Volume 10
Issue 3
Agricultural Engineering
JOURNAL OF
POLISH
AGRICULTURAL
UNIVERSITIES
Available Online: http://www.ejpau.media.pl/volume10/issue3/art-03.html
ON-LINE ESTIMATION OF THE MOISTURE CONTENT OF GRAIN DURING NEAR-AMBIENT DRYING ON THE BASIS OF THE DRYING AIR TEMPERATURE CHANGES
Dariusz Tomkiewicz^{1}, Antoni Ryniecki^{2}
^{1} Department of Control Systems Engineering,
University of Technology in Koszalin, Poland
^{2} Institute of Food Technology of Plant Origin,
Agricultural University of Poznan, Poland
The post-harvest drying and cooling of cereal grain in silos are becoming an increasingly popular methods of grain preservation for long-term storage. Grain in silos is dried in a thick layer and, in order to reduce costs of this process, an low-cost and reliable method for the measuring of changes in the moisture content in the grain bed is needed. Acting on the assumption that the drying air enthalpy during this process does not change the authors presents in this article a stochastic mathematical model allowing moisture content estimation on the basis of the drying air temperature changes.
Key words: deep bed drying, stochastic model, monitoring of the moisture content.
NOTATION
A_{0} – mass of dry air, kg (dry air)
c – specific heat, J kg^{-1} K^{-1}
E – source of energy stream, J s^{-1}
G_{0} – mass of dry material, kg (dry mass)
i – enthalpy of moist air, J [kg (dry air)]^{-1}
j – j-th discrete spatial element
n – n-th discrete time element
r – heat of water desorption, J [kg (water)]^{-1}
S – surface area, m^{2}
t – time, s
T – temperature, °C
M – moisture content, kg [kg(dry matter)]^{-1}, or kg kg^{-1} d.b., or decimal dry basis (dec. d.b.)
v – air velocity, m s^{-1}
H – absolute humidity of air, kg [kg(dry air)]^{-1}
z – depth in bed from inlet, m
α – void ratio
ε – white noise with Gaussian distribution
ρ – specific density, kg m^{-3}
ψ – relative humidity of air (RH), 100·kPa (water vapor in air) kPa^{-1} (water vapour in saturated air), or %
Subscripts:
A – drying air
Atm. – ambient
F – final
M – material being dried
V – water vapour
IN – inlet
OUT – outlet
INTRODUCTION
One of the most popular methods of cereal grain preservation in many countries is drying and cooling in metal silo-bins. Grain preserved at near-ambient temperatures has lower breakage susceptibility and higher germination, than grain from high-temperature dryers [12]. Drying grain in silos can be defined as the process of moisture removal from deep static beds of grain by forced ventilation with air of evaporative capacity that comes mainly from the drying potential of the ambient air [2]. Therefore, the moisture transfer in this process is subjected to considerable disturbance from the stochastic fluctuations in the ambient air temperature and humidity [8].
Preservation of grain in metal silos has a number of advantages associated with the convenience of their utilization, taking care of the quality of the stored material and its turnover on the cereal grain market. However, there are also a series of disadvantages associated with the application of these stores. The principal problem is the drying process in silos of the grain harvested directly from the field. Directly after harvesting cereal grains often have excessively high moisture content and must be dried inside the stores down to the moisture content which will allow its further long-term storage. The structure of most silos requires the air used for drying to be blown into the bin from the bottom, then it flows through inter-granular spaces along the entire length of the bed. Therefore, in this situation, we deal with the process of thick layer drying. During the typical process of near-ambient drying in a thick, stationary grain layer moisture transfers from kernels to the air in those areas where the air relative humidity is lower than the equilibrium humidity. This occurs only in a relatively thin layer of grain, referred to as the ‘drying zone’ or ‘drying front’ [2, 6]. The drying zone moves slowly in the same direction as the air flow in the inter-granular spaces. When the air relative humidity increases to the level of the equilibrium humidity, moisture no longer flows from kernels to the air. This situation occurs in the grain layers above the drying zone. This means that the grain moisture content in layers above the drying zone remains on the level similar to the initial moisture content almost throughout the drying period.
