Anaerobic Co-Digestion of Cattle Manure and Sewage Sludge Using Different Inoculum Proportions

Abstract

Anaerobic digestion (AD) is a sustainable strategy for converting hazardous wastes into renewable energy while supporting Sustainable Development Goals (SDGs). This study aimed to evaluate the effect of inoculum on optimizing biogas production from sewage sludge (SS) and cattle manure (CM). Bench-scale digesters were fed with 0, 20, and 40% inoculum prepared at a 1:3 SS:CM ratio. Substrate and digestate were analyzed for physicochemical properties, and biogas production data were fitted using nonlinear models. Kinetic parameters ranged from 0.0770 to 0.4691 L·kg⁻¹ for Y_max, from 1.0263 to 2.1343 L·kg⁻¹·week⁻¹ for μ_max, and from 0.8168 to 8.0114 weeks for λ, depending on the ratio. The 1:3 SS:CM with 40% inoculum significantly improved biogas production by reducing the lag phase and increasing weekly yield, with the Gompertz model showing the best fit to the digestion kinetics. This was particularly evident due to the favorable conditions for microbial adaptation and efficient substrate degradation. The results reinforce the concept of optimization as defined in this study, wherein the application of inoculum enhances the performance of AD by improving the physicochemical conditions of the substrate and accelerating microbial activity, thereby resulting in increased methane (CH₄) generation and overall biogas yield.

1. Introduction

Globally, countries have been implementing regulations to limit greenhouse gas (GHG) emissions due to their high global warming potential. One of the key strategies for mitigating emissions involves the recovery and reuse of waste generated by urban and agro-industrial activities within their respective production chains. To this end, various technological routes can be employed, including physical (extraction), biological (AD and fermentation), and thermochemical (direct combustion, pyrolysis, and gasification) processes. Among these, AD stands out for its ability to convert environmentally harmful waste into valuable energy resources. This aligns with the global energy agenda focused on Low Carbon Agriculture, Energy Transition, and diversification of the energy matrix [1,2].

AD encompasses anaerobic mono-digestion (MoAD), co-digestion (CoAD), and the use of inoculum [3,4,5]. MoAD uses a single type of substrate as a carbon and energy source for microorganisms, while CoAD involves the combination of different residues, significantly enhancing the efficiency of the process [3,4]. The addition of inoculum can further enhance biogas production by introducing a robust microbial community already adapted to the methanogenesis process. The digestate produced in AD can itself be reused as inoculum, serving as a concentrated microbial consortium capable of accelerating subsequent digestion cycles [6,7]. Operationally, the use of inoculum is of great importance, as it reduces the hydraulic retention time, shortens the lag phase, and increases the rates of biogas and CH₄ production [8,9].

Among the waste materials with high bioenergy potential for inoculum use, SS from wastewater treatment plants and CM are notable. Despite their high content of organic matter and nutrients, which provide significant gains and considerable potential for both energy recovery and agricultural use, these substrates are still underutilized or poorly managed [10]. Several studies have demonstrated the effectiveness of using these residues in co-digestion systems, with methane yield [9,11,12,13]. However, the continuous evaluation of anaerobic digestion performance, specifically focused on inoculum application, remains essential, given its operational significance and the current lack of comprehensive studies addressing its systematic use in the scientific literature.

To better understand and optimize the anaerobic digestion process, mathematical modeling is widely adopted. Such models allow for more accurate prediction of process behavior and improved decision-making, enabling the detailed analysis of each stage of digestion and the influence of experimental variables on CH₄ production. Among the various modeling approaches, nonlinear regression models are particularly suited to describe the complexity of the biochemical transformations involved in biogas production. These models help identify the growth and decline phases of microbial populations, the dynamics of biogas production, and the transformation of substrates into digestate over time [8,9].

Therefore, the aim of this study was to evaluate the effect of different inoculum percentages (0, 20, and 40%) on the AD of CM and SS, as well as to apply and fit mathematical models to the biogas production data generated under these conditions.

2. Materials and Methods

2.1. Experimental Site and Raw Materials

This study was conducted at the Rural Energy Efficiency Laboratory, linked to the Multi-User Research Laboratory of the Renewable and Alternative Rural Energy Group (LabGERAR), located at the Institute of Technology/Department of Engineering of the Federal Rural University of Rio de Janeiro (UFRRJ), Seropedica campus, Rio de Janeiro, Brazil.

The substrates (S) used for MoAD, CoAD, and inoculum consisted of cattle manure and sewage sludge. The CM was collected from the dairy cattle sector at UFRRJ, where animals are raised under conventional management and fed with a diet composed of Tanzania grass (Panicum maximum), corn, soybean meal, and wheat bran. The CM was collected using a masonry trowel, carefully avoiding the inclusion of foreign materials such as soil, grass, and stones.

