Method for model-based determination of a temperature distribution of an exhaust gas post-treatment unit

Abstract

In a method for a model-based determination of a temperature distribution of an exhaust gas post-treatment unit, a differentiation is made between steady operating states and non-steady operating states by taking into account the axial and the radial temperature distribution, and, on the basis of virtual segmentation of the post-treatment unit, in particular the radial heat transfer to the surroundings is taken into account in the model-based determination for steady operating states, and for non-steady operating states the heat transfer from the exhaust gas which flows axially through the post-treatment unit to the segments is taken into account by a heat transfer coefficient k.

Claims

1. A method for a model, comprising: determining a theoretical temperature distribution of an exhaust gas post-treatment unit, wherein exhaust gas flows axially through the post-treatment unit and which the post-treatment unit is segmented at least axially in a model of the post-treatment unit, wherein the theoretical temperature distribution is determined from at least: (a) a theoretical axial heat transfer between the segments due at least predominantly to the exhaust gas, the radial heat transfer determined from at least a heat transfer coefficient (k) and; (b) a theoretical radial heat transfer from a circumference of the post-treatment unit to the surroundings, the radial heat transfer determined from at least a heat transfer resistance value (R.sub.c), determining a deviation of a theoretical temperature downstream of the post-treatment unit from an actual temperature downstream of the post-treatment unit, and in response to the determination of the deviation, (a) adjusting the heat transfer resistance value (R.sub.c) when the model is in a steady-state operating mode, and (b) adjusting the heat transfer coefficient (k) when the model is in a non-steady state operating mode are determined based upon a variation of an exhaust gas temperature measured upstream of the post-treatment unit at predetermined and regular time intervals with respect to a chronological mean value of the exhaust gas temperature; and applying an amount of reducing agent to the post-treatment unit, the amount determined from at least the theoretical temperature distribution.

2. The method as claimed in claim 1, wherein, for the modeling with respect to axial segmentation of the post-treatment unit is axially segmented into disks and radially segmented into rings, wherein the average calculated temperature downstream of the post-treatment unit is determined by averaging the temperatures calculated for each radial segment of the last disk in the axial direction.

3. The method as claimed in claim 1, wherein, for a steady-state operating mode which is based on a given operating state, the given heat transfer coefficient (k) for this operating state is retained in the model calculation.

4. The method as claimed in claim 1, wherein, for a non-steady-state operating mode which is based on a given operating state, a constant heat transfer coefficient (R.sub.c) is expected in the modeling for this operating, state.

5. The method as claimed in claim 1, wherein the heat transfer coefficient (R.sub.c) is dependent on the ambient conditions of the post-treatment unit.

6. The method as claimed in claim 1, wherein the direction of the change in the heat transfer coefficient (k), is determined at least by the derivatives of the measured and calculated average temperature profiles downstream of the post-treatment, wherein the heat transfer coefficient (k) is increased and decreased as a function of the relative timing of the inflection points which correspond to the maximum and minimum values of the derivatives.

7. The method for the model-based determination of the temperature distribution of an exhaust gas post-treatment unit using an SCR catalytic converter, as claimed in claim 1; wherein the SCR catalytic converter is integrated into a regulating structure with at least one SCR model, a pilot controller and a regulator, wherein a quantity of NH.sub.3 which is fed to the SCR catalytic converter is determined based upon at least an emission limiting value, by the pilot controller, wherein the SCR model supplies the input variables for the pilot controller, wherein in the pilot controller the NO.sub.x value corresponding to the supplied data is continuously calculated and compared with the predefined emission value, and wherein, by adapting the respective NH.sub.3 quantity which is fed to the SCR catalytic converter, the regulator approximates the NO.sub.x actual value measured downstream of the SCR catalytic converter to the a calculated NO.sub.x setpoint value downstream of the SCR catalytic converter.

8. The method as claimed in claim 7, wherein the approximation is performed incrementally in the steady-state mode in order to compensate deviations of the NO.sub.x actual value measured downstream of the SCR catalytic converter from the calculated NO.sub.x setpoint value downstream of the SCR catalytic converter.

9. The method as claimed in claim 7, wherein input variables provided for the pilot controller include at least: NO and NO.sub.2 downstream of an SCR ppm, the maximum amount of NO and NO.sub.2 mol/s which can be converted at the given load, the converted NO and NO.sub.2 mol/s, the maximum NH.sub.3 storage capacity NH.sub.3 max, mol which can be stored, and the NH.sub.3 storage load NH.sub.3 mol stored.

