The significance of biowaste drying analysis as a key pre-treatment for transforming it into a sustainable biomass feedstock

Biowaste sampling

Sampling was carried out in Morelia, Michoacan, Mexico. Despite the fact that Morelia city has regulations for solid waste management, it is not complied by any of the actors involved, which also makes it difficult to collect samples (Hernández et al., 2019). The sampling area was chosen randomly without considering the economic stratum, as defined in Mexico by the National Institute of Statistics, Geography and Information (INEGI), which categorizes income into four ranges: Low, Lower-Middle, Upper-Middle, and High Stratum (INEGI, 2017). The selected area falls into lower-middle stratum. Samples were collected from municipal solid waste collection trucks with an average weight of five kilograms (composed of fresh fruit and vegetable peels), ensuring that samples were not tampered with and that valuable materials were extracted. Biowaste sampling was conducted on six consecutive days during the third week of May 2019, and was refrigerated at 4 °C. Samples were divided into six batches based on collection day, with each batch containing three kilograms of FVBW. To homogenize sample particle sizes, waste greater than 0.0254 m width, 0.0508 m length, and 0.005 m thickness, was sliced according to NREL/TP-510-42621 (2008).

Drying of biowaste samples

Six batch of FVBW formed during sampling stage, was spread evenly on a metal surface measuring 0.9 m long by 0.5 m wide and dried under open-sun conditions for 10 h (from 9:00 a.m. to 7:00 p.m.). Drying process was performed during 16 days between June and July (2019). In that period weather conditions were: maximum relative humidity of 77.25%, temperature of 47 °C (direct sunlight exposition) and maximum wind velocity of 19.3 km/h. Each batch was weighed daily on a 5 kg digital scale with 0.01 g accuracy. For all batches, under these conditions each drying curve only exhibits the second falling rate period at environmental conditions, and the drying process occurs in a non-steady state. Given the nature of biomass that makes up each batch of FVBW, the initial moisture content (M_o) differs between batches as well as the drying exposed area (A). Dry mass for each batch was determined according to ASTM D 4442-92 (1992).

Influence of initial moisture content and drying exposed area on drying rate

The influence of A and M_o interaction on drying rate (N) was analyzed using a surface model for each batch (Eq. 1): (1)${\displaystyle N\left(A,M_0\right)=a_1{A}^2+a_{2}A\cdot M_0+a_3{M}_0^2+a_{4}A+a_5{M}_0+a_6.}$

For each batch, each constant of each model was calculated in three experimental key moments, using GNU Octave version 7.1.0^® software (Eaton et al., 2022): (1) initial conditions, when FVBW presented maximum moisture content; (2) on the fifth day, when FVBW reached the preservation optimum moisture content (10%); and (3) at the end of the experiment, when the equilibrium moisture content was reached. The coefficient of determination (R²) was calculated for each model to test the effectiveness of N (A, M_o) in predicting experimental data.

Biowaste mathematical drying models

The effectiveness of eight models in predicting drying rates was assessed, which have previously been applied to other types of biomass: (Arslan & Musa, 2010) in onion slice drying, (Erbay & Filiz, 2010) thin layer food drying studies, (Gaibor et al., 2016) maize cane drying, (Inyang, Oboh & Etuk, 2018) modeling food drying techniques, and (Wakchaure et al., 2010) mushroom (Agaricus bisporus) drying. Mathematical models presented in Table 1 were fitted from experimental results of moisture ratio vs. time (t); dimensionless model constants a,b,c,d and n and drying constants k, k_o and k ₁ (h⁻¹) were estimated by nonlinear least squares using the Levenberg–Marquardt algorithm (Levenberg, 1944; Gavin, 2022).

Effective diffusivity coefficient

Fick’s second law in one dimension was applied (Crank, 1975) (Eq. (2)) (2)${\displaystyle \frac{\partial MR}{\partial t}=D_{eff}\frac{{\partial }^{2}MR}{\partial x^2}}$

where MR is dimensionless moisture ratio; t drying time; x distance in the moisture transport direction; and D_eff, effective diffusivity coefficient.

