Download The Problems of Using USMs at Low Reynolds Numbers (High

The Use of Liquid USMs in the Transition and Laminar Flow Region- Measurement of High Viscosity Oils
The Problems of Using USMs at
Low Reynolds Numbers (High
Viscosity Oils)
Terry Cousins,
CEESI
Acknowledgement
• I must thank Dr. Gregor Brown of Cameron for some
of the data presented here.
INTRODUCTION
• Even with the low cost of oil there is still a “scrabble”
to find and bring on line more.
• In many cases the production now contains large
larger quantities of “heavier” oils.
• We now are aware the most (All!!) meters are
influenced by Reynolds number.
• In general the major effects of Reynolds number are
at the low values.
• This takes us into the TRANSITION and LAMINAR
regions of fluid operation.
• It is the “heavy” oils, the higher viscosity oils that pull
us into this region.
Reynolds Number
• Inertia Forces/Viscous Forces
Linearising USMs
• I hope that we all accept now that USMs of all
persuasions are not basically linear under all
conditions within the scope of most Custody transfer
lquid requirements.
• Reynolds number is one of those conditions that can
cause non-linearity.
• They have to be linearised to make them meet the
specifications and requirements for operation,
particularly for Custody transfer metering.
• This requires a knowledge of the Operating Reynolds
number.
High Viscosity Challenges for USMs
Signal Transmission
Flow Challenge
• The basic flow curve often non-linear even in
turbulent region.
• The flow changes from turbulent to transition flow and
then Laminar.
• In transition the flow is very unsteady.
• The starting and stopping points of transition vary with
conditions
• In laminar flow temperature gradients are an issue.
Examples of Non Linearity-USM
Profile Change
and Error due
to method and
temperature
Laminar
Region
Profile Change
and Error due
to method,
temperature
and erratic
changes
Transition
Region
Turbulent Region
1%
Profile Change and Error
due to method
Claimed Final Linearity +/- 0.15%
Transition
• I have become aware that even with some
knowledge of fluid mechanics there is a very
naïve understanding of the nature of
transition.
• A recent view as expressed to me that
transition happened between 6000 and 2000,
full stop.
– The assumption is therefore corrections
can be carried out in this area and they will
be the same in all applications!!!
Transition
• What does transition look like?
– In technical terminology it is a mess!
– During transition:
• The profile switches, for laminar to turbulent profile.
• The fluid changes turbulent levels from laminar to
turbulent.
• There is no control over the switching, so the two will be
in packets of indeterminate duration.
• The appears to be no discreet point of change-there is a
mixing region of indeterminate duration.
Transition
• What causes it start or stop?
– The onset and stopping of transition
appears to be a function of:
–Installation
–Roughness
–Molecular structure
–Fluid properties
–The mixture
–Fluid mechanical operation.
What Does it Look Like?
• It appears as “slugs” ,sections of fluid
changing from laminar to turbulent.
• There is a mixing region between them.
• The profile varies from parabolic to turbulent.
• The turbulence levels vary from full to very
little with all shades in between
• It is unstable
Transition
• “Reynolds found that the transition occurred
between Re = 2000 and 13000, depending on the
smoothness of the entry conditions. When extreme
care is taken, the transition can even happen
with Re as high as 40000. On the other
hand, Re = 2000 appears to be about the lowest
value obtained at a rough entrance.
Four Path USM
1.050
Normalised Velocity
1.000
0.950
0.900
0.850
0.800
0.750
1
2
3
Path Number
A - Diametric Meter
B - Chordal Meter
Outside paths
Inside paths
= Flatness ratio
4
Transition
Standard Deviation sometimes called Turbulence - Deviation of indivual path
velocities obtained from the meter
Path Velocity Standard Deviation
30%
Calibration at
Manufacturer
Calibration at SPSE
25%
20%
Outer
Paths
Path 1
Path 2
Path 3
Path 4
15%
10%
5%
0%
Inner Paths
1,000
10,000
Pipe Reynolds number
Velocity profile changes
Flatness ratio= (V1+V4)/(V2+V3)
0.900
12-inch meter, 100-140 cSt, 28-35 deg C
Turbulence
0.800
Flatness Ratio
6-inch, 100-200 cSt, 20-30 deg C
0.700
0.600
Transition
0.500
0.400
0.300
100
Laminar
1,000
10,000
Reynolds Number
100,000
Transition
Transition
Examples of Non Linearity-USM
Profile Change
and Error due
to method and
temperature
Laminar
Region
Profile Change
and Error due
to method,
temperature
and erratic
changes
Transition
Region
Turbulent Region
1%
Profile Change and Error
due to method
Claimed Final Linearity +/- 0.15%
Alleviation!
