A New Dynamic Injection System of Urea-Water Solution for a Vehicular Select Catalyst Reduction System

Abstract

Since the Euro-ІІІ standard was adopted, the main methods to inhibit NO_x production in diesel engines are exhaust gas recirculation (EGR) and select catalyst reduction (SCR). On these methods SCR offers great fuel economy, so it has received wide attention. However, there also exists a trade-off law between NO_x conversion efficiency and NH₃ slip under dynamic conditions. To inhibit NH₃ slip with high NO_x conversion efficiency, a dynamic control method for a urea water solution (UWS) injection was investigated. The variation phenomena of SCR conversion efficiency with respect to the cross-sensitivity characteristics of the NO_x sensor to NH₃ have been thoroughly analyzed. The methodology of “uncertain conversion efficiency curve tangent analysis” has been applied to estimate the concentration of the slipped NH₃. The correction factor “φ” of UWS injection is obtained by a comparative calculation of the NO_x conversion ability and subsequent NH₃ slip. It also includes methods of flow compensation and flow reduction. The proposed control method has been authenticated under dynamic conditions. In low frequency dynamic experiments, this control method has accurately justified the NH₃ slip process and inhibits the NH₃ emission to a lower level thereby improving the conversion efficiency to a value closer to the target value. The results of European transient cycle (ETC) experiments indicate that NH₃ emissions are reduced by 90.8% and the emission level of NO_x is close to the Euro-Ѵ standard.

1. Introduction

Direct injection diesel engines are preferred for their superior economy, power and emissions. Due to the high combustion temperature of the diesel engine, the nitrogen in the air is easily oxidized by oxygen and produces a large amount of NO_x which have a significant pollution impact on the environment. Therefore, NO_x emissions should be controlled. High pressure fuel injection and turbocharging technology have been used to change the ratio of particulate matter (PM) and NO_x by regulating the fuel injection strategy. From the Euro-ІІ to the Euro-ІІІ phase, the high injection pressure (high common rail fuel injection) system has been used to optimize in-cylinder combustion and regulate the ratio of PM and NO_x to reach the emission goals. From the Euro-ІІІ to the Euro-ІѴ phase, the main problem is how to significantly reduce PM and NO_x emissions. There are two methods at present: one is to use exhaust gas recirculation (EGR) to reduce in-cylinder NO_x, and out of the cylinder, with diesel particulate filter(DPF) to filter PM; the other method is to use select catalyst reduction (SCR) to eliminate NO_x and PM. In small diesel engines, the SCR system is limited by the exhaust gas temperature, so EGR + DPF technology is used as the main method to solve the emission problem. The exhaust temperature of medium and heavy diesel engines is high. At high exhaust temperatures, diesel engines with SCR + high-pressure common rail (HCR) technology are more economical than diesel engines with EGR + DPF technology, so SCR is more widely used in medium and heavy duty diesel engines. From the Euro-ІѴ to the Euro-Ѵ phase, how to further reduce NO_x has become the key problem. The main method is to optimize the SCR system to enhance the NO_x conversion efficiency and reduce the NH₃ leakage [1,2,3,4,5,6].

At present, almost 99% of diesel vehicles work under dynamic operating conditions and thus their NO_x emissions are also a dynamic process. Based on this condition, excellent dynamic performance is an essential characteristic of the SCR system. SCR control strategies mainly focus on optimizing the urea water solution (UWS) injection rate algorithms and NH₃ slip inhibition. However, there is a trade-off law between NO_x conversion efficiency and NH₃ slip under dynamic conditions. When the actual injection rate is lower than the theoretical one, the NO_x can’t be completely reduced. When the actual injection rate is higher than the theoretical value, NH₃ can’t be completely oxidized and thus generates secondary pollution [7,8,9]. Furthermore, NH₃ storage and catalyst release make the NH₃ slip inhibition more difficult.

Some researchers believe that an oxidation processor installed at the end of the exhaust pipe may inhibit NH₃ slip [10]. Nova and Tronconi [11] added an Ammonia Slip Catalyst (ASC) to the exhaust pipe downstream of the SCR system and completed some investigations by experiment and simulation. The results showed that the studied ASC could efficiently clean up the slipped NH₃. Shrestha et al. [12] did some experiments and simulation research on multi-functional wash coated monolith catalysts. They compared the catalysts for a range of temperatures, space velocities, and feed compositions in the presence of H₂O and CO₂. Based on the data acquired from the experiments, a dynamic model of the NH₃ oxidation process was established.

Some researchers supposed that it is necessary to investigate the processes of NH₃ storage, release and reduction reaction as well as the SCR catalyst [13,14]. Rauch et al. [15] monitored the ammonia loading of a vanadia-based SCR catalyst by a microwave-based method. Their experimental results showed that the method can be applied to different temperatures. It was also possible to determine the storage of ammonia from the ammonia-to-NO_x feed ratio. Zhang and Wang [16] focused on the simultaneous estimation of ammonia coverage ratios and input. They configured a three-state nonlinear model with the high-gain observer method by assuming the states of the SCR system are homogenous inside and the SCR cell was a continuous stirred tank reactor. The NO_x sensor was cross-sensitive to the NH₃ concentration, and the NO_x sensor reading was corrected by precise NH₃ sensor measurements. The simulation results showed that the designed observer worked well.