10. The method as claimed in claim 7, wherein deviations which occur in a variable-dependent fashion between the NO.sub.x value determined on the basis of the input variables in the pilot controller and the predefined, emission value are taken into account by changing the supply of NH.sub.3 in such a way that an increase or decrease occurs for the NH.sub.3 stored in the SCR model.

11. The method as claimed in claim 7, wherein a model adjustment arrangement, in which the time sequence of the difference between measured NO.sub.x values and those determined in the model is determined as a measure of model errors, is integrated into the regulating structure.

12. The method as claimed in claim 7, wherein NO.sub.x reactions in the SCR model are determined by subsequent main reactions
NO+NO.sub.2+2NH.sub.3.fwdarw.2N.sub.2+3H.sub.2O,  1.) as a fast reaction
4NO+4NH.sub.3+O.sub.2.fwdarw.4N.sub.2+6H.sub.2O  2.) as a standard reaction, and
6NO.sub.2+8NH.sub.3.fwdarw.7N.sub.2+12H.sub.2O,  3.) as a slow reaction.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Further details and features of the disclosure can be found in the claims, the following explanations and the drawings. In the drawings:

(2) FIG. 1 is a schematic illustration of an SCR catalytic converter which is divided axially into disks in a virtual fashion as an example also of exhaust gas post-treatment units which are formed by other kinds of catalytic converters and/or particle filters,

(3) FIGS. 2 and 3 show catalytic converter disks which are segmented in cross section with respect to the direction of through-flow,

(4) FIG. 4 shows a schematic illustration of the thermal sequences in an SCR model,

(5) FIG. 5 shows a schematic and comprehensive illustration of a regulating structure according to the disclosure in a flow chart,

(6) FIG. 6 shows a basic illustration of a dynamic correction with respect to the thermal sequences in an SCR model,

(7) FIG. 7 shows an overview of a regulating structure in relation to an SCR catalytic converter according to the disclosure which is controlled in a model-based fashion, and

(8) FIGS. 8 and 9 show illustrations of the graphic determination of the quantity of NH.sub.3 which is stored and removed from storage in the case of a quantity of NH.sub.3 which is to be stored or removed from storage in a corrective fashion by means of the model adjustment.

DETAILED DESCRIPTION

(9) As is known from practice and also often described in the literature, in particular the patent literature, there are in particular drive systems which are operated with diesel engines and in which exhaust gas post-treatment systems are used arranged downstream with respect to the engine by means of which certain exhaust gas components, in particular pollutants contained in the exhaust gas are to be as far as possible removed from the exhaust gas or at least made innocuous. In order to reduce the amount of nitrogen oxides contained in the oxygen-rich exhaust gas of diesel internal combustion engines, in particular what is referred to as SCR technology is used in which the nitrogen oxides are selectively reduced to form nitrogen and water using ammonia or a corresponding precursor which can be converted into ammonia.

(10) So that this is achieved with a high conversion rate of the nitrogen oxides, in particular the temperature-dependent NH.sub.3 storage capability of the catalytic converter has to be taken into account, which storage capability changes, in particular, as a function of the operating conditions of the internal combustion engine, and also the ambient conditions and over the through-flow length of the catalytic converter. These changes cannot be detected in a real fashion, in particular with acceptable expenditure. For this reason, parallel to the detection of the temperatures by measuring technology on the input side and the output side with respect to the catalytic converter, the temperature distribution therein is detected in a virtual, model-based fashion in order to obtain a picture of the temperature distribution which is as precise as possible while taking into account the temperature values which are detected by measuring technology and the temperature values which are determined virtually, and in order to be able to perform open- and/or closed-loop control of the metering in of the reducing agent, that is to say an ammonia-forming substance, also correlated to the storage behavior of the catalytic converter, in particular while taking into account said temperature distribution.

(11) FIG. 1 illustrates the segmentation of a catalytic converter body in a model, by axial sub-division into a relatively large number of disks, through the illustration of three disks 1 to 3 lying one behind the other in the through-flow direction of the catalytic converter, and 5 indicates, by way of dot-dashed lines, a casing which surrounds the catalytic converter body on the circumference side. In accordance with the exhaust gas flow which is directed via the catalytic converter, the disks 1 to 3 each have a mass flow {dot over (m)} gas applied to them which corresponds to this exhaust gas flow, as the temperature Tgas of the respective disk 1 to 3 changes.

