Methodology for Developing a Diesel Exhaust After Treatment Simulation Tool.
Exhaust gas from diesel engines consists of several harmful substances such as Hydro Carbons (HCs), Particulate Matter (PM), carbon monoxide (CO) and nitrogen oxides (N[O.sub.x]), which are hazardous to the environment and compromise urban air quality. Consequently, these exhaust gases are strictly regulated, so an efficient after treatment system is needed. In Europe, the standard that currently applies to Heavy-duty diesel engines is Euro VI . The after treatment system typically consists of four modules which each remove different pollutants from the exhaust gas. An example system can be seen in Figure 1. This is a typical configuration of a Euro VI system, but different configurations are possible. To make sure that the after treatment system meets the regulations under the highly transient operations that are typical for an engine, thorough, expensive and time-consuming laboratory tests are necessary. Enhancement of process understanding, gained from simulations of after treatment systems, may assist in strategic planning of experimental efforts and thereby reduce the total experimental efforts. As summarized in Table 2, the literature has numerous examples of simulations of individual catalysts (and pairs). However, by simulating the complete system in succession, it is possible to explore how one catalyst affects succeeding catalysts as well as how the entire system is affected by changes in different conditions, e.g. temperature, velocity or inlet concentrations. Simulating the entire system as a whole will also make it possible to test the consequences of changing the order of the modules, removing a module, or adding extra modules. It would be possible to test changes made to a certain module; e.g. different catalytic substrates, or different sizes of the catalysts. This sequential simulation may also enable system-wide optimization. Some software is already available. The commercial software Axisuite[R] is developed by Exothermia and it is able to simulate the entire system and to consider various types of modules . However in commercial software it is only the built-in models which can be used for simulations. This will limit the possibility to determine effects of different models or new and innovative units. By developing a flexible simulator that enables the user to be in complete control of which models and units to test, it will be possible to use any available set of models from the literature provided these are structurally compatible. Studies where the entire system is simulated in succession is to the authors knowledge not well-documented in literature. This paper presents a methodology to develop such a flexible simulation tool which can simulate the entire after treatment system, or parts of it. Both physical models as well as kinetic models will be exchangeable. This will make it possible for the user to easily simulate and optimize a wide variety of diesel exhaust after treatment systems.
Diesel Exhaust After Treatment System
The Euro VI standard for diesel exhaust after treatment systems was presented in 2009 and revised in 2013 . The current emission standards are shown in Table 1. This made it necessary for the automotive industry to improve the removal of hazardous pollutants from the exhaust gases. In Figure 1, it is shown how the first module in the system typically is the Diesel Oxidation Catalyst (DOC). This module removes carbon monoxide and HC by oxidation to carbon dioxide and water. The second module is a Diesel Particulate Filter (DPF), which removes PM. Usually the DPF is a wall-flow filter as shown in Figure 4 [3, 4]. The PM accumulates on the walls of the filter, and therefore to avoid pressure build-up, the filter must be regenerated either actively or passively by burning away the soot. Downstream of the DPF, the Selective Catalytic Reduction (SCR) catalyst is placed. This catalyst reduces nitrogen oxides (N[O.sub.x]) to [N.sub.2] and [H.sub.2]O. By-products such as [N.sub.2]O are also formed. N[H.sub.3] is used as a reductant, and is usually added to the system in the form of urea that hydrolyses into N[H.sub.3] in the hot exhaust gases. Depending on the amount of urea that is dosed to the system and the reaction conditions, a fraction of the ammonia can remain in the exhaust gas.
Since ammonia is hazardous to the environment the residual ammonia in the exhaust gas must be controlled. This is done in the Ammonia Slip Catalyst (ASC), which oxidizes remaining ammonia to [N.sub.2]. To solve the selectivity issues of oxidizing ammonia to [N.sub.2], a dual layered ASC can be used. A dual layered ASC consists of a Platinum Group Metal (PGM) layer coated with a layer of SCR catalyst [5, 6, 7].
