This chapter concerns the phenomenon of leaks (gryphons) caused by the growth of undetected cavities and fissures filled up by oil/vapor, between different layers in laminated structures, acted upon by the pressure and temperature of the penetrated fluid. This unaccounted process caused many catastrophes, including the Chernobyl and Fukushima nuclear power stations’ disasters, and the summer 2010 disaster in the Gulf of Mexico as a result of the breakthrough of gryphons in two boreholes. Therefore, a special attention is given to the development of casing string gryphons and cylindrical gryphon cracks. The problem solutions using invariant integrals are obtained in a closed, very effective shape. This chapter is for those who work or interested in oil and gas industry, and for those who design and operate nuclear power stations.
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