The SS was sourced from the Palatinato Sewage Treatment Plant (STP), operated by Águas do Imperador (Grupo Águas do Brasil), also located in the state of Rio de Janeiro. The SS was previously thickened in a sludge thickening tank.

Both raw materials were collected and stored in plastic containers for transport to LabGERAR, where they were homogenized to obtain a representative sample. It is important to note that the materials were not subjected to any type of prior treatment.

2.2. Anaerobic Biodigester Configuration

The anaerobic biodigester used in the experiment was based on the Indian model, consisting of a water-seal containment chamber, digestion chamber, gasometer, and U-tube manometer with water as the manometric liquid. The anaerobic biodigesters were placed on a workbench at ambient temperature, protected from direct sunlight and rainfall. The digestion chamber was used to hold the substrate, while the gasometer stored the biogas produced [14,15,16].

Each anaerobic biodigester operated in batch mode and was loaded with 1.7 kg of substrate. The substrates consisted of SS:CM ratios of 0:1 and 1:0 for MoAD, and 1:3, with inoculum addition at 0, 20, and 40% of total volume, for CoAD. The inoculum percentages adopted were based on studies conducted by Paes et al. [15,16].

The inoculum used in the CoAD experiments was obtained from a prior 17-week AD of the 1:3 SS:CM (Figure 1) under mesophilic conditions (23.4 °C). The choice of inoculum was based on its higher biogas production potential, as reported by Paes et al. [16].

2.3. Analysis of Physicochemical Characteristics

The physicochemical characterization of the S and digestate (D) included total solids (TS), volatile total solids (VTS), pH, total alkalinity (TA), volatile fatty acids (VFA), chemical oxygen demand (COD), and nitrate nitrogen (N-NO₃), in accordance with Brazilian CONAMA Resolution 375/06 [18].

TS, VTS, pH, TA, and VFA were determined following the standard procedures of the American Public Health Association (APHA) standard procedures [19]. COD and N-NO₃ were analyzed using a DR3900 spectrophotometer (Hach, Loveland, CO, USA) with Alfakit^® test kits. All analyses were performed in triplicate.

The digestion temperature was monitored using a digital K-type thermocouple (TM902C, Shenzhen Hongxin Hardware Co., Ltd., Shenzhen, China) with ±0.1 °C accuracy. The probe was inserted into the gasometer with the sensor tip immersed in the substrate at the midpoint of the digestion chamber.

2.4. Biogas Analysis

The biogas volume was estimated as the product of the vertical displacement of the gasometer and its cross-sectional area during 12 weeks of anaerobic digestion. Displacement was visually measured using a graduated scale fixed to the gasometer. Corrections to standard temperature (20 °C) and pressure (1 atm or 101.32 kPa) were applied based on Paes et al. [14,15,16], assuming ideal gas behavior.

Biogas yield was calculated based on the weekly production and the amount of substrate added to the anaerobic biodigesters (1.7 kg). Cumulative biogas production potential was obtained by summing the previous week’s production with that of the current week’s data collection. The values were expressed in liters of gas per kilogram of substrate (L kg⁻¹) [14,15,16].

2.4.1. Flame Test

The presence of CH₄ was confirmed through a flame test conducted during the gasometer discharge. A torch was connected to the biogas outlet using a flexible hose and lit. A self-sustained flame after removal of the external heat source was used as an indicator of sufficient CH₄ to support combustion [14]. The moment at which a substance begins to burn rapidly and in a self-sustained manner is referred to as the onset of combustion (OC).

2.4.2. Biogas Temperature

Biogas temperature was measured using a Benetech GM1365 Humidity and Temperature Data Logger (Benetech, Guangzhou, China). For this purpose, a 30 mL biogas sample was collected using a syringe and transferred into an insulated glass chamber containing the data logger.

2.4.3. Biogas Composition

Biogas composition was determined using the Alfakit^® Biogas Analysis Kit (Alfakit, Santa Catarina, Brazil), measuring CH₄ (%) and carbon dioxide (CO₂, %) by Orsat’s volumetric method, ammonia (NH₃-ppmv) by the indophenol blue colorimetric method, and hydrogen sulfide (H₂S-ppmv) by the methylene blue colorimetric method. This method was developed by the Brazilian Agricultural Research Corporation (Embrapa, Brasília, Brazil) Swine and Poultry, in partnership with the company Alfakit^® LTDA [20].

2.4.4. Kinetics Modeling

Biogas yield data from MoAD and CoAD were fitted to three nonlinear regression models—Boltzmann Sigmoidal, Gompertz, and Logistic models (

Table 1. Nonlinear regression models used to fit biogas yield.

