Dynamic Pressure Optimization in Drilling Operations

In the drilling of oil wells, the need to accurately manage downhole formation pressure has long been established as critical for safety and economics. This thesis presents the research work conducted to improve the reliability of the pressure interpretations from drilling performance data to support optimal operational decision making. The evolution of differential pressure in the drilling wellbore is investigated using the modified ?-exponent (d_mod) as an applicable source of diagnostic data for the downhole drilling system. Design experiments were conducted to study the response of the d_mod variable to changes in factor effects and systemic error. The results and analysis from the experiments established the interactions of the two main exogenous factors (differential pressure and lithology) that contribute to the variations in rate of penetration (ROP) and the unique effects of these often coalescing factors are extracted. Subsequently, the differential pressure (∆P) system is modelled as a hidden 3 state continuous time Markov process with the signal process of its evolution identified in the changes in the observable ROP encoded in drilling performance data. The state and observation parameters of the hidden Markov model (HMM) are estimated using the Expectation Maximization (EM) algorithm and we show, for a univariate system with a depth dependent time relationship, that the model parameter updates of the EM algorithm equation have explicit solutions. A Bayesian inference model, to determine the safety threshold of the system and early failure prediction at each sampling epoch, is thereafter proposed and illustrated with a hindcast case example. Finally, we introduce a new problem, the Down Hole Drilling Pressures (DHDP) optimization problem for the drilling process, framed as an accelerating performance system subject to random failure in time. The parameters of the problem are formulated within a semi Markov decision process (SMDP) framework and a modified policy iteration approach is used to provide a first solution to the DHDP optimization problem. The optimization algorithm maximizes the sojourn time in the optimal differential pressure (∆P) state, and we show that the system yields the lowest long run average cost for drilling the wells. The decision model developed can be used to optimize the management of down hole drilling pressures in the wellbore especially in offshore and deepwater wells. The potential to predict the differential pressure state transitions ahead of the bit represents a capability not currently available in the industry and these solutions offer significant opportunity for value creation. They ultimately also open up potential for new frontiers of capabilities in the industry that can deliver substantial savings in oilwell construction costs and other associated systems or applications with similar performance conditions.

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