The optimal well-rate allocation problem (OWRA) can be stated as the following: given a model of a reservoir and locations of injecting and producing wells, find the well rates (defined over time) that maximize profit. Recent work led to a mathematical formulation of OWRA as an optimization problem, using the Black-Oil equations to characterize flow in the reservoir. In this talk I introduce the necessary mathematical background to understand the mathematical formulation of OWRA. I then discuss improvement of the solution by using adaptive (as opposed to fixed time-step) simulations.  

This talk will be split into three parts. First, I introduce unconstrained optimization, and discuss how this technology can be coupled with the IMPSAT (Implicit Pressure and Saturation) approach to solve the Black-Oil equations. I then address the well-rate bound requirement for OWRA, which motivates the use of constrained optimization algorithms. Finally, I show how to incorporate adaptive simulations for OWRA -- leading to quick convergence and physically meaningful results. Time permitting, I will also talk about computational storage issues and algorithms to circumvent these problems, such as the checkpointing algorithm for adaptive simulation.