Раимбаева Н.Т., Курманов Б.К. SIMULATION MODELING OF GRAIN STORAGE TECHNOLOGICAL PROCESSES

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Математика/5. Математическое моделирование

Raimbayeva N.T., Kurmanov B.K.

Almaty technological university, Republic of Kazakhstan

SIMULATION MODELING OF GRAIN STORAGE TECHNOLOGICAL PROCESSES

In the report herein we consider the issues of simulation modeling device usage for analyzing the performance capability of grain storage technological processes. Through the example of the grain elevator L2´100 there has been developed the structural scheme of its operation process model in Q-scheme symbolics.

Research outcomes can be used upon designing new or modernizing the existing grain elevators to assess their operation efficiency.

1. Introduction

For accepting, treatment (cleaning, drying, etc.), storing and releasing various culture types there used the grain elevators. Enumerated above operations are fulfilled by means of receiving and outloading devices of automobile and railway transport, powerful grain cleaning and grain drying machinery, storage reservoirs of warehouse and silo type. Devices, machinery and storage reservoirs are connected between with materials-handling vehicles (see fig.1).

Let us consider the L2´100 linear elevator’s technological process (twin bucket elevator with a capacity 100t/hour each). Figure 1 presents the given type elevator’s principal scheme. Elevator’s receiving unit consists of an unloading mechanism, receiving tanks, conveyors for the grain housing from under the tanks. Bucket conveyers (vertical conveyers) is the main equipment of the grain elevator, the performance of which defines the elevator’s capacity (volume of grain, handling by an elevator per time unit). The grain, loaded with an elevator, is weighted and dependent on its condition, by means of swing pipes, is delivered by gravity either for handling in separator operative tanks or to grain-storage section. For the aim of simplicity the figure 1 does not show a dryer. Grain cleaning machines have been designed for cleaning grain from foreign substances, differing according to the length, and separators – according to the width and thickness. Handled with help of separator grain is initially raised up, afterwards, in case of necessity, it can be fed into one of the equipment for rehandling or sent to a silo for storage and release. The grain in the silo periodically, by means of underground conveyors, is supplied into the equipment for reprocessing, which secures its storage quality.

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Figure 1 – Grain elevator

(1- headhouse, 2- grain storage section, 3 – receiving unit, 4 - infeed conveyor, 5 – bucket elevator, 6 - operative hopper, 7 - balance, 8 – swing pipes, 9 - gallery conveyor, 10 - separators, 11 - grain-cleaning machines, 12 – separator tanks, 13 – under separator tanks, 14 –collecting conveyor)

The aim of elevator’s technological scheme operation is gaining the maximum profit for the prescribed time interval at the expense of the increasing the volume of being stored and handled grain at minimal expenditures due to stored grain’s quality degradation, vehicles idle time owing to undue acceptance, uneconomical energy use and expenditures on the grain elevator equipment maintenance. Let us construct a simulation model of the grain elevator to assess the operation goal achieving extent.

2. Statement of problem

Grain mass condition changes upon storage dependent on the intensity of physiological processes, taking place in it and environmental conditions and depends on great number of factors (temperature, contamination status, freshness, humidity, germinative capacity, emergence rate, etc.). To prevent developing undesirable processes in the grain mass it is necessary to handle systematically the grain in the silo.

For the sake of simplicity let us suppose, that the quality of i–sample grain degraded upon its storage in the silo without reprocessing in excess of allowed time , at that, expenditures due to the quality loss of one ton of i-sample grain we will define according to the formula:

(1)

where t_i - i-sample grain storage duration without reprocessing, - i-sample grain’s storage cost coefficient . At that it is assumed, that in case , then .

Vehicles idle time expenses due to the queue formation in the receiving device we evaluate according to the formula:

, (2)

where , is the total queueing time of r-type transport (in vehicle/hour); - queueing expense ratio for r–type transport.

Expenditures for equipment installation and maintenance within the time Т we will define according to the formula

(3)

where n_j - quantity of j-type equipment; - expenses on purchasing and assembling the j-type equipment; - expenses on j-type equipment maintenance per time unit.

Expenses due to the electric power spending within Т time we define according to the formula:

(4)

Where h_j - j-type machines work load, - expenses due to the electric power spending by j-type equipment per the time unit.

With account of (1)-(4) the total expenditures are defined according to the formula

(5)

where Q_i- quantity of i-sample grain tons, taken as T time, - average expenditures due to the quality loss for i-sample grain ton storage.

