Apparatus and method for injecting a chemical to facilitate operation of a submersible well pump

A well pump assembly has a motor operatively connected to a well pump that has an intake. The well pump assembly has a capillary tube that extends alongside the tubing and has an outlet at the well pump assembly. A chemical injection pump is connected to an upper end of the capillary tube adjacent a wellhead of the well. A logic system detects well fluid falling back downward in the tubing and out the intake into the well, and in response turns on the chemical injection pump, which pumps a chemical down the capillary tube into the well adjacent or within the well pump assembly. Once upward flow of well fluid in the tubing has been established, the chemical injection pump may be turned off.