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Hydraulic Fracturing Basic Relations
Basic Relations
• Necessary to understand to apply to fracturing pressure analysis and design parameters
• Material balance – provides basic design requirements for fluid volumes and proppants
Rock deformation • Compliance of fracture describes the ease of fracture deformation
• Principle of crack advance and stresses at the crack tip
• The strain in the formation created by hydraulic fracturing is minor.
• As a result, formation deformation is linear elastic
• Based on the linear elastic assumption, the behavior of a fracture can be modeled using Sneddon’s classical solutions: 2D crack or radial crack Both are: • 2D with one-dimension infinite in extent • Elliptic shaped cracks • Inversely proportional to E’…plain strain modulus • Proportional to a characteristic dimension and net pressure
Fluid flow in fracture Pressure gradient exists along the fracture Local pressure gradient is given by the fluid rheology, velocity, and fracture width. where k’ and n’ are consistency and behavior indices, respectively, for a power law
model. If k’ = m and n’ = 1, then this equation reduces to Newtonian fluid.
Fluid flow in fracture: pressure gradient correction Classical fracture models assume pressure in the fracture is constant. However, the fluid flow relation indicates a gradient from pwf to pc. Thus define, where pf is average pressure within the fracture. Consequently, substitute for pf – smin in width equations with, • Includes the pressure gradient effect from flow and fluid rheology
• Fracture closure pressure is a global parameter which defines the fluid pressure for which the fracture effectively closes. It is the average of formation heterogeneities.
• The minimum stress is a local parameter which generally varies over the plane of the fracture.