Physical modelling of the electromagnetic heating of oil sand and other earth-type and biological materials

Maxwell's equations and the thermal equation for heat flow are examined and scaling criteria are developed which show that it is possible to construct scaled physical models in which the electromagnetic and thermal phenomena of the full scale system can be modelled simultaneously. Simultaneous modelling is made possible by simulating electromagnetic frequency and thermal events on different time scales. It is also shown that simultaneous modelling of electromagnetic and thermal phenomena can be carried out when the electrical conductivity of the medium of the full scale system is temperature dependent. In this case electromagnetic frequency and thermal events are still modelled on different time scales; the time variation of the envelope of the electromagnetic field distribution, however, is modelled on the same time scale as thermal events. The electrical and thermal properties of oil sand and the general problem of in-situ recovery of oil therefrom have been used to guide the development of the modelling criteria. The results obtained can be applied to a large class of other problems as well, such as electromagnetic heating of earth-type materials in the mining and construction industry, as well as the electromagnetic heating of food stuffs and biological tissue.