Over the past two decades, modeling the hydrolysis stage has been recognized as critical for understanding its behavior and determining optimal operating conditions for anaerobic digestion (AD). Traditional approaches, such as first-order and Michaelis–Menten kinetic models, account for substrate concentration and enzymatic activity, respectively, but neglect mass-transfer effects. In this work, we propose a semi-empirical model that integrates enzymatic catalysis with molecular diffusion phenomena in the microbial boundary layer. We derive a hydrolysis rate expression by combining Michaelis–Menten kinetics with Fick’s law of diffusion and validate it against experimental data from a thermophilic batch reactor treating cattle manure (55 <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12155_2025_10873_Article_IEq1.gif" Format="GIF" Height="7" Rendition="HTML" Resolution="72" Type="Linedraw" Width="9" /> </InlineMediaObject> <EquationSource Format="TEX">$^{\circ }$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mo>∘</mo> </mmultiscripts> </math></EquationSource> </InlineEquation>C, 62 <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12155_2025_10873_Article_IEq2.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="64" /> </InlineMediaObject> <EquationSource Format="TEX">$g\,\text {VS}\,\text {L}^{-1}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>g</mi> <mspace width="0.166667em" /> <mtext>VS</mtext> <mspace width="0.166667em" /> <msup> <mtext>L</mtext> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation>). Compared to the first-order model (R<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12155_2025_10873_Article_IEq3.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="TEX">$^2$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>2</mn> </mmultiscripts> </math></EquationSource> </InlineEquation> = 0.940), our model achieves a superior fit (R<InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12155_2025_10873_Article_IEq3.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="TEX">$^2$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>2</mn> </mmultiscripts> </math></EquationSource> </InlineEquation> = 0.973), demonstrating that diffusion resistance can significantly influence hydrolysis kinetics. By formulating the kinetic model in terms of explicit biochemical and mass-transfer parameters (<InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12155_2025_10873_Article_IEq5.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="41" /> </InlineMediaObject> <EquationSource Format="TEX">$r_{h,\text {max}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>r</mi> <mrow> <mi>h</mi> <mo>,</mo> <mtext>max</mtext> </mrow> </msub> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12155_2025_10873_Article_IEq6.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="29" /> </InlineMediaObject> <EquationSource Format="TEX">$K_M$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>K</mi> <mi>M</mi> </msub> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12155_2025_10873_Article_IEq7.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">$k_d$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>k</mi> <mi>d</mi> </msub> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12155_2025_10873_Article_IEq8.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">$\alpha $</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>), it becomes possible to identify optimal operational strategies for enhancing hydrolysis efficiency. The results indicate that coupling enzymatic catalysis with diffusion provides a more accurate theoretical description than the first-order model and enables improved prediction of biopolymer solubilization in AD.

Theoretical Analysis of the Hydrolysis Mechanism of Biopolymers in the Anaerobic Digestion Process of Livestock Manure

期刊论文
发表日期：

2025年8月7日

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Sebastián Villegas-Moncada,
Mario Luna-delRisco,
Catalina Arroyave-Quiceno,
Mauricio González-Palacio,
Carlos Peláez-Jaramillo

摘要

Over the past two decades, modeling the hydrolysis stage has been recognized as critical for understanding its behavior and determining optimal operating conditions for anaerobic digestion (AD). Traditional approaches, such as first-order and Michaelis–Menten kinetic models, account for substrate concentration and enzymatic activity, respectively, but neglect mass-transfer effects. In this work, we propose a semi-empirical model that integrates enzymatic catalysis with molecular diffusion phenomena in the microbial boundary layer. We derive a hydrolysis rate expression by combining Michaelis–Menten kinetics with Fick’s law of diffusion and validate it against experimental data from a thermophilic batch reactor treating cattle manure (55 $^{\circ }$ $^{\circ}$ C, 62 $g\,\text {VS}\,\text {L}^{-1}$ $g VS L^{- 1}$ ). Compared to the first-order model (R $^2$ $^{2}$ = 0.940), our model achieves a superior fit (R $^2$ $^{2}$ = 0.973), demonstrating that diffusion resistance can significantly influence hydrolysis kinetics. By formulating the kinetic model in terms of explicit biochemical and mass-transfer parameters ( $r_{h,\text {max}}$ $r_{h, max}$ , $K_M$ $K_{M}$ , $k_d$ $k_{d}$ , $\alpha $ $α$ ), it becomes possible to identify optimal operational strategies for enhancing hydrolysis efficiency. The results indicate that coupling enzymatic catalysis with diffusion provides a more accurate theoretical description than the first-order model and enables improved prediction of biopolymer solubilization in AD.