GB2403165A

GB2403165A - Correlating reductant injection with NOx leve

Info

Publication number: GB2403165A
Application number: GB0414061A
Authority: GB
Inventors: William Frederick Ball; Alexander David Beavan; Claus Friedrich Goersmann; Andrew Peter Walker
Original assignee: Johnson Matthey PLC; Eminox Ltd
Current assignee: Johnson Matthey PLC; Eminox Ltd
Priority date: 2003-06-23
Filing date: 2004-06-23
Publication date: 2004-12-29
Also published as: GB0322963D0; GB2403165A8; GB0314463D0; GB0414061D0

Abstract

A method of mapping the rate of reductant injection required to reduce NOx catalytically in a lean-burn internal combustion engine exhaust gas, to meet a required standard, comprises measuring the NOx in the exhaust gas as the vehicle is driven and correlating the measured value with at least one measurable parameter indicative of a condition of the engine. The at least one measurable parameter may be at least one of exhaust gas temperature, mass flow of exhaust gas, manifold vacuum, ignition timing, engine speed, throttle position, the lambda value of the exhaust gas, quantity of fuel injected into the engine, amount of exhaust gas recirculation, and boost pressure. The correlated value may be used to determine the amount of reductant required to reduce the measured value of NOx to a desired level or by a desired amount.

Description

METHOD OF CALIBRATING REDUCTANT INJECTION

The present invention relates to a method and apparatus for mapping the rate of injection of a reductant required to reduce NOX catalytically over a drive cycle in vehicular lean-burn internal combustion engine exhaust gas for the purpose of inter alla reducing the NOX to N2 to meet a desired emission standard.

By "NOX" herein, we mean "nitrogen oxides" including nitrogen monoxide (NO) and nitrogen dioxide (NO2). By "NOX sensors" herein, we mean sensors that measure total NOX, sensors that can selectively detect the amount of NO in the NOX present, sensors that can selectively detect the amount of NO2 in the NOx present and also NOX sensors which are cross-sensitive against ammonia for providing feedback control of reductant delivery in an exhaust system including a SCR catalyst. NOx sensors of the latter sort are described in "Development and evaluation of a DeNOx system based on urea SCR", by Martin Elsener et al., MTZ worldwide, 11/2003, Volume 64, p. 28-31 (incorporated herein by reference) and are available from NGK, for example.

It is has been suggested to use neural networks (or fuzzy logic) in process design and process modelling in exhaust systems for internal combustion engines (see e.g. SAE 2000-01-0212 "Three-way Catalytic Converter Modelling: Neural Networks and Genetic Algorithm for the Reaction Kinetics Submodel", L. Glielmo et al., incorporated herein by reference). In computing terms, neural networks have a number of advantages over theoretical modelling or modelling based on experimentally measured input-output data to build an empirical model. They can learn from experience; generalise from examples; and abstract essential information from "noisy" data. However, they can only provide good results for certain types of problem, and then only when a great deal of care is taken over neural network design and input data pre-processing data.

Reductant injection into exhaust systems of lean-burn internal combustion engines for the purpose of reducing NOX to N2 over a suitable catalyst is known. Where the reductant is a hydrocarbon, such as the fuel used to power the engine, the technology is generally called lean NOX catalysis and the catalysts are called lean NOX catalysts, denox catalysts, lean NOx reduction catalysts or NOx occluding catalysts. Typical lean NOX catalysts are copper exchanged zeolite e.g. ZSM5 or platinum on alumina. NOX in the exhaust gas competes with other oxidising agents such as oxygen (O2) for the hydrocarbon, and NOX conversion in a drive cycle is of the order of about 40%.

Where the reductant is a NOx specific reactant, the technique is generally termed "selective catalytic reduction" or SCR and reduction is more selective than lean NOX catalysis. Typical catalysts comprise platinum, vanadium (V2O5) supported e.g. on titania (TiO2) or zeolites such as mordenite.

By "NOX specific reactant" herein, we mean a reducing agent that, in most conditions, preferentially reduces NOX over other components of a gaseous mixture.

Examples of NOx-specific reactants include nitrogenous compounds such as nitrogen hydrides, e.g. ammonia (NH3) or hydrazine, or an NH3 precursor.

