You are here
Home > BLOG > Hydrulic Fracture > Modeling hydraulic fractures in finite difference simulators using amalgam local grid refinement (LGR)

Modeling hydraulic fractures in finite difference simulators using amalgam local grid refinement (LGR)

Fig. 2 Overview of the static model

Appendix 1: The different stress profile scenarios

See Figs. 16, 17, 18, 19.

Fig. 16 Stress profile scenario # 1 (base case)

Fig. 16 Stress profile scenario # 1 (base case).

Fig. 17 Stress profile scenario # 2

Fig. 17 Stress profile scenario # 2.

Fig. 18 Stress profile scenario # 3

Fig. 18 Stress profile scenario # 3.

Fig. 19 Young’s modulus profile

Fig. 19 Young’s modulus profile

Appendix 2

See Figs. 20, 21, 22, 23.

Fig. 20 Frac design optimization

Fig. 20 Frac design optimization.

Fig. 21 Fracture profile assuming rock mechanic model scenario # 1 (base case) and medium proppant size (16–20)

Fig. 21 Fracture profile assuming rock mechanic model scenario # 1 (base case) and medium proppant size (16–20).

Fig. 22 Fracture profile assuming rock mechanic model scenario # 2 and medium proppant size (16–20)

Fig. 22 Fracture profile assuming rock mechanic model scenario # 2 and medium proppant size (16–20).

Fig. 23 Fracture profile assuming rock mechanic model scenario # 3 and medium proppant size (16–20)

Fig. 23 Fracture profile assuming rock mechanic model scenario # 3 and medium proppant size (16–20).

Appendix 3

Matrices and vectors involved in Eq. (3) are defined as follows:

In which Ω is the domain and Np, Nu are pressure and displacement shape functions, respectively, and can be defined as follows:

Discretizing the governing equations of poroelasticity by using the finite element method (FEM) (Zienkiewicz and Taylor 2000) results in the following coupled linear systems of equations:

where nx, ny are the x, y components of unit normal vector to the boundary.

References

Castagna JP, Batzle ML, Eastwood RL (1985) Relationships between compressional wave and shear-wave velocities in clastic silicate rocks. Geophysics 50:571–581

Charlez PA (1997) Rock mechanics—petroleum application, 2nd edn. Technip, Paris

Chen HY, Teufel LW, Lee RL (1995) Coupled fluid flow and geomechanics in reservoir study—I. Theory and governing equations. Proceeding of the SPE annual technical conference and exhibition, Dallas, Texas, pp 507–519

Detournay E, Cheng AHD (1988) Poroelastic response of a borehole in a nonhydrostatic stress field. Int J Rock Mech Min Sci Geomech Abstract 25(3):171–182

Gidley J et al (1989) Recent advances in hydraulic fracturing, SPE Monograph 12, Richardson, Texas, pp 62–63

Salz LB (1977) Relationship between fracture propagation pressure and pore pressure. Paper SPE 6870 presented at the SPE annual technical conference and exhibition, Denver, Oct. 7–12

Williams DM (1990) The acoustic log hydrocarbon indicator. 31st Annual Logging Symposium, Society of Professional Well Log Analysts

Zienkiewicz OC, Taylor RL (2000) The finite element method — basic formulation and linear problems 1. Butterworth-Heinemann, Oxford

About this article

Cite this article as:
Azim, R.A. & Abdelmoneim, S.S. J Petrol Explor Prod Technol (2013) 3: 21. https://doi.org/10.1007/s13202-012-0038-6

Abbreviations

LGR

Local grid refinement, it is a widely used expression for the process of dividing one or several grids in the reservoir model into smaller sized grids allowing enhanced grid definition, which is useful for modeling wells or hydraulic fractures and other complex reservoir structures

DOE

Department of Energy, governmental department whose mission is to advance energy technology and promote related innovation in the United States
Tailored pulse fracturing

Employed to control the extent and direction of the produced fractures by the ignition of precise quantities of solid rocket fuel-like proppants in the wellbore to create pressure ‘pulse’ which creates fractures in a more predictable pattern

Foam fracturing

Using foam under high pressure in gas reservoirs. It has the advantage over high-pressure water injection because it does not create as much damage to the formation, and well cleanup operations are less costly

e-mail: [email protected]
Copyright information

© The Author(s) 2012

Open Access

This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

Emanuel Martin
Emanuel Martin is a Petroleum Engineer graduate from the Faculty of Engineering and a musician educate in the Arts Faculty at National University of Cuyo. In an independent way he’s researching about shale gas & tight oil and building this website to spread the scientist knowledge of the shale industry.
http://www.allaboutshale.com

Leave a Reply

seven − six =

Top