Moisture Sorption Isotherms of Fresh Compost

1 Moisture sorption isotherms of fresh compost Apolinar Picado*, Luis Moreno† Department of Chemical Engineering, KTH Royal Institute of Technology, Stockholm, Sweden ORCiD Apolinar Picado https://orcid.org/0000-0002-4138-8043 Luis Moreno https://orcid.org/0000-0001-8241-2225 *Corresponding author. Apolinar Picado, Department of Chemical Engineering, KTH Royal Institute of Technology, 100 44 Stockholm, Sweden. E-mail addresses: [email protected]; [email protected] (A. Picado). †Deceased 2 Moisture sorption isotherms of fresh compost In this study, the moisture sorption isotherm of fresh compost was experimentally determined using a modified gravimetric method. The experiments were conducted at a temperature of 50 C with an airflow rate of approximately 28 m/h. The results indicated that the moisture sorption isotherm exhibited a type II S-shaped curve. Notably, capillary condensation became significant at relative humidity levels exceeding 75%. A nonlinear regression analysis was performed to fit fifteen moisture sorption isotherm models from the literature to the experimental data. The models were evaluated based on their statistical parameters, specifically R2, SSE, and RMSE. Among the models, the Smith model was identified as the most accurate for predicting the relationship between equilibrium moisture content and relative humidity. Additionally, the Halsey, Henderson, and Luikov models also demonstrated good fit. Keywords: Fresh compost; Isotherm; Model; Regression analysis 3 1. Introduction Compost is a biologically-stable, nutrient-rich, soil-like amendment created through the aerobic decomposition of organic materials. Generally, compost products intended for commercial sale undergo thermophilic composting, a process that involves high temperatures to help eliminate pathogens. The composting process requires a balanced ratio of carbon-rich materials (e.g., dry leaves, woodchips, etc.) to nitrogen-rich materials (e.g., food scraps, grass clippings, etc.). To ensure that microorganisms can effectively break down organic materials into high-quality compost, it is important to maintain adequate moisture levels, oxygen flow, particle size, and temperature. Composting can be done at various scales and in a wide range of locations, from urban to rural areas (EPA, 2022; Haug, 1993). One important physical factor to consider when mixing materials and maintaining suitable conditions during the composting process is moisture content. Water is essential for microbial activity, as it supports the metabolic processes of microorganisms. It serves as a medium for chemical reactions, transports nutrients, and allows microorganisms to move freely. If the moisture content is too low, microbial activity will be limited. Conversely, if the moisture content is too high, excess water can displace air from the pore spaces, thus leading to anaerobic conditions within the material. Additionally, high moisture levels can weaken the structural integrity of the material, making it more susceptible to compression. This reduction in structural strength also decreases porosity, which can further contribute to the formation of anaerobic regions. Even if the compost materials are initially mixed to achieve an appropriate moisture content, maintaining that moisture level throughout the entire composting process can still be a challenge. Moisture can move within the compost matrix through the diffusion of water vapour and due to both forced and natural air movement. These mechanisms can lead to 4 water vapour from warmer areas condensing in cooler surface regions or result in the overall loss of moisture from the composting mass (Agnew and Leonard, 2003; Richard et al., 2002). Moisture content plays a crucial role in influencing both the material and matrix properties, as well as microbial activity, which have significant implications for the physical and biological aspects of the composting process. Additionally, biological materials will either gain or lose moisture to reach equilibrium with their surrounding environment. However, there has been limited research conducted on the equilibrium moisture content of compost. For instance, Meiering et al. (1972) conducted experiments to determine the sorption isotherms of compost at three different temperatures: 20, 60, and 80 °C. The compost consisted of a mixture of irregularly shaped particles with diameters ranging from 2 mm to a few microns. Many of these particles had a fibrous shape, resembling fine tobacco. The experiments were performed