Reduced basis method for managed pressure drilling based on a model with local nonlinearities

Abstract

To circumvent restrictions of conventional drilling methods, such as slow control actions and inability to drill depleted reservoirs, a drilling method called managed pressure drilling (MPD) has been developed. In MPD, single‐phase flow processes can be modeled as a feedback interconnection of a high‐order linear system and a low‐order nonlinear system. These nonlinearities appear locally both inside and at the boundaries of the computational domain. To obtain a fast simulation platform for real‐time purposes (eg, online model‐based controller implementation), model order reduction is required for MPD. However, the local nonlinearities render applying model order reduction techniques challenging. In this study, a new approach is proposed to deal with such nonlinearities within the reduced basis (RB) context and it is successfully tested on a model for MPD. Contrary to the classical RB technique, the proposed approach not only does not generate nonphysical spikes at the locations of these local nonlinearities but also yields high speedup factors. The obtained reduced‐order model can be used for efficient online simulation and controller design for drilling systems with MPD.

Advances in Well Control: Early Kick Detection and Automated Control Systems

“…Model order reduction techniques have been proposed for the construction of models that combine reduced complexity with high predictive capacity. A reduced bias method capable of handling localized nonlinearities has been applied for the modeling of well dynamics under MPD [40]. An alternate approach, the use of real-time high fidelity flow modeling approximates the results of offline complex PDEs but relaxes the model accuracy during the transient phases by assuming a fixed temperature profile and the linear Bingham Plastic model [41].…”

Model complexity reduction and controller design for managed pressure drilling automation

“…Low-to medium-resolution spatial discretization is another model reduction approach which has been pursued in drilling automation [10,14,16,17]. A recently developed approach to constructing low-order, but accurate, hydraulics models is to apply automatic model order reduction techniques to the models resulted from the high-resolution spatial discretization [12,18,19]. A new perspective to this problem has been presented in our recent preliminary work [20], the rationale of which is explained next.…”

Special Issue on Credible High‐Fidelity and Low‐Cost Simulations in Computational Engineering

“…The 12 manuscripts in this special issue cover a wide range of techniques related to the above mentioned topics, including: accurate high‐order 1,2 and fast lowest‐order discontinuous Galerkin discretisations; 3,4 mesh, 1‐3,5 degree, 1 and modal basis 6,7 adaptivity; a priori error estimates, 8 a posteriori error indicators, 1,3 error bounds, 5,7,9,10 and error estimates in quantities of interest; 2,6,9,10 a priori 5,10,11 and a posteriori 2,6‐9,12 reduced order models.…”