Mathematical modelling of waste activated sludge thermal disintegration

Chemical Oxygen Demand (COD) solubilisation was used to evaluate the impact of thermal pretreatment on the transfer of sewage sludge from particulate to soluble phase. It was gathering the experimental data needed for building of empirical mathematical model describing the relation between applied temperature and time and rate of COD solubilisation and degradation. In view of repeated measurements, in order to describe the relationship between changes in the fraction of dissolved COD and the time and temperature, mixed models have been adopted where by fixed factor measurement conditions have been adopted: time and temperature, while the random factor changes the characteristics of waste activated sludge. Linear and logistic nonlinear mixed models were analyzed. The tests demonstrated that all variables are statistically significant in assessing their impact on the efficiency of liquefaction of sludge. On the basis of the estimated model, the temperature rise of 10C increases degree of disintegration 1.7% above the average treatment time for 0.5h, by 2.6% for 1 hour, and by 3.9% for 2h. COD values decrease between 3 to 23% at temperatures in the range of 55 to 115°C. At higher temperatures COD was reduced in the range of 32 to 44%. Disintegration time did not have the significant impact on the degradation effect.


Introduction
The processing and disposal of sewage sludge is one of the most important and complex problems in the operation of municipal wastewater treatment plants. Anaerobic digestion is an attractive technology for the treatment of organic waste, which is a series of biochemical processes by different microorganisms to degrade organic matter under anaerobic conditions. Anaerobic degradation of particulate materials and macromolecules is considered to occur in four steps: hydrolysis, acidogenesis, acetogenesis, and methanogenesis. In sludge digestion, hydrolysis is the rate-limiting step. If the substrates consist of particulates, bacteria release extracellular enzymes that break down and solubilize organic particulate matter [1].
To improve process efficiency, the most expected approach is to destroy the microbial cells in the sludge. Use of pre-treatment of sewage sludge is aimed at breaking microorganisms' cells and release of intracellular organic matter to the liquid phase. Thermal disintegration of sludge has therefore been introduced to solubilize and convert slowly biodegradable, particulate organic materials to readily biodegradable lowmolecular-weight compounds. The hydrolysate liquid is rich in organic compounds, since carbohydrates and fats are transformed into easily decomposable forms, and proteins lose the protective enzymatic structure. Thermal pretreatment is an often used method to improve the properties of sewage sludge, which can not only improve the hydrolysis rate of organic substrates. The positive impact of the disintegration of sludge is considered in the following aspects, too: -the higher degree of substrates transformation of volatile fatty acids (VFA), -the decrease in the final waste mass through greater effectiveness of the dewatering processes and the required volumes of waste treatment and sludge treatment facilities, -the increase in the biogas production, -the increase in the degree of mineralisation of the organic matter of sludge, -the increase in the use of conditioning agents before the dewatering and mechanical thickening processes, -the recovery of certain desirable components from the sludge, for instance, plant-available nitrogen [2][3][4]. When thermal disintegration is combined with anaerobic digestion, energy required to perform thermal treatment can be positively balanced by biogas production [5,6].
Thermal disintegration of activated sewage sludge increases biogas production by 30% up to 225%, methane by 60% and decreases stabilized sludge organic mass by at least 30% [7]. For primary and activated sewage sludge, an increased susceptibility to dewatering was observed [8]. The energy balance demonstrates that, compared to the conventional methane fermentation, the system with thermal disintegration of sewage sludge provides a positive energy balance and allows fermentation chambers of smaller volumes. Li and Noike [9] managed to shorten the required fermentation time by 5 days for excess sludge disintegrated at 170°C for 60 min. Assuming the reduced dry matter and sludge susceptibility to hydration as the evaluation criterion, the literature data show that the optimal temperature for the process of sewage sludge thermal hydrolysis should be constrained to the range of 160 -175°C. According to Fisher and Swanwick [10], heating the sewage sludge to the temperature exceeding 180°C before the fermentation process leads to considerable loss of dry matter and the formation of refractory organic compounds (non-degradable COD fractions) in the process liquid. Conducting the process at lower temperatures (60 -80°C) increases the content of obtained hydrolysate, but requires longer reaction times. Elbing and Dünnebeil [11] demonstrated that the effect of the retention time of sewage sludge in the hydrolyser at the tested temperature on the liquidation result is not as crucial as the treatment temperature.

