Petroleum Reservoir Engineering by Non-linear Singular Integral Equations

Abstract

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.

Impact of uniform and non-uniform heated rods on free convective flow inside a porous enclosure: finite element analysis

“…Free convection in permeable enclosure has gained major attention in past years due to its numerous applications in medical, engineering, geophysics and industries such as circulatory system, biomass transport, cooling of electronic equipment, combustion technology, thermal insulation of buildings, solar energy systems, petroleum reservoir, energy storage, deep bed filtration, solar air heater, reduction of aerodynamic noise, greenhouses and geothermal reservoirs [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. Many researchers have adopted experimental, numerical and theoretical approaches to explore fluid flow and thermal distribution in several porous cavity.…”