Review on Particle Swarm Optimization Approach for Optimizing Wellbore Trajectory

Introduction

In the oil and gas industry cost minimization is a major concern for drilling engineers. From the very beginning, the advantages of drilling deviated wellbore have been very well-known to the industry. Though it is costly, this drilling makes it possible to place the well-path within productive intervals. In the beginning of the 19^th century near Texon, Texas, USA the first horizontal well drilled. Before 1950 only a horizontal section of just a few tens of meters drilled during wellbore drilling, but gradually technology developed(Pratt, 2004). Directional drilling technology became a commercially-viable technology between the 1980s to 1990s. Directional drilling technology was the most preferred technology at that time, but it was quite different from today. From previous studies, it is found that the cost of drilling directional is 1.4 times costlier than the drilling of vertical well(Joshi, 2003). But in both cases, the cost of drilling is directly proportional to two factors such as the length of a wellbore and computational time. So, under all geological constraints and limitations if it is possible to reduce the length of the wellbore trajectory it will typically decrease the time to reach the desired target destination. Finally, it will reduce the overall drilling cost. At the same time, it also reduces the probability of risk(Karimpour et al., 2016). There are some reasons which made directional drilling popular since 1990(Short, 1993). Such as it increases well productivity, increases the net productive section length, it can improve the production by penetrating more fractures in a fractured reservoir, better control etcetera. From the literature review, it is found that in the early era due to lack of strong mathematical model and related optimization theories, well design strongly depends on the experiences of an engineer. There was no automated way. Due to this, the researchers did the selection and adjustment of parameters again and again. The repeated selection and adjustment are very time consuming and inefficient(Amara & Martin, 1990; Miska & Skalle, 1981; Rampersad, Hareland, & Pairintra, 1993). In 1998 Helmy(Helmy, Khalaf, Darwish, & completion, 1998) established the first nonlinear optimization theory-based practical good design method. In that method, he considered some constraints such as build-up rate, drop-off rate, casing setting depth, inclination angle, azimuth angle, kick off point, etc(Helmy et al., 1998). But the model was in 2D. After that, another optimization work of wellbore trajectory completed which was based on the 3D model(Shokir et al., 2004). But these types of traditional optimization methods used direct search methods like random search which is inefficient to find the global optima in a vast search area. If the search is gibbous these methods also show their lacking. All those methods only deal with the continuous variable. The perfect design of a wellbore trajectory during good planning may reduce the probability of borehole failure(Awal, Khan, Mohiuddin, Abdulraheem, & Azeemuddin, 2001). Thus to reduce the cost and computational time trajectory optimization of a complex wellbore is the main purpose in drilling engineering. In recent years optimization has been used frequently in the petroleum industry. There are so many AI techniques and algorithms for optimization(Vasant & DeMarco, 2015; Vasant & Vasant, 2012). It has been used for various purposes such as plant optimization, transport schedule optimization, process optimization etcetera (Atashnezhad, Wood, Fereidounpour, Khosravanian, & Engineering, 2014; Guria, Goli, & Pathak, 2014; Shokir et al., 2004). The heuristic algorithm tries to find a solution to the problem through trial and error method. They take a reasonable amount of time. Whether the solution will be acceptable and reasonable it completely depends on the type of optimization task. Usually, the heuristic algorithm does not give a guarantee to find the best or global optimal solution. Rather it can provide an acceptable solution within a reasonable amount of time. Metaheuristic means a higher level heuristic algorithm(Bianchi, Dorigo, Gambardella, & Gutjahr, 2009; Yang, 2009) which is a combination of several low-level heuristic algorithms. A modern heuristic algorithm has two key feature such as “intensification” and “diversification”. If an algorithm can produce a diverse range of solutions and have the potentiality to find global optima we can mark it as an effective optimization algorithm. Furthermore, it should have the ability to explore the whole search area and to intensify its investigation radius around the neighbourhood of an acceptable solution. Heuristic algorithms have been applied to the constrained problem from the 1940s (Polya, 1945). Started with Genetic Algorithm (GA)(Gallagher, Sambridge, & Geosciences, 1994) the application of a metaheuristic algorithm in the form of a nature-inspired evolutionary algorithm (EA) escalated since the 1990s. And in many cases where those algorithms tried to solve effectively some nonlinear, non-smooth optimization challenges those performed better than the nonlinear gradient based optimizers. And this metaheuristic algorithm in the form of EA showed better and easier adaption power than others(Yang, 2010).