NOx model

Abstract

Methods are provided for estimating the NO.sub.x content of exhaust gas produced by an internal combustion engine. The method includes determining one or more operating parameters. The method further includes applying the determined operating parameter(s) to a global NO.sub.x model. The global NO.sub.x model may be derived using a plurality of steady state data points relating to local NO.sub.x emission models. The steady state data points may be derived using a plurality of set and variable operating parameters. The global NO.sub.x model allows for prediction of the engine-out NO.sub.x content of exhaust gas in real time and without a NO.sub.x sensor, even if engine operating parameters change.

Claims

1. A method for controlling an aftertreatment device based on estimating an engine-out NO.sub.x content of exhaust gas produced by an internal combustion engine, without the need to determine cylinder pressure, the method comprising: determining an engine speed and sending a signal indicative of the determined engine speed; determining an engine load and sending a signal indicative of the determined engine load; determining an intake oxygen level and sending a signal indicative of the determined intake oxygen level; determining a fuel pressure and sending a signal indicative of the determined fuel pressure; determining a fuel quantity and sending a signal indicative of the determined fuel quantity; and sending each of the signals indicative of the determined engine speed, engine load, intake oxygen level, fuel pressure, and fuel quantity to a control unit which is programmed to receive and process each of the signals indicative of determined engine speed, engine load, intake oxygen level, fuel pressure, and fuel quantity using a NO.sub.x model which utilizes a linear relationship between the intake oxygen level and engine-out NOx for the signal indicative of predetermined engine speed, and which utilizes a linear relationship between the intake oxygen level and engine-out NOx for the signal indicative of engine load, and which utilizes a linear relationship between the intake oxygen level and engine-out NOx for the signal indicative of intake oxygen level, and which utilizes a linear relationship between the intake oxygen level and engine-out NOx for the signal indicative of fuel pressure, and which utilizes a linear relationship between the intake oxygen level and engine-out NOx for the signal indicative of fuel quantity to arrive at an estimate of the engine-out NO.sub.x content; and controlling an aspect of the aftertreatment device based on the estimated engine-out NOx content.

2. The method of claim 1, wherein the NO.sub.x model applied by the control unit is based at least in part on a map emission response surface model that is a function of engine speed and engine torque.

3. The method of claim 1, wherein the NO.sub.x model applied by the control unit is based on a plurality of local NO.sub.x models that are generated using one or more set operating parameters and one or more variable operating parameters.

4. The method of claim 3, wherein the one or more variable operating parameters include at least one of the following: a local intake oxygen level; a local fuel pressure; and a local fuel quantity.

5. The method of claim 4, wherein the one or more set operating parameters include a constant engine speed and/or a constant engine torque.

6. The method of claim 5, wherein the plurality of local NO.sub.x models are derived using the design of experiments method.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 illustrates an exemplary schematic depiction of an internal combustion engine and an SCR system for reducing NO.sub.x from exhaust gas generated by operation of the engine.

(2) FIG. 2 provides a chart illustrating the formation of in-cylinder NO.sub.x being directly proportional to available inlet oxygen concentration.

(3) FIG. 3 illustrates steady state data points provided by the application of the design of experiments method to create local NO.sub.x emission response surface models as a function of engine speed and load/torque.

(4) FIG. 4 illustrates a second order polynomial for a global NO.sub.x emission model for selected steady state data points.

(5) FIG. 5 illustrates a comparison of actual bench test data for NO.sub.x levels and predicted NO.sub.x levels using a second order polynomial for a global NO.sub.x emission model.

(6) FIG. 6 illustrates a comparison of actual bench test data for NO.sub.x levels and predicted NO.sub.x levels using a third order polynomial for a global NO.sub.x emission model.

DETAILED DESCRIPTION

(7) FIG. 1 illustrates an exemplary schematic depiction of an internal combustion engine 10 and an SCR system 12 for reducing NO.sub.x from exhaust gas generated by operation of the engine 10. The engine 10 can be used, for example, to power a vehicle such as an over-the-road vehicle (not shown). The engine 10 can be a compression ignition engine, such as, for example, a diesel engine, including light-duty and heavy-duty diesel engines, among others, that receives fuel from a fuel supply system 14. The SCR system 12 includes a catalyst 20, a reductant supply 22, and a reductant injector 24.

