https://orcid.org/0009-0008-1443-5204
ABSTRACT
Developing small-volume composting systems can help improve sustainable sanitation and waste management at a household scale in constrained environments. In this work, an accessible analytical model that describes the container-based composting process is presented. The model focuses on the compost temperature as the main process parameter and was validated with an initial experiment and then used as a simulation tool for scaling a compost reactor with a mixture of feces and sawdust commonly found in dry toilets. Following literature thresholds for pathogen inactivation, the compost in the second experiment surpassed the required temperatures of 55 °C for more than 3 days. This work demonstrates that pathogen-inactivation temperatures can be achieved for a self-heating, container-based compost system at a household scale with a minimal experimental setup. Furthermore, the process can be described with an accessible analytical model that ensures ease of replication even in constrained environments.
HIGHLIGHTS
The accessible analytical model describes small-volume, container-based composting.
An experimental composting system was designed for ease of implementation.
The model was validated with the experimental data from the container-based composting system.
The model was used to configure a small-volume system that achieved pathogen-inactivation temperatures.
The experiment demonstrated the feasibility of a household-scale composting system.
INTRODUCTION
In recent years, composting has been increasingly utilized as an approach to sustainable waste management. The composting process, if managed appropriately, can promote thermal pathogen inactivation for a range of applications, from municipal organic waste to household-level organic waste and dry toilet feedstocks (Rynk et al. 2022). However, the required volumes for meeting the temperature threshold for pathogen inactivation without external heat sources are often large, making the solution challenging in small or resource-constrained dwellings (Epstein 1997).
Models are useful for describing composting operations. Using models, researchers and technology developers can understand different factors that influence the thermal performance of the process. This understanding can help scale it appropriately and make it accessible in resource-constrained environments where it can make a substantial impact on sustainable waste management.
Researchers have been actively developing models of the compost process. According to the reviews by (Hamelers 2004; Mason 2006; Ajmal et al. 2020b), the basic approach that has been used to model composting processes couples empirically derived substrate degradation kinetics with thermal balance equations. Models have been deterministic and their parameters either lumped, representing the whole reactor or discretized into individual reactor layers.
Researchers have modeled the energy generated from biological decomposition with first-order or Monod-type kinetics, predicting either volatile solids degradation, O2 consumption or CO2 production (Keener et al. 2005). Unfortunately, these models tend to be complex due to the thermal, microbiological and physicochemical phenomena involved. Some of the models reviewed included the mass balance of degraded solids, gases and water (Petric & Selimbašić 2008). Since the existing models are complex, measuring the process parameters to validate them requires expensive laboratory equipment. This makes their use and replication challenging, especially for use by organizations in resource-constrained settings. Furthermore, some researchers suggest increasing the complexity and precision of these models instead of making them more approachable (Mason 2006; Walling et al. 2020).
Taking the opposite route, this work develops an accessible analytical model that can be easily validated without the need for complex laboratory settings. The objectives of this research are to develop the simplified model, use this model to configure a simple, small-volume composting system, and then demonstrate the feasibility of attaining pathogen inactivation in small volumes.
The model was simplified by selecting only the compost temperature as the key process parameter. This parameter was chosen as research has shown that maintaining 55 °C for 3 days provides adequate pathogen reduction for compost (EPA 1993). More complex models have previously presented mass balances and gas exchange but here they were excluded as they are not strictly required to describe the compost temperature behavior.
A composting system can be described with the following inputs: (a) organic matter (OM) composition, (b) water content and (c) oxygen, and the outputs: (d) carbon dioxide/volatiles, (e) water, (f) compost matter and (g) heat (Petric & Selimbašić 2008). For the composting process to successfully transform the OM and maintain the required metabolic conditions, the inputs need to be in the desired ranges. First, the carbon-to-nitrogen ratio should be approximately 30:1 to allow for microbial growth (Haug 1993). Moisture content should be around 55% since water acts as a transport media and temperature buffer (Rynk et al. 2022). Also, the free air space should be approximately 35% to allow for airflow, which is usually achieved with a compost particle size of around 2–12 mm (Rynk et al. 2022). This parameter also defines the bulk density. Finally, a minimum airflow rate calculated from the stoichiometric demands should be present to ensure a complete oxidation process, however, higher rates are usually required to manage compost temperatures (Haug 1993; Epstein 1997; Rynk et al. 2022). The recommended ranges for these parameters can be found in Table 1.