Model	Equation
Boltzmann Sigmoidal	${\mathrm{Y}}_{\mathrm{i}}={\mathrm{Y}}_0+{\displaystyle \frac{\left({\mathrm{Y}}_{\mathrm{m}\mathrm{a}\mathrm{x}}-{\mathrm{Y}}_0\right)}{1+{\mathrm{e}}^{\frac{\mathsf{\lambda }-\mathrm{x}}{{\mathrm{\mu }}_{\mathrm{m}\mathrm{a}\mathrm{x}}}}}}+{\mathrm{u}}_{\mathrm{i}}$	(1)
Gompertz	${\mathrm{Y}}_{\mathrm{i}}={\mathrm{Y}}_{\max }\times {\mathrm{e}}^{-{\mathrm{e}}^{\left({\mu }_{\max }\times \left(\lambda -\mathrm{x}\right)\right)}}+{\mathrm{u}}_{\mathrm{i}}$	(2)
Logistic	${\mathrm{Y}}_{\mathrm{i}}={\displaystyle \frac{{\mathrm{Y}}_{\max }}{1+{\mathrm{e}}^{{\mu }_{\max }\times \left(\lambda -\mathrm{x}\right)}}}+{\mathrm{u}}_{\mathrm{i}}$	(3)

where Y_i is the biogas yield at week x (L kg⁻¹), i is the 1,…., n, x is the anaerobic digestion period (weeks), n is the number of cumulative biogas measurements, Y₀ is the initial biogas production (L kg⁻¹), Y_max is the maximum biogas production (L kg⁻¹), µ_max is the maximum specific production rate (L kg⁻¹ week⁻¹), λ is the lag phase duration (weeks), e is the 2.71828, and u_i is the residuals.

)—using the SigmaPlot v16 Trial Version (Grafiti LLC, Palo Alto, CA, USA).

2.5. Statistical Analysis

A completely randomized design (CRD) was adopted in a 5 × 2 factorial scheme, with five treatment ratios (0:1 and 1:0 SS:BM for MoAD and 1:3 SS:CM with 0, 20, and 40% inoculum for CoAD) and two analysis times (S and D). Each treatment was conducted in triplicate.

The physicochemical data were subjected to analysis of variance (ANOVA), as well as Tukey’s test at a 5% probability level using SISVAR^® Statistical Software Version 5.8 Build 92 [21].

Temperature profiles (substrate and biogas) and biogas yield curves were generated using SigmaPlot v16 Trial Version (Grafiti LLC, Palo Alto, CA, USA) [22].

To select the most appropriate model to represent the cumulative biogas production potential as a function of AD period, the following statistical criteria were considered: adjusted coefficient of determination (R²), mean relative error (P), standard error of the estimate (SE), and root mean square deviation (RMSD) [8,9].

SigmaPlot v16 Trial Version was used to compute the adjusted coefficient of determination (R²), while the mean relative error (P), standard error of the estimate (SE), and root mean square deviation (RMSD) were calculated using Equations (4), (5), and (6), respectively.

$$\mathrm{P}={\displaystyle \frac{100}{\mathrm{n}}}\sum {\displaystyle \frac{\left|\mathrm{Y}-\mathrm{Ŷ}\right|}{\mathrm{Y}}}$$

(4)

$$\mathrm{S}\mathrm{E}=\sqrt{{\displaystyle \frac{\sum {\left(\mathrm{Y}-\mathrm{Ŷ}\right)}^2}{\mathrm{G}\mathrm{L}\mathrm{R}}}}$$

(5)

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{D}=\sqrt{{\displaystyle \frac{\sum {\left(\mathrm{Y}-\mathrm{Ŷ}\right)}^2}{\mathrm{n}}}}$$

(6)

where Y is th observed value, Ŷ is the predicted value, n is the number of observations, and GLR is the degrees of freedom of the residuals (n—number of model parameters).

3. Results and Discussion

3.1. Biomass Characterization

A significant variation was observed in the parameters of TS and VTS between the substrate and the digestate. TS and VTS decreased throughout the AD process (

Table 2. Mean values (n = 3) of total solids (TS) and volatile total solids (VTS) in the substrate (S) and digestate (D) for cattle manure (CM) and sewage sludge (SS), and their different ratios (0:1 and 1:0 SS:CM) in anaerobic mono-digestion (MoAD) and (1:3 SS:CM) in anaerobic co-digestion (CoAD) with 0, 20, and 40% inoculum.

