Assessing entropy changes in urban sewer systems during pollutant degradation

The urban sewer system is a fundamental component of public infrastructure, responsible for managing sewage and rainwater (Mathioudakis & Aivasidis 2009). In these systems, complex organic matter undergoes degradation, with microorganisms playing a crucial role by utilizing organic pollutants as nutrients and substrates for metabolism (Hvitved-Jacobsen et al. 2002). Microbial biofilms that adhere to the rough surfaces of sewer pipes facilitate microbial growth (Gu et al. 2024). Variations in water quality during sewage transport lead to shifts in dominant microbial communities, which utilize carbon and nitrogen sources to carry out biochemical reactions that degrade pollutants. The interaction of microbial populations in the sewage biofilm with the external environment alters the material composition of the sewage.

Anaerobic digestion is the primary biological reaction process responsible for the decomposition of the sewer matrix (Cruz et al. 2021). The transformation of pollutants in sewers entails the breakdown of macromolecular organic matter into smaller molecules and the conversion of unsaturated organic matter into saturated organic (Jin et al. 2015). This transformation process is always accompanied by entropy transfer and thermal energy exchanges with the surroundings (Zhang et al. 2023a). Additionally, the degradation of environmental pollutants by microorganisms increases the entropy of waste emissions. This is consistently accompanied by entropy transfer (Ebeling & Volkenstein 1990). A portion of the chemical oxygen demand (COD) in sewers is converted into methane (CH₄) and carbon dioxide (CO₂) through leaks in the pipe network, resulting in inevitable COD loss (Auguet et al. 2015).

Thermodynamic entropy has limited applications in pollutant evaluation and water quality research. Existing studies on thermodynamic entropy primarily focus on ecosystem evolution, system sustainability, environmental degradation, and quantitative assessments of pollutant discharge impacts on aquatic systems (Aoki 1989; Luo et al. 2012; Steinborn & Svirezhev 2000; Svirezhev 2000). Some scholars have employed the effective energy method to evaluate pollutant degradation, assess water environmental costs, and determine the environmental impact index of sewage treatment plants (Huang et al. 2007; Valero et al. 2009; di Cicco et al. 2020). However, despite the involvement of entropy changes in pollutant degradation, no established method currently exists for evaluating pollutant conversion from a thermodynamic perspective (Shi et al. 2018). Research on entropy has predominantly focused on information entropy, which aids in determining the weight coefficients of water pollution indicators, thereby facilitating water quality evaluation (Liu et al. 2010). In water resources, information entropy is applied to hydrological frequency distribution and water availability assessment (Maruyama et al. 2005). However, this approach does not account for the entropy effect of pollutant conversion in pipeline networks. Consequently, this study assesses entropy in pipeline networks by examining the heat changes associated with pollutant degradation processes.

The sewage transportation process undergoes stages such as fermentation, hydrogen production, acetic acid production, and methane production, all of which are closely related to anaerobic processes. The gases emitted during sewage transportation are a typical example of human interference with nature, resulting in increased entropy. This entropy increase, driven by greenhouse gas emissions, impacts natural ecological changes. Viewing the sewage pipeline transportation process as a closed system, the degradation of pollutants and gas emissions during urban sewage transportation is an irreversible process that leads to an increase in the natural environment's entropy. This increase is attributed to the heat emitted during pollutant degradation and the heat released from greenhouse gas emissions. Due to the migration and transformation of pollutants within the sewage network, environmental temperature and pressure experienced minimal changes. The heat emitted during pollutant degradation equals the heat absorbed by the pipe system. Although these values are equal, the signs of endothermic and exothermic reactions are opposite. By assigning a negative value to endothermic reactions and a positive value to exothermic reactions, the entropy change process in the pipeline network can be calculated based on the thermal changes occurring during pollutant migration and transformation (Jin et al. 2019).

