + ...
(19)
For typical parameter values, takes values of the order of 10-3. It is, therefore, a very good approximation to solve only for the leading order terms of T h , y, w j. Moreover, it can be shown that T0 is independent of x. Following the solution method of Bissett and Shadmann (1985) and taking into account the incomplete oxidation terms introduced above, the dynamic behavior of the leading order terms is expressed by the following equations:
(
y0 ) yi exp -
kh (T0) R(xj + w0) T0F h
( ) { ( ( )) ( (
y0 ) yi exp -
kh (T0) Rw0 T0 F h
)
xj e 0
(20)
xj > 0
F h (th) dT0 1 ) ∆ hH h yi(th) 1 dt C h p1w0 + C h p2w js R kh (T0)w0 R +T h i(th) - T0 exp T0F h dw0 k(T0)w0 1 R ) -M hF h (th)yi(th) 1 - exp dth R T0F h (th)
))
}
(21)
(22)
In the following, the energy and mass balances represented by eqs 21 and 22 will be modified to take into account the effects of the catalytically induced regeneration reaction by the metal oxides, based on the theoretical approach presented above. The metal additive oxides are accumulated in the deposit soot layer, and we may define
ξ)
moles of metal oxides present in soot (23) carbon moles present in soot
The fraction ξ is a function of the metal additive concentration in the fuel as well as the engine soot emissions produced during the trap-loading operation. Metal additive oxides are generally present in the deposit layer in both the lower and the higher oxidation state. We define
(15)
(16)
During catalytic regeneration the oxidation state of the metal oxides may be changed by reacting either with oxygen of the exhaust gas or with the carbon atoms of the deposit layer. Thus, if we assume that the metal additive Me forms oxides with both its 3- and 4-valent state, the following redox reactions take place:
with the boundary conditions:
for xj ) -w j: y ) yi
(18)
ψ) “higher oxidation state” metal oxides present in soot total metal oxides present in soot (24)
(14) 1 )M hF h y|0-wj R
)0
The solution method for the above system of equations is presented by Bissett and Shadmann (1985). The solution is obtained by perturbation expansions of T h , y, and w j in the small parameter . For example,
The initial conditions for the system eqs 3, 5, and 7 are
T(x,t)0) ) Tb
(17)
Ind. Eng. Chem. Res., Vol. 35, No. 1, 1996 7
2MeO2 + C f Me2O3 + CO
(25)
Me2O3 + 1/2O2 f 2MeO2
(26)
The carbon monoxide produced may then react to CO2 similarly as in the thermal (noncatalyzed) regeneration. The reactions 25 and 26 represent a continuous oxidation/reduction process of the metal oxides present in the deposit soot layer. The rate of the reduction reaction 25 is assumed to follow an Arrhenius-type temperature dependence according to the following equation:
Rred ) krede-Ered/RT
(27)
The rate of the heterogeneous oxidation reaction 26 is expected to be proportional to the oxygen content of the exhaust gas, as well as to the availability of “lower oxidation state” metal oxides, which is expressed by 1 - ψ. The Arrhenius-type temperature dependence is also assumed here. The reaction rate for 27 is then
Rox ) kox[O2](1 - ψ)e-Eox/RT
(28)
The total rate of change of ψ may then be written as
dψ ) Rox - Rred dt
(29)
By defining the dimensionless oxidation and reduction time constants as given in the Nomenclature, we can rewrite eq 29 using nondimensional numbers in the following form:
dψ 1 1 ) dth ht ox ht red
(30)
The additional soot consumption due to metal oxide reactions should be accordingly taken into account in the energy and mass balances written above. Considering the stoichiometry of the reduction reaction, eqs 21 and 22 are modified to give
{
(
F h (th) dT0 1 ) ∆ hH h yi(th) 1 dth C h p1w0 + C h p2w js R k h (T0)w0 ξ∆ hH h R +T h i(th) - T0 + exp T0F h 2M h ht red
(
(
))
dw0 1 ) -M hF h (th)yi(th) 1 dth R
(
exp -
k h (T0)w0 R T0F h (th)
))
-
}
(31)
ξ (32) 2thred
Equations 30-32 can be solved numerically by RungeKutta fourth-order techniques with the initial conditions:
T0 ) w0 ) 1, ψ ) ψeq(yi)
(33)
