**6.2 Estimation of stress rotation**

The knowledge of differential stress is important to predict the ability of creating fracture complexity and increased surface contact. Areas with higher differential stress will produce highly anisotropic hydraulic fractures with reduced surface contact. This problem will be further complicated if the maximum horizontal stress

### *Exploitation of Unconventional Oil and Gas Resources - Hydraulic Fracturing...*

#### **Figure 8.**

*Engineered completion using the differential stress as a reference log to adjust stage length and number of clusters.* 

SHmax direction is not locally perpendicular to the wellbore, leading to undesirable parallel hydraulic fractures. Hence the need to estimate both the differential stress and the local direction of the maximum stress around the wellbore.

A good example that can illustrate this critical issue is the Grisham fault in the Permian basin, USA where stress rotates by up to 90°. **Figure 9** shows the public domain faults [19–20] used as input in the geomechanical simulation [11] to estimate the stress orientation.

 When the Woodford faults are subjected to a dominant E-W tectonic stress, rotations in the maximum horizontal stress direction arise as shown in **Figure 9**. It is important to note that faults which are oriented parallel or perpendicular to in-situ maximum stress direction, such as the N-S trending fault, cause little perturbation and critically stressed faults (roughly 30–60° from local maximum stress direction) cause large perturbations. While much of the basin is still subject to a SHmax within 10° of the input orientation, several areas evidence large deflections from this input orientation. These deflections can be further refined if using seismic data to define the local faults. Given the variability of the differential stress and the direction of the maximum stress direction, both captured with the plane strain modeling the next step is to evaluate the actual strain resulting from the hydraulic fracturing.

#### **6.3 Estimation of strain for laterally constrained 3D planar hydraulic fractures**

The 2D plane strain MPM modeling provides valuable stimulated reservoir volume (SRV) information by modeling the effect of a large increase in the stress around the wellbore and its distribution throughout the reservoir volume and interaction with fractures and faults as well as accounting for any variable geomechanical properties and pore pressure of the rock. This is achieved numerically by applying a large pressure on a hydraulic fracture plane with a given length varying between 100 and 200 ft. which is used to model the effects of the pumping pressure in the reservoir. The real surface contact available to the fluid to apply its pressure and create a stress front is much larger than the numerical hydraulic fracture assumed to be around 150 ft. Thus, the pressure applied to this limited surface must be higher than

*Surface Drilling Data for Constrained Hydraulic Fracturing and Fast Reservoir Simulation… DOI: http://dx.doi.org/10.5772/intechopen.84759* 

#### **Figure 9.**

*Stress orientation around the Grisham fault showing distinct behaviors of the stress field orientation north and south of the fault, and also along strike of the fault.* 

the pumping pressure and is approximately, in most realistic unconventional wells, about 2.5 times the minimum stress value. Since this stress can be modeled with a dynamic simulation, the pressure applied to the hydraulic fractures can be applied sequentially, in parallel, or in a zipper mode. This ability to simulate the sequence of hydraulic fracturing allows the proper representation of stress shadow effects between stages as well as those seen between wells. These stress shadowing effects are considered along with the complex geology present between the stages and wells. For each hydraulic fracturing sequence, the resulting strain will be able to provide useful indication on the resulting SRV as shown in **Figure 10**.

One simple way to account for the lateral stress gradients captured by the geomechanical simulation, is to estimate the geomechanical half lengths (**Figure 5C**) from an interpreted envelope of the strain (**Figure 10B**) that could represent a proxy for the SRV. These interpreted asymmetric geomechanical half lengths are used at each cluster or stage as a constraint in a 3D planar hydraulic fracture design. It is important to reemphasize that the use of the planar representation of the hydraulic fractures is not an indication that the hydraulic fractures are indeed planar but a simple mathematical discretization of an SRV estimated by the full geomechanical simulation.

 Having a constraint in the lateral direction is very helpful for a better estimation of the fracture height when using a 3D planar hydraulic fracturing approach. In this model, the vertical fracture growth occurs in the simplified world of perfect interfaces where debonding does not occur in a layered anisotropic rock. Unfortunately, the fracture growth does not depend only on the lateral stress but also on the geologic nature of the laminations and the characteristics of their interfaces which could be weak and could shear and consume hydraulic fracturing energy thus reducing the hydraulic fracture height. Since we have successfully estimated and validated with microseismic data the lateral stress gradients estimated with 2D plane strain MPM model, this information can be used as an input in a 2D vertical problem where we will focus on the geologic factors affecting the vertical fracture growth.

#### **Figure 10.**

*(A) Equivalent fracture model (EFM) derived by CFM using only surface drilling derived fracture indicators logs. The EFM is used as input in the reservoir geomechanics that provides the initial perturbed stress field and the subsequent (B) asymmetric strain resulting from the hydraulic fracturing of the wells and (C) comparison to microseismic events (note: the heel section of the wells was not monitored due to operations). (D) and (E) The envelope of strain provides the gross geomechanical half lengths which provide the lateral stress gradients needed to constrain the 3D planar hydraulic fracturing simulator.* 