Experimental procedures
It was accompanied the sewage sludge thermal disintegration process with a number of tests. The waste activated sludge (WAS) used during the tests was collected from the secondary settlement tank in a mechanical-biological wastewater treatment plant with the capacity Q = 6,450 m 3 d -1 . This plant is working under the low-loaded active sludge technology. This technological system does not include a primary settlement tank and the process of biological treatment is conducted in nitrification, denitrification and dephosphatation processes. Additionally, phosphor removal is supported by the precipitation reaction.
Activated sewage sludge was treated at the following temperatures: 55, 75, 95, 115, 135, 155 and 175°C for 0.5, 1 and 2 hours. Samples were treated at the given temperature in an autoclave Zipperclave 1.0., Autoclave Engineers. The autoclave warm-up time lasted 10 -20 min depending on the required temperature, and the maximum cooling time was 15 min. In each time and temperature three repetitions were made. Each measurement was made separately for a certain heating time at the changing temperature.
The evaluation of WAS thermal disintegration effect on the change of the hydrolysates profile was performed on the basis of physical and chemical analyses of raw and post-treatment samples. The degree of disintegration was measured as a fraction of the solubilised organic matter. In this case COD with its fractions were performed according to the current methodology before and after the disintegration process. For this paper, COD measured on hydrolysates will be called "soluble COD" (SCOD) and the difference between total COD and soluble COD will be called "particulate COD" (PCOD). Mathematical method to describe the results of final effectiveness of pretreatment was used [Eq. 1].
The indicator for the direct assessment of effectiveness, which is most frequently encountered in the literature [12], is the quotient of COD growth for compounds solubilised during the hydrolysis after disintegration (ΔSCOD) and COD of the particulate fraction in the substrate before disintegration (PCOD) or total COD (TCOD) of the substrate, expressed as follows: where: η D1 -degree of disintegration, %; SCOD -COD of the compounds solubilised in the raw substrate, gO 2 m -3 ; SCOD D -COD of the compounds solubilised after disintegration, gO 2 m -3 ; ΔSCOD -growth of COD of the compounds solubilised after disintegration, gO 2 m -3 ; PCOD -COD of the solid substances in the substrate, before disintegration, gO 2 m -3 ; TCOD -total COD of the substrate, gO 2 m -3 .

Characteristic of waste activated sludge
Value of the total COD in raw WAS added to thermal disintegration was changed in the range of from 6,625 to 6,940 gm -3 , with an average value at 6,843 ± 107 gm -3 . The content of COD soluble fraction was 4.6% (average value 272 gm -3 ). And loss on ignition determined for raw sludge was 70.2% TS and COD/TS average quotient was 1.53.

Statistical analysis and mathematical modelling
Statistical analysis was performed using the statistical software package R distributed under an open-source license (GPL) R core team [13]. R software was used in order to determine the relation between changes in soluble COD and TCOD decomposition values and both time and disintegration temperature.
These relations were described using two approaches: the mixed linear and mixed nonlinear models. The mixed model approach takes into account the correlated nature of the outcomes. Parameters of mixed models were estimated using the maximum likelihood method. In each model was testing random effects with a likelihood ratio test. To verify the significance of fixed effects the Wald test was used. In the case of all statistical tests, the significance level was defined at 0.05. In each model were required model assumptions verified.
In view of repeated measurements, in order to describe the relationship between changes in the fraction of dissolved COD (SCOD) in hydrolysates and the loss of organic matter (ΔTCOD) and the time and temperature, mixed models have been adopted where by fixed factor measurement conditions have been adopted: time and temperature, while the random factor changes the characteristics of waste activated sludge.
Linear and logistic nonlinear mixed models were analyzed. In the modelling of changes in COD fractions it is accepted that the processing time is a categorical variable with 3 levels, where the time of 0.5h was established as the reference category.