Supposing, that a_i is the elevator’s revenue for treatment and storage of i-sample 1 ton, them the profit of the given enterprise for certain time interval (Т) constitutes:

(6)

Maximum profit (6) is maintained at the account of the equipment effective using, finding the optimal features of the transport input flow, grounded selecting the number of receiving and operating tanks, defining the best modes of various devices operation.

3. Assumptions, variables and model parameters

Grain elevator’s technological process study shows, that, based on the principle of the grain’s portions quantization it can be represented as a discreet system [1]. Proceeding from the modeling problem description, one may suppose, that the processes, taking place both in the internal (elevator-equipment-silo), and in the external (transport- receiving mechanism, silo-transport for shipment) elevator stages, are maintenance processes by definition. Therefore, it is reasonable to describe those processes Q-schemes language (continuous-stochastic model) [2], i.e. in terms of the mass service network systems. It is known, that the processes, presented in Q-schemes language, convenient to model applying the simulation system GPSS[3].

Let’s simulate the process of the grain elevator operation in the heaviest duty work – within the harvesting.

Let us introduce the following assumptions, which do not introduce big disturbances and allow the model simplifying:

1. Grains is delivered from the fields with the only means of transport – automobiles, at that, an incoming automobiles stream is - Poisson.

2. Grain’s quality characteristics upon storage are taken into account merely through the storage expense coefficients, at that i-sample storage costs are not available, if (see formula (1).

3. There is not considered the extent of a bin block filling influence at the elevator’s internal work (a bin block excessive filling is excluded).

4. Grain shipping from the silo is fulfilled with automobiles, where automobiles downstream is as well Poisson. Inasmuch, that grain release is maintained uniformly and proportionally within a year, and harvesting activity lasts approximately 1 month, the automobiles downstream intensity is selected in average as 12 times less than that of an upstream. Thus, there is simulated the elevator’s work during procurement, i.e., there is considered merely the regime of the grain accumulation in the silos.

5. Automobiles income and outcome streams intensity are constant within the considered period.

6. Not taken into account elevators’ transport and technological equipment dead time due to their fault conditions (a supposition thereof is just for a teaching example simplicity).

7. The first bucket elevator serves an input (external) stream, the second – an internal one (grain stream from the silos) .However, upon a long income queue there is admitted the service by the second income stream bucket elevator.

8. We neglect the time spent on grain portions weighting on a balance, a swing pipe change over and grain delivery with separator, silos and receiving conveyers.

9. Accepting and releasing devices are considered as the systems of mass servicing smoothly with unlimited queue.

10.Deemed a priori specific the expectancy of various foreign substances presence in the grain input mass and handling possibility of the income grain portion at the dryer.

11.Average automobile capacity is expected equal to 5 t, which corresponds to one charge of grain. For programming convenience we associate such grain charge with the transaction in terms of GPSS.

12.Due to the fact, that there exists restriction on the active transacts number, we simulate the elevator’s work for a shift, Т = 8 hours.

Simulation should result in getting the data on the grain storage life in silos without repeated handling, automobiles queuing time at the income, principal equipment loading, etc., which is indispensable for the criterion assessment (6).

Model variables are:

1. Main equipment capacity (incl.): bucket elevators - u_b, grain cleaners - u_c, dryers - u_d, separators - u_s.

2. Expectancy of various foreign substances presence in the grain input mass, causing the need in its handling in the cleaner (P_c) and (or) in a separator (P_s) and probability of incoming the wet grain charge , which shall be dried (P_d).

3. Quantity of equipment main types: bucket elevator - n_b, cleaner - n_c, dryer - n_d, separator - n_s, separator tanks - n_st, under separator tanks - n_ut, receiving tanks - n_rt.

4. Number of samples, the seeds of which are stored in the elevator - m.

5. i-sample grain’s allowable storage life continuously without handling (in hours) – .

6. Cost coefficient of the dead time of an automobile , waiting for an accepting device or tanks release (KZT/machine hours) - k_q.

7. Expenditures on equipment maintenance (KZT/h.): bucket elevator - C_mb, cleaners - C_mc, dryers - C_md, separators - C_ms, separator tank- C_mst, beneath separator tank - C_mut, receiving tank - C_mrt.

8. Expenses on electric power, consumed with principal equipment (KZT/h.): elevator - C_eb, cleaner - C_ec, dryer - C_ed, separator - C_es.

