title: A Mathematical Model of Stratified Bi-Directional Flow Through the Railroad Causeway Embankment of Great Salt Lake
Creators: name: Cameron, James T.
Publisher: name: Utah State University
Year: 1978

description: A two-dimensional, finite-element, porous-media flow model is developed to simulate stratified bi-directional flow of brine through the earth embankment carrying the Southern Pacific Railroad across Great Salt Lake. The model is part of a two-year research program whose objective is to develop a computer model of circulation in Great Salt Lake. This overall model is to be used as a predictive device for salinity distributions and circulation patterns in the lake. The porous media flow model is designed to establish flow rates through the Southern Pacific Railroad causeway embankment which traverses the north central part of he lake and divides it into two bodies of water.
The study first develops the mathematical equations which describe two-dimensional stratified bi-directional flow of a fluid through porous media. Next , the problem is numerically posed as a boundary value problem in terms of pressure. This formulation is then solved by an iterative finite element scheme which employs quadratic, isoparametric, quadrilateral elements.
The study also investigates two possible means of performing an analysis of stratified bi-directional flow with a pressure formulation by either posing the problem as a single boundary value problem with two densities of fluid within, or as two single-density boundary value problems coupled at the density interface. The single boundary formulation did not converge with the techniques attempted due to numerical instability at the density interface.
The numerical model developed enables one to calculate fluid flow rates as well as the locations of the free surface and density-interface. The model simulation investigates many lake variables which affect brine flows through the embankment. Realistic model parameters are used which cover the range of actual values observed on the lake for the years 1968 through 1972. The numerical results presented in the study are given in terms of generalized dimensionless variables.
The numerical results appeared to be in agreement with previously performed stratified bi-directional Hele-Shaw model studies. The major lake parameters affecting flow rates through the causeway were the free surface head difference, the southside lake surface elevation and the difference in fluid densities between the upper and lower layers of the embankment . The southward density flow was found to be completely cut off for certain combinations of lake parameters.
Lack of adequate field data collected on the embankment has left both the geometry and the coefficient of permeability of the fill in question, preventing a rigorous verification of the model' s ability to predict actual flows. More field data are also necessary to establish whether there is stratification on the north side of the embankment which can greatly affect flow calculations.
A high Reynold's number was found for flow through the embankment, raising a question as to the validity of the Darcian flow assumption used in the analysis. However, the establishment of the true Reynold's number can only be verified through the collection of more empirical data.