Optimal Control Model, Algorithm And Its Application For Well Trajectory In Non-Straight Wells

Well trajectory for non-straight wells, which includes directional wells, horizontal wells, siedtracking and /or horizontal wells, long-reach wells and multibranches, is one of key techniques in non-straight drilling.The main results, obtained in this dissertation, may be summarized as follows.1. Engineering background and some terms used in this dissertation are firstly introduced in Chapter One. Researches involved in this study are derived from reviewing and summarizing the history of well trajectory for non-straight wells.2. Chapter Two presents an optimized model named CORA with multi-constraints based on analyzing and reviewing some conventional methods been used in petroleum industry nowadays. And three specific model such as CORA-2D, CORA-3A and CORA-3S induced respectively. Some constraints such as kick-off-point, build-up rate of bottom-hole assembly(BHA), toolface orientation, inclination and azimuth etc. are involved in this novel model quantitatively for the first time. Its high design efficiency and accuracy are validated after used in more 22 non-straight wells.3. Two kinds of algorithms presented in Chapter Three: Working-set strategy based on Huang in ABS-class algorithms and Dual algorithm based on revised Lagrangian function. An convergence theorem proved and in order to speed convergence of working-set algorithm, constrained matrix derived from ABS in working-set method corrected. In latter part of Chapter Three, some exciting properties of the revised Lagrangian function discussed first, which leads to form a dual algorithm of CORA or COT. Convergence theorem proved by Banach perturbation theorem, Bertsekas implicit function theorem II and by analyzing Hesse matrix of revisedLargrangian function. Dual algorithm shows its advantage over other algorithms for its non-need for finding initial feasible point.4. Chapter Four analyzes the characteristics of optimal control system. A dynamic model and then an optimal control model established, which regards the minimum length of well trajectory as the index of characteristic and meets the terminal conditions. And the necessary condition of optimal solutions for the optimal control system then discussed. A new method to solve this model developed based on uniform design method and revised Hooke-Jeeves method. Optimal control model and its algorithm validated by numerical tests.5. A new software system with fine GUI and powerful functions and its applications introduced in Chapter Five. Then 3 typical case histories discussed hereinafter demonstrates its advantages and its leading rank with comparison to WellLead Software imported.