# Mathematical Modeling of Fluid Spills in Hydraulically Fractured Well Sites

5-2012

Dissertation

## Degree Name

Doctor of Philosophy in Engineering (PhD)

## Department

Chemical Engineering

Gregory J. Thoma

Mark E. Arnold

Robert R. Beitle

## Third Committee Member

Jackson D. Cothren

Jerry A. Havens

## Keywords

Applied sciences, Earth sciences, Computational hydraulics, Fluid spills, Fractured well sites, Mathematical modeling, Shallow water equations

## Abstract

Improved drilling technology and favorable energy prices have contributed to the rapid pace at which the exploitation of unconventional natural gas is taking place across the United States. As a natural gas well is being drilled, reserve pits are constructed to hold the drilling fluids and other materials returned from the drilling process. These reserve pits can fail, and when they do, plant and animal life of the surrounding area may be adversely affected. This project develops a screening tool for a suitable location for a reserve pit. This work will be a critical piece of the Infrastructure Placement Analysis System (IPAS) created by the Low Impact Natural Gas and Oil (LINGO) project.

A terrestrial spill model was developed that can be used as a decision support system in the Fayetteville Shale Play. There is currently no hydraulic model built with oil and gas production sites in mind. The model was developed by using equations describing shallow water flow and the transport of pollutants and sediments. Mass and momentum conservation laws together with physically reasonable assumptions were used in deriving these equations. The equations were solved numerically using the MacCormack time-splitting finite difference scheme. Novel techniques allowed us to solve the shallow water equations over very steep slopes (>30%) and starting with very low fluid depths without encountering unrealistically high values of velocities or negative flow depths.

The model takes as input the following: the Digital Elevation Model (DEM) of the terrain, predominant soil type, amount or rate of spill and initial concentration of pollutant species. The model gives as output the following: flow depth, flow velocities, the areal extent of pollutant contamination and the amount of sediment run-off. Data from the Fayetteville Shale Play was used in testing the model and the results were as expected. The computer program implementing the model is written in MATLAB. If the program is translated into a more optimally efficient language and run on a supercomputer, it would be computationally fast and still accurate enough to make its use in a real-time decision support system justified.

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