The catalysts are chemically different. However their physical designs are similar. They share the monolithic structure, shown in Figure 2. This is a honeycomb-like structure based on long, narrow channels of different shapes. Synthetic cordierite is most often used to make these structures, and the different catalytic materials are coated onto the walls of the monolith. The monolith can be coated either once or twice with different active material, which gives the different structures that are shown in Figure 3. The structure of the DPF is typically a wall-flow filter, where the channels are plugged alternately, as it is shown in Figure 4. This allows the exhaust gas to flow into one channel, through the walls and into the four adjacent channels, while depositing PM on the walls as shown in Figure 4b). The filter may also have other structures, which may have different advantages over the wall-flow monolith, e.g. a V-shaped foam filter .
As seen in Figure 1, the exhaust gas in this system flows from the engine, through the different modules and out to the ambient. This makes the system a good candidate for a modular simulation tool as will be shown later. This implies that all chemical species in the system (reactants, products and inert) have to be ordered in a structured variable which will serve as an input and output variable for each of the unit models respectively.
Modelling of the Catalytic Units
When developing models for the catalysts, the models should reflect the intended use of the model. For example, one may prioritize monitoring the pressure drops of the DPF, rather than getting the exact output concentrations. If not, one may assume no pressure drop across the filter. Such situations require different models.
A regular monolithic structure, which is coated with a single catalytic layer, is usually modelled in one dimension (1D) since the absence of radial flow and gradients is often assumed [9, 10]. However, diffusion in the porous catalytic layer can be important. If so, a one-plus-one-dimensional (1D+1D) model can be used. In case the gradients in the monolith channel cannot be neglected a full 3 D Computational Fluid Dynamic (CFD) model will have to be developed and solved. This type of complexity is usually reserved for design studies as the simpler models are often sufficient to describe operational performance of a given after treatment system. Variations of the types of models are listed in Table 2.
A dual layered catalyst differs significantly from the single-layered catalyst when it is modelled. The modelling focuses on the two different wash coats which must be modelled separately. The result is three mass balances (two for the wash coats and one for the bulk phase) per specie and the level of complexity of the model depends on how the mass transfer between the wash coat layers is handled. One way to model this type of catalyst, is to treat both layers as surfaces, assuming no radial flows . In this type of model, mass and heat transfer only takes place between phases, as well as in the axial direction. Alternatively, one may consider diffusion in the upper layer, but not in the lower layer. This is called a Layer-Surface Model (LSM) . It is also possible to model the catalyst, so that diffusion is considered in both layers.
It is usually necessary to consider variations in space as well as time. Therefore the model will result in a Partial Differential Equation (PDE) system. To solve a PDE system, it is necessary to discretize the model. This can be done by using a finite differences method, since most of the models are regular flow models, which is well suited for backwards difference discretization schemes .
By choosing a model with more dimensions, the computational time may increase due to the more complicated models. if the simulation requires high enough accuracy a high computational time and complexity can be tolerable. However, it may be advantageous to choose a less complex model in order to get satisfactory results, in a shorter time. The filter is the module, which stands out the most. The different physical appearance of the filter along with the necessity of monitoring the pressure drop across the filter makes it necessary for the filter model to be quite different from the models of modules with regular flow.
Methodology for Model Structure Development
When developing a simulation tool, a structure is required to facilitate exchange of different model elements. Replacing a 1D reactor model by a 2D model, or a change of kinetic model, can be done conveniently if each model (reactor or kinetic) is expressed consistently based on a common framework. It is important to ensure that the variable structure of the in- and outputs of each module are identical to ensure that the modules can be simulated in any order. Therefore all species considered in the system should be part of the inputs and outputs of all modules. When a species is an input to a module where it does not react, it will simply be treated as inert and there will be no changes in the molar flow of this species. Previous work in this area has been published in .
