Petroleum Reservoir Engineering by Non-linear Singular Integral Equations

For the determination of the properties of several reservoir materials, when oil reserves are moving through porous media, a new mathematical approach is proposed. Such problem is very much important for petroleum reservoir engineering. Thus, the above mentioned problem is reduced to the solution of a non-linear singular integral equation, which is numerically evaluated by using the Singular Integral Operators Method (S.I.O.M.). Beyond the above, several properties are analyzed and investigated for the porous medium equation, defined as a Helmholtz differential equation. Finally, an application is given for a well testing to be checked when an heterogeneous oil reservoir is moving in a porous medium. Hence, by using the S.I.O.M., then the pressure response from the well test conducted in the above heterogeneous oil reservoir, is numerically calculated and investigated.