Parameters of the composting process
| Parameters | Exp. A | Exp. B | Optimal range |
|---|---|---|---|
| Moisture | 57 | 54 | 50–60% |
| CN ratio | 22 | 30 | 20–40 |
| Bulk density | 420 | 400 | 400–600 g/L |
| Particle size | 3–6 | 3–6 | 2–12 mm |
| Airflow rate | 1.00 | 0.23 | 0.11–1.00 LPM/kgVS |
| Parameters | Exp. A | Exp. B | Optimal range |
|---|---|---|---|
| Moisture | 57 | 54 | 50–60% |
| CN ratio | 22 | 30 | 20–40 |
| Bulk density | 420 | 400 | 400–600 g/L |
| Particle size | 3–6 | 3–6 | 2–12 mm |
| Airflow rate | 1.00 | 0.23 | 0.11–1.00 LPM/kgVS |
Optimal ranges from other studies (Haug 1993; Epstein 1997; Rynk et al. 2022) and the values used in experiments A and B.
When developing a model that is focused on temperature, we need to analyze the composting process using the heat generation and heat loss terms. In a composting system, a wide range of microorganisms coexist and compete at different stages depending on the varying conditions. The microbial growth process inherently generates heat that makes some organisms thrive while others die off. The heat is also mainly lost from evaporative, convective and conductive phenomena (Epstein 1997). The metabolic heat generation, when properly managed to maintain temperatures in the thermophilic range, can be leveraged to inactivate pathogens within the compost. The EPA standards require a compost temperature of 55 °C for at least 3 days to ensure safe pathogenic loads (EPA 1993).
Many researchers and operations have successfully managed the heat generated from the compost process to deactivate pathogens from dry toilets both at the community (Kramer 2011) and household scales (Jenkins 2019). However, this was completed in compost volumes of at least 1,000 L, where self-heating of the substrate can maintain the thermophilic temperatures required for pathogen inactivation. In laboratory-scale or composting systems smaller than 1,000 L, however, the heat losses from evaporation and conduction become significant and detrimental to the objective of achieving high thermophilic temperatures for pathogen inactivation (Mason & Milke 2005). These required pathogen-inactivation temperatures have been successfully achieved in laboratory-scale systems under optimal conditions using sealed containers and controlled aeration (Mason & Milke 2005) however, these experiments require expensive sensors and electronics as well as complex aeration systems, putting them out of reach for resource-constrained applications.
Here, we demonstrate that a simple, low-cost system, made from off-the-shelf components can achieve pathogen inactivation temperatures in small volumes. This configuration enables replication and validation in resource-constrained environments.
METHODS
This paper presents a simplified model that describes the composting process of a mixture of feces and sawdust commonly found in dry toilets, nevertheless, it could also be applied to other organic mixtures with proper CN ratio. It is based on lumped parameters with substrate decomposition kinetics predicting volatile solids degradation. The aim of the model is to describe the process for feces composting, and it has been adapted to include only parameters that can be easily measured with minimal setup and resources so that the system can be replicated in constrained environments. The validation experiments were designed from a realistic and accessible perspective to be as close as possible to a final household-scale composting operation. The following assumptions for the model have been made:
a. The feedstock consists of a homogeneous mixture of feces and sawdust undergoing a microbial degradation process.
b. Active aeration is supplied at the center of the compost reactor at regular time intervals to ensure aerobic degradation conditions (Mohee et al. 1998).
c. A cylindrical insulated reactor is used to minimize heat losses (Bergman & Levine 2019).
d. Air vents at the top lid allow for gas release and constant pressure.
e. Input and output air flow rates are equal.
f. The gas mixture and outflow air are saturated with water. This has been shown to be valid for a compost moisture content above 50% (Bach et al. 1987).
g. Changes in mass and volume are less than 10% for the short duration of the experiments.
h. Heat generation terms and heat loss terms are expressed on a rate basis (kJ/day).
i. Heat input, pH, and radiation heat losses are not accounted for due to their small effects (Mason 2006).