9. Elevator’s profit for 1 t i-sample grain handling and storage (KZT/t) - .

10. Storage cost coefficient (KZT/h²) - and automobiles downtime expenses (KZT/h) - k_q.

11. Automobile maximum waiting time in the income queue (h.) - . Upon a lot of automobiles in the income queue and high cleaning machine work load on the given time expiry, the grain charge, being accepted might be sent to a silo without cleaning from foreign substances. Exception is in the case, when the grain in-coming mass, is wet. Uncleaned grain in the silo according to the cleaning equipment load decrease shall be handled.

In view of the fact, that the elevator’s equipment quantity in the example under consideration is not a model’s parameter, expenditures on its procurement are not accounted, therefore the equipment and its assembling cost within the variables we do not denote.

As a model parameter we select the in-coming stream intensity of the automobiles, loaded with i-sample grain (h^-1) - l_i. Practically, the parameter l_i can be adjusted through the rational choice of the elevator’s maintenance zone and distribution of available machinery (combine harvesters, vehicles) per zones during harvesting. The given parameter changing limits are selected proceeding from the elevators main equipment’s throughput capability restrictions. To simplify the considered example let us suppose, that l_i = l/m, where l - the incoming flow total intensity. Such simplification allows m of model parameters reducing to one - l. With account of the bucket elevator capacity – elevator’s main equipment (100 t/h) and automobile’s average capacity (5 t), let us assume, that l changes within a period from 5 to 20 h^-1.

Characteristics, measured in the course of simulation are:

1. Storage time of i-sample grain charge in the silo continuously without processing (per hour) - t_i.

2. Waiting duration of unloading with a vehicle (per hour) - t_q .

3. Main equipment loading (в %) : bucket elevator (h_b), cleaner (h_c), dryer (h_d), separator (h_s).

4. i-sample grain volume, taken to be a simulated time domain T (in tones) - Q_i.

Enumerated characteristics are initial for the profit computation (6), In the result of simulation there might be obtained a number of other characteristics as well: income queue’s average length, tanks loading, features of out-coming queue and the data on each cost element, calculated according to the formulae (1)-(4).

4. Simulation model

Structural scheme of the elevator’s operation model in Q-schemes symbolics has been shown on the figure 2, where it is designated: S1÷SЗ –stream source of the vehicles with grain (program generator of various sample grain incoming charges, in the given example m=3); S4 - stream source of the vehicles for shipment; InQ –incoming queue of the automobiles, waiting for unloading; AT – accepting tanks (presented as a storage tank with restricted number of places, defined n_rt); BE1 and BE2 – bucket elevators 1 and 2; B1 and В2 - balance 1 and 2; ST and BST – separator and beneath separator tanks (presented as storage tanks restricted number of places n_ut and n_st ); C1 and C2 - cleaners (in the considered example n_c=2); SP1 and SP2 - separators (n_s=2); D1 and D2 - dryers (n_d=2); T1÷TЗ - silo tanks for dirty grain storage, accordingly of 1-st, 2-nd and 3-rd samples; T4÷T6 - silo tanks for cleaned grain storage, accordingly of 1-st, 2-nd and 3-rd samples (T1÷T6 considered as storage tanks with unlimited places); V1÷V12 - valves, permitting or prohibiting the grain stream motion in compliance with a definite logics.

Using introduced representations and designations let us describe elevator’s technological process. Vehicles arrival and three sample types grain income are simulated the sources S1÷S3. Incoming grain enters accepting tanks AT. If all AT are occupied, then the valve V1 shuts, which brings to a queue InQ. Control link (dashed line) between AT and V1 denoted the necessity of blocking the grain entrance into AT upon reaching the amount of the grain charge in the accepting tanks n_rt.

Further for simplification let us assume, that each tank (receiving, operative, upper weighing hopper) is designed to accept only one grain charge (5 t). Grain from AT ascends to a upper weighing hopper (fig.2 through B denotes both upper weighing hopper and the balance itself).

Valve V2 blocks the incoming of the next grain charge into BE1 until the previous charge transportation finishes and upper weighing hopper discharges. Upon shutting V2 the next transact (grain portion) tries to go through VЗ. It means, that the entering seeds flow from AT might be raised up by the second bucket elevator, provided: а) if BE2, accordingly В2 are not occupied; b) in ST and BST there is the place to accept the next transact.

Need in checking the BST is connected with the fact, that BE2 mainly serves the gun-loading cage. The transact, having been served with the equipment (C, SP, D) might bring to the machines idle time due to the absence of free space in BST.