(12) In accordance with the engine emissions and the metering in of reducing agent into the exhaust gas flow, the latter contains mass fractions m of NO, NO.sub.2 and NH.sub.3 to which corresponding molar amounts n correlate, said amounts changing in accordance with the respective conversion rates over the throughput through the disks 1 to 3. In accordance with the illustration, the output values of the one disk, for example disk 1, constitute the input values of the following disk, for example the disk 2. Taking into account the reactions which take place in each of the disks, a corresponding temperature Tdisk and also the molar amount nNH.sub.3 in mol stored in the disk are obtained for each of the disks, wherein the temperature effect arising from the reactions in the disks is substantially less compared to the inputting of heat from the exhaust gas flow.

(13) In a refinement of the detection of temperature for the disks, it is also possible to detect the conduction of heat between successive disks (not illustrated). The entire molar amount of NH.sub.3 which is stored in the catalytic converter corresponds to the sum of the molar amounts NH.sub.3 stored in the disks.

(14) FIG. 1 models the axial temperature profile across the catalytic converter across the disks, and initially determines a respective temperature Tdisk for each of the disks, but the radial temperature distribution over each of the disks is assumed to be constant. However, in the radial direction, it is obtained in a real fashion, now in each case within the respective disk, a temperature stratification with a decrease in the temperature towards the casing 5, for which the ambient temperature in the case of regulation is significantly below the temperature of the catalytic converter.

(15) If, as in the disclosure, the radial temperature distribution is not assumed to be constant for each of the virtual disks, this requires per se for each of the disks 1 to 4 to be divided virtually into segments, as is illustrated in the schematic view in FIGS. 2 and 3. FIG. 2 shows in this regard virtual segments 6 which enclose one another radially, wherein in the illustration a central segment is enclosed by a relatively large number of annular segments.

(16) Another type of segmentation is illustrated by FIG. 3, wherein, in contrast to the illustration in FIG. 2, a casing 5 in annular form is not provided but instead a rectangular casing 5 is provided, the disks 1 to 4 being segmented virtually into squares 7 corresponding to their cross section which is rectangular transversely with respect to the direction of through-flow.

(17) In FIGS. 2 and 3, the arrangement of temperature detection elements, in particular sensors 8, 9, is illustrated with respect to the catalytic converter body which is respectively segmented in the model, for the purpose of detecting the temperature of the exhaust gas flow on the inflow side and outflow side of the catalytic converter body.

(18) With respect to the radial segmentation which is provided in the model and the associated possibility of detecting the radial temperature distribution over the respective virtual disk, temperature detection can take place in different radial regions in a real fashion on the output side of the catalytic converter, as shown in FIG. 3, by two sensors 9 and 10 which are arranged in various radial positions on the output side. An averaged output-side temperature can be determined by virtue of the fact that the temperatures which are calculated for the segments are detected in accordance with their area components, and averaged. An alternative to this is to detect the exhaust gas temperature by sensor at a distance from the catalytic converter at which the emerging exhaust gases have already mixed and there is an average temperature which can be detected by one sensor.

(19) One inventive possibility for taking into account the axial and radial temperature distribution is illustrated in FIG. 4 and also provides, in particular, advantages with respect to the implementation of a model-based regulating structure, which is also referred to below.

(20) FIG. 4 illustrates a thermal model of an SCR catalytic converter in its outlines, in which, according to FIG. 1, the temperature T upstream of the CAT and the exhaust gas mass flow {dot over (m)} gas form the input variables which are fed to a virtual heat accumulator gas mass 16 via a pole position compensation arrangement 15 for computationally compensating for the sensor inertia—and also having been verified and checked for plausibility—in which heat accumulator the heat content of the gas mass is detected in relation to the respective disk volume at the given temperature, and from which the heat transfer to the following disk owing to the transfer of the gas mass takes place, this being symbolized by the heat accumulator 17. Insofar as a rise in temperature occurs in the exhaust gas owing to exothermal reactions, this is taken into account in block 18 and leads, with respect to the heat content of the exhaust gases changing from the heat accumulator gas mass 16 to the heat accumulator gas mass 17, to a certain increase in temperature, which is sometimes even relatively strong in effect, for example in the DOC (Diesel Oxidation Catalyst), and in some cases is negligible.

(21) The heat transfer occurs from the flowing gas mass, detected respectively on a disk-related basis, to the catalytic converter material taking into account the heat transfer coefficient k, wherein the catalytic converter material of the respective disk is illustrated symbolized as a heat accumulator 19 or 20. Oriented with the real catalytic converter, a thermal gradient results for the catalytic converter body symbolized by the heat accumulators 19, 20, with respect to the circumference of the catalytic converter, corresponding to the given temperature differences. With respect to the illustration according to FIG. 4 and the symbolic indication of the casing 5 there, a heat transfer resistance is provided with respect to the surroundings, symbolized by the heat transfer resistance R.sub.c in FIG. 4.