NO_x sensors are used to measure the NO_x concentration downstream from the SCR system and feed it back to the SCR controller. However, research results have showed that NO_x sensors have an enhanced cross sensitivity to NH₃ [17,18,19]. According to the structural characteristics of NO_x sensors, the NH₃ inside the sensor is easily oxidized to NO_x. There are mainly three chemical reactions in this process, as described in Equations (1)–(3) [20,21,22,23]:

$$2{\mathrm{NH}}_3+2{\mathrm{O}}_2\to {\mathrm{N}}_2\mathrm{O}+3{\mathrm{H}}_2\mathrm{O}$$

(1)

$$2{\mathrm{NH}}_3+2.5{\mathrm{O}}_2\to 2{\mathrm{NO}+3\mathrm{H}}_2\mathrm{O}$$

(2)

$$2{\mathrm{NH}}_3+3.5{\mathrm{O}}_2\to 2{\mathrm{NO}}_2+3{\mathrm{H}}_2\mathrm{O}$$

(3)

Wang [24] believed that the main factor is temperature, which may affect the three chemical reactions. The cross sensitivity factor of the NO_x sensor is changed as the temperature changes. Experiments proved that this factor was between 0.5 and 2 for a range of diesel engine exhaust temperatures.

This paper focuses on the trade-off law between NO_x conversion efficiency and NH₃ slip by using a presented method of “uncertain conversion efficiency curve tangent analysis” based on the NH₃ cross sensitivity characteristics of the NO_x sensor. The degree of NH₃ slip will be obtained from the calculation of the parameters which may affect the shape and locations of this tangent. Subsequently, the UWS injection correction factor “φ” will be calculated with the dynamic flow compensation and flow reduction. Finally the accuracy of the UWS correction model and the effectiveness of NH₃ slip inhibition will be verified under low-frequency and high-frequency (ETC cycle) dynamic working conditions.

2. Correction Strategy Mathematical Analysis

For the SCR system control strategy, the corrected UWS injection rate is calculated by Equation (4):

$$q_{\mathrm{uws},\mathrm{Act}}=\left(1+\mathsf{\phi }\right)\times q_{\mathrm{uws},\mathrm{Bas}}$$

(4)

where q_UWS,Act is the real-time UWS injection rate after correction, q_UWS,Bas is the basic UWS injection rate before correction and φ is the correction factor of the UWS injection rate. The Simulink model of the correction strategy is shown in Figure 1.

The model consists of two sub-models. The “Basic UWS Injection Rate Model” sub-model collects three pieces of data: (1) engine operating data EngineMsg, which include speed, torque, original emissions, etc.; (2) exhaust gas processor data EGPMsg, which include exhaust temperature before and after the catalyst, gas flow, etc.; (3) injection system data UDSMsg. These data are combined to calculate q_UWS,Bas.

The “UWS Correction Model” sub-model collects four sets of data: (1) engine operating data; (2) waste gas treatment data; (3) urea injection system data; and (4) NO_x sensor data. These data are processed in the module to obtain the UWS injection rate correction factor φ. The q_UWS,Act is calculated using the factor φ and q_UWS,Bas.

The change rule of q_UWS,Act can be obtained from Equation (5):

$$a_{\mathrm{UWS},\mathrm{Act}}=\frac{\partial q_{\mathrm{uws},\mathrm{Act}}}{\partial t}=q_{\mathrm{uws},\mathrm{Bas}}\frac{\partial \mathsf{\phi }}{\partial t}+\left(1+\mathsf{\phi }\right)\frac{\partial q_{\mathrm{uws},\mathrm{Bas}}}{\partial t}$$

(5)

where a_UWS,Act is the acceleration of q_UWS,Act, and t is the time.

The “φ” (the initial value is “0”) is the key factor to correct the UWS injection and keep the SCR system at a low NH₃ slip level with a high conversion efficiency. The UWS correction model is shown in Figure 2.

The UWS correction model consists of five sub-models:

The “K_T Model” sub-model calculates the real-time NH₃ sensitivity factor of the sensor based on the exhaust gas temperature near the NO_x sensor. The NO_x emission was measured by a NO_x sensor under dynamic conditions. The surrounding NH₃ may be converted into NO_x easily in the NO_x sensor. Therefore, the values of NH₃ and NO_x at the same time will be influenced by the data which is measured by the NO_x sensor, as given by Equation (6):

$$C_{\mathrm{N},\mathrm{Act}}=C_{{\mathrm{NO}}_x,\mathrm{Act}}+K_{\mathrm{T}}{C}_{{\mathrm{NH}}_3,\mathrm{Act}}$$

(6)

where C_N,Act is the NO_x concentration measured by the NO_x sensor. C_NOx,Act is the actual NO_x concentration at the testing position. K_T is the NH₃ cross sensitivity factor of the NO_x sensor which could be obtained from the K_T map and C_NH3,Act is the actual NH₃ concentration at the testing position.

The “Engine Emission Model” sub-model is used to calculate the original engine NO_x emissions, the target conversion efficiency, the ammonia-nitrogen ratio and the target NO_x emission concentration which would support service for the other models as shown in Figure 3. For example the targeted conversion efficiency could be calculated using Equation (7):

$$C_{{\mathrm{NO}}_x,\mathrm{Trg}}=C_{{\mathrm{NO}}_x,\mathrm{Ori}}\cdot P_{\mathrm{Con},\mathrm{Trg}}$$

(7)

where P_Con,Trg is the target conversion efficiency (the highest value without NH₃ slip) which can be obtained from the engine emission map, C_NOx,Ori is the original NO_x concentration of the engine before after treatment and can be obtained by inserting the value calculation of the steady map and C_NOx,Trg is the target NO_x concentration.

The “NH₃ Slip Situation Model” sub-model is based on the output of the first two models to determine the current NH₃ leak situation; more details can be seen in Section 2.1. The “UWS Flow Dynamic Reduction Model” sub-model is triggered when an NH₃ leak occurs. When there is no NH₃ leakage, it is necessary to consider whether there is little UWS injection and trigger the “UWS Flow Dynamic Compensation Model”.

The “UWS Flow Dynamic Compensation Model” and “UWS Flow Dynamic Reduction Model” sub-models are used to calculate the correction factor and compensation factor of the UWS injection rate, respectively (see Section 2.2 and Section 2.3 for more details).