Ratio	TS (%)		Removal Efficiency (%)	VTS (%)		Removal Efficiency (%)
	S	D		S	D
0:1 SS:CM	13.0 Aa	10.6 Ba	18.5	11.0 Aa	7.9 Ba	28.2
1:0 SS:CM	4.6 Ac	3.3 Bc	28.3	2.6 Ac	2.4 Bd	7.7
1:3 SS:CM—0%	9.4 Ab	6.0 Bb	36.2	7.9 Ab	4.8 Bbc	39.2
1:3 SS:CM—20%	10.7 Ab	7.5 Bb	29.9	8.6 Ab	5.7 Bb	33.7
1:3 SS:CM—40%	10.9 Ab	6.5 Bb	40.4	7.7 Ab	4.3 Bc	44.2

Means followed by different uppercase letters in the same row (substrate and digestate) for each variable differ statistically according to the Tukey test at a 5% probability level. Means followed by different lowercase letters in the same column for each variable indicate significant differences between ratios, according to the Tukey test at a 5% probability level.

). The reduction in these parameters is a strong indicator of organic matter conversion into biogas. CoAD showed greater reductions in TS and VTS compared to MoAD, with the highest organic matter removal rates observed at 40% inoculum (Table 2).

When evaluating the effect among the different substrate ratios, CoAD and the inoculum addition did not significantly affect these parameters, regardless of the inoculum percentage. However, a statistically significant difference was found between MoAD and CoAD systems (Table 2). This outcome was anticipated, as SS typically has high moisture content, contributing to lower TS and VTS values, whereas CM exhibits opposite characteristics. Nonetheless, the combination of both substrates results in a more balanced feedstock with ideal characteristics for biogas production [8]. The observed values may be attributed to a higher amount of digestible organic matter, potentially enhancing biogas yield.

The efficiency of the AD process was confirmed by the removal of COD and N-NO₃ throughout the digestion period (

Table 3. Mean values (n = 3) of chemical oxygen demand (COD), total nitrogen—nitrate (N-NO₃), and their removal efficiency (%) for cattle manure (CM), sewage sludge (SS), and their different ratios (0:1 and 1:0 SS:CM) in anaerobic mono-digestion (MoAD) and (1:3 SS:CM) in anaerobic co-digestion (CoAD) with 0, 20, and 40% inoculum.

Ratio	COD (mg L−1)		Removal Efficiency (%)	N-NO3 (mg L−1)		Removal Efficiency (%)
	S	D		S	D
0:1 SS:CM	14,296 Aa	13,200 Ba	7.7	17.4 Ab	2.7 Ba	84.5
1:0 SS:CM	7321 Ac	3146 Be	57.0	30.0 Aa	2.5 Ba	91.7
1:3 SS:CM—0%	12,746 Ab	11,679 Bb	8.4	2.5 Ae	0.9 Bb	64.0
1:3 SS:CM—20%	13,059 Ab	8900 Bd	31.8	5.8 Ad	1.1 Bb	81.0
1:3 SS:CM—40%	11,600 Ab	9921 Bc	14.5	10.0 Ac	1.5 Bab	85.0

Means followed by different uppercase letters in the same row (substrate and digestate) for each variable differ statistically according to the Tukey test at a 5% probability level. Means followed by different lowercase letters in the same column for each variable indicate significant differences between ratios, according to the Tukey test at a 5% probability level.

). Similar to the trends observed for TS and VTS (Table 2), the use of inoculum promoted the reduction of both COD and N-NO₃⁻. The reductions were more pronounced in treatments with higher inoculum percentages, indicating greater substrate biodegradability and availability of organic matter for microbial conversion. Moreover, inoculum addition introduces acclimated microbial communities, enhancing hydrolysis and acidogenesis rates—factors that are positively correlated with increased biogas and CH₄ production [8,9].

The substrate without inoculum showed the lowest COD removal, suggesting that native microbial populations alone were insufficient to ensure effective organic matter degradation. However, higher microbial adaptation was observed in the treatments with 20% and 40% inoculum, with 20% resulting in the highest COD reduction. Paes et al. [15] reported similar findings, where COD was reduced by 48% in treatments with 20% inoculum, compared to only 20% in the absence of inoculum during AD of cattle manure.

Nitrogen, an essential nutrient for microbial metabolism, also showed a consistent decline. The highest N-NO₃⁻ concentration in the substrate was recorded for the MoAD with SS treatment (30.0 mg L⁻¹), while the lowest was observed in the CoAD treatment with 20% inoculum (5.8 mg L⁻¹). In the digestate, N-NO₃⁻ values ranged from 2.7 mg L⁻¹ (MoAD with CM) to 0.9 mg L⁻¹ (CoAD without inoculum). All treatments demonstrated a high nitrate removal efficiency (Table 3).

Previous studies using AD systems treating sewage sludge reported COD and nitrogen reductions ranging from 45% to 80% [23], confirming that the results presented herein are consistent with the current literature on AD performance.