If wet grain is allowed to remain for prolong periods of time in air of high humidity and temperature, its quality parameters can deteriorate or it may undergo spoil and, in extreme cases, the silo can even be damaged. That is why the relative humidity, temperature and the flow intensity of the drying air must be controlled very precisely. In order to optimize this process, it is essential to know changes in the moisture content of the dried material along the height of the store [7].
There are several methods allowing the measurement of the moisture content in cereal grain but, unfortunately, they are not suitable for measurements in conditions found inside silos. Moreover, there are methods allowing the taking of the measurements only in a specific spatial points of a store. In order to ensure comprehensive monitoring of stored grain, it would be necessary to install a number of sensors which would incur high costs. However, the problem could be solved if grain moisture content were determined on the basis of the thermodynamic parameters of the air flowing through the consecutive grain layers. The air passing through individual grain layers changes its thermodynamic parameters. These parameters depend on changes in the moisture content in the dried material and it is possible, on the basis of changes in their values, to estimate the moisture content in the dried material [11]. Air temperature is just one of such parameters. This parameter can be measured easily and sensors which allow to do it even in difficult conditions are relatively cheap.
The main goal of the performed investigations was to carry out initial tests of an on-line monitoring of changes in the moisture content of grain dried in a metal silos on the basis of the drying air temperature changes inside a thick layer of grain. The research assumption was made that above mentioned monitoring of grain moisture content will make it possible the automatic identification of the termination of near-ambient barley grain drying in a deep bed on the basis of the information obtained on-line from sensors of drying air temperature (located inside the bed of grain) and some constants stored in memory of a microcontroller.
MATHEMATICAL MODEL
The measurement of the moisture content on the basis of measurements of the drying air temperature is an indirect evaluation which requires the employment of a mathematical model capable of describing correlations occurring between the content of moisture in the dried material and air temperature. The process of drying, in which a simultaneous exchange of mass and energy takes place, is difficult to describe mathematically. Moreover, drying is a non-stationary process which means that the values of the model parameters describing this process keep altering both in time and space. The process is affected by many factors which would be very difficult to take into consideration in a deterministic model and would require taking into account frequently of very complex interrelationships.
Moreover, in order to ensure an accurate description of the system by the applied model, the measuring process must also be taken into account. In such case, the model of drying in a thick layer together with the disturbance model will adopt the form of a stochastic differential equation. Such model consists of two segments. The first of them describe changes of the mean value of the moisture content in the material in space and time, while the second one describes stochastic dispersion of this value modeled by a definite probability distribution:
(1) |
where:
– function describing changes of mean values of selected process values,
– additive stochastic component of the process.
This equation can be solved using methods of stochastic integration.
On the basis of the model and the description of disturbances which it contains, it is possible to develop an estimator which will allow to filter the disturbances and to calculate changes in the moisture content in the material. Figure 1 shows a block diagram of such an estimator. All additional factors not considered in the model are treated as stochastic disturbances of additive nature with properties of white noise with Gaussian distribution.
Fig. 1. Diagram illustrating functioning of the measuring system estimating moisture content in material being dried |
The relationship between the temperature of the drying air and the content of moisture in the material can be obtained from the equation describing the mass balance for the elementary layer of the static-bed drying [1, 3, 5]:
(2) |
Equation (2) does not contain the temperature of the drying air. The relationship which describes the link of the temperature of the drying air and its moisture content is enthalpy. If we apply the following formula for air enthalpy,
(3) |
then for a single spatial element of a stratum of dz thickness, the equation which describes the change of heat in time and along spatial variable z can be described in the following form:
(4) |
where: the spatial dimension of the process is contained in the area: ; the time of the run of the process is contained in the interval: ; the boundary conditions of the process are determined at points: and amount to: , [11].
