Optimal 3-D Directional & Horizontal Wells Planning Using Genetic Algorithm

Abstract

This paper introduces a new software that uses the genetic algorithm to givethe optimum drilling depth of directional &horizontal wells in 3-D. Aspecial penalty function, mutation, crossover probabilities, and a specialaccuracy of the stopping criterion were used to get the global minimum of theproblem. The minimum drilling depth is achieved at the minimum values forkick-point, inclination, and angle build-up and drop-off rates. The minimumparameters reduce the dogleg severity, which in turn reduce the chances foroperational problems like high torque and drag. The optimized design has beencompared with the conventional design (based on trial and error method) andWELLDES program (based on Sequential Unconstraint minimization Technique) for awell drilled in the Gulf of Suez (application I) and with conventional designfor a theoretical well (Application II). Results of the comparison have beenvalidated by genetic algorithm software. The optimization model reduced thetotal drilling length of the two applications. This was achieved while allother operational parameters were kept within the limiting constraints andcasing setting depths were taken into consideration. In contrast, WELLDESprogram and conventional design have some variables within their constraintlimits and the casing setting depths are outside their consideration. Introduction Minimizing the drilling cost of the directional or the horizontal well is amajor concern of the drilling engineers. Cost is traditionally optimizedthrough improving elements of the operations like bit selection, weight androtary speed, drilling time, casing length... etc. Optimizing well trajectoryin case of 3D deviated wells directly impacts well cost since it is casinglength, cemented parts, mud volumes, drilling time...etc. Review of thepublished literature in the last two decades shows that well design dependstrongly on the designers, experience, judgment and tuition, and the resultsobtained can be not be guaranteed to be the best due to lack of strictmathematical models and corresponding optimization theories. Furthermore, repeatedly selecting and adjusting of the design parameters is time consumingand inefficient 1–3. Helmy4 proposed the first practical well-design modelbased on nonlinear optimization theory, in which the constraints such askickoff point, build up rate, drop-off rate, inclination, casing - settingdepth were involved. The building of this model was in 2D and was solved usingsequential unconstrained minimization technique. This work followed by anotherwork also in Cairo University to optimize the well trajectory in 3D, due toconsideration constrained from casing setting depth in its simulator program5.Today no body knows if some faster exact algorithm exists. Proving ordisproving this remains as a big task for new researchers. Today many peoplethink that such an algorithm does not exist and so they are looking for somealternative methods6.