Method for estimating the amount of polluting species in the exhaust gas of an internal combustion engine, provided with at least one three-way catalyst

Abstract

A method for estimating the amount of polluting species in the exhaust gases of a motor vehicle equipped with an internal combustion engine and at least one three-way catalyst, the estimation method making it possible to estimate the amount of polluting species in the exhaust gases, in particular before a possible concentration sensor is hot enough to carry out measurements, comprising the following steps: a. the chemical reactions are identified (1) in the at least one three-way catalyst having the polluting species as a reactant or product, b. the reaction rates of each identified chemical reaction are determined (2), c. a mass balance is carried out (3) in the at least one catalyst considered as an open system, for each polluting species, and d. the amount of polluting species in the exhaust gas is determined (4) as a function of the mass balance.

Description

[0001]DESCRIPTION Method for estimating the amount of polluting species in the exhaust gas of an internal combustion engine, provided with at least one three-way catalyst. TECHNICAL FIELD The technical field of the invention is the estimation of the polluting species produced by an internal combustion engine, and more precisely, the polluting species produced by an internal combustion engine provided with at least one catalyst. PRIOR ART The new Euro 7 standard, which will come into force from 2025, requires a reduction in pollutant emissions, compared to the current standard (Euro 6e), for vehicles marketed in Europe. Among the polluting emissions, the Euro 7 standard is particularly strict with regard to emissions of nitrogen oxides ^^^and ammonia ^^^. Among these gases, the particularities of the ^^^and of the ^^^are noted. Nitrogen dioxide ^^^is a toxic gas that produces inflammation of the respiratory tract and contributes to the formation of acid rain. Ammonia ^^^contributes to the formation of secondary particles, associated with cardiovascular and respiratory diseases, and is harmful to aquatic environments. The Euro 7 standard comprises an OBM (English acronym for "On-Board Monitoring") on-board diagnostic obligation. It will be mandatory to monitor, on each journey made by the vehicle, the amount of nitrogen oxides ^^^(mainly nitrogen monoxide ^^ and nitrogen dioxide ^^^) and the amount of ammonia ^^^emitted at the exhaust. The vehicle will have to transmit these values not only via the OBD (On- Board Diagnostic) socket but also via OTA (Over the Air) wireless communication to a dedicated platform. If the emissions of nitrogen oxides ^^^or ammonia ^^^exceed a predefined limit, built by multiplying the regulatory threshold of the species considered by a predetermined factor greater than 1, called conformity factor CF, then the vehicle must alert the driver by lights on the dashboard and impose the repair of the vehicle via engine torque and vehicle speed limitations, or even by the prohibition of starting. In other words, if the emissions are greater than, for example, 1.5 or 2 times more than predetermined thresholds, generally obtained during the approval of the vehicle, calculated on a number of valid journeys, the alert must be given. In order to determine these values, a concentration sensor to determine the concentration of these pollutants in the exhaust gases must be provided in vehicles seeking Euro 7 approval. An on-board sensor diagnostic system is also required. However, existing types of sensors are not capable of carrying out a measurement as long as their sensitive element has not yet reached a threshold temperature, called the operating temperature. The temperature rise of the sensor can last up to 90 seconds from the start of driving for spark-ignition vehicles. It thus appears that it is not possible to meet the Euro 7 standard with the only existing sensors because of the absence of measurement until 90 seconds after the start of driving. There is a need for a determination of the emissions of nitrogen oxides and ammonia at the exhaust outlet of a controlled internal combustion engine, before the operating temperature is reached by the sensor for measuring these pollutants. In the prior art, many documents deal with estimating the amount of nitrogen oxides. Mention may be made in particular of documents US8225595, US20170044962, US9771846, US9304061, EP2832965, EP2910758 and EP3819483 dealing with the specific case of diesel engines, which does not apply to the present problem. Mention may also be made of the documents US11028753, JP2009287410, US2008 / 108212 and WO2016 / 159019A1 describing models for determining the amount of nitrogen oxides but only at the engine outlet, and not at the exhaust outlet after the after treatment device (s). Documents EP3736418 and EP3956549 disclose models for estimating these emissions as a function of the measurement of sensors. These documents are inapplicable here due to the impossibility of taking a measurement until the sensor has reached its operating temperature. The technical problem is therefore not solved by the prior art. EXPLANATION OF THE INVENTION The subject of the invention is a method for estimating the amount of polluting species in the exhaust gases of a motor vehicle provided with an internal combustion engine, and with at least one first three-way catalyst, the estimation method making it possible to