Well Placement Optimization Using Mixed Integer Programming

Placement and design of wells in high potential regions within hydrocarbon reservoirs is a critical step in field development planning. Identification of high potential regions, serving as pivotal extraction zones, doesn't address the challenges in maximizing ultimate hydrocarbon recovery. This identification needs to be complemented by optimizing wellbore placement and design. This paper presents an efficient mathematical optimization method for well placement that maximizes the contact with the productive zones with best locations in the reservoir. The method starts by transforming the high potential 3D grid cells in the reservoir model into a set of nodes. The relationships between each node with its neighboring nodes are defined using the concept of graph theory. Several governing mathematical equations are formulated to define the objective function and constraints to satisfy the requirements for the well design. The objective function in this work is the maximization of the contact of well trajectory with the best grid cells represented by the nodes in space. An MIP (Mixed-Integer Programming) solver is used to solve these equations to maximize the predefined objective function subject to the formulated constraints. The solver represents an effective mathematical modelling approach to solve complex optimization tasks. In addition, it identifies the potential trade-offs between conflicting objectives, which can provide a better understanding of bioenergy systems and support decision-makers elaborating the sustainable pathways towards bioenergy targets. Moreover, it creates meaningful connections between the nodes which define practical wellbore trajectory paths that adhere to constraints such as area of interest, well geometry and anti-collision. The proposed optimization method was tested on a synthetic reservoir model with a size of six million grid-cells to place twenty-five producers on a 3D sweetspot map. The method was able to find the best proposal of new wells, which were accurately positioned in the most lucrative and highest-quality grid-cells, ensuring smooth pathways across multiple grid layers. The method doesn't only aim for well placement, but for a joint relationship between optimal design and reservoir potential. Furthermore, the proposed method leads to approximately 80% reduction in turnaround time compared to traditional and manual well placement and other optimization methods. The design capability coupled with the mathematical optimization in this work enables exploring innovative approach in the realm of advanced field development strategies. The approach facilitates employing advanced mathematical modeling techniques to devise optimum and economically feasible full-field development plans.