As presented in

Table 4. Mean values (n = 3) of pH, total alkalinity (TA), volatile acidity (VFA), and AFV/TA ratio for cattle manure (CM), sewage sludge (SS), and their different ratios (0:1 and 1:0 SS:CM) in anaerobic mono-digestion (MoAD) and (1:3 SS:CM) in anaerobic co-digestion (CoAD) with 0, 20, and 40% inoculum.

Ratio	pH		TA (gCaCO3 L−1)		VFA (g eq HAc L−1)		VFA/TA
	S	D	S	D	S	D	S	D
0:1 SS:CM	8.0 Ab	7.6 Bb	5.20Aa	4.73 Bb	4.56 Bc	4.88 Aa	0.88 Ac	1.03 Ba
1:0 SS:CM	6.7 Bd	8.2 Aa	2.00 Bc	3.00 Ac	8.16 Aa	2.08 Bc	4.08 Aa	0.69 Bb
1:3 SS:CM—0%	8.4 Aa	7.7 Bb	3.33 Bb	7.00 Aa	5.76 Ab	3.52 Bb	1.73 Ab	0.50 Bc
1:3 SS:CM—20%	7.4 Ac	7.6 Ab	4.00 Bb	5.33 Ab	5.28 Ab	4.96 Ba	1.32 Ab	0.93 Ba
1:3 SS:CM—40%	7.4 Ac	7.6 Ab	3.00 Bb	5.60 Ab	5.56 Ab	5.24 Ba	1.85 Ab	0.94 Ba

Means followed by different uppercase letters in the same row (substrate and digestate) for each variable differ statistically according to the Tukey test at a 5% probability level. Means followed by different lowercase letters in the same column for each variable indicate significant differences between ratios, according to the Tukey test at a 5% probability level.

, pH b variation exhibited distinct patterns across treatments during the AD process. In MoAD, pH decline was observed in the cattle manure (CM) treatment, whereas an increase was recorded for SS. In CoAD without inoculum, a pH reduction was also observed, likely influenced by the higher proportion of CM in the substrate. In contrast, pH remained stable throughout the digestion process when inoculum was applied. The observed pH reduction may reflect the system’s natural buffering as it attempts to reach neutrality, creating favorable conditions for microbial survival and activity [8,24].

The CoAD with inoculum showed lower pH values compared to MoAD with CM and CoAD without inoculum, achieving values closer to the optimal range for biogas production, which remained near neutrality (Table 4). Despite minor fluctuations, all treatments maintained pH within the optimal range for CH₄ production (6.5–8.0) [12].

Overall, TA increased, while VFA decreased throughout AD, with the exception of MoAD with CM (Table 4). This behavior supports the stability of the digestion process [25]. This is further confirmed by the reduction in the VFA/TA ratio. However, the ratio ranged from 0.69 to 4.08, indicating potential instability in certain treatments. Ratios between 0.1 and 0.5 are considered optimal for stable AD; values above this range may suggest system overload or process imbalance [24].

Regarding the inoculum effect, no statistically significant differences were found in the substrate for TA, VFA, or the VFA/TA ratio. The pH and TA values were consistent with those reported in previous studies [26]. However, in the digestate, CoAD without inoculum showed statistically significant differences for all the parameters analyzed (Table 4).

3.2. Digestion, Biogas, and Ambient Environment Temperature Profile

Digestion temperature directly influences the microbial community involved in AD and, consequently, biogas production. Mesophilic bacteria, which dominate the process, are most active within the 30–40 °C temperature range [27]. Therefore, higher substrate temperatures tend to promote microbial activity and enhance biogas yields [3].

The initial stage of AD is characterized by the lag phase, during which the microbial community adapts to anaerobic conditions and the substrate environment. After the first week, temperature fluctuations were minimal (1–3 °C), decreasing only towards the end of the process. These conditions align with practical mesophilic digestion scenarios and do not compromise the relevance of the findings (Figure 2). It is important to emphasize that for the 0:1 and 1:0 SS:CM ratios, as well as for the 1:3 SS:CM ratio with 0% and 20% inoculum, the digestion (Figure 2A) and biogas (Figure 2B) temperatures showed no significant variation among them throughout the anaerobic digestion process.

The digestion temperature in the 1:3 SS:CM ratio with 40% inoculum was higher than that of the other treatments and the ambient temperature. For the remaining treatments, substrate temperature remained relatively stable throughout the process and consistently higher than the ambient level. The average digestion temperature during digestion was 29 °C, while the average ambient temperature was 27 °C (Figure 2A).

