Recently, a method for removing contaminants from soil (several meters under the ground) has been proposed by McMillan-McGee Corp. The process can be described as follows. Over a period of several weeks, electrical energy is introduced to the contaminated soil using a multitude of finite length cylindrical electrodes. Current is forced to flow through the soil by the voltage differentials at the electrodes. Water is also pumped into the soil via the injection well and out of the ground at the extraction well. The soil is heated up by the electrical current and the contaminated liquids and vapours are produced at the extraction well. The temperature of the contaminated soil, during the process, is believed to reach the maximum value (the boiling temperature of water). Normally, the electrodes are placed around the contaminated site and the extraction well is located in the centre of the contaminated region. The distance between the electrodes is usually seven to eight meters. The distance between the extraction well and an electrode is about four meters. The diameter of the electrodes is 0.2 meter and the extraction well is 0.1 meter in diameter. The reason for using the electrical current is that “flushing” the soil using water alone is not effective for removing the contaminants. By heating up the soil and vaporizing the contaminated liquid, it is anticipated that rate of extraction will increase as long as the recondensation is not significant. A major concern, therefore, is whether recondensation will occur. Intuitively, one might speculate that liquid phase may dominate near the injection well. Moving away from the injection site towards the extraction well, due to the combined effects of lower pressure and higher temperature (from heating), phase change occurs and a mixture of vapour and liquid may co-exist. There may also be a vapour-only region, depending on the values of temperature, pressure, and other parameters. In the two-phase zone, since vapour bubbles tend to rise due to the buoyancy force, and the temperature decreases along the vertical path of the bubbles out of the heated region, it is possible that the bubbles will recondense before reaching the extraction well. As a consequence, the probability exists that part of the contaminants stay in the soil. Obviously, to predict transition between single-phase and two-phase regions and to understand the transport phenomenon in detail, a thermal capillary two-phase flow model is needed. However, to simplify the problem, here we only consider the case when two-phases co-exist in the entire region
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