Systems and methods for determining exhaust flow rate

An aftertreatment system for treating an exhaust gas produced by an engine, the aftertreatment system comprising:

• a selective catalytic reduction system;
• a first sensor comprising a NOx sensor configured to measure an amount of NOx gases in the exhaust gas flowing into the selective catalytic reduction system, the first sensor further configured to measure an amount of oxygen included in the exhaust gas;
• and
• a controller communicatively coupled to the first sensor, the controller configured to:
• receive a first sensor signal from the first sensor;
• receive a fuel rate signal corresponding to a rate of fuel consumption by the engine;
• determine an oxygen fraction in the exhaust gas from the first sensor signal;
• determine an air-fuel ratio from the oxygen fraction;
• determine a fuel rate from the fuel rate signal;
• and
• determine an exhaust flow rate from the air-fuel ratio and the fuel rate.

A method of determining an exhaust flow rate of an exhaust gas produced by an engine, the method comprising:

• determining an oxygen fraction in the exhaust gas;
• determining an air-fuel ratio of the exhaust gas based on the oxygen fraction;
• determining a fuel rate corresponding to a rate of consumption of a fuel by the engine;
• determining the exhaust flow rate from the air-fuel ratio and the fuel rate;
• generating an exhaust flow rate signal indicative of the exhaust flow rate;
• and
• adjusting an amount of a reductant inserted into the exhaust gas based on the determined exhaust flow rate.

A control circuitry for determining an exhaust flow rate of an exhaust gas produced by an engine, the control circuitry comprising:

• a controller configured to be a communicatively coupled to a first sensor, the first sensor configured to measure an amount of NOx gases in the exhaust gas, the controller being configured to:
• receive a first sensor signal from the first sensor;
• receive a fuel rate signal corresponding to a rate of fuel consumption by the engine;
• determine an oxygen fraction in the exhaust gas from the first sensor signal;
• determine an air-fuel ratio from the oxygen fraction;
• determine a fuel rate from the fuel rate signal;
• determine the exhaust flow rate from the air-fuel ratio and the fuel rate;
• and
• generate an exhaust flow rate signal indicative of the exhaust flow rate.