Similar trends were observed for biogas temperature, with average values higher than ambient (31 °C vs. 27 °C). Except for the 1:3 SS:CM ratio with 40% inoculum, which exhibited the highest temperatures, there were no significant differences among the other treatments throughout the digestion period (Figure 2B).

This temperature difference between the internal environment of the digester and ambient conditions was also reported by Nindhia et al. [12], who emphasized the positive impact of elevated internal temperatures on biogas production. However, they caution that temperatures exceeding 38 °C can eliminate up to 99.9% of pathogens, which should be considered depending on the intended use of the digestate.

This experiment was conducted under naturally occurring mesophilic conditions, with temperatures maintained between 30 and 35 °C throughout most of the process. These conditions reflect the operational reality of decentralized energy generation systems, in which maintaining a fixed temperature in low-cost contexts may be economically unfeasible. Several studies have confirmed that efficient biogas production can be achieved within this temperature range [28,29].

3.3. Biogas Yield

Biogas production peaks were observed in the third, first, and second weeks for 0, 20, and 40% inoculum additions, respectively, with the highest values recorded for 40%, followed by 20% inoculum. For MoAD, only CM showed a biogas production peak in the ninth week, while SS peaked in the first week, with values 48 and 88% lower, respectively, than CoAD with 40% inoculum (Figure 3).

The OC was observed in the first week for CoAD treatments with 0, 20, and 40% inoculum, with corresponding CH₄ concentrations of 50, 55, and 60%, respectively. In contrast, for MoAD treatments, biogas combustion began in the second week, with CH₄ contents of 45% CM and 40% for SS, as shown in Figure 4.

At the first production peak, the highest CH₄ concentration was obtained for CoAD with 40% inoculum (85%), followed by 20% and 0%. MoAD using sewage sludge and CoAD without inoculum presented CH₄ peaks of 75% and 70%, respectively. As expected, CO₂ concentrations decreased proportionally with increasing CH₄ content, confirming the efficiency of the microbial consortia involved in the methanogenesis phase (Figure 4).

These results demonstrate the synergistic effect of co-digestion and inoculum addition on biogas quality, particularly regarding CH₄ enrichment. The CH₄ concentration levels achieved in this study are considered suitable for energy recovery and combustion applications, aligning with values reported by Nindhia et al. [12]. However, CH₄ concentration alone should not be used as the sole indicator for determining the most efficient treatment conditions.

The average values obtained from the characterization of the substrate and digestate (Table 2, Table 3 and Table 4), combined with weekly biogas potential (Figure 3) and CH₄ yield (Figure 4), suggest that co-digestion promoted a synergistic interaction between the substrates and the inoculum, enhancing microbial activity and, consequently, the AD process. In addition, Figure 2 clearly shows that methane production peaked during the periods when the temperature was highest, despite minor fluctuations. These results reinforce the importance of co-digestion and inoculum addition as effective strategies for optimizing AD.

The outcomes of this study regarding TS, VTS, and COD removal, as well as CH₄ content in the biogas, were superior to those reported in AD systems using sewage sludge with iron nanoparticles, which aimed to boost biogas production and reduce the lag phase. In that study, the maximum reduction achieved was 37% for TS, 50% for VTS, and 33% for COD, with CH₄ concentrations ranging from 50% to 65% over 40 days of digestion [9].

H₂S is a corrosive gas capable of damaging metallic components, necessitating mitigation strategies to prevent sensor and equipment degradation. Likewise, NH₃, especially in aqueous environments, is corrosive and poses risks to health and the environment [30].

In this study, H₂S concentrations remained stable at 20 ppmV throughout the entire digestion process, regardless of treatment condition. This concentration is within acceptable limits for biogas utilization in energy systems, eliminating the need for desulfurization.

NH₃ concentrations, however, varied across treatments. The highest NH₃ levels (525 ppmV) were recorded in CoAD systems with 0 and 40% inoculum, both peaking in the 12th week. In MoAD with CM, the maximum NH₃ concentration was 350 ppmV, also peaking in the 12th week. Conversely, MoAD with SS and CoAD with 20% inoculum showed lower NH₃ values (175 ppmV), with peaks occurring in the first week.

These NH₃ and H₂S concentrations are within acceptable thresholds for biogas utilization as an energy source [31,32], indicating that the biogas produced under the studied conditions is suitable for combustion and other energy applications requiring extensive post-treatment.

The mathematical models applied to the experimental data on cumulative biogas production potential yielded high adjusted coefficients of determination (R²), ranging from 98.77% to 99.83%—with the exception of the 1:3 SS:CM ratio with 20% inoculum, which presented an R² of 93.69%. Although this value is lower than those observed in the other treatments, it is still considered acceptable due to the low mean relative error (p = 1.04%), standard error of the estimate (SE = 0.02013), and root mean square deviation (RMSD = 0.01643), as previously discussed by [33].

