Fracture Modeling for PWRI

1. Fracture Modeling for PWRI R. D. Barree Marathon Oil Company April 25, 2000

2. 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

3. Effect of Distributed Load

4. Sneddon (1945) Developed Equivalent Solutions for Simple Geometries

7. 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 Almost all frac simulators in use today are based on basically the same fracture width equation. This equation comes from a general solution of elastic displacement in three-dimensional space. The equation used by these models is a simple closed-form solution resulting from a strict set of assumptions and boundary conditions applied to the general solution. The plane-strain solution assumes that the fracture is elliptical in cross section, has a fixed characteristic �height� and is infinite in �length�. So, variations in fracture width only occur along the axis of the ellipse. The fracture width is assumed constant outside the plane of the ellipse, so the fracture is described as an �infinite line crack�. The equation also assumes that the entire rock mass, both in the plane of the ellipse and to infinity in all directions, is a perfectly elastic medium which is fully coupled. No shear planes, natural fractures, bedding planes, or other discontinuities exist. Almost all frac simulators in use today are based on basically the same fracture width equation. This equation comes from a general solution of elastic displacement in three-dimensional space. The equation used by these models is a simple closed-form solution resulting from a strict set of assumptions and boundary conditions applied to the general solution. The plane-strain solution assumes that the fracture is elliptical in cross section, has a fixed characteristic �height� and is infinite in �length�. So, variations in fracture width only occur along the axis of the ellipse. The fracture width is assumed constant outside the plane of the ellipse, so the fracture is described as an �infinite line crack�. The equation also assumes that the entire rock mass, both in the plane of the ellipse and to infinity in all directions, is a perfectly elastic medium which is fully coupled. No shear planes, natural fractures, bedding planes, or other discontinuities exist.

8. 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 The figure shows an illustration of the perfect plane-strain crack and the equation representing its width.The figure shows an illustration of the perfect plane-strain crack and the equation representing its width.

9. 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 All width-pressure solutions used in current fracture models are based on linear-elastic deformation models (Griffith, England & Green, Sneddon). Most also assume plane-strain deformation. These assumptions may result in grossly overestimated fracture widths in real treatments. The assumptions inherent in the plane strain solution lead to high stress concentrations at the fracture tips. In fact, a stress singularity exists at the tips of the crack where stress becomes infinite. All width-pressure solutions used in current fracture models are based on linear-elastic deformation models (Griffith, England & Green, Sneddon). Most also assume plane-strain deformation. These assumptions may result in grossly overestimated fracture widths in real treatments. The assumptions inherent in the plane strain solution lead to high stress concentrations at the fracture tips. In fact, a stress singularity exists at the tips of the crack where stress becomes infinite.

10. Elastically Coupled Displacement Linear-elastic models assume that deformations occur over the entire surface of the elastic material in response to a load applied at any point. Deformations die out slowly with distance (1/r). The total displacement at any point is the resultant superposition of displacements caused by all applied loads on the surface. Under these assumptions, each local width is affected by a change in applied load at any point. Stresses around the perimeter of the fracture are likewise affected by all loads applied on the fracture surface.Linear-elastic models assume that deformations occur over the entire surface of the elastic material in response to a load applied at any point. Deformations die out slowly with distance (1/r). The total displacement at any point is the resultant superposition of displacements caused by all applied loads on the surface. Under these assumptions, each local width is affected by a change in applied load at any point. Stresses around the perimeter of the fracture are likewise affected by all loads applied on the fracture surface.

11. Containment in a Coupled System The elastically coupled plane strain models treat fracture propagation like a wedge being driven into a log. All the pressure applied to the walls of the fracture is transmitted through the elastic deformation of the rock to the crack tip where it is concentrated. So, the larger the fracture gets the more stress is concentrated at the tip and the faster the frac tends to grow. As the height increases the width also increases because the fracture opening is directly proportional to its characteristic height. All this behavior is rooted in the assumed boundary conditions used to derive the simple closed-form equation. The elastically coupled plane strain models treat fracture propagation like a wedge being driven into a log. All the pressure applied to the walls of the fracture is transmitted through the elastic deformation of the rock to the crack tip where it is concentrated. So, the larger the fracture gets the more stress is concentrated at the tip and the faster the frac tends to grow. As the height increases the width also increases because the fracture opening is directly proportional to its characteristic height. All this behavior is rooted in the assumed boundary conditions used to derive the simple closed-form equation.