2.1. NH₃ Slip Situation Analysis

In order to justify and analyze the real-time NH₃ slip situation of the engine, a method called “uncertain conversion efficiency curve tangent analysis” is presented. From the real-time measured value C_N,Act, the uncertain conversion efficiency P_Con,Fuz can be calculated using Equation (8). The absolute conversion efficiency P_Con,Abs can be obtained from the calculated valve C_NOx,Act by Equation (9):

$$P_{\mathrm{Con},\mathrm{Fuz}}=\frac{C_{{\mathrm{NO}}_x,\mathrm{Ori}}-C_{\mathrm{N},\mathrm{Act}}}{C_{{\mathrm{NO}}_x,\mathrm{Ori}}}=1-\frac{C_{\mathrm{N},\mathrm{Act}}}{C_{{\mathrm{NO}}_x,\mathrm{Ori}}}$$

(8)

$$P_{\mathrm{Con},\mathrm{Abs}}=\frac{C_{{\mathrm{NO}}_x,\mathrm{Ori}}-C_{{\mathrm{NO}}_x,\mathrm{Act}}}{C_{{\mathrm{NO}}_x,\mathrm{Ori}}}=\frac{\left[C_{{\mathrm{NO}}_x,\mathrm{Ori}}-\left(C_{\mathrm{N},\mathrm{Act}}-K_{\mathrm{T}}{C}_{{\mathrm{NH}}_3,\mathrm{Act}}\right)\right]}{C_{{\mathrm{NO}}_x,\mathrm{Ori}}}=P_{\mathrm{Con},\mathrm{Fuz}}+\frac{K_{\mathrm{T}}{C}_{{\mathrm{NH}}_3,\mathrm{Act}}}{C_{{\mathrm{NO}}_x,\mathrm{Ori}}}$$

(9)

According to the results of Equations (8) and (9), the relative conversion efficiency can be calculated with Equation (10):

$$P_{\mathrm{Con},\mathrm{Rel}}=P_{\mathrm{Con},\mathrm{Abs}}-P_{\mathrm{Con},\mathrm{Trg}}=P_{\mathrm{Con},\mathrm{Fuz}}+\frac{K_{\mathrm{T}}{C}_{{\mathrm{NH}}_3,\mathrm{Act}}}{C_{{\mathrm{NO}}_x,\mathrm{Ori}}}-P_{\mathrm{Con},\mathrm{Trg}}$$

(10)

The change rules of P_Con,Fuz, P_Con,Abs, and P_Con,Rel can be obtained from Equations (11)–(13):

$$v_{\mathrm{Con},\mathrm{Fuz}}=\stackrel{•}{P_{\mathrm{Con},\mathrm{Fuz}}}=-\frac{\partial \left(\frac{C_{\mathrm{N},\mathrm{Act}}}{C_{{\mathrm{NO}}_x,\mathrm{Ori}}}\right)}{\partial t}$$

(11)

$$v_{\mathrm{Con},\mathrm{Abs}}=\stackrel{•}{P_{\mathrm{Con},\mathrm{Abs}}}=\frac{\partial P_{\mathrm{Con},\mathrm{Fuz}}+\partial \left(\frac{K_{\mathrm{T}}{C}_{{\mathrm{NH}}_3,\mathrm{Act}}}{C_{{\mathrm{NO}}_x,\mathrm{Ori}}}\right)}{\partial t}$$

(12)

$$v_{\mathrm{Con},\mathrm{Rel}}=v_{\mathrm{Con},\mathrm{Abs}}-v_{\mathrm{Con},\mathrm{Trg}}=\frac{\partial P_{\mathrm{Con},\mathrm{Fuz}}+\partial \left(\frac{K_{\mathrm{T}}{C}_{{\mathrm{NH}}_3,\mathrm{Act}}}{C_{{\mathrm{NO}}_x,\mathrm{Ori}}}\right)-\partial P_{\mathrm{Con},\mathrm{Trg}}}{\partial t}$$

(13)

where v_Con,Abs, v_Con,Rel, and v_Con,Fuz are their velocities. There are several kinds of NH₃ slip situations, as follows:

(1)

P_Con,Fuz > P_Con,Trg

For the original map of P_Con,Trg obtained from the engine calibration experiments, from the theoretically point of view, with the P_Con,Fuz ≤ P_Con,Trg under any circumstances. In the actual conditions when the engine calibration points are not enough, engine working instability or sensor testing errors might occur and lead to an abnormal circumstance (like P_Con,Fuz > P_Con,Trg). For such an instance the NH₃ slip is assumed to be zero, thus the UWS need not be corrected.

(2)

0 ≤ P_Con,Fuz ≤ P_Con,Trg, and tanθ < 0 (v_Con,Fuz < 0)

In this case, the uncertain conversion efficiency is lower than its target and stays away from the target value gradually. According to Equation (8), P_Con,Fuz becomes smaller due to the increase of the C_N,Act. The enlargement of the C_N,Act may be caused by the following two cases:

• The first case is that the excessively injected UWS caused an acceleration of the process and subsequently an increasing NH₃ slip due unreacted ammonia.
• The second case is that insufficient UWS may cause a slowing the process and lead to a growing amount of NO_x remaining unreduced due to unavailability of reactant.

Therefore, it may be concluded that with the condition a_UWS,Act ≤ 0 and P_Con,Abs ≤ P_Con,Trg, there is no NH₃ slip, thus UWS compensation could be continued. When a_UWS,Act > 0 and P_Con,Abs = P_Con,Trg, NH₃ slip is severely increased, thus UWS injection should be reduced.

(3)

0 ≤ P_Con,Fuz ≤ P_Con,Trg, and tanθ ≥ 0 (v_Con,Fuz ≥ 0)

In this case, the uncertain conversion efficiency is lower than its target and becomes close to the target value gradually. In this case it can be concluded that when a_UWS,Act > 0 and P_Con,Abs ≤ P_Con,Trg, there is no NH₃ slip like the previous cases, thus UWS compensation should be continued. With the condition a_UWS,Act ≤ 0 and P_Con,Abs ≥ P_Con,Trg, UWS injection should be reduced as NH₃ slip is going to increase.