estimate the amount of polluting species in the exhaust gases, in particular before a possible concentration sensor is hot enough to carry out measurements, the method comprising the following stages: the chemical reactions involved in the first three-way catalyst are identified, having as reagent or product the polluting species whose amount in the exhaust gases must be estimated, the reaction rates of each identified chemical reaction are determined, a mass balance is carried out in the first catalyst considered as an open system, for each of the polluting species whose quantity is to be determined, and the amount of polluting species in the exhaust gas is determined as a function of the mass balance. The polluting species may be nitric oxide and ammonia, the estimation method may then comprise the following steps: the temperature in the first catalyst, the flow rate in the first catalyst, and the torque of the internal combustion engine are determined, the molar fraction of nitrogen oxide in the gases leaving the internal combustion engine is determined by applying a first mapping as a function of the estimated torque of the engine, the molar fraction of nitrogen oxides in the gases leaving the first catalyst, arranged downstream of the internal combustion engine, is determined as a function of the molar fraction of nitrogen oxides produced by the engine, the flow rate in the first catalyst and the volume of the first catalyst, as well as a second 1D mapping dependent on the temperature in the first catalyst and a third 1D mapping dependent on the flow rate in the first catalyst, the molar fraction of ammonia in the gases leaving the first catalyst is also determined, as a function of a fourth 1D mapping dependent on the temperature in the first catalyst and the molar fraction of nitrogen oxides in the gases issued by the internal combustion engine. When, as is frequently the case, the motor vehicle is provided with a second three-way catalyst upstream of the first three-way catalyst, the method may comprise the following steps: the molar fraction of ammonia in the gases leaving the second catalyst is determined as a function of a fifth temperature-dependent 1D mapping in the second catalyst and as a function of the value of the number of ammonia adsorption sites, the molar fraction of nitric oxide in the gases leaving the second catalyst is determined as a function of the molar fraction of nitric oxide in the gases leaving the first catalyst, the flow rate in the second catalyst and the volume of the second catalyst, as well as a sixth temperature-dependent 1D mapping in the second catalyst and a seventh flow-dependent 1D mapping in the second catalyst. The mappings can be calibrated as a function of measurements made during tests. Polluting species can be carbon dioxide, carbon monoxide, hydrocarbons, ammonia, nitric oxide, nitrogen dioxide or nitrous oxide. The invention also relates to a motor vehicle provided with an estimation system configured so as to carry out the estimation method as described above, in particular within an on-board diagnosis. The motor vehicle may further comprise a partial exhaust gas recirculation circuit at the intake. BRIEF DESCRIPTION OF THE DRAWINGS Other aims, characteristics and advantages of the invention will become apparent on reading the following description, given solely by way of non-limiting example, and made with reference to the appended drawings in which: - figure [Fig 1] illustrates the main steps of a method for estimating the amount of polluting species in the exhaust gases. DETAILED DESCRIPTION The following concepts specific to the determination of reaction rates in general in a given system, which can be open or closed, are recalled. The following generic chemical reaction is applied: ^^ + ^^ → ^^ + ^^ with a,b,c,d: stoichiometric coefficients A,B: reagents from the reaction C,D: products of the reaction. The rate v of this chemical reaction is defined in moles per unit time: [Eq.1] v = Vol ∙ f^T^ ∙ ^A^^^B^!With: Vol: The volume of the system "^#^: a function of the system temperature T [A], [B]: the volume concentrations of reagents A and B respectively. α, β: the powers applied to these concentrations The function f is often modelled by an Arrhenius law: [Eq.2] ke&'(+ )*where: k: a pre-exponential factor of the reaction Ea: the activation energy of the reaction R: the universal constant of the ideal gases (~8.3145 J / K) T: the reaction temperature, in Kelvin However, this expression only provides two degrees of freedom, the pre- exponential factor k and the activation energy Ea, to adjust it. Experimentally, the dependence of the reaction rate on temperature can have a more complex form. In the rest of the present description, the more generic form "^#^ will therefore be used. If the system is open, as is the case with an exhaust-mounted catalyst of an internal combustion engine, the function f may also have a dependency on the axial velocity of the gases, obtained as the volume flow rate of the gases divided by the cross-sectional area of the system. For a constant cross-section, equation [Eq.1] can be rewritten: [Eq.3] , = -. / ∙ "^#, 1^ ∙ ^^^^^^^2For an open system, the mass balance for a species A, in moles, is written: With: E7HE>: Change per unit time in the number of moles of species A in the system 167: Molar flow of gases entering the system 849:: Molar fraction of species A in the gases entering the system 1<=>: Molar flow of gases exiting the system 84?