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Dynamic Simulation Model for tracking grain lots in an

elevator AE 503 Term Project

Maitri ThakurAgricultural and Biosystems

Engineering May 2, 2007

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Food TraceabilityISO definition

Traceability is the “ability to trace the history, application, or location of that which is under consideration.”

A grain of wheat or a truckloadA standard location size (field, farm, or

county)A list of processes that must be

identified (pesticide applications or animal welfare)

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Food Traceability Respond to security threats Respond to food safety problems Document chain-of-custody Document production practices (e.g.

organic) Meet consumer desires or social preferences Provide due diligence for safety/quality

assurance Protect integrity of brand name Authenticate claims (e.g. Bordeaux wine)

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Traceability ?

February 2007: Peter Pan Peanut Butter

Product Recall Salmonella Outbreak

March 2007: Simply Fresh Fruit Inc. Recall of

Fresh Cut Fruit Trays: Possible Salmonella Contamination

March 2007: Frito-Lay Recall of 2 oz. Bags of Fritos

Original Corn Chips: Undeclared Milk and Wheat March 2007: Recall of Pet Foods Manufactured by

Menu Foods, Inc. (Melamine found in wheat gluten)

September 2006: FDA Warning on Serious Foodborne E.coli Outbreak in Several States

Source: Food and Drug Administration

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Movement of grains for export in the U.S.

Source: U.S. Grains Council

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Traceability in Bulk Grain Handling

SourceA

SourceB

SourceC

Common Storage Silo

Manufacturing Plant

Cookies

Source: Food and Drug Administration

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Problem Statement Grain lots commingled:

To meet buyer specifications as close as possible and to maximize the profit.

Lot identity is not maintained.

Recent experiences with regulatory issues have introduced a growing need to track product identity

Grain elevators facing the problem of having to segregate their incoming products in batches of different end use quality (e.g. GMO and non-GMO)

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Storage Bin- Grain Flow Methods

FIFO – First In, First OutMass Flow

LIFO – Last In, First Out Funnel Flow

NIFO – Next In, First Out Simultaneous Bin emptying and filling with Funnel Flow

Source: Hazardous Occupations Safety Training in Agriculture

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Objective

The objective of this project is to build a dynamic simulation model that tracks individual grain lots in the outbound load from a grain bin following funnel flow

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Grain and Bin Specifications

Shape : Cylindrical, Flat-bottom, Bottom-draw

Diameter (D): 15 feet (4.6 m)

Opening diameter (d) : 30 cm (0.3 m)

Grain : Soybeans Angle of Repose (Θ) : 35° Coefficient of friction (c) :

0.3 Bulk Density (ρ) : 770 Kg/m3

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m1s m1s

m1gx

Fc Fc

m1

m2

m2s m2sh

ρgAh

Dd

Grain Forces

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Differential EquationsForces acting on m1:

m1g + ρgAh – Fc - Fc=m1d2x/dt2 ……. (1)

where,

m1 = Mass of load 1 g = Acceleration due to Gravity ρ = Bulk Density of GrainA = Surface area of mass m2

h = Height of mass m2

Fc = Frictional Force = cdx/dtc = Coefficient of friction of grain

x = Displacement of mass m1

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Differential Equations

dm1/dt = ρAdx/dt ……. (2)

Σ Q = -dm1/dt + 2*dm1s/dt + dm2/dt = 0

dm2/dt = dm1/dt – 2*dm1s/dt ……. (3)

m1s: f (c, dx/dt, Θ) m1s = k*(cdx/dt)*cos Θ k = 10

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Differential Equations

c1 = m1/(m1+m2) ……. (4)

c2 = m2/(m1+m2) ……. (5)

where,

c1 = Proportion of mass m1 in outbound load

c2 = Proportion of mass m2 in outbound load

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Model Inputs and Outputs Inputs

Mass of load 1 (m1)

Mass of load 2 (m2)

Outputs Proportion of load 1 in outbound load (c1) Proportion of load 2 in outbound load

(c2)

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Simulink Model

x'' x' x

m1'

m2'

m1

m2

c21

m2

215.6

m1

9.81

g

c 1

simout

To Workspace

Subtract

Scope

4.94Ro*g*A*h/m1

54.4

Ro*A

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K

1sxo

Integrator4

1s

Integrator3

1s

Integrator2

1s

Integrator1

0.3

C

0.0028

2c*x'/m1

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Inputs

1. m1 = 2000 bu and m2 = 2000 bu

2. m1 = 2000 bu and m2 = 1000 bu

3. m1 = 2000 bu and m2 = 500 bu

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Results

m1 = 2000 bu, m2 = 2000 bu

0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time (min)

Pro

po

rtio

n o

f M

1 a

nd

M2

Proportion of Loads M1 and M2 in outbound load

M 2

M 1

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0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time (min)

Pro

po

rtio

n o

f M

1 a

nd M

2Proportion of Loads M1 and M2 in outbound load

M 2

M 1

m1 = 2000 bu, m2 = 1000 bu

Results

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Results

0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time (min)

Pro

po

rtio

n o

f M

1 a

nd

M2

Proportion of Loads M1 and M2 in outbound load

M 2

M 1

m1 = 2000 bu, m2 = 500 bu

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Conclusions Proportions of loads m1 and m2 in the outbound load

can be determined at any given time

At t = 0:Proportion of m1 = 1 and Proportion of m2 = 0

Proportion of m1 decreases and m2 increases with increasing time (FUNNEL FLOW).

As m2 empties out, proportion of m1 starts increasing exponentially till it reaches an equilibrium value

Profiles of c1 and c2 vary depending on m1 and m2

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Further Development

More grain loads

Experimental determination of flow dynamics – Relation with Angle of Repose Model applicable for different grains

LIFO (Real world application)Simultaneous filling and emptying

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Thank you for your attention !