The simulation tool should determine the state of the exhaust gas passing through all modules of the after treatment system. The models for each module are developed following the methodology in Figure 5. Step 1 in Figure 5 defines the assumptions for the module in question, leading to the list of variables to be included. These can be (but are not limited to):
* Concentrations of all reacting species,
The variables necessary to describe the behaviour of the module, dictate which balances must be set up in the reactor model. If temperature variations are required, energy balances are needed. Concentrations of various species require balances in species. If the pressure drop across the module is of interest, momentum balances must be used. A decision that should be made in step 1 in Figure 5 is whether the model should be for a single channel, or if it is necessary to consider gradients across the monolith. It is common to use single channel models, where identical inlet conditions into every channel are assumed, but 3D CFD models can be of use if for example gradients across the monolith are of interest due to differences in inlet concentration between channels. The conservation balances being set up for each of the different modules do not have to have identical dimensions to be included in a unit simulation but it is important that they only include species which are present in the common variable structure. Step 1 also involves deciding whether or not the model should be dynamic. By developing a dynamic model, transient simulations can be done and the results can be compared with the WHTC regulations shown in Table 1. It will furthermore be possible to make control studies of the urea dosing. It will still be possible to run steady state simulations and compare results with the WHSC regulations.
In step 2 in Figure 5, it is necessary to establish the reactor model, which describes the system. One may either choose a model from the literature, and adapted it to the situation, or develop a new model, either from first principles or from simpler approaches.
In step 3 in Figure 5, the species that should be considered in the module are chosen. A high amount of chosen species will result in a high number of differential equations in the final reactor model. This will make the simulations slower. Therefore it may be beneficial to ignore species that have little influence on the system. Species that are of great abundance in the system, for example [N.sub.2] and [O.sub.2], can be considered constant if not a very detailed kinetic model is needed. It must also be remembered that in order to simulate the changes in the molar concentration of a certain species, a rate expression concerning this species must be present in the kinetic model.
Step 4 in Figure 5 establishes the kinetic model. When doing this, it is important to make sure that the kinetic model includes all the chosen species. It should also be decided which reactions to take into account. The reactions which remove the harmful substances are usually included in the kinetic model since these are the desired reactions. However side-reactions also occur, which can sometimes be ignored for simplicity. If a kinetic model is developed, it is necessary to experimentally estimate the kinetic parameters. Certain kinetic models consider only a limited amount of species or reactions, and this will limit the possibilities of adding extra species or reactions to the model. Furthermore, a kinetic model found in literature may only be valid in a limited temperature range. The calibration of the kinetic parameters must be studied carefully as well. If kinetic parameters have been calibrated while the system is affected by specific mass and heat transfer conditions, these may not be valid for any other system that is affected by different conditions. It is therefore important that an intrinsic kinetic model within the desired temperature range and with all the necessary species is used. Due to these requirements it may be advantageous to develop a kinetic model, which fits the requirements of the final program.
Methodology of Implementation
Once the modelling has been completed, the reactor and kinetic models for each module must be implemented, before the system can be simulated in succession. Each module must be implemented in a certain way in order to ensure the desired flexibility which allows the build program to be a valuable simulation tool. A suggested implementation strategy that has been applied in this work can be seen in Figure 6. The call function should be called in a main script, which connects the entire program, and the idea is that once the system is implemented, the user only has to work with the main script.
Parameter Object This object contains information about the module in question; e.g. length, diameter, CPSI or heat transfer coefficients. This object will be used as input to both the call and reactor functions.
Call Function This function begins the simulation of the module. Here, the results of the simulation can be saved. It will be in this function the initial and boundary conditions used in solving the reactor model will be defined. In this function the model is solved using an ODE solver. The inputs of this function should be data on the exhaust gas as well as the parameter object of the module in question. The only output will be the updated exhaust object.
Reactor Function The discretized system of differential equations in the reactor model is defined here. The rates of reaction are computed using the kinetic function. The input of this function will be the parameter object and the exhaust data, and the output will be the states for the catalyst. This function should be called by an appropriate ODE solver.
Kinetic Function All kinetic parameters are defined and these are used along with temperature and concentrations of the species to compute the reaction rates. To do this, temperature and concentrations must be inputs to this function. The output should be the rates of the reactions and heat generation.