For a rectangular slab with thickness of 2L and symmetrical plane at x = 0; the initial (i) and boundary (ii, iii) conditions are: ${\displaystyle \begin{array}{c}\hfill \left(i\right)t=0,0<x<L,M=M_0\hfill \\ \hfill \left(ii\right)t>0,x=0,\frac{\partial M}{\partial x}=0\hfill \\ \hfill \left(iii\right)t>0,x=L,M=M_e\hfill \end{array}}$

where M₀: indicates the initial moisture content; M_e: equilibrium moisture content and M: moisture content at any time.

Equation (2) is solved by power series; when internal mass transfer is the controlling transport mechanism in one dimension, assuming an infinite slab (Eq. (3)) (Crank, 1975; Derossi, Severini & Cassi, 2011; Cai et al., 2017). (3)${\displaystyle MR=\frac{8}{{\pi }^2}\sum _{i=0}^{\mathrm{\infty }}\frac{1}{{\left(2i+1\right)}^2}exp\left[\frac{-{\pi }^2{\left(2i+1\right)}^2}{4L_0^2}{D}_{eff}\cdot t\right].}$

For long drying periods, when i = 0 and the drying process is carried out under unsteady-state conditions, Eq. (3) can be further simplified to only the first term of the series (Eq. (4)) (Pisalkar et al., 2014). (4)${\displaystyle MR=\frac{8}{{\pi }^2}exp\left[\frac{-{\pi }^2}{4L_0^2}{D}_{eff}\cdot t\right].}$

According to Lewis (1921); MR is expressed as Eq. (5): (5)${\displaystyle MR=\frac{\left(M-M_e\right)}{\left(M_0-M_e\right)}.}$

Substituting MR from the Eq. (5) in Eq. (4), Eq. (6) is obtained: (6)${\displaystyle MR=\frac{\left(M-M_e\right)}{\left(M_0-M_e\right)}=\frac{8}{{\pi }^2}exp\left[\frac{-{\pi }^2}{4L_0^2}{D}_{eff}\cdot t\right].}$

Finally, when logarithms are applied on Eq. (6), Eq. (7) is obtained: (7)${\displaystyle lnMR=ln\left[\frac{8}{{\pi }^2}\right]-\left[\frac{{\pi }^2}{4L_0^2}{D}_{eff}\cdot t\right].}$

Statistical analysis

The Fickian model and semi-theoretical mathematical models presented in Table 1 were assessed using goodness-of-fit tests; coefficient of determination (R²), reduced Chi-square (χ²), and root mean square error (RMSE) were calculated for each model. Highest R² values and lowest χ², and RMSE values were used as criteria to define the effectiveness of the best model in predicting experimental data.

The Kruskal-Wallis test (df = 5 and α = 0.05) was used to compare the mean values of N among the six batches with respect to A and M_o.

Characterization of biowaste samples based on drying area and initial moisture

The components of FVBW within and among batches, were heterogeneous respect to A and M_o (Table 2).

Drying process at constant rate, A and M_o are inversely related, this suggests that batches with higher values of M_o may take longer to dry; according to M_o values of batch one (B1) and batch two (B2) samples, it can be inferred that it takes a longer drying time than the rest of batches; however, in this work, where drying process took place under unsteady-state, the drying rate exhibits a different response to M_o.

Behavior of drying rate and its relationship with the initial moisture and drying area

Every surface mathematical models N(A, M_o), presented R² values of 0.999. Which demonstrated the effectiveness of N(A, M_o) to predict N values with high accuracy at three key moments of the experiment (Table 3).

At initial conditions of drying process, interaction among the experimental data of A with M_o and its influence on N, B6 sample reached the highest value of N, which is associated with the lowest values of A and M_o (Fig. 1A). The behavior of N, estimated as a function of A and M_o, from the surface mathematical model, is increasing in the maximum values of A and M_o as well as at the opposite side associated with minimum values of A and M_o (Fig. 1B).

In Fig. 2A, results of N with respect to A and M ₀ at fifth day are presented. B6 kept highest N value. At this moment, N trending observed is similar that at experiment’s start (Fig. 2B). Biggest N values appear at highest interactions between A and M ₀, as well as opposite side where batches presented lowest A and M ₀ values.

At final stage of experiment (day 16), FVBW samples reached equilibrium moisture (Fig. 3A). N follows same pattern as observed at the first and fifth day (Fig. 3B). In general, it is observed that highest values of A associated with highest values of M_o promote N to reach highest values. Analogously, same behavior tends to occur at opposite conditions where lowest values of A are associated with lowest values of M_o.

