Mathematical analysis of potentiometric oxygen sensors for combustion‐gas streams

Baker, Daniel R.

doi:10.1002/aic.690400909

Cited by 9 publications

(8 citation statements)

References 36 publications

(47 reference statements)

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“…6 also displays another important property of the sensor that is not apparent from the data in the left panel: the K-value associated with zero current is slightly lean, not exactly at stoichiometry. This lean shift has also been observed in potentiometric sensors, 8 where it was noted that the amount of the shift is largest when the adsorption of combustible gases onto the platinum electrode is equilibrated. 20 10 E C C.) When the adsorption reactions become hindered, the shift grows with the size of the diffusion length fi.…”

Section: Simplifications Of the Model Equationsmentioning

confidence: 72%

“…A more detailed analysis leads to modeling transport using the Stefan-Maxwell equations. 8 The ratios of forward to backward combustion rate constants are assumed to take the values of the equilibrium constants for the associated reaction; thus kfC/kb,, = 3.72 X iO exp[33,800/T] and k88/k88 = 9.78 X 10 exp [30,200/11.844 Values for the forward rate constants must be chosen to fit sensor data.…”

Section: Discussionmentioning

confidence: 99%

“…Because a large diffusion resistance is essential to maintain transport-limited conditions over a wide range of k-values, the adsorption reactions on the working electrode of an amperometric sensor are expected to be very close to equilibrated, and this assumption has been incorporated into the kinetic expressions for the combustion reactions in this work (compare with Ref. 8). It follows that such sensors should exhibit a pronounced lean shift.…”

Section: Simplifications Of the Model Equationsmentioning

confidence: 97%

“…For the more complicated formulations without this assumption, see Ref. 8. We note only that a large transport resistance in the porous layer, used to obtain the transport-limited conditions necessary for this sensor, makes it more likely that the adsorption processes can be treated accurately as equilibrated.…”

Section: Vv//41 Pt Electrodementioning

confidence: 99%

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Theory and Simulation of Solid‐Electrolyte Wide‐Range Sensors for Combustion‐Gas Streams

Baker

1996

J. Electrochem. Soc.

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Clarification of the complex chemical processes governing polarized wide-range air-to-fuel-ratio sensors should enable one to determine characteristics of the system geometry and physical properties necessary for successful sensor operation. To develop a mathematical description of these sensors, we have combined well-established theories for electron, electron-hole, and oxygen-vacancy transport within yttria-stabilized zirconia with transport equations that apply to gaseous diffusion within the dense, porous layer that covers the solid electrolyte. Along the interface between the solid electrolyte and the porous layer, a thin platinum electrode catalyzes various chemical reactions and an electrochemical charge-transfer reaction. The model equations have been simplified using an asymptotic analysis which is valid over a broad range of conditions of practical interest; in particular, it is valid for all simulations presented in this work. Model calculations are shown to compare well with experimental data, and acceptable ranges for the four dimensionless groups that dictate sensor performance are considered.lnfroduction The need to improve fuel economy and reduce unwanted emissions associated with internal combustion engines has promoted research into sensors that can determine airto-fuel ratios over a wide range of operating conditions, which can lead to an improved closed-loop control system.' It is possible that a wide-range sensor (WRS) will eventually replace the present potentiometric exhaustoxygen sensor (EOS),2-4 which provides only a binary response that indicates whether the engine is operating lean or rich.58 Before a WRS is to become used widely, it is likely that an economical catalyst system capable of reducing nitrogen oxides in a lean exhaust stream will be required, so that advantages such as fuel savings and reductions in hydrocarbon emissions obtained by operating an engine in the lean condition can be realized without excessive nitrogen oxide emissions.9 Conversely, when high power is demanded from an engine, a feed stream rich in fuel is often required; under such conditions, a WRS could determine quantitatively the degree to which the exhaust is rich in combustibles, and the resulting airfuel control system could reduce hydrocarbon emissions.A schematic illustration of a WRS based on an oxygentransporting solid electrolyte is shown in Fig. 1. The importance of these sensors has led to a large number of publications and patents over the past 20 years. The patent by Bhagat and Howarth'2 and those by Wang et al.13 provide a substantial listing of early United States patents issued on this topic area. References 14-27 describe sensors constructed with materials and geometries close to or analogous to that which is addressed in this communication, and references cited in these documents can be consulted for related studies. In addition, a number of relatively recent review articles discuss the construction and operation of zirconia-based wide-range sensors,2831 and the reviews in Ref. 32-35 presen...

