This work presents the basic of steady-state productivity index behavior for a well with finite conductivity fracture complicated by presence of damaged zone around the fracture. Two kinds of fracture damage parameters are studied: • a damaged zone width around the fracture; • a damaged zone permeability reduction caused by the fracturing fluid loss in the formation.` This paper emphasizes that damage effects on well productivity are quite different for different values of dimensionless fracture conductivity, fracture penetration ratio and damage factor. Special type curves for steady-state productivity index can be used to identify different cases when damaged zone influence on well productivity index becomes quite significant


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