By "NH3 precursor" we mean one or more compounds from which NH3 can be À.

derived, e.g. by hydrolysis. These include urea (CO(NH2)2) as an aqueous solution or as..

a solid or ammonium carbamate (NH2COONH4). If the urea is used as an aqueous.

solution, a eutectic mixture, e.g. a 32.5% NH3 (aq), is preferred. Additives can be included in the aqueous solutions to reduce the crystallisation temperature. À. À

Urea hydrolyses at temperatures above 160 C according to equation (1) to liberate NH3 itself. It is also believed to decompose thermally at this temperature and above according to equations (2) and (3) resulting in reduction of NOx, as evidenced by formation of CO during SCR processes with urea (see SAE 900496 and SAE 930363 (both incorporated herein by reference)).

CO(NH2)2 + H2O 2NH3 +CO2 (1) CO(NH2)2.NH2+ CO (2) NH2 + NO N2 + H2O (3) The NH3 can be in anhydrous form or in the form of an aqueous solution, for

example.

The application of NH3 SCR technology to treat NOx emissions from IC engines, particularly lean-burn IC engines, is well known. Several chemical reactions occur in the NH3 SCR system, all of which represent desirable reactions which reduce NOx to elemental nitrogen. The overall desired reaction is represented in equation (4). s

4No+4NH3+O24N2+6H2O (4) Competing, non-selective reactions with oxygen can produce secondary emissions or may unproductively consume NH3. One such non-selective reaction is the complete oxidation of NH3, represented in equation (5).

4NH3 + 5O2 4NO + 6H2O (5) Presently, urea is the preferred source of NH3 for mobile applications because it is less toxic than NH3, it is easy to transport and handle, is inexpensive and commonly available.

Early methods of using urea as a source of NH3 in exhaust systems involved injecting urea directly into the exhaust gas, optionally over an in-line hydrolysis catalyst (see EP-A-0487886 (incorporated herein by reference)). However, not all urea is hydrolysed in such arrangements, particularly at lower temperatures.

Incomplete hydrolysis of urea can lead to increased PM emissions on tests for meeting the relevant emission test cycle because partially hydrolysed urea solids or droplets will be trapped by the filter paper used in the legislative test for PM and counted as PM mass. Furthermore, the release of certain products of incomplete urea hydrolysis, such as cyanotic acid, is environmentally undesirable. Another method is to use a pre injection hydrolysis reactor (see US-A-5,968,464 (incorporated herein by reference)) held at a temperature above that at which urea hydrolyses.

It will be appreciated that at lower temperatures, below about 100-200 C, NH3 can also react with NO2 to produce an explosive mixture of ammonium nitrate and ammonium nitrite according to equation (6): 2NH3+2NO2 + H2O NH4NO3 + NH4NO2 (6) For the avoidance of doubt, in so far as the invention uses NH3-SCR, the present invention does not embrace such reactions or the promotion of conditions which bring them about. For example, the reaction can be avoided by ensuring that the temperature does not fall below about 200 C or by supplying into a gas stream less than the precise amount of NH3 necessary for the stoichiometric reaction with NOX (1 to 1 mole ratio).

For cold start applications, measures to prevent water from contacting the catalyst can be adopted. These can include locating a water trap, e.g. a zeolite, upstream of the catalyst I to reduce the amount of water vapour contacting the catalyst until it is heated sufficiently. A water trap can also be positioned downstream of the catalyst, to prevent atmospheric humid air from travelling up the exhaust pipe. An electric heater can also be employed to drive off moisture from the catalyst pre- cold start. Such arrangements.

are described in our EP 0747581, (incorporated herein by reference). ...

One problem in adopting SCR or lean NOX technology is in controlling the À..

addition of the reductant: if too little reductant is added, NOX conversion may be:. . insufficient to meet a relevant emission standard. On the other hand, if there is too much À . reductant it may be exhausted to atmosphere - hydrocarbon is a legislated pollutant and À NH3 is a biological poison and is detected as NOX in tests for meeting such standards. À À In order to avoid such problems, extensive bench testing and modelling is carried out to establish engine maps and look-up tables to match e.g. urea injection to engine-out NOX. However, such testing is time consuming and extremely expensive.

