Processes 2021 , 9 , 1117
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rise. The above idealized scheme occurs if drying conditions are similar over the entire drying process. In commercial dryer sections, the constant rate phase does not often exist. The schematic diagram of the evaporation heat measurement based drying curve is shown in Figure 1. It shows that the one-to-one correspondence function between the evaporation heating curve (Figure 1a) and the drying curve (Figure 1b) can be established theoretically during the paper drying. The specific derivation process is as follows:
1 / K W W M u t ' ' E t K ' ' ' '
E
'
Assumptions: 1) Drying conditions are consistent; 2) Ignoring the energy loss, the energy provided by the drying system is only used for paper drying.
E K W W ' ' t ' '
H ' |
H
'
H ' |
W
'
dp
Assumptions: 3)The absolute dry weight of paper does not change during drying
dp W M u ' '
E K t ' | '
u
u
u
(a) Evaporation heat curve ( ə H ~ u )
(a) Evaporation heat curve ( ə H ~ u )
(a) Evaporation heat curve ( ə H ~ u )
Theoretical analysis: 1) It is feasible to estimate the heat of evaporation by measuring the drying curve. 2) Another key problem is to determine the parameters K and M dp .
u
t
(b) Drying curve ( u ~ t )
Figure 1. Schematic diagram of evaporation heat measurement based drying curve: ( a ) Evaporation heat curve; ( b )Dry- ing curve.
The evaporation heat ( Δ H ) in the paper drying process refers to the energy consumed by the evaporation of water inside the paper sheet and the final release. As shown in Figure 1a, it is a curve where the y -axis is evaporation heat ( Δ H ) and the x -axis is the moisture of the paper ( u ), u is a state variable, which can be easily obtained by weighing the paper sheet. Δ H is a process variable, which can be calculated by Equation (3).
Δ E Δ W
Δ H =
(3)
Energy consumption( Δ E ) is difficult to measure directly. According to the principle of energy conservation, it can theoretically be measured indirectly by measuring the energy consumption of the drying system. As shown in Equation (4), K is the effective horsepower of drying system. In a period of time ( t 1 ~ t 2 ), energy consumption ( Δ E ) can be calculated by an integral formula. The right side approximation holds in the assume that K is a constant. Δ E = t 2 t 1 Kdt ≈ K · Δ t (4) Water evaporation ( Δ W ) is also a process variable, which is a function of the drying rate ( R ) and time ( t ), as shown in Equation (5). M dp is the mass of the dry paper. Δ W Δ t = R = M dp Δ u Δ t (5) From Equations (3)–(5), evaporation heat ( Δ H ) can be calculated by Equation (6), under the following assumptions: (1) drying conditions are consistent; (2) ignoring the
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