Complex and expensive downhole tools have been employed increasingly in modern drilling. Downhole tool failures include motor failures, bit failures, and MWD failures. Any of these failures may result in reduction of rate of penetration (ROP), repair or replacement of the damaged tools, wasted trips, and rig downtime, and thus add substantially to the drilling cost. The causes of downhole tool failures are compound, embracing material, quality, design, and operating conditions. It is possible to monitor operating conditions and adjust operating parameters to avoid downhole tool failures and mitigate damages to downhole tools. In this thesis, game theory is considered for the prediction of downhole tool failures.
Game theory is a branch of mathematics for decision making in the conflict of interests. A game theory model has four important components: players, information, actions, and payoff. An appropriate approach, i.e., a two-player non-zero-sum game, has been established for downhole tool failure. Namely, one player holds interest of the drilling time free of tool failures while the other cares the probability of tool failure. The information includes all pertinent data to calculate the drilling time and the probability of tool failure. The first player may take actions such as drilling operations to maximize his payoff, e.g., minimal drilling time, while the second player tries to reduce the probability of tool failures as much as possible.
We utilized Game Theory Explorer to solve the two-player non-zero-sum game. Based on the game theory model, two payoff tables in terms of ROP and tool reliability, respectively, have been constructed and the optimal strategies have been found.