Understanding the Uncertainty when Using a Type Coefficient for Temperature Corrections of a Coriolis meter. Dean M. Standiford Emerson-Micromotion

Transcription

1 Understanding the Uncertainty when Using a Type Coefficient for Temperature Corrections of a Coriolis meter Dean M. Standiford Emerson-Micromotion

2 Temperature Correction of Micro Motion, Inc. Coriolis Mass Flowmeters Dean Standiford Director Global Calibration Quality

3 Overview Purpose: To help Micro Motion, Inc. (MMI) customers understand the impact of using a Type coefficient as the temperature correction factor with MMI Coriolis flowmeters. Scope: Mass flow with MMI Coriolis flowmeters Historical data available for Elite meters Temperature calibration with water Approximately 20 C to 60 C fluid temperature Ambient room conditions 3

4 Agenda Real World Application (Why does it matter?) MMI Temperature Correction Factors Determining the Temperature Correction Factor Understanding the Uncertainty Conclusion Other Items to Consider (Best Practices) 4

5 Real World Applications Export system from a production platform North Sea UK applications follow DECC 1 Guidelines that define uncertainty limits of ±0.25% for dry mass in single phase liquid applications. 1 Department of Energy and Climate Change 5

6 Real World Applications Platform Example CMF300M (stainless steel) Calibration at 20 C, operating conditions at 70 C Continuous flowrate, Imperial bbl/day Fluid density, 797 kg/m³ Mass measurement uncertainty of ± 0.25% at $50 per bbl. 11,000 bbl/day x $50/bbl x 0.25% x 365 day/yr > $500K / yr How much of this is influenced by a temperature Type coefficient? 6

7 Temperature Influence A Coriolis flowmeters measurement of mass flow and density is influenced by the stiffness of the vibrating tube(s). This stiffness changes with temperature. Coriolis flowmeters utilize a temperature correction factor to account for this change in stiffness. Mass Flow Stiffness Term Density m = FCF t = E I t FCF = flow calibration factor t = time difference E = modulus of elasticity 7 ω 2 = L m = k t m = E I m t + m f

8 Temperature Influence Young s Modulus (modulus of elasticity) known as the tensile modulus or elastic modulus, is a measure of the stiffness of an elastic material and is a quantity used to characterize materials. Young's modulus From Wikipedia, the free encyclopedia 8

9 Temperature Influence Temperature correction values are applied to each unique equation for mass flow and density measurements and therefore have different values and sensitivities. Sensitivity in relation to Mass Flow m E m = FCF t = E I t Change in modulus directly related to change in mass flow 9

10 Ratio "Modulus of Elasticity" to "Modulus of Elasticity at 0 C" Temperature Correction Factors How are they determined? Method #1 Theoretical value during design based on published material properties 316 Stainless Steel * y = E-04x E Normalized Modulus * Re: 1) Ledbetter, Journal Applied Physics Volume 52, No 3, March ) Peckner and Bernstein, HandBook of Stainless Steels, McGraw Hill, Temperature, C 10

11 Error, % Error, % Temperature Correction Factors How are they determined? Method #2 1.0 Experimentally determined temperature correction based on temperature flow test Typical test, (8) temperatures with (4) flowrates at each temperature DIGITAL BATCH ACCURACY vs MASS FLOW RATE (0.048% / 33 C) x 100 C ~ 0.15% per 100 C DIGITAL BATCH ACCURACY v Flow Temperature Coefficient (FTC) FTC Current: 4.45 FTC Difference: FTC Actual: % error over 33 C Mass Flow Rate, lb/min Mass Flow Ra

12 Temperature Correction Factors How are they determined? Method #3 Experimentally determined temperature correction based on density measurement error of pure water at ~20 C and 60 C. Water is flowing through sensor at ~10% of nominal flowrate Temperature is measured both up and downstream of sensor» Must be within ±0.1 C and cannot vary more than 0.05 C for 5 minutes before measurements can be made 12

13 Temperature Coefficient Variation Understanding the Uncertainty Method #3 provides historical data with low process uncertainties 4.8 CMF300M years of data Large sample size /13/ /17/ /21/ /25/ /29/ /03/ /07/ /11/2014 Calibration Date, mm/dd/yyyy DTC 13

14 Temperature Coefficient, % per 100 C Understanding the Uncertainty Data shows stability over time (8 yrs) Normal Distribution High confidence in average value Population Average % per 100 C 4.8 CMF300M % uncertainty in the mean < 0.006% per 100 C /13/ /17/ /21/ /25/ /29/ /03/ /07/ /11/2014 Calibration Date, mm/dd/yyyy DTC

15 Calibrated Standard Deviation % per 100 C Understanding the Uncertainty Elite Temperature Coefficient Variation Population Std Dev Population Std Dev Average = 0.039% per 100 C CMF025M CMF050M CMF100M CMF200M CMF300M CMF400M 15

16 Understanding the Uncertainty Process capability Repeat Repeat Sensor Population Population Population Meter Meter Model Qty DT Std Dev Qty Std Dev CMF025M CMF050M CMF100M CMF200M CMF300M CMF400M Averages Individual Meter Std Dev Less than Population Std Dev Indicates process is capable 16

17 Real World Applications Platform Example CMF300M (stainless steel) Calibration at 20 C, operating conditions at 70 C Continuous flowrate, Imperial bbl/day Fluid density, 797 kg/m³ Answer: (k=2) or $66K / yr Mass measurement uncertainty of ± 0.25% at $50 per bbl. 11,000 bbl/day x $50/bbl x 0.25% x 365 day/yr > $500K / yr How much of this is influenced by a temperature Type coefficient? 17

18 Conclusions Process uncertainty is ~0.026% per 100 C (k=2) about 1/3 of average population Std Dev Mass error due to utilizing a Type coefficient for temperature results in ~0.078% per 100 C (k=2) Calibration at process conditions must have a lower uncertainty than the Type coefficient to provide additional benefit. 18

19 Other Items to Consider Type of material contributes to modulus sensitivity with temperature Hastelloy (C22) is about 40% less sensitive than stainless steel Large differences between fluid temperature and ambient temperature can lead to additional measurement errors Effects can be minimized with proper insulation 19

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