@A: Molar fraction of species A in the gases leaving the system ∑6 CD<E 4,46: Number of moles of species A generated per second by reactions where species A is a product ∑6 F<7G 4,46: Number of moles of species A consumed per second by reactions where species A is a reagent It is recalled that the estimation method presented here is intended to estimate the production of nitrogen and ammonia ^^^oxides ^^^between the start of rolling and the obtaining of the operating temperature at a possible measurement sensor. For this purpose, the species for which the above mass balance is applied are nitric oxide NO, and ammonia ^^^. In the example considered here (spark-ignition engine) the nitrogen oxides ^^^present at the output of the engine or the catalyst are considered as being solely nitric oxide NO. In a catalyst, in particular a three-way catalyst, the main reactions involving nitric oxide NO and ammonia ^^^are as follows: NO reduction reaction CO Reduction of NO by hydrocarbons ^^ + 2 / ^4 + O^ ^^D,→^2 / ^4 + O^ ^^^+ O / ^4 + O^ ^^^ + ½ ^^ Reduction Formation of ammonia ^^^and reduction of nitric oxide NO by dihydrogen ^^ Formation of ammonia ^^^and reduction of nitric oxide NO by dihydrogen ^^and carbon dioxide CO ^^ + 2 ^^ + ^^^ + ½ ^^,→S^^^+ 2 ^^^Oxidation of ammonia ^^^to dinitrogen ^ ^^^+ ¾ ^^,^→U½ ^2 + 3 / 2 ^^^ Oxidation of ammonia ^^^to nitrous oxide ^^^ ^^^+ ^^,→W½ ^^^ + 3 / 2 ^^^ Oxidation of ammonia ^^^to oxide NO Ammonia adsorption reaction in an ammonia ^^^adsorption site noted as ^^^+ ^Y,→Z^^^_^Y Ammonia desorption reaction from an ammonia ^^^adsorption site noted as In this set of reactions, the reagents NO, ^^^, CO^^D, ^^and ^^are in the gaseous state. A balance of moles in the catalyst is then carried out for nitrogen oxide NO, ammonia and adsorbed ammonia ^^^^^^_^Yy considering their rates of formation or consumption: [Eq.5] ^3]^^5= 167∙ 8]^9:− 1<=>∙ 8]^?@A− ,J− ,^− ,^− ,R− ,S+ ,X With: vJ^mol / s^ = Vol ∙ fJ^T, Q^ ∙ ^NO^^J^CO^!Jv^^mol / s^ = Vol ∙ f^^T, Q^ ∙ ^^^^^^^CHi^!^v^^mol / s^ = Vol ∙ f^^T, Q^ ∙ ^NO^^^^This^O^^!^vR^mol / s^ = Vol ∙ fR^T, Q^ ∙ ^NO^^R^H^^!RvS^mol / s^ = Vol ∙ fS^T, Q^ ∙ ^NO^^S^CO^!SvU^mol / s^ = Vol ∙ fU^T, Q^ ∙ ^NH^^^U^O^^!UvW^mol / s^ = Vol ∙ fW^T, Q^ ∙ ^NH^^^W^O^^!WvX^mol / s^ = Vol ∙ fX^T, Q^ ∙ ^NH^^^X^O^^!XvZ^mol / s^ = Vol ∙ fZ^T, Q^ ∙ ^NH^^^Z^as^!ZvJ\^mol / s^ = Vol ∙ fJ\^T, Q^ ∙ ^^^^_^Y^^J\ coefficients The internal temperature of the catalyst T and the exhaust gas flow rate Q through the catalyst are determined, i.e. either measured or estimated by an electronic control unit of the motor vehicle, and are subsequently considered as input data. In a theoretical approach such as presented above, it is necessary to calibrate as many two-dimensional functions,"6^#, 1^,s,as there are reactions considered. In the case presented above, ten two-dimensional functions are to be calibrated for the reactions affecting nitric oxide NO and ammonia alone ^^^. It is also necessary to estimate, in addition, the concentrations of the rest of the reagents involved in each of the reactions identified above (here carbon monoxide CO, hydrocarbons ^^D, cesium oxide ^P^^^, dihydrogen ^^and dioxygen ^^) which will in turn be determined via new reaction schemes. In addition, the parameters must be determined for each of these new reactions. It thus appears that the determination and calibration of an exact model taking into account all the reactions affecting the concentration of nitric oxide NO and ammonia ^^^becomes very complex. Indeed, there are many more functions to calibrate than observed phenomena (i.e. the production of nitric oxide NO and ammonia NH3 at the outlet of the catalyst in the system considered here) and different solutions would be possible, all correctly adjusting the experimental results, but without the certainty that one of them correctly describes the physical and chemical phenomena involved. Moreover, the very high dynamic nature of the reactions would make it necessary to choose very small sampling stages (due to the stability of the calculations), which would make it difficult to integrate this solution into a computer, which would be overloaded. In the process detailed below, a number of assumptions will be made in order to solve these two problems and to arrive at a solution that is, at the same time, easy to calibrate and to embed in a computer. The following assumptions and considerations apply identically regardless of the type of issue to be determined. In the present case, they will be described for a system comprising the internal combustion engine and at least one first three-way catalyst, and for which it is sought to estimate emitted amounts of nitric oxide NO and ammonia ^^^. Nevertheless, it will be understood that the teaching below can be applied to other chemical reactions. The system is considered homogeneous in space, i.e. the temperature and concentrations are the same at all points of the considered system. In other words, the model is a 0D model. The molar fractions inside and at the outlet of the system are identical and it is therefore possible to write: With 8]^and 8]_`the molar fractions at the output of the system that we are trying to determine. The system is considered quasi-stationary. The variations in the number of moles of the gaseous species are instantaneous. In addition, the flow rate at the inlet is very close to that at the outlet: [Eq.11] 167≈ 1<=>≈ 1 Based on these assumptions, the equations [Eq.8] to [Eq.10] are