**2. UFM model specifics**

**Figure 1.** Evolution of natural fracture opening [10]

290 Effective and Sustainable Hydraulic Fracturing

The HF models [28-32] do not account for permeability of natural fractures explicitly. The 2D model in [33] uses approach from [13] to simulate interaction between induced propagating fracture and natural fracture. A modified leak-off model for an intersecting fracture based on poro-elasticity was introduced to account for the increased leakoff at the intersections. A poroelastic solution for the stresses in the HF/NF interaction zone has been used as a basis for hydraulic/natural fracture interaction criteria. A fully coupled finite element based approach was used to simulate HF propagation in a poroelastic formation with existing natural fractures.

A complex fracture network model, referred to as Unconventional Fracture Model (UFM), had recently been developed [1, 39, 40]. The model simulates the fracture propagation, rock deformation, and fluid flow in the complex fracture network created during a treatment. The model solves the fully coupled problem of fluid flow in the fracture network and the elastic deformation of the fractures, which has similar assumptions and governing equations as conventional pseudo-3D fracture models. Transport equations are solved for each component of the fluids and proppants pumped. A key difference between UFM and the conventional planar fracture model is being able to simulate the interaction of hydraulic fractures with preexisting natural fractures, i.e., determine whether a hydraulic fracture propagates through or is arrested by a natural fracture when they intersect and subsequently propagates along the natural fracture.

To properly simulate the propagation of multiple or complex fractures, the fracture model takes into account the interaction among adjacent hydraulic fracture branches, often referred to as "stress shadow" effect. It is well known that when a single planar hydraulic fracture is opened under a finite fluid net pressure, it exerts a stress field on the surrounding rock that is proportional to the net pressure. The details of stress shadow effect implemented in UFM are given in [40].

The branching of hydraulic fracture when intersecting natural fracture gives rise to the development of a complex fracture network. A crossing model that is extended from the Renshaw-Pollard [12] interface crossing criterion, applicable to any intersection angle, has been developed, validated against the experimental data [16, 17], and was integrated at first in the UFM. The crossing model, showing good comparison with existing experimental data, did not account for the effect of fluid viscosity and flow rate on the crossing pattern. More recently a new advanced OpenT crossing model, taking into the account the impact of fluid and NF properties, have been developed [2] and integrated in UFM [18].

Hydraulic fractures propagating in the rock are modeled in accordance with existing approach in UFM model. The Schematic of the complex HF interaction with permeable NF is shown in

Hydraulic fracture

Fracturing fluid invasion into the two wings of the NF needs to be considered separately. Four

**1.** Opened part filled with invaded fracturing fluid (fluid pressure exceeds the normal

**2.** Invaded closed part of NF (filtration zone) filled with fracturing fluid (fluid pressure

**3.** Closed pressurized part filled with pressurized original reservoir fluid (fluid pressure

**4.** Closed undisturbed part of NF filled with reservoir fluid under original pore pressure

When a natural fracture is intercepted by the hydraulic fracture, the fluid pressure in the hydraulic fracture transmits into the natural fracture. If the fluid pressure is less than the normal effective stress on the natural fracture, the natural fracture remains closed. Even closed natural fractures may have hydraulic conductivities much larger than the surrounding rock matrix, and in this case fracturing fluid will invade the natural fractures more than leakoff into the surrounding matrix. If the portion of injected fluid is lost into closed natural fractures from

possible regions can co-exist in each wing of the NF encountered by HF (Figure 4):

above pore pressure but below the closure stress) with length *L filtration* >0

Pressurized Reservoir Fluid in NF

Hydraulic Fracturing in Formations with Permeable Natural Fractures

Original (not disturbed) Reservoir Fluid in NF

http://dx.doi.org/10.5772/56446

293

Opened part of NF

Figure 2 and Figure 4.

Natural Fracture filled with

reservoir fluid Closed invaded part of NF

**Figure 2.** Hydraulic fracture intercepting natural fracture and possible situation to model

effective stress on NF), with length of opened part *L opened* >0

above the pore pressure) with length *L pressurized* >0

the main HF, the HF growth could be affected.

Hydraulic fracture

conditions.

The modelling approach used in UFM to predict the leakoff into the NFs is presented below.