Inspired by studies on thermal entropy calculations, this paper uses a 1,200-m-long urban sewer pilot system to analyze and summarize the main pollutant transformation processes in a three-stage anaerobic sewer based on chemical reaction equations. By establishing an entropy calculation method based on standard molar reaction enthalpy changes and calculating the entropy change of the reaction process induced by pollutant conversion, the study systematically reveals the entropy change characteristics of pollutant degradation in the sewage pipeline network. This calculation method provides a foundation for analyzing the entropy change characteristics of pollutant degradation at each stage of actual sewer systems and offers insights for developing entropy-based calculation methods and multidisciplinary applications for researchers in related fields.

Second, the following assumptions are made to simplify the analysis:

• (1) Pipeline network conditions:

• • The pipeline network operates under gravity flow conditions.

• • The sewage flow pattern is treated as a continuously operating plug flow system.

• • The pilot system simulates a long-distance trunk pipe with no confluence, reflecting a relatively closed pipe network without branch pipes, network overflow, leakage, or gas escape.

• (2) Entropy change considerations:

• • The primary focus is on the changes in heat and the emission of CO₂ and CH₄ into the atmosphere during the degradation of pollutants in the pipeline network.

• • Entropy change (ΔS) in this context is composed of two parts:

• • Δ_eS represents external contributions from the environment.

• • Δ_iS represents internal contributions from reactions within the system (Ludovisi & Poletti 2003).

In research, the following assumptions are made:

• (1) The system operates as a conditionally closed system free from human interference.

• (2) The external natural environment's circulation system on a large scale has self-repair capabilities and relatively dynamic stability.

These assumptions and conditions provide a foundation for analyzing the entropy change characteristics of pollutant degradation during sewage transportation in the pipeline network. This approach facilitates the calculation of thermodynamic entropy changes and provides insights into the impact of human activities on the natural ecological environment.

Chemical thermodynamics primarily deals with the conversion and transfer of heat in materials. In the quantitative analysis of chemical reactions, the entropy change of the reaction is used to determine whether the chemical process can occur spontaneously. While enthalpy change alone cannot determine the direction of chemical reactions, it serves as the foundation for calculating entropy changes.

For a given pollutant i within the urban sewage pipe network, the reaction enthalpy of its transfer transformation reaction in the pipe network is represented by Δ_rH. Typically, the temperature range of the pipe network falls within 0–30 °C. In this temperature range, the reaction enthalpy of chemical reactions exhibits minimal variation with temperature. The average temperature of the pipe network is calculated to be 25 °C. Since the system operates at approximately constant pressure and temperature, the heat of the reaction is equal to the change in enthalpy. In addition, the temperature difference within the pipe network has little effect on the final result of the entropy change calculation. For example, the annual average temperature difference in the water body temperature of the pipe network is ΔT = 5 °C, which results in only a 1.3% variation in the entropy change result.

The standard molar enthalpy of the formation of organic substances can be obtained from the ‘Standard thermodynamic properties of chemical substances’ (Haynes 2011). For organic substances not listed, the standard molar enthalpy can be calculated by Giese's equation.

The enthalpy change in the process of degradation of protein A₀–A₁ to produce amino acids is Δ_rH_m⁰ = 454.91 kJ/mol

Thus, the entropy change can be calculated using the provided formula.

This hydrolysis process persists throughout the entire pipeline, as depicted in the figure. However, the production stages and processes of these substances vary. Under the influence of methanogenic archaea, VFAs are eventually decomposed into gases such as methane and carbon dioxide, with this process predominantly occurring after 600 m along the pipeline (details on the entropy changes during these reactions are provided in Sections 3.2).

The degradation, migration, and transformation of pollutants in sewers generally result in minimal pressure variations, allowing the degradation process to be treated as a constant pressure reaction. According to thermodynamic principles, the heat of a reaction under constant pressure equals the enthalpy change. Pollutant degradation during urban sewage transportation involves heat exchange through various biochemical reactions. Protein hydrolysis, amino acid hydrolysis, fatty acid degradation, hydrogen production, and acetic acid production are predominantly endothermic processes. In contrast, glucose degradation and methanogenesis are primarily exothermic reactions. Therefore, the entropy change in sewers can be determined by the thermal changes accompanying the chemical reactions during pollutant degradation.

