A continuous fracture front tracking algorithm with multi layer tip elements (MuLTipEl) for a plane strain hydraulic fracture

Hydraulic fracturing is critical in breaking underground rock to free oil and gas reserves. It involves injecting sand, water and appropriate chemicals into wells to create new fractures on the existing rocks or increase the connectivity or sizes of existing fractures to avail more space for oil and gas extraction. Hydraulic fracturing is widely used in low-permeability rocks like shales and tight sandstone despite being a well-defined stimulation technique. Techniques similar to hydraulic fracturing can enhance permeability in underground geothermal reservoirs and increase the efficiency of heat extraction in low-permeability rock formations.

For low-permeability shale formations, hydraulic fracture involves drilling multiple wells adjacent to each other. These wells are then fractured in phases following a well-defined protocol. Additionally, the highly laminated rock formations and the ability to distinguish layer formations on any length scale have raised fundamental questions on how the associated properties can be upscaled and to what resolution. To this end, running a numerical simulator on high-resolution data in a hydraulic fracturing model has attracted research attention. A big obstacle in developing such a model is the associated complexity.

While using a coarse mesh has emerged as a promising approach for incorporating high-resolution data into the algorithm, its effectiveness can be enhanced by developing an efficient approach for tracking the fracture front. Most of the existing numerical simulators for hydraulic fracture modeling fail to account for the effects of thin layers smaller than the size of the elements mainly because they assume opening of one element at a time. Other methods, like homogenization, moving mesh approaches, and using Implicit Level Set Algorithm (ILSA), have also been developed, but their feasibility is limited by numerous drawbacks.

To overcome these challenges, Dr. Egor Dontsov, the chief scientists at ResFrac corporation developed a numerical Multi-Layer tip Element (MulTipEl) algorithm to continuously track fracture front considering the problem of plane strain hydraulic fracture propagating in a layered formation. The algorithm was based on fixed mesh, assuming that in-situ stress, fracture toughness and leak-off coefficient vary by layer while the elastic properties remained constant throughout the domain. The work is currently published in the Journal of Petroleum Science and Engineering.

The author showed that the problem associated with the propagation of plane strain hydraulic fracture in a layered formation was effectively addressed with low mesh dependence using elements even those larger than the layer size. In order to achieve this outcome, an additional fictitious stress was introduced to the tip element. When the additional stress was sufficiently large, it prevented the partially filled tip elements containing the fracture front from being fully open such that the tip element volume was equal to the tip asymptotic solution volume. As a result, it was possible to mimic the true local behavior of the fracture front within the element. Moreover, when the fictitious stress decreased to zero, the solution transitioned to one with an increase in length.

A theoretical basis for the proposed concept was established and validated. The effects of the layers were incorporated by varying the layer properties as a function of the front location. Several examples (including some with thick and thin layers as well as randomly generated layers) were presented. The algorithm’s ability to tackle multiple thin layers, even in situations when the layer size was much smaller than the element size, with remarkable accuracy was demonstrated. Additionally, the number of layers had no significant influence on the algorithm’s computational efficiency.

In summary, Dr. Egor Dontsov provided a simple alternative method for fracture front tracking based on local boundary conditions and a fixed mesh approach. Unlike most existing approaches, this approach is able to include the effect of layers that are smaller than the element size. Overall, the presented approach provides a better opportunity for evolving apparent fracture length and tracking fracture front by altering the magnitude of the additional fictitious stress.

In a statement to Advances in Engineering, Dr. Dontsov noted that it lays the foundation for developing advanced hydraulic fracturing models. In particular, the approach is incorporated into a fully coupled hydraulic fracturing and reservoir simulator ResFrac, which helps optimize hydraulic fracturing operations for E&P companies on a daily basis