(8) A control unit 26 or other control module (collectively referred to as ECU) is configured to control the delivery of a reductant, such as ammonia, from the reductant supply 22 and into the exhaust gas through the reductant injector 24. According to certain embodiments, the reductant supply 22 may include one or more canisters that store ammonia in solid, liquid, or gaseous form. Further, according to certain systems, the one or more canisters may, upon depletion of the ammonia contained therein, be replaced with other canisters and/or recharged to replenish at least a portion of the previously consumed ammonia. In such systems, the reductant supply 22 may also include a heating jacket that is positioned around the canister(s) and which is configured to elevate the temperature of the solid ammonia in the canister(s) to a sublimation temperature. Further, according to such systems, ammonia in the reductant supply 22, such as ammonia in the canisters that has been converted to a gaseous state, may be directed from the reductant supply 22 and to the reduction injector 24.

(9) The reductant injector 24 is positioned in or adjacent to the exhaust system upstream from the catalyst 20, and is configured to inject reductant from the reductant supply 22 into the exhaust gas stream. As the ammonia is injected into the exhaust system, the ammonia mixes with the exhaust gas to provide a diesel exhaust fluid that flows through the catalyst 20. The catalyst 20 is configured to cause a reaction between NO.sub.x present in the exhaust gas and a NO.sub.x reducing agent (e.g., ammonia) to reduce/convert the NO.sub.x into nitrogen and water, which then passes out of the tailpipe 30 and into the environment. According to certain embodiments, exhaust gas may also flow through a diesel particulate filter (DPF) 28 before being released into the environment through a tailpipe 30.

(10) In addition to controlling the dosing or metering of ammonia, the ECU 26 can also store information such as the amount of ammonia being delivered to the exhaust gas, the canister providing the ammonia, the starting volume of deliverable ammonia in the canister, and other such data which may be relevant to determining the amount of deliverable ammonia in each canister. The information may be monitored on a periodic or continuous basis. When the ECU 26 determines that the amount of deliverable ammonia is below a predetermined level, a status indicator (not shown) that is electronically connected to the ECU 26 may be activated.

(11) While the SCR system 12 has been described in the context of solid ammonia, it will be appreciated that the SCR system 12 could alternatively use, for example, a reductant such as pure anhydrous ammonia, aqueous ammonia, or urea.

(12) The ECU 26 controls operation of the SCR system 12, including operation of the reductant injector 24, based on a plurality of operating parameters. As explained in greater detail, the engine-out NO.sub.x level is determined or predicted by the ECU 26, or other control module, using a global NO.sub.x emission model that utilizes one or more engine operating parameters. For example, in the exemplary embodiment, the global NO.sub.x emission model may employ a mathematical formula that utilizes one or more of the following operating parameters: fuel pressure (FuP), engine speed (N) (i.e., rotational speed), engine load or torque (L), the start of injection timing (SOI), the fuel quantity (m.sub.f) involved in the injection(s), and oxygen concentration, among other possible parameters. The fuel pressure (FuP) may be determined via a pressure sensor 52 that is operably positioned to sense the pressure in the engine's intake manifold and produce a responsive output signal. Engine speed (N) may be determined using a sensor 54 to detect the rotational speed of the engine, e.g., crankshaft revolutions per minute (rpm). According to certain embodiments, engine load or torque (L) can be based on the position of an accelerator pedal or throttle 57, as measured by a sensor 58 or fuel setting, for example. Further, as the operation of fuel injectors 60 are typically controlled by the ECU 26, the SOI and fuel quantity may be determined by the ECU 26 based on the timing and/or duration that a fuel injector 60 is operated.

