A wellbore system with a tubular string extending from an earth surface down into a wellbore in the earth, a packer system with a selectively settable packer element, and a disconnect located between an end of the tubular string and the packer system, the disconnect operable from the surface by imposing a downward force on the tubular string. In one aspect the packer system's packer element is a tension-set packer element. A wellbore disconnect with a top sub (122), a mandrel (126) having an upper end secured to the top sub and a portion below the upper end releasably secured with at least one releasable member (138) to a carrier member (136), the carrier member having apparatus (156) for selectively gripping the mandrel, the apparatus for selectively gripping the mandrel also selectively gripping a bottom sub (144) within which the mandrel is moveable, the at least one releasable member releasable in response to a downward force on the disconnect.