Abstract
By using a non-linear 3-D elastic waves real-time expert system, the new theory of ‘real-time expert seismology’ is proposed, for the exploration of the on-shore and off-shore oil and gas reserves all over the world. This highly innovative and groundbreaking technology is working under real time logic for searching the on-shore and off-shore petroleum reserves developed on the continental crust and in deeper water ranging from 300 m to 2,500 m, or even deeper. Furthermore, for the determination of the properties of the reservoir materials, when oil reserves mixed with water in multiphase flows are moving through porous media, a new mathematical device is proposed. The above problem is very much important for petroleum reservoir engineering and the oil industry. Hence, such a problem is reduced to the solution of a non-linear singular integral equation, which is numerically evaluated by using the singular integral operators method (SIOM). Also, several properties are analysed and investigated for the porous medium equation, defined as a Helmholtz differential equation.
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