Patent Publication Number: US-2010122520-A1

Title: System for Controlling Urea Injection Quantity of Vehicle and Method Thereof

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     The present application claims priority to Korean Patent Application No. 10-2008-0113489 filed on Nov. 14, 2008, the entire contents of which are incorporated herein by reference. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a vehicle that is fitted with a selective catalytic reduction (SCR) device. More particularly, the present invention relates to a system for controlling urea injection quantity of a vehicle, and the method thereof. 
     2. Description of the Related Art 
     Post-processing devices includes a diesel oxidation catalyst (DOC) that is disposed at a downstream side of an engine to transform non-methane hydro-carbons (NMHC), a catalyzed particulate filter (CPF) that filters particulate matter (PM), and an SCR catalytic convertor that reduces NOx through a reduction reaction. 
     The selective catalyst reduction (SCR) system uses ammonia (NH3) as a reducing agent so as to purify NOx. The NOx of an exhaust gas reacts with the NH3, the ammonia that is absorbed in the catalyst. The ammonia has good selectiveness to the NOx, and even when oxygen exists, the ammonia reacts with well the NOx. 
     A dosing module that is disposed in the front of the SCR catalytic convertor injects a urea solution so as to sustain the purification performance of the SCR catalytic convertor, and the injected urea is transformed to ammonia such that the SCR system maintains a uniform amount of the ammonia. 
     The urea injection controlling method according to the conventional art calculates a necessary ammonia amount corresponding to the NH3/NOx ratio, calculates a necessary urea solution corresponding to the necessary ammonia, and operates an injector of a dosing module to inject the calculated urea solution. 
     In another method thereof, the necessary ammonia is calculated according to the ammonia amount that is stored or attached in the SCR catalytic convertor, the necessary urea is calculated according to the necessary ammonia amount, and the injector of the dosing module is operated to inject the necessary urea solution. 
     However, there is a problem in effectively correspondence in a case in which the exhaust condition of the vehicle is abruptly varied. 
     The information disclosed in this Background of the Invention section is only for enhancement of understanding of the general background of the invention and should not be taken as an acknowledgement or any form of suggestion that this information forms the prior art already known to a person skilled in the art. 
     BRIEF SUMMARY OF THE INVENTION 
     Various aspects of the present invention are directed to provide a urea injection amount control apparatus of a vehicle having advantages of accurately calculating an entire ammonia consumption amount that is affected by an ammonia amount only consumed by NOx, an accumulative absorbed ammonia amount, an absorbed and detached amount of HC, an oxidized amount of ammonia, an deterioration, and so on in a SCR catalytic convertor to control a necessary absorbed ammonia amount such that purification efficiency and purification performance thereof can be improved. 
     In an aspect of the present invention, the urea injection amount control apparatus of a vehicle, may include an engine, an SCR catalytic convertor that is configured to purify NOx through a reduction reaction of the NOx and NH3 that is included in exhaust gas, a dosing module that is configured to inject a urea solution at the front of the SCR catalytic convertor, and a control portion that is configured to estimate a necessary ammonia amount by predicting an entire ammonia consumption amount that is necessary in the SCR catalytic convertor so as to estimate an injection amount of a urea according to the necessary ammonia amount. 
     The control portion may apply an ammonia amount consumed by the NOx, an absorbed ammonia amount, an ammonia reaction rate, an absorbed HC amount, and a deterioration according to exposure time to a predetermined temperature so as to predict the entire necessary ammonia consumption amount, and controls an absorbed ammonia amount according to the predicted entire necessary ammonia consumption amount. 
     The control portion may apply a function of “NOx exhaust amount×stoichiometric ratio (NH 3 /NOx)×the ammonia reaction rate” to estimate the ammonia amount consumed by the NOx. 
     The control portion may apply a function of “a present absorbed ammonia amount+an ammonia inflow amount−an ammonia amount consumed by the NOx (a reacted ammonia amount+a detached ammonia amount)” to estimate the absorbed ammonia amount. 
     The control portion may divide a reacted amount of an ammonia into a reacted amount with the NOx and a reacted amount with oxygen, and applies a NOx purification ratio, in which a specific gravity of a reaction route is applied according to a variation of an exhaust condition and the stoichiometric ratio to estimate the reacted amount with the NOx. 
     In another aspect of the present invention, the method for controlling the urea injection amount of a vehicle, may include calculating an entire consumption amount of an ammonia that is necessary in an SCR catalytic convertor by applying an ammonia consumption amount according to a NOx exhaust amount, an absorbed ammonia amount, an ammonia reaction rate, an absorbed HC amount, and an deterioration, calculating a necessary urea amount by calculating a necessary ammonia amount corresponding to the calculated entire ammonia consumption amount, and injecting the necessary urea amount when a temperature of the SCR catalytic convertor is in a predetermined range. 
     The ammonia reaction rate may include a reaction rate with NOx and a reaction rate with oxygen. 
     The absorbed ammonia amount may be “an accumulatively absorbed amount that is absorbed in the SCR catalytic convertor plus a new inflow amount minus a reacted amount and a detached amount.” 
     In the present invention by the above composition, the ammonia consumption amount is accurately predicted in the SCR catalytic convertor based on the ammonia consumption amount, and the absorbed ammonia amount is controlled to improve the purification performance of the NOx and the responsiveness to the rapid variation of the driving condition, such that the purification efficiency is enhanced. 
     The methods and apparatuses of the present invention have other features and advantages which will be apparent from or are set forth in more detail in the accompanying drawings, which are incorporated herein, and the following Detailed Description of the Invention, which together serve to explain certain principles of the present invention. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  shows a urea injection amount control apparatus of a vehicle according to an exemplary embodiment of the present invention. 
         FIG. 2  is a graph showing a NOx concentration value after start-up of an engine. 
         FIG. 3  is a graph showing a relationship between the ammonia amount that is attached in the SCR catalytic convertor and the temperature thereof. 
         FIG. 4  is a graph showing the NOx purification rate according to the temperature of the inlet. 
         FIG. 5  is a flowchart for a urea injection amount control in a vehicle according to an exemplary embodiment of the present invention. 
         FIG. 6  is a flowchart for calculating the ammonia reaction rate in a vehicle according to an exemplary embodiment of the present invention. 
         FIG. 7  is a flowchart for calculating a control value of the absorbed ammonia amount in a vehicle according to an exemplary embodiment of the present invention. 
         FIG. 8  is a flowchart for calculating the absorbed ammonia amount in a vehicle according to an exemplary embodiment of the present invention. 
         FIG. 9  is a flowchart for calculating the absorbed HC amount in a vehicle according to an exemplary embodiment of the present invention. 
     
