Evaluation of Lyapunov-based Adaptive Observer using Low-Order Lumped Model for Estimation of Production Index in Under-balanced Drilling

Abstract

A distributed drift-flux model and a low-order lumped model describing a multiphase (gas-liquid) flow in the well during Under-Balanced Drilling (UBD) has been presented. This paper presents a novel nonlinear adaptive observer to estimate the total mass of gas and liquid in the annulus and production constant of gas and liquid from the reservoir into the well during UBD operations. Furthermore, it describes a joint unscented Kalman filter to estimate parameters and states for both the distributed drift-flux and lumped model by using real-time measurements of the choke and the bottom-hole pressures. The performance of the adaptive observers are evaluated for typical drilling scenarios. The results show that all adaptive observers are capable of identifying the production index, although the adaptive observers based on the low-order lumped model achieves better convergence rate than adaptive observer based on the drift-flux model. The results show that the LOL model is sufficient for the purpose of estimating the production parameters.

Multi-phase flow measurement in a gas refinery using decentralized Lyapunov–based adaptive observer

“…where S fr is the friction loss, Δ φ is the mean angle between the gravity direction and the well positive flow direction ( Δ φ value is close to zero), g is the gravitational constant, and A is the pipe cross-section. All these relations can be found in Aarsnes et al (2014) and Nikoofard et al (2015).…”

“…Topside measurement is one of the widely-used ways to estimate down-hole parameters. For example, in Nikoofard et al (2015), the authors have used OLGA simulator for the estimation of the production of oil and gas from the underground reservoir during a UBD operation. Several formulations are available for modeling the one-dimensional flows in the pipelines, for example, homogeneous equilibrium model (HEM), no-pressure-wave model (NPW), drift-flux model, and two-fluid model.…”

Reservoir characterization in under-balanced drilling using low-order lumped model

“…In [16], the performance of the adaptive estimators was compared and evaluated for pipe connection procedure using a simple simulation model. In [17] the extended version of adaptive observer used in [16] was directly using real-time measurements of the choke and the bottom-hole pressures to estimate states and parameters. The performance of the adaptive observers was compared and evaluated for typical drilling case to estimate only production constant of gas using a simulated scenario with drift-flux model.…”

“…The performance of the adaptive observers was compared and evaluated for typical drilling case to estimate only production constant of gas using a simulated scenario with drift-flux model. In the present paper, the adaptive observers from [17] is compared and evaluated for an UBD case study to estimate both production constants of gas and liquid using some simulated scenarios with the OLGA simulator. The OLGA dynamic multiphase flow simulator is a high fidelity simulation tool which has become the de facto industry standard in oil and gas production, see [18].…”

State and Parameter Estimation of a Drift-Flux Model for Underbalanced Drilling Operations

“…Nikoofard et al [9] designed a Lyapunovbased adaptive observer, a recursive least squares estimation and a joint unscented Kalman filter based on a low-order lumped model to estimate states and parameters during UBD operations. This model was the extended version of an adaptive observer used in [9] for directly using real-time measurements of the choke and the bottom-hole pressures to estimate states and parameters [13]. The performance of the adaptive observers was compared and evaluated for a typical drilling case to estimate only production index of gas using a simulated scenario with a drift-flux model.…”