In order to estimate the energy consumption for the preliminary drying of apple pomace, it was necessary to perform experimental studies of the kinetics of filtration drying, which was chosen because of its efficiency confirmed by authors [21], [23]. Three series of experiments were conducted, the peculiarity of which was the change of a certain process parameter – the thermal agent temperature T, the thermal agent filtration rate v₀, the layer height of the wet material H.

When one of the studied parameters was changed, the other two parameters remained unchanged. As a result, we obtained curves of changes in the moisture content of the stationary layer of apple pomace over time at different heights of the wet material (Figure 1), different temperatures of the thermal agent (Figure 2), and different velocities of its movement through the stationary layer of apple pomace (Figure 3). Additionally, the value of the equilibrium moisture content of apple pomace $w_e^c$ was determined, which was conditionally taken as the lowest value at a certain temperature: for 60 °C, 70 °C, 80 °C, and 90 °C, the values were 0.221, 0.201, 0.151, and 0.099 kg H₂O ⁄ kg dry material, respectively.

Figure 1.

Changes in the moisture content of a stationary layer of apple pomace over time at different heights of the stationary layer of wet material

Figure 2.

Changes in the moisture content of a stationary layer of apple pomace over time at different temperatures of the thermal agent

Figure 3.

Changes in the moisture content of a stationary layer of apple pomace over time at different velocities of the thermal agent

Figure 4.

Graph-analytical method for determining the critical moisture content and the time of its achievement at different stationary layer heights of wet material

Figure 5.

Graph-analytical method for determining the critical moisture content and time of its achievement at different temperatures of the thermal agent

Figure 6.

Graph-analytical method for determining the critical moisture content and the time of its achievement at different velocities of the thermal agent

Using the graph-analytical method [21], the critical moisture content $w_{cr}^c$ and the time of its achievement τ_cr were determined at different stationary layer heights of apple pomace (Figure 4), different temperatures of the thermal agent (Figure 5), and different velocities of the thermal agent (Figure 6). The results of the graphical analysis are given in Table 1.

According to the methodology of [21], using the graphical method, the kinetic coefficients a and η were determined for the first conditional drying period, the period of complete moisture saturation (Figure 7). The results of the graphical determination of the kinetic coefficients are given in Table 2.

Figure 7.

Determination of the kinetic coefficients a and η in the first conditional drying period

Having determined the coefficients A = 1.237×10^-5, m = 1.06, n = 0.422 to express the kinetic coefficient η in the first drying period of complete saturation of the thermal agent with moisture [21], write down an expression to describe the kinetics of filtration drying of apple pomace in this drying period:

$w^c=w_0^c\left(1-1.237\times {10}^{-5}\times T^{1.06}\times v_0^{0.422}\times \tau \times e^{-10.075\times H}\right)$ (1)

To generalize the regularities of the filtration drying rate of apple pomace in the second conditional drying period, graphical dependencies are constructed to determine the drying coefficient K (Figure 8 - Figure 10). The coefficient K allows us to find the relative drying coefficient χ at a known value of the drying rate in the second conditional period of partial saturation of the thermal agent with moisture N [21]. The results of the graphical analysis are summarized in Table 3.

Figure 8.

Determination of the coefficient K at different stationary layer heights of wet material

Figure 9.

Determination of the K coefficient at different temperatures of the thermal agent

Figure 10.

Determination of the coefficient K at different velocities of the thermal agent

Figure 11.

Dependence of drying coefficient K on drying rate N for filtration drying of apple pomace

The graphical dependence K = f (N) (Figure 11) indicates that for apple pomace the relative drying coefficient is χ = 0.211 kg H₂O ⁄ kg dry material.

Thus, the generalized equation describing the drying rate in the period of partial saturation of the thermal agent with moisture will be as follows:

$w^c=\left(w_{\text{cr}}^c-w_{\text{e}}^c\right)\times e^{-0.211\times N\times \left(\tau -{\tau }_{\text{cr}}\right)}+w_{\text{e}}^{\text{c}}$ (2)