•Move the outer transducers away
from the walls. (other errors will
come into play)
•Accept a larger error and
repeatability in this range.
•Use a flow noise producer close to
the meter
Solution!
Use a reduced bore meter.
• The sudden contraction causes the flow to:
• Flatten, so profile changes are less.
• The relative turbulence is reduced.
• The apparent Reynolds number increases.
• Like so much in fluid mechanics ideas have been there for
a long time. It is a standard method used in windtunnels
since the 1930s to reduce turbulence
Modified profile behaviour
With reducing nozzle
1.4
1.4
1.3
1.3
1.2
1.2
Normalised Path Velocity
Normalised Path Velocity
No reducing nozzle
1.1
1.0
0.9
Re = 1,000
0.8
Re = 7,000
0.7
0.6
0.5
1.1
1.0
0.9
Re = 1,000
0.8
Re = 7,000
0.7
0.6
0.5
0.4
0.4
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
Path Radial Location
0.6
0.8
1
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
Path Radial Location
0.6
0.8
1
Modified profile behaviour
1.000
6-inch, 100-200 cSt, 20-30 deg C
0.900
Flatness Ratio
6-inch meter with reducing nozzle
0.800
0.700
0.600
0.500
0.400
0.300
100
1,000
Reynolds Number
10,000
Modified statistical/ repeatability behaviour
No reducing nozzle
With reducing nozzle
30%
Path 1
Path 2
Path 3
Path 4
25%
Path Velocity Standard Deviation
Path Velocity Standard Deviation
30%
20%
15%
10%
5%
0%
Path 1
Path 2
Path 3
Path 4
25%
20%
15%
10%
5%
0%
1,000
10,000
Pipe Reynolds number
1,000
10,000
Pipe Reynolds number
Laminar Flow
• At face value laminar flow should be easy,
there is no turbulence.
• With no temperature difference between the
pipe walls and the fluid it is easy to measure.
• As soon as there is a difference a temperature
gradient forms in the pipe.
• This causes large errors if not resolved.
Laminar Flow
• Because oil has a poor thermal conductivity
the different temperature layer form around the
pipe wall.
• This causes the ultrasound to refract, and the
angle of transmission changes.
Thermal gradients
• In laminar flows
there is no turbulent
mixing of the oil
• Therefore if the pipe
wall is cooler (or
hotter) than the oil
temperature,
thermal gradients
will form
Thermal gradients
Correct
Transmission
Refracted
Transmission
6-inch full bore meter
1.040
1.3 cSt
4 cSt
11 cSt
22 cSt
75 cSt
215 cSt, 20 deg C, NEL
55 cSt, 45 deg C, NEL
120 cSt, 30 deg C, NEL
20 deg C NEL repeat
30 deg C NEL repeat
1.035
1.030
1.025
1.020
Meter Factor
1.015
1.010
1.005
1.000
0.995
0.990
0.985
0.980
0.975
0.970
100
1,000
10,000
Reynolds Number
100,000
1,000,000
How can I tell if I have a gradient problem?
• Fortunately, with a chordal multipath design the
‘inside’ paths respond differently to the ‘outside’ paths
• Even the top path responds differently to the bottom
path, owing to partial gravity based stratification
• The effects are most noticeable in terms of the
velocity of sound variations path to path
Solutions
•They are difficult:
•Insulation of the pipes
•Heating of the pipes
•Mixers upstream
•There is a patented calculation to
correct for the refraction
•All work to a greater or lesser
extent.