    
    
     It should be understood that the appended drawings are not necessarily to scale, presenting a somewhat simplified representation of various features illustrative of the basic principles of the invention. The specific design features of the present invention as disclosed herein, including, for example, specific dimensions, orientations, locations, and shapes will be determined in part by the particular intended application and use environment. 
     In the figures, reference numbers refer to the same or equivalent parts of the present invention throughout the several figures of the drawing. 
     DETAILED DESCRIPTION OF THE INVENTION 
     Reference will now be made in detail to various embodiments of the present invention(s), examples of which are illustrated in the accompanying drawings and described below. While the invention(s) will be described in conjunction with exemplary embodiments, it will be understood that present description is not intended to limit the invention(s) to those exemplary embodiments. On the contrary, the invention(s) is/are intended to cover not only the exemplary embodiments, but also various alternatives, modifications, equivalents and other embodiments, which may be included within the spirit and scope of the invention as defined by the appended claims. 
     As those skilled in the art would realize, the described embodiments may be modified in various different ways, all without departing from the spirit or scope of the present invention, and the drawings and description are to be regarded as illustrative in nature and not restrictive. 
       FIG. 1  shows a urea injection amount control apparatus of a vehicle according to an exemplary embodiment of the present invention. 
     The present invention includes an engine  2  as a power source, an exhaust pipe  6  for exhausting exhaust gas from the engine  2 , an SCR catalytic convertor (or filter)  10 , a first NOx sensor  12 , a second NOx sensor  14 , a temperature sensor  16 , a control portion  18 , a dosing module  20 , a mixer  22 , a urea tank  30 , a pump  32 , a urea supply line  34 , and a pressure sensor  36 . 
     The SCR catalytic convertor  10  is made up of V 2 O 5 /TiO 2 , Pt/Al 2 O 3 , or zeolite, an is disposed in a position of the exhaust pipe  6  that is connected to the engine  2  as a power source to purify the NOx through a reduction reaction of the NOx and ammonia that is formed from the urea that is injected from the dosing module  20 . 
     The first NOx sensor  12  is disposed in the inlet side of the SCR catalytic convertor  10  to detect the NOx amount that is included in the exhaust gas flowing into the SCR catalytic convertor  10 , and transmits the related information to the control portion  18 . 
     The second NOx sensor  14  is disposed in the outlet side of the SCR catalytic convertor  10  to detect the NOx amount that is included in the exhaust gas that is processed through the reduction reaction of the SCR catalytic convertor  10 , and transmits the related information to the control portion  18 . 
     The temperature sensor  16  detects the temperature of the SCR catalytic convertor  10  that is activated by the exhaust gas temperature, and transmits the information thereof to the control portion  18 . 
     The control portion  18  analyzes the driving condition of the engine  2 , the exhaust gas temperature, and the information of the first and second NOx sensors  12  and  14  to calculate a entire necessary ammonia amount that is to be process in the exhaust system, and decides a urea injection amount according to the necessary ammonia amount to control the dosing module  20  to inject the urea. 
     The control portion  18  applies an ammonia amount only consumed by the NOx, the absorbed ammonia amount, the reacted ammonia amount, the absorbed HC amount, and the aging rate according to the exposure time at a predetermined temperature so as to predict the entire ammonia consumption amount, and injects the urea solution according to the predicted entire ammonia consumption amount to control the absorbed ammonia amount. 