Boundary conditions should be received as inputs to the call function and the reactor function, as illustrated in Figure 6. In the first module, engine data should be used as boundary conditions. When this module has been simulated, the outlet conditions are used as boundary conditions for the next module, and so forth. To do this as efficiently as possible, all information about the exhaust gas can be stored in an object, which should be used as input to the call functions and the physics functions. When the first module is simulated, the object contains the data from the engine, which will be the boundary conditions. After the simulation of the first module, the object is updated to contain the output values from the module. The next module receives the updated object as an input, so the output from the first module will be the input to the next module. This continues until all the desired modules have been simulated.
When all of the modules have been modelled individually, they can be simulated in succession by implementing a main script. In the main script, the call functions for each module should be called in a way so the desired order is used. It should be simple to change the order of the modules and adding or removing modules. This can be achieved by first defining which modules to simulate and the order of these. A way to do this is to develop a function, which initializes the system. For usability, this function should be the only function which is accessed and changed. This means that every factor should be defined in this function. These factors can be concentrations of all species in the exhaust as well as the desired order of the modules.
The methodology described in the previous section has been used to develop a program that can simulate the entire after treatment system. The order of the modules in the simulations, operating conditions and the types of catalysts can be modified. The methodology presented in Figure 5 is used, and the resulting simulation tool is used to analyze some system configurations.
As shown in Figure 5, the first step of developing the models is to define the assumptions for the module in question. All four reactor models are based on a single channel inside the monoliths. It has been assumed that:
1. The channels are identical and square-shaped.
2. There is no heat transport by conduction.
3. There is no heat loss to the surroundings.
4. Temperature, concentrations and velocity are identical at the inlet of all channels of the catalysts.
5. All flow in radial direction has been neglected.
Assumption 1 is common, since channels are usually similar throughout the catalyst. Assumption 2 has been made because the DOC reactor model was implemented with and without heat conduction and the results showed that it was justified to neglect the heat conduction. Assumption 3 is not very good in a test situation, since the system is not isolated during testing. However on the road, the system is surrounded by an exhaust silencer which isolates and causes reduced heat loss to the surroundings, thus making this assumption better in real life. In practice, assumption 4 is questionable since it will not be possible to have completely even inlet concentrations for all channels. The error is however evaluated to be irrelevant when only overall unit performance is being monitored. Assumption 5 will result in all the reactor models being one-dimensional.
The second step in Figure 5 is to develop the reactor models. In this work it was decided to adapt models found in the literature. The reactor models used in this paper for the DOC, SCR and ASC have been found in literature and they have all been simplified, since the aim of this work is not to analyze the detailed behavior of the exhaust system, but rather show that the suggested methodology works for developing a simulation tool for the entire system. For the DPF, a simple model has been set up which describes the major trends of the DPF. The reactor model for the DOC is developed by Kim and Kim . It consists of coupled ordinary and partial differential equations which are the mass and energy balances for the gas and the solid phase. The reactor model for the SCR also consists of the mass and energy balances for the gas and solid phase, as developed by Opitz et al. . The ASC which has been simulated in this study is a dual layer ASC and the reactor model used for this catalyst is a 1D+1D reactor model  and consists of mass and energy balances for the gas phase, the SCR layer and the PGM layer. In the reactor model by Sukumar et al. , steady state has been assumed in the gas phase and this assumption has not been used in the implementation of the reactor model.
The reactor models for the DOC, SCR and ASC are very similar but the DPF usually differs from the other units, since the pressure drop should be monitored. In order to simplify the implementation of the models, a simple reactor model has been set up for the DPF. This reactor model has been based on the assumption that 99% of the soot is removed in the filter. It has also been assumed that the gas simply flows through one channel, and that the reaction takes place in the gas phase. These assumptions will result in a mass balance for the gas phase, as in equation (1),
[mathematical expression not reproducible] (1)
where i = N[O.sub.2] and NO. This mass balance estimates how much N[O.sub.2] is converted into NO when N[O.sub.2] oxidizes the soot in the DPF. The assumption that 99% of the soot is removed will result in the following mass balance:
[mathematical expression not reproducible] (2)
Step 3 in Figure 5 is to decide which species to monitor in each module. The species are shown in Table 3. Based on these species it is possible to move to step 4 in Figure 5. The kinetic model for the DOC module consists of rate expressions for the three reactions which take place in the catalyst, as developed by Kim and Kim .
