Mathematical Modeling of an Anaerobic Moving Bed Biofilm Reactor

Introduction Biofilm accumulation on plastic carriers in an Anaerobic Moving Bed Biofilm Reactor (AnMBBR) depends on the (1) surface loading of biodegradable organics (g COD/m2-d), (2) time for the syntheses of microorganisms and biofilm accumulation, and (3) net rate of biofilm attachment/detachment. We developed and used mathematical models of an AnMBBR, 1-D biofilm, and biochemical transformations by bacteria, archaea, and enzymes. Objectives were to simulate experimental scenarios and describe total chemical oxygen demand (TCOD) removal, methane (CH4) generation, and biofilm structure and function. Materials and Methods Physical System: di Biase et al. (2018) investigated the effects of increasing TCOD volumetric loading rate (VLR) on its removal and CH4 production in three 4-L AnMBBRs treating brewery wastewater. Each AnMBBR had a 40% volumetric fill of ActiveCellTM 920 plastic carriers, which has a reported 680-m2/m3 specific surface area (SSA). The TCOD VLR was increased from 3.9 to 19.5 kg CODT/m3-d, and each loading condition lasted for 25 days. Process Model: A process model of biological and enzymatic processes included eight soluble and eight particulate state variables. Heterotrophic bacteria (XF) and acetate-cleaving methanogenic archaea (XM) syntheses and endogenous decays were modeled. Heterotrophic bacteria fermented readily biodegradable COD (SB) into volatile fatty acids (SVFA). Methanogenic archaea fermented SVFA into dissolved CH4 (SCH4) and carbon dioxide. Substrate transformations led to synthesis of active biomass, utilization associated products (SUAP), protein-extracellular polymeric substance (XEPS,P), carbohydrate-extracellular polymeric substances (XEPS,C), and hydrolytic enzymes (XHYD). Endogenous-decay products included XEPS,P, XEPS,C, biodegradable endogenous decay products (XEDP), and unbiodegradable endogenous decay products (XEDP,U). Extracellular enzymes catalyzed the hydrolysis of slowly biodegradable COD (XB), XEDP, XEPS,P, and XEPS,C. Protein-EPS and XEDP were hydrolyzed into protein-biomass associated products (SBAP,P), XEPS,C hydrolyzed into carbohydrate-biomass associated products (SBAP,C), and XB hydrolyzed into SB. Biofilm Model: A numerical, 1-D biofilm model following Wanner et al. (2006) and protocols from the Good Biofilm Reactor Modeling Practice (Rittmann et al. 2018) were applied. The modeled biofilm had a thickness (LF) that was discretized as 10 layers. Biofilms were modeled on the protected interior surfaces of plastic carriers, and biofilm area (AF) was modeled to decrease as LF increases, as illustrated by Figure 1. A mass-transfer boundary layer (MTBL) with variable thickness (LL) modeled mass-transfer resistance external to the biofilm. The transformation of soluble substrate i inside the biofilm was modeled as simultaneous diffusion and reaction. The ratio of DF,i to DW,i was set to 0.80. The rate of particle attachment to the biofilm surface was modelled as the product of the total suspended solids (TSS) concentration in the water (XTSS) and an attachment rate coefficient (katt). The rate of total solids (TS) detachment from the biofilm surface was modeled with a second-order expression that multiplied a detachment rate coefficient (kdet) by LF^2. LF, katt, and kdet were adjusted to maintain a TS concentration less than 300,000 g CODX/m3 inside each biofilm layer. Bioreactor Model and Simulator: The laboratory AnMBBR was modeled as a continuous flow stirred tank reactor. Water displacement by plastic carriers was included. The WWTP simulator SUMO (Dynamita, France) was utilized. Results and Discussion Simulations matched the experimental results of di Biase et al. (2018), see Figure 2. Most of the effluent COD was soluble COD (SCOD) that consisted of SB, SVFA, SUAP, SBAP,P, and SBAP,C, see Figure 3. Most of the SCOD was SVFA. Furthermore, the sum of COD in the effluent, including SCH4, was less than the influent TCOD. Thus, 25 days was not long enough to establish a steady-state LF. Although increasing the TCOD VLR led to increased COD removal rates and conversion to CH4 (expressed in kg COD/m3-d), the fractional conversions declined. The CH4-production rate increased from 0.012 to 0.043 kg COD/d from the first to the sixth stage, but the fractional COD conversion to CH4 dropped from 85 to 59%. The modeled LF increased with TCOD VLR, but the biofilm SSA decreased as the carrier channels filled with biofilm, see Figure 4. This AF loss was an important reason why TCOD removal and CH4 production rates did not increase linearly with the increasing TCOD VLR. Figure 5, which includes 1-D profiles of solids concentrations inside the biofilm, indicates that increasing TCOD VLR led to increased accumulation of endogenous-decay products and methanogenic archaea near the substratum, while the outer portion of the biofilm was enriched in fermenting heterotrophic bacteria. Methanogenic archaea accumulation near the substratum contributed to the relative slowdown of CH4 production for high TCOD VLR. Conclusions Integrated models described measured results from the experimental study by di Biase et al. (2018). Increasing the TCOD VLR led to lower ratios of COD removal and its conversion to CH4. Although higher TCOD VLR led to greater LF, it also was associated with lower SSA and increased accumulation of endogenous-decay products and methanogens deep in the biofilm, which contributed to less conversion of TCOD to CH4.