     The ammonia amount only consumed by the NOx is calculated from the equation of “the NOx exhaust amount×stoichiometric ratio (NH 3 /NOx)×the ammonia reaction rate,” and the absorbed ammonia amount is calculated from the equation of “the present absorbed ammonia amount+the ammonia inflow amount−the ammonia amount consumed by the NOx (the reacted ammonia amount+the desorbed ammonia amount.)” 
     The reacted ammonia amount is divided into the reacted amount with the NOx and the reacted amount with the oxygen, and the NOx purification rate, in which the specific gravity variation of the reaction route is reflected according to the variation of the exhaust condition, and the stoichiometric ratio are applied to calculate the reacted amount with the NOx. 
     The absorbed HC amount is the accumulatively absorbed amount plus the HC inflow amount minus the desorbed HC amount minus the reacted HC amount. 
     According to the control of the control portion  18 , the dosing module  20  has the injector to inject the urea solution that is estimated in the temperature condition. 
     The pressure sensor  36  detects the pressure that is formed in the urea supply line  34  to transmit the related information to the control portion  18  such that the predetermined pressure thereof is continued during the operation of the engine  2 . 
     First, the characteristics of the SCR catalytic convertor are explained as follows. 
       FIG. 2  is a graph showing a NOx concentration value after start-up of an engine. 
     As shown in the  FIG. 2 , while the urea is uniformly injected after start-up of the engine at 200 g/h, the NOx exhaust amount decreases in an “A” area thereof. 
     A greater ammonia amount than a predetermined amount is to be absorbed inside the SCR catalytic convertor  10  for effective reaction with the NOx, and it takes a time to stabilize the reaction thereof. More specifically, it takes a long time to stabilize at a low temperature due to the high absorbed ammonia amount, and it takes a short time to stabilize at a high temperature due to the low absorbed ammonia amount. 
     Further, the responsiveness for the NOx purification can be enhanced in a vehicle in which the driving condition thereof varies irregularly, in a case in which the greater amount of ammonia than a predetermined amount is previously absorbed. 
       FIG. 3  is a graph showing a relationship between the ammonia amount that is attached in the SCR catalytic convertor and the temperature thereof. 
     As shown in the graph, as the temperature of the SCR catalytic convertor  10  increases, the absorbed ammonia amount abruptly decreases, and it is sustained at a predetermined level at a temperature higher than 260° C. 
     However, in a low temperature condition in which the temperature of the SCR catalytic convertor  10  is lower than 220° C., the ammonia is absorbed to the maximum, and if the temperature of the SCR catalytic convertor  10  is abruptly increased to a high temperature of higher than 260° C., the ammonia absorption capacity of the SCR catalytic convertor  10  is lowered, that is, the absorbed ammonia amount exceeds the ammonia storage capacity thereof, such that the ammonia is detached therefrom to cause “ammonia-slip.” 
     Although the ammonia is previously absorbed, it is necessary to decrease the maximum absorption capacity considering variations of possible conditions, it is also necessary to accurately detect the absorption amount at specific timing so as to control the absorption amount, and it is also necessary to detect the reacted amount thereof. 
     A variety of reactions inside the SCR catalytic convertor  10  are shown in Table 1 below. It can be known that there are many kinds of ammonia NH3 consumption routes in addition to the NOx reaction, and the ammonia can be actively oxidized at a high temperature such that calculation of the necessary ammonia amount has to be considered. 
     