The kinetic model used for the SCR is developed by Pant and Schmieg  and considers several different reactions that take place in the catalyst. However, only the adsorption and desorption of ammonia and the three SCR reactions are taken into account in the implemented kinetic model. The kinetic model for the ASC consists of a model for both the SCR layer and the PGM layer. The kinetic model used for the SCR layer is the same one that has been used in the implementation of the SCR catalyst, and the kinetic model used for the PGM layer is developed by Scheuer et al. . This kinetic model consists of rate expressions for nine reactions which take place in the PGM layer. In the DPF module, it has been assumed that only 20% of the soot is oxidized by N[O.sub.2] according to the following reaction.
C + 2N[O.sub.2] [R] C[O.sub.2] + 2NO (3)
The kinetic model has been set up as the rate expression for reaction (3), since only one reaction is considered:
[mathematical expression not reproducible] (4)
The models have been discretized using a backwards difference scheme and implemented in Matlab according to the methodology given in the section "Methodology of implementation". The models were first simulated individually to make sure that they gave realistic results. When analyzing the results, it must be kept in mind that the models were not validated by comparison with experimental data, and therefore the results can only be used to observe the tendencies of the modules. Such a simulation of a single module has been done for the SCR and the results are shown in Figure 7. The concentration profiles clearly shows the trends of this module; decrease in ammonia until all, or nearly all, NO and N[O.sub.2] has been reduced. It also shows how the outlet stream of the SCR will contain a certain amount of ammonia, which should be removed using an ASC after the SCR. When all four models had been implemented and tested, the implementation of the program was done with the methodology described above. In order to test if the program could simulate the entire system, different simulations have been run. The program should be able to simulate the system under different conditions and this has been tested by running simulations at 200[degrees]C, 300[degrees]C and 400[degrees]C. The results from these simulations are seen in Figure 8, 9, 10. These results are as expected. It is clear from the figures that the ratio between NO and N[O.sub.2] changes in the output of the DOC. This is because the NO is oxidized in the DOC. The difference in temperature also affects the amount of ammonia exiting the SCR because desorption of ammonia is temperature-dependent. This temperature dependence results in less adsorbed ammonia at higher temperatures, which can be seen in Figure 10. The reactions in the different catalysts are affected by the temperature changes. However, the changes in the composition of the outlet gas are so small that they can hardly be seen in the figures. Physical data, catalyst parameters, and simulation conditions used for the simulations can be seen in Table. 4.
Another important feature in the program is that the system can be simulated with different configurations of the modules. This can be done by rewriting a single string in the initialization of the simulation. To test this, a simulation has been run in which the order of the modules was defined as SCR-ASC-DOC-DPF. The simulation was run at 200[degrees]C, and the simulation result is seen in Figure 11. When this is compared to Figure 8, it can clearly be seen that this setup results in different outlet conditions. This is because the SCR is the first module, and without the DOC being upstream of the SCR, the N[O.sub.2]/NO ratio will lower. The effect of the N[O.sub.2]/NO ratio on the SCR is explained by Koebel et al. .
By using the methodology presented in this article, a flexible simulation tool is achieved. The program will be able to simulate any desired models and it will be possible to change the complexity of the models and thereby the computational time and accuracy of the simulations.
