David Tomasko

An analytical model for simulating step-function injection in a radial geometry

An analytical model is developed for analyzing underground injection of wastes that undergo advection, dispersion, sorption, and first-order degradation. The model uses a time-dependent, step-function source that simulates intermittent waste injection in a continuous fluid injection well. The governing equations for a cylindrically symmetrical system are cast in nondimensional form and then transformed and solved in Laplace space. The Laplace space solution is inverted with the Crump algorithm, which uses the real and imaginary parts of a Fourier series. The numerical solution is verified by replicating the step-function source at the point of injection, and the behavior of the model is demonstrated in a series of figures. The model is recommended for quick, scoping calculations in which there is little site-specific information and periods of discontinuous radial injection.

Disposal of NORM waste in salt caverns

Some types of oil and gas production and processing wastes contain naturally occurring radioactive materials (NORM). If NORM is present at concentrations above regulatory levels in oil field waste, the waste requires special disposal practices. The existing disposal options for wastes containing NORM are limited and costly. This paper evaluates the legality, technical feasibility, economics, and human health risk of disposing of NORM-contaminated oil field wastes in salt caverns. Cavern disposal of NORM waste is technically feasible and poses a very low human health risk. From a legal perspective, there are no fatal flaws that would prevent a state regulatory agency from approving cavern disposal of NORM. On the basis of the costs charged by caverns currently used for disposal of nonhazardous oil field waste (NOW), NORM waste disposal caverns could be cost competitive with existing NORM waste disposal methods when regulatory agencies approve the practice.

A Simple Quantitative Model to Estimate Consumptive Evaporation Impacts of Discharged Cooling Water with Minimal Data Requirements

This paper provides a early-stage analysis tool with minimal data requirements that can be used to quantify the consumptive water use from cooling operations and determine if additional data gathering or more detailed analysis is required. We develop and present a quantitative model to predict increased evaporation rates from the discharge of heated cooling water to a receiving water body. This model can be a screening tool for policy and decision makers, requiring minimal data to quickly estimate water loss from evaporation for various alternatives and impact evaluations. The model is based on standard evaporation estimation methods, modified to consider the higher atmospheric saturation gradient resulting from the heated water. The model requires minimal data; ambient air temperature, heated plume temperature, relative humidity, and wind speed. When comparing impacts from various alternatives, the change in evaporation is more important than the total evaporation and we show that the change in evaporation from the discharge of heated cooling water is independent of relative humidity, further reducing data requirements. We present graphs of model behavior over a range of expected conditions and discuss this behaviour.

Exact Analytical Solution to the One-Dimensional Advective-Dispersive Equation with a Decaying Source Term

This paper presents an exact analytical solution of one-dimensional transport of a contaminant undergoing advection, dispersion, sorption, and first-order decay, subject to unique boundary conditions, a first-order decaying contaminant concentration in time at the source with a constant concentration at infinity. This exact solution provides a method to study a new area of physical processes and to evaluate approximate methods and models that have been developed to analyze these problems. Recently two fields have developed interest in modeling physical processes that are best conceptualized using a decaying source boundary condition. These two fields are long-term modeling of recalcitrant non-aqueous phase liquid (NAPL) spills and radioactive waste disposal. Both of which can be approximated using a decaying source term. This paper briefly introduces some general field transport problems that can conceptually be described using a decaying source boundary condition. The paper then describes the governing equations, boundary and initial conditions, and the solution techniques used to develop the analytical solution. Next the analytic solution is provided and discussed along with some example cases. The results of the exact analytical solution are compared to another similar solution from the literature.