PSI - Issue 66

Amani J. Majeed et al. / Procedia Structural Integrity 66 (2024) 212–220 Author name / Structural Integrity Procedia 00 (2025) 000–000

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Table1. Fracture Properties and Material Parameters (Nasiri, 2015) Items Magnitude Shear modulus (G) 8.702*e5 [psi] Drained Poisson's ratio (V) 0.2 [-] Fluid viscosity ( ) 1 [cp] In-situ stress ( σ min) 400 [psi] Pumping rate (Q) 75 [bbl/min] Wellbore radius (r w ) 0.3 [ft] Passed Time (t f ) 0.3 [min]

3. Result and Discussion The present work enhances Arash's work by incorporating an amendment to align it more closely with reality. The PKN model suggests that with increasing fracture length, there is a proportional increase in the anticipated wellbore pressure. In contrast, the KGD model predicts that the wellbore pressure will converge towards the in-situ stress σ _min as the length increases, see Fig. 1. In Fig. 2, the fraction factors' behavior over time is depicted, showcasing an increase over time. The current modifications aim to portray a more realistic scenario, where the fracture grows naturally rather than in a linear fashion as seen in Arash's work (Nasiri, 2015). The progress of fracture length and width over time is illustrated in Fig. 2 (a, and c), with a detailed depiction in Fig. 2 (b, d, and f) to clarify the zigzag pattern more distinctly. The fracture's shape concerning KGD is represented as an ellipse in Fig. 2 (c), although in reality, fractures do not occur precisely in this manner. The current work presents a portrayal closer to reality by considering the potential tortuosity during growth. Moreover, Fig. 3 depicts a 3D surface for the developed model, where it can see the tortuosity path clearly in Fig. 3 (b).

Fig. 1. Pressure changes vs time curves predicted by two models, where; (a) KGD model, and (b) PKN model