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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 !