Large-Scale Computer Models
for Environmental Systems


ENVR 265
Multiphase Transport Phenomena
Spring Semester 2003

1. Summary

This course is focused on the development of models to describe transport phenomena in multiphase porous medium systems. Of special interest is systems that involve more than one fluid phase and a solid phase. Such systems occur routinely in both engineered and natural contexts. Porous medium systems lying below the Earth’s surface (e..g., soil, groundwater, petroleum reservoir systems) are of special interest. Conservation of mass, momentum, angular momentum, energy, and entropy are considered for phases and species in volumes, interfaces, common lines, and common points. Multiphase thermodynamics are developed and used to constrain the development of closure relations. Models are developed across a range of scales, and recent computational and experimental approaches to close these models are addressed.

This course will be offered at the Statistical and Applied Mathematical Sciences Institute (SAMSI) in Research Triangle Park. The content is suitable for a wide range of scientists, engineers, mathematicians, and statisticians interested in the formulation of conservation principle-based models to describe transport phenomena in complex systems.

2 General Information

3 Grading Bases

Grades will be based upon a course project. The format of this project is described below.

4 Course Objectives

5 Background Required

The subject matter of this course is broad and quantitative in nature. A good background in mathematics through partial differential equations, vector and tensor calculus, calculus-based physics, and fluid mechanics are needed. A background in statistics, thermodynamics, and physical chemistry would be helpful. Rarely does a student have a complete grounding in each of these areas. Thus, it is usually necessary for all students to do some background reading in areas in which their background is deficient for the material covered in this course.

6 Course Reference Materials

Because the focus of this course is on evolving methods for modeling multiphase flow, a suitable book does not yet exist. Therefore, other forms of reference materials will be relied upon, including periodic course notes, reprints, reports, computer codes, and literature references. These materials will be placed on blackboard to facilitate electronic distribution.

7 Course Project

The course project will consist of original independent work done by the student in an area related to the course. Topics will be arrived at mutually by the student and the instructors. The instructors will supply a list of potential topics, and each student may tailor a topic to an area of special interest. A suitable project will investigate some aspect of evolving models of multiphase systems: model formulation, constitutive equation determination for model closure, model solution methods, or model analysis. The subject material of the course is rich in potential topics, many of which have not yet been investigated or published in the literature. The course project should be typed in a manuscript format, including abstract, introduction, background, formulation, results, discussion, conclusions, and reference sections. Further guidance will be provided.

8 Course Outline