Here we have studied the fingering phenomena in fluid flow through Fracture porous media with inclination and gravitational effect and investigate the applicability of Adomian decomposition method to the nonlinear partial differential equation arising in this phenomena and prove the convergence of Adomian decomposition scheme, which leads to an abstract result and an analytical approximate solution to the equation. Finally developed a simulation result of saturation of wetting phase with and without considering the inclination effect for some interesting choices of parametric data value and studied the recovery rate of the oil reservoir with dimensionless time.

The interpretation of the pressure data of naturally Fractured reservoirs (NFRs) has particular significance. The most famous theory for analyzing the pressure data of NFRs is the dual-porosity model presented by Warren and Root. Recent studies have shown that the dual-porosity model may not be appropriate for interpreting well test from all NFRs because this model has limits. In this study, the pressure transient response of naturally Fractured reservoirs was investigated by using numerical simulation without considering analytical and semi-analytical methods. To this end, a set of models including connected and disconnected Fracture networks was simulated in the numerical simulator. The Warren and Root well-testing signature was observed in all simulations but it was highly evident for a well was located in the matrix and was negligible for a well that was intersected by Fractures. The results of the simulation for the well that was intersected by Fractures showed the bilinear flow regime with the slope of 1/4. The period of this flow regime increased in the unconnected Fracture network and changed to the linear flow regime with a slope of 1/2 in two cases: firstly, by increasing Fracture permeability in the connected Fracture network, secondly, in the small-unconnected Fractures. Moreover, the sensitivity analysis was performed on the well location in the connected Fracture network. This research showed that by decreasing the distance between well and Fracture network, the transition period becomes deeper and appears earlier.

The present investigation is concerned with the reflection and transmission of plane waves at a interface between two swelling porous elastic half-spaces in welded contact. It is found that their exist two longitudinal waves and two transverse waves. The expression for various amplitude ratios due to the incidence of longitudinal wave in solid (PS) /longitudinal wave in fluid (PF) / transverse wave in solid (SVS) / transverse wave in fluid (SVF) have been obtained and depicted graphically. It is found the amplitude ratios of reflected and transmitted waves are the functions of angle of incidence and are a effected by the swelling porousity of the media. Surface response at the interface have also been obtained. The results so obtained have been compared with (without swelling porous) elastic medium (EL).The present investigation has immense application in structural problems.