Fracture Modeling for PWRI

R. D. Barree

Marathon Oil Company

April 25, 2000

Critical Factors for Modeling Fracture Growth During PWRI

- Fracture geometry
  - containment
    - effects of layering
    - effects of stress contrast
    - effects of pore pressure variation
  - length development

- Fluid leakoff
  - typically very low efficiency

Effect of Distributed Load

Consider, by superposition, the effect of a distributed load

over some area:

The deflection of the surface of the half-space is

Integrating this for a circle gives expressions for the

displacement at the center and edge of the loaded area

These solutions were developed by J. Boussinesq in 1885

Sneddon (1945) Developed Equivalent Solutions for Simple Geometries

For a pressurized circle:

where a is the radius of the loaded area, a<=c.

Note that for a=c, the displacement at the center is

which is similar in form to the previous solution. However,

Sneddon’s equation assumes that the displacement is zero

outside the area of the circle.

PPT Slide

Sneddon equation for an infinite

(plane-strain) crack

These simplified-geometry solutions assumed two-dimensional

plane-strain behavior with an implied stress singularity

(infinite stress) at the crack tip.

These equations are used in most 2-D and pseudo 3-D frac

models.

PPT Slide

Sneddon’s equation applied to

two common models:

For the KGD model, the crack half length (c) is given by L:

For the PKN geometry, the total fracture height (H) is 2c:

Note that these are the same equations solved with different

characteristic crack lengths and assume an infinite stress

and zero displacement at the crack tips.

The Plane-Strain Solution

- Applied in most fracturing simulators

- Assumed in many theoretical analyses
  - Griffith
  - Sneddon
  - England and Greene

- Implies that the entire rock mass is elastically coupled

Plane-Strain Solution

- Applies for cracks of large aspect ratio

- Width is a function of net pressure and characteristic length

- Width is constant along frac length

Elastically Coupled Displacement

- A net pressure applied at any point causes displacements over the entire surface

- Displacement magnitude decreases with distance from the point of application of force

- Total displacement at a point is the integration of all displacement increments caused by all loads

Elastically Coupled Displacement

A point-load causes deformation of the

entire surface

Containment in a Coupled System

Internal frac fluid pressure

displaces frac walls.

Stresses at the frac tip

concentrate from elastic

displacements transmitted

through the rock.

Frac extends by “wedge”

action and fluid pressure.

Containment depends on

stress contrast.

Field observations suggest:

- High net treating pressures are common

- Fracture widths are often less than predicted

- Height containment is often better tan expected

- Shear failure occurs in the rock mass (microseisms)

- Shear slip occurs at some bed boundaries

Shear Failure in Rock

- Internal angle of friction determines how much shear stress can be supported at any normal stress

- Allowable shear stress decreases with decreasing normal stress

- High pore fluid pressures decrease normal stress on shear plane

Shear Failure in Rock

Failure depends on net confining stress.

High pore pressure leads to low net stress.

Displacement With Shear

Shear Plane

Slippage along shear-planes restricts

displacement to a limited area

Containment in a Decoupled System

Internal frac fluid pressure

displaces frac walls.

Shear slip separates frac

into segments.

Frac extends by local

fluid pressure.

Containment depends on

stress contrast and system

connectedness.

Fracture Discontinuities

Core Containing Propped Fracture

Shear-Slip Model

- No displacement transmitted across a freely sliding shear plane

- No influence from any loads applied on opposite side of shear plane

- Integrate applied load over a small area

- No stress concentration at fracture boundary

- Very small fracture widths

Width Profiles for Various Shear-Dampening Radii

Infinite

100 ft

50 ft

20 ft

10 ft

PPT Slide

Frac Geometry After Water Injection

C Sand

Fracture contained in C sand interval

Most growth in upper half of sand until end of job

Microseisms After Water Injection

Frac Geometry at End of Gel Injection

C Sand

High viscosity x-linked gel injection

causes increased width and height

Microseisms After X-L Gel Injection

West Texas Injection Test

Injection Falloff Analysis

Injection SRT

SRT Falloff Analysis

Pinnacle Technologies Fracture Mapping results

- Four injection zones mapped

- Surface and downhole inclinometers

- Frac opening at 0.1 bpm water injection

- All fracs contained in zone at all rates

- Frac half lengths 400-600 feet

- Typically 20% vertical component of fractures

Fluid Leakoff Modeling in GOHFER

- Modified one-dimensional analytical leakoff model (FLIC)
  - non-Newtonian fluid invasion
  - filter cake erosion

- Coupled 3-D reservoir simulator
  - handles reservoir pressure transients
  - more accurate for very low efficiency

- Pressure dependent leakoff

Leakoff in PWRI fracturing

- Efficiency generally very low

- Frac growth rate controlled by material balance

- Small errors in leakoff dominate geometry

- Poorly constrained even by pressure falloff measurements