ψeq represents the metal additive oxidation state for which the oxidation and reduction rates are equal for the given temperature and oxygen content of the exhaust gas. Model Predictions versus Experimental Results The theoretical approach and the numerical model presented above will be applied in this section and the results will be discussed and compared with some
Table 1. Technical Data of the Particulate Filter Used in the Experiments and Model Applications Presented cell density diameter length
100 cells/in.2 143.8 mm 152.4 mm
wall thickness filter material porosity
0.43 mm cordierite 50%
experimental findings. Both the model and experimental results presented are based on the regeneration of a typical commercial filter used in vehicular applications, whose basic features are given in Table 1. It must be clear from the model presentation that the calculation of the parameter ξ is critical to the correlation of model predictions with real trap operation. For example, a series of observations related to the stochastic nature of regeneration may be assigned to the statistical variation of this parameter inside the trap. Three main series of input data are required to determine a mean value of this parameter for the soot layer at the beginning of regeneration: (1) a distribution of engine operation points that represent the actual vehicle driving during trap loading; (2) a particulate emissions map (engine-out, solid part) for the trap equipped engine (The particular catalyst-doped fuel must be used to produce this map, due to the significant effect of some fuel additives on the raw particulate emissions of diesel engines); (3) the concentration of catalyst in fuel. Three filter regenerations will be compared to assess the effect of the presence of a typical metal additive in the fuel at different concentrations. It will be assumed that the filter loading has taken place with the engine operating at constant load and speed, thus emitting soot at a constant rate of 2 g/h. The concentration of the additive in the fuel will now determine the concentration of metal oxides in the deposit layer, represented by ξ according to eq 23. The kinetic constants used for the thermal regeneration constants have been taken from a previous work (Koltsakis and Stamatelos, 1995), whereas these involving the catalytic reactions are chosen so as to closely resemble the behavior observed with cerium-based metal additives. In Figure 5 the computed filter temperature and deposit mass are plotted as function of time for three regenerations with fuel additive concentrations of 0, 50, and 100 ppm. The exhaust gas flow rate is kept constant at 38 g/s, and the oxygen concentration of the feed gas is 9.3%. A specific inlet temperature evolution is considered as shown in the plot. The initial filter loading is 20 g for all three cases. As expected, the catalytic regenerations are clearly initiated at significantly lower temperatures compared to the thermal (uncatalyzed) regeneration and the concentration of additive in the fuel seems to affect the onset of regeneration. On the other hand, little influence of the catalyst presence in the maximum developed filter temperature is observed in the specific computational case. As a second example, the influence of filter loading in the evolution of catalytic regeneration will be examined. The same regeneration conditions regarding the feed gas and the filter dimensions are considered as in the previous example. However, the results will be presented only for fuel additive concentration of 50 ppm. Figure 6 illustrates that the well-known strong dependence of the regeneration temperatures developed without any catalytic aids also applies for the additiveassisted regeneration. In a recent work, Lepperhoff et al. (1995) presented a series of experiments aiming at evaluating different additives and concentrations regarding their behavior for promoting filter regeneration. The work was con-
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Ind. Eng. Chem. Res., Vol. 35, No. 1, 1996
Figure 5. Comparison of typical filter regenerations with different catalyst concentrations.
