Continuous improvements during well completion in addition to stimulation technology renew the need for multi-fractured horizontal well modeling. The present work investigates the productivity of a well with fractures by means of semi-analytical late-time approximations. These expressions are related to a vertical and a horizontal well with a single-fracture production. The flow in a fracture that is coupled to a horizontal well is of uniform flux (or of infinite conductivity flow) and the fractures can be positioned transversally or longitudinally. To successfully measure the production efficiency of a fractured-horizontal well, the effective wellbore radius and the equivalent single-fracture half-length were introduced. The effective wellbore radius was defined for a vertical well and could be extended for its horizontal counterpart. The equivalent fracture half-length was defined for a horizontal well with a single-transversal and a single-longitudinal fracture. The late-time approximations were developed for a fractured horizontal well positioned in the middle of an infinite oil reservoir. The developed expressions were employed for a multi-fractured horizontal well in order to define an effective wellbore radius and an equivalent fracture half-length (for both the transversal and the longitudinal fractures). A series of solutions corresponding to various conditions were given in a multiple-fractured-horizontal well model. It was possible to verify derived effective parameters of a fractured horizontal well by using a fast, robust and facile software program, a screening-tool product, that has been of considerable benefit to companies in the petroleum industry.

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