(4)

P_Con,Fuz < 0

This particular case emerges on ruling out the test error and the engine calibration map error, thus under these circumstances C_NOx,Act ≤ C_NOx,Ori (theoretically), whereas, C_N,Act > C_NOx,Ori (P_Con,Fuz < 0), C_NH3,Act > 0 as shown in Equation (7). This case indicates a seriously high level of NH₃ slip therefore UWS injection must be stopped immediately.

2.2. Urea Water Solution Flow Dynamic Compensation

There was no NH₃ slip during the process of the UWS dynamic compensation. Therefore:

$$\{\begin{array}{c}{C}_{{\mathrm{NH}}_3,\mathrm{Act}}\equiv 0\\ C_{{\mathrm{NO}}_x,\mathrm{Act}}\equiv C_{\mathrm{N},\mathrm{Act}}\end{array}$$

(14)

It is indicated that the actual amount of injected UWS (including the NH₃ released from the catalyst) was less than the demand of SCR reaction. The condition is 0 ≤ P_Con,Abs ≤ P_Con,Trg and zero NH₃ slip. Therefore, the correction factor φ can be calculated using Equation (15):

$$\mathsf{\phi }\equiv \frac{\stackrel{•}{\Delta Q_{{\mathrm{NO}}_x,\mathrm{Red}}}}{\stackrel{•}{Q_{{\mathrm{NO}}_x,\mathrm{ActRed}}}}$$

(15)

where Q_NOx,Red (NO_x conversion potential) is the difference between the target value and actual value of the total reduced NO_x in a period as shown by Equation (16) and Q_NOx,AcRed is the actual value of the total reduced NO_x in a specific period given by Equation (17):

$$\begin{array}{cc}\Delta Q_{{\mathrm{NO}}_x,\mathrm{Re}}& ={\displaystyle \int C_{{\mathrm{NO}}_x,\mathrm{Ori}}{P}_{\mathrm{Con},\mathrm{Trg}}{q}_{\mathrm{Exh}}\mathrm{d}t-{\displaystyle \int \left(C_{{\mathrm{NO}}_x,\mathrm{Ori}}-C_{{\mathrm{NO}}_x,\mathrm{Act}}\right)}{q}_{\mathrm{Exh}}\mathrm{d}}t\hfill \\ & ={\displaystyle \int \left[C_{\mathrm{N},\mathrm{Act}}-C_{{\mathrm{NO}}_x,\mathrm{Ori}}\left(1-P_{\mathrm{Con},\mathrm{Trg}}\right)\right]}{q}_{\mathrm{Exh}}\mathrm{d}t\hfill \end{array}$$

(16)

$$Q_{{\mathrm{NO}}_x,\mathrm{ActRe}}={\displaystyle \int \left(C_{{\mathrm{NO}}_x,\mathrm{Ori}}-C_{{\mathrm{NO}}_x,\mathrm{Act}}\right)q_{\mathrm{Exh}}\mathrm{d}}t={\displaystyle \int \left(C_{{\mathrm{NO}}_x,\mathrm{Ori}}-C_{{\mathrm{NO}}_x,\mathrm{N}}\right)q_{\mathrm{Exh}}\mathrm{d}}t$$

(17)

$$\mathsf{\phi }=\frac{\partial \Delta Q_{\mathrm{N}{\mathrm{O}}_x,\mathrm{Red}}/\partial t}{\partial Q_{\mathrm{N}{\mathrm{O}}_x,Act\mathrm{Red}}/\partial t}=\frac{\left[C_{\mathrm{N},\mathrm{Act}}-C_{{\mathrm{NO}}_x,\mathrm{Ori}}\left(1-P_{\mathrm{Con},\mathrm{Trg}}\right)\right]q_{\mathrm{Exh}}}{\left(C_{{\mathrm{NO}}_x,\mathrm{Ori}}-C_{\mathrm{N},\mathrm{Act}}\right)q_{\mathrm{Exh}}}=\frac{C_{{\mathrm{NO}}_x,\mathrm{Ori}}{P}_{\mathrm{Con},\mathrm{Trg}}}{\left(C_{{\mathrm{NO}}_x,\mathrm{Ori}}-C_{\mathrm{N},\mathrm{Act}}\right)}-1$$

(18)

$$C_{\mathrm{N},\mathrm{Act}}\le C_{{\mathrm{NO}}_x,\mathrm{Ori}}$$

(19)

For the control method, the calculation of UWS injection rate and its acceleration may be accomplished with Equation (20) or Equation (21):

$$\{\begin{array}{c}{q}_{\mathrm{uws},\mathrm{Act}}=\frac{C_{{\mathrm{NO}}_x,\mathrm{Ori}}{P}_{\mathrm{Con},\mathrm{Trg}}}{\left(C_{{\mathrm{NO}}_x,\mathrm{Ori}}-C_{{\mathrm{NO}}_x,\mathrm{N}}\right)}{q}_{\mathrm{uws},\mathrm{Bas}}\\ \begin{array}{l}{a}_{\mathrm{uws},\mathrm{Act}}=q_{\mathrm{uws},\mathrm{Bas}}\frac{\partial \left(\frac{C_{{\mathrm{NO}}_x,\mathrm{Ori}}{P}_{\mathrm{Con},\mathrm{Trg}}}{C_{{\mathrm{NO}}_x,\mathrm{Ori}}-C_{\mathrm{N},\mathrm{Act}}}\right)}{\partial t}+\\ \left(\frac{C_{{\mathrm{NO}}_x,\mathrm{Ori}}{P}_{\mathrm{Con},\mathrm{Trg}}}{C_{{\mathrm{NO}}_x,\mathrm{Ori}}-C_{\mathrm{N},\mathrm{Act}}}\right)\frac{\partial q_{\mathrm{uws},\mathrm{Bas}}}{\partial t}\end{array}\\ C_{\mathrm{N},\mathrm{Act}}\le C_{{\mathrm{NO}}_x,\mathrm{Ori}}\end{array}$$

(20)

$$\{\begin{array}{c}{q}_{\mathrm{uws},\mathrm{Act}}=0\\ a_{\mathrm{uws},\mathrm{Act}}=0\\ C_{\mathrm{N},\mathrm{Act}}\le C_{{\mathrm{NO}}_x,\mathrm{Ori}}\end{array}$$

(21)

where NH₃ slip is assumed to be zero.