ducted on a passenger car diesel engine equipped with a commercial trap (geometrical characteristics given in Table 1). The results are presented by means of “regeneration maps”, in which the equilibrium regeneration temperature is plotted versus the filter loading (Figure 7). The filter loading is represented by means of normalized backpressure, that is, the pressure drop in the loaded filter normalized by a recalculation to 0 °C according to the perfect gas law, to eliminate the effect of temperature on pressure. The equilibrium temperature is characterized by the condition, at which the rate of soot reaction is equal to the soot accumulation rate on the filter. In this map the region of “stochastic” regenerations illustrates the observed differencies in the equilibrium temperatures measured for the same filter loading in the series of experiments conducted. A similar regeneration map was produced by use of the numerical model as presented in Figure 8. The equilibrium temperature is plotted versus filter loading for different fuel additive concentrations as well as for the uncatalyzed regeneration. The results refer to the exhaust gas conditions of the previous examples, which are also given in the figure. The experimentally observed strong dependence of the critical equilibrium temperature on the filter loading is also clear in the numerical results, whereas higher additive dosages shift the equilibrium curves to lower temperatures. Obviously, the stochastic nature of regeneration with fuel additives cannot be predicted by a numerical model. However, based on the parameter interactions presented above, we can figure some possible explanations of this apparent stochastic nature of the regeneration. We begin from the fact that, even in a very carefully
Figure 6. Effect of initial trap loading on the evolution of filter temperature during regeneration
controlled experimental test bench, nonuniformities regarding temperature, exhaust gas flow, as well as soot and additive loading are to be expected in different trap positions radially and axially. Since the onset of regenerations is sensitive to all the above parameters, the reaction may be initiated at a single favorable trap position; since the reaction is exothermic the regeneration may then easily expand to other channels and clear a significant portion of the filter, so that equilibrium conditions are attained. The fact that this stochastic nature is more common for catalytic rather than thermal regenerations leads to the assumption that the nonuniformity of fuel additive deposition in different filter positions may be the major factor contributing to the stochastic regeneration. Dimensional Analysis of the Catalytic Regeneration Process Dimensional analysis has been employed in a recent work (Koltsakis and Stamatelos, 1995) in order to raise some difficulties in assessing the relative importance of the parameters involved in the thermal regeneration process. In this section the analysis will be extended for the case of the fuel additive assisted regeneration. An idealized regeneration process with constant feed gas temperature and flow rate is analyzed. A representative temperature of 550 °C was selected for the thermal regeneration, whereas 400 °C were used for the catalytic regeneration in this study. The trap is supposed to be thermally equilibrated with the exhaust gas at the beginning of the regeneration. Perfect soot oxidation to CO2 is also assumed. The physical proper-
Ind. Eng. Chem. Res., Vol. 35, No. 1, 1996 9 Table 2. Physical Magnitudes and Dimensions Involved in the Idealized Regeneration Process Employed for the Dimensional Analysis F Fg Ti Tmax wb ws tmax treaction
force
length
time
temperature
1 1 0 0 0 0 0 0
-1 -4 0 0 1 1 0 0
1 2 0 0 0 0 1 1
0 0 1 1 0 0 0 0
According to Buckingham’s Π-theorem, we can formulate 8 - 4 ) 4 dimensionless numbers (Π-groups), that adequately describe the phenomenon. The numbers selected for this purpose are a dimensionless deposit layer thickness,
w j )
wb ws
(34)
the Damkoehler number, which is expressed as the residence time in the deposit layer divided through a characteristic reaction time, defined in the Nomenclature,
Dam )
mb
1 F(0) treaction
(35)
the dimensionless maximum temperature developed during regeneration (the temperatures are expressed in K),
Figure 7. Regeneration maps for different fuel additives and concentrations (Lepperhoff et al., 1995).
T h max )
Tmax Ti
(36)
and the dimensionless regeneration duration,
ht max )
Figure 8. Computed regeneration map for different fuel additive concentrations.
ties of the ceramic filter are taken equal to that of cordierite with 50% porosity. In the present case, we are interested in the maximum temperature Tmax developed during the regeneration process as well as the total regeneration duration tmax. The dimensions of the physical magnitudes involved in this regeneration process are expressed in the technical system as [force]m[length]n[time]o[temperature]p as shown in Table 2.
F(0) t mb max
(37)
The previous analysis, applicable to thermal regeneration, can be further extended for the case of fuel additive assisted regeneration by introducing one more dimensionless variable, namely ξ, which has already been defined in the model description. The kinetic constants involved in the catalytic reactions for the sake of this analysis are taken as above to resemble the behavior of cerium-based additives. After execution of a number of model simulations with variable input parameters and using the definitions above, the dimensionless regeneration duration and maximum temperature can be plotted as functions of the Damkoehler number with w j as independent parameter for different additive concentrations in the deposit layer (represented by ξ). Some interesting conclusions may be drawn from the interpretation of these graphs: For the case of thermal regeneration, the maximum temperature developed in a given filter is merely a function of the initial soot loading for Damkoehler numbers above 5 × 10-3, and becomes higher for higher initial loading. On the other hand, a filter with thicker walls is subjected to lower temperature peaks for the same initial soot loading. Figure 9 clearly shows for thermal as well as catalytic regenerations the existence of a critical Damkoehler number, under which regeneration “freezes”. The critical Damkoehler number is obviously a function of ξ, but is only slightly dependent on the w j values lying in the range of interest. On the
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Figure 9. Dimensionless representation of the maximum temperature developed during the idealized regeneration process described in the text for different ξ.