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Section: Simplifications Of the Model Equationsmentioning

confidence: 72%

Section: Discussionmentioning

confidence: 99%

Section: Simplifications Of the Model Equationsmentioning

confidence: 97%

Section: Vv//41 Pt Electrodementioning

confidence: 99%

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Theory and Simulation of Solid‐Electrolyte Wide‐Range Sensors for Combustion‐Gas Streams

Baker

1996

J. Electrochem. Soc.

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“…(Chapman et al, Report 30, 2010 andChapman et al, Report 31, 2010) When these parts of the model are combined, the voltage output of the EGO sensor given the exhaust gas composition can be determined. Comparing the new model to the data obtained by Baker and Verbrugge (1994), showed the correct shape for the output and a slight shift toward leaner values when methane reduction was included in the model compared to a model with no methane reduction as can be seen in Figure 8. (Chapman et al, Report 32, 2010) When the exhaust gas concentrations from the NSCR characterization study were examined, the puzzling points with identical EGO readings and very different emissions characteristics were explained.…”

Section: Ego Sensor Modelmentioning

confidence: 94%

Cost-Effective Reciprocating Engine Emissions Control and Monitoring for E&P Field and Gathering Engines

Hohn¹,

Nuss-Warren²

2011

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This final report describes a project intended to identify, develop, test, and commercialize emissions control and monitoring technologies that can be implemented by E&P operators to significantly lower their cost of environmental compliance and expedite project permitting. Technologies were installed and tested in controlled laboratory situations and then installed and tested on field engines based on the recommendations of an industry-based steering committee, analysis of installed horsepower, analysis of available emissions control and monitoring technologies, and review of technology and market gaps. The industry-recognized solution for lean-burn engines, a low-emissions-retrofit including increased airflow and pre-combustion chambers, was found to successfully control engine emissions of oxides of nitrogen (NO X ) and carbon monoxide (CO). However, the standard non-selective catalytic reduction (NSCR) system recognized by the industry was found to be unable to consistently control both NO X and CO emissions. The standard NSCR system was observed to produce emissions levels that changed dramatically on a day-to-day or even hour-to-hour basis. Because difficulties with this system seemed to be the result of exhaust gas oxygen (EGO) sensors that produced identical output for very different exhaust gas conditions, models were developed to describe the behavior of the EGO sensor and an alternative, the universal exhaust gas oxygen (UEGO) sensor. Meanwhile, an integrated NSCR system using an advanced, signal-conditioned UEGO sensor was tested and found to control both NO X and CO emissions. In conjunction with this project, advanced monitoring technologies, such as Ion Sense, and improved sensors for emissions control, such as the AFM1000+ have been developed and commercialized.

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Mathematical modeling of automotive three-way catalytic converters with oxygen storage capacity

Aimard

Sorine

1996

Control Engineering Practice

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Mathematical analysis of potentiometric oxygen sensors for combustion‐gas streams

Cited by 9 publications

References 36 publications

Theory and Simulation of Solid‐Electrolyte Wide‐Range Sensors for Combustion‐Gas Streams

Theory and Simulation of Solid‐Electrolyte Wide‐Range Sensors for Combustion‐Gas Streams

Cost-Effective Reciprocating Engine Emissions Control and Monitoring for E&P Field and Gathering Engines

Mathematical modeling of automotive three-way catalytic converters with oxygen storage capacity

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