Reservoir Flooding Optimization by Control Polynomial Approximations
Abstract
In this dissertation, we provide novel parametrization procedures for water-flooding
production optimization problems, using polynomial approximation techniques. The methods project the original infinite dimensional controls space into a polynomial subspace. Our contribution includes new parameterization formulations using natural polynomials, orthogonal Chebyshev polynomials and Cubic spline interpolation.
We show that the proposed methods are well suited for black-box approach with
stochastic global-search method as they tend to produce smooth control trajectories, while reducing the solution space size. We demonstrate their efficiency on synthetic two-dimensional problems and on a realistic 3-dimensional problem.
By contributing with a new adjoint method formulation for polynomial approximation,
we implemented the methods also with gradient-based algorithms. In addition to fine-scale simulation, we also performed reduced order modeling, where we demonstrated a synergistic effect when combining polynomial approximation with model order reduction, that leads to faster optimization with higher gains in terms of Net Present Value.
Finally, we performed gradient-based optimization under uncertainty. We proposed
a new multi-objective function with three components, one that maximizes the expected
value of all realizations, and two that maximize the averages of distribution tails from
both sides. The new objective provides decision makers with the flexibility to choose the
amount of risk they are willing to take, while deciding on production strategy or performing reserves estimation (P10;P50;P90).
Subject
OptimizationOptimal Control
Polynomial Approximation
Waterflooding
Reservoir Simulation
Reduced Order Modeling
Control Parameterization
Chebyshev
Spline Interpolation
Particle Swarm Optimization
Interior Point
LBFGS
BFGS
Adjoint Method
Optimization Under Uncertainty
Conditional Value at Risk
Conditional Value at Success
Citation
Sorek, Nadav (2017). Reservoir Flooding Optimization by Control Polynomial Approximations. Doctoral dissertation, Texas A & M University. Available electronically from https : / /hdl .handle .net /1969 .1 /166003.
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