       
         
           
               
               
               
               
               
               
             
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                   
                   
                 Reaction 
                 NH  NO x   
                   
               
               
                   
                 Kind 
                 Oxygen 
                 speed 
                 ratio 
                 Product 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 (1) 
                 4NH 3  + 6NO→5N 2  + 6H 2 O 
                 NO 
                 — 
                 Slow 
                 4/6 = 0.67 
                 N 2   
               
               
                 (2) 
                 4NH 3  + 4NO + O 2 →4N 2  + 6H 2 O 
                   
                 O 2   
                 Medium 
                 4/4 = 1.0 
               
               
                 (3) 
                 8NH 3  + 6NO 2 →7N 2  + 12H 2 O 
                 NO 2   
                 — 
                 Slow 
                 8/6 = 1.33 
               
               
                 (4) 
                 4NH 3  + 2NO 2  + O 2 →3N 2  + 6H 2 O 
                   
                 O 2   
                 Medium 
                 4/2 = 2.0 
               
               
                 (5) 
                 2NH 3  + NO + NO 2 →2N 2  + 3H 2 O 
                 NO + NO 2   
                 — 
                 Fast 
                 2/2 = 1.0 
               
               
                 (6) 
                 2NH 3  + 8NO→5N 2 O + 3H 2 O 
                 NO 
                 — 
                 — 
                 2/8 = 0.25 
                 N 2 O 
               
               
                 (7) 
                 4NH 3  + 4NO + 3O 2 →4N 2 O + 6H 2 O 
                   
                 O 2   
                   
                 4/4 = 1.0 
               
               
                 (8) 
                 6NH 3  + 8NO 2 →7N 2 O + 9H 2 O 
                 NO 2   
                 — 
                   
                 6/8 = 0.75 
               
               
                 (9) 
                 4NH 3  + 4NO 2  + O 2 →4N 2 O + 6H 2 O 
                   
                 O 2   
                   
                 4/4 = 1.0 
               
               
                 (10) 
                 2NH 3  + 2O 2 →N 2 O + 3H 2 O 
                 — 
                 O 2   
                   
                 ∞ 
                 N 2 O 
               
               
                 (11) 
                 4NH 3  + 3O 2 →2N 2  + 6H 2 O 
                   
                 O 2   
                   
                   
                 N 2   
               
               
                 (12) 
                 4NH 3  + 5O 2 →4NO + 6H 2 O 
                   
                   
                   