The degradation of amino acids is gradual, with acetic acid and propionic acid being the primary degradation products. The overall trend of entropy change shows a rapid shift at the front end of the pipeline, followed by a decrease in the 200–400 m section, primarily due to the extensive reaction of amino acids producing acetic acid and propionic acid. This reaction occurs after the significant degradation of proteins into amino acids (Figure 3(a)). After 400 m, the entropy change associated with amino acid degradation gradually slows down, reaching its highest value at the end of the pipeline. Between 800 and 1,000 m, further degradation of amino acids into acetic acid and propionic acid occurs, likely due to the complete consumption of oxygen in the pipeline, leading to anaerobic degradation, which is also supported by methane production later in the process.

The degradation of amino acids results in different entropy change trends, depending on the acids produced. As the pipeline progresses, the amount of acetic acid degraded decreases. For example, the degradation of methionine and proline primarily yields propionic acid, while the hydrolysis of aspartic acid, threonine, and lysine can produce butyric acid, with a notable increase in entropy primarily occurring in the middle and later segments of the pipeline. Additionally, the hydrolysis of leucine and proline predominantly results in valeric acid production.

The ‘entropy increase’ from amino acid degradation in sewers, leading to various acids (and amines), exhibits diverse trends in environmental entropy changes. The degradation process leading to valeric acid (throughout the full process) and propionic acid (in the initial and middle sections of the pipeline) contributes positively to environmental entropy. However, the degradation of butyric acid and methylamine contributes insignificantly to environmental entropy change. Most of the negative entropy in the environment results from amino acid degradation, particularly the formation of acetic acid and propionic acid at the front end of the pipeline. Overall, environmental entropy shifts to positive between 0 and100 m at the pipeline's front end. However, beyond 200 m, as amino acid degradation increases, entropy transitions to negative and gradually rises, aligning with the overall degradation trend of different amino acids along the pipeline.

Carbohydrate degradation, particularly for lactic acid, ethanol, and butyric acid, primarily occurs in the back-end section of the pipeline network. Previous studies have shown that the dominant genus in the pipeline shifts to anaerobic bacterial groups, such as Anaerolinea, which are proficient in degrading carbohydrates into small organic acids (Jin et al. 2018). Therefore, the process of sugar degradation into methanol, associated with negative entropy, mainly occurs in the front section of the pipeline network. Overall, the contribution to environmental entropy increase is primarily observed in the pipeline's front, with relatively modest entropy changes in the middle section; the rise in environmental entropy at the end of the pipeline section slightly decelerates.

During hydrogen and acetic acid production, fermentation byproducts such as propionic acid, butyric acid, and lactic acid serve as substrates for hydrogen-producing acetogenic bacteria. These bacteria convert organic acids and alcohols, which are not easily utilized by methanogens, into acetic acid, CO₂, and H₂. The significant amount of H₂ produced provides energy for methanogens, while CO₂ can also act as an electron donor for CH₄ production. Consequently, the reaction processes involved in hydrogen and acetic acid production inevitably cause changes in the entropy of the sewer environment.

Figure 6(b) depicts the change in environmental entropy along the pipeline network for acetic acid production. The increase in entropy during acetic acid production is primarily attributed to the degradation of methanol and lactic acid. Ethanol and butyric acid undergo degradation primarily in the middle section of the pipe network, while the generation of acetic acid from lactic acid, methanol, CO₂, and H₂ represents a process of entropy increase along the way. The overall entropy change of the acetic acid production process becomes a reduction process. The positive entropy observed in the pipeline network is mainly contributed by the rapid degradation of methanol into acetic acid. Lactic acid (400–1,100 m) contributes to acetic acid production as a positive entropy process, albeit with a small increase in entropy. The environmental negative entropy of the acetic acid production process in the pipe network is primarily contributed by propionic acid.

