Nonlinear Concentrated Parameter System Optimization Theory, Algorithms And Applications

The control of the trajectory is the core technique in horizontal well technique, while trajectory design and optimal design are the two key techniques. Trajectory designing has been a hot topic for the researchers and many methods have been presented. But most of methods nowadays for designing 3D horizontal wells are based on Trial-and-Error method. So well trajectory designing depend greatly on the experience of the designer, which lead to the time-consuming trial-and-error procedure while using those kinds of methods. What's more, the optimal solution cannot be guaranteed.According to the constraint nonlinear programming of designing horizontal trajectory presented by Jiang Shengzong in 2001, the paper constructs a nonlinear multilevel lumped parameter dynamical system by the nonlinear control theory and describes the existence of its solution and the controllability as well as the polykeys of this optimal control. In order to obtain the solutions to this system, Uniform Design is introduced to choose the initial points. Then based on these points decompose the admitted region into finite subregions, in which an improved Hooke-Jeeves algorithm is constructed to solve the subproblems. The new algorithm and its corresponding software we developed has been not only validated in several horizontal wells, but also show their advantages such as shorter length of trajectory designed, more accuracy of target hitting and less time-consuming comparison with present conventional methods. The practical trajectory often deviates the optimal trajectory of provisional design in practical application of horizontal wells. For this reason we propose an optimal control model for designing 3-dimension horizontal wells with deviation.