(13) The primary function governing NO.sub.x formation may be expressed by the following equations.
O+N.sub.2.Math.NO+N(Eq. 1)
N+O.sub.2.Math.NO+O(Eq. 2)
OH+N.Math.NO+H(Eq. 3)

(14) Further, based on chemical kinetics, the rate of NO.sub.x formation ({D[NO]/DT}) may be derived by the following equation:
{D[NO]/DT}={k.sub.4f[O].sub.e[N.sub.2].sub.e+k.sub.5f[N].sub.e[O.sub.2].sub.e+k.sub.6f[N].sub.e[OH].sub.e}{k.sub.4b[NO].sub.e[N].sub.e+k.sub.5b[NO].sub.e[O].sub.e+k.sub.6b[NO].sub.e[H].sub.e}(Eq. 4)
where: k.sub.4f and k.sub.4b are the forward and backward reaction rates, respectively, of above equation (1); k.sub.5f and k.sub.5b are the forward and backward reaction rates, respectively, of above equation (2); k.sub.6f and k.sub.6b are the forward and backward reaction rates, respectively, of above equation (3); [O].sub.e is the equilibrium species concentration; [O.sub.2].sub.e is the equilibrium oxygen species concentration; [N].sub.e is the species concentration; [N.sub.2].sub.e is the species concentration; [NO].sub.e is the species concentration; [H].sub.e is the species concentration; and [OH].sub.e is the species concentration.

(15) Using a steady state approximation and equilibrium assumption, the NO.sub.x formation recited in above Eq. 4 may be reduced to:

(16) $\begin{array}{cc}d\frac{\left[\mathrm{Nox}\right]}{\mathrm{dt}}=\frac{6{10}^{16}}{T^{0.3}}*e^{\left(-69000/T\right)}*{\left[O_2\right]}_e^{0.3}\left[N_2\right]& \left(\mathrm{Eq}.5\right)\end{array}$
where

(17) $d\frac{\left[\mathrm{Nox}\right]}{\mathrm{dt}}$
is the nitrogen oxide (NO) formation rate, T is the temperature in the engine cylinder 62, and the first instance of e (stated with respect to e.sup.(69000/T)) is activation energy in the cylinder 62 for the formation of NO.sub.x.

(18) As shown above by Eq. 5, the formation of in-cylinder NO.sub.x is directly proportional to available inlet oxygen concentration (O.sub.2). More specifically, Eq. 5 indicates that there is a linear logarithmic relationship between engine-out NO.sub.x and the intake oxygen concentration for given engine operating parameters. This linear relationship is demonstrated in FIG. 2, where fuel pressure (FuP), start of injection/injection timing (SOI), and fuel quantity (m.sub.f) have been held, in three different instances, constant. Moreover, the three lines in the chart of FIG. 2 reflect the use of data from three different constant, FuP, SOI, and m.sub.f values. Thus, knowing which one of the three constant FuP, SOI, and m.sub.f values apply to the given situation, the engine-out NO.sub.x concentration may be determined by knowing the intake oxygen concentration. Moreover, according to certain embodiments, the engine-out NO.sub.x concentration may be predicted based upon the intake oxygen concentration for a constant fuel pressure (FuP), start of injection/injection timing (SOI), and fuel quantity (m.sub.f).

(19) However, in at least certain engines, during operation, at least some operating parameters within the engine cylinder 62, such as fuel pressure, start of injection, and fuel quantity, among others, are often not constant. Accordingly, certain embodiments of the present technology provide for the prediction or determination of the level of NO.sub.x being generated by an internal combustion engine, without requiring the use of a NO.sub.x sensor and using variable engine operating parameters. For example, according to certain embodiments, the level of NO.sub.x being generated by an internal combustion engine may be determined using variable parameters that may include, but are not limited to, one or more of the following: engine speed (N); engine load (L); the concentration of the oxygen introduced into the cylinder 62 for the combustion event, also referred to as the intake oxygen concentration (O.sub.2); fuel pressure (FuP); start of injection/injection timing (SOI); and the fuel quantity (m.sub.f). By using such variables, the NO.sub.x emission model provided by the present technology is not constrained to input factors that are used as calibration set point tables. Moreover, by utilizing the actual variable parameters, rather than assuming such variables are constant, the model of the present technology provides for real time determination of NO.sub.x emission levels.

