Gaussian Elimination: A Comprehensive Review of History, Algorithms, and Applications

In this research paper, the authors aim to develop a mathematical optimization model to enhance oil recovery (EOR) processes. The model considers various factors that affect the optimization of EOR, including reservoir properties, injection rates, and production schedules. The authors use linear programming techniques to find the optimal solution that maximizes oil recovery while minimizing costs.
The paper begins by discussing the importance of EOR and the challenges associated with it. The authors explain that EOR is a complex process that involves injecting fluids into an oil reservoir to increase the amount of oil that can be extracted. They note that the optimization of EOR processes is critical to maximize oil recovery while minimizing costs, as it can significantly impact the profitability of oil production.
The authors then describe their approach to developing a mathematical optimization model for EOR. They explain that they use linear programming techniques to find the optimal solution that maximizes oil recovery while minimizing costs. The model considers various factors that affect the optimization of EOR, including reservoir properties, injection rates, and production schedules.
To illustrate how the model works, the authors provide an example of a simple reservoir with two wells. They show how the model can be used to find the optimal injection rate and production schedule to maximize oil recovery while minimizing costs. The authors note that their model is flexible enough to be applied to more complex reservoirs with multiple wells and different injection rates.
The authors then provide nearly matching upper and lower bounds on the optimal value of Program 3.5 for sufficiently large n, thereby proving Theorem 1.1. They explain that this result demonstrates the accuracy of their optimization model and highlights its potential to improve oil recovery processes.
Finally, the authors conclude by emphasizing the significance of their research and the potential impact it can have on the oil industry. They note that their optimization model can help oil companies reduce costs and increase profits while minimizing environmental impacts. Overall, the paper provides a valuable contribution to the field of EOR and highlights the importance of mathematical optimization in improving oil recovery processes.