Numerical simulation of catalytic converter of urea scr system based on matlab by menez

Scientific Journal of Control Engineering April 2014, Volume 4, Issue 2, PP.51-57

Numerical Simulation of Catalytic Converter of UREA-SCR System Based on MATLAB Pei Zhenga, Jingguan Yinb, Xiaolong Cuic College of Energy and Power Engineering, Inner Mongolia University of Technology, Hohhot 010051 China Email: a#zhengpei@imut.edu.cn, byinjinguan@163.com, c317164089@qq.com

Abstract In order to content more stringent emissions regulations, the purification measures about NOx must be taken. It’s confirmed that Selective catalytic reduction technology is useful for the exhaust gas purification. In this paper, we set up a catalytic converter model by the MATLAB software, and simulate its working process. Comparing the experimental data verifies the veracity and reliability of the model, and the results are shown. Keywords: UREA-SCR; Catalytic Converter; Numerical Simulation

1 Introduction In practical application, the emissions of diesel engine will be affected by many factors, if study these factors which impact on SCR catalyst conversion efficiency or the whole system performance separately in the actual experiments are very complicated and tedious work. But by the method of numerical simulation can make an accurate simulation on diesel engine exhaust components, temperature and the concentration. It provides a convenient way to separate research a particular factor's influence on the SCR system. Because there are a variety of structure on the catalysts, and catalytic converter’s parameters such as length to diameter ratio, porosity, channel width and the thickness of coating is different will have different effects on catalyst features. If it compared through the experiment research will be costly and time consuming, but numerical simulation can be flexible on the parameter changes. So through the way of combining experimental study and numerical simulation method, not only can save time, but also can save cost.

2 Numerical simulation In diesel engine’s UREA-SCR system, a typical monolithic catalyst has a porous structure. Each channel’s structure of the porous structure is same, and it’s internal flow field distribution and chemical reaction etc are similar, so a single-hole math model can represent the entire catalytic converter and the working process of the catalyst converter. When we study the monolithic catalyst, we can divide catalytic converter into several segments, in this paper, the catalytic converter will be split into 2 units, and each unit will be connected to simulate the working process of the overall catalyst. In addition, in order to simplify the model, this paper has the following assumptions: the system is adiabatic; the gas temperature diffusion on the axis and lengthways is negligible; the flowing gas into the catalyst is a homogeneous medium; the medium density through the catalyst cross-section is calculated. Based on the above assumptions, the model is divided into three parts: a. Reducing agent distribution b. Exhaust gas flow distribution c. The temperature distribution Reducing agent distribution simulation is very important, if reducing agent too much will lead to ammonia slip phenomenon, and reducing agent too little will cause reduction not enough. Nonuniform distribution phenomenon of reducing agent in channel cannot rely on excessive injection. And when - 51 http://www.sj-ce.org

reducing agent distribution is constant in the channel, exhaust gas flow too much leads to low conversion efficiency, and too little goes to the other extreme. Therefore excessive injection makes high conversion efficiency but cause secondary pollution by ammonia slip. So if the SCR system wants to meet the Euro IV, Euro V Standard, the closed-loop control is necessary.

2.1 Chemical reaction There are five mainly chemical reactions in the SCR system, respectively is: r1 CO( NH 2 )2  H 2O   2NH3  CO2

r2 S  NH 3   S  NH3

r3 S  NH3   S  NH3

1 r4 2S  NH 3  2 NO  O2   2S  2 N 2  3H 2O 2

(2.1) (2.2) (2.3) (2.4)

5 r5 (2.5) 2S  NH 3  O2   2S  3H 2O  2 NO 2 The active site on the surface of catalyst is shown by S. (2.1) represents the urea’s thermolysis and hydrolysis; it is the sum of two equations: first, the urea is decomposed in equimolar amounts of NH 3 and HNCO ; then HNCO is hydrolyzed to NH 3 and CO2 on surface of catalyst. The adsorption and desorption of NH 3 equations are given by (2.2) and (2.3). In the process of desorption, generally thinks that the desorption activation energy is reduced with the increase of coverage. In numerical simulation, there are two ways to simulate it: one kind is the linear decrease; the other kind is exponential decline. And at low temperature, ammonia adsorption speed, large amounts of ammonia adsorption on the catalyst, while at high temperature, the adsorption is slow than desorption, could lead to NH 3 slip. The reduction reaction of NO is described by (2.4), only consider standard reduction reaction when simulating because the ratio of NO and NO2 in the diesel engine exhaust is 9:1 in general. When the catalyst’s temperature is higher than 350 C , some of them will be oxidized, expressed by (2.5). The reaction rates of the five reactions are:

r1  k1Curea

(2.6)

r2  k2CNH3 (1   NH3 )

(2.7)

r3  k3 NH3

(2.8)

r4  k4CNO NH3

(2.9)

r5  k5 NH3

(2.10)

 NH is the NH 3 coverage, Coefficient ki is calculated by the Arrhenius Equation: 3

ki  Ai exp(

Ea ,i RTS

) ,1  i  5

(2.11)

Ai is frequency factor, Ea ,i is activation energy which can be seen as a constant which has no reference to T, R is molar gas constant, Ts is the temperature of catalyst.