We have now devised a method of establishing such maps and look-up tables which overcomes problems associated with the prior art and is particularly applicable to the retrofit market. In retrofit applications, the invention is based on the idea of fitting at least one NOx sensor to the exhaust system of the vehicle, preferably downstream of the SCR or lean NOx catalyst, to input measurements on NOX detected in the system to suitable processor means, e.g. the vehicle's electronic control unit (ECU) . The ECU may I be the engine control unit or separate therefrom but in communication with the engine control unit. In one embodiment, the ECU is used to correlate the detected NOx values . . . . with at least one detectable parameter indicative of the condition of the engine. The vehicle is then driven normally for a period sufficient to collect enough correlated data to enable the amount of NOX in the exhaust gas to be predicted to a desired level of accuracy by looking up a detected value of the at least one parameter. The at least one NOX sensor can then be removed, if desired, and the rate of reductant injection can be controlled in response to the detected input of the at least one parameter, so that the exhaust system meets the relevant emission standard.

Accordingly, the expense and time normally required to develop maps for reductant injection can be avoided. Furthermore, since certain embodiments of the invention comprise empirical determination of the amount of reductant required to treat NOX in the exhaust gas, the method is more likely to reduce NOx emissions than data generated from models or bench testing. A further advantage resides in the fact that, since NOx sensors can be removed following mapping, the problems of NOX sensor cost e and durability can be reduced or avoided. Moreover, it is known from e. g. EP 1054722 À.

that NOX conversion over certain SCR catalysts can be improved if the NO:NO2 ratio is...

adjusted to a particular range of values. Accordingly, by positioning at least one NOx.. À

sensor upstream of the SCR or lean NOX catalyst, it may also be possible to adjust NO:NO2 ratio e.g. at selected temperatures for optimal NOx conversion. À À.

The methods of the invention can use established techniques such as neural network technology. Adequate safeguards such as "mop-up" oxidation catalysts to prevent excessive emission of hydrocarbon or NH3 to atmosphere during collection of such generalization data or testing of training algorithm can be provided as necessary.

Therefore, according to a first aspect, the invention provides a method of mapping the rate of reductant injection required to reduce NOX catalytically over a drive cycle in vehicular lean-burn internal combustion engine exhaust gas flowing in an I exhaust system, thereby to meet a desired emission standard, which method comprising the steps of (i) measuring NOX in the exhaust gas as the vehicle is driven and (ii) correlating the measured NOX value with a value of at least one measurable parameter I indicative of a condition of the engine.

In one embodiment, the method comprises the step (iii) of determining what rate of reductant injection is required catalytically to reduce the measured value of NOX to/by a desired amount for the correlated parameter value.

In its broadest aspect, the collected correlated data is analysed "offvehicle", either by removing the means for collecting the data, or downloading the data from the means for collecting the data. Such analysis can include a determination of what rate of reductant injection is required catalytically to reduce a measured value of NOX to/by a desired amount for the correlated parameter value. However, in a preferred embodiment, such determination of what rate of reductant injection is required is also performed as the vehicle is driven by suitable processor means and appropriate feedback e.g. by measuring NOX and/or reductant e.g. downstream of the catalyst to provide empiric "finessing" of the rate of reductant injection to arrive at a recalculated rate of reductant injection, as necessary. Such a "learned" response is an aspect of neural network or e "fuzzy logic" technology. .. I À: Therefore, according to a further embodiment, the method comprises the step of: . (iv) injecting reductant at the rate determined in step (iii) when the correlated parameter value is detected as the vehicle is driven, analysing exhaust gas downstream of the À catalytic reduction step for the presence of reductant and/or NOX and recalculating the À.

rate determined according to step (iii) in order to reduce NOX emissions and/or prevent reductant slip as necessary.

In an embodiment the or each correlation step, the or each step of determining or recalculating what rate of reductant injection is required is performed by a processor.

Such processor can be part of an electronic control unit (ECU).

According to a further embodiment, the correlated values, the rates of reductant: injection determined and/or the recalculated rates of reductant injection are stored as look-up tables or maps, for example, in the ECU.

Ordinarily, modern vehicle ECU's for controlling engine function do not have the processor and/or storage capability necessary for applying the methods according to the first and second aspects of the invention. It is envisaged, therefore, that the vehicle ECU can be removed and replaced for the period of mapping with an ECU with the necessary processor andlor storage capacity. Following the mapping procedure, the original ECU can be re-programmed with the appropriate look up tables or maps and algorithms or a fresh ECU so-programmed can be inserted. Of course, if the original ECU of the vehicle has the required processor and/or storage capacity, no such ECU switching/re- programming is necessary. Alternatively, the capacity of the original ECU can be supplemented by additional processor/storage capacity for the period of the analysis.

