Abstract：
During hydraulic fracturing, the injected self-degradable diverters can bridge and form a tight plug within the hydraulic
fractures. The net fracture pressure can be enlarged to a great level and the natural fractures can be activated, thus the stimulated volume
is greatly enlarged. The investigation of the in-fracture temporary plugging and diverting fracturing (ITPDF) process is beneficial for
uncovering the mechanisms and the patterns of ITPDF. This paper systematically introduces the physical processes and the controlling
equations of the hydraulic fracturing problems during ITPDF. A 2D fluid-solid fully-coupled finite element model is developed to simulate
the overall fracture propagation when a hydraulic fracture intersects a natural fracture. In the model, cohesive elements are applied to
pre-define the fracture propagation paths and a cohesive zone model is applied to control the fracture initiation and propagation criteria.
In this way, the calculation of the stress singularity at the fracture tips can be avoided. Moreover, this paper assumes the diffusive term
from Darcy’s equation equals the conductivity term in Reynold’s equation, and the equivalent viscosity is modified to model the effects
of the tight plug on fluid flow. In this way, it is not necessary to change the governing equation of the fracturing fluid flow within the
hydraulic fracture. The simulation results of the developed model are consistent with the reported simulation results at various conditions,
which verifies the reliability of the developed model. Further, this paper simulates the dynamic process of ITPDF based on the established
model. The simulation results show the fluid pressure declines sharply within the tight plug, and the net fracture pressure and the fracture
width are enlarged dramatically, thus the NF(Natural Fracture) is activated. The whole process of ITPDF includes five stages: (1) the
hydraulic fracture initiates at the fluid injection point and then propagates and arrives at the intersection point of the hydraulic fracture
and the natural fracture; (2) the hydraulic fracture propagates from the intersection point to the position of the tight plug; (3) the hydraulic
fracture stops propagating and the upper branch of the natural fracture opens until arriving at the tip; (4) the upper branch of the natural
fracture stops propagating and the lower branch of the natural fracture opens until arriving at the tip; (5) both the hydraulic fracture and
the natural fracture swell continually. This work provides a robust model and method basis for the further investigation of the ITPDF.
