A mathematical model for soil vapor extraction of volatile organic compounds from soils rich in natural humic organic carbon by means of a single vertical well screened along its length and operating underneath an impermeable cap is described. The model includes a distributed diffusion treatment of diffusion kinetics. Partitioning of volatile organic compounds between the aqueous phase and the natural organic carbon is handled by a linear isotherm or by a Freundlich isotherm. Freundlich isotherm exponents n(f) chosen on the basis of published data lead to substantially more prolonged remediations than result from use of a similar linear isotherm.