written: [Eq.12] [Eq.13] 1 ∙ 8]_`9:− 1 ∙ 8]_`+ ,R+ ,S− ,U− ,W− ,X− ,Z+ ,J\= 0 [Eq.14] The dynamics of gas-phase species have been broken, which has the effect of modifying their balance equations from differential equations to algebraic equations. By definition, the concentration of species A is written: [Eq.15] Where XAis the molar fraction of species A in all species present in the catalyst, and n is the total amount of species in the catalyst, in moles For species in the gas phase, the ideal gas law is applied. [Eq.16] t. -. / = 3v# We can then reformulate the equation [Eq.15] as follows: [Eq.17] Neglecting the effect of pressure variations in reaction rates (i.e. considering P substantially constant) in a new generic function w^#, 1^, the following equations can be written: [Eq.18] v^mol / s^ = Vol ∙ g^T, Q^ ∙ Xz^X{!where v: the reaction rate for a two-reagent gas reaction [Eq.19] v^mol / s^ = Vol ∙ where v: the reaction rate for a reaction comprising a single reactant as a gas. For each reaction rate, only the dependence on a single gaseous reagent is retained, the one considered to be limiting. The other reagent is not taken into account if it is also in the gaseous state or if it is considered to be in excess. We then reformulate the equations [Eq.18] and [Eq.19] as follows: [Eq.20] v^mol / s^ = Vol ∙ g^T, Q^ ∙ Xz^where v: the reaction rate for a two-reagent gas reaction [Eq.21] v^mol / s^ = Vol ∙ where v: the reaction rate for a reaction comprising a single reactant as a gas. Returning to the case of estimating the quantities of nitric oxide NO and ammonia ^^^produced, nitric oxide NO and ammonia ^^^will be considered limiting species. carbon monoxide CO, hydrocarbons ^^D, dihydrogen ^^, dioxygen ^^, cesium oxide ^P^^^and as adsorption sites will be considered as excess species. The reaction rates defined in relation to the equations [Eq. 5] to [Eq. 7] are reformulated as follows: vJ^mol / s^ = Vol ∙ v^^mol / s^ = Vol ∙ v^^mol / s^ = Vol ∙ vR^mol / s^ = Vol ∙ vS^mol / s^ = Vol ∙ vU^mol / s^ = Vol ∙ vW^mol / s^ = Vol ∙ vX^mol / s^ = Vol ∙ vZ^mol / s^ = Vol ∙ vJ\^mol / s^ = Vol Specifically, carbon monoxide CO, hydrocarbons ^^D, dihydrogen ^^and cesium oxide ^P^^^are in excess if the richness of the fuel / air mixture is greater than 1. Conversely, the oxygen ^^will be considered in excess if the richness is less than 1. The assumptions made above will be valid or not as a function of the wealth value. Nevertheless, for a spark-ignition engine, regulated generally at richness equal to 1, the overestimates and underestimates of the model will be compensated through its calibration (for given regulation characteristics). The powers m of the gaseous reactants in the equations [Eq.20] and [Eq.21] are considered equal to unity in all reaction rates and the equations can be rewritten as follows: [Eq.22] v^mol / s^ = Vol ∙ g^T, Q^ ∙ Xzwhere v: the reaction rate for a two-reagent gas reaction [Eq.23] v^mol / s^ = Vol where v: the reaction rate for a reaction comprising a single reactant as a gas. The combination of equations [Eq.12] to [Eq.23] makes it possible to write the balance equations in a linear form with regard to the molar fractions X, which can be obtained explicitly, and therefore without the need for an iterative calculation, making it possible to use a calculation step of 100 to 1000 times greater in iterative simulations by exact model, with a negligible loss in precision. Applied to the determination of the amounts of nitric oxide NO and ammonia ^^^, the following equations are then obtained: With: m_^_^^^: Ammonia Desorption Power ^^^[Eq.27] w^^#, 1^ = wJ^#, Reactions consuming [Eq.28] wC_]^^#, 1^ = wX^#, 1^ NO-producing reactions Reactions consuming ^^^[Eq.30] wC_]_`^#, 1^ = wR^#, 1^ + wS^#, 1^ Reactions producing ^^^[Eq.31] wa_]_`^#, 1^ = wZ^#, 1^ Adsorption reaction of ^^^[Eq.32] Desorption reactions of the ^^^ The initial system contained ten two-dimensional functions to be calibrated (f1 to f10). The new system comprises only six, scored wF_]^, wC_]^, wF_]_`, wC_]_`, wa_]_`^3^ wE_]_`. Additionally, the molar fractions 8]^and 8]_`can be isolated from the first two equations and obtained explicitly. Adsorption phenomena are considered immediate: any species A entering the system is stored instantaneously. Instead of calibrating an adsorption rate and a desorption rate, only the desorption rate is taken into account. For the present case, ammonia ^^^can be adsorbed: [Eq.33] ,9 = 1 ∙ 8]_`9: The system is thus reduced to five functions to be calibrated, noted wF_]^, wC_]^, wF_]_`, wC_]_`, wE_]_`. The following assumptions apply, in the particular case of NO and ammonia emissions ^^^. The choice of these hypotheses was made by meeting purely empirical or simplification criteria. The oxidation of ammonia ^^^to nitric oxide NO is neglected. The reaction speed v8 is then considered zero. This makes the nitric oxide NO balance equation independent of the molar fraction of ammonia ^^^. Equations [Eq.34] to [Eq.36] are rewritten as follows. [Eq.37] 0 = 1 ∙ 8]^9:− 1 ∙ 8]^− -. / ∙ wF_]^^#, 1^ ∙ 8]^ This implies that the molar fractions of nitric oxide NO and ammonia ^^^can be written as follows: In order to simplify the calibration, the coefficient mE^^`can be considered equal to unity. The set of equations [Eq.40] to [Eq.42] is rewritten as follows: [Eq.43] [Eq.44] -. / ∙ wC^^^#, 1^∙ 8]^+ wE^^#, 1^∙ 3]_8` ^` `pq]_`= 1 + -. / ∙ wF^^`^#, 1^ [Eq.45] Empirically, we ask: [Eq.46] wF_]^^#, 1^ ≈ wF_]^_*^#^ ∙ wF_]^_^^1^ This simplification is based on experience, indeed the function wF_]^_^^1^ acts by modulating the function wF_]^_*^#^. Thus, for low flow rates, we have wF_]^_^^1^ = 1, but its value decreases as the flow rate becomes high. This transforms a two-dimensional function into two one-dimensional functions, easier to calibrate and with less risk of extrapolation. Empirically, we ask: [Eq.47] wE_]_`^#, 1^ ≈ 1 ∙ wE_]_`_*^#^ Indeed, experimentally, at iso-temperature, a variation in the function wE_]_`proportional to the flow rate through the catalyst is observed. Equations [Eq.43] and [Eq.45] can then be rewritten as follows: [Eq.48] [Eq.49] At this step, we thus have the set of equations [Eq.44], [Eq.48] and [Eq.49] in order to determine the production of nitric oxide NO and ammonia ^^^at the outlet of a catalyst. Nevertheless, depending on the placement of a catalyst, other simplifications can be achieved. In a three-way catalyst downstream of the internal combustion engine, ammonia adsorption / desorption phenomena are not considered ^^^Indeed, a catalyst thus arranged in the exhaust line, close to the engine, is subject to a fairly rapid rise in temperature. The value is then zero and it is then possible to rewrite the equation [Eq.44] as follows: [Eq.50] Then, by combining the equations [Eq.50] and [Eq.48], we obtain: In such a catalyst any dependence on the flow rate Q in the previous expression can be overlooked. We can then rewrite the equation [Eq.51] as follows: [Eq.52] 8]_`_J≈ wC7^^`^#^ ∙ 8]^9:The function wC7_]_`^#^ thus combines the ammonia formation ^^^function (wC_]_`) and the ammonia ^^^oxidation function (wF_]_`) in a single function, easier to calibrate. It can be seen as a "net" ammonia ^^^production speed. At this step, the equation [Eq. 52] makes it possible to determine the production of ammonia at the outlet of the catalyst. The amount of nitric oxide at the outlet of this same catalyst is determined by the equation [Eq.48]. In many cases, a second catalyst is provided in the exhaust line, downstream of the internal combustion engine and a first catalyst, in order to increase the efficiency of treatment of the different pollutants of the engine. In such a second catalyst, ammonia formation and oxidation ^^^are neglected. Indeed, either the first catalyst is already primed and therefore the second will lack nitric oxide NO to form ammonia ^^^, or the first catalyst is still cold and the second catalyst will be all the colder, which will prevent it from forming ammonia ^^^. Only adsorption / desorption phenomena will be considered in this second catalyst: The ease of calibration (over a few dynamic cycles carried out on a test bench) as well as the ease of integration into a computer due to the limited resources required, make this method an ideal candidate for application in the context of OBM on-board monitoring in a Euro 7 standardised vehicle. The physical approach used in this invention is advantageous over other statistical or machine learning approaches because of its explainability and the need for less testing (as a rule quite expensive) for its calibration. Indeed, the contribution of theory to the model makes it possible to better predict the response of the system in areas where there would be less training data. The area of use of the system is better covered. Finally, the simplifications made to the model facilitate the calibration task with negligible loss of accuracy. The steps of the estimation method are notably executed by a calculation means, included in the on-board electronic computer of the vehicle or in a specific computer. The computer comprises in all cases at least one processor, a memory and means of communication with the rest of the vehicle and in particular the sensors and estimation means, via a wired network, in particular of the can type or a wireless network. The estimation method illustrated by Figure [Fig 1] comprises four main steps. A first step 1 of measurement and estimation. A second step 2 of estimating the emissions at the output of the internal combustion engine. A third step 3 for estimating the emissions at the output of the at least one first catalyst. A fourth step 4 of estimating the emissions at the outlet of a second catalyst. Nitrogen oxides are ^^^formed at very high temperatures in the combustion chamber, when the dioxygen in ^^the ambient air is able to react with dinitrogen ^^. For a spark-ignition engine, it is mainly the formation of nitric oxide NO, but this can then be transformed into nitrogen dioxide ^^^with the ozone in ^^the ambient air. Ammonia ^^^is not formed in the engine but in the catalyst, as a by-product, from other combustion products such as nitric oxide NO and dihydrogen ^^. It will therefore not be estimated in this step. The nitrogen oxide concentration ^^^at the engine output (in ppm) is determined as a function of the torque estimated by the computer. This function can be given in the form of 1D mappings. Other variants are possible by also considering the dependence on the rotational speed of the internal combustion engine via 2D maps, which are then a function of the estimated torque and the rotational speed. Alternatively, 1D or 2D mapping may be provided for each combustion mode designated by MEA activation information. The MEA activation information is information indicating which phase of the catalyst heating the vehicle is in. Indeed, a three-way type pollution control catalyst must be heated to