, the rate of thermal energy generated from the degradation of OM by biological activity 
, the rate of heat loss through air as convection and latent heat of evaporation 
, and as conduction through the reactor walls 
:
Sensible heat
The model describes the temperature change inside the reactor during the composting process. It calculates the rate of change of the sensible heat of the compost mixture through a series of ordinary differential equations where temperature is the dependent variable.
(kJ/day), depends on the compost mass, m (kg), the specific heat capacity of the compost mixture, 
(kJ/kg°C), and the compost temperature, T (°C). Due to the slow rate of mass change, calculated from the experimental results at less than 10% per week, a constant compost mass was assumed:
(kJ/kg°C) can be calculated as (Van Lier et al. 1994):
is the specific heat of water (kJ/kg°C), and 
is the specific heat of OM (kJ/kg°C).Degradation kinetics
, but the present model also includes correction functions for moisture content, 
and CN ratio, 
, that reduce the rate coefficient when conditions are sub-optimal:
depending on system configurations. The model presented by (Haug 1993) based on the aerobic digestion of liquid wastes has been used previously by many researchers with good results (Ndegwa et al. 2000; Briški et al. 2007; Petric & Selimbašić 2008; Wang et al. 2014; Zhang et al. 2016) and the review from (Mason 2006) and the results from (Higgins & Walker 2001; Richard & Walker 2006) suggested that the cardinal temperature equation presented by (Rosso et al. 1993) could provide the best description, however, while its parameters are easy to determine experimentally, both Haug's and Rosso's models fail for temperatures higher than 80 °C and solving the analytical model can become complicated. (Ekinci et al. 2004) on the other hand, suggested a simple exponential model that closely resembles Haug's and requires only parameters a and b to be fitted experimentally, thus it was adapted for this research:
To achieve a successful composting process, several parameters need to be balanced at the beginning of the reaction. When kept within the ranges shown in Table 1, the influence from the moisture and CN ratio should account for less than 10% each on the degradation kinetics (Haug 1993; Walling & Vaneeckhaute 2021). A sensitivity analysis for these parameters is out of the scope of the work presented here, but if kept within the recommended ranges, close to the optimal values, the correction functions presented in Equations (7) and (8) could be simplified with a single correction value ranging from 0.20 to 1.00.
(kJ/day), is obtained by multiplying the substrate degradation kinetics Equation (4) by the heat of combustion of the reaction, 
(kJ/kg):
The kinetics of the system have been modeled using a value for the heat of combustion, 
, of 17,500 kJ/kg. Other authors have used the heat of combustion values for similar composting configurations ranging from 16,000 to 19,000 kJ/kg (Van Lier et al. 1994; Ahn et al. 2007; Wang et al. 2014, 2016), but the challenge for feces composting is the varied organic composition that can be encountered, thus a mean value within the presented range was selected here, acknowledging the importance of future work to better capture the influence of this parameter.
Aeration requirements
Container-based composting operations require an active aeration system to satisfy the oxygen demand for organic degradation. Without constant aeration, the oxygen in the free air space can be depleted in a matter of hours and stall the reaction (Rynk et al. 2022). Airflow helps to remove excess water and keep a balanced moisture content through evaporation. For big volumes, aeration also helps control the temperature of the compost pile by removing heat, however, in the case of small-volume container-based composting, this heat removal opposes the goal of increasing and maintaining high temperatures for pathogen inactivation.
, can be estimated as 1.744 
. For the sawdust fraction, which is mostly a cellulosic material, a carbohydrate composition undergoing the following reaction is assumed:
is estimated as 1.185 
. The total oxygen demand, 
(g), can be determined from the compositions of the feces and sawdust fractions and the weighted average oxygen demands:
are the wet weights of feces and sawdust respectively (g), 
the moisture contents (%) and 
the biodegradable volatile solids fraction that can be composted (%).
and a 
. The total BVS of the substrate, C (kg) for the kinetics Equation (4) is obtained by adding the volatile solids masses from the feces and sawdust:
(L), can be determined using a value for oxygen concentration in air of 23.2% by weight (Haug 1993) and an average air density, 
(g/L):
The total volume of air, 
gives the minimum required for a complete aerobic reaction. Using this value, the minimum aeration rate can be calculated. According to Haug 1993 and Ahn et al. 2007, the minimum aeration rate should be between 0.11 and 0.28 LPM/kgVS, with a recommended optimum range of 0.8–1.0 LPM/kgVS. The mass flow rate of air, 
(kg/day), can also be obtained by dividing the total air mass by the number of days where most of the thermophilic reaction takes place. To operate within the recommended optimum range, the experiments used a higher flow rate than the minimum calculated from stoichiometry (Table 1).
