Numerical modeling for potential relaxation of charged oil in containers

A numerical model that simulates the relaxation process for surface potential at the surface of a charged oil in a grounded metal vessel is developed. In the model, constant (ohmic) conductivity of the oil is assumed, and a surface conduction mechanism for the dissipation of electric surface charge is introduced. Calculations for a cylindrical vessel of diameter D_t, height H_t, and fill fraction F show that the charge relaxation is influenced by vessel geometry and fill level, as expected, and by the absolute size of the vessel as well. In fact, it is found that the effective relaxation time of the surface potential correlates quite well to a dimensionless quantity D_tκ/λ, where κ (in Siemens per meter) is the bulk conductivity of the oil, and λ (in Siemens) is the effective surface conductivity at the oil/air interface