TY - JOUR SP - 1095 SN - 21900558 AV - none PB - Springer Science and Business Media Deutschland GmbH EP - 1107 A1 - Nguyen, H.T. A1 - Lee, J.H. A1 - Elraies, K.A. N1 - cited By 6 JF - Journal of Petroleum Exploration and Production Technology KW - Fracture; Oil wells; Petroleum reservoir engineering; Petroleum reservoirs KW - Fracture model; Fracture network models; Height growth; Hydraulic fracture modeling; Hydraulic fracture propagation; Injection rates; Modeling approach; P3D model; Perkins; Three dimensional modelling KW - Hydraulic fracturing N2 - In the field of hydraulic fracture modeling, the pseudo-three-dimensional (P3D) approach is an efficient and practical computational tool serving as a compromise between two-dimensional and planar three-dimensional models. This review discusses the P3D modeling approach from its early developmental stage in the 1980s to the present. The evolution of P3D modeling is drawn over time based on the major differences in the governing formulation and assumptions considered by each model. The problems of equilibrium height growth and vertical viscous fluid resistance (i.e., non-equilibrium height growth) emphasize the primary differences among these models. Besides, the P3D-based complex fracture network models for shale oil and gas reservoirs accounting for the interaction between preexisting natural fractures and induced hydraulic fractures are discussed. Finally, in the application section, several simulations are reported to demonstrate the validation of the P3D numerical algorithm by comparing it with the Perkinsâ??Kernâ??Nordgren (PKN) large and small asymptotic solutions, as well as the effect of time-dependent variable injection rates on the hydraulic fracture propagation. The results showed a good matching between P3D and PKN solutions and a significant effect of the wellbore variable injection rate on the evolution of the fracture length. © 2021, The Author(s). ID - scholars16962 IS - 4 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85119593234&doi=10.1007%2fs13202-021-01373-1&partnerID=40&md5=919c57db0aaefc9816b61d2714205624 VL - 12 TI - Review of pseudo-three-dimensional modeling approaches in hydraulic fracturing Y1 - 2022/// ER -