The value of NO_x emission in this process may be obtained with:

$$\{\begin{array}{c}{Q}_{\mathrm{N}{\mathrm{O}}_x}={\displaystyle \int C_{\mathrm{N},\mathrm{Act}}{q}_{\mathrm{Exh}}\mathrm{d}t}\\ Q_{{\mathrm{NH}}_3}\equiv 0\end{array}$$

(22)

2.3. Urea Water Solution Flow Dynamic Reduction

During the UWS dynamic process, reduction is the response of increasing NH₃ slip. Therefore:

$$\{\begin{array}{c}{C}_{{\mathrm{NH}}_3,\mathrm{Act}}\ne 0\\ C_{{\mathrm{NO}}_x,\mathrm{Act}}+K_{\mathrm{T}}\cdot C_{{\mathrm{NH}}_3,\mathrm{Act}}=C_{\mathrm{N},\mathrm{Act}}\end{array}$$

(23)

The case of 0 ≤ P_Con,Abs ≤ P_Con,Trg and presence of evident NH₃ slip shows that the actual amount of injected UWS (including the NH₃ released from the catalyst) is much more than the demand of the SCR reaction. This current situation indicates that the SCR reaction is saturated as shown by Equation (24):

$$C_{{\mathrm{NO}}_x,\mathrm{Act}}=C_{{\mathrm{NO}}_x,\mathrm{Ori}}\left(1-P_{\mathrm{Con},\mathrm{Trg}}\right)$$

(24)

According to Equation (7):

$$C_{{\mathrm{NH}}_3,\mathrm{Act}}=\frac{C_{\mathrm{N},\mathrm{Act}}-C_{{\mathrm{NO}}_x,\mathrm{Ori}}\left(1-P_{\mathrm{Con},\mathrm{Trg}}\right)}{K_{\mathrm{T}}}$$

(25)

The correction factor φ can be calculated as Equation (26):

$$\mathsf{\phi }=-\frac{\stackrel{•}{Q_{\mathrm{N}{\mathrm{H}}_3}}}{R_{\mathrm{AN}}\stackrel{•}{\left(Q_{\mathrm{N}{\mathrm{O}}_x,\mathrm{TrgRed}}+\frac{Q_{\mathrm{N}{\mathrm{H}}_3}}{R_{\mathrm{AN}}}\right)}}=-\frac{\stackrel{•}{Q_{\mathrm{N}{\mathrm{H}}_3}}}{\stackrel{•}{\left(R_{\mathrm{AN}}{Q}_{\mathrm{N}{\mathrm{O}}_x,\mathrm{TrgRed}}+Q_{\mathrm{N}{\mathrm{H}}_3}\right)}}$$

(26)

where Q_NH3 is the total NH₃ emission amount in a specific period of time given by Equation (27), Q_NOx,TrgRed is the total reduced NO_x with target conversion efficiency of Equation (28) and R_AN is the ammonia nitrogen ratio constant set in the SCR system control strategy:

$$Q_{{\mathrm{NH}}_3}={\displaystyle \int C_{{\mathrm{NH}}_3,\mathrm{Act}}{q}_{\mathrm{Exh}}\mathrm{d}}t={\displaystyle \int \left[\frac{C_{\mathrm{N},\mathrm{Act}}-C_{{\mathrm{NO}}_x,\mathrm{Ori}}\left(1-P_{\mathrm{Con},\mathrm{Trg}}\right)}{K_T}\right]}{q}_{\mathrm{Exh}}\mathrm{d}t$$

(27)

$$\begin{array}{ll}\mathsf{\phi }& =-\frac{\partial Q_{\mathrm{N}{\mathrm{H}}_3}/\partial t}{\partial \left(R_{\mathrm{AN}}{Q}_{\mathrm{N}{\mathrm{O}}_x,\mathrm{TrgRed}}+Q_{\mathrm{N}{\mathrm{H}}_3}\right)/\partial t}\\ & =\frac{\left[C_{\mathrm{N}{\mathrm{O}}_x,\mathrm{Ori}}\left(1-P_{\mathrm{Con},\mathrm{Trg}}\right)-C_{\mathrm{N},\mathrm{Act}}\right]q_{\mathrm{Exh}}}{K_T\left(R_{\mathrm{AN}}{P}_{\mathrm{Con},\mathrm{Trg}}{C}_{{\mathrm{NO}}_x,\mathrm{Ori}}-\frac{C_{{\mathrm{NO}}_x,\mathrm{Ori}}\left(1-P_{\mathrm{Con},\mathrm{Trg}}\right)-C_{\mathrm{N},\mathrm{Act}}}{K_T}\right)q_{\mathrm{Exh}}}\\ & =\frac{C_{{\mathrm{NO}}_x,\mathrm{Ori}}\left(1-P_{\mathrm{Con},\mathrm{Trg}}\right)-C_{\mathrm{N},\mathrm{Act}}}{K_T{R}_{\mathrm{AN}}{P}_{\mathrm{Con},\mathrm{Trg}}{C}_{{\mathrm{NO}}_x,\mathrm{Ori}}-C_{{\mathrm{NO}}_x,\mathrm{Ori}}\left(1-P_{\mathrm{Con},\mathrm{Trg}}\right)+C_{\mathrm{N},\mathrm{Act}}}\end{array}$$

