A theoretical model for capacitance measurement of liquid films in an annular flow

Colin Atkinson,Ruoxi Huang

doi:10.1186/s40929-016-0003-6

Abstract

This paper develops mathematical models for a proposed production logging tool, which uses capacitance sensors to measure liquid annulus thickness and liquid type for a primarily gas-carrying wellbore. A semi-analytical method is devised which uses Fourier analysis to account for the complicated system geometry and reduces the problem to singular integral equations over a sensor electrode. Approximate solutions of these integral equations give expressions for capacitance, which is calculated for different liquids and varying liquid annuli thicknesses and electrode positions. These results are compared with capacitance values found using COMSOL Multiphysics, a finite element package. Good agreement is obtained between these two methods, with a discrepancy range of 1–8 %. Capacitance values obtained range from 32 to 93 pF/m, and sensitivity is estimated to range from 0.8 to 60 %, depending mainly on the proximity of the electrode to the liquid and also on the permittivity and thickness of the liquid layer. Practical implications of the study are also discussed. Realistically useful measurements, where ~0.2 mm of liquid is detectable, can potentially be made using an electrode 4–6 mm away from the inner wellbore wall.

Highlights

In oil and gas production, a technical service known as production logging (PL) is used to identify different fluid phases in the wellbore and measure the flow rates of each
The presence of boundaries creates image sources which contribute an interaction potential term. This term may be quite complicated due to the different natures and geometries of the boundaries and the geometry of the source and the potential cannot be solved in closed form
The geometric parameters do not need to be scaled for the theoretical results as the widths of the plates have already been taken into account

Summary

Introduction

In oil and gas production, a technical service known as production logging (PL) is used to identify different fluid phases in the wellbore and measure the flow rates of each. A sensor carrying tool can be deployed downhole to measure production rates at different depths, so that entry points of fluid flow can be located. This serves as a useful diagnostic tool and can help with well management. The presence of boundaries creates image sources which contribute an interaction potential term This term may be quite complicated due to the different natures and geometries of the boundaries and the geometry of the source and the potential cannot be solved in closed form. The total potential due to the distribution of sources and interaction potentials is Φ

Objectives

Results

Conclusion