The range within which the N values appear among batches and their means, for each day, shows low dispersion, according to obtained values of the standard deviation (Table 4). After five days of treatment the MR value is greater than 90%, half of the time required to dry cylindrical bodies of corn cane previously reported by Gaibor et al. (2016). This moisture content is within the desired range to prevent the development of biomass-decomposing bacteria; moreover, within this moisture range, the biomass can enter bio-refinery processes such as pyrolysis or densification of biomass (Bajwa et al., 2018).

Drying curves and semi-theoretical drying models

In Fig. 4A, results of N vs. t are presented, batch six (B6) sample presented the higher values of N followed by batch three (B3) sample. It is important to mention that initial moisture content and dry solid mass were variable among batches. On the fifth day, B3 sample presented the highest value of remaining moisture content; and batch five (B5) sample the lowest (Fig. 4B); in spite of this findings, when Kruskal-Wallis test was applied, significant differences were not found (p = 0.639, df = 5 and α = 0.05).

The experimental MR results among batches differed by 0.06% when the initial moisture content in samples was present; 0.02% when moisture content reach 10% value; and 0.00032% when drying process reach the equilibrium. According to goodness of fit test (Table 5), Two-term model presented best fitting to predict drying rate (R² = 0.999, χ² =4.666 × 10⁻⁵ and RMSE =0.00683).

Determination of effective diffusivity coefficient

In Fig. 5A, results of ln (MR) vs. t are shown. Different points in the graphic represent six different batches; D_eff is obtained for the curve slope of ln (MR) and t relationship (Fig. 5B). Kruskal-Wallis test showed that there is no significant difference (p = 0.723, α = 0.05) of D_eff among batches.

In all batches R² values were above of 95%. B1 sample presented the highest R² value (0.979), and B2 sample the lowest (0.952); despite of drying process occurred in unsteady-state, this finding demonstrate a significant linear relationship between ln(MR) and t (Table 6); hence, the model obtained from Fick’s second law is reliable to predict N values for biowaste samples under open sun-drying conditions.

Initial moisture content and heterogeneous physical composition of samples

The initial moisture content in FVBW is relatively higher than that of forest and agricultural biowaste (Libra et al., 2011; Pavi et al., 2017; Osman et al., 2019; Qu et al., 2021; Wang & Tester, 2023; Eixenberger et al., 2024). This implies a greater difference between M ₀ and M_e, which, along with meteorological conditions, is a critical factor in the decrease of the drying rate. The drying rate slowed as the moisture content approached equilibrium moisture, as reported by Zhen-dong et al. (2022) in the direct sun drying of corn seeds. This suggests that the drying period to reach the same final moisture content in FVBW would be longer in samples where the difference between M ₀ and M_e is greater, implying additional energy consumption, as mentioned by Kaveh, Abbaspour-Gilandeh & Fatemi (2021). Heterogeneous nature of physical composition of FVBW affected M₀ in each batch, resulting in M ₀ behaving randomly during sampling. However, M ₀ showed low variation among batch values, allowing for sufficient control over M ₀ to achieve uniform drying operation. When considering the projection of solar drying on a pilot scale, M ₀ values would be similar, and an effective treatment could be achieved. Based on this, final moisture content within a specific drying period would be consistent, in line with the observed values of MR and its standard deviation at initial conditions, after five days, and after 16 days of treatment.

Effectiveness of surface model and correlation of M₀ and A with maximum N

Drying rate and dimensionless moisture content are typically reported as functions of time; however, N has a multivariable dependence (Treybal, 1981). In this study, it was demonstrated that the surface model N(M ₀, A) is effective and highly accurate predicting N as a function of M ₀ and A. Through this model, it was identified that maximum drying rate of FVBW is correlated with higher values of M ₀ and A. It is of particular interest to observe the response of N as a function of M ₀ and A since, on one hand, M ₀ varies between batches and is expected to do so each time FVBW is collected due to its origin; on the other hand, the drying area is a variable that can be relatively easier to control to achieve more uniform treatment and greater control over the operation. The response of N at the beginning of the experiment, when the value of M = 10% is reached, and when equilibrium is reached, demonstrated that the behavior of N(M ₀, A) remains consistent over time. This supports the assertion that drying method is effective despite being conducted under non-constant drying conditions and that the mechanisms involved in the movement of water from the inner part of the solid to the surface are similar among samples from the six batches.