reach a threshold temperature from which it has a predetermined minimum treatment efficiency. This temperature is generally reached by degrading the combustion efficiency of the engine through, for example, delayed fuel injection. Nevertheless, the temperature increase thus generated being significant, and the degradation of the combustion efficiency being significant, this heating phase cannot be maintained indefinitely. There then appears a cycling between several operating phases of the internal combustion engine. The active phase is thus indicated by the MEA activation information. It is therefore not necessary to take into account other variables, such as the EGR partial exhaust gas recirculation rate or the richness l, which are taken into account in part via the engine operating point (rotational speed / load), the combustion mode (for a given engine setting) or the characteristics of their regulation. In the case of application described here, a 1d mapping depending on the estimated torque is preferred. Indeed, such a 1D mapping is simpler to calibrate, reduces the risk of extrapolation of the model and makes it possible to maintain sufficient accuracy on the cycle. Nitrogen oxides ^^^generated by the internal combustion engine are admitted into the first catalyst in order to reduce them. The reduction achieved is not total, and nitrogen oxides ^^^are still present at the outlet of the first catalyst. The residual nitrogen oxides ^^^and the ammonia ^^^generated in the latter are then optionally admitted into a second catalyst. This second catalyst then reduces the ^^^residual nitrogen oxides. The method for estimating the amounts of nitric oxide ^^ and ammonia ^^^in the polluting emissions of a vehicle provided with a spark-ignition internal combustion engine and an exhaust line with at least a first three-way catalyst according to the invention comprises the stages presented below. In a particular case, the internal combustion engine may also have other particularities, in particular a partial exhaust gas recirculation circuit at the intake, called EGR circuit (English acronym for "Exhaust Gas Recirculation"). The method for estimating the amount of nitric oxide and ammonia in the exhaust gases of a motor vehicle provided with at least one first three-way catalyst is illustrated in Figure [Fig.1] and comprises the following stages: In a first step 1, the temperature in the first catalyst, the flow rate in the first catalyst, and the torque of the internal combustion engine are measured or estimated. In a second step 2, the molar fraction of nitric oxide in the gases leaving the internal combustion engine is determined by applying a mapping as a function of the estimated torque of the engine forming a first map. In a third step 3, the molar fraction of nitric oxide in the gases at the outlet of the first catalyst, arranged downstream of the internal combustion engine, is determined by applying the equation [Eq.48], depending on the molar fraction of nitric oxide produced by the engine, the flow rate and volume of the first catalyst, as well as a 1D mapping (wF_]^_*) depending on the temperature in the first catalyst forming a second mapping, and a 1D mapping (wF_]^_^) depending on the flow rate in the first catalyst forming a third mapping. The molar fraction of ammonia in the gases leaving the first catalyst is also determined by applying the equation [Eq.51], as a function of a 1D mapping (wC7^^`) dependent on the temperature in the first catalyst and the molar fraction of nitric oxide in the admitted gases, equal to the molar fraction of nitric oxide in the gases issued by the internal combustion engine. Said 1D mapping forms a fourth map. When the motor vehicle is provided with a second three-way catalyst upstream of the first three-way catalyst, the process continues with a fourth step 4. In this fourth step 4, the molar fraction of ammonia in the gases leaving the second catalyst is determined by applying equation [Eq.53], a function of a 1D mapping (wE_]_`_*) dependent on the temperature in the second catalyst and the number of moles of ammonia adsorbed, the value of which is obtained by integrating equation [Eq.49]. Said 1D mapping (wE_]_`_*) forms a fifth map. The molar fraction of nitric oxide in the gases leaving the second catalyst is determined by applying the equation [Eq.48], dependent on the molar fraction of nitric oxide in the gases leaving the first catalyst, the flow rate and volume of the second catalyst, as well as a temperature-dependent 1D mapping (wF_]^_*) in the second catalyst forming a sixth mapping and a flow-dependent 1D mapping (wF_]^_^) in the second catalyst forming a seventh mapping. The model ([Eq.48], [Eq. 49], [Eq. 52] and [Eq. 53]) makes it possible to describe in a simplified but reliable manner the generation and catalysis of pollutant emissions in a motor vehicle provided with a spark-ignition internal combustion engine and at least one first three-way catalyst, and if necessary (frequently) provided with a second three-way catalyst. In order to be able to use this model, the following functions must be calibrated: - the 1D mapping as a function of the estimated engine torque or the 2D mapping as a function of the engine rotational speed and the estimated engine torque, giving the molar fraction of the ^^^at the engine output, by combustion mode and by fuel type, - the functions involved in determining the molar fraction of ^^^at the outlet of each catalyst ([Eq.48]), - the functions involved in determining the number of moles of adsorbed NH3 ([Eq.49]), - the functions involved in determining the molar fraction of the ^^^at the outlet of the first catalyst ([Eq.52]), and - the functions involved in determining the molar fraction of the at the ^^^outlet of the second catalyst (if present) ([Eq.53]). In other words, a mapping (1D or 2D) is to be calibrated for the engine output ^^^emissions in addition to the maps used to determine the emissions from ^^^and the ^^^output of the catalysts (wF_]^_*, wF_]^_^, wC7_]_`and wE_]_`_*). To carry out this calibration, dynamic tests are carried out sweeping the combustion modes, the engine field (rotational speed / torque), the flow rates and the temperatures in the at least one catalyst, likely to be observed during road use by the end customer. To carry out such a calibration, the following acquisitions are carried out, in particular at an acquisition frequency of 10 Hz: Engine Output Emissions: ^^^Emissions downstream first catalyst: ^^^Exhaust Output Emissions: ^^^, ^^^Internal temperatures in each catalyst Estimated Torque MEA Action Information Flow rate through each catalyst. The model is calibrated for a given technical definition, catalyst ageing status, ECU calibration, as well as ambient conditions (temperature, pressure, humidity). Based on the acquisitions made, the calibration is broken down into three steps: Calibration of the quantity of nitrogen oxides ^^^leaving the engine, Calibration of the amount of nitrogen oxides ^^^and the amount of ammonia ^^^leaving the first catalyst, and Calibration of the amount of nitrogen oxides ^^^and the amount of ammonia ^^^leaving the second catalyst (if present). As discussed above, the amount of nitrogen oxides ^^^generated by the engine can be determined based on a one-dimensional mapping dependent on the estimated torque, or based on a two-dimensional mapping dependent on the estimated torque and the rotational speed of the engine. According to the embodiments, a 1D or 2D mapping is provided for each combustion mode of the engine indicated the MEA activation information. To construct each map, the quantity of nitrogen oxides ^^^is determined by measurement [ppm] as a function of the inputs, i.e., in the case of application as an example, the indicated engine torque. The cutting of this mapping is quite fine, in particular with a pitch of 10 Nm for a 1D mapping depending on the motor torque. Several methods are possible to determine to complete the values of the mapping around the measured values. Mention may be made in particular of the use of a neural network or a Gaussian process model, for which a learning method is carried out on the measurements of the mapping. This is a static model calibrated on dynamic cycles, accordingly the measurement of nitrogen oxides ^^^at the engine output must be well synchronized beforehand with respect to the engine events used. The expression obtained ([Eq. 48]) to calculate the molar fraction of nitric oxide NO at the outlet of the catalyst is applied indifferently to each catalyst present. Only the origin and quantity of the pollutants received at the inlet, the flow rate, the temperature and the volume change depending on whether it is the first or the second catalyst. When equation [Eq. 48] is applied to the first catalyst, the value 8]^9:corresponds to the molar fraction of ^^^in the gases leaving the engine and calculated in the first step of the process and 8]^is the molar fraction of ^^^in the gases leaving the first catalyst. In the present case, Q denotes the flow rate passing through the first catalyst (including the low-pressure EGR if necessary), T the internal temperature of the first catalyst (homogeneous if a 0D model has been envisaged) and Vol the volume of the first catalyst. The wF_]^_*^#^ and wF_]^_^^1^ functions then take the form of 1D mappings. During calibration, these functions are adjusted or determined, in particular through mathematical modelling based on a sample of values obtained during bench tests. The function wF_]^_*^#^can be adjusted independently of the function wF_]^_^^1^ for small flows, the function wF_]^_^^1^ taking a value equal to 1 in such cases. For high flow rates, the function wF_]^_^^1^ takes values below 1, in order to account for the efficiency losses in the treatment of nitrogen oxides ^^^. The molar fraction of ammonia ^^^at the outlet of the first catalyst is given by the equation [Eq.52] wherein 8]^9:represents the molar fraction of nitrogen oxides ^^^exiting the engine, calculated in the first step and 8]_`_Jrepresents the molar fraction of ammonia ^^^exiting the first catalyst. The function wC7_]_`is determined by bench measurements. This function shows an increase in value when increasing the temperature to a maximum and then a decrease in amplitude when the temperature continues to increase until it becomes zero. The mechanisms of ammonia formation and oxidation of ammonia at high temperature are thus reported. The molar fraction of nitric oxide NO at the outlet of the second catalyst is calculated with an expression similar to that used for the first catalyst ([Eq. 48]) modified to account for gases from the first catalyst: The variables are: 8]^_^9:: molar fraction of nitrogen oxides ^^^leaving the first catalyst Q_2: Flow rate through second catalyst T_2: internal temperature of the second catalyst Vol_2: volume of the second catalyst 8]^_^: molar fraction of nitrogen oxides at ^^^leaving the second catalyst The method for calibrating the functions wF_]^_^_*^#_2^ and wF_]^_^_^^1_2^ for the second catalyst is identical to that used for calibrating the functions wF_]^_*^#^and wF_]^_^^1^ for the first catalyst. Ammonia production ^^^in the second catalyst only takes into account adsorption and desorption phenomena. In the model, two equations ([Eq.49] and [Eq. 53]) had been deducted to obtain the number of moles of ammonia ^^^stored and the fraction of ammonia ^^^leaving the catalyst. These equations are adapted to take into account the gases admitted from the first catalyst: [Eq.55] Where: 8]_`9:: molar fraction of ^^^leaving the first catalyst and calculated in the previous step. 3]_`_aG: number of moles of ^^^stored in the second catalyst. 