The method of displacing fluids in the annulus between pressurized casing strings inside an active oil or gas well by providing a controlled turndown insert and guides then inserting and retrieving a flexible hose without it folding or buckling while being pushed or pulled through a wellhead system orifice with relatively sharp edges at the annulus opening where the hose must make a 90 degree turn from horizontal to vertical within a short radius without cutting, crimping or tearing the hose then seating and holding the hose while fluids are injected, all the while providing protection against well blow out or other pressure problems.