During the transport process within a pipe network, the degradation of organic matter serves as the primary mechanism responsible for reducing COD. This degradation process generates byproducts such as CO₂ and CH₄, which not only contribute to the formation of greenhouse gases but also lead to significant entropy changes within the pipeline network, ultimately affecting the external environment. The current study investigates the primary mechanisms of pollutant degradation and the production of CO₂ and CH₄ through metagenomic analysis of microbial activity within biofilms. By understanding these processes, the study aims to elucidate the mechanisms behind entropy change.

Organic metabolism and the distribution of microbial communities are inseparably connected along sewer systems. To investigate the changes in the microbial community structure in the pipeline network and infer the biological reactions occurring in the sewer system, pyrophosphate sequencing has been employed. In the first 30 m of the sewage system, Ballistosporium and Cloacibacterium are the dominant genera (Jin et al. 2018). As the distance increases, Cloacibacterium gradually disappears. Ballistosporium is well adapted to environments rich in hydrolyzed substrates, especially macromolecular organic compounds. In the front section of the pipeline (0–400 m), due to the high concentration of macromolecular organic compounds, Ballistosporium is relatively abundant in this region. From 600 to 800 m, as macromolecular organic matter degrades and various small molecules are produced, the relative abundance of Ballistosporium sharply decreases. In contrast, the relative abundance of Xanthobacter significantly increases, becoming the dominant genus. This shift occurs because the small molecules provide substrates for its growth. After 800 m, as substrates are gradually consumed, the relative abundance of Xanthobacter continues to decline, indicating that other genera at the end of the pipeline are more efficient at utilizing the remaining material (Jin et al. 2020). Therefore, the degradation of organic matter during transport is primarily driven by changes in the microbial community.

By employing the Kyoto Encyclopedia of Genes and Genomes database, this analysis focuses on key genes involved in carbon conversion pathways and methane production during pollutant degradation. The abundance of specific microorganisms within biofilms dictates the degradation pathways of organic matter. Various enzymes, such as cyanate hydrolase (EC 4.2.1.104), glycine dehydrogenase (EC 1.4.4.2), and formate dehydrogenase (EC 1.4.4.2), play crucial roles in breaking down proteins, amino acids, sugars, lipids, and carbohydrates, leading to the formation of CO₂ through multiple pathways (Jin et al. 2020). These enzymes significantly influence microbial abundance and thus the overall degradation process.

CO₂ is further utilized in the synthesis of formylmethylfuran by tetrahydromethotrexate formyltransferase (EC 1.2.99.5) derived from Methanopyrus kandleri. The subsequent conversion of formylmethylfuran involves a series of methyltransferases (EC 2.1.1.86, EC 1.5.98.1, EC 3.5.4.7, and EC 23.1.101), eventually producing methyl-CoM methanol via methyl conversion lyase (MtaA, MtaB, and MtaC) and formazan Group-CoM. Further processing by methyltransferases (MfbA, MtmB, and MtmC) leads to the formation of methylamine and acetic acid, with methane being generated from methyl-CoM by microbial methyl-Coenzyme M reductase (EC 2.8.4.1). The abundance of methyl-coenzyme M reductase in biofilms enhances methane production and its subsequent conversion. The continuous accumulation of methane in the pipeline network contributes to significant changes in entropy.

Carbohydrate degradation and methane production are identified as the primary contributors to the increase in entropy, with carbohydrate degradation playing a particularly significant role. The increase in environmental entropy is predominantly observed in the degradation pathways of sugar to propionic acid (26.234%), sugar to acetic acid (8.322%), and methanol to acetic acid (14.747%). These findings indicate that sugars, which undergo significant degradation during long-distance transport within the pipe network, are highly influential in determining the biochemical performance of sewage.

The heat exchange occurring during the pollutant degradation process contributes to an increase in external environmental entropy. However, it is crucial to note that not all reactions lead to an entropy increase; some degradation processes, in fact, result in negative entropy. The pilot-scale simulation system reveals that environmental entropy in the pipe network is primarily influenced by carbohydrate degradation and acetic acid production.

