1 Dynamic Simulation Model for tracking grain lots in an elevator AE 503 Term Project Maitri Thakur Agricultural and Biosystems Engineering May 2, 2007

2 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)

3 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)

4 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

5 Movement of grains for export in the U.S. Source: U.S. Grains Council

6 Traceability in Bulk Grain Handling Source A Source B Source C Common Storage Silo Manufacturing Plant Cookies Source: Food and Drug Administration

7 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)

8 Storage Bin- Grain Flow Methods  FIFO – First In, First Out Mass 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

9 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

10 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/m 3

11 m1sm1sm1sm1s m1gm1g x Fc m1m1 m2m2 m2sm2sm2sm2s h ρgAh D d Grain Forces

12 Differential Equations Forces acting on m 1 : m 1 g + ρgAh – F c - F c =m 1 d 2 x/dt 2 ……. (1) where, m 1 = Mass of load 1 g = Acceleration due to Gravity ρ = Bulk Density of Grain A = Surface area of mass m 2 h = Height of mass m 2 Fc = Frictional Force = cdx/dt c = Coefficient of friction of grain x = Displacement of mass m 1

13 Differential Equations dm 1 /dt = ρAdx/dt ……. (2) Σ Q = -dm 1 /dt + 2*dm 1s /dt + dm 2 /dt = 0 dm 2 /dt = dm 1 /dt – 2*dm 1s /dt ……. (3) m 1 s : f (c, dx/dt, Θ ) m 1s = k*(cdx/dt)*cos Θ k = 10

14 Differential Equations c 1 = m 1 /(m 1 +m 2 ) ……. (4) c 2 = m 2 /(m 1 +m 2 ) ……. (5) where, c 1 = Proportion of mass m 1 in outbound load c 2 = Proportion of mass m 2 in outbound load

15 Model Inputs and Outputs  Inputs  Mass of load 1 (m 1 )  Mass of load 2 (m 2 )  Outputs  Proportion of load 1 in outbound load (c 1 )  Proportion of load 2 in outbound load (c 2 )

16 Simulink Model

17 Inputs 1. m 1 = 2000 bu and m 2 = 2000 bu 2. m 1 = 2000 bu and m 2 = 1000 bu 3. m 1 = 2000 bu and m 2 = 500 bu

18 Results m 1 = 2000 bu, m 2 = 2000 bu

19 m 1 = 2000 bu, m 2 = 1000 bu Results

20 Results m 1 = 2000 bu, m 2 = 500 bu

21 Conclusions  Proportions of loads m 1 and m 2 in the outbound load can be determined at any given time  At t = 0: Proportion of m 1 = 1 and Proportion of m 2 = 0  Proportion of m 1 decreases and m 2 increases with increasing time (FUNNEL FLOW).  As m 2 empties out, proportion of m 1 starts increasing exponentially till it reaches an equilibrium value  Profiles of c 1 and c 2 vary depending on m 1 and m 2

22 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

23 Thank you for your attention !