(22) In the illustration of the thermal model provided by FIG. 4, it is assumed that, corresponding to the conditions in the practical operation, steady-state and non-steady-state operating phases occur and that it is possible to differentiate between these operating phases in all cases and to differentiate when the exhaust gas temperature measured at regular time intervals upstream of the exhaust gas post-treatment unit, in particular therefore upstream of the catalytic converter, changes compared to a chronological mean value over corresponding time periods. If this is not the case, it is assumed that there is a steady state, and in the other case a non-steady state. Correspondingly different control circuits are used.

(23) Corresponding to the usually relatively small influence of the radial heat transfer, from the body thereof, in particular that is to say from the catalytic converter body, on the temperature of the exhaust gas post-treatment unit, which is embodied in particular as a catalytic converter, on the surroundings, in the steady-state case adaptation takes place by changing the heat transfer resistance R.sub.c by a regulating arrangement 22. The steady-state case is determined in the model under the conditions described above by steady-state detection indicated in the block 21. The regulating arrangement 22 takes into account the difference between the output-side temperatures T downstream of the exhaust gas post-treatment unit, with respect to an SCR catalytic converter as in the exemplary embodiment, that is to say downstream of the sensor CAT (measured) and T downstream of the model (calculated). If relevant deviations occur with respect to an exhaust gas temperature T measured over a chronological mean value of the input-side, upstream of the exhaust gas post-treatment unit, in particular upstream of the catalytic converter, the heat transfer coefficient k is changed. This is because the heat transfer coefficient k changes as a function of the flow rate of the exhaust gas, and therefore as a function of the load, and in addition the heat content of a respective storage disk, like also that of the body of the exhaust gas post-treatment unit, in particular of the catalytic converter as a whole, is influenced far more by the temperature of the through-flowing exhaust gas than by the heat transfer from the respective disk to the surroundings. The changing of the heat transfer coefficient k follows, starting from the block 23 taking into account the described dynamic factors.

(24) FIG. 5 shows an illustration of the sequence described above, in a block diagram, wherein again reference is also made to an SCR catalytic converter as an example of other exhaust gas post-treatment units, with the result that T downstream of CAT or T upstream of CAT also stands for T downstream of the exhaust gas purification unit or T upstream of the exhaust gas purification unit, whether measured or calculated. According to block 30, in the model calculation the dynamic correction of the measured exhaust gas temperature T, on the outlet side with respect to the exhaust gas post-treatment unit, takes place downstream of the CAT sensor, the calculation of the gas temperatures and the calculation of the temperature take place in the catalytic converter body with cross-distribution during the detection of the heat transfer to the surroundings by means of the heat transfer resistance R.sub.c and the heat transfer from the exhaust gas to the catalytic converter is calculated by the heat transfer coefficient k, wherein the model calculation is carried out from the front to the rear.

(25) The measured, inlet-side exhaust gas temperature, denoted as T upstream of CAT, is detected in block 31 and is processed according to block 30 in the model calculation, after passing through a pole position compensation arrangement according to block 32. The measured, outlet-side exhaust gas temperature, denoted as T downstream of CAT, according to block 33 is fed to a block 35 via a pole position compensation arrangement according to block 34, in which block 35 adjustment of the measured exhaust gas temperature T downstream of CAT sensor towards the calculated exhaust gas temperature T downstream of CAT model takes place. With respect to the calculated, outlet-side exhaust gas temperature T downstream of CAT model, weighted formation of mean values takes place in block 36 taking into account the results according to block 30, which mean values are fed as a result to the block 35 via the block 37 as a calculated, outlet-side temperature T downstream of CAT sensor.

(26) The differentiation between steady-state and non-steady-state operating behavior takes place taking into account the adjustment of measured outlet-side temperature T downstream of CAT sensor, carried out in the block 35, and the calculated outlet-side temperature T downstream of CAT model, wherein by the steady-state detection according to block 38 and the subsequent adjustment of the heat transfer resistance R.sub.c (block 40) the latter is fed as a parameter into the model calculation according to block 30. In the case of the non-steady-state detection according to block 39, provided by the adjustment according to block 35 between the measured and calculated, outlet-side temperature T downstream of CAT, the adjustment of the heat transfer coefficient k takes place in the block 41 with subsequent feeding into the model calculation according to block 30. In said model calculation, the ambient temperature T, which is made available according to block 42, is also taken into account.