To assess the correctness of the derived mathematical dependencies (1) and (2), it was analyzed the distribution of the deviations of theoretically calculated values from the experimentally obtained ones. It should be noted that the analysis of the nature of the kinetic curves and the obtained set of experimental data indicates an increase in the deviation of theoretically calculated values from the experimental data after reaching a certain value of moisture content. This is due to the nature and type of raw materials - the heat consumption for the evaporation of bound moisture and heating of wet material, which increases with a decrease in the tangent of the slope of the kinetic drying curve to the abscissa axis and requires a correction factor for the second conditional drying period [23]. Thus, the authors recommend the use of eqs. (1) and (2) for the following range of moisture contents, where the error of conformity of experimental data to theoretically calculated ones is acceptable for calculations of drying equipment and does not exceed ~32 % (Table 4):

For the recommended values (Table 4), the largest absolute value of the deviation of theoretically calculated values relative to experimental data is 32.29%, the average value of this deviation is 7.60%. A graphical representation of the distribution of deviations of theoretically calculated values relative to experimental data is shown in Figure 12.

Figure 12.

Distribution of deviations of experimental data to theoretically calculated ones for filtration drying of apple pomace

Eqs. (1) and (2) allow us to express the equations for determining the process duration in the first τ_I and second τ_II conditional drying periods, respectively:

${\tau }_{\text{I}}=\frac{1-\frac{w^c}{w_0^c}}{1.237\times {10}^{-5}\times T^{1.06}\times v_0^{0.422}\times e^{-10.075\times H}}$ (3)

${\tau }_{\text{II}}=\frac{0.211\cdot \left(w_0^c-w_{\text{cr}}^c\right)-ln\frac{\left(w^c-w_{\text{e}}^c\right)}{\left(w_{cr}^c-w_{\text{e}}^c\right)}}{0.211\times N}$ (4)

The second important parameter for the calculation of filtration drying equipment is the hydraulic resistance of a stationary layer of material. Experimental studies were conducted to determine the effect of the fictitious flow rate v₀ on the hydraulic resistance ΔP of the porous stationary layer of the material under study according to the method [22]. In addition, computer modeling was performed to generalize the obtained experimental values. Computer simulations of the hydrodynamics of the flow of the thermal agent were performed in the ANSYS Fluent 2022 R2 program [24], which is widely used for similar tasks [25], [26].

In accordance with the methodology of [22], the bulk density of dried apple pomace was experimentally determined to be 202.37 kg/m³ and the layer porosity of the studied material was 0.276.

The results of the hydrodynamics study of the thermal agent movement through a stationary layer of the studied material are presented in form of graphical dependence ΔP = f(v₀) for the recommended values of the material layer height during drying under industrial conditions H = 80÷120 mm (Figure 13) [22].

Figure 13.

Dependence of the fictitious velocity of the thermal agent on the change in the hydraulic resistance of the dried apple pomace layer at different heights

Figure 14.

Graphical comparison of the obtained simulation values (––– red lines) of the hydraulic resistance of dried apple pomace with the experimental one (––– black lines) from the fictitious velocity of the thermal agent at different layer heights

Table 5 shows the deviations of computer modeling from the values of hydraulic resistance obtained experimentally (Figure 14).

Analyzing the simulation data, the average deviation for all experimental points is 8.28 % (Table 5). Taking into account the results of modeling according to the methodology [22], the pressure loss in the layer of apple pomace ΔP can be determined according to equation:

$\Delta P=3073.572289\times H\times v_0+3397.456559\times H\times v_0^2$ (5)

The calculation of the technologically feasible parameters of filtration drying at the experimental installation was performed according to the methodology described in [23], which was based on [27], [28]. The energy costs for heating the thermal agent to remove 1 kg of moisture ${\text{Q}}_{\text{t}\text{.a}\text{.}}^{\text{lab}}$ and for overcoming the pressure drop to remove 1 kg of moisture ${\text{Q}}_{\Delta P}^{\text{lab}}$ were determined.

The determination of ${\text{Q}}_{\text{t}\text{.a}\text{.}}^{\text{lab}}$ was based on the parameters of the filtration drying process [23], [27], as well as its duration, determined by Eqs. (3) and (4). The calculation of ${\text{Q}}_{\Delta P}^{\text{lab}}$ was based [23], [28] on the determination of pressure losses in a stationary layer of apple pomace according to Equation (5).

Taking into account the recommendations [1], it is advisable to dry the initial plant material to a moisture content of 14%, which in terms of moisture content is approximately w^c ≈ 0.16 kg H₂O/kg dry material. Based on the analysis of dependence (4) and the previously determined values of the equilibrium moisture content of apple pomace $w_e^c$ for different temperatures, it is possible to achieve the required moisture content at temperatures of 80 °C and 90 °C, since for these temperatures the values of $w_e^c$ are less than the final w^c.