                   
                 NO 
               
               
                 (13) 
                 2NH 3  + 2NO 2 →NH 4 NO 3  + N 2  + H 2 O 
                 NO 2   
                 — 
                   
                 2/2 = 1.0 
                 N 2 , NH 4 NO 3   
               
               
                   
               
               
                     indicates data missing or illegible when filed 
               
            
           
         
       
     
       FIG. 4  is a graph showing the NOx purification rate according to the temperature of the inlet. 
     As the ratio of the NO 2 /NOx is low, the purification rate suddenly increases according to the temperature increase of the SCR catalytic convertor  10 , and as the ratio of the NO 2 /NOx is high, the purification rate suddenly increases at a low temperature and sustains its maximum purification rate at a predetermined temperature of about 200° C. 
     It can be known that the NO 2 /NOx ratio and the temperature are important factors for the stoichiometric ratio, the reaction speed, and the purification rate, and in a case in which the HC is absorbed in the SCR catalytic convertor  10 , the reaction with the NOx can be prevented such that the absorption and detachment of the HC and the oxidization thereof need to be considered. 
     In addition, it is necessary to consider the flow velocity (space speed) and the performance variation according to the deterioration of the filter (catalyst). 
     The above descriptions are arranged to obtain the following results. 
     It is necessary to obtain rapid responsiveness at a low temperature by previously attaching the ammonia in the SCR catalytic convertor  10 , it is necessary to accurately detect the reacted amount of the ammonia so as to control the absorbed ammonia amount, and in addition to the purification reaction with the NOx, the ammonia oxidization, the attachment and detachment of the HC, and the oxidization of the ammonia need to be considered. 
     Also, the flow velocity (space speed) and the deterioration of the catalyst need to be considered, and the NO 2 /NOx ratio, the stoichiometric ratio, the reaction speed, and so on are also important factors for determining the purification rate of the NOx. 
     The ammonia consumption amount is accurately calculated according to a variety of conditions of the SCR catalytic convertor as stated above, and accordingly the method for controlling the absorbed ammonia amount will be hereinafter specifically described as follows. 
     When the engine of the vehicle is started, the control portion  18  detects the operation conditions including the temperature of the SCR catalytic convertor  10 , the exhaust gas flow velocity, the NOx concentration, the accumulatively absorbed ammonia amount, the NO 2 /NOx ratio, the deterioration, etc., to calculate the ammonia stoichiometric ratio equivalent by multiplying the mass flow velocity of the NOx by the stoichiometric ratio (NH 3 /NOx) in S 101 . 
     The above stoichiometric ratio (NH 3 /NOx) is estimated as a function of the catalyst temperature, the NO2/NOx ratio, and the deterioration. 
     As stated above, if the ammonia stoichiometric ratio equivalent is calculated, the ammonia equivalent that is calculated in S 101  is multiplied by the ammonia reaction rate to calculate the ammonia amount only consumed by the NOx in S 102 . 
     Further, the absorbed ammonia amount is added to the ammonia amount consumed by the NOx of the exhaust gas, which is calculated in S 102 , to calculate the necessary ammonia amount in S 103 , the molecular weight ratio (urea/NH3) is multiplied by the necessary ammonia amount that is calculated in S 103 , and then the result thereof is divided by the urea mass ratio inside the urea solution to calculate the necessary urea amount in a S 104 . 
     When the necessary urea amount for the necessary ammonia is calculated according to the above procedures, the temperature of the SCR catalytic convertor  10  is detected through the temperature sensor  14  in S 105  to estimate whether the temperature of the SCR catalytic convertor  10  is higher than a predetermined value, for example 200° C., at which the NOx can be purified, in S 106 . 