Substituting equation (3) into equation (4) and putting the terms in order, with the assumption that values of the specific heat and the heat of evaporation are constant, the relationship between the air humidity change rate and temperature of drying air can be described:
(5) |
Further if we assume that the enthalpy of air passing through the thick layer of material during the process of drying does not change, i.e. and (which can be assumed for a slow process of near-ambient drying), then equation (5) can be simplified to the following form:
(6) |
The model described in equation (2) is a deterministic model and does not take into consideration disturbances that occur during the process. However, if we supplement this equation by a section describing stochastic changes in accordance with equation (1), then we will obtain a description of the drying process in the following form of a stochastic differential equation:
(7) |
The numerical methods were utilized to solve partial differential equation (6) and (7) and to optimally estimate changes of the drying air temperature.
NUMERICAL PROCEDURE
The equations (6) and (7) were substituted by discretized models along the spatial dimension and time. In his calculations, the authors used the method of finite differences and the Euler differential scheme. The following formulas were utilized for the approximation of the temperature of air changes:
(8) |
(9) |
Equation (8) requires to estimate the air temperature one time step ahead:
(10) |
Neural networks were used for approximation of this function. Due to the complex correlation describing the temperature change of the drying air during the drying process which occurs in equation (10) we treat it as a “black box”. Following a series of tests, the following network structure was adopted: three neurons in the input layer, two neurons with an activation function in the shape of a hyperbolic tangent in the hidden layer and one neuron with a linear activation function in the output layer. The Extended Kalman Filter (EKF) was used to teach the neural network [10].
The empirical constants, used for calculations: c_{A} = 1.005 J kg^{-1} K^{-1}, c_{V} = 1.88 J kg^{-1} K^{-1}, r = 2501 J kg^{-1}. ρ_{M} = 700 kg m^{-3} (for the barley), ρ_{A} = 1.25 kg m^{-3} were taken from Pabis [4] and Strumiłło [9]. The computer code has been written using the general-purpose software MATLAB R2006a.
VALIDATION OF THE SIMULATIONS
In order to check the operational appropriateness of the applied method, an empirical experiments were carried out in the course of which authors recorded the course of temperature changes of the drying air as well as changes in the moisture content during drying in the thick layer of barley. Empirical experiments were done using the laboratory stand, built for the mass and heat transfer research at the University of Agriculture in Poznań, Institute of Food Technology, Food Engineering Group (Fig. 2). The experimental station was equipped in the bin (1) consisted of several segments, each 0.1 m high and 0.3 m diameter, a fan (7) with a control system of the engine rotational speed (8) and a heater (11) with a pulse control system of electrical power (10). Such equipment allowed precise parameter control of the air blown into the mass of grain. In order to enforce moisture desorption from grain throughout the drying period, an electronic humidistat (9b) was applied which controlled the air heater which was responsible for ensuring that the air relative humidity (RH) blown into the grain bulk did not exceed 55%. The responsibility of the second humidistat (9a) was to switch off the fan whenever the air RH increased over the value of 95% (e.g. during periods of rainfalls). The mass of the material in each segment of the bin (1) was independently weighed during drying using for this purpose an electronic balance of 1 g accuracy (“AXIS B 10” of Sartorius, Germany). The grain moisture content (GMC) in individual layers can be calculated from the mass balance on the basis of mass losses. The velocity of the air flowing through grain layers was measured at the outlet from the drying chamber using the rotameter type airflow meter (2) of the resolution 0.00022 m s^{-1} per 1 mm length of the scale (Lokkes Maskinfabrik, Denmark).
