Transcript Dynamic simulation model for tracking grain lots in an elevator

Dynamic Simulation Model for
tracking grain lots in an elevator
AE 503 Term Project
Maitri Thakur
Agricultural and Biosystems Engineering
May 2, 2007
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Food Traceability
ISO definition
Traceability is the “ability to trace the
history, application, or location of that
which is under consideration.”
A grain of wheat or a truckload
A 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
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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
Source
B
Source
A
Source
C
Common
Storage
Silo
Cookies
Manufacturing
Plant
Source: Food and Drug Administration
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Problem Statement
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Grain lots commingled:
To meet buyer specifications as close as
possible and to maximize the profit.
Lot identity is not maintained.
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Recent experiences with regulatory issues
have introduced a growing need to track
product identity
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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
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FIFO – First In, First Out
Mass Flow
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LIFO – Last In, First Out
Funnel Flow
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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
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Shape : Cylindrical, Flatbottom, 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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Grain Forces
m2
m2s
m2s
ρgAh
h
Fc
Fc
m1
m1s
m1s
m1g
x
d
D
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Differential Equations
Forces 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 Grain
A = Surface area of mass m2
h = Height of mass m2
Fc = Frictional Force = cdx/dt
c = 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
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Inputs
 Mass of load 1 (m1)
 Mass of load 2 (m2)
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Outputs
 Proportion of load 1 in outbound load (c1)
 Proportion of load 2 in outbound load (c2)
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Simulink Model
Ro*g*A*h/m1 4.94
x''
9.81
x'
1
s
g
Integrator1
x
1
s
Integrator2
Scope
2c*x'/m1
0.0028
Ro*A
m1'
54.4
m2'
m1
1
xo s
1
s
c1
Integrator4
simout
Integrator3
To Workspace
m2
K
C
10
0.3
1
m2
c2
Subtract
215.6
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
Proportion of Loads M1 and M2 in outbound load
1
0.9
Proportion of M1 and M2
0.8
M2
M1
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
Time (min)
7
8
9
10
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Results
m1 = 2000 bu, m2 = 1000 bu
Proportion of Loads M1 and M2 in outbound load
1
0.9
Proportion of M1 and M2
0.8
M2
M1
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
Time (min)
7
8
9
10
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Results
m1 = 2000 bu, m2 = 500 bu
Proportion of Loads M1 and M2 in outbound load
1
0.9
Proportion of M1 and M2
0.8
0.7
M2
M1
0.6
0.5
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
Time (min)
7
8
9
10
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Conclusions
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Proportions of loads m1 and m2 in the outbound load
can be determined at any given time
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At t = 0:
Proportion of m1 = 1 and Proportion of m2 = 0
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Proportion of m1 decreases and m2 increases with
increasing time (FUNNEL FLOW).
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As m2 empties out, proportion of m1 starts increasing
exponentially till it reaches an equilibrium value
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Profiles of c1 and c2 vary depending on m1 and m2
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Further Development
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More grain loads
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Experimental determination of flow
dynamics – Relation with Angle of Repose
Model applicable for different grains
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LIFO (Real world application)
Simultaneous filling and emptying
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Thank you for your attention !
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