Modeling of Biogas Reactors

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190 6 Modeling of Biogas Reactors 6.4.2.2 Mathematical Modeling The structure of the mathematical models is shown in Figure 6.28. The mass balance of one module (i), including the interaction with an upper (i+1) and a lower module (i–1), leads to Eq. 26. V i dSS i dt = V · exchange,i–1(SS i –1–SS i)+V · exchange,i (SS ic1–SS i) +V · feed(SS i–1–SS i) – M · sedi,i–1 +M · sedi,i +M · prod V i SS i n � V k ·SS k kp1 In this equation V i denotes the volume of a module, SS i the concentration of suspended solids, V · feed, the volumetric feed rate of the reactor, and M · sedi,i the sedimenting mass flow between the modules. The produced biomass M · prod according to the growth of organisms could be calculated according to the TOC consumed (Eq. 27). M · prod = 0.1·V · feed(TOC in – TOC out) (27) The volumetric exchange flow V · exchange,i is calculated with Eq. 28 on the basis of measurements in Figure 6.26. Fig. 6.28 Structure of the mathematical model compared to two modules of the BTR. (26)
= 0.014 m s –1 V + 3.1· · exchange Aexchange The only parameter that is not known a priori, is the sedimenting mass flow rate M · sedi. This value was determined by regression analysis from the experiments performed as shown in Fig. 6.29. It can be clearly seen that the sedimentation capacity of active gassing sludge is much smaller compared to inactive (dead) sludge as used in the laboratory experiment. The sedimentation of active sludge follows Eqs. 29 and 30 where A reactor is the cross-sectional area of the reactor. SS~3 kg m –3 : = 0.0025 m s –1 M ·SS (29) · sedi A reactor SS`3 kg m –3 : = 0.04 kg s –1 m –2 + 0.015 m s –1 M ·SS (30) · sedi A reactor 6.4 Hydrodynamic and Liquid Mixing Behavior of the Biogas Tower Reactor V · gas A exchange In Figure 6.30 results of experiments and the calculation on the basis of the mathematical model are compared. The agreement between simulated data and measured suspended solid concentration is quite good. The relative deviation between measured and calculated values increases with decreasing concentration of suspended solids. The relative deviation ranges from 10%–15% of the concentrations in the BTR. To investigate the scattering of the measured concentration of suspended solids, 10 samples were taken at one sampling point during a laboratory scale experiment. The detected suspended solid concentrations deviated by up to 8% from the average value. This shows that part of the deviation might be due to sampling errors. Reinhold and Märkl (1997) also demonstrated that the mathematical model allows for realistic predictions of the dynamic behavior of the system, as was shown by simulating the start-up of a BTR. (28) Fig. 6.29 Sedimenting mass flow rate between adjacent modules on the laboratory scale and pilot scale as a function of the suspended solid concentration in the upper module. 191
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 23 and 24: 6.4.1.1 Model A Model A, which is a
Page 27: 6.4 Hydrodynamic and Liquid Mixing
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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