Analytical Solution for Vapor Flow to a Horizontal Well in Unsaturated Soils

We developed new solutions for soil vapor extraction from a finite horizontal well in unsaturated zones by Fourier and Laplace transforms. These solutions may be applied for problems with or without laterally impervious bounds and for covered, uncovered or leaking ground surface conditions. However, the solution for the problems with laterally impervious bounds is expressed in series form. To attain good accuracy, the required number of terms for the series solution may depend on the ratio of width and depth of the problem domain. Further, with the dimensionless permeability, kD (the ratio of permeability for the leakage layer and that for the unsaturated zone) and dimensionless depth, fD (the ratio of the leakage layer depth and the unsaturated soil depth), we may find lower and upper limit values of the ratio of kD and fD for the problems representing covered and uncovered surface condition, respectively.