Pseudo Steady State Gas Flow in Tight Reservoir under Dual Mechanism Flow

Gas reservoirs with low permeability (k<0.1 mD) are among the unconventional reservoirs and are commonly termed as "Tight Gas Reservoirs". In conventional gas reservoirs that have high permeability, the flow of gas is basically controlled by the reservoir permeability and it is calculated using the Darcy equation. In these reservoirs, gas flow due to gas diffusion is ignored compared to Darcy flow. However, diffusion phenomenon has a significant impact on the gas flow in tight gas reservoirs and the mechanism of gas diffusion can no longer be ignored in comparison to Darcy flow. In this study, a dual mechanism based on Darcy flow as well as diffusion is used for the gas flow modeling in tight gas reservoirs. The diffusivity equation is obtained using this method that it indicates the gas flow in a porous media. The conventional dry gas pseudo pressure function is not able to linearize the diffusivity equation including diffusion effect. Subsequently, a new real gas pseudo pressure function is used and a novel real gas pseudo time function is introduced. These pseudo functions consider changes in gas properties with pressure and linearize the diffusivity equation. The linear diffusivity equation is solved analytically for constant gas flow boundary condition under Pseudo Steady State (PSS) situation. Then, pseudo steady state analytical solution, based on new functions of pseudo pressure and pseudo time, is obtained. The calculation of reservoir parameters such as permeability, effective diffusion coefficient and original gas in place (OGIP) using reservoir data is the first application of analytical solution. Reservoir data is required to analysis the results of application of introduced model in low permeability gas reservoir.