(27) FIG. 6 serves to illustrate the dynamic correction, taken into account in block 30, of the temperature T, which is measured on the outlet side of the exhaust gas post-treatment unit, downstream of the CAT sensor, that is to say the temperature values which are sensed according to the sensor and therefore falsified in accordance with the inertia of the sensor. Said values are plotted (represented by dashed lines) in their profile against the time and the associated derivation, with low-pass smoothing, after pole position compensation which is symbolized in block 45 and which computationally compensates for the inertia of the sensor. For the same time period, the temperature T downstream of CAT model, determined on the model basis, that is to say calculated, is also determined in a corresponding way and represented in the diagram as a continuous line. The correction requirement is represented in the corresponding offset of the timing of the inflection points corresponding to the maximum and minimum values of the derivation curves, wherein the given chronological offset has to be minimized as part of the correction. This is done by correspondingly changing the k value with the effect of decreasing or increasing said value in the model calculation. For the correction of the k value, the latter is expediently corrected by the same order of magnitude in each case, for example approximately one percentage point plus or minus. The numerical values corresponding to the derivatives are determined in the blocks 46 and 47 and plotted in the diagram.

(28) By using a model-based calculation of the temperature distribution in a model of an exhaust gas purification unit, in particular by using the model-based calculation explained above, operation is carried out in a regulating structure for an exhaust gas purification unit, in particular an SCR catalytic converter according to FIG. 7.

(29) In FIG. 7, tailored as already above to an SCR catalytic converter as an example also for other exhaust gas purification units, an SCR catalytic converter is denoted by 50, and an SCR model by 51, in particular of the type mentioned and explained above, a pilot controller by 52, a regulator by 53 and a model adjustment arrangement 54.

(30) In the SCR model the temperature-dependent NH.sub.3 storage capability is additionally taken into account, in particular in parallel with the modeled temperature calculation, as a function of the NH.sub.3 concentration in the exhaust gas, in particular in a characteristic-diagram-related fashion on the basis of data determined on a test bench for the respective catalytic converter material. By taking into account this storage behavior and the main reactions represented below, the total conversion rate of NH.sub.3 is determined, said conversion rate correlating to the difference between the proportion of NO.sub.x upstream of the CAT and the proportion downstream of the CAT, and by means of it the NO.sub.x value which is respectively taken as the target value, for example the emission value which is to be complied with on the basis of legal prescriptions, can therefore be determined.

(31) The abovementioned main reactions are:
NO+NO.sub.2+2NH.sub.3.fwdarw.2N.sub.2+3H.sub.2O,  1.) as a fast reaction
4NO+4NH.sub.3+O.sub.2.fwdarw.4N.sub.2+6H.sub.2O  2.) as a standard reaction, and
6NO.sub.2+8NH.sub.3.fwdarw.7N.sub.2+12H.sub.2O  3.) as a slow reaction.

(32) For the model calculation, it can be assumed as an approximation that the more rapid reaction is ended in each case before the slower one begins, with the result that in terms of the computational technology the reactions can be assumed to occur in succession. After the respectively more rapid reaction, the converted quantities of NO and NO.sub.2 are subtracted from the initial quantities and after each reaction the quantity of NH.sub.3 which is still available in the volume of a disk is determined.

(33) With respect to the regulating structure according to FIG. 7, the SCR model 51 therefore provides a representation of the SCR catalytic converter 50 which is as accurate as possible in terms of the processed characteristic variables, such as also of the output values, in particular the NO.sub.x value.

(34) Correspondingly, the input parameters to the SCR model relating to the exhaust gas flowing via the SCR catalytic converter 50 are NO, NO.sub.2, exhaust gas mass, temperature T upstream and downstream of the CAT and NH.sub.3. On the outlet side the following are detected: NO.sub.x, NO/NO.sub.2 converted, NO/NO.sub.2 maximum converted, NH.sub.3 stored and NH.sub.3 maximum and stored. The calculation of the conversion requirement of NH.sub.3 and the quantity of NH.sub.3 which is to be stored and removed from storage takes place in the pilot controller 52, and is applied to the SCR model 51 and the SCR catalytic converter 50. The regulator 53 is assigned the function of determining any additional metering quantity to the SCR catalytic converter 50 in order to adjust the SCR catalytic converter 50 with the SCR model 51 on a case-by-case basis.

