Processes 2021 , 9 , 1117
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process, including water balance and weighing, needs to be kept under the same relative humidity. Many different relative humidity are needed to determine a complete sorption isotherm, as at each relative humidity the water balance of the sample takes a long time. Therefore, the measurement of sorption isotherm line is very time-consuming. The sorption isotherm of paper depends on the structure of the paper and the fibers and other raw materials used to manufacture the paper. Keränen [14] has studied hand- made paper’s sorption isotherms with different filler contents. Fitting the experimental data with the Soininen model, it was found that the model parameters was obviously different corresponding to the different filler content. Popescu [15] studied the adsorption isotherm of wood and got the similar conclusion. There are more than 1000 kinds of paper in the current paper-making industry; according to market demand, each kind of paper’s manufacturing process has been frequently adjusted in the actual production process. How to rapidly estimate the evaporation heat of the frequently changing paper, and then guide the dryer section to optimize the process parameters in time, is a new problem encountered in the process of paper enterprises in pursuit of energy saving and consumption reduction. The traditional estimation method based on sorption isotherm obviously can not achieve the purpose of rapid measurement, and can not adapt to the rapidly changing market demand. Therefore, developing a simple approach for rapidly measuring the evaporation heat of paper is urgent. The drying curve is an overall indication of the paper drying process, covering all the information during paper drying, and including paper’s evaporation heat [16,17]. The current study attempts to explore a simple method for rapidly measuring evaporation heat based on the drying curve measurement. Generally, the drying curve is a curve that changes in the moisture content of the material with the drying time. In the papermaking industry, it was also expressed by a correlation between paper moisture content and drying position (cylinder number) [18]. The new method starts from the measurement of the drying curve, and no longer needs to measure the sorption isotherm, which makes the measurement of evaporation heating time-saving and convenient.
2. Methodology 2.1. Theoretical Model Based on Drying Curve
The moist paper consists of water in different fractions, free water in large pores and bound water in micro pores. They have different thermodynamic and physical properties, such as different vapor partial pressures, enthalpies and so on. The thermodynamic and physical properties of free water being same as that of bulk water. The binding force of free water is small, generally, it evaporates first in the drying process. Drying decreases the level of fiber swelling by closing the pores in a fiber cell wall irreversibly. The removal of bound water needs to overcome such resistance, so with the passage of time, it is more and more difficult to remove water by drying, so it also needs to consume more heat energy. During the drying process, wet paper passes through three distinct phases, including the preheating phase, c, and the falling drying rate phase. In the preheating phase, part of the heat of the heating medium is used to heat the paper, and the paper temperature increases rapidly, but the moisture content of the paper changes little with the drying time. Then, the paper drying enters the constant drying rate phase, and the moisture content of the paper is basically linear with the drying time. The slope is constant, that is, the drying rate is constant. At this time, the heat transferred by the heating medium to the paper and the heat required by the evaporation of the water in the paper are in balance, and the surface temperature of the paper remains unchanged, which is just equal to the wet bulb temperature of the hot air around the paper surface. After a period of time, when the moisture content of the paper is lower than the critical moisture content (CMC), the paper drying enters the deceleration stage. In this stage, the drying characteristic curve tends to be flat, gradually approaching the equilibrium moisture content (EMC), and the drying rate decreases. Part of the heat provided by the heating medium is used to evaporate water, and part is used to heat the paper, and the surface temperature of the paper continues to
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