# Quantum-Based Analytical Techniques on the Tackling of Well Placement Optimization
## 1 Introduction  
In oil and gas industry, to maximize productivity, optimization of well placement is one of the most important issues in the field development process. The optimization techniques, based on contemporary research works on this field, can be indexed in three major categories. They are (i) classical methods, (ii) non-classical methods, and (iii) hybrid methods [1]. In the early novel research endeavors, focuses were mainly shown on classical methods to tackle well placement optimization problem and among them mixed-integer programming (MIP) [2], gradient-based finite difference method [3], multivariate interpolation algorithms [4], simultaneous perturbation stochastic approximation method [5, 6], and steepest ascent method [7] are significant. However, the gradient-based techniques might get trapped in local optima, which is one of the biggest bottlenecks of the gradient-based techniques. Moreover, the calculation of the gradients is complex. Hence,due to the nature of the well placement optimization problem, it is hardly solved by gradient-based techniques. On the other hand, derivative calculations are not required for non-classical methods, and less likely to get trapped in local optima than classical techniques [8; 9; 10]. Due to the robustness and parallelism nature, nonconventional methods with gradient-free approaches are more considered for well placement optimization. To make a model robust, consideration of risk management is important. Again, due to different heterogeneity in conventional and shale reservoirs, the production is different [11; 12; 13]. Hence, different search space will be produced that can be challenging for an optimization technique and the results may not be consistent. Unconventional reservoirs are relatively tight, exhibit strong heterogeneity, low permeability (<0.1 md), and possess a complex micropore structure, thus restricting the effective economic development of oil and gas. Boost up oil production from unconventional reservoirs is different from conventional reservoirs as it requires advanced technologies of multiple horizontal wells and multi-stage hydraulic fracturing. Due to the fact that in these unconventional reservoirs, the space between cracked wells is narrowed, the economic equations also need to take into account the effects of natural fractures and well interference through fracture communication. Smaller intervals connect more existing fracturing, creating a complex fracturing network during hydraulic fracturing [12; 13]. Hydraulic fracturing has been widely used in many regions. Despite having many economic benefits it can damage the formation and can reduce the production rate and recovery efficiency [14; 15; 16]. In the operational performance, formation damage is a profoundly important issue [16]. Nowadays, most reservoirs are facing pressure reduction due to the high production rate of hydrocarbons, which leads to low recovery efficiency [15]. During the drilling operations, ineffective implementation of drilling fluid damages the reservoir formation [14]. Nonconventional nature-inspired gradient-free methods such as artificial bee colony (ABC) [17], improved harmony search (IHS) [18], genetic algorithm ([19; 20], covariance matrix adaptation evolution strategy (CMA-ES) [21], differential evolution (DE) [22], cuckoo search (CS) [23], bat algorithm (BA) [24], ant colony optimization (ACO) [25], and imperialist competitive algorithm (ICA) [26], etc. have been applied in well placement optimization problem. Although these types of global optimization algorithms can provide better solutions than traditional techniques, they are still heavily affected by parameter tuning and tend to be trapped in a local optimum. To improve this situation, hybrid techniques are realized in different ways in different research aspects. In some aspects, researchers prefer to blend non-conventional techniques with classical methods [27], whereas in some cases incorporating two or more nonconventional approaches are used for developing a hybrid algorithm [28].