Results
The analysis of results indicates the influence of temperature and disintegration time on SCOD in hydrolysates. An increase of COD solid fraction liquidation (Fig. 1), were observed after increasing temperature of pre-treatment. The lowest value for SCOD (281 gm -3 ) was observed in the sample disintegrated at 55°C for 0.5 hour, and the highest value -3,793 gm -3 for the sample treated at 175°C for 2 hours. SCOD content in TCOD in these samples amounted to 4.1 and 97.7% respectively. Regardless of the disintegration time, a significant increase in SCOD values was observed in samples exposed to treatment at minimum 115°C. In disintegration time of 0.5h the highest SCOD value was achieved at 175°C -2,048 gm -3 . In the longer disintegration time similar effects were obtained at lower temperatures: 135°C (1h) and 115°C (2h), respectively (and disintegration becomes more complete at high temperatures).

Effect of thermal pretreatment on COD solubilization and decomposition
The effectiveness of the disintegration process is evaluated by, inter alia, the increase in soluble COD content in the hydrolysate with relation to the initial value of COD solid fraction according to the Eq. 1 (Fig. 2).
A 26.6% increase in SCOD value was obtained when sludge was pre-treated at 175C during 0.5 h, a 42.1% was reached at the same temperature when treatment time was 1 h. A 54.2% increase in SCOD was reported at 175C of the 2 h.
The process of WAS thermal pretreatment in every sample caused the decomposition of organic matter, and consequently resulted in diminishing of total COD value. Values of SCOD depending on the level of TCOD value decrease in thermal disintegration are illustrated in Figure 3 and 4.
The analysis of results demonstrates that the soluble COD content in hydrolysates at specific treatment temperature increases at a similar relative extent as total COD decreases (Fig. 3). Total COD decrease from 3 to 23% was observed at treatment temperatures in the range of 55 -115°C. While the disintegration of WAS at higher temperatures affected the reduction of the COD in the range of 32 to 44%. However, the disintegration time did not have the significant impact on the mineralization effect. The decrease of total COD was amounted about 20% in 0.5, 1.0 and 2.0 h pretreatment (Fig. 4).