other hand, the magnitude of T h max seems to be independent of the catalyst concentration in the deposit layer. We can get some physical explanations arising from the existence of this critical Dam number if we look at the variables appearing in it. The regeneration does not take place when one or more of the following occur: the feed gas temperature is too low; the oxygen content of the feed gas is too low; the residence time of the feed gas in the soot layer is too low. This may either occur due to high exhaust gas flow rates or due to low filter loading. Analogous conclusions can be drawn from Figure 10 showing the regeneration duration as function of Dam. For thermal regenerations, the critical Dam number leading to infinite regeneration durations is also recognized, whereas for Dam numbers higher than 5 × 10-3 the dimensionless duration approaches a constant value of about 40 × 10-3 practically independent of w j . Similar trends are observed in the catalytic regenerations as well, although no limiting value for the dimensionless regeneration duration can be clearly recognized. Comparative Assessment of Fuel Additives It should be clear from the discussion of international experience regarding fuel additive assisted regeneration presented above that we observe continuous efforts
Figure 10. Dimensionless representation of the duration of the idealized regeneration process described in the text for different ξ.
toward the discovery of an additive that is best suited for trap applications. Naturally, a complete procedure for the selection of a best-suited fuel additive for a specific trap application must take into account a number of practical problems related to the toxicity of the additive, its degree of retention in the filter, its effect on the injection equipment as well as on the combustion and engine out emissions, etc. However, the modeling approach presented here is focused on the assessment of the catalytic activity of fuel additives regarding regeneration of wallflow filters. Due to the multitude of parameters affecting fuel additive performance in trap regeneration (engine operation and particulate emissions, trap loading, fuel additive concentration etc.), it is not easy to devise a single experimental procedure by which a direct assessment of its catalytic activity would be possible. According to the reasoning presented in this paper, the selection of a suitable test procedure should be based on the determination of the fuel additive oxygen storage and release properties. These properties are embodied in the model by means of the four additional parameters presented in Table 3. These parameters along with the corresponding equations (eqs 27 and 28), allow a more fundamental description of the fuel additive activity. Determination of these parameters for each specific fuel additive allows the prediction of its catalytic activity
Ind. Eng. Chem. Res., Vol. 35, No. 1, 1996 11 Table 3. Fuel Additive Characterization property
unit
physical meaning
kox Eox kred Ered
m/s J/mol m/s J/mol
rate coefficient for oxidation of additive activation energy for metal oxidation rate coefficient for reduction of additive activation energy for metal reduction
irrespective of its concentration in the fuel or soot. This constitutes the main innovation of the new modeling approach presented here. Laboratory testing of the validity of our approach is a rather demanding task that would require independent estimates of the oxidation and reduction rate constants and activation energies for various additives. To this end, derivation of Arrhenius plots should be separately carried out for reactions 25 and 26 under net reducing and net oxidizing conditions, respectively. The required experiments pose two major difficulties regarding the necessary equipment and the experimental procedure to be followed: 1. The measurements should be conducted on a special type of isothermal reactor. This reactor should have a special fixture able to hold a minitrap specimen in a way that the gas flow would be forced through the specimen walls. 2. The minitrap specimens should be easily dismountable, in order to allow their loading with engine soot with the specific fuel additive concentration in fuel and a specific engine operating point. The soot loading of the specimens in a full scale engine-trap layout presents significant problems by itself. Naturally, such a complicated and time-consuming set of experiments would only be required for a thorough testing of model validity. For the purposes of the engineering approach presented in this paper, full scale measurements could also be employed for model tuning and preliminary assessment of catalytic activity. The experiments employed for model tuning in this paper are due to Lepperhoff et al. (1995), and their results may be presented in the form of Figure 7. According to the discussion of the preceding section, dimensional analysis indicates that this approach takes into account the major parameters affecting fuel aditive performance. The experiments of Figure 7 embody the effect of engine load (variable exhaust temperature), trap loading versus flow rate (normalized backpressure). A series of measurements of this type may be used for a comparative assessment among various types of additives in varying concentrations in fuel. Thus, the approach presented in Lepperhoff et al. (1995) is fully consistent with the catalytic activity model presented here. A further series of experiments would be required for a finer tuning of the model regarding the computation of CO emissions during regeneration. This aspect of fuel additive activity plays an important role in the accurate determination of the heat of soot oxidation reaction. It is dependent on the type of additive, the temperature, and the oxygen availability during regeneration (Wiedemann and Neumann, 1985; De Soete, 1987). Model Applications: Regeneration Control The primary area of application of regeneration models is the design of trap systems and optimization of regeneration control systems. In this section, application of the model will be illustrated in a case study related to regeneration rate control. The durability of regenerable trap systems probably presents the major obstacle in their wider application
Figure 11. Filter protection by limiting oxygen content of the exhaust gas during a trap failure scenario.