As the case study reveal the advantage of constructing an in house simulator give the ability to tailor the simulations for a given desired purpose; that being e.g. the evaluation of a given steady state or dynamic performance of an individual unit or the whole system. Since the engine exhaust gas in a diesel car or truck changes dramatically in terms of flow, composition and temperature as the driving conditions change, detailed studies of the benefit and disadvantages for the after treatment system design needs to be tested for a large variety of scenarios which implies that simulation can be a very valuable supplement to full scale engine test. The simulations can help to show the effect of having all units in the system in terms of thermal mass, which means that the temperature variations from the engine is dampened after each unit which can be very important in terms of preventing too high ammonia desorption from the SCR unit. As the SRC needs a controlled dosing of urea, simulations can also be useful in testing a large variety of control strategies and closed loop scenarios to optimize the dosing when the full system is taken into account.
The main advantage of the presented methodology is that the users freely can chose which model complexity to use, and therefore have the possibility to for example do detailed optimization of the system components and their effect on each other. This will also allow new and innovative types of modules to be simulated. This could be a combination of two models, e.g. the SCR and DPF, or the SCR and ASC. Furthermore, if a simulation tool is developed, it can be customized to fit the exact needs by adding more features. Another advantage to developing a program is that it is free as long as a programming tool is available. When a simulation tool has been developed in-house, it will be easier to make optimizations using whichever software is available.
A simulation tool based on the methodology presented in this paper will make it possible to simulate the modular processes in a diesel exhaust after treatment system. This tool will allow testing and optimizing any desired configuration of an after treatment system including both state of the art and new and innovative units. A methodology for the development of models for each module has also been presented in this paper along with a methodology for implementation of the system. In the final system it will be possible to test very different systems, e.g. the size of a module or the catalytic substrate, by making only minimal changes to the code of the program.
Jakob Kjobsted Huusom
The financial support from Innovation Fund Denmark under Grant number 103-2012-3 is gratefully acknowledged.
1D - One-dimensional
2D - Two-dimensional
3D - Three-dimensional
ASC - Ammonia Slip Catalyst
CFD - Computational Fluid Dynamics
CPSI - Cells Per Square Inch
DOC - Diesel Oxidation Catalyst
DPF - Diesel Particulate Filter
HC - Hydrocarbons
LSM - Layer-Surface Model
ODE - Ordinary Differential Equation
PDE - Partial Differential Equation
PGM - Platinum Group Metals
PM - Particulate Matter
SCR - Selective Catalytic Reduction
WHSC - World Harmonized Steady state Cycle
WHTC - World Harmonized Transient driving Cycle
[C.sub.ig]- concentration of species i in gas phase [mol/[m.sup.3]]
[C.sub.i,s] - concentration of species i in solid phase [mol/[m.sup.3]]
[E.sub.A] - activation energy [J/mol]
[k.sub.0] - pre-exponential factor [[m.sup.6]/([mol.sup.2] s)]
[N.sub.R] - number of reactions [-]
r - rate of reaction [mol/([m.sup.3] s)]
R - gas constant [J/(K mol)]
t - time [s]
[T.sub.s] - temperature in solid phase [K]
u - exhaust gas velocity [m/s]
v - stoichiometric coefficients [-]
x - axial placement in the catalyst [m]
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Tine Christiansen, Technical University of Denmark