12. 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 When field observations of fracture behavior are made, the traditional plane strain models are found wanting. Better diagnostic techniques point out basic flaws in the underlying assumptions made by these models. One apparent disconnect is that microseismic measurements record energy created by shear failures. If rock shears as a result of deformation, all the assumptions of elastic coupling in the rock mass are invalid. When field observations of fracture behavior are made, the traditional plane strain models are found wanting. Better diagnostic techniques point out basic flaws in the underlying assumptions made by these models. One apparent disconnect is that microseismic measurements record energy created by shear failures. If rock shears as a result of deformation, all the assumptions of elastic coupling in the rock mass are invalid.

13. 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 is controlled by rock strength, internal friction, and applied external load (net stress). In the area around the fracture that is affected by leakoff, the pore fluid pressure may be greatly elevated. In the extreme, the pore pressure may be close to the frac fluid pressure in the open fracture. In this case, one of the net stresses will be near zero and possibly the second principal stress may be considerably reduced. This sets up a condition where shear failure and slip can occur even if the rock were originally intact. Shear failure in rock is controlled by rock strength, internal friction, and applied external load (net stress). In the area around the fracture that is affected by leakoff, the pore fluid pressure may be greatly elevated. In the extreme, the pore pressure may be close to the frac fluid pressure in the open fracture. In this case, one of the net stresses will be near zero and possibly the second principal stress may be considerably reduced. This sets up a condition where shear failure and slip can occur even if the rock were originally intact.

14. Shear Failure in Rock In soft formations, the tendency to fail in shear is dependent onthe applied normal stress. For most Gulf-Coast unconsolidated sediments the failure envelope can be aproximated by a cohesion of 50-200 psi and an angle of internal friction of 25-30 degrees. As pore pressure surrounding the fracture increases, net stress decreases and the sand becomes more likely to fail in shear. In soft formations, the tendency to fail in shear is dependent onthe applied normal stress. For most Gulf-Coast unconsolidated sediments the failure envelope can be aproximated by a cohesion of 50-200 psi and an angle of internal friction of 25-30 degrees. As pore pressure surrounding the fracture increases, net stress decreases and the sand becomes more likely to fail in shear.

15. Displacement With Shear Displacement damping by shear planes is schematically illustrated.Displacement damping by shear planes is schematically illustrated.

16. Containment in a Decoupled System When shear slippage occurs, either at bed boundaries or induced shear planes, the fracture no longer assumes a nice elliptical shape. The local width becomes a function of local rock properties and stresses, and may no longer increase directly with frac height or length. The stresses transmitted to the fracture tip are also reduced because they are not concentrated over the entire fracture body. As a result, fracture containment improves and frac width may be less than previously expected. The illustration of the expected fracture shape looks much more like those seen in borehole televiewer and image log pictures. When shear slippage occurs, either at bed boundaries or induced shear planes, the fracture no longer assumes a nice elliptical shape. The local width becomes a function of local rock properties and stresses, and may no longer increase directly with frac height or length. The stresses transmitted to the fracture tip are also reduced because they are not concentrated over the entire fracture body. As a result, fracture containment improves and frac width may be less than previously expected. The illustration of the expected fracture shape looks much more like those seen in borehole televiewer and image log pictures.

