Processes 2021 , 9 , 1117
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often treat the dryer section as a “black box”. Nevertheless, rising energy costs are forcing papermakers to pay more attention to the dryer section, and especially steam usage. The thermal energy consumption during paper drying is mainly used to evaporate the water in the moist paper. According to the diverse binding force, the water in the moist paper can be divided into different types, such as free water and bound water, of which thermodynamic and physical properties are different. For the bound water, evaporation heat is used not only to vaporize water, but also to overcome the interaction between cellulose fibers and water. The quantitative measurement of evaporation heat is important to understand the interaction between fibers and water (drying mechanism) and the resulting impact on the paper drying behavior for optimizing the capital and operating costs of the dryer section. At present, there are few studies on the quantitative measurement of evaporation heat, mainly because heat energy flow is difficult to measure directly. Heikkilä [5] studied the evaporation heat of coated paper and found that the evaporation heat of bound water was composed of two parts, latent heat of vaporization and an extra amount of energy called heat of sorption. The latent heat of evaporation is the same as that of pure water, which can be easily obtained by consulting the physical property data of water, but the data of sorption heat is difficult to obtain. At present, the traditional method to obtain the sorption heat is to establish its theoretical model based on the Clausius–Clapeyron equation, and the theoretical model estimation needs to use the data of paper sorption isotherm [1]. Taking mechanical pulp as an example, the theoretical estimation equation of sorption heat is as follows: Δ H sorp = R v 1 − ϕ ϕ c 3 u c 4 T p + 273.15 2 (1) ϕ = 1 − exp − c 1 u c 2 − c 3 T p u c 4 (2) where Equation (1) is the calculation model of sorption heat ( Δ H sorp ), R v is the gas constant, T p is the paper temperature, and u is the paper moisture, Equation (2) is an example of fitting equation of sorption isotherm( ϕ ), c 1 , c 2 , c 3 and c 4 are the equation parameters. This model had been widely used in modeling and simulation of the paper drying process. For instance, Slätteke [6] established a complete simulation model for the drying section that is implemented in the object-oriented modeling language Modelica. The pur- pose is to study the feedback control of paper drying. Roonprasang [7] made a theoretical study on the modeling and simulation of the impact of new design configuration geometry on the drying process, with means of theoretical estimation model of evaporation heat. Karlsson [8,9] presented several models for the drying section to describe the phenomena at a steady state. New control strategies applicable for both steady-state control and for grade changes were derived. Heo [10] used the theoretical estimation model of evaporation heat to model and simulate the state change of paper in the drying section, trying to solve the problem of the “black box” in dryer section. Åkesson [11] used the theoretical estimation model of evaporation heat to present a Modelica library, DryLib, which enables users to rapidly develop complex models of dryer section. In addition, parameter optimization by means of non-linear model predictive control is treated. Nevertheless, there were still many inconveniences in the practical application in the process of using the above model based on the sorption isotherm. The main reason is that the data of sorption isotherm curves of different paper grades in the industry are very few. The sorption isotherm is a correlation between relative humidity and the equilibrium moisture content. The measurement of the sorption isotherm is time-consuming and difficult, requiring strict test conditions such as constant temperature and humidity [12,13]. Measurement of sorption isotherms is a common practice in many fields of science and engineering, such as food science, material science, and so on. Traditional methods to determine sorption isotherms usually rely on conditioning above saturated salt solutions that keep constant relative humidity and gravimetric methods to determine the moisture content in the sample. In order to reduce the systematic error caused by the change of relative humidity around the sample during sampling and weighing, the whole experiment
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