in a column-shaped dryer with a cross-section of 0.125 m2 (0.5 m  0.25 m) and a height of 2 m. The sorption isotherms obtained at the different temperatures were relatively close to one another. Furthermore, Baker et al. (1999) determined the equilibrium moisture isotherms of synthetic food waste and biosolids compost using a closed loop, dynamic method. They investigated the effect of substrate type and the level of degradation on the equilibrium relationship between moisture content and relative humidity. Their findings indicated that mixtures composted for 20 to 30 days had isotherms resembling those of the raw materials, thus suggesting that the degradation process did not significantly alter the equilibrium relationships. The Chung-Pfost equation was used to describe the experimental data. Bloom and Richard (2002) conducted bench-scale measurements using a static method to correlate the compost’s moisture content with water activity and matric potential. The compost used was a blend of poultry manure and wood shavings. They found that for moisture contents exceeding 35% (wet basis), the water activity remained consistently above 0.98. Maia et al. (2011) 5 determined sorption isotherms for a compost material sieved into four different particle size ranges (4.76 mm > PS1 > 3.36 mm > PS2 > 2.38 mm > PS3 > 2.00 mm > PS4 > 1.68 mm). The compost material used was a blend of horse manure, cattle manure, chicken waste, woodchips, sawdust, leaves, ground hay, tobacco stalks (seasonal), grass hay, and others. The Henderson model provided the best fit for all four particle size ranges tested. Many studies have investigated the production and utilisation of compost; however, there is a lack of information on moisture sorption isotherms in existing literature. This study aimed to experimentally determine the moisture sorption isotherm of fresh compost and evaluate the effectiveness of various theoretical, semi-theoretical, and empirical models in describing the relationship between equilibrium moisture content and relative humidity in fresh compost. 2. Materials and methods 2.1. Materials The fresh compost, consisting of raw or undigested materials, is composed of a blend of shredded household refuse (70%) and dewatered sewage sludge (30%) sourced from wastewater treatment plants in Stockholm, Sweden. The average composition of the household refuse is detailed in Table 1. The moisture content of the household refuse ranges from approximately 39% to 42% on a wet basis. The dewatered sewage sludge serves as a valuable source of nitrogen and moisture. The amount of dewatered sewage sludge that can be added to the fresh compost without disrupting the composting process depends on its moisture content, as reported by Moreno (1982). 6 {Table 1 Placeholder} 2.2. Experimental apparatus A schematic diagram of the experimental apparatus is illustrated in Figure 1. The apparatus comprises two main sections: the humidification section and the adsorption section. A blower generates an airflow at a velocity of approximately 28 m/h (2 m3/h), as measured by a rotameter positioned before the humidification section. In the humidification section, the air is passed through water maintained at a constant temperature to achieve a desired level of humidity. After this humidification process, the air is heated to the temperature required for determining the moisture sorption isotherm. The temperature is regulated using a contact thermometer (TIC) linked to a heating device (HD). 2.3. Experimental procedure In the adsorption section, fresh compost was placed in a column with a diameter of 30 cm and packed to a height of approximately 20 cm. The adsorption experiments were performed at a temperature of 50 °C using a modified gravimetric method. The temperature within the fresh compost was monitored using thermocouples. Air with a specific temperature and humidity was passed through the fresh compost until equilibrium was reached. Once equilibrium was achieved, the fresh compost was removed from the column, and samples were collected. These samples were then dried at 105 °C for 48 hours to determine the moisture content. The experiments were conducted in duplicate. {Figure 1 Placeholder} 7 2.4. Moisture sorption isotherm models Experimental data for equilibrium moisture content (Xeq) versus relative humidity (  ) are fitted to the sorption models outlined in Table 2, which are commonly used for foods and other materials. Sorption models with five or more model constants are not included. It is important to note that these models have a