Method for operating a delivery device for a reducing agent and motor vehicle having a delivery device

A method for operating a delivery device for a reducing agent, the method comprising the following steps:

• providing the delivery device with a tank for a liquid reducing agent, an injector for supplying the liquid reducing agent to an exhaust gas treatment device of an internal combustion engine, and a reducing agent line running from the tank to the injector and having at least one pump for delivering reducing agent in a delivery direction from the tank to the injector and at least one pressure sensor;
• a) determining and providing an adequate and achievable supply pressure for the injector in the delivery device with the pump;
• b) calculating an injector opening time from a defined injection quantity and the achievable supply pressure;
• c) opening the injector for the calculated injector opening time;
• and
• carrying out, at a predefined point in time, an air removal procedure including at least the following steps:
• i) determining an actual slope of a pressure/delivery volume characteristic in the delivery device;
• ii) calculating an air bubble volume by comparing the determined slope to a target slope;
• and
• iii) delivering a delivery volume through the injector if the air bubble volume calculated in step ii) is greater than a maximum permissible air bubble volume.