Anaerobic digester (hydrolysis + acidogenesis + methanogenesis) simulation

1 inlet -> 2 outlets [biogas, digestate]

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Governing equations

The exact equations the solver works for a anaerobic digester (hydrolysis + acidogenesis + methanogenesis) — the same math shown in the app's "Theory" panel, not a black box.

D = \dot V/V,\qquad S_p = \frac{D\,S_{p,in}}{D+k_{hyd}},\qquad r_{hyd} = k_{hyd}\,S_p\quad(\text{first-order hydrolysis, CSTR steady state})

\mu_a = \mu_{max,a}\,\frac{S_s}{K_{s,a}+S_s} = D + \mu_{d,a}\quad(\text{acidogen chemostat, } S_{s,in}=r_{hyd}/D)

\mu_m = \mu_{max,m}\,\frac{S_{vfa}}{K_{s,m}+S_{vfa}}\cdot\frac{K_{i,m}}{K_{i,m}+S_{vfa}} = D + \mu_{d,m}\quad(\text{methanogen chemostat, Haldane self-inhibition by its own substrate})

\mathrm{CH_3COOH} \rightarrow \mathrm{CH_4} + \mathrm{CO_2}\quad(\text{acetoclastic, exactly 1:1 molar})

$D$: dilution rate [1/s] — volumetric feed divided by reactor volume, shared by every stage (one well-mixed CSTR)
$S_p$: particulate/polymeric substrate concentration [mol/m³] remaining after hydrolysis
$k_{hyd}$: first-order hydrolysis rate constant [1/s]
$r_{hyd}$: soluble-substrate production rate from hydrolysis [mol/(m³·s)]
$\mu_a, \mu_m$: specific growth rate of the acidogen / methanogen population [1/s]
$\mu_{d,a}, \mu_{d,m}$: specific death rate of each population [1/s]
$S_s$: soluble substrate concentration feeding acidogenesis [mol/m³]
$S_{vfa}$: volatile fatty acid (VFA, acetate-equivalent) concentration [mol/m³] — both the methanogens' substrate and, via K_{i,m}, their own inhibitor
$K_{s,a}, K_{s,m}$: Monod half-saturation constant for each stage [mol/m³]
$K_{i,m}$: Haldane self-inhibition constant for methanogenesis by VFA [mol/m³]

Parameters

substrate (feed component), volume [m^3, required], mu_max_acidogen [1/s, required], mu_max_methanogen [1/s, required]; optional k_hyd [1/s, first-order hydrolysis rate constant, default 1e-5], Ks_acidogen/Ks_methanogen [mol/m^3], yield_xa/yield_xm [mol biomass/mol substrate], vfa_yield [mol VFA/mol soluble substrate, default 0.8], Ki_methanogen [mol/m^3, Haldane self-inhibition of methanogenesis by VFA — omit for no inhibition], maintenance_acidogen/maintenance_methanogen [mol substrate/(mol biomass*s)], death_rate_acidogen/death_rate_methanogen [1/s], soluble_substrate/vfa/acidogen_biomass/methanogen_biomass [pseudo-component name overrides], pressure_drop [Pa]. Two-stage reduced model (hydrolysis+acidogenesis, then methanogenesis, solved sequentially — see the module docstring for the disclosed bound); biogas CH4:CO2 is exactly 1:1 by acetoclastic stoichiometry

Anaerobic digester (hydrolysis + acidogenesis + methanogenesis) simulation

Governing equations

Parameters

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