A further advantage of the present invention is that a plurality of vehicles sharing similar drive cycles can be fitted with appropriately programmed ECUs, whereas the data need be collected from only one such vehicle.

The method of the present invention is particularly applicable to the retrofit IS market, e.g. so that vehicles can meet certified standards to enter areas, such as parts of cities, wherein access is denied to vehicles not meeting proscribed emissions standards Therefore, according to a second aspect, the invention provides a method of retrofitting a vehicle comprising a lean-burn internal combustion engine with a system for meeting a desired emission standard for NOX, which system comprising means for injecting a reductant into exhaust gas and a catalyst for reducing NOx to N2 with the reductant, which method comprising fitting the existing exhaust system with at least one NOx sensor for measuring NOX in the exhaust gas as the vehicle is driven and means for correlating a measured NOX value with a value of at least one measurable parameter indicative of a condition of the engine In one particular embodiment according to the second aspect of the invention, NOX is detected using at least one NOX sensor fitted either upstream and/or downstream of the catalyst. However, since NOX sensors are expensive and have limited durability, the invention comprises the steps of removing the at least one NOx sensor from the exhaust system when sufficient data points have been collected for the correlation of measured NOX with the at least one measurable parameter to determine what rate of reductant injection is required to reduce NOX on the catalyst over a drive cycle to meet a relevant emission standard.

The at least one measurable parameter can be any parameter indicative of a condition of the engine. It is envisaged that one or more of the following may be used: exhaust gas temperature; mass flow of exhaust gas in the system; manifold vacuum; ignition timing; engine speed; throttle position (accelerator position); the lambda value of the exhaust gas; the quantity of fuel injected in the engine; the position of the exhaust gas recirculation (EGR) valve and thereby the amount of EGR; boost pressure; and engine coolant temperature. Sensors for measuring all these parameters are known to the skilled person.

The reductant can be a hydrocarbon and the catalyst can be a lean NOX catalyst e.g. any of those mentioned above, or the reductant can be a NOX specific reactant, such as a nitrogen hydride, e.g. ammonia (NH3) or hydrazine, or an NH3 precursor and the catalyst can be a SCR catalyst such as a platinum-based catalyst, a supported vanadium such as V2O5/TiO2 or a zeolite, such as mordenite. The NH3 precursor can be urea (CO(NH:)2) or ammonium carbarnate (NH2COONH4), for example.

According to a third aspect, the invention comprises an apparatus for mapping the rate of reductant injection required to reduce NOx catalytically in exhaust gas of a vehicle comprising a lean-burn internal combustion engine and an exhaust system comprising a catalyst for reducing NOx to N2 with the reductant, thereby to meet a desired emission standard for NOx, which apparatus comprising at least one NOx sensor for measuring NOx in the exhaust gas, means for measuring at least one measurable parameter indicative of a condition of the engine and means for correlating the measured NOX value with the value for the at least one measurable parameter.

In one embodiment, the at least one NOX sensor is located downstream of the catalyst. Where the system also includes a reductant sensor, this can also be positioned downstream of the catalyst. The system can also comprise a source of reductant, e.g. a hydrocarbon fuel such as diesel or a NOx specific reactant as defined herein.

According to a fourth aspect, the invention provides a vehicle comprising an apparatus according to the invention. Such vehicle can be powered by any suitable fuel such as gasoline or preferably diesel. Alternative fuel such as liquid petroleum gas, natural gas and methanol may also be used. J Where the vehicle comprises a diesel engine, it can be a heavy-duty diesel engine or light duty diesel engine according to the relevant legislation.

In order that the invention may be more fully understood, reference will be made I to the accompanying drawings, in which: Figure 1 is a flowchart illustrating the method steps involved in replacing a NOx J sensor with a NOX calculation algorithm, according to the invention; and Figure 2 is a flowchart illustrating the bin concept of threshold comparisons. ..

Referring to Figure 1, at step 1, the function creation algorithm readsin À. I parameters A, X2, X3 and ye The function determines a relationship between A, x2 and X3 À .e that would allow y' to be calculated without the sensor ye being connected to Engine: . Control Unit (ECU).

