Analyzing Oil Reservoir Dynamics: Leveraging Separated Variable Solution of Radial Diffusivity Equation with Constant Bottom Flux

The demand for oil and its subproducts is steadily increasing, making the study of oilfields and in particular oil wells a crucial aspect of exploitation engineering.Information obtained from fluid filtration and the study of pressure drop in reservoir conditions is of great importance in determining the productive capabilities of the oilfield reservoir.The behavior of fluid flow in a reservoir is usually modeled by a nonlinear partial differential equation (PDE), which is often simplified to a linear form in the petroleum industry for practical applications.This paper presents an analytical solution using the separable-variable technique for the constant-flow radial diffusivity equation, which describes the pressure drop in the near-wellbore region under conditions of constant oil production.The production data for the Amonica oilfield were provided by the Geological Institute of Oil and Gas in Fier, Albania.Our findings underscore the importance of depletion time, production rate, and reservoir radius in calculating pressure drops.A sensitivity analysis shows that the primary factors influencing the pressure profile are several parameters such as permeability, porosity, and viscosity.Additionally, we determined that the radial diffusivity equation solution for a finite constant flow rate during the initial transient flow period can be derived using the separable-variable method, which was approximated by the so-called linear solution.It is assumed that, in comparison to infinite reservoirs, the well radius is negligible, and the area near the wellbore can be treated as a point source.