in vehicle applications. Filter failure may result either from overheating above the melting point or from local high temperature gradients that cause severe thermal and mechanical stresses. This occurs under several failure scenarios, a typical one comprising an engine operation at high load and subsequent braking leading to idle operation with low exhaust flow rates. It is necessary to develop regeneration control strategies in order to eliminate reaction rates during failure scenaria. Considering the well-known behavior of the regeneration process and bearing in mind the theoretical results presented in the previous sections, we can state four major directions for limiting the undesired high regeneration rates: (1) maintaining low mean trap loading; (2) cooling of the filter; (3) reduction of the exhaust gas oxygen content; (4) decreasing the exhaust gas residence time in the soot layer. Apart from the first one, the above approaches may have two secondary effects of minor importance, namely increasing the regeneration duration and inhibiting a complete soot combustion. The above theoretical possibilities could be realized in practice by a number of techniques (limiting trap loading by controlling regeneration frequency, limiting oxygen availability in the exhaust gas by controlling A/F, limiting oxygen availability by keeping a low exhaust flow rate, filter cooling by keeping a high exhaust flow rate). As a case study, we may consider the principle of trap protection by limiting the oxygen content of the feed exhaust gas, which has recently been shown to be effective in a number of trap failure scenarios (Pattas et al., 1995). Figure 11 shows the measured trap temperatures developed during a failure scenario comprising a sudden vehicle braking following engine operation at high load and speed. This scenario causes the onset of a very fast regeneration, due to the combination of relatively high temperatures, low exhaust flow rates, and high oxygen content. In this specific case, exhaust gas recirculation is activated at t ) 155 s in order to control the regeneration. It is obvious that regeneration control is successful in this case. Figure 12 compares model predictions of such a failure scenario, with and without application of trap protection. The parameters used in this run are given in Table 4, and are characteristic for conditions met in
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Discussion
Figure 12. Simulation of a trap failure scenario with a corresponding filter protection technique. Table 4. Model Parameters Used as Input for the Simulation of a Trap Failure Scenario mode
mass flow rate (kg/s)
O2 concn (%)
full load idle EGRa
50 10 5
4 17 4
a
Exhaust gas recirculation.
passenger car applications. Data regarding the filter are given in Table 1. The trap loading in this experiment amounted to 12 g. According to the model the lack of regeneration rate control would lead to much higher temperature levels that could possibly damage the filter. The experience gained by a significant number of experiments of this kind, along with the respective model runs, indicates that the design of a control system for this technique is a complex task. This is mainly due to the fact that the levels of exhaust gas recirculation necessary for trap protection in each specific failure scenario are variable. The evolution of a regeneration like that of Figure 11 could be significantly different even with small changes in trap loading, exhaust flow rate, temperature, and oxygen content. Additionally, one must take into account variation in fuel additive concentration in soot for different trap-loading modes. Control system design in this case is probably impossible without assistance from regeneration modeling. Another significant area of model application is related to the design of fuel additive assisted trap systems. Model predictions are very helpful toward the determination of optimal filter size (together with a backpressure model) and (constant or variable) levels of additive concentrations for a given vehicular application. Finally, another very important aspect of trap modeling applications is related to the rising concern of onboard diagnostics (OBD) for emission control systems in all vehicle types (Koltsakis and Stamatelos, 1995). Due to special aspects of the design of trap systems (wide variety of filter types with significantly varying filtering efficiencies regarding the solid and the soluble organic fraction of the particulate, also varying with engine operation point, etc.), it is absolutely necessary to computationally support any OBD development efforts.
