Author(s)

R. C. Callarotti

Abstract

We analyze the problem of the capacitive measurement of the height of a liquid in a cylindrical storage tank whose outer structure is connected to the ground. The system is excited electrically by applying a time varying voltage between a disk shaped electrode (located at the centre of the tank) and the external tank wall. The theoretical solution for the pertinent Maxwell’s equations is derived for a liquid characterized by a given real permittivity ε_L and zero conductivity. The space above the liquid is air. The problem is reduced to the solution of the Laplace equation for a multiply connected region. The validity of the analytical solution is checked against a numerical based on an equivalent circuit for the system. The case where the liquid is considered as having a given conductivity is also considered. Finally, we include a discussion concerning the application of this type of instrumentation in the case of storage tanks used in the petroleum industry.

Keywords

inductive measurements, numerical procedures, oil production