Subsequent to weighing the grain mass depending on its condition can be sent either to the silo T4÷T6 (mass is dry and without foreign substances), or to ST via V4 (mass is dry, but with foreign substances), or V5 (mass is wet, but might be with foreign substances). The dry grain with foreign substances, while waiting for automobiles in InQ over t_q is sent to the silo T1÷T3. The operation thereof is conducted in order to avoid losses due to expenses increase connected with the vehicles idle town. Such situation is possible upon intensive incoming of the grain with foreign substances to the elevator.

Valves V6÷V8 block the transacts income to C, SP and D in case of their occupancy, and V9 – to BST upon the absence of a free tank. Valve V10 blocks an exit of the silos T1÷T3 unless and untill: а) the vehicles waiting time in InQ no lees than - t_q; b) appropriate equipment for cleaning from foreign substances is occupied. Valve V3 as well blocks those silos exits (also of silos T4÷T6). Условия открытия V3 opening conditions have been described above.

Grain charges storage in the silos T4÷T6 is possible until the continuous storage duration t_i exceeds - (such excess can lead to expenditures due to the stored grain quality fall of ). Therefore, the valve V11, blocking the exits T4÷T6, opens at . The valve VI2 opens exits T4÷T6 to ship the grain upon arrival of the vehicle for shipping. According to the assumption 4, the intensity S4 in average 12 times less than the total intensity of the sources S1÷SЗ. At that it is supposed, that with equal probability there shipped the seeds of one sample.

Figure 2 – Structural scheme of the elevator operation process model in Q-schemes symbolics

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C1

V8

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InQ

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BE1

BE2

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SP2

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V9

BST

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T5

T6

T4

V11

V12

OutQ

S4

Let us describe modeling algorithm of the elevator operation process per steps:

Step 1. There generated vehicles income streams per each type of sample. For each grain charge (GCH) or a transact in terms of GPSS there is defined presence of foreign substances and moisture condition in it.

Step 2. There is broken out the following: vehicles occupy InQ (see figure 2), unloaded upon releasing the space for accepting GCH in AT (valve V1 - open) and leave InQ. At the given step there is conducted time calculation and, accordingly, transport idle time expenditures according to the formula (2),

Step 3. At open valve V2, which corresponds to BE1 and space availability in ST, there simulated the processes of lifting GCH by the first bucket elevator and occupying B1. Otherwise there is checked the VЗ status. At open VЗ GCH there is lifted BE2. If V2and VЗ shut, the transacts wait for opening one of them in BST. Transfer to the step 4, if GCH is lifted to BE1 and to the step 5 - BE2.

Step 4. Subsequent to weighing simulation at B1 there is checked the V4 valve status. V4 open, if there is demanded the GCH handling (presence of foreign substances or GCH is wet). But under dry GCH and vehicles continuous waiting in InQ ( ) the valve V4 shuts irrespective of various foreign substances presence in GCH. Under shut V4 GCH with B1 are sent to the silos T_i (transfer to the step 8), if GCH admixtures, and silos T_i (transfer to the step 9), if GCH without foreign substances, where m- quantity of samples. At that in silos T1 and T_m+1 there stored the first sample grain, in silos T2 and T_m+2 - the second sample, etc. It should be noted, that the amount of silos in the elevator sufficiently increases 2m, each «model» silo T_i corresponds to dozens of real silos.

Step 5. There is fulfilled the operation, described in the step 4, for GCH with B2. Conditions of opening (shutting) of V5 are similar to V4.

Step 6. There is fulfilled draw of the line GCH ST. It is checked whether there is needed the dryer GCH. In case of necessity, the GCH occupies one of the free D. Valve V8 is closed, if both dryers are occupied, and GCH waits in ST. If a dryer is not required, then there is checked the necessity to clean GCH from admixtures, different per length. If it is required, then GCH occupies one of free C. The valve V6 is closed, if both cleaners are occupied and GCH waits in ST. Similarly, if there is necessity to clean from foreign substances, deferring per width and thickness, GCH enters one of the separators, if V7 is opened.

Step 7. Having been served by the equipment (D, C or SP) GCH occupies BST, if the valve V9 open, V9 open, provided the BST has space for accepting the handled GCH. Transfer to the step 5, if the valve V3 open, which corresponds to a free BE2 and availability of space in ST and BST. If VЗ closed, then GCH waits for its opening in BST.

