Mathematical model for estimating perforation penetration depth

This article presents a simplified mathematical model based on the energy-work method to estimate the penetration depth in well perforation. The model uses casing and formation properties in the estimation. It uses the initial speed of the bullet and the failure strengths of the materials resisting penetration as model input. An automated computer program was developed to compute the penetration depth in terms of various field parameters. It was found that bullet penetration increases with increasing jetting velocity and decreasing effective bullet surface area, and that the use of explosive-type HMX1 yields higher penetration depth for the same bore size. The results also showed that the productivity ratio becomes much higher for larger borehole diameters and higher explosive speeds. Overall, the study showed that the model can be used to design for optimum penetration depths leading to an optimum productivity ratio.