An analytical solution for transient gas flow in a multi-well system

Soil vapor extraction (SVE) combined with air injection provides an efficient way for the cleanup of vadose zone contaminated by volatile organic chemicals (VOCs). A successful design of an SVE system, however, relies on a good knowledge of the induced gas flow field in the vadose zone. Analytical solutions are available to help understand the gas flow field at steady-state. However, most SVE systems must pass a transient period before reaching steady (or quasi-steady) state and the length of the period should be system-specific. This paper presents an analytical solution for transient gas flow in a vadose zone with extraction and injection wells. The transient solution approaches the steady-state solution as time increases. Calculations have shown that for a shallow well (screened in a depth of less than 10 m) in a vadose zone with an air permeability of 1 darcy (10-12 m2) or larger, the system reaches steady-state in just several hours. Decreasing the air permeability or increasing the screen depth increases the time to reach steady-state. In practical applications the transient solution may be relatively insignificant in an SVE design. However, the solution can be important in site characterization through pneumatic tests. A procedure is provided for applying the dimensionless solution in estimating air permeability and air-filled porosity. An example is also given to use the transient solution for verifying numerical codes