(28)

Due to q_UWS,Act ≥ 0 and 1 + φ ≥ 0:

$$C_{\mathrm{N},\mathrm{Act}}\ge C_{{\mathrm{NO}}_x,\mathrm{Ori}}-\left(1+K_T{R}_{\mathrm{AN}}\right)P_{\mathrm{Con},\mathrm{Trg}}{C}_{{\mathrm{NO}}_x,\mathrm{Ori}}$$

(29)

In the presence of NH₃ Slip, the control method may be applied to calculate the UWS injection rate and its acceleration is given by Equation (30) or Equation (31):

$$\{\begin{array}{c}{q}_{\mathrm{uws},\mathrm{Act}}=\left(1-\frac{1}{K_T{R}_{\mathrm{AN}}}+\frac{C_{{\mathrm{NO}}_x,\mathrm{Ori}}-C_{\mathrm{N},\mathrm{Act}}}{K_T{R}_{\mathrm{AN}}{P}_{\mathrm{Con},\mathrm{Trg}}{C}_{{\mathrm{NO}}_x,\mathrm{Ori}}}\right)q_{\mathrm{uws},\mathrm{Bas}}\\ \begin{array}{l}{a}_{\mathrm{uws},\mathrm{Act}}=q_{\mathrm{uws},\mathrm{Bas}}\frac{\partial \left(\frac{C_{{\mathrm{NO}}_x,\mathrm{Ori}}-C_{\mathrm{N},\mathrm{Act}}}{R_{\mathrm{AN}}{P}_{\mathrm{Con},\mathrm{Trg}}{C}_{{\mathrm{NO}}_x,\mathrm{Ori}}}-\frac{1}{K_T{R}_{\mathrm{AN}}}\right)}{\partial t}+\\ \left(1-\frac{1}{K_T{R}_{\mathrm{AN}}}+\frac{C_{{\mathrm{NO}}_x,\mathrm{Ori}}-C_{\mathrm{N},\mathrm{Act}}}{K_T{R}_{\mathrm{AN}}{P}_{\mathrm{Con},\mathrm{Trg}}{C}_{{\mathrm{NO}}_x,\mathrm{Ori}}}\right)\frac{\partial q_{\mathrm{uws},\mathrm{Bas}}}{\partial t}\end{array}\\ C_{\mathrm{N},\mathrm{Act}}\ge C_{{\mathrm{NO}}_x,\mathrm{Ori}}-\left(1+K_T{R}_{\mathrm{AN}}\right)P_{\mathrm{Con},\mathrm{Trg}}{C}_{{\mathrm{NO}}_x,\mathrm{Ori}}\end{array}$$

(30)

$$\{\begin{array}{c}{q}_{\mathrm{uws},\mathrm{Act}}=0\\ a_{\mathrm{uws},\mathrm{Act}}=0\\ C_{\mathrm{N},\mathrm{Act}}\ge C_{{\mathrm{NO}}_x,\mathrm{Ori}}-\left(1+K_T{R}_{\mathrm{AN}}\right)P_{\mathrm{Con},\mathrm{Trg}}{C}_{{\mathrm{NO}}_x,\mathrm{Ori}}\end{array}$$

(31)

The amount of NO_x emission and NH₃ emission in this process could be determined by:

$$\{\begin{array}{c}{Q}_{\mathrm{N}{\mathrm{O}}_x}={\displaystyle \int C_{\mathrm{N},\mathrm{Act}}{q}_{\mathrm{Exh}}\mathrm{d}t={\displaystyle \int C_{{\mathrm{NO}}_x,\mathrm{Ori}}\left(1-P_{\mathrm{Con},\mathrm{Trg}}\right)q_{\mathrm{Exh}}\mathrm{d}t}}\\ Q_{{\mathrm{NH}}_3}={\displaystyle \int \left[C_{\mathrm{N},\mathrm{Act}}-C_{{\mathrm{NO}}_x,\mathrm{Ori}}\left(1-P_{\mathrm{Con},\mathrm{Trg}}\right)\right]}{q}_{\mathrm{Exh}}\mathrm{d}t\end{array}$$

(32)

2.4. Special Case

For the special case of P_Con,Abs > P_Con,Trg, the actual value is more than the target value of the system conversion efficiency and NH₃ slip is assumed to be zero, as can be seen Equation (33):

$$\{\begin{array}{c}{C}_{{\mathrm{NH}}_3,\mathrm{Act}}\equiv 0\\ C_{{\mathrm{NO}}_x,\mathrm{Act}}\equiv C_{\mathrm{N},\mathrm{Act}}\end{array}$$

(33)

The UWS injection rate doesn’t require any dynamic adjustment thus $\mathsf{\phi }$ $\equiv$ 0. Therefore, it can be described with Equation (34) as follows:

$$\{\begin{array}{c}{q}_{\mathrm{uws},\mathrm{Act}}=q_{\mathrm{uws},\mathrm{Bas}}\\ a_{\mathrm{uws},\mathrm{Act}}=\frac{\partial q_{\mathrm{uws},\mathrm{Bas}}}{\partial t}\end{array}$$

(34)

The amount of NO_x emission and NH₃ emission in this process are:

$$\{\begin{array}{c}{Q}_{\mathrm{N}{\mathrm{O}}_x}={\displaystyle \int C_{\mathrm{N},\mathrm{Act}}{q}_{\mathrm{Exh}}\mathrm{d}t}\\ Q_{{\mathrm{NH}}_3}\equiv 0\end{array}$$

(35)

While in another special case where P_Con,Fuz < 0 indicates that NH₃ slip is very high. Thus UWS injection must be stopped immediately. Now $\mathsf{\phi }$ $\equiv$ 0, and:

$$\{\begin{array}{c}{q}_{\mathrm{uws},\mathrm{Act}}=0\\ a_{\mathrm{uws},\mathrm{Act}}=0\end{array}$$

