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Diffusion of Substrate and Oxygen in Aerobic Granules
Published in Yu Liu, Wastewater Purification, 2007
The Thiele modulus is a measurement of the ratio of granule surface reaction rate to the mass diffusion rate. If the Monod kinetics for microbial reaction is applied, Y. Q. Liu, Liu, and Tay (2005) proposed the following modified Thiele modulus (φ) by introducing dimensionless concentrations: () ϕ=R(XoμmYX/SSoDes)1/2
Methanol Conversions
Published in Saeed Sahebdelfar, Maryam Takht Ravanchi, Ashok Kumar Nadda, 1 Chemistry, 2022
Saeed Sahebdelfar, Maryam Takht Ravanchi, Ashok Kumar Nadda
The effectiveness factor (η) is a criterion for describing the degree of catalyst utilization (Levenspiel, 1999). When the Thiele modulus is low (φ → 0), full utilization of catalyst particle (η → 1) is observed. In contrast, φ = 10 leads to η = 0.1 which is equivalent to 10% of catalyst surface utilization. Characteristic length of diffusion (L), efficient diffusivity (Deff) and intrinsic reaction rate constant (k) are parameters used for the calculation of the Thiele modulus (φ). As for a given reaction and molecular sieve, k is fixed, for decreasing Thiele modulus, diffusion length (L) must be shortened and/or effective diffusivity (Deff) in the pores must be increased (Zhong et al., 2017).
Mass Transfer in Binary Systems without Bulk Flow: Steady-State Examples
Published in İsmail Tosun, Fundamental Mass Transfer Concepts in Engineering Applications, 2019
Large values of the Thiele modulus correspond to cases in which the diffusion rate is very slow and the surface reaction is very rapid. Under these conditions, the effectiveness factor becomes η=1Λ
Effect of catalyst and feed properties on the deactivation parameters of an ARDS process model for HDS and HDM reactions
Published in Chemical Engineering Communications, 2021
Dduha Chehadeh, Mohammad Khajah, Hamza Albazzaz, Dawoud Bahzad
It can be observed from Figure 1 that the Thiele moduli are different for the three tested catalyst systems (cases 1, 2, 3) using the same feed. This is in line with the fact that Thiele modulus is related to the diffusion and reaction in the porous catalyst. Diffusion restrictions are present for Thiele moduli larger than 1 (Marafi et al. 2010). Catalyst system S1 presented relatively lower values of Thiele moduli; thereby minimum diffusion limitations are expected, especially since the catalysts in this system have the highest pore volume among the others (Table 1). Catalysts with large pores give paths for reactant and product molecules and have a high metal storage capacity. On the other hand, the Thiele moduli for the same fresh catalyst system (S3) followed the same trend (cases 3, 4, and 5) for the three different feeds. The loading profile of catalyst system S3 was the same in the reactors, and most catalysts contributed in the same way regardless of the feed type. This supports the fact that Thiele modulus is directly related to the catalyst itself.
Modeling of bioethanol production through glucose fermentation using Saccharomyces cerevisiae immobilized on sodium alginate beads
Published in Cogent Engineering, 2022
Astrilia Damayanti, Zuhriyan Ash Shiddieqy Bahlawan, Andri Cahyo Kumoro
As presented in Figure 2, all the corresponding experimental data and calculation results exhibit the same trend. Glucose concentrations in the fermentation and became close to zero at 16 hours because glucose rapidly entered the Na-alginate bead pores and was followed by a quick diffusion to the microbial film. Thiele modulus (φ) can be used to identify the effect of internal diffusion on the biochemical reaction rate (Galaction et al., 2010). Vives et al. (1993) also reported that the observable Thiele modulus (φ) values for both glucose and ethanol were always in the range between 1 × 10−3 to 6 × 10−2, which confirm that there were no internal and external diffusion limitations in the alginate beads. Scott et al. (1989) also found that the diffusivity coefficient of glucose solution with 10–200 g/L concentration to 2 mm alginate beads at 30°C ranged between 6.0 × 10−6 to 6.8 × 10−6 cm2.s−1. The diffusivity coefficient of ethanol in water was 1.98 × 10−5 cm2.s−1. This condition denotes that the mass transfer rate in the alginate beads with entrapped cells is very fast relative to the fermentation rate. However, this glucose is also simultaneously consumed by S. cerevisiae cells in the microbial film to support their growth and production of ethanol. As a result, ethanol concentration increased significantly within the same period due to the conversion of glucose. Ethanol concentration continued to increase gradually until 32 hours of fermentation. Unfortunately, beyond 32 hours, ethanol concentrations became almost constant for fermentation using 0.5, 0.75, and 1.0 g dry yeast, which indicate exceptionally low ethanol production rates caused by the attenuation of glucose as substrate. The slowest glucose consumption and ethanol production rates can be observed for fermentation using 0.25 g dry yeast. Meanwhile, glucose concentration on the surface of the Na-alginate beads was almost linear in the first 8 hours of fermentation and was followed by a gradual increase to reach the maximum value at about 16 hours of fermentation. This phenomenon proved the existence of mass transfer resistance of glucose from the bulk fermentation broth to the surface of the Na-alginate beads and followed by fermentation by S. cerevisiae cells entrapped the pores of the Na-alginate beads. Prolong fermentation time caused a gradual reduction of glucose concentration on the surface of the Na-alginate beads because glucose is consumed by S. cerevisiae cells as a substrate for their growth and is converted to ethanol.