2.2 Model of the conservation of mass and conservation of energy - 52 http://www.sj-ce.org

According to the main reaction in catalyst and ignore the impact of other gases, the conservation of mass model is set up by (2.2) ~ (2.5).This model includes: the concentration of the NH 3 flow; the concentration of the NO flow; Ammonia coverage on catalyst surface. Respectively as follows: 

V C NO  FCNO,in  r4   r5  FCNO

(2.12)



 NH  r2  r3  r4  r5 3

(2.13)



V C NH3  FCNH3,in  r2   r3  FCNH3

(2.14)

(2.15)   V F is waste gas flow rate. In the case, the waste gas flow rate from catalyst import to the export is constant. CNH3 ,in is the input of Ammonia, CNO ,in is the input of the exhaust gas concentration. The volume of the catalysts represents by V,  is reaction space, it can be showed by the ammonia storage capacity of catalyst (  ).Consolidate the dynamic equation into a state space is as follows:  F F     CNO ,in  k4 CNO NH3   k5 NH3   CNO   CNO   V V      k2CNH 3   NH 3 (CNH 3 k2  k3  CNO k4  k5 )    NH3        F CNH   CNH ,in  k2 CNH (1   NH )  k3 NH   F CNH  3 3 3 3 3 3     V V 

(2.16)

The conservation of energy is represented as: M tot c p (Tin  T )  hA(T  Ts )

(2.17)

M tot is exhaust molar flow, c p is specific heat, h is heat transfer coefficient of inside of catalyst channel, A is the area of catalyst cross profile, T is the temperature of inside of catalyst.

3 State space analysis and design 3.1 State space analysis The closed-loop control of NH 3 is indispensable if it want to meet higher emission regulations. In practical application, we have a feedback of ammonia slip by NH 3 sensor signals aim to build a closed-loop control of the whole system; in numerical simulation, we set up a NH 3 controller for closed-loop control. For the convenience of analysis the state space which in the previous section, we will refer to the states as: x1  CNO , x2   NH3 , x3  CNH3

So (2.16) can be shown as: 

x  Ax  BU ; Y  Cx

(2.18)

As the input of the model, U is the NH 3 concentration and NO concentration of the catalyst import. And the output of the model Y is NH 3 concentration.  A11 A   A21  A31 A11  k4 x2  

A12 A22 A32

F  V   CNO ,in  A13       A23  , B   0  , U     , C  0 0 1 F  CNH ,in  A33  3     V 

F , A12  k5  , A13  0 , A21  0 , V

A22  ( x3k2  k3  x1k4  k5 ) , A23  k2 , A31  0 , A32  k3 ,

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F V For a linear system’s state space, it can be analyzed from two aspects: the state space’s controllability and observability condition. Now we analyze the observability of the state space, according to the necessary and sufficient condition, we can get the observability discriminant matrix:

A33  k2 (1  x2 ) 

1 N   A11  A112

   A12 A23 

0 A12

0 0

A11 A12  A12 A22

(2.19)

When the matrix rank N equals 3, the state space is observed. But there has some situations that the rank did not equals 3, although it will cause state space isn’t observed in theory, in practice it is impossible to happen: one situation is A12  0 .In this situation, the oxidation reaction of NH 3 is not happen. In fact, when T  400 C , basically the oxidation reaction rate is far less than the reduction reaction rate, but oxidation reaction has been existed forever, so this kind of special situation won't appear. The other situation is A23  0 . In this situation the ammonia adsorption is not exist, it clearly not right. Therefore the state can be observed. The controllability of state space explains if the every change of the state affected by the input or not, the controllability discriminant matrix is:  0  M 0   F  V

   F ( A22 A23  A23 A33 ) V  F  ( A23 A32  A332 ) V  A12 A23

F V F A33 V

A23

F V

(2.20)

The characteristics of the controllability discriminant matrix is similar to the observability discriminant matrix, we can make sure the state space can be controlled with the rank M.

