The zonostrophic instability that leads to the emergence of zonal jets in barotropic beta-plane turbulence is analyzed through a geometric decomposition of the eddy stress tensor. The stress tensor is visualized by an eddy variance ellipse whose characteristics are related to eddy properties. The tilt of the ellipse principal axis is the tilt of the eddies with respect to the shear, the eccentricity of the ellipse is related to the eddy anisotropy, while its size is related to the eddy kinetic energy. Changes of these characteristics are directly related to the vorticity fluxes forcing the mean flow. The statistical state dynamics of the turbulent flow closed at second order is employed as it provides an analytic expression for both the zonostrophic instability and the stress tensor. For the linear phase of the instability, the stress tensor is analytically calculated at the stability boundary. For the non-linear equilibration of the instability the tensor is calculated in the limit of small supercriticality in which the amplitude of the jet velocity follows Ginzburg-Landau dynamics. It is found that dependent on the characteristics of the forcing, the jet is accelerated either because the jet primarily anisotropizes the eddies so as to produce upgradient fluxes or because the jet changes the eddy tilt. The instability equilibrates as these changes are partially reversed by the non-linear jet-eddy dynamics.
No abstract
Well network simulation and optimization is an established technology within BP for production optimization. However, for simplicity, the processing facilities are usually only considered as fixed oil, gas and water flow rate constraints. Actual production limits vary as a function of operating conditions and/or cannot be measured directly (e.g. True Vapour Pressure (TVP) or gas velocity at the inlet separator nozzles). To improve on existing workflows, BP has expanded its existing petroleum engineering-focused toolkit and is now globally deploying an end-to-end production system digital twin that extends from the well choke to the facility export for system surveillance and optimization. The end-to-end production system digital twin is a cloud-based system that links sensor data from the asset historian with an equipment data model and third-party first principle steady state simulation tools for an accurate representation of the well network and processing facilities. It supports multi-discipline collaboration, particularly between Petroleum Engineers and Process Engineers, and is remotely accessible by a globally dispersed team. This integrated digital twin can be used in two modes: monitoring and what-if. In monitoring mode, the models are automatically updated hourly with real time data and key simulation results extracted and stored. These monitoring simulations generate virtual sensor output, providing insights that cannot be measured by real sensors. In what-if mode, engineers test scenarios risk-free to explore optimization opportunities. As well as routine optimizations to align with production forecast updates, this can also include scenarios during planned abnormal operations (e.g. facility equipment offline for maintenance or well flowback). An early pilot in a key production region delivered significant production upside and was foundational for the subsequent global roll-out program. This paper will illustrate two practical applications from early deployment activities: (1) condensate recovery optimization (2) well routing optimization / feasibility against variable processing facility limits.
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