Integral models for bubble, droplet, and multiphase plume dynamics in stratification and crossflow

Anusha L Dissanayake,Jonas Gros,Scott A Socolofsky

doi:10.1007/s10652-018-9591-y

Abstract

We present the development and validation of a numerical modeling suite for bubble and droplet dynamics of multiphase plumes in the environment. This modeling suite includes real-fluid equations of state, Lagrangian particle tracking, and two different integral plume models: an Eulerian model for a double-plume integral model in quiescent stratification and a Lagrangian integral model for multiphase plumes in stratified crossflows. Here, we report a particle tracking algorithm for dispersed-phase particles within the Lagrangian integral plume model and a comprehensive validation of the Lagrangian plume model for single- and multiphase buoyant jets. The model utilizes literature values for all entrainment and spreading coefficients and has one remaining calibration parameter kappa , which reduces the buoyant force of dispersed phase particles as they approach the edge of a Lagrangian plume element, eventually separating from the plume as it bends over in a crossflow. We report the calibrated form kappa = [(b - r) / b]^4 , where b is the plume half-width, and r is the distance of a particle from the plume centerline. We apply the validated modeling suite to simulate two test cases of a subsea oil well blowout in a stratification-dominated crossflow. These tests confirm that errors from overlapping plume elements in the Lagrangian integral model during intrusion formation for a weak crossflow are negligible for predicting intrusion depth and the fate of oil droplets in the plume. The Lagrangian integral model has the added advantages of being able to account for entrainment from an arbitrary crossflow, predict the intrusion of small gas bubbles and oil droplets when appropriate, and track the pathways of individual bubbles and droplets after they separate from the main plume or intrusion layer.

Highlights

Jets and plumes occur often in our surroundings, formed due to both manmade and natural reasons
We present the development and validation of a numerical modeling suite for bubble and droplet dynamics of multiphase plumes in the environment
We present this general modeling system for multiphase plumes in stratification and crossflow, its validation to laboratory and field experiments, and we discuss its predictions for canonical test cases of accidental oil-well blowouts in deep water to illustrate the complex role that thermodynamics and mass transfer often plays in multiphase plumes

Summary

Introduction

Jets and plumes occur often in our surroundings, formed due to both manmade and natural reasons They vary in scale from small, rising hot air plumes formed from smoke stacks to large multiphase plumes created due to volcanic eruptions or subsea oil-well blowouts. Jets and plumes attract our attention due to their role in the advection and dispersion of the energy and materials that they carry and the alterations they create in the ambient environment where they are discharged. Due to their small lateral scale compared to the length along their trajectory, buoyant jets and plumes are often modeled using an integral approach based on self-similarity. This work is important to demonstrate the proper applicability range of different modeling approaches from the literature, to highlight some of the limitations of available validation data, and to quantify model performance for predicting important metrics that describe the dynamics and impact of both single- and multiphase plumes in the environment

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