3.2 The NH 3 sensor observer and controller design In the study of SCR system, it must design the NH 3 sensor observer in order to prevent secondary pollution by ammonia slip. The Linear observation equation is: 

xob  f ( xob ,U , t )  L(CNH3  CNH3 ,ob )

(2.21)

where xob  CNO,ob  NH3 ,ob CNH3 ,ob  is the observed elements, f is the dynamic nonlinear equation which is T presented in (2.18). Pick L   5 2 5 ensure characteristic value in the left half plane. So that can ensure that the state observer have enough fast convergence speed, make sure the state of observed by observer fully close with the original system. Set up the state controller in order to make the NOx , NH 3 concentration of the export of SCR system is least; traditionally what we call the conversion efficiency refers to the ratio of the NOx concentration of exports and imports. In order to more convenient to observe and control the ammonia slip, to redefine the conversion efficiency as:



CNO,in  CNO,out  CNH3 ,out CNO,in

1

x1   x3 CNO,in

According to this define, pick the switching function s  pout  p , p  x1   x3 .it’s reaching condition is: 



s s  0  s   sgn( x),   0 - 54 http://www.sj-ce.org

(2.22)

so the control equation is: 1 x3,in  x3,ob   ( x1,ob  x1,in )   sgn( x) V  ( x 3,ob  k2 x3,ob (1  x2 )  k3 x2 ) F V '  ( pout  k4 x1 x2   k5 x2 ) F

(2.23)

When   0 , the NH 3 closed-loop is achieved.

4 Model validation and results Select a type four-cylinder diesel engine as the original engine to simulation, select 13 test points and experimental date are shown in table 1: TABLE.1 TEST POINTS AND EXPERIMENTAL DATE Speed

Power

Torque

Gas T

(r/min)

(KW)

(NM)

(℃)

714

0.4

5.8

130.8

1333

198

1418.2

531.8

1655

118

683

380

1655

178

1029.8

421.6

1333

99.3

710.88

432.5

1333

148.8

1065.7

494.4

1333

351.5

333.6

1655

273.5

1370.2

477.4

1655

58.5

337.8

308

1980

244.5

1180.1

452.2

1980

297.6

282.4

1980

182.6

881.9

368.3

1980

121.8

588.3

328.2

Test point

The NO concentration of SCR system’s upstream and downstream on original engine as shown in figure 1: 2500 2000 1500

upstream dowmstream

1000 500 0 1 2 3 4 5 6 7 8 9 10 11 12 13

FIG. 1 THE NO CONCENTRATION OF SCR SYSTEM’S UPSTREAM AND DOWNSTREAM

Compare the NO volume fraction from simulation and experimental data, has a result is shown in figure 2. From figure 2 in points 7, 8, 9, 10, the simulation results have a large deviation with the experimental data; the other points can be good match. The reason of errors occurring in the model is the model is one-dimensional homogeneous steady flow has difference with the actual working condition, which leads to the simulated data is low than the experimental data. - 55 http://www.sj-ce.org

Analysis the catalytic converter with the model, first step when we establish the model we divide the catalytic converter into two segments, it demonstrated that can be good mach with the performance of the catalytic converter. Figure 3 shows the conversion efficiency of two segments. From the figure, the first segment of the catalyst’s conversion efficiency is significantly higher than the second segment, which indicates that catalyst efficiency is declining following the exhaust flow, which because  NH3 of the first segment is less than the second one leads to the conversion efficiency is down. And when idling, the conversion efficiency is very low, close to zero, this is mainly because the exhaust temperature of idle condition is very low, and it hasn't reached the SCR working temperature. 800 experiment simulation

NOx volume fraction/ppm

700

600

500

400

300

200

100

6 8 test point

FIG.2 NO VOLUME FRACTION OF EXPERIMENT AND SIMULATION OF CATALYSTS DOWNSTREAM 80 SCR1 SCR2

conversion efficiency /%

60 50 40 30 20 10 0

6 8 test point

FIG. 3 THE CONVERSION EFFICIENCY OF TWO SEGMENTS

Can be seen from figure 4 when idle the NH 3 emissions are high, the reason is the exhaust temperature is very low leads to the NH 3 slip. In the excess coefficient larger point, the NH 3 slip also has increased. 60

NH3 volume fraction/ppm

6 8 test point

FIG. 4 NH 3 VOLUME FRACTION OF CATALYSTS DOWNSTREAM - 56 http://www.sj-ce.org

5 Conclusion In this paper we study the model of the catalytic converter. The catalytic conversion working is mainly concentrated in the front of the catalyst; the catalytic conversion function declined obviously following the gas flow direction; Catalyst needs certain operating temperature (200~550), when idle condition emission performance is poor, the NH 3 slip still need further control.

REFERENCES [1] Claes Ericson, I.Odenbrand. A state-space simplified SCR catalyst model for real time pplications[C]. SAE Technical papers, 2008-01-0616 [2] Walker A, et al. The Development and In-Field Demonstration of Highly Durable SCR Catalyst Systems[C]. SAE Paper 2004-01-1289 [3] TaoZeMin Song Chonglin, Lv Gang, etc. Dynamic response characteristics of vanadium base SCR catalyst engine test research [J], journal of internal combustion engine, 2009, 27(5) [4] Tong De, Hui Li, Guo xiang, TaoJian Zhong etc. Amino SCR catalytic reaction of numerical simulation and analysis [J]. Journal of internal combustion engine, 2008, 26(4) : 335-340

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