Accuracy of Continuous Level Measurement Systems in Dry

Bulk Applications and Performance Expectations

By

Greg DeRudder,

Technical Sales Support Manager

Monitor Technologies LLC

Copyright © 2004, Monitor Technologies LLC. All rights reserved

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CM Console Picture

Multi-Station and Single Station CM3A and CM4 Control Console

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Weight, the Final Frontier!

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Factors Contributing to Errors in Calculated Values

• Error in Height & Width

• Cone Height

• Inside Diameter

• Corrugated Walls

• Bulk Density

• Packing Factors

• Bridges & Rat Holes

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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 176.714ft3.

Using the radius of 7.46, the volume is 174.834ft3. The difference is 1.88ft3 per linear foot. If your Bulk Density is 40lbs/ft3, the weight error is 75.2 lbs/ft.

A 30ft straight wall would represent an error of 2,256lbs. 40 feet would represent 3,008 lbs.

R 7.50'

R 7.46'

To Outside

To Inside

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Terms and Other Considerations

• Direct Distance Measurement

• Calculated Level Measurement

• Calculated Volume Measurement

• Bulk Density

• Calculated Weight Representation

• Angle of Repose

• Packing Factor

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• Distance to material is actually measured• Material Level is calculated

• Level = Vessel Height - Distance Measured

11.54'

Vol cone

Vol cylinder

Vol repose

11.46'

Distance

Level

23.00'

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• Calculated Volume Measurement

11.54'

Vol cone

Vol cylinder

Vol repose

Distance

6.60'

4.85'2.00'

1.00'3.85'

10.00'Vcyl = π r2 H

=3.14 x 56.25 x 4.85

=856.63ft3

Vcone = .2618(D2 + Dd + d2) H

= .2618(225 +15 + 1) 6.6

= 416.42ft3

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Definitions

• Bulk Density is weight as a function of volume

= ___________

3

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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

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Assumptions• The Vessel is center filled from a single point on center

• The sensor (if smart weight & cable) is mounted at 1/6th Diameter from the outer wall

• The vessel is discharged from the bottom on center15.00'

2.50'

10.00'1.00'

2.00'

When a SiloPatrol unit is mounted at 1/6D, the volume of air represented in Green equals the volume of material represented in Red

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15.00'

2.50'

10.00'1.00'

2.00'

Vred = π r2 h/3 = (3.14 x 25 x 2) / 3

=52.33ft3

Vgreen = Volume of 1 ft of straight wall = VCyl minus VOrange

VCyl = π r2 h = 3.14 x 56.25 x 1

= 176.625ft3

VOrange = .2618 (D2 + Dd + d2) h

=.2618(225 + 150 + 100) x 1

= 124.35ft3

Vgreen =176.625 - 124.35 = 52.275ft3

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15.00'

2.50'

10.00'1.00'

2.00'

VGreen = Volume of 1 ft of straight wall (VCyl) minus Vorange

VCyl = 176.625ft3

VOrange = 124.35ft3

VGreen = 176.625ft3 - 124.35ft3 = 52.275ft3

Vred = 52.33ft3 VGreen = 52.275ft3

= .055ft3

or about 2.2 lbs. @40 lbs/ft3

Proving 1/6D Volume Analysis

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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

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11.54'

11.46'

Distance

Level

23.00'23.43'

11.01'

(@ 1/6 D)

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23.00'23.61'

21.22'20.64'

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18.64'16.43'

14.83'

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.

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

23.00'

19.16' 18.26' 17.34'

2.50'

2.50'

6.50'

16.50'

Distance Calculated Calculated Calculated DifferenceMeasured Cone Level Volume Weight From Actual

RED 16.5 6.5 410.11 16,404 2,120Magenta 17.34 5.66 357.11 14,284 ActualBlue 18.26 4.74 299.06 11,963 -2,322Black 19.16 3.84 242.28 9,691 -4,593

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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.

1.00'

15.00'

8.00'

47.00'

Actual Adjust H Adjust D Adjust Cone H Adjust BDSilo Height 55.00 54.50 54.50 54.5 54.5Silo Diameter 15.00 15.00 14.92 14.92 14.92Cone Height 8.00 8.00 8.00 7.5 7.5Discharge Diameter 1.00 1.00 1.00 1.00 1.00Bulk Density (lbs./cubic foot) 40.00 40.00 40.00 40.00 39.00Total Volume (Cubic Feet) 8,806.13 8,718.06 8,471.77 8225.52 7757.17Total Weight (Pounds) 352,245.02 348,722.50 338,870.63 329,020.81 302,529.78Volume Error 0 88.06 334.36 492.54 714.59Weight Error 0 3,522.52 9,851.87 9,849.81 26,491.04

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Published Accuracy of SiloPatrol equipment is:

<.5% of the Distance Measurement

Published Accuracy of Ultrasonic Equipment is:

.2% of the distance/.05% of the range

Published accuracy of Load Cell System is:

.2% Full Scale

Consider a Silo That can Hold 133,036 lbs of Material

23.00'

6.50'

3326 ft3

133,305 lbs.

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Published Accuracy of SiloPatrol equipment is:

<.5% of the Distance Measurement = .08feet

so, worst volume error = 14.13ft3 = 565lbs

Published Accuracy of Ultrasonic Equipment is:

.2% of the distance/.05% of the range = .032 feet

so, worst volume error = 5.6 ft3 = 226.08 lbs.

Published accuracy of Load Cell System is:

.2% Full Scale = 233.26 lbs worst case

A Distance measurement of 16 feet is taken ...

23.00'

2.50'

6.50'

16.00'

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List Price Comparison for four Silos

• 16 Load Cells & Mounting Plates $17,680

• Display, Analog Card, Scanner 2,885– List less installation costs $20,565

• SMU for 4 Silos $4,480

• 8 Channel HMI 745– List for SiloPatrol less installation $5,225

• Ultrasonic and Accessories $6,020– Does not include Display Device

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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

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