**Abstract**

[7] Moos, D, Vassilellis, G, & Cade, R. Predicting shale reservoir response to stimulation in the Upper Devonian of West Virginia. In: proceedings of SPE Annual Technical Conference and Exhibition, SPE-145849, 30 October-2 November (2011). Denver, Col‐

[8] Vassilellis, G. D, Li, C, Moos, D, et al. Shale engineering application: the MAL-145 Project in West Virginia. In: proceedings of Canadian Unconventional Resources Conference, CSUG/SPE-November (2011). Calgary, Alberta, Canada., 146912, 15-17.

[9] Barton, C, Zoback, M. D, & Moos, D. Fluid Flow Along Potentially Active Faults in

[10] Moos, D, & Barton, C. A. Modeling uncertainty in the permeability of stress-sensitive fractures. In: proceedings of 42nd US Rock Mechanics Symposium and 2nd U.S.-Can‐ ada Rock Mechanics Symposium, ARMA June- 2 July (2008). San Francisco, USA.,

[11] Hossain, M. M, Rahman, M. K, & Rahman, S. S. A Shear Dilation Stimulation Model for Production Enhancement From Naturally Fractured Reservoirs, SPE 78355, SPE

[12] Moos, D, & Zoback, M. D. Utilization of Observations of Well Bore Failure to Con‐ strain the Orientation and Magnitude of Crustal Stresses: Application to Continental, Deep Sea Drilling Project and Ocean Drilling Program Boreholes, Journal of Geo‐

[13] Heidbach, O, Tingay, M, Barth, A, Reinecker, J, Kurfe, D, & Müller, B. The World Stress Map database release (2008). doi:10.1594/GFZ.WSM.Rel2008.http://

Crystalline Rock, Geology(1988). , 23(8), 683-686.

orado, USA.

1038 Effective and Sustainable Hydraulic Fracturing

08-312.

Journal; June , 2002-183.

physical Research (1990). , 95, 9-305.

www.world-stress-map.org

Hydraulic fracturing of naturally fractured reservoirs is a critical issue for petroleum indus‐ try, as fractures can have complex growth patterns when propagating in systems of natural fractures. Hydraulic and natural fracture interaction may lead to significant diversion of hy‐ draulic fracture paths due to intersection with natural fractures which causes difficulties in proppant transport and eventually job failure. In this study, a comparison has been made between numerical modeling and artificial intelligence to investigate hydraulic and natural frcature interaction. First of all an eXtended Finite Element Method (XFEM) model has been developed to account for hydraulic fracture propagation and interaction with natural frac‐ ture in naturally fractured reservoirs including fractures intersection criteria into the model. It is assumed that fractures are propagating in an elastic medium under plane strain and quasi-static conditions. Comparison of the numerical and experimental studies results has shown good agreement. Secondly, a feed-forward with back-propagation artificial neural network approach has been developed to predict hydraulic fracture path (crossing/turning into natural fracture) due to interaction with natural fracture based on experimental studies. Effective parameters in hydraulic and natural fracture interaction such as in situ horizontal differential stress, angle of approach, interfacial coefficient of friction, young's modulus of the rock and flow rate of fracturing fluid are the inputs and hydraulic fracturing path(cross‐ ing/turning into natural fracture) is the output of the developed artificial neural network. The results have shown high potentiality of the developed artificial neural network ap‐ proach to predict hydraulic fracturing path due to interaction with natural fracture. Finally, both of the approaches have been examined by a set of experimental study data and the re‐ sults have been compared. It is clearly observed that both of them yield promising results

properly cited.

© 2013 Keshavarzi and Jahanbakhshi; 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, distribution, and reproduction in any medium, provided the original work is © 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, and reproduction in any medium, provided the original work is properly cited.

while numerical modeling yields more detailed results which can be used for further inves‐ tigations but it is computationally more expensive and time-consuming than artificial neural network approach. On the other hand, since artificial neural network approach is mainly da‐ ta-driven if just the input data is available (even while fracturing) the hydraulic fracture path (crossing/turning into natural fracture) can be predicted real-time and at the same time that fracturing is happening.

