TY  - JOUR
KW  - Fracture; Hydraulic fracturing; Numerical models; Velocity control
KW  -  Chronological order; Dependent variables; Modeling and computation; Modeling technique; Particle velocities; Robust algorithm; The standard model; Three-dimensional model
KW  -  Three dimensional computer graphics
KW  -  computer simulation; flow field; future prospect; hydraulic fracturing; model test; nonlinearity; numerical model; petroleum engineering; three-dimensional modeling
ID  - scholars12451
TI  - A review of PKN-type modeling of hydraulic fractures
N2  - Many numerical modeling techniques have been employed to understand the phenomena occurring during hydraulic fracturing. Despite the various complex models developed, such as the planar three-dimensional and pseudo three-dimensional models, the one-dimensional Perkinsâ??Kernâ??Nordgren (PKN) model is still of great interest because it serves as a starting point for the development of more efficient and robust algorithms. This work reviews all PKN-type models from the first published model in 1961 to recent advancements in the model design. The underlying assumptions of the fundamental physical processes of the PKN model are first analyzed. Developments of and notable contributions to PKN models are then summarized into four main groups and discussed in a relatively chronological order. The differences between the standard modeling approach that employs the fluid flux as a dependent variable and the other that utilizes the particle velocity are highlighted. The trend of accounting for the poroelastic effect in the leak-off process and the effect of turbulence in the flow regime is also discussed. A number of challenges in modeling and computations caused by the strong nonlinear and degenerate governing system and how they have been tackled are then discussed in detail. Finally, some open suggestions for future work are mentioned. © 2020 Elsevier B.V.
N1  - cited By 15
AV  - none
VL  - 195
UR  - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85088117447&doi=10.1016%2fj.petrol.2020.107607&partnerID=40&md5=e9d6d80f9a61a3bce4f0f18368eeac22
JF  - Journal of Petroleum Science and Engineering
A1  - Nguyen, H.T.
A1  - Lee, J.H.
A1  - Elraies, K.A.
SN  - 09204105
PB  - Elsevier B.V.
Y1  - 2020///
ER  -