Pump device and method for operating a pump device

The device (12) has a low pressure line (20) for conducting fluid with low pressure. A transfer pump (18) compresses and conveys the fluid from a tank (14) into the low pressure line. A high pressure pump (28) compresses and conveys the fluid from the low-pressure line into a high pressure line (38). A low pressure storage unit (34) is connected with the low pressure line for storing a part of the conveyed fluid at storage pressure. The low pressure line has a stop valve (26) present between the transfer pump and the low pressure storage. An independent claim is also included for a method for operating a pumping device.