significant limitation: their applicability is not suitable across the entire range of relative humidity (0    1). {Table 2 Placeholder} In this study, a non-linear regression analysis is performed to fit the experimental data to the sorption models using MATLAB’s Curve Fitting Toolbox and the non-linear least squares method. The coefficient of determination (R2) is the primary criterion for selecting the best model to describe the experimental data, with the highest R2 value being required. In addition to R2, the root-mean-square error (RMSE) and the sum of squared errors (SSE) are also used to assess the model’s fit. To determine the goodness of fit, it is necessary to have the highest R2 value along with the lowest SSE and RMSE values. These statistical parameters can be calculated as follows (Vega-Gálvez et al., 2009): ( ) 2 ,, 1 N eq,exp,i eq pred i i SSE X X = =−  (1) ( ) 2 1 , N eq,exp,i i eq exp SST X X = =−  (2) 8 21SSE RSST =− (3) ( ) 1/2 2 ,, 1 1N eq,exp,i eq pred i i RMSE X X N=  =−    (4) where Xeq,exp,i is the ith experimental equilibrium moisture content, Xeq,pred,i is the ith predicted equilibrium moisture content, X eq,exp is the average of the experimental values, and N is the number of observations. Various regression analysis methods for fitting these models to experimental data have been discussed in the literature. Direct nonlinear regression has several advantages over indirect nonlinear regression (Mujumdar, 2014). 3. Results and discussion 3.1. Experimental observations The moisture sorption isotherm was determined at a temperature of approximately 50 °C. To adjust the experimental values, an equation reported by Harmathy (1969) was applied that connects the moisture content to the average normal curvature of the liquid surface in the pores. This equation is derived from the Kelvin equation. Although it strictly applies only to the capillary condensation region, it can be utilised across nearly the entire sorption range. Experimental data for Xeq versus  are presented in Figure 2. As expected, Xeq increased with rising  levels. The results indicated that capillary condensation became significant at relative humidity levels above 75%. A moisture sorption isotherm that exhibits a vertical step, which is commonly observed in porous materials, suggests the occurrence of capillary condensation 9 alongside pore-filling phenomena. This phenomenon occurs when water vapour condenses within the pores of a material at relative humidity levels below the saturation vapour pressure of bulk water (Mudoi et al., 2022). According to the literature, moisture sorption isotherms can be classified into six distinct types (I to VI) based on their shape (Sing et al., 1985). In this case, the moisture sorption isotherm displayed a type II sigmoid pattern, which is typical of macroporous material matrices, such as fresh compost. Two well-defined zones were observed (see Figure 2). At low values of  (< 0.75), small changes in the Xeq corresponded to significant changes in  , while at high values of  (> 0.75), the opposite occurred. The S-shaped isotherm represents a sorption curve that reflects both monolayer and multilayer moisture adsorption. At low values of  , the sorption process primarily involves monolayer adsorption, characterised by gradual increases in Xeq as  rises. When  values surpass 0.75, the transition to multilayer sorption occurs, resulting in a rapid increase in Xeq (Sing et al., 1985). Additionally, the presence of plastic in the fresh compost may result in lower values for the moisture sorption isotherm. {Figure 2 Placeholder} 3.2. Moisture sorption isotherm models Although some of the models listed in Table 2 do not account for capillary condensation, all available experimental data were used to determine the constant values for the sorption models employed. The experimental data (Xeq versus  ) were analysed and fitted to all the models outlined in Table 2. The models were evaluated based on their statistical parameters, specifically R2, SSE, and RMSE. The results of the regression analysis are summarised in Table 3. Only models that showed an R2 of approximately 0.90 or higher were included in 16 Maia, G.D.N., Day, V., Gates, R.S., & Taraba, J.L. (2011). Biofilter media characterization using water sorption isotherms. Transactions of the ASABE, 54(4), 1445-1451. doi: 10.13031/2013.39025 Meiering, A.G., Clifford, W.H., & Bakker-Arkema, F.W. (1972). Drying of a bed of composted waste. Transactions of the ASAE, 15(1), 116-0120. doi: 10.13031/2013.37844 Moreno, L. (1982). Composting household