Minimization of Downhole Tool Failures Using Nash Equilibrium and Downhole Data

Abstract

Abstract Complex and expensive downhole tools have been increasingly employed in modern drilling. Downhole tools may fail and result in a reduction in the rate of penetration (ROP), repair or replacement of the damaged tools, wasted trips, and rig downtime, which can substantially add to the drilling cost. The causes of downhole tool failures are compound, ranging from material, quality, and design to operating conditions. Accurate modeling and prediction of downhole tool failure may be useful for tool maintenance, preventive measures, and the determination of optimal operation windows to avoid downhole tool failures and mitigate damages. The risk of tool failure as well as the drilling cost may be evaluated simultaneously. To model these two objective functions, a two-player, non-zero-sum game theory model is proposed. In the game theory model, the first player takes actions, such as drilling operations, to maximize his/her payoff in terms of ROP, while the second player tries to reduce the probability of tool failure as much as possible. The payoff tables in terms of ROP and tool reliability have been constructed respectively. Based on the payoff tables, the Nash equilibrium (i.e., optimal strategies) has been determined.