A downhole well system for producing hydrocarbon-containing fluid from a reservoir downhole includes a well tubular structure having first and second annular barriers for isolating an annulus outside the well tubular structure. Each annular barrier has a tubular part adapted to be mounted as part of the well tubular structure, the tubular part having an outer face, an expandable metal sleeve surrounding the tubular part, and an annular space between the inner sleeve face of the expandable sleeve and the tubular part. An inflow valve assembly is arranged between the first and the second annular barriers for providing fluid communication between the production zone and the inside of the well tubular structure through a passage in the inflow valve assembly by adjusting a closing member in relation to the passage.