Stationary Problem and Optimal Control

Abstract

Soil venting is an in-situ process to remove the volatile organic compounds from the unsaturated zone. The extraction well creates a negative differential pressure which generates a gas flow towards the probe. After removal the VOCs existing in the equilibrium conditions, VOC will enter the gaseous phase from the liquid phase due the phase change. Hence the discharges of the active probes must be relatively small, in the other case the concentration of VOCs in the extracted gas will be low. Differential pressures applied to the extraction well typically range from 15“-350” of water (cf. Hiller [Hill). The influence of a vapor extraction system depends on many parameters (stratigraphy, soil type, length and position of the probes, discharge, VOC distribution and its concentration in the soil matrix, soil surface, depth of the vadose zone). In the case when the soil surface is not covered, the range of influence of a single well is relatively small. In order to increase the radius of influence one can use full or partially cover of the soil surface. According to the field tests, the time required to develop the steady state flow and the effective radius ranges between 15-30 minutes (cf. Hiller [Hill). On the other hand the movement of the air inside the porous matrix is slow (it can take days to arrive from the range of the remediation site into the active probe) and the whole soil venting process takes place over a few years. From this point of view it is natural to study the steady state problem first.