Application of fuel additives in the regeneration of diesel particulate filters over the past decade has been assisted by a significant number of research studies. However, the necessity still exists for a valid modeling approach that would be capable of explaining the complex aspects of fuel additive assisted regeneration. A new approach to the catalytic activity of fuel additives during trap regeneration is presented in this paper. The approach takes into account the quantified oxygen storage and release properties of the metal additives used in such applications. A zero-dimensional regeneration model with a minimal number of tunable parameters was developed on the basis of this approach. The model was tuned on the basis of a valid series of experiments recently conducted by other researchers in this field. The results show good correlation with real-world observations, taken from the authors, and others’ previous experience. The dimensional analysis of an idealized regeneration process provided a more concise presentation of the relative significance of the model parameters. Further work is necessary in order to further improve the model-tuning approach, aiming at higher accuracy. This would require the exploitation of the results of dedicated kinetics experiments that would further investigate the regeneration characteristics of the different types of fuel additives. Even in its current status of development, that is, tuned to the results of routine full scale fuel additive assessment tests, the model is successfully used in trap and regeneration system design as well as optimization of regeneration rate control system parameters. Further applications include on-board diagnostics for trap systems and optimization of catalyst dosimetry. Nomenclature A ) filtration area, m2 A/F ) air to fuel mass ratio Cpg ) specific heat capacity of exhaust gas, 1090 J/(kg K) Cp1 ) specific heat capacity of soot deposit, 1510 J/(kg K) Cp2 ) specific heat capacity of ceramic wall, 1120 J/(kg K) C h pj ) dimensionless heat capacity, CpjFj/(CpgF1) Dam ) Damkoehler number, mb/[F(0)treaction] E ) apparent activation energy of soot oxidation, 150 × 103 J/mol Eox ) activation energy for metal additive oxidation Ered ) activation energy for metal additive reduction F h ) dimensionless exhaust gas mass flow rate, F(t)/F(0) F(t) ) mass flow rate of exhaust gas, kg/s F(0) ) value of F(t) at t ) 0 ∆H ) “combined” reaction enthalpy of soot oxidation, J/mol ∆H(i) ) specific heat of CO2 formation, 3.61 × 105 J/mol ∆H(ii) ) specific heat of CO formation, 0.90 × 105 J/mol kj ) rate coefficient for the reaction in region j, m/s k ) collisions frequency factor, 6.0 m/(s K) kox ) rate coefficient for oxidation of additive, m/s kred ) rate coefficient for oxidation of additive, m/s k h j ) dimensionless rate coefficient, (s1wbApMakj)/[RTbF(0)] Ma ) molecular weight of exhaust gas, 29 × 10-3 kg/mol Mc ) atomic weight of deposit, 12 × 10-3 kg/mol M h ) molecular weight ratio m ) accumulated soot mass, kg p ) exhaust gas pressure, 101 × 103 Pa ∆P ) trap backpressure, Pa R ) gas constant, 8.31 m3 Pa/(mol K) s1 ) specific area of deposit layer, 5.5 × 107 m-1 T ) temperature, K T h ) dimensionless temperature, T/Tb Tb ) temperature at t ) 0, K
Ind. Eng. Chem. Res., Vol. 35, No. 1, 1996 13 Ti(t) ) inlet temperature, K T h i ) dimensionless inlet temperature, Ti/Tb Tmax ) maximum temperature developed during regeneration, K T h max ) dimensionless maximum temperature developed during regeneration t ) time, s ht ) dimensionless time, F(0)t/mb htmax ) dimensionless total regeneration duration treaction ) characteristic reaction time, F1/(s1Fgkjyi), s v ) superficial velocity, m/s w ) thickness of the deposit layer, m w j ) dimensionless deposit layer thickness, w/wb ws ) channel wall thickness, m w j s ) dimensionless wall thickness, ws/wb x ) distance, m xj ) dimensionless distance, x/wb y ) oxygen concentration of the exhaust gas (mole fraction) yi(t) ) mole fraction of oxygen at inlet Greek Letters R ) index for the completeness of soot oxidation ) dimensionless group CpgF(0)wb/Aλ1 λ ) bulk thermal conductivity λhj ) ratio of thermal conductivities, λj/λ1 ξ ) defined in eq 23 F ) exhaust gas density, kg/m3 F1 ) bulk density of the deposit layer, 550 kg/m3 F2 ) bulk density of porous ceramic, 1400 kg/m3 ψ ) defined in eq 24 Subscripts b ) initial condition i ) inlet condition j ) 1, 2 ) indication of region 1 (deposit) or 2 (ceramic wall)
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Received for review May 16, 1995 Accepted August 24, 1995X IE950293I
X Abstract published in Advance ACS Abstracts, November 15, 1995.
