Abstract Compressibility needs to be accounted for when estimating productivity decline in closed gas and oil reservoirs, and in closed aquifers. Previous works derived an analytical model and well index for inflow performance accompanied by fines migration and consequent permeability damage for incompressible flow towards well. In the present work, we account for fluid and rock compressibility. The problem with given and constant well production rate is investigated. Mathematical model is developed, which provides well productivity index decline with time. Under this model, the solution of damage-free compressible flow in a closed reservoir is matched with the impedance growth formulae for incompressible flow in the well vicinity. The well production data have been successfully matched by the model; the tuning parameters have the common values. It allows indicating the fines mobilization, migration and straining as possible well impairment mechanism in wells under investigation.