Parametric analysis of diffusivity equation in oil reservoirs

The governing equation of fluid flow in an oil reservoir is generally non-linear PDE which is simplified as linear for engineering proposes. In this work, a comprehensive numerical model is employed to study the role of non-linear term in reservoir engineering problems. The pervasive sensitivity analysis is performed on rock and fluid properties, and it is shown that rock permeability and fluid viscosity are the most significant parameters which influence the pressure profile. Moreover, the critical reservoir radius was determined in four different cases including heavy and light oil along with high and low permeable rocks, in which the pressure difference of linear and non-linear diffusivity equation is significant. Results of this study give an insight into proper simplification of diffusivity equation and provide an engineering-based decision strategy for different reservoir properties having certain rock and fluid properties in oil reservoirs. The results show the significance of depletion time, production rate, and reservoir radius in calculation of pressure drop.