This three years research project was funded by the The Federal Ministry for Education, Science, Research and Technology (BMBF), Grant Number 03-HO7BWM. The project was one out of fiftysix projects in the program Application Oriented Joint Projects in Mathematics managed by the Project Management Condensed Matter Research and New Technologies in the Arts (PFR) at the Research Centre Jülich (KFA).
Time period: 1.11.1993 - 30.6.1997
Contaminant transport.
Benzene, mineral oil, solvents, or other organic compounds entering the subsurface may be a serious and potentially long-term hazard for the environment e.g., soils and groundwater systems. For removing volatile organic compounds (VOC) from the water-unsaturated zone of contaminated soils commonly the vapor extraction method is used. During the operation of soil venting systems the vapor phase of the nonaqueous phase liquid VOC is being removed by imposing a convective air stream and enhancing the evaporation of the fluid phase of the VOC in contaminated regions of the soil. Frequently, soil venting systems are designed empirically, yet, using extensive experimental studies and observations. Theoretical approaches and simulation models for optimization of the lay-out and the operation of venting systems are often based on narrow physical and simplified mathematical descriptions of the key processes and, furthermore, relatively inefficient numerical methods are frequently applied for the solutions of systems of differential equations.
The objective of the current project is to develop a model-based computer program package for optimization of soil venting systems that may assist companies in designing and dimensioning of such systems prior to its application and in controlling vapor extraction rates and remediation progress during its operation. In this project, the components required for simulating soil venting systems such as process models, numerical solution procedures, and optimization algorithms will be combined to a comprehensive program package. The mathematical description of the basic transport and transformation processes will lead to systems of non-linear partial differential equations which will be treated using efficient numerical methods such as mixed finite elements, domain decomposition, and multigrid techniques. The numerical methods will be formulated as parallel algorithms in order to use powerful computers for the simulations like, e.g., workstation clusters. Eventually, methods for optimal control of partial differential equations will be employed.
In cooperation with a German consulting company model and optimization procedures will be developed and tested utilizing data obtained from a typical example of a clean-up case. However, the program package is intended to become generally applicable for solving problems of soil contaminations with VOC. Variables such as size, position and number of extraction wells, or air extraction rates will be considered as control variables for the optimization procedure. The technical goals are to increase the efficiency, to decrease the costs, to calculate impact-radii, and to predict duration, remediation progress, and the output of the pollutants. The partner company will further develop the simulation package for optimizing the soil venting systems to a level of applicability. Considering the relatively large number of old contaminations and recent or new pollution by VOC significant improvements of the soil venting technique could be of great interest for companies, clients, and the public certainly, because of the costs connected with the remediation of contaminated soils.
Gas flow for a single extraction well with an open soil surface.
On one of the remediation sites in Germany an estimated 100 tons of VOCs have seeped to the upper three to five meters of the soil in an area of about 20,000 m^2. This area contains several buildings with basements. Its surface is partially sealed by an asphalt layer. Boreholes with soil patterns are denoted by colored points.
Remediation
site.
The 3-D domain is insulated at the top and bottom boundaries. The vertical thickness is small compared with the horizontal lengths. The soil matrix is horizontally layered. The air flow is essentially horizontal. These assumptions allow the vertical integration of the air permeability. Buildings are considered with basements.
Vertically
integrated air permeability = 2-D air transmissivity.
The following figures show the concentration of chemicals on this site. Measurement points are black colored. The concentration outside the measurements points was found by method of ``Kriging'' (cf. Journel and Huijbregts: Mining Geostatistics, Academic Press, London 1978).
cis-1,2-Dichlorethen 
Tetrachlorethen 
Trichlorethen
Air
flow field and pressure for given discharges at active wells.
Flow
field. Colors denote the length of the flow velocity.
Optimization
The optimal control aspect of soil venting consists of optimizing the remediation process with respect to its efficiency. There are several conflicting goals:
It is by no means obvious how to formulate an appropriate mathematical objective/cost functional that adequately takes all these points into account (the choice of the ``objective'' function is highly ``subjective'').
Positions
and the sum of discharges (= 431.646 [g/s]) for all active wells are given.
Optimal distribution of discharges with maximal extraction rate of chemicals
(J = 0.119 [g/s]) from the whole remediation site is shown in the figure.
The extraction of NAPLs is denoted by a rectangle (width=discharge, hight=concentration,
area=extraction of NAPLs) at each active well. Color of streamlines denotes
the concentration of NAPLs.
New
positions and the sum of discharges (= 10 [g/s]) for all active wells are
given. For this case, the maximal extraction rate of chemicals (J = 0.107
[g/s]) from the whole remediation site was obtained.
The second picture shows how important the placement of active wells is. Generally, they should be placed into the center of a polution. But the question how to find the optimal place for extraction wells remains an open question.