Heat losses and overall thermal balance
The energy rate Equation (1), expressed as the rate of change of sensible heat, is a thermal balance between heat generated from the biological activity and heat losses through the system. As the main objective of the process is to reach and maintain the required pathogen inactivation temperatures, it is important to minimize thermal losses. The three main components for heat loss are forced convection, latent heat of evaporation and conductive heat loss through the container walls, where the last two are the most significant terms (Mason 2006; Ahn et al. 2007). The forced aeration into the system will influence both the evaporative and convective heat losses while the insulation material and compost container geometry will influence the conductive heat loss.
(kJ/day), is equal to the sensible and latent heat gained as air passes through the compost and is related to the mass flow rate of air, 
(kg/day), and the difference in enthalpies, 
(kJ/kg), at the system outlet and inlet:
and 
are the specific heat of dry air and water vapor respectively (kJ/kg°C), 
are the humidity ratios at inlet and outlet, and 
is the latent heat of water evaporation (kJ/kg). These parameters were obtained from the ASHRAE handbook moist air tables (ASHRAE 2021).
), can be determined for the saturated conditions by regression of the psychrometric charts as (de Guardia et al. 2012; ASHRAE 2021):
The humidity ratio at the system outlet 
can be obtained from the above equation evaluated at the compost temperatures since outlet air is regarded as saturated. For the inlet conditions 
a relative humidity of 50% was assumed and the humidity ratio evaluated at the ambient temperature.
(°C·day/kJ), that depends on the insulation thickness and the reactor geometry following the equations presented by (Bergman & Levine 2019). The total thermal resistance of the container was obtained by adding the resistance of each insulation material calculated with the following equation:
(m) are the radii for insulation thickness, L (m) is the cylinder height, and (W/m°c) is the thermal conductivity coefficient.
Numerical modeling
The development of the analytical model with its corresponding assumptions yields a system of two ordinary differential equations, the first one based on the degradation rate of OM (Equation (4)) and the second one based on the rate of change of the compost temperature (Equation (21)). To obtain the output values for compost temperature, the differential equations were solved with a Runge-Kutta single-step solver (ode45) using the MATLAB® software.
All the parameters described in Equations (2)–(21) are required to run the model, these were either obtained from literature, measured directly from the experimental setup or calculated from other referenced equations. Only the parameters a and b for the temperature correction function (Equation (6)) had to be regressed from the experimental results. The values used for the experiments described in this work can be found in Table 2.