At step 2, the signal from the function determining a relationship between x,, x2 À.

and X3 that calculates zag is compared to the signal from the sensor y'. If the NOX sensor signal y' and the calculated NOX signal z' are not close enough to meet the threshold comparisons then the function determining the relationship between A, x2 and X3 and y' continues to be adapted until the difference between calculated signal z, and the real sensor signal y, is within the pre-deterrnined comparison threshold at a variety of conditions. However, if the difference between calculated signal z' and the real sensor signal ye is within the pre-determined comparison threshold at a variety of conditions and! for a sufficient time, the ECU is configured to alert the operator that the sensor can be removed.

Referring now to Figure 2, it can be seen that most of the temperature/load i windows in the table have bins in them; some of the windows do not have bins in them because the conditions are not reached by the vehicle. The height of the bin is related to the length of time the vehicle has spent at each of the windows. The tallest bins represent a few hours, the smallest just a few minutes. Each of the bins has a "fill" level; the level of fill indicates how much time the sensor signals y' and z' (see Figure 1) have been within the comparison threshold (see Figure 1). The example illustrated in Figure 2 shows an early level of the function calculating zig. It can be seen that in the 50% load, 1 50 C window, the signals zag and ye are within the threshold 100% of the time, whereas in the 75% load 300 C window, it can be seen that there is less than 5% correlation between z' and ye. À. À À À À. Àe À À. À.- À À. À À A. À. À À e. :. Àe

Claims

CLAIMS: 1. A method of mapping the rate of reductant injection required to

reduce NOx catalytically over a drive cycle in vehicular lean-burn internal combustion engine exhaust gas flowing in an exhaust system, thereby to meet a desired emission standard, which method comprising the steps of (i) measuring NOX in the exhaust gas as the vehicle is driven and (ii) correlating the measured NOX value with a value of at least one measurable parameter indicative of a condition of the engine.
2. A method according to claim 1, comprising the step (iii) determining what rate of reductant injection is required catalytically to reduce the measured value of NOX to/by a desired amount for the correlated parameter value.
3. A method according to claim 2, comprising the step of (iv) injecting reductant at the rate determined in step (iii) when the correlated parameter value is detected as the vehicle is driven, analysing exhaust gas downstream of the catalytic reduction step for the presence of reductant and/or NOx and recalculating the rate determined according to step (iii) in order to reduce NOX emissions and/or prevent reductant slip as necessary.
4. A method according to claim 1, 2 or 3, wherein the or each correlation step and/or the or each step of determining or recalculating what rate of reductant injection is required is performed by a processor.
5. A method according to claim 4, wherein the processor is part of an electronic control unit (ECU).
6. A method according to any of claims 1 to 5, wherein the correlated values, the rates of reductant injection determined and/or the recalculated rates of reductant injection are stored as look-up tables or maps.
7. A method according to claim 6, wherein the correlated values and/or rates are stored on an ECU. 12 1
8. A method according to claim 5 or 7, wherein the ECU used to perform the or each correlation step, to determine the or each rate of reductant injection and/or to determine the or each recalculated rate of reductant injection is replaced with an ECU S programmed with look-up tables or maps comprising the determined or recalculated rate of reductant injection required for any detected value of the at least one measurable parameter. I
9. A method according to any preceding claim, wherein the at least one measurable parameter is at least one of exhaust gas temperature; mass flow of exhaust gas in the system; manifold vacuum; ignition timing; engine speed; throttle position; the lambda: value of the exhaust gas; the quantity of fuel injected in the engine; the position of the exhaust gas recirculation (EGR) valve and thereby the amount of EGR, and boost., . pressure. À
10. A method according to any preceding claim, wherein the reductant is a NOx...