The influence of time and temperature on disintegration process efficiency
Values SCOD/TCOD in the pre-treated sludge were clearly higher than that in the raw sludge (Fig.1), thereby indicating that thermal pretreatment had a strong effect  A mixed linear model with regard to the interaction time and temperature has been adopted in modelling the increase in the degree of η D1 disintegration. Preliminary analysis demonstrated the absence of a statistically significant random effect in this model (p-value = 0.49), therefore the model has been simplified to the model without considering such an effect: where y i corresponds to the i th response η D1 , x temp to temperature (C), x time.1h and x time.2h are categorical variables coded with dummy variables 0 or 1, for a heating time 1 and 2h respectively, and ɛ i are independent and normal with mean zero and variance  2 , i=1,2,…,63. In this model the heating time 0.5 h was chosen to be the reference category.
In order to verify the relevance of the effect of temperature, time and their interaction on the growth of the degree of η D1 disintegration, sequential testing was conducted (Table 1). The tests demonstrated that all of these variables are statistically significant in assessing their impact on the efficiency of liquefaction of waste activated sludge. Hence, the impact of temperature on the degree of disintegration is significantly conditioned by the time of treatment (p-value <0.0001). On the basis of the estimated model (Table 2) the temperature rise of 10C increases the degree of η D1 disintegration approximately 1.7% above the average treatment time for 0.5 h, by 2.6% for 1 hour, and by 3.9% for 2 h. Regression lines estimated using a linear model (Eq. 2) illustrating the process of η D1 change for temperatures of measurements varied by treatment time is presented in Fig. 6. Analysis of the mean values (Fig. 5) and boxed charts (Fig. 4) demonstrated that the treatment time does not significantly affect the reduction of organic material, measured by COD loss, therefore in this case the dependency of ΔTCOD changes only with respect to temperature was considered. The confidence intervals for the mean ΔTCOD value (Fig. 7) demonstrate that changes in the average COD loss together with increasing temperature of the process are non-linear. The growth rate of TCOD loss is not constant, though varies depending on the temperature. This course suggests that the non-linear logistic model is the adequate model for the description of ΔTCOD changes.  A mixed logistic model was used to analyze the observed behaviour. All parameters were assumed to be fixed and random [15]. The mixed effects logistic model can be expressed as: where y ij represents the j th measurement ΔTCOD on the i th sludge sample (cluster), x ij is the corresponding temperature, and Ɛ ij are independent and normal with mean zero and variance  e 2 . In this case i =1, 2,…, 9 and j =1, 2,…7 and all three parameters Φ i1 , Φ i2 and Φ i3 have both a fixed and random component: The model was analyzed during the construction process and its parameters were determined, assuming a random component. Under normality assumptions, alternative models were evaluated by Akaike information criterion (AIC) ( Table 3). A model was selected that only includes the Φ i2 parameter (both fixed and mixed components). In addition, it was verified that the random factor is statistically significant in a predetermined fixed effects (p-value=0.001 and 2 σ sludge,2 = 12.183, 2 e σ = 3.327). The estimates of fixed logistic parameters obtained with mixed effects models (Eq.3) are presented in Table  4. The predicted logistic curve is shown in Fig. 8, precisely this is the mean curve, i.e., the fitted curve with b i2 =0 for all i. Model analysis of the logistic model (Table 4) of ΔTCOD changes in relation to temperature differences. At a temperature of 117.7C (23.53% TCOD loss) the COD loss shows the largest temperature dependence (Fig. 8). More specifically, this temperature is below the rapid depletion of COD during the disintegration process, and above the gradual decrease, the rate of organic matter decreases.  The graphical evaluation of logistically adjusting the mixed model for ΔTCOD is presented on the diagnostic chart ( Fig. 9). The results are in compatible with that presented in literature. Climent [16] established that the time and temperature have similar influence on the performance of high temperature thermal treatment as well as the combined effect of the two parameters. It should be noted that the degree of solubilisation is in most cases linearly dependent on temperature, especially for hightemperature disintegration. Tanaka [14] were evaluated the effectiveness of thermal treatment by means of SCOD concentration, too. A 25% increase in SCOD value was obtained when sludge was pretreated at 130C during 30 min, a 30% was reached at the same temperature when treatment time was 60 min. A 60% increase in SCOD was reported at 170C independently of the time of treatment. Under the same conditions, in Zipperclave reactor, was excessive sludge disintegrated [17,18] during 15, 30 and 60 min. During the one-hour treatment, the SCOD share increased from 2.7% to 25.3, 43.9 and 59.5% at process temperatures of 130, 150 and 170°C, respectively. Bougrier [19] obtained a solubilisation of the COD fraction in the range of 40 to 45% in 30 and 60 min. However, Aboulfoth [1] at 175ºC found an increase in COD solubilisation from 11.2% to 15.1 and 25.1% after increasing the treatment time from 1 to 2 and 3 hours, respectively. Thermal treatment processes are associated with the simultaneous mineralization of organic components, however, it is possible to establish conditions limiting the decomposition [19]. For example Caraballa [20] obtained a reduction of organic mass of sewage sludge below 5%, leading to disintegration at 130°C during 60 min.

Conclusions
Thermal (low and high temperature) disintegration is effective in waste activated sludge solubilisation as reflected in the increase of SCOD in hydrolysates. COD solubilisation was found to increase linearly with treatment temperature. The maximum SCOD value and the majority of the particulate organic matter removals were achieved for the sample treated at 175°C for 2 hours.
It was found, that time and temperature have similar influence on the performance of temperature thermal treatment as well as the combined effect of the two parameters as derived from the coefficients of the mathematical model that results of the experimental data.