Drying curves and the controlling mechanism of drying kinetics

When the controlling mechanism of drying kinetics is due to internal factors within the solid, the properties of the drying air and its velocity become insignificant (El-Amin, 2011). If the controlling mechanism of drying kinetics is due to internal factors, the internal morphology of the solid influences the trend of the drying curve that characterizes the drying of the solid (Zhao et al., 2023). The close similarity between the batches in the trends of drying curves N vs t (Fig. 4A), and MR vs t (Fig. 4B), suggests that there is sufficient resemblance in the arrangement of the channels and voids that define internal structure of substrate. This means that the path that water molecules have to take in order to move from the inner part of the substrate to the surface would generally encounter the same difficulty across the six batches of FVBW. This fact is reflected in the similarity among the drying curves of the six batches and demonstrates the repeatability and efficacy of the method. The trend of drying-curves is similar to those reported by Agbede et al. (2023) in the drying of banana stalks, dried under sun drying. As seen in the results of the MR vs t curves, discrepancies in MR among the batches over time are small. In these curves, it is more notable that these discrepancies are related to differences between M_o and M_e. This fact demonstrated that, despite these discrepancies, drying remained uniform over time and become more evident after MR reached 100 h of drying and approached equilibrium. This trend is consistent with other studies in which agricultural products and by-products were dried under sun-drying (Suherman et al., 2020; Simo-Tagne & Ndukwu, 2021; Zhen-dong et al., 2022; Zhao et al., 2023). Sun-drying is the most economical, environmentally friendly, and widely used technique for drying agricultural products and by-products (Zhao et al., 2023). However, to handle the daily volume of FVBW generated, it is necessary to incorporate an environmentally friendly technological adaptation to the method to reduce the moisture content just below 10% within a few hours, instead of five days, as other researchers have successfully done in drying other types of biomass using solar energy (El-Sebaii & Shalaby, 2012; Badaoui et al., 2019; Devan et al., 2020).

Drying models and their response under non-constant drying conditions

The drying models evaluated in this study have been successfully employed in sun-drying operations, as well as under constant drying conditions, and in drying thin layers of agricultural and food products (Henderson, 1974; Erenturk, Gulaboglu & Gultekin, 2004; Sobukola et al., 2007; Gaibor et al., 2016; Goud et al., 2021; Dhake et al., 2023). These models have proven to be particularly useful predicting drying rate in falling rate period (Henderson, 1974). Consistent with the above, in present study, Logarithmic, Two-Term, and Midilli models provided best fit to experimental data, with as much effectiveness and precision as reported in the drying operations of food and agricultural products. Sobukola et al. (2007) dried leafy vegetables under direct sunlight and found that the Logarithmic and Midilli models were the most reliable, with the Midilli model being the most accurate (R² = 0.999). Badaoui et al. (2019) dried tomato residues in a greenhouse-type solar dryer and, among conventional models they evaluated, Midilli-Kucuk model achieved an R² value of 0.999, while Logarithmic model achieved an R² of 0.998. Castillo-Téllez et al. (2024) dried oregano leaves directly under sun and found that Modified Page, Page, and Logarithmic models provided best fit, with Logarithmic model being the most reliable ( R² = 0.998). Suherman et al. (2020) dried cassava flour in a hybrid solar dryer and found that Midilli model was the most accurate (R² = 0.994). Logarithmic and Two-Term models proved to be the best for predicting drying rate of rosehip under constant conditions, with Logarithmic model achieving an R² value of 0.994 (Erenturk, Gulaboglu & Gultekin, 2004). The MR vs t curve exhibits a trend similar to that indicated by Henderson (1974), suggesting that the mechanism controlling water transport is diffusion. Given that the effective diffusivity coefficient is sensitive to temperature (Baldán et al., 2020), it is inferred that temperature changes throughout the day affected dispersion of ln(MR) vs. t relationship results, particularly when MR approached 10%. However, the D_eff values showed low dispersion according to their standard deviation. Moreover, values obtained from six batches fall within the acceptable range of D_eff values for agricultural products and food, which are between 10⁻¹¹ and 10⁻⁹ m²/s (Sobukola et al., 2007).