Accuracy of Continuous Level Measurement Systems in Dry

Accuracy of Continuous Level Measurement Systems in Dry Bulk Applications and Performance Expectations By Greg De. Rudder, Technical Sales Support Manager Monitor Technologies LLC Copyright © 2004, Monitor Technologies LLC. All rights reserved

CM Console Picture Multi-Station and Single Station CM 3 A and CM 4 Control Console 2

Weight, the Final Frontier! 3

Factors Contributing to Errors in Calculated Values • • Error in Height & Width Cone Height Inside Diameter Corrugated Walls Bulk Density Packing Factors Bridges & Rat Holes 4

Factors Contributing to Errors in Calculated Values • Inside Diameter vs: Outside Diameter The dimensions shown at left represent a difference of 1 inch of silo diameter error. Using the OD of 15 feet (a radius of 7. 5’) calculates a volume per linear foot of 176. 714 ft 3. To Outside To Inside Using the radius of 7. 46, the volume is 174. 834 ft 3. The difference is 1. 88 ft 3 per linear foot. If your Bulk Density is 40 lbs/ft 3, the weight error is 75. 2 lbs/ft. A 30 ft straight wall would represent an error of 2, 256 lbs. 40 feet would represent 3, 008 lbs. 5

Terms and Other Considerations • • Direct Distance Measurement Calculated Level Measurement Calculated Volume Measurement Bulk Density Calculated Weight Representation Angle of Repose Packing Factor 6

• Distance to material is actually measured • Material Level is calculated • Level = Vessel Height - Distance Measured 7

• Calculated Volume Measurement Vcyl = π r 2 H =3. 14 x 56. 25 x 4. 85 =856. 63 ft 3 Vcone =. 2618(D 2 + Dd + d 2) H =. 2618(225 +15 + 1) 6. 6 = 416. 42 ft 3 8

Definitions • Bulk Density is weight as a function of volume = ______ 3 9

Definitions • Calculated Weight Representation – Weight Approximations can be easily calculated when the volume of material and the Bulk Density of the Material are known Material Weight = Material Volume x Bulk Density 10

Assumptions • The Vessel is center filled from a single point on center • The sensor (if smart weight & cable) is mounted at 1/6 th Diameter from the outer wall • The vessel is discharged from the bottom on center When a Silo. Patrol unit is mounted at 1/6 D, the volume of air represented in Green equals the volume of material represented in Red 11

Vred = π r 2 h/3 = (3. 14 x 25 x 2) / 3 =52. 33 ft 3 Vgreen = Volume of 1 ft of straight wall = VCyl minus VOrange VCyl = π r 2 h = 3. 14 x 56. 25 x 1 = 176. 625 ft 3 VOrange =. 2618 (D 2 + Dd + d 2) h =. 2618(225 + 150 + 100) x 1 = 124. 35 ft 3 3 Vgreen =176. 625 - 124. 35 = 52. 275 ft 12

Proving 1/6 D Volume Analysis VGreen = Volume of 1 ft of straight wall (VCyl) minus Vorange VCyl = 176. 625 ft 3 VOrange = 124. 35 ft 3 VGreen = 176. 625 ft 3 - 124. 35 ft 3 = 52. 275 ft 3 Vred = 52. 33 ft 3 VGreen = 52. 275 ft 3 =. 055 ft 3 or about 2. 2 lbs. @40 lbs/ft 3 13

Considerations for Equipment that does not use Gravity • When using Ultrasonic measurement equipment there will almost always be an angle in the measurement to consider that, because of gravity, does not exist with plumb bob type measurement 14

(@ 1/6 D) 15

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Ultrasound Flight Characteristics A Sensor that is aimed straight down in an empty silo condition is prone to false material Distance measurements. In this example, with 23 feet being programmed as the maximum measuring distance, we can expect the display to reflect the time of flight of Echo 1 to be interpreted as the Valid Echo for the following pulse. The net result would be a displayed distance of around 8 feet. 17

Effects of Angle of Repose and Sensor Mounting location @ 200 of Material Slope 18

Accumulation of Error In the chart above, 4 of 5 variables are slightly altered one at a time. See the error figures in each column and how the accumulate. Please note that Bulk Density has the most severe impact on the accuracy of volume and weight calculations. 19

Consider a Silo That can Hold 133, 036 lbs of Material Published Accuracy of Silo. Patrol equipment is: <. 5% of the Distance Measurement Published Accuracy of Ultrasonic Equipment is: 3326 ft 3 133, 305 lbs. . 2% of the distance/. 05% of the range Published accuracy of Load Cell System is: . 2% Full Scale 20

A Distance measurement of 16 feet is taken. . . Published Accuracy of Silo. Patrol equipment is: <. 5% of the Distance Measurement =. 08 feet so, worst volume error = 14. 13 ft 3 = 565 lbs Published Accuracy of Ultrasonic Equipment is: . 2% of the distance/. 05% of the range =. 032 feet so, worst volume error = 5. 6 ft 3 = 226. 08 lbs. Published accuracy of Load Cell System is: . 2% Full Scale = 233. 26 lbs worst case 21

List Price Comparison for four Silos • 16 Load Cells & Mounting Plates • Display, Analog Card, Scanner – List less installation costs • SMU for 4 Silos • 8 Channel HMI – List for Silo. Patrol less installation • Ultrasonic and Accessories – Does not include Display Device $17, 680 2, 885 $20, 565 $4, 480 745 $5, 225 $6, 020 22

Summary • • Obtain Accurate Dimensional Data Obtain Accurate Bulk Density Information Follow Factory Installation Guidelines You should get acceptable - repeatable calculated measurement data • If you still need better accuracy numbers, employ the use of a Linearization Table or Curve-Fit-Weight Table 23

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