Application of derivative-free methodologies to generally constrained oil production optimization problems

Abstract

Oil production optimization involves the determination of optimum well controls (e.g., well pressures, injection rates) to maximize an objective function such as cumulative oil production or net present value. In practice, this problem additionally requires the satisfaction of physical and economic constraints. Thus, the overall problem represents a challenging nonlinearly constrained optimization. The cost function and constraints involve calls to a reservoir simulator. Therefore, in many situations gradient information cannot be obtained efficiently. This fact motivates the use of derivative-free (non-invasive, black-box) optimization methods. This work entails a comparative study of a number of these methods applied to the solution of generally constrained production optimization problems. The derivativefree techniques considered include two pattern search methods (generalized pattern search and Hooke-Jeeves direct search) and a genetic algorithm. A gradient-based algorithm, in which derivatives are estimated numerically, is also considered. The performance of the derivative-free algorithms is shown to be quite satisfactory and can be improved significantly when implemented within a distributed computing environment. In order to address the solution of the generally constrained production optimization problem, different constraint handling techniques are investigated. Penalty functions can be used successfully for this purpose, but they typically involve a tuning/iterative process that is not exempt, in theory, from potential pitfalls. The results indicate that the filter method combined with pattern search suitably addresses this issue while keeping the scheme efficient. We have also explored a parameterless penalty method for genetic algorithms that appears promising when hybridized with pattern search techniques. In total, the results of this study demonstrate the applicability of derivative-free methods for challenging reservoir management problems.

Adjoint formulation and constraint handling for gradient-based optimization of compositional reservoir flow

“…Refer to [21] for a more complete overview of adjoint-based optimization methods. We note additionally that, although not considered here, derivative-free methods can also be applied for production optimization problems -see [16] for discussion and examples.…”

Fracture Characterization in Enhanced Geothermal Systems by Wellbore and Reservoir Analysis

“…Researchers at the Stanford Department of Energy Resources Engineering are actively working on the topic, specifically within the Smart Fields Consortium. A few publications of 45 interest are those by Sarma et al (2006), Cardoso et al (2009) andEcheverria Ciaurri et al (2011). Professor Jan-Dirk Jansen at the Delft University of Technology also runs an active research group with an interest in production optimization.…”

Joint optimization of oil well placement and controls

“…In order to simplify notation we introduce the well position feasible set X = {x ∈ Z n1 ; x d ≤ x ≤ x u } and the well control feasible set U = {u ∈ R n2 ; u d ≤ u ≤ u u }. Non-linear constraints, which could include rate or water-cut specifications, can be handled using different techniques such as penalty functions or filter methods, as described in Echeverría Ciaurri et al (2011a).…”

“…The optimization bounds define upper and lower BHP limits for both injectors and producers. Other operational constraints (e.g., minimum oil and/or maximum water production over all wells) can be addressed in an efficient manner by the filter method (Nocedal and Wright, 2006;Echeverría Ciaurri et al, 2011a). The filter method is really an add-on that can be combined with most (derivative-based and gradientfree) optimization algorithms.…”

“…Well control optimization is commonly stated in terms of continuous variables (well flow rates or pressures), and in some cases (bound-constrained optimization problems) has been observed to present smooth optimization landscapes with multiple optima but similar cost function values (see e.g., Jansen et al, 2005 andEcheverría Ciaurri et al, 2011a). This observation is for problems with linear constraints (which have been studied the most), and its validity is unclear for more general cases.…”