A new mathematical model for estimating perforation penetration length

Penetration depth has been studied by a number of scholars both in ballistic science and also in the oilfield. A number of models have been developed for estimating oil well perforation depths and also assessing perforation gun performance under sub-surface conditions. Earlier derived models have been found to be narrow in scope and did not accommodate a wide range of factors that affect perforation gun performance. The intent of this study is to develop a new mathematical model that can extend the scope of previous models and provide room for factors like target strength, explosive load, gun-to-casing clearance, effective impact area of jet/bullet, and velocity of perforator already known to affect perforation gun performance. The approach to the development of the new model was based on the energy conservation theorem. The translational kinetic energy of the jet/bullet was equated to the summation of the gun penetrative work and accompanying heat energy loss. The kinetic energy was represented by a simple relation of half the product of mass and square of velocity of the jet/bullet. The expression for the penetrative work done was based on the one-dimensional Bernoulli's hydrodynamic theorem, while the heat loss was derived using Fourier's law of heat conduction across a cylindrical composite media at steady state. Heat convention through completion fluid was assumed negligible. The new model finds its applications in perforation operation design as well as in appropriate gun selection.