5. Mechanics of fluid driven fractures

This document is a draft. Find hand written notes here: https://github.com/dnicolasespinoza/GeomechanicsJupyter/tree/master/ClassNotes.

5.1 Fracture initiation in a wellbore

Figure 5.1: Pressure for tensile fracture initiation in an uncased vertical wellbore.

Figure 5.2: Breakdown solution cases based on level of horizontal stress anisotropy.

5.1.1 Fracture injection/shut-in tests

Figure 5.3: Typical signature of a fracture injection/shut-in test as a function of time.

5.1.2 Ideal orientation of hydraulic fractures

Figure 5.4: Ideal orientation of hydraulic fractures: planes perpendicular to local least principal stress.

5.2 Coupled fluid-driven fracture propagation

5.2.1 Overview

Figure 5.5: Schematic of processes happening in a fluid-driven fracture.

Figure 5.6: Physical processes and key equations for fluid-driven fractures.

5.2.2 Linear elastic fracture mechanics

Figure 5.7: Net pressure concept for free-body diagrams and abstraction

Figure 5.8: Solution for stress and displacements around a planar crack pressurized at constant pressure.

Figure 5.9: Derivation of stress intensity factor for plane-strain fracture with constant pressure

Figure 5.10: Critical stress intensity factor for fracture propagation.

5.2.3 PKN solution and other cases

Figure 5.11: PKN model: main assumptions and geometry.

Figure 5.12: Determination of fracture height (from stress logs) and fracture width.

Figure 5.13: Fluid fllow along the fracture and mass conservation equations.

Figure 5.14: PKN derivation (1).

Figure 5.15: PKN derivation (2).

Figure 5.16: PKN derivation (3).

Figure 5.17: Summary pseudo 3D models: PKN, KGD and Radial.

5.2.4 Fluid-driven fractures in porous media

Figure 5.18: Schematic and relevant parameters for fracture propagation in porous media.

Figure 5.19: Dimensionless space for fracture propagation in porous media.

Figure 5.20: Summary of key points.

5.3 Hydraulic fracturing in tight formations

5.3.1 Design: Pads, wellbores, stages and clusters

Figure 5.21: Comparison between single fracture vertical well and horizontal well with multiple clusters per stage .

5.3.2 Fracture interference and interaction

Figure 5.22: Fracture interference in a stage with multiple clusters.

5.3.3 Typical hydraulic fracturing parameters

Figure 5.23: Typical fracture design in the Permian Basin.

Figure 5.24: Typical injection schedule.

5.3.4 Fracture swarms

5.3.4.1 Impact of heterogeneity

TBA (high permeability layers)

5.3.4.2 Fracture branching and splitting

Figure 5.25: Pure and mixed-mode fracture propagation.

Figure 5.26: Conceptual image of fracture swarms.

5.3.4.3 Subcritical fracture propagation

Figure 5.27: Concept of subcritical fracture propagation.

Figure 5.28: Subcritical fracture propagation in hydraulic fracturing.

5.3.4.4 Nucleation from diffuse excess pore pressure

5.3.5 Monitoring: microseismicity and fiber optics

Figure 5.29: Conceptual image of fracture swarms and microseismic events.

Figure 5.30: The Stimulated Reservoir Volume and relationship with seismic and aseismic slip.

Figure 5.31: Velocity strenghtening and weakening shear slip.

5.4 WP9: Hydraulic Fracturing

5.4.1 Stress shadows and interference

Read the paper “Roussel, N. P., and Sharma, M. M. (2011). Optimizing fracture spacing and sequencing in horizontal-well fracturing. SPE Production and Operations, 26(02), 173-184.” https://doi.org/10.2118/127986-PA.

1. Calculate the point of principal stress reversal (isotropic point in Fig. 11 of the paper) with a constant pressure and plane-strain solution utilizing your FreeFEM++ linear elasticity code. Use all parameters as in Table 1. Note: $\Delta S_{yy} = \nu (\Delta S_{xx}+\Delta S_{zz})$.
2. Repeat the previous task for fracture width 6 mm, 8 mm, and 10 mm. Plot stress reversal distance as a function of fracture width. Hint: You may need to calculate the required net pressure from the analytical solution.

Figure 5.32: $S_{Hmax}$ direction around a propped hydraulic fracture (Roussel and Sharma, 2011).

5.4.2 Coupled hydraulic fracturing modeling

A single hydraulic fracture treatment will be performed in a tight sandstone. The hydraulic fracture height is expected to be $h_f$ = 170 ft. The tight sandstone has a plane-strain modulus $E' = 8.9 \times 10^6$ psi. The (two-wing) injection rate will be 50 bbl/min (constant) during 1 hour.

Compute:

1. The expected fracture half-length $x_f$, fracture width at the wellbore $w_{w,0}$, and net pressure $p_{n}$ as a function of time with the PKN model (no leak-off) assuming the fracturing fluid has a (constant) viscosity 2 cP.
2. The expected fracture half-length $x_f$, fracture width at the wellbore $w_{w,0}$, and net pressure $p_n$ as a function of time with the PKN model (no leak-off). Now the fracturing fluid has a viscosity 2 cP with no proppant (initial 10 min), and increases in steps of 10 min with 2 cP in each step (due to increasing proppant concentration).
3. What should you do to your solution in order to consider leak-off? Justify and explain briefly the algorithm to calculate $x_f$, $w_{w,0}$, and $p_n$.

Hint: convert all quantities to the SI system first

5.5 Suggested reading

• Fracture injection/shut-in tests for geothermal: https://doi.org/10.1016/j.ijrmms.2023.105521
• Integrated analysis of HTFS2 https://doi.org/10.15530/urtec-2021-5396
• Buoyant fractures in Delaware Basin https://doi.org/10.15530/urtec-2022-3722883