refuse by forced aeration [PhD Thesis, KTH Royal Institute of Technology]. Mudoi, M.P., Sharma, P., & Khichi, A.S. (2022). A review of gas adsorption on shale and the influencing factors of CH4 and CO2 adsorption. Journal of Petroleum Science and Engineering, 217, 110897. doi: 10.1016/j.petrol.2022.110897 Mujumdar, A.S. (Ed.). (2015). Handbook of industrial drying (4th ed.). CRC Press. Oswin, C.R. (1946). The kinetics of package life. III. The isotherm. Journal of the Society of Chemical Industry, 65(12), 419-421. doi: 10.1002/jctb.5000651216 Papadakis, S.E., Bahu, R.E., McKenzie, K.A., & Kemp, I.C. (1993). Correlations for the equilibrium moisture content of solids. Drying Technology, 11(3), 543-553. doi: 10.1080/07373939308916843 17 Peleg, M. (1993). Assessment of a semi‐empirical four parameter general model for sigmoid moisture sorption isotherms1. Journal of Food Process Engineering, 16(1), 21-37. doi: 10.1111/j.1745-4530.1993.tb00160.x Richard, T.L., (Bert) Hamelers, H.V.M., Veeken, A., & Silva. T (2002). Moisture relationships in composting processes. Compost Science & Utilization, 10(4), 286-302. doi: 10.1080/1065657X.2002.10702093 Schuchmann, H., Roy, I., & Peleg, M. (1990). Empirical models for moisture sorption isotherms at very high water activities. Journal of Food Science, 55(3), 759-762. doi: 10.1111/j.13652621.1990.tb05223.x Sing, K.S.W., Everett, D.H., Haul, R.A.W., Moscou, L., Pierotti, R.A., Rouquérol, J., & Siemieniewska, T. (1985). Reporting physisorption data for gas/solid systems with special reference to the determination of surface area and porosity (Recommendations 1984). Pure and Applied Chemistry, 57(4), 603-619. doi: 10.1351/pac198557040603 Smith, S.E. (1947). The sorption of water vapor by high polymers. Journal of the American Chemical Society, 69(3), 646-651. doi: 10.1021/ja01195a053 United States Environmental Protection Agency (EPA) (2022, September 14). Composting. URL: https://www.epa.gov/sustainable-management-food/composting Vega-Gálvez, A., López, J., Miranda, M., Di Scala, K., Yagnam, F., & Uribe, E. (2009). Mathematical modelling of moisture sorption isotherms and determination of isosteric heat of 18 blueberry variety O′Neil. International Journal of Food Science and Technology, 44(10), 20332041. doi: 10.1111/j.1365-2621.2009.02027.x 19 Tables Table 1. Average composition of the household refuse. Component wt%, refuse Non-volatiles wt%, dry material Plastics 5.5 - Newspapers, magazines 10.0 5.5 - 19.0 Kraft paper, corrugated board, grease-proof paper 4.0 8.0 Paper board 7.0 7.0 Other paper components 15.0 13.0 Animal matter 4.0 24.0 Vegetable matter 32.0 10.0 Textiles 2.0 9.0 Rubber, leather 1.0 24.0 Metals 5.0 - Glass 5.0 - Other combustible components 2.0 17.0 Other non-combustible components 0.5 - Fines (less than 10 mm) 6.0 41.0 20 Table 2. Moisture sorption isotherm models. No. Model Model equation References 1 Langmuir 1 eq AB XB   =+ Langmuir (1918) 2 BET ( )( ) 11 eq AB XB     =− − + Brunauer et al. (1938) 3 GAB ( )( ) 11 eq ABC XA A AB     =− − + Anderson (1946) 4 Oswin 1 B eq XA    = −  Oswin (1946) 5 Smith   ln 1 eq X B A  = − − Smith (1947) 6 Halsey 1 ln B eq X A T  −   =    Halsey (1948) 7 Henderson 11 ln 1 B eq XA T    =  −   Henderson (1952) 8 Chung and Pfost 1ln ln eq RT XBA   = − −   Chung and Pfost (1967) 9 Kühn   ln eq A XB  =+ Kühn (1967) 10 Luikov 1 1 ln eq A X BT  = +  Luikov (1968) 11 Iglesias and Chirife 1 eq X A B    =+  −  Iglesias and Chirife (1981) 12 Schuchmann et al. 11 ln 1 11 ln 1 eq AT X BT       −   =  −  −   Schuchmann et al. (1990) 13 Keey 31 1 ln eq A X BT  = +  Keey (1992) 14 SPS 1 exp ln eq X A BT    =−     Papadakis et al. (1993) 15 Peleg CD eq X A B  =+ Peleg (1993) 21 Table 3. Regression analysis results for fresh compost at 50 °C. Model R2 SSE RMSE Model constants Smith 0.9573 0.00015 0.0037 a = 0.02571; b = 0.02789 Halsey 0.9534 0.00016 0.0039 a = 0.2984; b = 0.3446 Henderson 0.9547 0.00016 0.0038 a = 18.27; b = 0.4661 Luikov 0.9472 0.00019 0.0041 a = 0.09462; b = 0.004549 SPS 0.8974 0.00036 0.0057 a = 0.08397; b = 0.002392 Peleg 0.8974 0.00036 0.0063 a = 0.04197; b = 0.04197; c = 0.7772; d = 0.7772 22 Figures Figure 1. A schematic diagram of the experimental apparatus. 23 Figure 2. Average equilibrium moisture data for fresh compost at a temperature of 50 C. 24 Figure 3. Moisture sorption isotherm for fresh compost using the Smith model at a temperature of 50 °C. 25 Figure 4. Comparison of the experimental and predicted equilibrium moisture content values for fresh compost using the Smith model at a temperature of 50 C.