Step 8. Detected the name (number) of sample type, considered by GCH, i-type GCH is sent to silo T_m+1 and leaves it, in case the valves VЗ and V5 open (transfer to the step 5). If at least of those valves shut, then the GCH waits their opening in the appropriate silo. Conditions of V10 closing were described aboveо.

Step 9. Detected the name (number) of the sample type, considered by GCH. i-type GCH is sent to T_i and leaves it, if open simultaneously V11 and VЗ, or open V12. Conditions of V11 opening were described above. V12 opens at presence of the transact in the queue OutQ, which corresponds to arriving the vehicle for shipping.

Processes of the vehicles outcoming stream generation, lines and release of OutQ are simulated independently and in parallel with the described algorithmс. Number of passing through V12 transacts defined by quantity of incomes into OutQ. For each transact, entering the OutQ there is drawn a random number i , uniformly and proportionally distributed in the interval [1,m]. Number i determines the sample type of GCH being shipped. In the step 9 upon appearing in OutQ the transact with a character i GCH is unloaded from the silo T_i. At empty T_i the transact with a feature i waits in OutQ till appearing GCH in T_i.

5. Example of modeling

Based on the above described algorithm there has been elaborated the program using the simulation system GPSS World. Simulation experiments have been conducted upon the following initial data: m=3, i.e., the elevator receives three types of grain - wheat (i =1), barley (i=2) and oat (i =3); u_b =100 t/hr; u_c =100 t/hr; u_d =100 t/hr; u_s=10 t/hr; P_c=0,5; P_d=0,3; P_s=1; n_b=2; n_d=2; n_c=2; n_st=n_ut=80; n_rt=4 (it is assumed that the volume of each tank ST, BST and AT - 5 t); =1hr; ; k_q=0,6 thousand KZT/automobile.hr.; C_mb=0,25 thousand KZT/hr; C_mc=0,1 thousand KZT/hr; C_md=0,15 thousand KZT/hr; C_ms= 0,05 thousand KZT/hr; C_mst=C_mut=C_mrt=0,01 thousand KZT/hr; C_eb=1,2 thousand KZT/hr; C_ec=0,12 thousand KZT/hr; C_ed=0,44 thousand KZT/hr; C_es=0,13 thousand KZT/hr; =0,6 thousand KZT/hr.^-2 ; a₁=1,3 thousand KZT /t; a₂=a₃=1 thousand KZT/t. In the program the above enumerated data shall be designated with preliminary translation them into minutes and tiyns .

Elevator’s work was simulated during one shift (Т=8 hour) at 11 values l. Based on the formulae (5) and (6) there was computed the profit, common costs and elevator gaining in thousand tenge (KZT). Obtained outcomes study shows, that the profit depends on the automobiles input stream intensity l. Comparing the results of carried out experiments, given in the figure 3, we single out, that at the selected version of initial data the highest profit is provided at the parameter value l » 10 hr^-1.

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Figure 3 – Simulation outcomes

(1- profit, 2- gaining, 3- total expenses)

6. Conclusion

In the work herein we presented the methodology of conducting the simulation experiments of the grain storage technological processes. Developing different version of decision taking upon processes control using the principle «what, if …» it is possible to find the best parameters of technological processes and the best variants of using the available resources, securing the minimal expenses. Simulation experiments allow assessing the performance of processes on such showings as equipment useful loading, works execution terms, interrelated technological processes regularity of pace, as well on complex factors, such as, expenses and profit. Applying the simulation modeling device for analysis of the elevator technological processes, representing a complicated system of interrelated mechanisms and processes, is a correct solution of the problem without doubt. Modular principle of constructing the simulation models, accepted in GPSS World, allows working out in detail the processes being studied with the desirable accuracy rate.

List of references

1. Raimbayeva N.Т., Kurmanov B.К. Analysis of the grain elevator technological processes by means of the simulation system GPSS World. In the book.: VII-th International scientific-technical conference "Engineering and technology of food productions". Theses. May 21-22, 2009. Mogilyev, Republic of Belarus. –Mogilyev: Publishing house of the MTU, 2009. p.215.

2. Sovetov B.Ya., Yakovlev S.А. System modeling. - Moscow: Higher school, 2007.- 322 p.

3. Kurmanov B.К., Kurmanov G.B. Development of simulation models at GPSS World. Study guide. –Almaty: Publishing center of JSC «KBTU», 2011. 221p.