An analytical solution to equations describing rate‐limited soil vapor extraction of contaminants in the vadose zone

Soil vapor extraction (SVE) is a technique that is commonly used to remove volatile organic compounds from the vadose zone. Recent research has demonstrated that rate‐limited sorption and desorption of these compounds can have a profound impact on the concentration reductions achievable by SVE. In this note, one‐dimensional equations presented by Brusseau (1991), which describe rate‐limited transport of sorbing organic compounds in the vadose zone, are modified to model a SVE remediation at an idealized site and analytically solved. The analytical model presented herein describes transport of a sorbing organic contaminant in a converging radial flow field in the vadose zone, with sorption rate limitations described by first‐order rate expressions. The model equations are solved in the Laplace domain and numerically inverted to simulate contaminant concentrations at an extraction well. A Laplace domain solution for the total contaminant mass remaining in the vadose zone is also derived. It is shown that under certain conditions, rate‐limited sorption can have a significant impact upon SVE remediation in the vadose zone. The solutions presented in this note may be useful in verifying numerical codes which are being developed to model organic transport in the vadose zone under conditions of rate‐limited sorption.