Well Placement Optimization via Gradient-Based Continuous Variables
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current methods for optimizing well placement in oilfields are inefficient, particularly for large-scale simulation models, as they rely on stochastic gradient-free algorithms that require numerous simulations and do not guarantee global optimality, and indirect applications of gradient-based methods are limited by discrete parameter issues.
Innovation Solution
A direct method using gradient-based techniques and adjoint models with continuous well location variables, allowing for the calculation and adjustment of well locations to optimize well placement, enabling efficient and rigorous optimization by representing wells in a continuous spatial domain and using pseudo-wells to approximate the objective function.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If stochastic gradient-free algorithms are used for well placement optimization, then the method is easy to apply and global in nature, but the computational efficiency is poor requiring hundreds of simulations
Solution Approach 1:
The patent transforms the discrete well location parameters into continuous parameters, enabling the use of gradient-based optimization methods. This parameter transformation allows calculation of gradients with respect to well locations, fundamentally changing the optimization approach from stochastic gradient-free to deterministic gradient-based methods, thereby improving computational efficiency while maintaining ease of application
Solution Approach 2:
The patent introduces adjoint models as intermediary tools to efficiently calculate gradients of the objective function with respect to well locations. These adjoint models serve as mediators between the reservoir simulation and optimization algorithms, enabling gradient computation without requiring hundreds of simulations, thus resolving the efficiency bottleneck
2Productivity
If gradient-based algorithms with adjoint models are used, then computational efficiency is improved requiring only tens of iterations, but the discrete nature of well location variables prevents direct application
Solution Approach 1:
The patent applies parameter changes by representing discrete well location indices (i, j) as continuous spatial coordinates. This transformation enables the direct application of gradient-based algorithms to well placement optimization, allowing efficient computation of gradients with respect to well locations while maintaining the physical meaning of well positions in the reservoir grid
Solution Approach 2:
The patent segments the optimization problem into two parts: (1) treating well locations as continuous parameters for gradient calculation, and (2) applying appropriate constraints to ensure final well locations correspond to valid grid block positions. This segmentation allows gradient-based methods to be applied while respecting the discrete nature of the reservoir model
3Loss of information
If indirect gradient methods using pseudo-wells are used, then gradient information can be obtained, but only limited search directions are available corresponding to pseudo-well locations
Solution Approach 1:
The patent changes the parameter representation from discrete pseudo-well positions to continuous well location variables. This allows gradients to be computed with respect to any direction in the continuous space, not just along the fixed directions of pseudo-wells. The continuous parameterization enables arbitrary search directions while still providing accurate gradient information for optimization
Data Source
AI summary
The disclosed methods, systems, and software are described for optimizing well placement in a reservoir field. A geological model of a reservoir field, a grid defining a plurality of cells, one or more wells to be located within the plurality of cells, and an objective function are all provided. The geological model is associated with the grid defining the plurality of cells. The locations of the wells are represented by continuous well location variables associated with a continuous spatial domain. A gradient of the objective function is calculated responsive to the continuous well location variables. The locations of the wells are then adjusted responsive to the calculated gradient of the objective function. Iterative calculation of the gradient and adjustment of the wells continue until the well locations are optimized. A visual representation of the reservoir field can be generated based on the optimized well placements.