**Author details**

N. Nagel, F. Zhang, M. Sanchez-Nagel and B. Lee

\*Address all correspondence to: nnagel@itascahouston.com

Itasca Houston, Inc., USA

### **References**


[4] King, G. E. (2010). Thirty Years of Gas Shale Fracturing: What Have We Learned?", Paper SPE 133456 presented at the SPE Annual Technical Conference and Exhibition, Florence, Italy, September., 19-22.

optimization (wherein the goal is to maximize natural fracture shear, i.e., maximize 'complexity') requires the evaluation and consideration of natural fracture orientation.

**•** As natural fracture friction controls the depth and amount of natural fracture shear, multiwell completion optimization requires the evaluation and consideration of natural fracture

**•** The optimum hydraulic fracture separation distance for multi-well completions (i.e, the separation of hydraulic fractures along their respective wellbores) must be determined in consideration of natural fracture properties (e.g., orientation and friction properties) and

**•** For multi-well completion schemes, the design length of the second hydraulic fracture (Xf2) should be kept less than the point of overlap with the first hydraulic fracture (Xf1) and be

**•** Overall, the simulation results presented suggest that there is the potential for only modest improvements in stimulation complexity from the modified zipper-frac completion scheme while the potential for well-to-well communication (and possible screenout conditions)

[1] Agarwal, K, Mayerhofer, M. J, & Warpinski, N. R. (2012). Impact of Geomechanics on Microseismicity", Paper SPE 152835 presented at the SPE/EAGE European Uncon‐ ventional Resources Conference and Exhibition, Vienna, Austria, March., 20-22.

[2] Clover Global SolutionsLP, (2012). The Seven Major U.S. Shale Plays", http://c1wsolu‐

[3] Ground Water Protection Council and ALL Consulting(2009). Modern Shale Gas De‐ velopment in the United States: A Primer", prepared for the US DOE, Office of Fossil

tions.wordpress.com/2012/09/13/the-seven-major-u-s-shale-plays

optimized in conjunction with the hydraulic fracture separation distance.

friction properties.

544 Effective and Sustainable Hydraulic Fracturing

the in-situ stress ratio.

increases.

**Author details**

Itasca Houston, Inc., USA

**References**

N. Nagel, F. Zhang, M. Sanchez-Nagel and B. Lee

Energy, DE-FGNT15444., 26-04.

\*Address all correspondence to: nnagel@itascahouston.com


[14] U.S. Energy Information Administration, 2012, "Annual Energy Outlook 2012 Early Release Overview", U.S. Dept. of Energy, Washington D.C., USA, www.eia.gov

**Section 8**

**Flow Paths and Flow Networks**

[15] U.S. Energy Information Administration, 2013, "Annual Energy Outlook 2013 Early Release Overview", U.S. Dept. of Energy, Washington D.C., USA, www.eia.gov

**Flow Paths and Flow Networks**

[14] U.S. Energy Information Administration, 2012, "Annual Energy Outlook 2012 Early Release Overview", U.S. Dept. of Energy, Washington D.C., USA, www.eia.gov [15] U.S. Energy Information Administration, 2013, "Annual Energy Outlook 2013 Early Release Overview", U.S. Dept. of Energy, Washington D.C., USA, www.eia.gov

546 Effective and Sustainable Hydraulic Fracturing

**Chapter 26**

**Modeling of Proppant Permeability and**

Bruce R. Meyer, Lucas W. Bazan and Doug Walls

proppant bed conductivity under realistic flowing conditions.

understanding of fluid flow and transport phenomena in porous media.

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/56299

**Abstract**

2

**Inertial Factor for Fluid Flow Through Packed Columns**

Standard industry testing procedures provide proppant quality control and methods to determine long term reference conductivity for proppants under laboratory conditions. However, test methods often lack repeatable results. Additionally, the testing procedures are not designed to account for fundamental parameters (e.g., proppant diameter, porosity, wall effects, multi-phase/non-Darcy effects, proppant and gel damage) that greatly reduce absolute

A constitutive model for permeability and inertial factor for flow through packed columns has been formulated from fundamental principles. This work provides a detailed deterministic proppant permeability correlation and defines a methodology to help explain why different proppant types behave differently under stress. The theory also characterizes the origin of inertial, or non-Darcy flow, based on a unique approach formulated from the extended Bernoulli equation based on minor losses. The physical model provides insight into the dominant parameters affecting the pressure drop in a proppant pack and improves our

The fundamental solution for flow through packed columns can be characterized by the sum of viscous (Blake-Kozeny) and inertial forces (Burke-Plummer) in Ergun's equation. Coupling Ergun's equation with the Forchheimer equation results in a deterministic set of equations that describe the fracture permeability and inertial factor as functions of the proppant diameter, pack porosity, sphericity, and fracture width. Plotting the dimensionless permeability, (k/dp

), versus the characteristic proppant porosity parameter, Ω, is a very useful diagnostic tool that can indicate: 1) sphericity, 2) channeling, 3) crushing, 4) non-uniform sphere size distri‐ bution, 5) embedment and 6) deviation of the friction multiplier *λ<sup>m</sup>* from Ergun's equation.

and reproduction in any medium, provided the original work is properly cited.

© 2013 Meyer et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

© 2013 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

distribution, and reproduction in any medium, provided the original work is properly cited.
