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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.