Modeling of Biogas Reactors

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184 6 Modeling of Biogas Reactors Fig. 6.21 Mixing of a Dirac impulse in the upper module of the laboratory scale reactor (Fig. 6.19). Fig. 6.22 Mixing of a Dirac impulse (3rd module) in the pilot scale BTR (Fig. 6.20). The structure of the mathematical model developed is shown in Figure 6.23. The structures of the two models A and B follow the modular structure of the reactor concept. Both models couple two neighboring modules by the flow of the feed (V · feed), which is constant within the tower reactor and is directed from the bottom to the top of the reactor. The central idea of both models is to predict the coupling between two modules by the so-called “exchange flow rate”. This virtual flow rate (V · exchange) accounts for the situation of a turbulent exchange of volume elements in the area between two modules (A exchange). This turbulent flow is driven by the bubbles passing this area. V · feed is kept at zero during the experiment. Also, in reality the contribution of V · feed is usually small compared to the turbulent exchange flow V · exchange.
6.4.1.1 Model A Model A, which is a more detailed one, is able to describe mixing within a module as well as intermixing between modules. Each module is composed of four compartments. Riser and downcomer are mathematically replaced by tube reactors with axial dispersion. At the bottom and the top of each module, riser and downcomer join in mixing zones which are regarded as stirred vessels. The four zones are linked by the circulation flow rate V · circ. Since the cross-sectional area of the riser A riser and the downcomer A downc. as well as the flow rate through the riser V · riser and the downcomer V · downc. are equal, the mean circulation velocity w m is given by Eq. 19. V · riser Ariser V · downc. Adownc. 6.4 Hydrodynamic and Liquid Mixing Behavior of the Biogas Tower Reactor Fig. 6.23 Structure of models A and B as compared to the BTR for describing the mixing behavior of the liquid phase. w m = = (19) Each real module of the reactor is thus replaced by a “ring structure” of four reactors. The transport and mixing mechanisms in this ring structure are convection and axial dispersion. The mathematical equations of model A can be derived from the mass balances of each of the four compartments. Model A needs three parameters for calculating the mixing behavior: the liquid circulation velocity w m, the axial dispersion coefficient D ax, and the exchange rate V · exchange. All these parameters depend on the gas flow rate entering the module from the lower module. For more details of the model, the mathematical structure, and the procedure of solving the partial differential equations, the publication of Reinhold et al. (1996) should be consulted. 185
Page 1 and 2: 6 Modeling of Biogas Reactors Herbe
Page 3 and 4: tom (Fig. 6.1), the question of mix
Page 5 and 6: Table 6.2 Characteristic data of th
Page 7 and 8: desalinated water and wastewater in
Page 9 and 10: 6.3 Kinetics Fig. 6.7 Combined meas
Page 11 and 12: dx dt dc Ac dt = µ (c Ac, c i) x -
Page 13 and 14: For example, the acetic acid HAc is
Page 15 and 16: On the abscissa the concentration o
Page 17 and 18: c HAc µ = µ max · · (18) cHAc+K
Page 19 and 20: 6.4 Hydrodynamic and Liquid Mixing
Page 21: 6.4 Hydrodynamic and Liquid Mixing
Page 29 and 30: = 0.014 m s -1 V + 3.1· · exchang
Page 31 and 32: The effect of gas recirculation can
Page 33 and 34: high (5.13 g L -1 ), the concentrat
Page 35 and 36: culated k La values in the pilot sc
Page 37 and 38: 6.7 Outlook Altogether at a higher
Page 39 and 40: References tance in the production

Modeling of Biogas Reactors

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