Using the Boltzmann Sigmoidal, Gompertz, and Logistic models, the R² values obtained were consistent with ranges reported by the literature [34,35], confirming the reliability of the fitted models (

Table 5. Adjusted coefficient of determination (R²), mean relative error (P), standard error of the estimate (SE), and root mean square deviation (RMSD) for adjusting the kinetic models of the cumulative biogas production potential for cattle manure (CM), sewage sludge (SS), and their different ratios (0:1 and 1:0 SS:CM) in anaerobic mono-digestion (MoAD) and (1:3 SS:CM) in anaerobic co-digestion (CoAD) with 0, 20, and 40% inoculum.

Ratio	Model	R2 (%)	P (%)	SE (Decimal)	RMSD (Decimal)
0:1 SS:CM	Boltzmann Sigmoidal	0.9971	10.59	0.01035	0.00845
	Gompertz	0.9913	23.43	0.01875	0.01531
	Logistic	0.9970	8.74	0.01100	0.00898
1:0 SS:CM	Boltzmann Sigmoidal	0.9983	0.64	0.00111	0.00090
	Gompertz	0.9952	0.71	0.00194	0.00158
	Logistic	0.9867	1.19	0.00323	0.00264
1:3 SS:CM—0%	Boltzmann Sigmoidal	0.9952	2.85	0.01005	0.00820
	Gompertz	0.9955	3.40	0.01022	0.00834
	Logistic	0.9897	2.64	0.01553	0.01268
1:3 SS:CM—20%	Boltzmann Sigmoidal	Did not converge	-	-	-
	Gompertz	0.9622	2.10	0.01555	0.01270
	Logistic	0.9369	1.04	0.02013	0.01643
1:3 SS:CM—40%	Boltzmann Sigmoidal	0.9877	1.33	0.02023	0.01652
	Gompertz	0.9941	1.15	0.01475	0.01204
	Logistic	0.9835	1.80	0.02467	0.02015

).

Although a high R² is an important indication of a model’s goodness of fit, it should not be the only parameter considered. Associating R² with additional statistical metrics such as P, SE, and RMSD increases the robustness and confidence in model selection [8,28]. Most P values obtained were below 10% across all models, indicating strong model performance in explaining data variability and statistical significance, except for the Boltzmann and Gompertz models applied to the MoAD of CM.

Moreover, SE and RMSD values were consistently below 0.03 across all treatments, indicating that the predicted values closely approximated the regression line, thereby enhancing the models’ precision and predictive accuracy.

Therefore, the Boltzmann Sigmoidal model was found to be the most suitable for representing AD under the 1:0 SS:CM and 1:3 SS:CM ratios without inoculum, while the Gompertz model best described the CoAD with inoculum. However, the Boltzmann model was inadequate for the 1:3 SS:CM ratio with 20% inoculum due to convergence issues, likely stemming from its limitations in handling certain data distributions. For the MoAD of CM, only the Logistic model proved adequate, with all parameters falling within the acceptable range, as previously discussed.

Table 6. Maximum cumulative biogas production potential (Y_max), maximum biogas production rate (μ_max), and lag phase duration (λ) estimated by the selected kinetic models.

Ratio	Model	Ymax (L kg−1)	µmax (L (kg Week)−1)	Λ (Week)
0:1 SS:CM	Logistic	0.4691	0.8418	8.0114
1:0 SS:CM	Boltzmann Sigmoidal	0.0770	1.3675	0.8959
1:3 SS:CM—0%	Boltzmann Sigmoidal	0.3738	2.1343	4.7371
1:3 SS:CM—20%	Gompertz	0.2413	1.0514	0.8168
1:3 SS:CM—40%	Gompertz	0.4538	1.0263	1.9866

presents the maximum cumulative biogas production potential (Y_max), the maximum biogas production rate, and the lag phase, as estimated by the selected kinetic models outlined in Table 5.

The results highlight the influence of substrate composition, including the presence of inoculum, on the AD process and subsequent biogas production. CM, due to its high organic matter content, exhibited the highest Y_max among all treatments. In contrast, SS, characterized by a more balanced ratio between organic load and microbial population, led to a higher μ_max and shorter λ, as shown in Table 6.

The μ_max value—representing the acceleration rate of biogas production kinetics—was highest in the 1:3 SS:CM ratio without inoculum, as estimated by the Boltzmann Sigmoidal model, although this condition also presented the longest lag phase (λ = 4.7371 weeks). When evaluating the effect of inoculum in CoAD systems, it was observed that maintaining 40% inoculum in the 1:3 SS:CM ratio resulted in higher Y_max but lower μ_max. Regarding λ, this treatment showed an intermediate adaptation period compared to CoAD systems with and without inoculum. These outcomes may be attributed to the adaptation requirements of methanogenic bacteria and the need to metabolize a greater proportion of available organic matter, as suggested by [8].

