A gas storage well with a tubing string that is disposed within a wellbore communicating an underground storage cavern with the surface. A surface controlled subsurface safety and flow control system is provided within the wellbore so that all flow into or out of the well can be shut down rapidly in the event of an emergency. The safety and flow control system features a dual opening-style packer element that provides an annulus seal between the surrounding casing and the tubing string and between the casing and a pup joint that is located within the annulus. Both the tubing string and the pup joint contain surface controlled subsurface safety valves that are capable of quickly shutting off flow through both the flowbore and the annulus. Each valve can be opened or closed independently of the other.