(35) Taking as a basis the fact that the quantity of NH.sub.3 which is respectively matched to the predefined emission value, that is to say NO.sub.x downstream of the CAT, and which is to be sprayed in as a reducing agent by the pilot controller on the basis of the prescriptions of the SCR model 51 and that corresponding spraying in is brought about, by the model adjustment arrangement 54 an evaluation is carried out to determine whether a relatively large deviation is present between the SCR model 51 and the SCR catalytic converter 50, and this is done for the case in which the “quantity for removal from storage is unequal to zero” in the pilot controller. If this is the case, in the model the maximum storage capability is changed, and therefore also the pilot controller is adapted for the next load change since the pilot controller 52 itself operates on the basis of data which is made available by the SCR model 51. Said data comprises: NO downstream of SCR CAT ppm, NO.sub.2 downstream of SCR CAT ppm, maximum convertible NO mol/s, maximum convertible NO.sub.2 mol/s, NO converted mol/s, NO.sub.2 converted mol/s, NH.sub.3 max mol storable and NH.sub.3 mol stored. According to the definition that the model adjustment takes place only if “quantity for removal from storage is unequal to zero” is in the pilot controller, model adjustment takes place only in the phase of removal from storage.

(36) According to the data predefined by the SCR model 51, the pilot controller adjusts the injected quantity of NH.sub.3 to the effect that the respectively predefined emission value, that is to say, for example, a legal emission value, is complied with. For this purpose, in the pilot controller the output-side NO.sub.x value is calculated continuously on the basis of the data supplied by the SCR model 51 and is compared with the predefined emission value. If relatively large deviations occur, the fed-in quantity of NH.sub.3 is increased or decreased by changing the quantity of NH.sub.3 which is metered by the pilot controller 52 and is to be injected in the SCR model 51.

(37) For example, an NO.sub.x value of 0.5 g/kWh which is calculated by the pilot controller 52 can bring about an excessively large rate of conversion of NO.sub.x with respect to an emission value, that is to say, for example, the legal emission value of 0.67 g/kWh. Accordingly, the injection of NH.sub.3 is decreased by the pilot controller 52. If the conversion of NO.sub.x is smaller than the predefined emission value, the pilot controller 52 brings about the increase in the NH.sub.3 injection quantity. The storage of NH.sub.3 is performed in such a way that a risk of slip is ruled out.

(38) The time profile between an NO.sub.x which is set in a real fashion downstream of the CAT and the NO.sub.x calculated according to the model is detected at defined times using the model adjustment arrangement 54. If there is a resulting difference between these values and if these values are plotted in a diagram as NO.sub.x values over time in curves, the area between the curves is a measure of the model error. If this model error exceeds a threshold value, the storage capability in the model is changed. Such changes are preferably performed according to the invention only during the removal from storage, since the storage capability changes only slowly due to CAT aging and model errors become significantly more visible compared to the storage. In conjunction with such a correction using the model adjustment means 54, the aging of the catalytic converter is also preferably taken into account automatically.

(39) Whether the SCR model 51 also has to be corrected in terms of its maximum storage capability under the respective conditions, that is to say whether an increase or decrease of the storage capability is necessary, depends on the NO.sub.x values which are determined by sensor, that is to say measured. The following applies: NO.sub.x model−NO.sub.x real>0: increase the storage capability of the model, <0: decrease the storage capability of the model.

(40) In the steady-state operating mode, in the case of relatively small deviations of the NO.sub.x values, calculated in the SCR model 51, from the measured NO.sub.x values downstream of the SCR catalytic converter 50, the regulator 53 is assigned the function of performing adaptation of the sprayed-in mass of NH.sub.3 in a way which is superimposed with respect to and independently of the definitions of the pilot controller 52, in order to ensure rapid adaptation with respect to compliance of the NO.sub.x emission values.

(41) The said adaptation preferably takes place in that the conversion rate of NO.sub.x or NH.sub.3 is detected over the load of the accumulator, and deviations of the actual load from the load corresponding to the setpoint conversion are determined as a measure for what quantity is to be stored or removed from storage. In the case of storage, the quantity which is to be stored corresponds to the difference between the actual load and the setpoint conversion rate of a corresponding load with respect to a linear interpolation of the load curve between the actual load value and the maximum load. In the case of removal from storage, the quantity which is to be removed from storage corresponds to the difference between the actual load and a linear interpolation of the load curve between the actual load and the passage thereof through the point of intersection of the axes, as illustrated in FIGS. 8 and 9.