Resistance Monitoring

Westbrook, Rex and Bohun, Sean C. (2002) Resistance Monitoring. Canadian Industrial Problem Solving Workshops > 6th IPSW [Vancouver 27/5/2002 - 31/5/2002].

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Abstract/Summary

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.

Item Type:	Study Group Report
Study Group:	Canadian Industrial Problem Solving Workshops > 6th IPSW [Vancouver 27/5/2002 - 31/5/2002]
Company Name:	McMillan-McGee Corporation
Industrial Sector:	Materials None/Other
Additional Contributors:	Barannyk, Lyudmyla and Bolton, Matthew and Donaldson, Roger and Frigaard, Ian and Gilmore, Jeff and Han, Ying and Huang, Huaxiong and Lehr, Heather and McGee, Bruce and Mubayi, Anuj and Myers, Tim and Pierce, Anthony and Roy, Bidhan and Segin, Tatyana and Zou, Quinze
ID Code:	179
Deposited By:	Michele Taroni
Deposited On:	13 October 2008

Problem Statement

MacMillan McGee Corp. is involved in the removal of soil contaminants using a process in which a set of electrodes is placed in the soil and the soil is heated by passing a current through it. The electrical conductivity of the soil, and hence the heat generated, is enhanced by pumping heated water in at some of the electrodes and removing it at a well (or set of wells). The heated water also provides some convected heating, which in the case of soil, far exceeds the conductive heating.

The problem of interest is that of estimating the temperature field in the region of interest, the contaminated region, using measurements of electrical potential and current and also of temperature, at accessible points such as the wells and electrodes and the soil surface. These measurements in conjunction with the field equations for the electrical potential and temperature provide a mathematical "Inverse Problem".

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