(20) Referencing FIG. 3, the design of experiments (DOE) method may be applied to map emission response surface models as a function of engine speed and load/torque, with calibration parameters also being used as set point tables in the control strategy. The steady state data points mapped in FIG. 3 reflect the different results of local NO.sub.x emission modeling. Moreover, the local NO.sub.x emission modeling is generated using particular set operating parameters, in this instance engine speed and load/torque, and corresponding values for other, variable engine operating parameters used to attain the set operating parameters. For example, to attain a particular engine speed and torque/load for a particular type of engine, the value or range of a combination of other variable parameters may need to be determined, referred to as determined operating parameters. Such other determined operating parameters may include, but are not limited to: the concentration of the oxygen introduced into the cylinder 62 for the combustion event, also referred to as the intake oxygen concentration (O.sub.2); fuel pressure (FuP); start of injection/injection timing (SOI); and the fuel quantity (m.sub.f). The steady state data points reflected in FIG. 3 were carried out based on a MaxxForce 15 engine that was certified for 2010 emissions, and which had a 15.2 L displacement, a inline 6-cylinder configuration, a bore by stroke of 5.6 inches by 6.75 inches, a dual stage turbocharger with inter-cooler and after-cooler air system, a Bosch common rail direct injection combustion system, and a rated horsepower of 550 HP.

(21) The set operating parameters and the determined operating parameters may be used, such as in a local design of experiments (DOE), to determine or predict a level of NO.sub.x emission under those parameters, also referred to as a local NO.sub.x emission model. For example, the set and determined operating parameters may be used in a DOE test matrix for data collection. The measured NO.sub.x emission responses may then be used to create the local NO.sub.x emission model.

(22) The DOE used to generate the local NO.sub.x model may be limited to data that falls within the operating and/or emission constraints of the corresponding engine. For example, brake specific fuel consumption (BSFC) model, which may be a measure of fuel efficiency within a shaft reciprocating engine, and pressure and temperature models may be employed to govern whether the particular set and determined operating parameters used in obtaining the local NO.sub.x emission model, and/or the local NO.sub.x emission model itself, is within the operating limits of the engine 10.

(23) The DOE process may be repeated a number of times for different set operating parameters, and the associated determined operating parameters for those set parameters, so as to map a plurality of different local NO.sub.x emission models. FIG. 3 illustrates a map containing the steady state points for a plurality of the local NO.sub.x emission models for set engine speeds and loads/torques. At least some, if not all, of the plurality of local NO.sub.x emission models may then be used to generate a global NO.sub.x emission model. For accuracy purposes, a minimum number steady state points for various local NO.sub.x emission models may be required for the generation of the global NO.sub.x emission model. For example, according to certain embodiments, one or more the of the steady state points that correspond to local NO.sub.x emission models may be used in generating a global NO.sub.x emission model.

(24) Various methods may be employed for the selection of which, if not all, of the mapped local NO.sub.x emission models are to be used in generating the global NO.sub.x emission model. For example, according to certain embodiments, the local NO.sub.x emission models to be used in generating a global NO.sub.x emission model may be selected based at least in part on a lug curve, a ramped mode cycle (such as using a 13 mode test cycle), and/or a Federal Test Procedure transient cycle that may be used for emission testing. Additionally, according to certain embodiments, particular local NO.sub.x emission models may be selected to capture specific engine operating conditions, such as, for example, operating conditions relating to high or low engine idling at different loads/torque, not-to-exceed (NTE) emissions, and different drive cycles, including city, severe service, and highway conditions, among others.