Fig. 2. The laboratory stand for empirical experiments: 1 – drying bin (L2 ... L4 – layers 2–4), 2 – rotameter type airflow meter, 3 – temperature sensors, 4 – air RH probes, 5 – data acquisition system’s unit (Taiwanese ICP_CON I-7018), 6 – computer PC with a data acquisition program “Vi-dry”, 7 – fan, 8 – a control system of the engine rotational speed, 9 – humidity controller, 10 – pulse control system of electrical power, 11 – electrical heater, 12 – wall of building; symbols ψ and T are explained in the text |
In the course of each drying process, every 10 minutes, temperature was registered in eight and the air RH in four places of the research station. The temperature was measured with the assistance of Cu-Konstantan thermocouples (3), whereas the air RH – using probes with a sensor that works according to the capacitive measuring principle (4) (type EE21-FT6B53/T24 of the E+E Elektronik Comp., Austria). The temperature was measured at the place where the ambient air was sucked in by fan (T_{Atm.}), in the channel supplying the plenum air to the grain bulk (T_{IN}) and in segments of the drying chamber (T_{L2}-T_{L4}). The RH of the atmospheric air (ψ_{Atm.}) and the plenum air (ψ_{IN}) were measured. All thermocouples and humidity probes were connected to the computer system of data acquisition (5) and (6) (ICP-CON I-7018 of the ICP Taiwanese company) which allowed registration, visualization and archiving of measurement results. Temperature and humidity probes were calibrated before trials. After calibration, the repeatability of results and maximum differences of measurements between the applied eight temperature probes did not exceed ±0.2°C. However, due to differences between characteristics of individual sensors and their nonlinearity, the accuracy of the temperature measurements amounted to ±0.5 K. The measurement accuracy of the air RH in the important range of 10%-95% guaranteed by the manufacturer of probes was ±2.5%. In order to improve their accuracy, probes were calibrated prior to experiments and checked after the trials in a humidistat chamber with saturated NaCl solution (reference humidity 75%). However, due to the phenomenon of the hysteresis of sensors, it was not possible to reduce the range of error below ±2%.
Fig. 3. The laboratory stand for empirical experiments: 1 – drying bin (L2 ... L4 – layers 2–4), 2 – rotameter type airflow meter, 3 – temperature sensors, 4 – air RH probes, 5 – data acquisition system’s unit (Taiwanese ICP_CON I-7018), 6 – computer PC with a data acquisition program “Vi-dry”, 7 – fan, 8 – a control system of the engine rotational speed, 9 – humidity controller, 10 – pulse control system of electrical power, 11 – electrical heater, 12 – wall of building; symbols ψ and T are explained in the text |
The results of the empirical experiment as well as results of the estimation are presented in Figure 3. Mean of differences between the estimated and measured grain moisture content is equal to 0.001 kg kg^{-1} d.b. (with the standard deviation of 0.003 kg kg^{-1} d.b.).
CONCLUSIONS
The performed analysis and experiments corroborated the experimental hypothesis about the possibility of automatic identification of the termination of near-ambient barley grain drying in a metal silo on the basis of the drying air temperature measured on-line inside the bed of grain. The applied method of moisture content estimation in a thick layer of dried grain on the basis of data concerning the temperature changes of the drying air is based on the assumption that the drying air enthalpy does not undergo change. On the basis of the experiment carried out on the test station in which barley grain was dried, it can be concluded that the estimation quality was satisfactory for a 0.4 m bed depth. Mean of differences between the estimated and measured grain moisture content is equal only 0.001 kg kg^{-1} d.b. and the standard deviation of the above differences 0.003 kg kg^{-1} d.b. The authors continue their experiments with the aim, among others, to check the elaborated method in more cases of higher bed depths.
The numerical procedures of the moisture content estimation are not complicated and not time and memory consuming. Therefore they can be easily adopted in a control or monitoring systems.
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Accepted for print: 25.06.2007
Dariusz Tomkiewicz
Department of Control Systems Engineering,
University of Technology in Koszalin, Poland
Racławicka 15-17, 75-620 Koszalin, Poland
Phone: (+48 94) 347 82 72
email: dariusz.tomkiewicz@tu.koszalin.pl
Antoni Ryniecki
Institute of Food Technology of Plant Origin,
Agricultural University of Poznan, Poland
Wojska Polskiego 31, 60-624 Poznan, Poland
Phone:(+48 61) 848 72 69
email: ryniecki@au.poznan.pl
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