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.