(36)

The amount of NO_x emission and NH₃ emission in this case can be described as follows:

$$\{\begin{array}{c}{Q}_{\mathrm{N}{\mathrm{O}}_x}={\displaystyle \int C_{\mathrm{N},\mathrm{Act}}{q}_{\mathrm{Exh}}\mathrm{d}t={\displaystyle \int C_{{\mathrm{NO}}_x,\mathrm{Ori}}\left(1-P_{\mathrm{Con},\mathrm{Trg}}\right)q_{\mathrm{Exh}}\mathrm{d}t}}\\ Q_{{\mathrm{NH}}_3}={\displaystyle \int \left[C_{\mathrm{N},\mathrm{Act}}-C_{{\mathrm{NO}}_x,\mathrm{Ori}}\left(1-P_{\mathrm{Con},\mathrm{Trg}}\right)\right]}{q}_{\mathrm{Exh}}\mathrm{d}t\end{array}$$

(37)

3. Experiments and Result Analysis

The low-frequency dynamic working conditions of the engine are reproduced as shown in Figure 1. The detailed dynamic process is shown in Figure 3. The related parameters of the SCR system are changed in a slower manner for this process by an explicit analysis of their relationships and interaction factors. Changes of NO_x emission and NH₃ slip are compared before and after the UWS dynamic correction. The ETC cycle was adopted for the high-frequency dynamic process for further verification of the UWS control method performance. The engine experiment platform is shown in Figure 4.

The specifications of main equipment in the engine experiment platform are listed in

Table 1. Specifications of main equipment.

Name	Type	Manufacturer	Location	Remark
Diesel engine	ISDe270 40	DCEC	Xiangfan, China	L6
Dynamometer	GWD300	POWERLINK	Changsha, China	Eddy current style
Fuel consumption	FC2210	POWERLINK	Changsha, China	Quality style
Air flow meter	ToCeil	Shanghai ToCeil Engine Testing Equipment	Shanghai, China	Hot film style
Emissions analyzer	SESAM4.0	AVL	Graz, Austria	Fourier transform infrared spectroscopy

.

The heavy duty diesel engine parameters used in the experiment are given in

Table 2. Parameters of ISDe270 40 diesel engine.

Cylinder Number	Bore/Stroke	Capacity	Compression Ratio	Rated Power/Speed	Max Torque	Fuel Supply Type
-	mm/mm	L	-	kW/rpm	Nm/rpm	-
L6	107/124	6.7	17.3:1	198/2500	970/1400	high pressure common rail

.

3.1. Mathematical Model Validation

As shown in Figure 5 (in this paper, A indicates the values after correction, B indicates the values before correction, T indicates the values obtained from equipment testing, C indicates the values obtained from calculation and M indicates the values obtained from the maps). The UWS injection was started at the 6th second. It can be seen in Figure 5 that the C_N,Act curve declined gradually in the first 30 s, became stable at a very low level in the second 30 s, and two noticeable humps can be observed in the last 60 s. Considering the NH₃ cross sensitivity of the NO_x sensor, it could be initially assumed that the conversion efficiency was low in the first 30 s as the UWS injection was not sufficient. The NH₃ slip increased significantly in the position of the two humps with the severely overloaded UWS injection. The UWS correction under dynamic conditions is critical for improving SCR conversion efficiency and NH₃ slip inhibition.

The change rules of the four kinds of conversion efficiency which have been discussed in Section 2.1 are shown in Figure 6.

(1)

In the beginning, P_Con,Abs was less than the target valve P_Con,Trg. However, these two values are the same as that after the 30th second.

(2)

P_Con,Fuz and P_Con,Abs remain the same as that before the 60th second. Then, two serious sinks appeared in the P_Con,Fuz curve.

(3)

After the beginning of UWS injection, P_Con,Rel was stable near a 0 value between the 20th and 60th second and fluctuated in a range of ±30% between the 60th and 120th second.

As a result, between the 30th and 60th second, the NH₃ slip is assumed to be zero thus the UWS needs no correction. Between 60th and 90th or 100th and 120th second, NH₃ slip is severely increased, thus UWS injection should be reduced. Between the 0th and 30th second there is no NH₃ slip, thus UWS compensation be continued. The calculated value and actual experimental value of the NO_x and NH₃ are compared in the low-frequency process. The results are shown in Figure 7.

(1)

From the 0 to the 60th second and the 90th to 100th second, the experimental value of the NH₃ concentration downstream from the SCR system is almost 0 ppm. The NO_x concentration and NH₃ concentration calculated by the correction model completely overlap with the experimental values.

(2)

From the 60th to 90th second and the 100th to 120th second, there are slight deviations in the hump position between the calculated value and the experimental value of the NH₃ concentration. The two compared values of NO_x concentration no longer completely overlap, but the range and the change rate are apparently the same.

(3)

At zero NH₃ slip condition, the calculation deviation of NH₃ concentration was between −10 and 0 ppm and that of the NO_x concentration was between −20 and 20 ppm.

(4)

Under high NH₃ slip conditions, the calculation deviation of NH₃ concentration was between −40 and 100 ppm and that of NO_x concentration was between −70 and 70 ppm.

3.2. Low-Frequency Dynamic Process Correction Result

The low-frequency process has been repeated with the dynamic correction of the UWS injection. The NO_x and NH₃ emissions after the correction are shown in Figure 8.

(1)

From the UWS injection starting position to 60th second there was no NH₃ slip. Between the 60th and 120th second the second two humps appeared in the NH₃ concentration curve at less than 80 ppm. That’s because of the fractionally unreacted NH₃ slip downstream of the SCR system.

