Bjarne Foss

Global optimization of multiphase flow networks using spline surrogate models

Abstract A general modelling framework for optimization of multiphase flow networks with discrete decision variables is presented. The framework is expressed with the graph and special attention is given to the convexity properties of the mathematical programming formulation that follows. Nonlinear pressure and temperature relations are modelled using multivariate splines, resulting in a mixed-integer nonlinear programming (MINLP) formulation with spline constraints. A global solution method is devised by combining the framework with a spline-compatible MINLP solver, recently presented in the literature. The solver is able to globally solve the nonconvex optimization problems. The new solution method is benchmarked with several local optimization methods on a set of three realistic subsea production optimization cases provided by the oil company BP.

Well placement optimization subject to realistic field development constraints

This work considers the well placement problem in reservoir management and field development optimization. In particular, it emphasizes embedding realistic and practical constraints into a mathematical optimization formulation. Such constraints are a prerequisite for the wider use of mathematical optimization techniques in well placement problems, since constraints are a way to incorporate reservoir engineering knowledge into the problem formulation. There are important design limitations that are used by the field development team when treating the well placement problem, and these limitations need to be articulated and eventually formalized within the problem before conducting the search for optimal well placements. In addition, these design limitations may be explicit or implicit. In this work, various design limitations pertaining to well locations have been developed in close collaboration with a field operator on the Norwegian Continental Shelf. Moreover, this work focuses on developing constraint-handling capability to enforce these various considerations during optimization. In particular, the Particle Swarm Optimization (PSO) algorithm is applied to optimize for the well locations, and various practical well placement constraints are incorporated into the PSO algorithm using two different constraint-handling techniques: a decoder procedure and the penalty method. The decoder procedure maps the feasible search space onto a cube and has the advantage of not requiring parameter tuning. The penalty method converts the constrained optimization problem into an unconstrained one by introducing an additional term, which is called a penalty function, to the objective function. In contrast to the penalty method, only feasible solutions are evaluated in the decoder method. Through numerical simulations, a comparison between the penalty method and the decoder technique is performed for two cases. We show that the decoder technique can easily be implemented for the well placement problem, and furthermore, that it performs better than the penalty method in most of the cases.

Dual adaptive model predictive control

Abstract We present an adaptive dual model predictive controller ( dmpc ) that uses current and future parameter-estimation errors to minimize expected output error by optimally combining probing for uncertainty reduction with control of the nominal model. Our novel approach relies on orthonormal basis-function models to derive expressions for the predicted distributions for the output and unknown parameters, conditional on the future input sequence. Propagating the exact future statistics enables reformulating the original stochastic problem into a deterministic equivalent that illustrates the dual nature of the optimal control but is nonlinear and nonconvex. We further reformulate the nonlinear deterministic problem to pose an equivalent quadratically-constrained quadratic-programming ( qcqp ) problem that state-of-the-art algorithms can solve efficiently, providing the exact solution to the probabilistically constrained finite-horizon dual control problem. The adaptive dmpc solves this qcqp at each sampling time on a receding horizon; the adaptation is a result of updating the parameter estimates used by the dmpc to decide the control input. The paper demonstrates the application of dmpc to a single-input single-output ( siso ) system with unknown parameters. In the simulation example, the parameter estimates converge quickly and the probing vanishes with increasing accuracy and precision of the estimates, improving the future control performance.

Echo State Networks for data-driven downhole pressure estimation in gas-lift oil wells

Process measurements are of vital importance for monitoring and control of industrial plants. When we consider offshore oil production platforms, wells that require gas-lift technology to yield oil production from low pressure oil reservoirs can become unstable under some conditions. This undesirable phenomenon is usually called slugging flow, and can be identified by an oscillatory behavior of the downhole pressure measurement. Given the importance of this measurement and the unreliability of the related sensor, this work aims at designing data-driven soft-sensors for downhole pressure estimation in two contexts: one for speeding up first-principle model simulation of a vertical riser model; and another for estimating the downhole pressure using real-world data from an oil well from Petrobras based only on topside platform measurements. Both tasks are tackled by employing Echo State Networks (ESN) as an efficient technique for training Recurrent Neural Networks. We show that a single ESN is capable of robustly modeling both the slugging flow behavior and a steady state based only on a square wave input signal representing the production choke opening in the vertical riser. Besides, we compare the performance of a standard network to the performance of a multiple timescale hierarchical architecture in the second task and show that the latter architecture performs better in modeling both large irregular transients and more commonly occurring small oscillations.

Gas Lift Optimization under Uncertainty

Abstract In this paper, we consider the problem of production optimization under uncertainty applied to gas lifted well networks. Worst-case and scenario optimization methods are presented to explicitly handle the uncertainty. We also compare the performance and computation time of the presented methods with nominal and ideal cases using Monte Carlo simulations. We show that the scenario optimization method is able to reduce the conservativeness, however at the cost of computation time. We also show that the performance can be improved by parameter adaptation using an extended Kalman filter for combined state and parameter estimation.

An augmented Lagrangian method for optimal control of continuous time DAE systems

This works presents an algorithm for solving optimal control problems (OCP) of differential algebraic equations (DAE) based on the augmented Lagrangian method. The algorithm relaxes the algebraic equations and solves a sequence of OCPs of ordinary differential equations (ODE). The major benefits of this approach are twofold. First, the state and algebraic variables can be bound constrained, even when the solution methods are indirect. Second, by reducing the system to an ODE, the representation is more compact and can be handled by computationally efficient methods. Experiments show that the algorithm converges to the objective value of the original OCP and the violation of the relaxed algebraic equation goes to zero.

Steady-state real-time optimization using transient measurements

Abstract Real-time optimization (RTO) is an established technology, where the process economics are optimized using rigourous steady-state models. However, a fundamental limiting factor of current static RTO implementation is the steady-state wait time. We propose a “hybrid” approach where the model adaptation is done using dynamic models and transient measurements and the optimization is performed using static models. Using an oil production network optimization as case study, we show that the Hybrid RTO can provide similar performance to dynamic optimization in terms of convergence rate to the optimal point, at computation times similar to static RTO. The paper also provides some discussions on static versus dynamic optimization problem formulations.

Multiple shooting applied to robust reservoir control optimization including output constraints on coherent risk measures

The production life of oil reservoirs starts under significant uncertainty regarding the actual economical return of the recovery process due to the lack of oil field data. Consequently, investors and operators make management decisions based on a limited and uncertain description of the reservoir. In this work, we propose a new formulation for robust optimization of reservoir well controls. It is inspired by the multiple shooting (MS) method which permits a broad range of parallelization opportunities and output constraint handling. This formulation exploits coherent risk measures, a concept traditionally used in finance, to bound the risk on constraint violation. We propose a reduced sequential quadratic programming (rSQP) algorithm to solve the underlying optimization problem. This algorithm exploits the structure of the coherent risk measures, thus a large set of constraints are solved within sub-problems. Moreover, a variable elimination procedure allows solving the optimization problem in a reduced space and an iterative active-set method helps to handle a large set of inequality constraints. Finally, we demonstrate the application of constraints to bound the risk of water production peaks rather than worst-case satisfaction.