Optimization of petroleum production under industrial constraints using alternative objective functions and adjoint gradient-based techniques

Summarization: The optimization of oil production is a tedious and computationally intensive pro- cess that requires the solution of time dependent nonlinear set of partial differ- ential equations describing the flow of hydrocarbons in anisotropic porous me- dia. Optimization of production is usually performed using either gradient free techniques like genetic algorithms, particle swarm algorithms, or gradient-based techniques where the gradients are computed through the solution of the adjoint problem. A gradient-based optimization method, in which the gradient is com- puted using an adjoint formulation, is often the method of choice since in con- trast to numerical perturbation techniques that require as many objective function evaluations as the number of control parameters, the gradient using adjoint-based techniques is obtained only at a small fraction of the time spent for the evaluation of the objective function. It is well known that for non-convex optimisation prob- lems, gradient-based techniques are likely to get trapped in poor local optima. A common practise is to lunch several independent optimisation runs from different initial guesses or to combine ideas from gradient-free algorithms with gradient- based to benefit from the merits of both. An adequate sampling of the search space would require an intractable number of simulations and it is thus impossible. The aim of this work is to exploit an observation in homogeneous reservoirs, where the global optimum, when optimising cumulative oil recovery, is usually achieved from practically any initial guess. This observation suggest to optimize cumulative oil by adopting a “geology continuation” method. In this novel ap- proach the porosity and permeability fields, gradually switch from some average homogeneous values chosen heuristically for the particular benchmark, to the in- homogeneous geological properties characterizing the reservoir. The optimal con- trols from each step become the initial controls to the next step. In addition instead of maximizing the cumulative oil we suggest to minimize mod- ified versions of the residual oil function which are likely to be more convex and thus less likely to lead in poor local optima.