Analytical model parameters used in experiments A and B
| Symbol | Parameter | Exp. A | Exp. B | Units | Reference |
|---|---|---|---|---|---|
 | Total compost mass | 2.43 | 5.10 | kg | Experiment |
 | Compost moisture | 57 | 54 | % | Experiment |
 | Specific heat mixture | 2.873 | 2.782 | kJ/kg°C | Calculated |
 | Specific heat water | 4.186 | 4.186 | kJ/kg°C | (Haug 1993) |
 | Specific heat OM | 1.133 | 1.133 | kJ/kg°C | (Haug 1993; Van Lier et al. 1994) |
 | BVS fraction compost mass | 0.269 | 0.562 | kg | Calculated |
 | Reaction order | 1 | 1 | – | (Haug 1993) |
 | Temp. correction coefficient | 0.20 | 0.20 | 1/day | Regressed |
 | Temp. correction coefficient | 0.10 | 0.10 | – | Regressed |
 | Free air space | 56 | 55 | % | Experiment |
 | CN ratio | 22 | 30 | – | Experiment |
 | Heat of combustion | 17,500 | 17,500 | kJ/kg | (Van Lier et al. 1994; Ahn et al. 2007) |
 |  Demand feces | 1.744 | 1.744 |  | Calculated |
 |  Demand sawdust | 1.185 | 1.185 |  | Calculated |
 | Wet weight of feces | 1,575 | 3,045 | g | Experiment |
 | Wet weight of sawdust | 855 | 2056 | g | Experiment |
 | Moisture content feces | 81 | 83 | % | Experiment |
 | Moisture content sawdust | 14 | 11 | % | Experiment |
 | BVS fraction feces | 42 | 42 | % | (Funamizu 2019) |
 | BVS fraction sawdust | 19 | 19 | % | (Haug 1993) |
 | Density of air | 1.2 | 1.2 | g/L | (Haug 1993) |
 | Mass flow rate of air | 1.7 | 0.85 | kg/day | Calculated |
 | Specific heat dry air | 1.006 | 1.006 | kJ/kg°C | (ASHRAE 2021) |
 | Specific heat water vapor | 1.860 | 1.860 | kJ/kg°C | (ASHRAE 2021) |
 | Latent heat of evaporation | 2,501 | 2,501 | kJ/kg | (ASHRAE 2021) |
 | Humidity ratio at inlet | 0.0095 | 0.0095 |  | Calculated |
 | Ambient temperature | 24 | 24 | °C | Experiment |
 | Thermal resistance insulation | 0.074 | 0.077 | °C·day/kJ | Calculated |
 | ON time for aeration fan | 17 | 15 | sec/cycle | Calculated |
| Symbol | Parameter | Exp. A | Exp. B | Units | Reference |
|---|---|---|---|---|---|
| | Total compost mass | 2.43 | 5.10 | kg | Experiment |
| | Compost moisture | 57 | 54 | % | Experiment |
| | Specific heat mixture | 2.873 | 2.782 | kJ/kg°C | Calculated |
| | Specific heat water | 4.186 | 4.186 | kJ/kg°C | (Haug 1993) |
| | Specific heat OM | 1.133 | 1.133 | kJ/kg°C | (Haug 1993; Van Lier et al. 1994) |
| | BVS fraction compost mass | 0.269 | 0.562 | kg | Calculated |
| | Reaction order | 1 | 1 | – | (Haug 1993) |
| | Temp. correction coefficient | 0.20 | 0.20 | 1/day | Regressed |
| | Temp. correction coefficient | 0.10 | 0.10 | – | Regressed |
| | Free air space | 56 | 55 | % | Experiment |
| | CN ratio | 22 | 30 | – | Experiment |
| | Heat of combustion | 17,500 | 17,500 | kJ/kg | (Van Lier et al. 1994; Ahn et al. 2007) |
| | Demand feces | 1.744 | 1.744 | | Calculated |
| | Demand sawdust | 1.185 | 1.185 | | Calculated |
| | Wet weight of feces | 1,575 | 3,045 | g | Experiment |
| | Wet weight of sawdust | 855 | 2056 | g | Experiment |
| | Moisture content feces | 81 | 83 | % | Experiment |
| | Moisture content sawdust | 14 | 11 | % | Experiment |
| | BVS fraction feces | 42 | 42 | % | (Funamizu 2019) |
| | BVS fraction sawdust | 19 | 19 | % | (Haug 1993) |
| | Density of air | 1.2 | 1.2 | g/L | (Haug 1993) |
| | Mass flow rate of air | 1.7 | 0.85 | kg/day | Calculated |
| | Specific heat dry air | 1.006 | 1.006 | kJ/kg°C | (ASHRAE 2021) |
| | Specific heat water vapor | 1.860 | 1.860 | kJ/kg°C | (ASHRAE 2021) |
| | Latent heat of evaporation | 2,501 | 2,501 | kJ/kg | (ASHRAE 2021) |
| | Humidity ratio at inlet | 0.0095 | 0.0095 | | Calculated |
| | Ambient temperature | 24 | 24 | °C | Experiment |
| | Thermal resistance insulation | 0.074 | 0.077 | °C·day/kJ | Calculated |
| | ON time for aeration fan | 17 | 15 | sec/cycle | Calculated |
Experimental setup
The analytical model was calibrated with two small-volume composting experiments (experiments A and B, described in the following) that were conceived for low-cost installation and ease of replication. These twofold objectives facilitate a democratization of research. First, designing a low-cost experiment with off-the-shelf components and accessible materials allows a wide audience to reproduce the system, even in resource-constrained environments. Second, the minimum process parameters were selected for the model of the compost process, which can be measured with simple sensors. This enables others to easily build on research results to advance accessible, low-cost sanitation solutions. All the process parameters used for the model are listed in Table 2 and only mass, moisture, CN ratio and temperature measurements are required besides the mathematical calculations.