Will the advancing hydraulic fracture cross the natural fracture or will it turn into it?

**2. Interaction between hydraulic and natural fractures**

hydraulic and natural fracture interaction.

growing hydraulic fractures [2].

**Figure 1.** A weakly bonded fracture cement in a shale sample [26].

For the purpose of this study, a 2D eXtended finite element method (XFEM) has been compared with a feed-forward with back-propagation artificial neural network approach to account for

Investigation of Hydraulic and Natural Fracture Interaction: Numerical Modeling or Artificial Intelligence?

http://dx.doi.org/10.5772/56382

1041

The interaction between pre-existing natural fractures and the advancing hydraulic fracture is a key issue leading to complex fracture patterns. Large populations of natural fractures are sealed by precipitated cements (Figure 1) which are weakly bonded with mineralization that even if there is no porosity in the sealed fractures, they may still serve as weak paths for the

In this way, experimental studies [4, 5, 6] suggested several possibilities that may occur during hydraulic and natural fractures interaction. Blanton [4] conducted some experiments on naturally fractured Devonian shale as well as blocks of hydrostone in which the angle of approach and horizontal differential stress were varied to analyze hydraulic and natural fracture interaction in various angles of approach and horizontal differential stresses. He concluded that any change in angle of approach and horizontal differential stress can affect hydraulic fracture propagation behavior when it encounters a natural fracture which will be referred to as opening, arresting and crossing. Warpinski and Teufel [5] investigated the effect of geologic discontinuities on hydraulic fracture propagation by conducting mineback

#### **1. Introduction**

Hydraulic fracture growth through naturally fractured reservoirs presents theoretical, design, and application challenges since hydraulic and natural fracture interaction can significantly affect hydraulic fracturing propagation. Although hydraulic fracturing has been used for decades for the stimulation of oil and gas reservoirs, a thorough understanding of the inter‐ action between induced hydraulic fractures and natural fractures is still lacking. This is a key challenge especially in unconventional reservoirs, because without natural fractures, it is not possible to recover hydrocarbons from these reservoirs. Meanwhile, natural fracture systems are important and should be considered for optimal stimulation. For naturally fractured formations under reservoir conditions, natural fractures are narrow apertures which are around 10-5 to 10-3 m wide and have high length/width ratios (>1000:1) [1].Typically natural fractures are partially or completely sealed but this does not mean that they can be ignored while designing well completion processes since they act as planes of weakness reactivated during hydraulic fracturing treatments that improves the efficiency of stimulation [2]. The problem of hydraulic and natural fracture interaction has been widely investigated both experimentally [3, 4, 5, 6, 7, 8] and numerically [9, 10, 11, 12, 13, 14, 15, 16, 17, 18]. Many field experiments also demonstrated that a propagating hydraulic fracture encountering natural fractures may lead to arrest of fracture propagation, fluid flow into natural fracture, creation of multiple fractures and fracture offsets [19, 20, 21, 22] which will result in a reduced fracture width. This reduction in hydraulic fracture width may cause proppant bridging and conse‐ quent premature blocking of proppant transport (so-called screenout) [23, 24] and finally treatment failure. Although various authors have provided fracture interaction criteria [4, 5, 25] determining the induced fracture growth path due to interaction with pre-existing fracture and getting a viewpoint about variable or variables which have a decisive impact on hydraulic fracturing propagation in naturally fractured reservoirs is still unclear and highly controver‐ sial. However, experimental studies have suggested that horizontal differential stress, angle of approach and treatment pressure are the parameters affecting hydraulic and natural fracture interaction [4, 5, 6] but a comprehensive analysis of how different parameters influence the fracture behavior has not been fully investigated to date. In this way, in order to assess the outcome of hydraulic fracture stimulation in naturally fractured reservoirs the following questions should be answered:

What is the direction of hydraulic fracture propagation?

How will the propagating hydraulic fracture interact with the natural fracture?

Will the advancing hydraulic fracture cross the natural fracture or will it turn into it?

For the purpose of this study, a 2D eXtended finite element method (XFEM) has been compared with a feed-forward with back-propagation artificial neural network approach to account for hydraulic and natural fracture interaction.
