Resistance Monitoring

The problem considered was that of estimating the temperature field in a contaminated region of soil, using measurements of electrical potential and current and also of temperature, at accessible points such as the wells and electrodes and the soil surface. On the timescale considered, essentially days, the equation for the electrical potential is static. At any given time the potential $V$ satisfies the equation $\nabla \cdot (\sigma \nabla V ) = 0$. Time enters the equation only as a parameter since $\sigma$ is temperature and hence time dependent. The problem of finding $\sigma$ when both the potential $V$ and the current density $\sigma \partial{V} / \partial{n}$ are known on the boundary of the domain is a standard inverse problem of long standing. It is known that the problem is ill posed and hence that an accurate numerical solution will be difficult especially when the input data is subject to measurement errors. In this report we examine a possible method for solving the electrical inverse problem which could possibly be used in a time stepping algorithm when the conductivity changes little in each step. Since we are also able to make temperature measurements there is also the possibility of examining an inverse problem for the temperature equation. There seems to be much less literature on this problem, which in our case is essentially, a first order equation with a heat source.(We neglect thermal conductivity, which is small compared with the convection). Combining the results of both inverse problems might give a more robust method of estimating the temperature in the soil

In-Situ Thermal Remediation of Contaminated Soil

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

SIMPLE MODELS FOR AN INJECTION

ABSTRACT. We develop simple models that can be used to predict the forces of impact that occur during the injection molding process involving a magnesium alloy. We model the impact of the injection molding screw tip on the molten material entering the mold, and the impact of the piston flange on the machine housing, which can occur when the amount of material that has been injected into the mold is insufficient to completely fill the mold. We consider the effects due to the elasticity of the molten material and machine parts, those due to the presence of a thin film of hydraulic fluid between the piston flange and machine housing, the variation of the viscosity of the hydraulic fluid, and those due to the leakage of molten metal past the screw tip. With the simple models developed here, an injection molding machine designer can predict how varying the process parameters may affect the impact forces, and thus, may be able to more efficiently design the machine so that damage is less likely to occur during operation. This will result a longer life for the machine, which will lead to increased cost effectiveness for the manufacturer