A mathematical formulation and solution methodology for placing proppant to create open channels and propped pillar packs in hydraulic fractures is presented. The advantage of this methodology is increased fracture conductivity by creating open channels and/or pillars that support the unpropped (or open) fracture region. The technique requires reduced proppant mass and results in enhanced fracture conductivity. The work illustrates that high conductivity proppant is not required.

The paper presents the governing equations, assumptions and a solution methodology for designing open channels and for flow around pillars in propped fractures. The governing equations and assumptions for calculating the surface displacement (in the loaded and unloaded regions) for pressure loading of a strip and circular region in an elastic half-space are formulated in the appendices. Four cases are presented: 1) uniform pressure distribution over an infinite strip, 2) uniform (constant) distribution (i.e., rigid line punch) over an infinite strip, 3) uniform pressure applied to a circular region, and 4) uniform normal displacement over a circular region.

The effects of the closure stress on the proppant and the formation modulus on embedment are discussed and illustrate the advantage of this methodology in formations with high Young's modulus and low confining stress contrasts. Disadvantages and limitations of the procedure are also discussed. A formulation for the equivalent fracture permeability for flow through channel and pillar type propped fractures is also presented and demonstrates the advantage of creating pillars and open channels for enhanced fracture conductivity. Fractures with open channels and pillars have much greater permeability than traditionally propped fractures. However, proppant permeability is not important in pillar and channel type fracture designs. A proppant that is more ductile and one that creates few fines when crushed is more advantageous for channel and pillar type designs.

The design formulae present a simple methodology to allow for easy field implementation based on a volumetric ratio of fluid to proppant stages. The treatment design can be accomplished with standard industry pumping equipment and methods are provided for the fracture design engineer to create treatment schedules that can be employed by current hydraulic pumping technology. The methodology, if implemented correctly, will greatly increase the dimensionless fracture conductivity (by orders of magnitude) resulting in enhanced production while minimizing operational costs associated with proppant quality.