Shell 1

Background

The model is an extension of Koning’s model for waterflood-induced fracturing.  The fracture is assumed to fully penetrate a permeable layer and is bounding above and below by impermeable material.  The fracture is surrounded by four elliptically shaped zones that include:

 

1.     an impaired zone where oil and/or solids have penetrated,

2.     a cooled (or heated depending on the injected fluid) zone,

3.     a zone flooded by injected water that “has warmed up,” and,

4.     a virgin oil zone.

 

Each zone is characterized by its own temperature, saturant viscosities, and relative permeabilities.  The extent of each zone is determined from mass balance as well as heat capacities of the water and the target formation (using the methods outlined in Koning’s thesis).  The fracture face is covered with an external filter cake consisting of injected oil and solids that have not penetrated into the formation.  Eventually, the fracture may be filled with solids (oil) that have not penetrated into the formation, leading to a finite fracture conductivity.  This is a significant departure from Koning’s model.

 

Propagation

For clean water injection, the fracture is infinite conductivity, poro- and thermoelastic back stresses are applied and propagation is based on a critical stress intensity factor criterion.  A geometry factor is included to account for whether the fracture has a KGD or PKN geometry.  Poroelasticity is incorporated using analytical solutions for elliptical regimes.  Thermoelasticity is based on the concepts of Perkins and Gonzalez.

 

Damage

The damage is represented as:

 

1.                 A damage zone around the fracture which is characterized by a “uniform permeability impairment factor.”  The boundary is calculated from the volume of injected oil (solids) that deeply penetrates (analogous to an internal filter cake).  It is assumed that this is roughly equal to the extent of the residual oil saturation.  A determination must be made of what percentage of the oil/solids deeply penetrates.

 

2.                 An external filter cake on the fracture face with uniform permeability.  The thickness of this filter cake is assumed to be elliptical.  If the fracture conductivity is infinite this implies a uniform pressure drop over the entire surface.  Thickness of the filter cake is calculated from the volume of injected solids/oil that remains in the fracture and the fracture surface areas.

 

3.                 Internal plugging of the fracture.  When the external cake starts to form it is assumed that supplementary deposition of solids will be against the external filter cake and will progressively fill the fracture.  Elliptical symmetry is lost but this is resolved mathematically in the model.  Consequently, a finite conductivity fracture can result.  It is visualized that wormholes will evolve.  “This picture allows one to calculate the fracture conductivity by requiring that at any moment in time, the fracture volume should be equal to the total volume of injected solids.”

 

Movement of fines towards the tip is envisioned and two extremes in fracture permeability are envisioned (one uniform permeability profile and one with an impermeable tip plug).