Modeling buoyant droplet plumes in a stratified environment

This work describes the formulation and application of a novel two-phase integral plume model. This model describes the characteristics of a vertical plume driven by the continuous release of dissolving buoyant droplets from a fixed point in a stratified, stagnant environment. Model development is motivated by a specific application, the injection of CO 2 into the deep ocean by means of a buoyant droplet plume. This application is one method of sequestering anthropogenic C02 emissions from the atmosphere. The goal of such measures is to reduce the environmental risks associated with atmospheric emissions. Of course, sequestration of C02 in the ocean introduces other environmental concerns, as dissolved CO 2 tends to lower seawater pH. It is also necessary to ensure that the CO 2 is delivered to a depth where it will not be transported to the surface over short time scales. To assess the feasibility and begin to estimate the potential for environmental impacts, a multinational group of researchers plans to conduct a pilot-scale field experiment in 2001. The aim of this work is to build a model of a buoyant droplet plume that will aid both design and interpretation of the field experiment, as well as any production-scale C02 releases. Such a model is also applicable to other two-phase plume flows. To that end, an integral model is formulated which accounts for the dynamics of the primary processes associated with a droplet plume: buoyant forces acting upon the droplets and plume water, dissolution of the droplets, turbulent entrainment of ambient water into the plume, and buoyant detrainment, or "peeling. " The resulting model, at its core, is expressed as a set of nonlinear, coupled differential equations. Typical integral plume models are one-dimensional, initial-value problems which require a single integration to solve the governing equations. The particular nature of the class of plumes under investigation (droplet plumes where droplet buoyancy decreases with height due to dissolution, and dissolved C02 increases fluid density), however, is characterized by regions of upward flow, driven by the buoyant droplets, and downward flow, driven by stratification and other density effects. As these flows are coupled, solution of the governing equations for flow in each direction is iterative, increasing the complexity of the solution scheme. One implicit model assumption is that plume fluid in the vicinity of the droplets advects in the same direction as the droplets. As some coarse grid models predict that the fluid actually flows in the opposite direction, some scoping experiments were carried out to verify the nature of the velocity profile in a countercurrent droplet plume. The model is analyzed for sensitivity to both design variables, such as the flow rate of droplets at the source, and parameters which are uncertain, such as turbulent entrainment coefficients and droplet dissolution rates. In the case of C02 droplets, the dissolution rate is quite uncertain due to the formation of hydrates on the droplet surface, whose effect on mass transfer is poorly understood. Fortunately, it is clear that reduced mass transfer rates can be offset by reducing the size of the droplets. Also, while plume characteristics such as plume height are sensitive to parameter uncertainty, the dilution of C02 is strongly controlled by quantifiable factors such as the C02 mass flux and the ambient stratification. This is attributable to the density effect of dissolved C02; high concentrations of dissolved C02 creates negative buoyancy which induces mixing. This mixing aids dilution. The model is also compared to datasets describing different plume regimes in order to assess its validity. Though, when tuned to a given situation, the model agrees well with the data, there is no set of parameters which is universally applicable. Although the reasons why some parameters, such as the entrainment coefficients, change from case to case are partially understood, parameter uncertainty limits the accuracy of the model. In the case of a C02 droplet plume, the rise height predictions are estimated to be accurate to within ±30 percent. Thesis Supervisor: E. Eric Adams Title: Senior Research Engineer Acknowledgments I would like to acknowledge the the National Science Foundation for providing me with a Graduate Research Fellowship, and to the many sponsors of the C02 field experiment project, including the United States Department of Energy. On the international front, I wish to thank Guttorm Alendal of the Nansen Center and Toru Sato of the University of Tokyo for sharing their work. I would also like to acknowledge all those involved with the C02 sequestration experiment with whom I have worked, including, but not limited to, Perry Bergman of the U.S. DOE, Stephen Masutani of the University of Hawaii, Lars Golmen of NIVA, Rick Coffin of NRL, and Howard Herzog of the MIT Energy Lab. There are several more people at MIT whom I would like to thank. These include fellow Parsons Lab students Scott Rybarczyk, Durelle Scott, and Megan Kogut, for their good humor, and Assistant Director of the Parsons Lab, Sheila Frankel, for keeping things lively. I would also like to thank fellow graduate student Scott Socolofsky for all his help, which ranged from configuring Linux installations to editing manuscripts to teaching me how to body-surf in Hawaii. Tim Harrison, an MIT senior, was instrumental in carrying out the scoping experiments of Chapter 3. I also wish to thank my thesis advisor, E. E. Adams, for his kindness and patience. I was always amazed by how often a quick stop by his office evolved into a lengthy, constructive discussion. Finally, I would like to thank my family for supporting me these past few months. I especially thank my wonderful wife, Madeleine. I am lucky to be married to her. I dedicate this work to my father, Jerome B. Crounse.