Identifiability and physical interpretability of hybrid, gray-box models -- a case study

Model identifiability concerns the uniqueness of uncertain model parameters to be estimated from available process data and is often thought of as a prerequisite for the physical interpretability of a model. Nevertheless, model identifiability may be challenging to obtain in practice due to both stochastic and deterministic uncertainties, e.g. low data variability, noisy measurements, erroneous model structure, and stochasticity and locality of the optimization algorithm. For gray-box, hybrid models, model identifiability is rarely obtainable due to a high number of parameters. We illustrate through an industrial case study - modeling of a production choke valve in a petroleum well - that physical interpretability may be preserved even for non-identifiable models with adequate parameter regularization in the estimation problem. To this end, in a real industrial scenario, it may be beneficial for the model's predictive performance to develop hybrid over mechanistic models, as the model flexibility is higher. Modeling of six petroleum wells on the asset Edvard Grieg using historical production data show a 35\% reduction in the median prediction error across the wells comparing a hybrid to a mechanistic model. On the other hand, both the predictive performance and physical interpretability of the developed models are influenced by the available data. The findings encourage research into online learning and other hybrid model variants to improve the results.Comment: 6 pages, 4 figure

Fault diagnosis of downhole drilling incidents using adaptive observers and statistical change detection

Downhole abnormal incidents during oil and gas drilling cause costly delays, and may also potentially lead to dangerous scenarios. Different incidents will cause changes to different parts of the physics of the process. Estimating the changes in physical parameters, and correlating these with changes expected from various defects, can be used to diagnose faults while in development. This paper shows how estimated friction parameters and flow rates can be used to detect and isolate the type of incident, as well as isolating the position of a defect. Estimates are shown to be subjected to non-Gaussian, $t$-distributed noise, and a dedicated multivariate statistical change detection approach is used that detects and isolates faults by detecting simultaneous changes in estimated parameters and flow rates. The properties of the multivariate diagnosis method are analyzed, and it is shown how detection and false alarm probabilities are assessed and optimized using data-based learning to obtain thresholds for hypothesis testing. Data from a 1400 m horizontal flow loop is used to test the method, and successful diagnosis of the incidents drillstring washout (pipe leakage), lost circulation, gas influx, and drill bit nozzle plugging are demonstrated

Drillstring Washout Diagnosis Using Friction Estimation and Statistical Change Detection

In oil and gas drilling, corrosion or tensile stress can give small holes in the drillstring, which can cause leakage and prevent sufficient flow of drilling fluid. If such \emph{washout} remains undetected and develops, the consequence can be a complete twist-off of the drillstring. Aiming at early washout diagnosis, this paper employs an adaptive observer to estimate friction parameters in the nonlinear process. Non-Gaussian noise is a nuisance in the parameter estimates, and dedicated generalized likelihood tests are developed to make efficient washout detection with the multivariate $t$-distribution encountered in data. Change detection methods are developed using logged sensor data from a horizontal 1400 m managed pressure drilling test rig. Detection scheme design is conducted using probabilities for false alarm and detection to determine thresholds in hypothesis tests. A multivariate approach is demonstrated to have superior diagnostic properties and is able to diagnose a washout at very low levels. The paper demonstrates the feasibility of fault diagnosis technology in oil and gas drilling

Hierarchical nonlinear model predictive control of offshore hybrid power systems

This paper presents an approach for controlling ofshore hybrid power systems consisting of gas turbines, offshore wind, and batteries for satisfying an exogenous power demand. A hierarchical controller is developed comprising a high-level economic nonlinear model predictive controller that distributes the power demand according to some economic objective, a low-level nonlinear tracking model predictive controller that actuates on the hybrid power system, and a nonlinear moving horizon estimator to estimate the system state. Simulation results and concluding remarks reveal the advantage of such a hierarchical approach for a simple simulation study.Hierarchical nonlinear model predictive control of offshore hybrid power systemspublishedVersio

Incident detection and isolation in drilling using analytical redundancy relations

Early diagnosis of incidents that could delay or endanger a drilling operation for oil or gas is essential to limit field development costs. Warnings about downhole incidents should come early enough to allow intervention before it develops to a threat, but this is difficult, since false alarms must be avoided. This paper employs model-based diagnosis using analytical redundancy relations to obtain residuals which are affected differently by the different incidents. Residuals are found to be non-Gaussian - they follow a multivariate $t$-distribution - hence, a dedicated generalized likelihood ratio test is applied for change detection. Data from a 1400 meter horizontal flow loop test facility is used to assess the diagnosis method. Diagnosis properties of the method are investigated assuming either with available downhole pressure sensors through wired drill pipe or with only topside measurements available. In the latter case, isolation capability is shown to be reduced to group-wise isolation, but the method would still detect all serious events with the prescribed false alarm probability

On Gradient Computation in Single‐shooting Nonlinear Model Predictive Control

Abstract: This paper gives an overview of methods for computing derivative information in dynamic optimization with path constraints. Efficiency of forward and adjoint techniques are discussed in a discrete-time setting and some algorithms are derived. Next, the discussion is extended to also include continuous-discrete systems. Dimensions in the model, signal parameterization, horizon length and sampling interval affect each of the methods differently. The key contributions of this paper is to give an overview of these methods, how they can be combined, and how different parameters affect efficiency

Adaptive sampling for UAV sensor network in oil spill management

In this paper we propose a method for adaptive sampling using Unmanned Aerial Vehicles (UAVs) in oil spill management. The goal is to measure and estimate oil spill concentrations at the sea surface, while at the same time identify the leak rates of sources at known positions. First we construct a cost which approximates the benefit of sampling locations at specific times. This cost is based on measures of observability and of persistency of excitation for the oil spill model. A receding horizon Mixed-Integer Linear Programming (MILP) problem is solved in order to find UAV trajectories which are optimal with respect to the cost. For UAV trajectory tracking we use a Lyapunov based controller. The oil spill concentration measurements taken by the UAVs by following these tracks are used in an adaptive observer, which provides state (concentration) and parameter (leak rate) estimates. Under the assumption that the sampling strategy described above lead to uniform complete observability and persistency of excitation, we prove Uniform Global Asymptotic Stability (UGAS) of the state estimation, parameter identification and UAV trajectory tracking errors. Finally, we provide a simulation of the proposed strategy, and compare it with two other strategies.acceptedVersio

Bayesian Neural Networks for Virtual Flow Metering: An Empirical Study

Recent works have presented promising results from the application of machine learning (ML) to the modeling of flow rates in oil and gas wells. Encouraging results and advantageous properties of ML models, such as computationally cheap evaluation and ease of calibration to new data, have sparked optimism for the development of data-driven virtual flow meters (VFMs). Data-driven VFMs are developed in the small data regime, where it is important to question the uncertainty and robustness of models. The modeling of uncertainty may help to build trust in models, which is a prerequisite for industrial applications. The contribution of this paper is the introduction of a probabilistic VFM based on Bayesian neural networks. Uncertainty in the model and measurements is described, and the paper shows how to perform approximate Bayesian inference using variational inference. The method is studied by modeling on a large and heterogeneous dataset, consisting of 60 wells across five different oil and gas assets. The predictive performance is analyzed on historical and future test data, where an average error of 4-6% and 8-13% is achieved for the 50% best performing models, respectively. Variational inference appears to provide more robust predictions than the reference approach on future data. Prediction performance and uncertainty calibration is explored in detail and discussed in light of four data challenges. The findings motivate the development of alternative strategies to improve the robustness of data-driven VFMs.Comment: 34 pages, 11 figure