Fractured Well Performance: Key to Fracture Treatment Success
Authors: Mukherjee Hemanta 
Published: June 2014

Distinguished Author Series articles are general, descriptive representations that summarize the state of the art in an area of technology by describing recent developments for readers who are not specialists in the topics discussed. Written by individuals recognized as experts in the area, these articles provide key references to more definitive work and present specific details only to illustrate the technology. Purpose: to inform the general readership of recent advances in various areas of petroleum engineering.

Summary
Best production practice requires the optimum production rate from a well with maximum bottomhole flowing pressure (BHFP). This can be engineered only by reducing pressure losses in the reservoir-flow conduit that comprises the reservoir rock and the near-wellbore completion at or near the perforation. Under most producing conditions, an induced fracture with appropriate geometry minimizes near-wellbore pressure losses very efficiently. This paper explores this role of the hydraulic fracture, which results in many applications under different reservoir conditions. Problems concerning placement of an optimally designed hydraulic fracture and common solutions also are discussed.

Introduction
The basic objectives of hydraulic fracturing are to increase productivity or injectivity and to improve the efficiency of steam injection in thermal floods. A more fundamental and alternative view to explain the role of induced fracturing comes from Prats'1 contention that hydraulic fractures extend the wellbore radius. There are a few ways to explain the profound implications of extended wellbores.2 The most practical explanation derives from understanding the pressure losses in the area of drainage. Darcy'slaw states that the pressure gradient in the direction of flow is directly proportional to the velocity. This is stated mathematically in consistent unitsby
dp/dx=vµ/k, (1)
where v=q/A. This relationship also implies that the lower the velocity, the lower the pressure gradient in the path of flow. In radial drainage, with constant volumetric rate, the flow velocity in the radial-flow path is maximum at the wellbore. Fig. 1 explains this point with real dimensions. The velocity at a wellbore of 6-in. radius is 2,000 times that at the entry into the drainage (1,000 ft from the wellbore), assuming negligible fluid entry within this drainage. From Darcy's law, this implies that, at the wellbore perimeter, the pressure gradient is 2,000 times greater than at the drainage surface 1,000 ft from the wellbore. This also suggests that, if the wellbore diameter is increased to 100 ft from 6 in., the entry velocity into this wellbore increases 10 times that at drainage. This translates to a substantial net increase in BHFP by effectively increasing the wellbore radius from 6 in. to 100 ft. Such an increase in the BHFP can be used to produce the well at higher rates; at lower drawdown; or at a combination that considers sand-, water-, or gas-control problems.
For a fixed velocity, Darcy's law also implies that the pressure gradient is inversely proportional to the reservoir permeability: the lower the effective permeability of the flowing phase, the higher the pressure gradient. Near the wellbore, permeability is reduced through different radial-damage mechanisms, such as drilling-fluid invasion and production-induced mechanisms (e.g., condensate dropout from gas, solids/fines deposit, sublimation of sulfur, paraffin deposit, and other scale deposits).
Consequently, the pressure gradient at the wellbore increases as a result of both increased velocity and the reduced permeability caused by damage. Induced hydraulic fractures not only reduce pressure gradients near the wellbore by increasing the surface area of fluid entry but also inhibit some production-induced-damage mechanisms by reducing drawdown and physically bypassing these damaged areas. In many such production-induced-damagemitigations, fracturing can postpone the need for frequent matrix acid treatments.

Fracture Optimization
A fracture can be idealized as a slot induced in the rock, possibly open between acid-etched surfaces or filled with proppant to resist closure. It can be shown analytically that the permeability of an open slot is proportional to the square of slot width; this can be presented as
k=54.4×10 6w2, (2)
where permeability, k, is in darcies and slot width, w, is in inches.
The permeability of a 0.01-in.-wide open slot is 5,440 darcies.3Because permeability is inversely proportional to the pressure loss through porous media, the pressure losses at or near the wellbore can be minimized if the fluid flow can be directed through a fracture or a high-permeability slot from the reservoir to the wellbore. Consequently, the extent of this pressure-loss control determines the major fracture properties, such as its physical dimensions and the permeability with or without proppant.