This paper presents a new technique for analyzing the performance of hydraulically fractured vertical wells in bounded reservoirs. The main objective is to present a new set of practical equations, based on the recently introduced concepts in well testing, for evaluating the effective length of the hydraulic fracture contributing to unrestricted production. It is determined that the performance of a hydraulically fractured vertical well with mechanical skin and fracture half-length xf1 can be substituted by the performance of a fractured half-length xf2 with no skin. New equations presented in this paper can be used to determine pseudo skin factor effective fracture half-length, mechanical skin factor, shape factor, and productivity index of fractured vertical wells. The new equations and guidelines given in this paper can be used to determine the magnitude of formation damage around hydraulically fractured vertical wells and to evaluate the success of the stimulation treatment. An example based on simulated well test data is presented to illustrate the application of the new technique.


Hydraulic fracturing plays an important role in increasing the productivity of a damaged well or wells producing from low permeability formations. At the present time, 35 to 40% of all vertical wells drilled are hydraulically ractured and 25 to 30% of total US oil reserve have been exploited by this technique. I The net increase in the oil eserve for North America as a result of hydraulic fracturing is believed to be about 8 billion barrels.1 Pressure transient analysis of hydraulically fractured wells can be used to evaluate the performance of these wells, During the last three decades extensive studies have been done to determine the fracture characteristics and formation properties using pressure transient analysis.2–10 These studies made it possible to analyze the entire pressure history of a well test, not just long time data as in conventional analysis. Determination of wellbore storage skin and permeability can now be determined with the aid of statistical analysis. These investigators presented solutions for the infinite-conductivity, uniform-flux and finite conductivity fractures. Different aspects of the subject such as the effects of boundaries, production at constant flowing bottom-hole pressure, flow restrictions caused by fracture damage, wellbore storage, and non-Darcy flow were also investigated. Lower than expected productivity of hydraulically fractured vertical wells can be attributed to problems associated with:

  • proppant transport.

  • proppant embedment in soft formations.

  • fracture extending into the gas cap, bottom-water, and non-reservoir rock.

  • Flow restriction caused by mechanical skin damage around the fracture plane.

  • lack of control of the induced vertical fracture direction.

  • presence of an impermeable barrier near the vicinity of the induced vertical fracture.

  • decrease in fracture conductivity with time as a result of proppant not withstanding the in-situ stresses of the rock.

These problems cause the effective length of the fracture to be shorter than its designed length, thus reducing the expected productivity of these wells.

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