8]_`_^: molar fraction of the ^^^leaving the second catalyst. The function wE_]_`_*is determined from values measured on a bench. It has a zero value as long as the temperature does not reach a predetermined value accounting for the storage by adsorption of ammonia ^^^, then an increase accounting for the release by desorption of the ^^^stored ammonia. This function is very sensitive to temperature, its calibration is important in order to be precise during the first moments of running when the catalyst is cold, while the measurement sensor ^^^^^^has not yet reached the operating temperature and adsorption / desorption phenomena are present. The invention has been described above in the context of estimating the quantities of nitrogen oxides ^^^and ammonia ^^^produced. Nevertheless, the invention can be adapted to reactions involving other species as products and reagents, in particular carbon dioxide ^^^, carbon monoxide ^^, hydrocarbons HC, nitrogen dioxide ^^^or nitrous oxide ^^^.

Claims

CLAIMS 1. Method for estimating the amount of polluting species in the exhaust gas of a motor vehicle provided with an internal combustion engine and at least one first three-way catalyst, the estimation method making it possible to estimate the amount of polluting species in the exhaust gas, in particular before a possible concentration sensor is hot enough to carry out measurements, the method comprising the following steps: a. the chemical reactions involved in the first three-way catalyst are identified, having as reagent or product the polluting species whose amount in the exhaust gases must be estimated, b. the reaction rates of each identified chemical reaction are determined, c. a mass balance is carried out in the first catalyst considered as an open system, for each of the polluting species whose quantity is to be determined, and d. the amount of polluting species in the exhaust gas is determined as a function of the mass balance.

2. Estimation method according to claim 1, wherein the polluting species are nitric oxide and ammonia, the estimation method comprising the following steps: a. the temperature in the first catalyst, the flow rate in the first catalyst, and the torque of the internal combustion engine are determined, b. the molar fraction of nitric oxide in the gases leaving the internal combustion engine is determined by applying a first mapping as a function of the estimated torque of the engine, c. the molar fraction of nitrogen oxides in the gases leaving the first catalyst, arranged downstream of the internal combustion engine, is determined as a function of the molar fraction of nitric oxyde produced by the engine, the flow rate in the first catalyst and the volume of the first catalyst, as well as a second 1D mapping dependent on the temperature in the first catalyst and a third 1D mapping dependent on the flow rate in the first catalyst, d. the molar fraction of ammonia in the gases leaving the first catalyst is also determined, as a function of a fourth 1D mapping dependent on thetemperature in the first catalyst and the molar fraction of nitrogen oxides in the gases issued by the internal combustion engine.

3. Estimation method according to claim 2, wherein, when the motor vehicle is provided with a second three-way catalyst upstream of the first three-way catalyst, the method comprises the following steps: a. the molar fraction of ammonia in the gases leaving a second catalyst is determined as a function of a fifth temperature-dependent 1D mapping in the second catalyst and as a function of the value of the number of ammonia adsorption sites, b. the molar fraction of nitric oxide in the gases leaving the second catalyst is determined as a function of the molar fraction of nitric oxide in the gases leaving the first catalyst, the flow rate in the second catalyst and the volume of the second catalyst, as well as a sixth temperature-dependent 1D mapping in the second catalyst and a seventh flow-dependent 1D mapping in the second catalyst.

4. Estimation method according to claim 2 or 3, wherein the mappings are calibrated as a function of the measurements made during tests.

5. Estimation method according to claim 1, wherein the polluting species are carbon dioxide ^^^, carbon monoxide CO, hydrocarbons HC, ammonia ^^^, nitric oxide NO, nitrogen dioxide ^^^or nitrous oxide ^^^.

6. Motor vehicle equipped with an estimation system configured so as to carry out the estimation method according to any one of claims 1 to 5, in particular within an on-board diagnosis.

7. Motor vehicle according to claim 6, further comprising a partial exhaust gas recirculation circuit at the intake.

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