     If the temperature is lower than the predetermined value, that is, the temperature is not at an injection-able condition temperature in S 106 , the control portion  18  closes the injector of the dosing module  20  so as to not inject the urea in S 111 , and if the temperature is at in an injection-able condition temperature, it is estimated that the necessary urea amount is larger than a minimum amount that can be injected in S 107 . 
     If the necessary urea amount is less than the injection-able minimum amount in S 107 , the control portion  18  stops injecting the urea in S 111 , and if the necessary urea amount is larger than the injection-able minimum amount, it is estimated that the necessary urea amount is less than an injection-able maximum amount in S 108 . 
     If the necessary urea amount is less than the injection-able maximum in the S 108 , the control portion  18  controls the dosing module  20  to inject the necessary urea amount, which is calculated in S 104 , in S 109 . 
     However, if the necessary urea amount is larger than the injection-able maximum in S 108 , the control portion  18  controls the injector of the dosing module  20  to inject the urea at a predetermined injection-able maximum in S 110 . 
     The injection-able maximum is set according to the hardware specifications of the dosing module  20 , the temperature and flow velocity of the exhaust gas, and the temperature of the catalyst inside the SCR, and the set value thereof is varied corresponding to the deviation. 
       FIG. 3  is a graph showing a relationship between the ammonia amount that is attached in the SCR catalytic convertor and the temperature thereof. 
     In S 102  of the  FIG. 5 , the ammonia reaction rate, which is applied to calculate the ammonia amount only consumed by the NOx, is calculated as follows. 
     The reaction rate of the ammonia with the NOx is calculated from a function including the catalyst temperature and the exhaust gas flow velocity, the NOx concentration, the accumulatively absorbed ammonia amount, the NO2/NOx ratio, the deterioration corresponding to the exposure to a high temperature, and the absorbed HC amount in S 201 , and the reaction rate of the ammonia with the oxygen is calculated from the function including the catalyst temperature and the exhaust gas flow velocity, the oxygen concentration, the accumulatively absorbed ammonia amount, the NO2/NOx ratio, the deterioration corresponding to the exposure to a high temperature, and the absorbed HC amount in S 202 . 
     Further, the reaction rate of the ammonia with the NOx that is calculated from S 201  is added to the reaction rate of the ammonia with the oxygen that is calculated from S 202  to calculate the ammonia reaction rate in S 203 . 
       FIG. 7  is a flowchart for calculating a control value of the absorbed ammonia amount in a vehicle according to an exemplary embodiment of the present invention. 
     The control value of absorbed ammonia amount, which is applied so as to calculate the necessary ammonia amount in S 103  of the  FIG. 2 , is calculated as follows. 
     The objective value of the absorbed ammonia amount is calculated from a function including the catalyst temperature, the exhaust gas flow velocity, the deterioration, and the absorbed HC amount in S 301 , and the difference value of the absorbed ammonia amount is calculated by subtracting the calculated objective valve of the absorbed ammonia amount from the present accumulatively absorbed amount in S 302 . 
     Next, the control value of the absorbed ammonia amount is calculated from the function including the difference value of the absorbed ammonia amount that is calculated in S 302 , the exhaust gas temperature, the exhaust gas flow velocity, and the catalyst temperature in S 303 . 
       FIG. 8  is a flowchart for calculating the absorbed ammonia amount in a vehicle according to an exemplary embodiment of the present invention. 
     The reacted ammonia amount, which is consumed according to the present driving condition, is calculated by the absorbed ammonia amount that is accumulated in the SCR catalytic convertor  10 . 
     That is, the ammonia amount consumed by the NOx exhaust amount and the reaction rate of the ammonia with the oxygen are applied to calculate the reacted ammonia amount. 
     The reacted ammonia amount, which is calculated in S 401 , is subtracted from the accumulatively absorbed ammonia amount to calculate the absorbed amount that is absorbed in the SCR catalytic convertor (catalyst)  10  in S 402 . 
