# Non-Vertical Well Trajectory Design Based on Multi-Objective Optimization
## 2 Related Work  
### Non-Vertical Well Trajectory Classification and Characteristics Analysis  
As an important part of drilling engineering, the design of a wellbore trajectory involves the knowledge of mathematics, physics, geology, and other fields. It usually includes the determination of a coordinate system, the selection of a well type, the establishment of an objective function, the selection of an optimization algorithm, and so on. With the continuous development of the oil and gas industry, directional drilling technology is more and more widely used in complex geological conditions. As the core part of directional drilling, the wellbore trajectory design directly affects the success rate and economic benefits of drilling [26]. The following will focus on several common types of non-vertical well tracks and analyze their characteristics and applicable scenarios. (1) Three-stage  
The first type of trajectory is composed of the vertical well section, build-up section, and stable section. It is customarily called the three-section wellbore trajectory. This type of wellbore trajectory has a shallow build-up point, convenient construction, and easy control. Generally, the maximum deviation angle can be reached only in the surface casing, and then the wellbore is drilled to the bottom of the well. Due to the simple design process, this type of well trajectory is suitable for the surface layer of the geological structure and the area, which can effectively reduce the difficulty and cost of drilling construction, and the overall drilling construction process is more direct. The construction personnel can easily grasp and control the drilling parameters in the actual drilling process to ensure that the well trajectory is carried out in accordance with the design requirements. Therefore, this type of well trajectory is mainly used in traditional vertical deep vertical wells and simple directional wells. (2) Five-stage  
The second type of trajectory is composed of the vertical well section, build-up section, stable section, build-up section, and stable section, which is usually called the five-section wellbore trajectory. This kind of wellbore trajectory is mostly used for horizontal wells. The upper drilling trajectory is along the vertical deep well section, and then gradually increases the well deviation angle from the build-up section to the set maximum well deviation angle. The stable section maintains the well deviation angle in order to maintain stability to prepare for entering the increase section. Then, after increasing the inclination again in the increase section to make it close to the horizontal state, the second stable section is used to keep the wellbore at this angle until it reaches the target layer. The five-stage wellbore trajectory type is complex, but flexible, so this type of trajectory can be applied to more horizontal wells with special drilling requirements, which is conducive to achieving the maximum possible contact area with the reservoir, so as to achieve the highest production level. (3) 'S' shape  
The third type of trajectory is the 'S'-shaped wellbore trajectory. This kind of wellbore trajectory is relatively shallow, and the drilling is stabilized after the surface casing is completed. The 'S'-shaped wellbore trajectory is characterized by two build-up sections, which are similar to the 'S' shape. First, drilling starts from the vertical section, and then enters the first build-up section, that is, the wellbore is deviated from the vertical well trajectory. After the build-up is completed, the surface casing is cemented, and the inclined drilling is stabilized, and then the second build-up section is entered to adjust the well deviation and continue drilling. Finally, through the last stable section, the original well angle drilling is maintained, and finally the target layer is reached. The 'S'-shaped wellbore trajectory is suitable for complex formations, and it is suitable for drilling to avoid geological conditions or multi-layer reservoirs.