17. Fracture Discontinuities

18. Core Containing Propped Fracture

19. 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 If there are shear planes in the medium which are free to slip, or capable of slipping with some loss of energy across the plane, displacements cannot be fully transmitted throughout the medium. Loads applied on one side of a shear plane will not generate displacements on the opposite side of the plane. Displacements from all applied loads die out at shear plane boundaries. This results in much smaller fracture widths at a given applied load. Also, stresses transmitted to the fracture boundary will only be generated by areas elastically coupled to the bounding layer. If free shear occurs at a bed boundary, little or no stress will be transmitted to the boundary and fracture containment is greatly increased. If there are shear planes in the medium which are free to slip, or capable of slipping with some loss of energy across the plane, displacements cannot be fully transmitted throughout the medium. Loads applied on one side of a shear plane will not generate displacements on the opposite side of the plane. Displacements from all applied loads die out at shear plane boundaries. This results in much smaller fracture widths at a given applied load. Also, stresses transmitted to the fracture boundary will only be generated by areas elastically coupled to the bounding layer. If free shear occurs at a bed boundary, little or no stress will be transmitted to the boundary and fracture containment is greatly increased.

20. Width Profiles for Various Shear-Dampening Radii In GOHFER the degree of coupling is modeled using the Shear Dampening Radius (DSmax). This value represents the area integrated in determining the widt hat any point on the fracture wall. As DSmax increases the fracture comes closer to the fully coupled solution. As shown in the figure, larger values of DSmax increase the stress concentration at the fracture tips and increase the predicted width. The higher stress concentration leads to poorer height containment and further increases in width.In GOHFER the degree of coupling is modeled using the Shear Dampening Radius (DSmax). This value represents the area integrated in determining the widt hat any point on the fracture wall. As DSmax increases the fracture comes closer to the fully coupled solution. As shown in the figure, larger values of DSmax increase the stress concentration at the fracture tips and increase the predicted width. The higher stress concentration leads to poorer height containment and further increases in width.

21. The plot shows measured surface and bottomhole treating pressures (yellow) in the M-Site C-sand injection. The red curves show the predicted pressures using the shear-decoupled model formulation. The first two injections were treated water. After the long shut-in a crosslinked borate-guar fluid was pumped. Pressure matching indicates that the model may be functionally correct but does not indicate an accurate model of the treatment results.The plot shows measured surface and bottomhole treating pressures (yellow) in the M-Site C-sand injection. The red curves show the predicted pressures using the shear-decoupled model formulation. The first two injections were treated water. After the long shut-in a crosslinked borate-guar fluid was pumped. Pressure matching indicates that the model may be functionally correct but does not indicate an accurate model of the treatment results.

22. Frac Geometry After Water Injection The frac geometry created by each pump-in is a better illustration of the model performance. The decoupled model predicts fracture containment within the C-sand. Most of the frac length is developed in the upper half of the sand. After extending to the limit of the sand at about 500 feet from the wellbore, the frac grows down into the rest of the zone. Traditional plane-strain models could not predict this degree of containment using the rock property and stress data measured. The decoupled model used only the directly measured stress and rock data. The frac geometry created by each pump-in is a better illustration of the model performance. The decoupled model predicts fracture containment within the C-sand. Most of the frac length is developed in the upper half of the sand. After extending to the limit of the sand at about 500 feet from the wellbore, the frac grows down into the rest of the zone. Traditional plane-strain models could not predict this degree of containment using the rock property and stress data measured. The decoupled model used only the directly measured stress and rock data.

23. Microseisms After Water Injection Microseisms recorded during the water injections show containment in the sand, as modeled. Most of the growth is in the upper part of the sand with later events in the lower half. Microseisms recorded during the water injections show containment in the sand, as modeled. Most of the growth is in the upper part of the sand with later events in the lower half.

24. Frac Geometry at End of Gel Injection The model of croslinked gel injection preedicts a much larger frac width amd upward height growth out of zone.The model of croslinked gel injection preedicts a much larger frac width amd upward height growth out of zone.

25. Microseisms After X-L Gel Injection Microseisms recorded during the gel injection agree with the model results. Offset inclinometers shoed a large increase in fracture width. These data confirm that fluid rheology can significantly affect fracture geometry, treating pressure, width and containment.Microseisms recorded during the gel injection agree with the model results. Offset inclinometers shoed a large increase in fracture width. These data confirm that fluid rheology can significantly affect fracture geometry, treating pressure, width and containment.

26. West Texas Injection Test

27. Injection Falloff Analysis

28. Injection SRT

29. SRT Falloff Analysis

30. 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

31. 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

32. 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