(25) The selected steady state data points from FIG. 3 may be represented in a global mathematical formula that is used to determine NO.sub.x formation at the various set and determined operating parameters. For example, FIG. 4 illustrates a global NO.sub.x emission model for the selected steady state data points, such as those shown in FIG. 3, that was generated using a numerical computation program, such as, for example, MATLAB from Mathworks, Inc. As shown, the selected steady state data from the local NO.sub.x emission models shown in FIG. 3 have been translated into a second order polynomial that represents a global NO.sub.x emission model. More specifically, in this particular example, the second order polynomial mathematical model generated from the selected, mapped steady state data points from FIG. 3 is represented by the equation:
Engine-out NO.sub.x level=x.sub.1+x.sub.1.sup.2+x.sub.1x.sub.2+x.sub.1x.sub.3+x.sub.1x.sub.4+x.sub.1x.sub.5+x.sub.1x.sub.6+x.sub.2+x.sub.2.sup.2+x.sub.2x.sub.3+x.sub.2x.sub.4+x.sub.2x.sub.5+x.sub.2x.sub.6+x.sub.3+x.sub.3.sup.2+x.sub.3x.sub.4+x.sub.3x.sub.5+x.sub.3x.sub.6+x.sub.4+x.sub.4.sup.2+x.sub.4+x.sub.4.sup.2+x.sub.4x.sub.5+x.sub.4x.sub.6+x.sub.5+x.sub.5.sup.2+x.sub.5x.sub.6+x.sub.6+x.sub.6.sup.2(Eq. 6)
where x.sub.1 is engine speed, x.sub.2 is engine load, x.sub.3 is fuel pressure, x.sub.4 is injection timing, x.sub.5 is intake oxygen concentration, and x.sub.6 is fuel quantity.

(26) However, the particular formula that may be used to represent the global NO.sub.x emission model may vary based on a variety of different factors, including the size and configuration of the engine 10, and which operating parameters are, or are not, generally constant. For example, the above model utilized five different variable operating parameters. However, one or more of these five parameters may be relatively constant during at least some periods of engine 10 operation. In such situations, those relatively constant operating parameters may not be used in deriving the local NO.sub.x emission model, and thus by the global NO.sub.x emission model in predicting engine-out NO.sub.x emissions.

(27) The accuracy of the global NO.sub.x emission model may be improved by increasing the polynomial degree or order of the formula of the model. For example, FIG. 5 illustrates a comparison of the actual test data and predicted NO.sub.x levels. The bench testing involved the use of a NO.sub.x sensor having accuracy ranges of +/15 PPM for 0-100 PPM and +/15% for 100-1500 PPM. The predicted NO.sub.x levels, represented by a line in FIG. 5, were derived using a second order polynomial of the model represented by Eq. 6. As shown, a large portion of the bench test data is aligned with, or is in close proximity to, the predicted NO.sub.x levels. Moreover, omitting some of the outer layer test data reveals that the second order polynomial of the global NO.sub.x emission model represented by Eq. 6 had a root mean square error of 9.5 with an accuracy of the correlation of 0.957.

(28) FIG. 6 provides a similar comparison as shown in FIG. 5, but for a third order polynomial. As shown, omitting some of the outer layer test data revealed the third order polynomial of the global NO.sub.x emission model obtained a root mean square error of 9.9, with an accuracy of the correlation of 0.988.

(29) As previously mentioned, the ECU 26 may use the global NO.sub.x emission model to determine or predict engine-out NO.sub.x levels. While increasing the order of the polynomial of the formula used by the global NO.sub.x emission model may improve the accuracy of the model, the increased order may increase the number of polynomial coefficients. Such increases in polynomial coefficients may delay the speed at which the ECU 26 is able to determine the engine-out NO.sub.x, and thereby interfere with the real time ability of the global NO.sub.x emission model.

(30) The global NO.sub.x emission model of the present technology provides the ability to predict, in real time, variations in engine-out NO.sub.x emissions even when certain engine 10 operating parameters change. For example, a change in exhaust gas recirculation rate may vary the concentration of oxygen, which typically alters the level of NO.sub.x emissions. However, as the global NO.sub.x emissions model may include intake oxygen as at least one of the variable operating parameters used to determine NO.sub.x emission levels, the effect for a change, or failure, in exhaust gas recirculation rate or system may be accounted for by the global NO.sub.x emissions model. Thus, in this capacity, the global NO.sub.x emissions model has the capacity to predict or estimate NO.sub.x emission values even with issues or faults pertaining to engine combustion events.