Challenges in Hydraulic Fracture Simulation: Evidence from Observations Spanning Laboratory-Scale Experiments to Tectonic-Scale Dyke Swarms

IMA, May 2015

Andrew BungerDept of Civil and Environmental EngineeringDept of Chemical and Petroleum Engineering

University of Pittsburgh, Pittsburgh, PA, USAbunger@pitt.edu

Role of Geometry and Propagation Regime in Multiple HF Growth

IMA, May 2015

Andrew BungerDept of Civil and Environmental EngineeringDept of Chemical and Petroleum Engineering

University of Pittsburgh, Pittsburgh, PA, USAbunger@pitt.edu

Uniformly Stimulated Volume: The Elusive Goal

Soliman et al. , J Pet Tech, August 1990

Early 1950s frac pump, from Montgomery and Smith, J Pet Tech, December 2010

Direction drilling ad from 1954 issue of World Oil

Example from Barnett ShaleFisher et al. 2004, SPE 90051

“…regularly spaced cross-cutting fractures that tend to appear at roughly 500 ft intervals regardless of perforation cluster location.”

Success not the norm: Example from US tight sand reservoir

Mace et al. 2011. SPE 140444.

Giant Dyke Swarms- 1000s of km length

- 10s of km height

- Lateral propagation with blade-like geometry

- >119 on Earth

- >163 on Venus

- “Abundant" on Mars

Goal: Simulator to predict multiple hydraulic fracture growth versus localization

…in order to explore possible approaches to promote multiple growth

Premise: Our simulator will be consistent with basic physical principles found throughout nature and will therefore give energy-minimizing solutions

Basic Question: Can we use a 2D geometry and/or ignore fluid-solid coupling and still grasp the leading order behavior of the system?

Approach: Examine role of dimensionality of the problem and of fluid-solid coupling in energetics of the system

PI = pfo Q = Rate of energy input

PI = Sum from N HFs =Pi

If:•constant rate injection•uniformly growing array

Q=Qo, Qi=Qo/(N-1)~Qo/N, N>>1

PI=N Pi

•PI depends on N: PI=PI[N,Pi(…,Qo/N)]•Objective: Clarify nature of this dependence

Bunger AP. 2013. Analysis of the Power Input Needed to Propagate Multiple Hydraulic Fractures. International Journal of Solids and Structures, 50:1538-1549.

Input energy via the fluid and it either does work on the solid or is dissipated in fluid flow

Expression for Pi

Input energy via the fluid and it either does work on the solid or is dissipated in fluid flow

Pressure drop through perforations

Flow in fracture channel

Expression for Pi

Input energy via the fluid and it either does work on the solid or is dissipated in fluid flow

Counteract work done on crack by far field stress

Counteract work done on crack by nearby HFs

Increases elastic strain energy stored in the rock

Dissipated through rock fracturing

Expression for Pi

Radial Geometry – Viscosity Dominated Regime

Radial Geometry – Viscosity Dominated Regime

Bunger AP, Jeffrey RG, Zhang X. 2014. Constraints on Simultaneous Growth of Hydraulic Fractures from Multiple Perforation Clusters in Horizontal Wells. SPE Journal, 19(4): 608-620.

Requires less power

to propagate MORE HFs

Until interactions

become strong

enough

Very little influence

from perforations

Radial Geometry – Viscosity Dominated Regime

Bunger AP, Peirce AP. 2014. Numerical Simulation of Simultaneous Growth of Multiple Interacting Hydraulic Fractures from Horizontal Wells. Proceedings ASCE Shale Energy Engineering Conference, Pittsburgh, PA, USA, 21-23 July 2014.

Radial Geometry – Toughness Dominated Regime

Radial Geometry – Toughness Dominated Regime

Bunger AP, Peirce AP. 2014. Numerical Simulation of Simultaneous Growth of Multiple Interacting Hydraulic Fractures from Horizontal Wells. Proceedings ASCE Shale Energy Engineering Conference, Pittsburgh, PA, USA, 21-23 July 2014.

Bunger AP, Jeffrey RG, Zhang X. 2014. Constraints on Simultaneous Growth of Hydraulic Fractures from Multiple Perforation Clusters in Horizontal Wells. SPE Journal, 19(4): 608-620.

