Radial Curvilinear Motion in a Free Flow of Compressible Viscoplastic Oil in a Homogeneous Formation

Abstract

The paper presents a solution to a steady-state hydrodynamic problem dealing with one-dimensional free-surface radial flow of compressible viscoplastic oil in a horizontal homogeneous circular formation. A vertical producing oil well is located in the centre of the formation, penetrating the pay zone fully, with no well casing or perforation present. We used generalised Darcy's law and equations of state for a compressible fluid to determine mass flow rate of the compressible viscoelastic oil and derive equations for current density, oil flow rate, current pressure distribution in the drainage area, and current pressure gradient. The equations take into account oil compressibility and initial pressure gradient. We also determined the time it takes an oil particle to reach the well starting from the current radius vector and from the external boundary. This is the case when the oil deposit lies close to the earth surface. This depth range features no shale beds or interbedded formations. Since subsurface mining is possible with shallow oil deposits, both wells and tunnels may be used for production.