The objective of this paper is to show the results of an industrial project dealing with modelling of anaerobic digesters. A multi-scale mathematical approach is developed to describe reactor hydrodynamics, granule growth/distribution and microbial competition/inhibition for substrate/space within the biofilm. The main biochemical and physico-chemical processes in the model are based on the Anaerobic Digestion Model No 1 (ADM1$ADM1$) extended with the fate of phosphorus (P$P$), sulfur (S$S$) and ethanol (Et−OH$Et-OH$). Wastewater dynamic conditions are reproduced and data frequency increased using the Benchmark Simulation Model No 2 (BSM2$BSM2$) influent generator. All models are tested using two plant data sets corresponding to different operational periods (#D1$\#D1$, $\#D2$). Simulation results reveal that the proposed approach can satisfactorily describe the transformation of organics, nutrients and minerals, the production of methane, carbon dioxide and sulfide and the potential formation of precipitates within the bulk (average deviation between computer simulations and measurements for both #D1$\#D1$, $\#D2$ is around 10%) Model predictions suggest a stratified structure within the granule which is the result of: 1) applied loading rates, 2) mass transfer limitations and 3) specific (bacterial) affinity for substrate. Hence, inerts (X_I$(X_{\text{I}}$) and methanogens (X_ac$(X_{\text{ac}}$) are situated in the inner zone, and this fraction lowers as the radius increases favouring the presence of acidogens ($X_{\text{su}},X_{\text{aa}}$, $X_{\text{fa}}$) and acetogens ($X_{\text{c}4},X_{\text{pro}}$). Additional simulations show the effects on the overall process performance when operational (pH) and loading (S:COD$S:COD$) conditions are modified. Lastly, the effect of intra-granular precipitation on the overall organic/inorganic distribution is assessed at: 1) different times; and, 2) reactor heights. Finally, the possibilities and opportunities offered by the proposed approach for conducting engineering optimization projects are discussed.

中文翻译：

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使用多尺度方法对工业厌氧颗粒反应器进行建模

本文的目的是展示一个处理厌氧消化池模型的工业项目的结果。开发了一种多尺度数学方法来描述反应器的流体动力学，颗粒生长/分布以及微生物对生物膜内基质/空间的竞争/抑制作用。该模型中的主要生化和理化过程基于1号厌氧消化模型（ADM1$\mathrm{一个}d\mathrm{中号}\mathrm{1个}$）与磷的命运（P$P$），硫（S$\mathrm{小号}$）和乙醇（Et-OH$EŤ-ØH$）。使用基准模拟模型2（BSM2$乙\mathrm{小号}\mathrm{中号}\mathrm{2个}$）进水发电机。所有模型均使用两个工厂数据集进行了测试，这些数据集对应于不同的运营时间段（＃D1$＃d\mathrm{1个}$， $＃d\mathrm{2个}$）。仿真结果表明，所提出的方法可以令人满意地描述有机物，营养物和矿物质的转化，甲烷，二氧化碳和硫化物的产生以及大量沉淀物的潜在形成（＃D1计算机模拟和测量值之间的平均偏差）$＃d\mathrm{1个}$， $＃d\mathrm{2个}$大约10％）模型预测表明颗粒内有分层结构，其结果是：1）施加的负载率，2）传质限制和3）对底物的特异性（细菌）亲和力。因此，惰性（X _I$（X_{\text{一世}}$）和产甲烷菌（X _ac$（X_{\text{交流电}}$）位于内部区域，并且随着半径的增加，该分数降低，有利于酸原的存在（$X_{\text{su}}，X_{\text{a}}$， $X_{\text{F A}}$）和产乙酸素（$X_{\text{C}4}，X_{\text{亲}}$）。其他仿真显示了在操作（pH）和装载（S：COD$\mathrm{小号}：CØd$）条件已修改。最后，在以下时间评估颗粒内沉淀对总体有机/无机分布的影响：1）不同的时间；2）反应堆高度。最后，讨论了所提出的方法进行工程优化项目所提供的可能性和机会。