In the CoAD treatments, the highest cumulative biogas production potential was observed for the 1:3 SS:CM ratio with 40% inoculum. Under this condition, both biogas and CH₄ production began in the first week (Figure 4), with process stabilization reached by the seventh week (Figure 5). When 20% inoculum was applied, biogas production also started in the first week, but stabilization occurred earlier—by the fifth week. Although the onset of biogas production was earlier for the 20% inoculum treatment compared to the 40% (Table 6), it resulted in a lower cumulative production potential and an earlier plateau (Figure 5).

In MoAD scenarios, SS exhibited immediate biogas production; however, it had a lower biogas yield compared to CoAD treatments and CM, reaching stability by the fifth week. For CM, the production dynamics were similar to the 1:3 SS:CM 0% CoAD ratio, with biogas generation starting from the second week and continuing without stabilization throughout the 12-week period. However, CM alone achieved a higher cumulative production potential than the 0% and 20% inoculum CoAD treatments, starting from the eighth and ninth weeks, respectively.

The cumulative biogas production potential results (Figure 4) are consistent with the weekly production trends observed (Figure 5). The varying responses observed under different AD conditions may be attributed to insufficient initial microbial activity and the presence of a microbial adaptation phase. Once this adaptation period was completed, a rapid increase in methanogen populations likely occurred, driving accelerated biogas production in the early stages of the process.

The microbial behavior throughout the anaerobic digestion process was closely associated with temperature trends, as illustrated in Figure 2. Each substrate ratio exhibited distinct dynamics, with the highest biogas production peaks occurring during periods of elevated temperature. The process began with lower initial temperatures and showed a decline toward the end of the 12-week period, which contributed to the overall average reduction. Notably, the substrate combination that yielded the highest cumulative biogas production potential (1:3 SS:CM with 40% inoculum) maintained a temperature range between 30 and 35 °C, which falls within the optimal mesophilic zone. Therefore, the temperature data support the trends observed in weekly and cumulative biogas production potential and CH₄ and CO₂ (Figure 3, Figure 4 and Figure 5), underscoring the relevance of thermal stability in enhancing AD performance.

A satisfactory fit of the Gompertz model was observed in describing the cumulative biogas production potential as a function of the AD period, as the observed values are close to the predicted ones (Figure 6). The same was reported by Sumardiono et al. [36], who noted that the cumulative experimental and estimated biogas production values were closely aligned, thereby confirming the predictive accuracy of the referred model.

4. Conclusions

In this study, optimization was defined as the enhancement of process performance through improved physicochemical conditions of the substrate and accelerated microbial adaptation, both promoted by the application of inoculum. This was evidenced by increased CH₄ yield, reduced lag phases, and enhanced operational stability. These findings offer a valuable contribution to the development and refinement of AD technologies under economically viable and scalable conditions.

The physicochemical characterization of the substrates and digestates revealed consistent improvements across all evaluated ratios, highlighting the significant energy potential of SS and CM for AD. Notably, 20 and 40% inoculum additions led to shorter start-up periods, with the 1:3 SS:CM ratio combined with 40% inoculum yielding the highest cumulative biogas and CH₄ production, as well as improved process stability.

The kinetic behavior of biogas production was accurately described using nonlinear regression models, with model suitability varying as a function of substrate composition and inoculum percentage. The logistic model best fitted the mono-digestion of SS (0:1 SS:CM), the Boltzmann Sigmoidal model was most appropriate for the mono-digestion of CM and co-digestion with 0% inoculum, and the Gompertz model demonstrated superior fit for co-digestion with 20% and 40% inoculum—confirming its relevance under enhanced microbial activity conditions.

Although thermal stabilization at 36–37 °C is standard in industrial AD systems, the present study was conducted under naturally mesophilic conditions (30–35 °C), which proved sufficient to maintain microbial performance. Given the economic limitations of thermal control in decentralized or small-scale applications, this approach reflects realistic operational conditions without compromising scientific rigor.

Overall, maintaining 40% inoculum in the digester at the end of each cycle and refeeding with a new 1:3 SS:CM mixture significantly improved process kinetics, reduced the lag phase (1.9866 weeks), and maximized biogas production (µ_max = 1.0263 L (kg Week)⁻¹, Y_max = 0.4538 L·kg⁻¹). These results reinforce the critical role of inoculum in optimizing AD by enhancing substrate quality and microbial dynamics, thereby contributing to the development of more efficient, robust, and scalable biogas systems.