The cross-sensitivity of a gas sensor can be mitigated by installing a catalytic filter upstream. The objective of the filter is to convert interferents into species that interact weakly with the recognition element of the sensor. Mathematical models may be useful for optimizing the design parameters of the catalytic filter. Particularly, if the catalyst is not perfectly selective for the interferent over the analyte, we hypothesize the existence of an optimal residence time of the gas in the filter. Short residence times allow too much interferent to reach the sensor and corrupt its response, while long residence times degrade too much of the analyte, diminishing the signal-to-noise ratio. Herein, we develop a toy mathematical and probabilistic model of a catalytic filter and gas sensor in series. We model (a) the catalytic filter as an isothermal, packed-bed reactor that decomposes the interferent and analyte with first-order kinetics and reactant-selectivity for the interferent and (b) the cross-sensitive gas sensor as gravimetric, producing a response with contributions from the analyte and interferent, governed by the competitive Langmuir adsorption model. Under distributions of (a) concentrations of interferent and analyte in the sensing environment and (b) measurement noise corrupting the response of the sensor, we simulate deployment of the model catalytic filter-gas sensor, where the objective is to accurately predict the concentration of the analyte in the gas phase from the response of the sensor. The performance of the catalytic filter-gas sensor is measured by the expected error in the predicted concentration of the analyte. Indeed, our toy model shows an optimal residence time of gas in the catalytic filter, which depends on the reactant-selectivity of the catalyst. While just a caricature of a catalytic filter-gas sensor, our toy model illustrates the utility of mathematical and probabilistic models for optimizing their design parameters.
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