). 
Schematic and pictures of the reactor system. (1) Temperature sensors inside compost, (2) air distribution pipe, (3) exhaust vents, (4) DC fan, (5) Raspberry Pi microcomputer and (6) polyester fiber insulation.
Schematic and pictures of the reactor system. (1) Temperature sensors inside compost, (2) air distribution pipe, (3) exhaust vents, (4) DC fan, (5) Raspberry Pi microcomputer and (6) polyester fiber insulation.
The reactor was wrapped in polyester fiber for insulation (6) and located inside a 120-L container. For experiment (A), 12.5 cm of polyester fiber (
W/m°c) was used around the 7-L container; for experiment (B), 8 cm of polyester fiber was used around the 14-L container plus the 2.5 cm polyurethane foam (
W/m°c). Cylindrical reactors were selected because this geometry allows for improved heat retention (Bergman & Levine 2019) and because these container types are readily available.
The energy generated from biological activity, 
, increases the temperature inside the compost matrix, while the inlet airflow, 
, moves the air volume that gets heated and leaves the system through the exhaust gas, 
. Heat also gets lost through the container walls and the insulation material from the conductive process, 
.
Setting up the experiment requires that the compost parameters be within the ranges presented in Table 1, to ensure this, the dry toilet feedstock needs to be mixed into a homogeneous matrix. Moisture content and free air space were measured as described by (Rynk et al. 2022), the CN ratio was calculated and balanced following the procedures and equations presented by (Trautmann & Krasny 1997). The particle size was ensured at the beginning of the process by sieving sawdust and the airflow rate was calculated from Equation (12). Once the mixture and the sensors are in place, the reactor is insulated and located inside the bigger container, the sensors are connected, and the data logging and fan activation occur automatically as programmed in the microcomputer. The experiment is then left to run without any further intervention.
RESULTS AND DISCUSSION
Temperature behavior experiment A
By numerically solving the differential Equations (4) and (21), we can estimate the degraded mass, C, and the compost reactor temperature, T, over time. The model uses the parameters specified in Table 2. The data obtained from the experiment comprises the temperature values from six sensors logged every 15 min and is presented for a period of 5 days. The temperature values were averaged to represent the reactor temperature and are plotted alongside the model results as well as the +− 5% model margins.
Model and experiment (A) temperature (5 days).
The highest compost temperatures will occur during the first hours when most of the BVS mass is available (Equation (9)). As seen in Figure 2 since the model closely describes the temperature behavior, even if this experiment didn't reach the required temperatures, the model can be used as a tool to simulate the required system conditions to achieve the 55 °C for 3 days.
Energy rates
(9). As shown in Figure 3, the energy generated from biological activity increases during the first hours and then starts decaying. This graph presents the modeled results for 8 days which is the time when the compost reached ambient temperature. 
Rate of heat generated (
), heat loss rate through aeration (
) and conduction (
) calculated for the model results from experiment (A) (8 days).
Rate of heat generated (), heat loss rate through aeration () and conduction () calculated for the model results from experiment (A) (8 days).
The vector representing the compost temperature was evaluated in the equations for energy loss through exhaust gasses, 
(Equation (18)) and through conduction, 
(Equation (19)). According to the reviews by (Mason 2006; Ajmal et al. 2020a), the latent heat of evaporation tends to be the most significant loss term followed by conduction trough the reactor walls. Since this experiment has a very small mass and the aeration requirement was also small, the heat losses through evaporation are very close to the conductive losses.