Johanne Jensen, Andreas Aberg, Jens Abildskov, and Jakob Huusom, Technical University of Denmark
e-Available: 16 Sep 2017
TABLE 1 Euro VI emission standards for heavy duty diesel engines. WHSC: World Harmonized Steady state Cycle. WHTC: World Harmonized Transient driving Cycle . All units are given in mg/kWh, except ammonia which is in ppm. CO THC N[O.sub.x] N[H.sub.3] PM WHSC 1500 130 400 10(ppm) 10 WHTC 4000 160 460 10(ppm) 10 [c] SAE International TABLE 2 Overview of modelling work of varying complexity. Reactor Kinetic Kinetic model model parameters Remarks DOC X X X * 1D reactor model. X X * Solid phase energy balance is 3D. reactor model is 2D. * The kinetic model considers oxidation of multiple types of hydrocarbons. X X * Considers oxidation of [H.sub.2] by oxygen. * Considers oxidation of hydrocarbons by both oxygen and N[O.sub.2]. DPF X * 1D reactor model. * Does not consider regeneration by N[O.sub.2]. X * 1D reactor model. * Nearly identical to Bissett's model, but considers regeneration by N[O.sub.2]. X X X * 1D+1D reactor model for a Catalyzed DPF. * Heat loss to the surroundings is considered. X * 3D CFD reactor model. SCR X X * 1D reactor model. * Kinetic model includes an empirical correction for the rate of ammonia oxidation in the presence of NO/N[O.sub.2]. X X * Kinetics of SCR over Cu-ZSM-5. X * 2D reactor model. * No energy balances. * Only NO and N[H.sub.3] are taken into account. X * Kinetics of SCR over Cu-ZSM-5. * Based on work by Olsson et al.  but examines consequences of higher temperatures. X * Kinetic comparison of Fe-ZSM-5 and Cu-Chabazite catalysts. X X X * 3D reactor model. * No energy balances. * Only NO and N[H.sub.3] are taken into account. X X X * 1D reactor model * Full-scale monolith data validation ASC X X * 1D+1D reactor model. * Heat loss to surroundings is considered. X X * Single and dual layer ASC are simulated and compared. X X * Layer-Surface reactor model. * The SCR layer is modelled two-dimensionally and the PGM layer is modelled one-dimensionally. * Should only be used at temperatures above 250 [degrees]C. Developed by DOC Kim and Kim 2009  The rest of the Lafossos et al. 2011  Pandya et al. 2015  DPF Bissett 1984  Zheng and Banerjee 2009  Peck and Becker 2009  Piscaglia et al. 2008  SCR Opitz et al. 2014  Olsson et al. 2007  Forzatti et al. 2000  Pant and Schmieg 2011  Metkar et al. 2012  Chen and Tan 2011  Aberg et al. 2016  ASC Sukumar et al. 2012  Scheuer et al. 2011  Colombo et al. 2012  [c] SAE International TABLE 3 It is shown for each module which species are assumed to react. The species, which have not been marked are assumed inert in the unit. Module DOC DPF SCR ASC [O.sub.2] X X X CO X HC X PM X NO X X X X N[O.sub.2] X X X X N[H.sub.3] X X [c] SAE International TABLE 4 Parameters used in the simulations. Factors Exhaust gas p [c.sub.p] x p [C.sup.In.sup.CO] [mathematical expression not reproducible] [C.sup.In.sup.HC] [C.sup.In.sup.C] [C.sup.In.sup.NO] [mathematical expression not reproducible] ANF DOC L S [phi] DPF L SCR L S [D.sub.h] [[OMEGA].sub.max] [GAMMA] ASC L S [phi] [[epsilon].sub.WC] [GAMMA] Cordierite [lambda] [c.sub.p] [rho] Value Unit Exhaust gas 101 325 Pa 5.0 x [10.sup.4] J/([m.sup.3]K) 56.4 ppm 7.0 x 104 ppm 94.0 ppm 197.5 ppm 202.1 ppm 27.7 ppm 1.2 - DOC 0.1016 m 2610 [m.sup.2]/[m.sup.3] 0.5 - DPF 0.1524 m SCR 0.2286 m 2784 [m.sup.2]/[m.sup.3] 1.16 x [10.sup.-3] m 95 mol/[m.sup.3] 31 mol-sites/[m.sup.3] ASC 0.1016 m 1431 [m.sup.2]/[m.sup.3] 0.4 - 0.5 - 11.6 mol/[m.sup.3] Cordierite 0.85 W/(m K) 1.52 x [10.sup.3] J/(kg K) 140 kg/[m.sup.3] [c] SAE International
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|Author:||Christiansen, Tine; Jensen, Johanne; Aberg, Andreas; Abildskov, Jens; Huusom, Jakob|
|Publication:||SAE International Journal of Commercial Vehicles|
|Article Type:||Case study|
|Date:||Mar 1, 2018|
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