(2)

In the low-frequency process, the actual tested value of the NO_x emission was almost the same as the target value. The actual tested value was slightly lower than the target value in the hump region of the NH₃ slip. That’s because of the undue UWS injection and more NO_x was restored by the excessive NH₃.

(3)

In the hump region of the NH₃ slip, the measured value is slightly higher than the target value of the NO_x concentration. That’s because the NO_x sensor was influenced by NH₃ and NO_x at the same time as shown in Equation (7).

Comparing the engine emissions before and after the UWS dynamic correction:

(1)

The C_NOx,Act was slightly reduced in the last 60 s on application of the UWS dynamic correction. However, the control method has no significant effect on the value of C_NOx,Act in the low-frequency process.

(2)

The C_NH3,Act was also significantly reduced in the last 60 s after the UWS dynamic correction application. The values of C_NH3,Act in the low-frequency process are also greatly influenced by the application of the correction.

(3)

Overall, the application of UWS dynamic control method has reduced ∫C_NH3,Act dt by 92.68%, respectively. Moreover it has also improved ∫C_NOx,Act dt by 5.58%.

The change trends of the all four kinds of conversion efficiencies are compared after applying the control method as shown in Figure 9.

(1)

In the beginning of the low-frequency process, P_Con,Abs was smaller than P_Con,Trg. However, the two curves overlapped after the 15th second.

(2)

From 0 to 60th second, P_Con,Fuz was the same as P_Con,Abs, whereas, after the 60th second P_Con,Fuz started to deviate with a slightly sinking trend.

(3)

Initially P_Con,Abs was less than 0 with a rising trend, whereas, it became stable when close to 0 and 15th to 60th second, while from 60th to 120th second it fluctuated many times with an amplitude between −15% and 15%.

(4)

P_Con,Abs and P_Con,Trg were achieved in a shorter period as compared to Figure 4. The sinking amplitude of the P_Con,Fuz curve has significantly decreased after the 60th second and became stable in the last 60 s.

The calculated values and experimental values of the NO_x and NH₃ were further compared to ensure that the revised data can be well trusted as shown in Figure 10.

(1)

In the corrected low-frequency process the trend of the calculated NH₃ concentration was the same with that of the experimental value. The deviation of the calculation was more obvious in the region of high NH₃ slip as compared to the results shown in Figure 7. The deviation oscillated between −10 to 0 ppm and −5 to 0 ppm with NH₃ slip and between −40 to 100 ppm and −20 to 15 ppm without NH₃ slip.

(2)

Moreover, during the corrected low−frequency process trend of the calculated NO_x concentration was the same as the actual tested value. The calculation deviation was uniformly distributed and oscillated between −70 to 70 ppm and −20 to 20 ppm as compared with Figure 7.

(3)

NO_x concentration calculation and NH₃ concentration downstream of the SCR system would become more accurate with application of the UWS dynamic correction.

It is compared by the correction factor φ before and after applying the UWS dynamic control method as illustrated in Figure 11 (φ_A and φ_B indicate the correction factors after and before applying the control method, respectively).

(1)

From the UWS injection starting to 20th second, φ_B remained at more than 0 with a gradually declining trend. That is for the catalyst NH₃ storage characteristic therefore UWS injection should be compensated.

(2)

From 20th to 60th second, φ_B remained constant and close to 0. Now catalyst NH₃ storage has been saturated without NH₃ slip so UWS injection may not be corrected.

(3)

From 60th to 120th second, φ_B was less than 0. As compared to Figure 7 it is observed that the change trend of φ_B was contrary to the change trend of NH₃ concentration. It is because of the severely increasing NH₃ slip and UWS injection must be reduced.

(4)

φ_A and φ_B were greater than 0 and declined gradually from the starting position of UWS injection till the 20th second. However, the decrease of φ_A was faster than that of φ_B.

(5)

φ_A and φ_B remained close to 0 from 20th till the 60th second.

(6)

Values of both the factors (φ_A and φ_B) became less than 0 during the last 60 s. Both factors shared two troughs. The trough values of φ_B ranged from −5 to −8 and that of the φ_A was −1 to 0 in curve.

The uncertain conversion efficiency P_Con,Fuz and its velocity v_Con,Fuz before and after applying the UWS dynamic correction are compared as shown in Figure 12:

(1)

P_Con,Fuz and v_Con,Fuz were changed in the last 60 s on applying UWS injection dynamic correction during a high level of NH₃ slip.

(2)

The P_Con,Fuz after correction appeared more close to P_Con,Trg and its range was reduced from −250%–95% to 40%–95% compared to the values before correction.

(3)

The range of the v_Con,Fuz was reduced from −70%–30% to −10%–10% compared to the value before correction.

3.3. High-Frequency Dynamic Process Correction Result

The emission data comparison in ETC cycle before and after the UWS dynamic control method application is shown in Figure 13.

The result indicated a great high efficiency of NO_x conversion in the two tests. The NO_x emission was improved by 53.9% and the NH₃ slip was reduced by 90.8% with the application of the control method. The NH₃ slip was also inhibited significantly. The levels of engine NO_x emissions and NH₃ slip were improved and conform to the Euro-V standard.

4. Conclusions

(1)

It can be generalized that the “uncertain conversion efficiency curve tangent analysis” method can accurately justify the different NH₃ slip situation.

(2)

The calculation deviation can be controlled with NO_x between −20 ppm and 20 ppm and NH₃ between −20 ppm to 15 ppm by application of UWS dynamic correction in a low-frequency process. The NO_x emission was improved by 5.58% and NH₃ slip was reduced by 92.68%.

(3)

In the application of UWS dynamic correction in high-frequency process (i.e., during of ETC test), in spite the fact the NO_x emission has been improved by 53.9%, the NH₃ slip was reduced by 90.8%. The level of engine NO_x emissions and NH₃ slip has been improved up to Euro-IV and closer to the Euro-V standard. The newly developed method presents a significant NH₃ slip inhibition.