These results show that increasing the thermal resistance with better or more insulation could be an alternative to increasing the compost temperature, but it would also increase the system cost, thus the best path would be to increase the compost mass so more energy can be generated biologically. Eventually, the whole system can be designed to balance energy generated and energy loss through convection/evaporation and through conduction. These three terms can be modified in simulations by changing the compost mass, airflow rate and insulation material respectively. The advantage of having this model as a tool is that it can show the limitations of a designed system and simulate expected behaviors.
SIMULATIONS
, or by decreasing the aeration rate 
. The latter is limited by the stoichiometric demands but even if using the minimum required, there is a risk of creating anaerobic conditions. The advantage of the model is the ease with which different scenarios can be simulated, thus the following design changes were explored: The compost mass was increased to 5 kg, and assuming a compost density of around 400 g/L a bigger composting reactor of 14 L was proposed. This time a cylindrical container with a 2.5 cm polyurethane foam wall was selected, thus improving also the thermal resistance. Figure 4 presents the simulated temperatures for this configuration at three different aeration rates: 0.42 kg/d as the minimum required by stoichiometric demands and then twice (0.85 kg/d) and four times (1.7 kg/d) that requirement. The simulation assumed a moisture content of 55% and a CN ratio of 30. According to the results, an aeration rate of 0.85 kg/d should be enough to achieve the required pathogen-inactivation temperatures of 55 °C for 3 days, so these were the design parameters selected and used for experiment (B). 
Simulation for a 5 kg compost experiment with three different aeration rates and experiment (A) results as reference.
Simulation for a 5 kg compost experiment with three different aeration rates and experiment (A) results as reference.
Temperature behavior experiment B
As described previously, for experiment (B) a 14-L container with polyurethane insulation was used as the main compost reactor. This container was filled with the compost mixture of feces and sawdust in the configuration shown in Figure 1, including the six temperature sensors and the central air distribution pipe. All the parameters used for this experiment were calculated based on the results from the simulation shown in Figure 4 and are listed in Table 2.
Simulation and experiment (B) results showing average, maximum and minimum temperatures. The compost reached 55 °C for more than 3 days.
Simulation and experiment (B) results showing average, maximum and minimum temperatures. The compost reached 55 °C for more than 3 days.
These results show that the objectives of the experiment were accomplished, demonstrating the usefulness of the simple model to design and refine a simple experimental compost reactor. As far as to the authors’ knowledge, this is the first time a small-volume (<20 L) compost experiment with limited controls is able to meet the pathogen-inactivation requirements.
Simulations and average-measured temperatures for both experiments A and B.
CONCLUSIONS
This work presented an accessible analytical model for container-based composting that was simplified by selecting only the compost temperature as the key process parameter. The model, validated through a low-cost experimental setup, demonstrated its usefulness for predicting compost temperature at different experimental volumes and aeration regimes. The final experiment achieved the objectives of attaining pathogen-inactivation temperatures in a small volume with the ease of replication that the experimental setup and the simplified analytical model allow. This work aims at facilitating a wide audience of researchers and practitioners to reproduce the results even in constrained environments.
The advantage of the model presented here is its applicability and ease of implementation. By focusing on the main system parameters, the sizing of self-heating compost reactors can be determined only from the compost mass, the reactor geometry and insulation, and the aeration regime. The authors recommend further research focusing on the influence of the startup parameters of CN ratio and moisture on the precision of the model, and its applicability toward the development of better composting systems for dry sanitation solutions.
ACKNOWLEDGEMENT AND FUNDING
The authors are thankful to the Natural Sciences and Engineering Research Council (NSERC) of Canada for the NSERC Discovery Grant, to the School of Graduate Studies and the Department of Mechanical and Industrial Engineering at the University of Toronto for their Fellowships. P.C.R. is grateful for the Paul Cadario Doctoral Fellowship in Global Engineering and the Doctoral Scholarship from the Mexican National Council for Science and Technology (CONACYT).
AUTHOR CONTRIBUTIONS
P.C.R. contributed to conceptualization, formal analysis, investigation, methodology, project administration, software, visualization, writing – original draft, writing – review & editing. A.B. contributed to conceptualization, funding acquisition, methodology, validation, writing – review & editing, supervision.
DATA AVAILABILITY STATEMENT
All relevant data are included in the paper or its Supplementary Information.
CONFLICT OF INTEREST
The authors declare there is no conflict.
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