Modeling Hydraulic Fractures in Unconsolidated Sands
Authors: Denney Dennis 
Published: February 2015

This article, written by Technology Editor Dennis Denney, contains highlights of paper SPE 96246, "A New Approach to Modeling Hydraulic Fractures in Unconsolidated Sands," by Z. Zhai, SPE, and M.M. Sharma, SPE, U. of Texas at Austin, prepared for the 2005 SPE Annual Technical Conference and Exhibition, Dallas, 9-12 October.
Field data show that traditional models for brittle, linear-elastic rocks do not adequately represent fracturing in poorly consolidated rocks. A model was developed for describing the propagation of "fractures" in unconsolidated sands. The model departs radically from current models in that brittle-rock fracture mechanics is not used. Instead, the propagation of pore pressure is computed, and the porosity and permeability of the sand are specified as functions of the effective stress. This region of enhanced porosity defines a "fracture" in unconsolidated sands. The physics of creation and propagation of this oriented high-permeability zone is modeled.

Introduction
The application of frac packs in poorly consolidated reservoirs has been effective to prevent sanding problems. In conventional hydraulic-fracture simulations, to which linear-elastic fracture mechanics (LEFM) is applied, fracture initiation and propagation are governed by in-situ stresses, fracture toughness, tip dilatancy, and the process zone. Unlike competent formations, unconsolidated-sand beds have little or no tensile strength. LEFM is adequate for hard rocks, but the fracture-geometry predictions fall short when applied to fracturing soft rocks. For example, when using classical fracture models for simulating this process, it has been reported that millions of barrels of solid-waste slurry can be injected easily into soft formations over a period of several years. To accommodate such a large volume of solids, fracture lengths of several miles would be required, even with fractures that are several centimeters wide.
Experimental and simulation studies identified mechanisms of fracture propagation and initiation in unconsolidated-sand formations. Many of those studies rely on classical brittle-rock fracture mechanics and in some cases do not account for shear failure. Permeability anisotropy induced by in-situ stresses is not considered. An approach to modeling the mechanical behavior of unconsolidated sands that are subjected to injection of water-based slurries is detailed in the full-length paper.

Model for Stress Distribution Around an Injection Well
To study fracture initiation and propagation, the effective-stress distribution around the well must be obtained and then the permeability and porosity updated in accordance with the appropriate constitutive relationships.
The stresses around the wellbore can be divided into three parts.Stresses induced by far-field, in-situ stresses.Stresses induced by wellbore pressure.Flow-induced stresses (poroelastic stresses).
On the basis of stress distribution, the anisotropic stress tensor can be determined as well as where and when tensile or shear failure occurs. This approach has been applied widely to wellbore-stability problems for homogeneous isotropic rocks. In this paper, the stress distribution is coupled with the pore pressure, and the model is applied to hydraulic-fracturing problems in unconsolidated sands. This iterative, coupled program was developed to calculate the pore pressure, stress/strain distribution, porosity, and permeability in the formation.