In particular, the degradation pathways of sugar to propionic acid (26.234%), sugar to acetic acid (8.322%), and methanol to acetic acid (14.747%) are responsible for significant increases in environmental entropy. On the other hand, reactions such as lactic acid to H₂ (2.603%) and lactic acid to acetic acid (2.934%) have a comparatively minor effect. The contributions of sugars to lactic acid (0.213%), sugars to butyric acid (0.185%), carbohydrates to H₂ (0.375%), CO₂ to acetic acid (0.145%), and H₂ to acetic acid (1.145%) are negligible in terms of entropy change.

Negative entropy contributions primarily stem from the degradation of proteins and amino acids, as well as from the hydrogen and acetic acid production processes. Notably, the degradation of propionic acid, including pathways such as protein to amino acid (−6.887%), amino acid to acetic acid (−2.455%), protein to H₂ (−3.564%), amino acid to H₂ (−2.693%), and propionic acid to acetic acid (−18.613%), significantly contributes to environmental negative entropy. Additionally, fatty acid and glycerol degradation have a relatively smaller impact on negative entropy, while the entropy increase associated with methane production (0.606%) has a notable effect on the overall external system.

In long-distance sewage pipelines without significant confluence, environmental entropy within the network gradually increases. Throughout the pollutant degradation process, both negative and positive entropy changes occur alternately, with the rate of entropy increase typically slowing toward the end of the pipeline. This entropy pattern aligns with the expected degradation behaviors of pollutants. Although some negative entropy may manifest near the end of the network, the overall trend still reflects an increase in environmental entropy. In practical sewage pipeline sections, as sewage is transported over long distances, the rate of entropy increases and diminishes gradually. However, the introduction of sewage from branch lines into the main pipeline can induce fluctuating entropy changes, resulting in a dynamic equilibrium of entropy within the sewage pipe network.

Urban sewage pipe networks predominantly operate under anaerobic conditions, where abundant carbon and nitrogen sources undergo a series of biochemical reactions, leading to changes in sewage quality. Using chemical equation analysis, this study examines and summarizes the specific transformation processes of primary pollutants within the sewer system and calculates the associated entropy changes. The results of this study could help predict the actual influent quality of wastewater treatment plants and promote the optimization of wastewater treatment. The key conclusions derived from this analysis are as follows:

• Thermodynamic reactions during pollutant degradation: Pollutant degradation during urban sewage transportation involves heat exchange. Processes such as protein hydrolysis, amino acid hydrolysis, fatty acid degradation, hydrogen production, and acetic acid production are predominantly endothermic, whereas glucose degradation and methanogenesis are primarily exothermic reactions.

• Entropy dynamics in urban sewage transport: Urban sewage transportation generally increases entropy in the external environment. However, not all reactions contribute to an entropy increase; some pollutant degradation processes result in negative entropy. Sugar degradation and acetic acid production are the main contributors to environmental entropy increases within the pipe network, while methane production has a minimal impact. Acid and fatty acid degradation, as well as glycerol degradation, contribute relatively minor amounts of negative entropy to the environment.

• Spatial variability of entropy change: The comprehensive entropy changes along the pollutant degradation pathway exhibit variability throughout the pipe network. Initially, at the beginning of the pipe section, the rate of entropy increase is relatively slow. As degradation progresses, there is an alternation between negative and positive entropy changes. Entropy increases more significantly in the middle sections of the pipe network and gradually rises in the last sections. Negative entropy becomes more pronounced at the terminal end of the pipe network, reducing the overall rate of entropy increase. By the time sewage reaches the end of the long-distance pipeline, most degradable organic matter has been decomposed, aligning the observed entropy changes with the expected degradation patterns of pollutants along the network.

• Human impact and environmental entropy: The gases emitted during sewage transportation represent a typical example of human interference with natural processes, contributing to an overall increase in entropy. The primary drivers of this increase are the heat released during pollutant degradation and the heat associated with greenhouse gas emissions.

This research was supported by the Major Special Project for Water Pollution Control and Treatment Technology under the sub-project titled ‘Research on Flow Mass Transfer and Pollutant Transfer and Transformation Patterns in Urban Sewage Pipe Networks’ (Project No. 2012ZX07313-001-01).

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.