It should be noted that to calculate the time of filtration drying at temperatures of 80 °C and 90 °C for the second conditional period, it was necessary to take into account the additional heat consumption for the evaporation of bound moisture using the refinement coefficient Kτ_τII [23] – 0.45 and 0.55, respectively.

The results of calculating the technologically feasible parameters of filtration drying of apple pomace in the experimental installation are summarized in Table 6.

Thus, the following parameters are taken as technologically feasible parameters of filtration drying of apple pomace: the height of the dried material layer H = 120 mm, the temperature of the thermal agent T = 90 °C, and the filtration velocity of the thermal agent v₀ = 1.76 m/sec. With these process parameters, the energy consumption for removing 1 kg of moisture is 21990.02 kJ/kg H₂O or 6.11 kWh/kg H₂O.

If to estimate the industrial dehydration from the moisture content of raw materials of 83 % wt. to 14 % wt. by the filtration method and, for comparison, by the common method in a rotary dryer [29], according to the methodology [23], then in terms of dehydration of ≈ 1000 kg of apple pomace, the results will be as follows (Table 7):

Note that the heat capacity of apple pomace was calculated according to [30]. The parameters of the thermal agent were determined using the I-d state of humid air [31].

The data of the theoretical calculation of the filtration drying use in industry (Table 7) and the experimentally obtained data (Table 6) are close, which indicates the correctness of the calculation. Also, the calculation data of industrial drying methods indicate the efficiency of using filtration drying according to the indicators of specific energy costs for moisture removal and, above all, according to the duration of the process.

The calorimetric combustion method was used to determine three main indicators of the studied solid material (Figure 15) and the briquetted solid fuel sample created from it (Figure 16): residual moisture content, ash content, and higher calorific value in accordance with the State Standards of Ukraine [1].

Figure 15.

Dried apple pomace

Figure 16.

Briquetted sample of solid fuel obtained from apple pomace

Due to the heterogeneity of the apple pomace composition, 3 parallel experiments were conducted to determine the average values. The results are presented in Table 8. Calorimetric studies of dried apple pomace showed the prospects of creating solid fuel briquette samples; briquetting conditions are described in the section “Experimental part”.

The moisture content of all the samples was < 1%. The values of calorific value, ash content, and residual moisture are close to or meet the requirements of European standards for solid fuels: German standard DIN 51731 (calorific value 15512÷19515 kJ/kg, ash content <1.5 %, residual moisture <12 %); Swedish standard SS 187120 (calorific value >16910 kJ/kg, ash content <1.5 %, residual moisture <10 %); etc. [32]. The obtained experimental data indicate the prospects of using apple pomace as an alternative solid fuel.

Comparison of the obtained calorimetric combustion results of solid fuel samples obtained from apple pomace (Table 8) and the calculation of specific energy consumption for removing excess moisture from the material (Table 7) indicate the following: theoretically, 92977.11 kJ/kg of material should be spent for filtration drying of apple pomace to be able to obtain ≈ 19438 kJ/kg of energy as a result of using them as solid fuel. The values of energy consumed for the preliminary preparation of 1 kg of initial raw material exceed the potential energy that can be obtained as a result of burning 1 kg of the resulting fuel differ by 79.09 %. This balance can be corrected by using secondary heat at the factory to dry the raw materials, since the energy for heating the thermal agent makes up the largest part of the required energy consumption. It is also possible to consider the option of drying wet material in several stages, for example, initial mechanical pressing of moisture and filtration drying to the required moisture content of the raw material.

On the other hand, society lives not only in terms of economics, but also the need to improve the environmental situation in the world. The use of secondary raw materials of plant origin as an alternative solid fuel can replace the use of slowly renewable or non-renewable sources (such as wood and fossil fuels) and, at the same time, solve the problem of accumulating excessive amounts of industrial waste with a limited shelf life.

Of course, this estimate does not take into account energy costs for briquette production, warehouse rent, investments in new equipment, logistics, etc. However, given the availability and low cost of recycled materials, it can be argued that with a rational scheme of recycled material preparation, the use of apple pomace as an alternative solid fuel is a promising and rational area for practical use.