Analytical and numerical analysis on rock penetration in pulsed power drilling technology

Pulsed power for rock fragmentation, liberation of mineral inclusions, comminution, and drilling is a well-established technology that has seen success applied across multiple industrial contexts. This includes mining and processing, downhole drilling for oil and gas exploration, and deep geothermal drilling. Penetration of plasma channels into rock material is a key mechanism for pulsed power drilling technology. It has previously been assumed that the downward development of plasma channels is limited by the rapid decay of the electric field away from the drilling electrode gap. However, quantitative theoretical analysis remains scarce and could be further improved, advancing analytical understanding.

The main objective was to revisit analytical models of pulsed power rock fragmentation and compare the predicted tendencies to advanced numerical simulations, focusing specifically on per-pulse penetration depth of plasma channels. Expressions established for theoretical penetration depths are assessed by comparison to statistical distributions extracted from Monte-Carlo simulations of plasma channel trajectories based on a stochastic biased random walk breakdown model.

An analytical approach based on conformal mapping techniques allows the electric field around a pair of drilling electrodes to be approximated. Expressions for the normalised penetration depth as a function of the electrode separation provides similar tendencies to those attained from simulation.