Sensitivity analysis for a 4-sensor probe used for bubble velocity vector measurement

In recent years, there has been an increase in the level of interest shown in making flow rate
measurements in multiphase flow. This in part has been brought about by the metering requirements
of the oil and natural gas industries. Measuring the volumetric flow rate of each of the flowing
components is often required and this is particularly true in production logging applications, where it
may be necessary to measure the flow rates of oil and water down hole in vertical and inclined oil
wells. Within the University of Huddersfield [1], work has been undertaken on the study of vertical and
inclined multiphase flow. Previous work was based on the use of local, dual-sensor conductance
probes to obtain the local axial velocity and volume fraction of the bubbles in multiphase flows [1]. The
purpose of this research presented in this paper is to investigate the sensitivity of 4-sensor-probes,
used for bubble velocity vector measurement to dimensional measurement errors of the probe and to
errors in measuring the time intervals between the surfaces of the bubble contacting the sensors in the
probe.

The probe was manufactured from 0.3mm diameter stainless steel acupuncture needles due to their
high level of rigidity. The acupuncture needles were mounted inside a stainless steel tube with an
outer diameter of 4mm [2]. A procedure was carried out whereby an error on a specific probe
dimension was introduced (errors in the range of -10 % to +10% of the true value of the dimension
were used). The error in the measured bubble velocity vector was then investigated. A similar
procedure was used to investigate the effect of measurement errors in the probe ‘time intervals’δt11 ,
22 δt and 33 δt on the measured bubble velocity vector. NB:The bubble velocity vector is quantified in
terms of a polar angle α an azimuthal angle β and a velocity magnitude v .
Results demonstrate that it is crucial to measure probe dimensions precisely (within the range of ±1%)
as small errors in the probe dimensions or measured time intervals can give rise to large errors in the
values ofα , β and v .