PKN Geometry – Viscosity Dominated Regime

Minimum power is associated with an INTERMEDIATEnumber of HFs

PKN Geometry – Viscosity Dominated Regime

Global min – but can’t get there

Expect h~1.2-2 H

Perforation diameter

PKN “Linguine” Case – Energetically Preferred Spacing

Stress shadow –

pushes apart

Min viscous dissipation –

brings together

Predicted Emergent

spacing

Natural spacing ->energy minimum resulting from combination of stress shadow and viscous dissipation

Early Successes – Example from Barnett ShaleFisher et al. 2004, SPE 90051

“…regularly spaced cross-cutting fractures that tend to appear at roughly 500 ft intervals regardless of perforation cluster location.”

H~350 ft h~1.4 H

– Mean distal spacing in 1270 Ma Mackenzie (<h>~27 km) Swarm, Ontario, Canada in range of estimated H~20-40 km

– Krafla rifting episode, Iceland, <H>~2.8 km

– Tertiary Alftafjördur dyke swarm, Iceland, <h>~2.5 km

– Next steps:

– Earth in greater detail

– Contrast Earth, Mars, Venus

Bunger AP, Menand T, Cruden AR, Zhang X, Halls H. 2013. Analytical predictions for a natural spacing within dyke swarms. Earth and Planetary Science Letters, 375:270-279.

Approximate with plane strain model?

Compare 2D and Radial Geometry

ˆ inqHQ ˆ inq

RQ

The Difference: Characteristic Flux

Fixed height means characteristic flux is constant

Growing radius means characteristic flux decreases with time

Compare 2D and Blade-Like Geometry

W PLE W PH

E

The Difference: From Elasticity

Growing length means crack compliance decreases with time

Fixed height means crack compliance is constant

PKN/Visc

Maxwell et al. 2002, SPE 77400

Spacing of lineaments: 300 ft

Approximate with plane strain model?

2D model much more prone to localization

Approximate with uncoupled model (fracture mechanics only)?

Compare Viscosity and Toughness

IcKPR

3inP

WQ

The Difference: Characteristic Pressure

Pressure scale from LEFM propagation condition

Pressure scale from Poiseuillefluid flow equation

Approximate with plane strain model?

2D model much more prone to localization

Approximate with uncoupled model (fracture mechanics only)?

Misses the main driving physical mechanism – and again gives a prediction that is much more prone to localization

Conclusions

• Predictions of swarm-like multiple HF growth versus localization are profoundly different for different geometries and propagation regimes

• Toughness dominated and/or 2D HFs are not expected to exhibit swarm-like growth (in absence of perforation losses)

• Radial, viscosity-dominated HFs favor multiple growth until the radius attains a similar value to the spacing

• Blade-shaped, viscosity-dominated HFs swarm with a characteristic spacing coming from fracture height H

Note: Applications now are aimed at forcing spacing to be less than H.

33

C2Frac – Energy and Asympotics-Based Simulator

C Cheng and A P Bunger, In Review ~1 sec ~1 week

- Penny-shaped crack solution- Far field approx of interaction- Update pressure using global

energy balance

34Good match until R~0.6Z

35

36

37

• An additional N equation is obtained from the interaction stresses. The main challenge and focus of the problem is due to interaction and the impact of the interaction on hydraulic fracture growth, including the effect on the partitioning of the fluid embodied by Qi.

where , By letting be the mean injection rate to the jthhydraulic fracture and and , where Rj is the radius of the jth hydraulic fracture and hi,j is the separation between the jth and the ith hydraulic fracture; we can approximate the interaction stresses exerted on the ith hydraulic fracture as

)(25

1091;, 42

23

'

Oh

tQEQ i

iI

Rh / jQ

jji,ij Rh / jj Rr /

,

i ,j 1

ˆ , , ;N j i

I j i j jr t Q

38

• However, the interaction stresses remain uncoupled from the other 4N equations. The proposed solution for this issue, which is the critical component of the C2Frac algorithm, is to replace the estimate of the pressure, with an updated estimate that obtains its correction via an energy balance equation for each hydraulic fracture of the form derived by Bunger(IJSS, 2013). This energy balance is given by

• : increases the elastic strain energy stored in the rock

• : overcome the negative work being created on each hydraulic fracture by the stress interactions from its neighbors

• Dc: breaking the rock (assume equals zero)

• Df: viscous fluid flow

• σmin: is constant at uniform reservoir condition

fcIfii DDWUtpQ ..

min,0

IW

U

Epilogue: Promoting multiple fracture initiation and growth

Peirce AP, Bunger AP. Interference Fracturing: Non-Uniform Distributions of Perforation Clusters that Promote Simultaneous Growth of Multiple Hydraulic Fractures. SPE Journal, In Press. Pre-print: http://hdl.handle.net/2429/45492