specific reactant, such as a nitrogen hydride, e.g. ammonia (NH3) or hydrazine, or an. ; NH3 precursor. ....
11. A method according to claim 10, wherein the NH3 precursor is urea (CO(NH2)2) ÀÀÀ or ammonium carbamate (NH2COONH4).
12. A method of retrofitting a vehicle comprising a lean-burn internal combustion engine with a system for meeting a desired emission standard for NOX, which system comprising means for injecting a reductant into exhaust gas and a catalyst for reducing NOX to N2 with the reductant, which method comprising fitting the existing exhaust system with at least one NOx sensor for measuring NOX in the exhaust gas as the vehicle is driven and means for correlating a measured NOX value with a value of at least one measurable parameter indicative of a condition of the engine.
13. A method according to claim 12, wherein the at least one NOX sensor is removed from the exhaust system when sufficient data points have been collected for the correlation of measured NOX with the at least one measurable parameter to determine what rate of reductant injection is required to reduce NOX on the catalyst over a drive cycle to meet a relevant emission standard.
14. Apparatus for mapping the rate of reductant injection required catalytically to reduce NOX in exhaust gas of a vehicle comprising a leanburn internal combustion engine and an exhaust system comprising a catalyst for reducing NOX by a desired amount with the reductant, thereby to meet a desired emission standard for NOx, which apparatus comprising at least one NOX sensor for measuring NOx in the exhaust gas, means for measuring at least one measurable parameter indicative of a condition of the engine and means for correlating the measured NOX value with the value for the at least one measurable parameter.
15. Apparatus according to claim 14, comprising reductant injection means and means for controlling the injection means to inject reductant into the exhaust gas at a desired rate.
16. Apparatus according to claim 15, comprising means for using the correlated parameter value to determine the rate of reductant injection required catalytically to reduce the NOx to N2.
17. Apparatus according to claim 16, comprising means for measuring exhaust gas downstream of the catalyst for the presence of reductant and NOx and recalculating the rate of reductant injection for that measured parameter value to reduce NOX emissions and/or prevent reductant slip, as necessary.
18. Apparatus according to claim 14, 1 5, 1 6 or 1 7, wherein the correlating means, the reductant rate injection determining means, the injection controlling means and/or the reductant rate recalculating means comprises a processor.
19. Apparatus according to claim 14 to 18, comprising means for storing the correlated values, the rates of reductant injection determined and/or the recalculated rates of reductant injection as look-up tables or maps.
20. Apparatus according to claim 18 or 19, wherein the processor and/or the storing means is part of the electronic control unit (ECU).
21. Apparatus according to any of claims 14 to 20, wherein the at least one NOX sensor is positioned upstream and/or downstream of the catalyst.
22. Apparatus according to any of claims 14 to 21, comprising means for detecting reductant in exhaust gas downstream of the catalyst.
23. Apparatus according to any of claims 14 to 22, wherein the catalyst comprises copper exchanged zeolite, such as Cu/ZSM5, or platinum e.g. platinum on alumina.
24. Apparatus according to any of claims 14 to 22, wherein the catalyst comprises supported vanadium such as V2Os/TiO2 or a zeolite, such as mordenite. À a e sea
25. Apparatus according to any of claims 14 to 24, further comprising a source of.e..

reductant. , À,
26. Apparatus according to any of claims 14 to 25, wherein the means for measuring at least one measurable parameter indicative of a condition of the engine measures at I: least one of exhaust gas temperature; mass flow of exhaust gas in the system; manifold vacuum; ignition timing; engine speed; throttle position; the lambda value of the exhaust gas; the quantity of fuel injected in the engine; the position of the exhaust gas recirculation (EGR) valve and thereby the amount of EGR; and boost pressure.
27. A vehicle comprising an apparatus according to any of claims 14 to 26.
28. A vehicle according to claim 27, wherein the engine is a diesel engine, such as a heavy-duty diesel engine.
29. A method of mapping the rate of reductant injection required catalytically to reduce NOx over a drive cycle in vehicular lean-burn internal combustion engine exhaust gas thereby to meet a desired emission standard substantially as described herein.
30. A method of retrofitting a vehicle comprising a lean-burn internal combustion engine with a system for meeting a desired emission standard for NOx, which system comprising means for injecting a reductant into exhaust gas and a catalyst for reducing NOx to N2 with the reductant substantially as described herein.
31. Apparatus for mapping the rate of reductant injection required catalytically to reduce NOx in exhaust gas of a vehicle comprising a leanburn internal combustion engine and an exhaust system comprising a catalyst for reducing NOx to N2 with the reductant, thereby to meet a desired emission standard for NOx substantially as described herein.
32. A vehicle comprising an apparatus according to the invention substantially as described herein. À Àe À. À À.e À. À Àe À À À e.. A. À A. : - À.-