     In addition, a new inflow amount, which is formed by injecting the urea through the dosing module  20 , is calculated in S 403 . 
     The result value, which is calculated by multiplying the urea injection amount by the mass ratio of the urea, is divided by the molecular weight so as to calculate the new inflow amount. 
     Thereafter, the absorbed maximum amount that the SCR catalytic convertor  10  can store is calculated from a function including the catalyst temperature, the exhaust gas flow velocity, and the deterioration in S 404 , and the saturation degree of the SCR catalytic convertor  10  is calculated through the absorption amount/maximum absorption amount in S 405 . 
     The ammonia detached amount is calculated in the SCR catalytic convertor in a S 406 , and the actual absorbed ammonia amount is calculated in S 407 . 
     The accumulatively absorbed ammonia amount, which is calculated in S 402 , plus the new inflow amount, which is calculated in S 403 , minus the detached amount, which is calculated in S 406 , is the actual absorbed ammonia amount that is calculated in S 407 . 
     Further, it is estimated whether the actual absorbed ammonia amount ranges from “0” to the maximum in S 408 , and in a case that the actual absorbed ammonia amount is out of the range, it is estimated as “0” or the maximum, and if it is larger than zero or smaller than the maximum, the calculated actual absorbed ammonia amount is applied in S 409 . 
       FIG. 9  is a flowchart for calculating the absorbed HC amount in a vehicle according to an exemplary embodiment of the present invention. 
     A function including the catalyst temperature, the exhaust gas temperature, and the deterioration is applied to the accumulatively absorbed HC amount in the SCR catalytic convertor  10  to calculate the reacted HC amount in S 501 , and the accumulatively absorbed HC amount, which is accumulated in the SCR catalytic convertor  10 , minus the reacted HC amount, which is calculated in S 501 , is an actual absorbed HC amount that is substantially absorbed in the SCR catalytic convertor  10  in S 502 . 
     Further, a function including the catalyst temperature, the exhaust gas flow velocity, and the saturation degree is applied to the HC inflow amount to calculate the absorbed HC amount that is absorbed new in the SCR catalytic convertor  10  in S 503 , and a function including the catalyst temperature, the exhaust gas flow velocity, and the deterioration is applied to calculate the absorbed HC maximum amount in S 504 . 
     Thereafter, the HC saturation degree of the SCR catalytic convertor  10  is calculated in S 505  from the accumulatively absorbed amount that is calculated from S 502  and the absorbed maximum that is calculated from S 504 , and a function including the catalyst temperature, the exhaust gas temperature, and the saturation degree is applied to the accumulatively absorbed amount that is calculated in S 502  to calculate the detached HC amount from the SCR catalytic convertor  10  in S 506 . 
     The accumulatively absorbed HC amount, which is calculated in S 502 , plus the new absorbed HC amount, which is calculated in S 503 , is the actual absorbed HC amount that is calculated in S 507 . 
     It is estimated whether the actual absorbed HC amount ranges from “0” to the maximum in S 508 , and in a case that the actual absorbed HC amount is out of the range, it is estimated as “0” or the maximum, and if it is larger than zero or smaller than the maximum, the calculated actual absorbed HC amount is applied in S 509 . 
     The foregoing descriptions of specific exemplary embodiments of the present invention have been presented for purposes of illustration and description. They are not intended to be exhaustive or to limit the invention to the precise forms disclosed, and obviously many modifications and variations are possible in light of the above teachings. The exemplary embodiments were chosen and described in order to explain certain principles of the invention and their practical application, to thereby enable others skilled in the art to make and utilize various exemplary embodiments of the present invention, as well as various alternatives and modifications thereof. It is intended that the scope of the invention be defined by the Claims appended hereto and their equivalents.