Effective Wellbore Parameters and the Productivity of a Multi-Fractured Horizontal Well

Abstract

Summary 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. Introduction Fractured wells are frequently considered in reservoir and production engineering. They constitute either hydraulically fractured wells to improve oil production or wells intersecting natural fractures. Hydraulically fractured horizontal wells represent a proven technology for producing oil and gas from tight formations. Hydraulic fractures reduce well drawdown, increase the productivity of horizontal wells by increasing the surface area in contact with formation, and provide high conductivity paths to the wellbore. Depending on the in-situ stress orientation, hydraulic fractures can be parallel (longitudinal) or perpendicular (transverse) to the horizontal well axis. Usually, two main fracture directions relative to the well direction appear. If a horizontal well is drilled perpendicularly to the axis of the least principal formation stress, a longitudinal fracture along the wellbore is generated by hydraulic fracturing. If, on the other hand, it is drilled parallel to the least principal stress direction, multiple transverse fractures can be generated. In general, horizontal wells with transverse fractures are favorable in low permeability reservoirs provided that a high conductive fracture conductivity can be obtained. Project economics in tight formations, however, depend strongly on well spacing and the number of hydraulic fractures required for the efficient draining of the reservoir. The present study aims at establishing an understanding of the influence of the (fracture-wellbore) system intersection angle on various predictions made through single-well modeling. This modeling was based on the developed mathematical models, able to reproduce the responses of acute systems to various forms of disturbances under a variety of conditions. The differential equation governing flow in conceptualized acute systems was derived from basic principles. Analytical solutions to this equation were reached for transient flowing conditions. The vertical well effective wellbore radius, rwv, which is greater than the actual wellbore radius, rw, constitutes a measure of the multi-fractured well efficiency. This efficiency can also be related to a single fracture with an equivalent half-length, Lfe, positioned transversally or longitudinally along a horizontal well.