Bubble wake solids content in three-phase fluidized beds

El‐Temtamy, Seham A.; Epstein, Norman

doi:10.1016/0301-9322(78)90022-8

Cited by 53 publications

(18 citation statements)

References 21 publications

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“…The values of el calculated from the previously published It may be seen that the present data of el in the three-phase fluidized beds can be represented well by the correlation of Kato et al (1981) with a coefficient of variation of 7.8%, although the deviation between the predicted and experimental liquid holdups becomes significant in the range of higher gas flow rate ( Ug > 10 cm/s). The predictions of E, by the correlation of Darton and Harrison (1975) based on the solid free wake model and by the correlation based on the generalized wake model proposed by Bhatia and Epstein (1974) and refined by El-Temtamy and Epstein (1978) also agree fairly well with the experimental points, within a coefficient of variation of 10.4% and 8.7%, respectively. The predictions based on the empirical correlation of Begovich and Watson (1978) result in a coefficient of variation of 18.3% for the whole data and give poor agreement with the data for low density particles.…”

Section: Liquid Holdupsupporting

confidence: 64%

Wall‐to‐bed heat transfer coefficient in gas—liquid—solid fluidized beds

1984

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Wall to bed heat transfer has been studied in three‐phase fluidized beds with a cocurrent up‐flow of water and air. Six sizes of glass beads, two sizes of activated carbon beads and one size of alumina beads, varying in average diameter from 0.61 to 6.9 mm and in density from 1330 to 3550 kg/m3, were fluidized in a 95.6 mm diameter brass column heated by a steam jacket. Complementary heat transfer experiments have been performed also for a gas–liquid cocurrent column and liquid–solid fluidized beds. The wall‐to‐bed coefficient for heat transfer in the gas–liquid–solid fluidized bed is evaluated on the basis of the axial dispersion model concept. The ratio of the wall‐to‐bed heat transfer coefficient in the gas–liquid–solid fluidized bed to that in the liquid–solid fluidized bed operated at the same liquid flow rate is correlated in terms of the ratio of the velocity of gas to that of liquid and the properties of solid particles. A correlation equation for estimating the wall‐to‐bed heat transfer coefficient in the liquid–solid fluidized bed is also developed.

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Section: Liquid Holdupsupporting

confidence: 64%

Wall‐to‐bed heat transfer coefficient in gas—liquid—solid fluidized beds

1984

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“…Later, Yu and Rittmann 20 proposed another correlation equation for k, which was a modification from that of El-Temtamy and Epstein; 7 as shown in eqn (12):…”

Section: Gas Hold-up and Kmentioning

confidence: 98%

“…Thus, the generalized wake model 5 was simplified by setting x = 0, as most researchers have done, 7,9,20 as shown in eqn (1):…”

Section: Theory and Model Formulation Wake Model Terminal Settling Vmentioning

confidence: 99%

“…6 -8 Efremov and Vakhrushev 9 were the earliest researchers to establish the wake model with x = 0 (ie the liquid wakes are particle free), which is accurate for large and/or dense particles. 5,7 Other researchers primarily considered the establishment of correlation equations for gas and liquid hold-ups. 6,10 -12 External gas injection was commonly used for the study of the fluidization of bioparticles in biological FBRs.…”

Section: Introductionmentioning

confidence: 99%

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Expansion characteristics of an anaerobic fluidized bed reactor with internal biogas production

Wu¹,

Huang

Gou

2005

J of Chemical Tech & Biotech

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More realistic dynamic bed-expansion experiments using a three-phase anaerobic fluidized bed reactor (AFBR) with and without internal biogas production were conducted for the establishment of correlation equations for the mean volume ratio of wakes to bubbles (k). A predictive model was also developed for the expansion characteristics of the three-phase AFBR with internal biogas production. The predicted bed-expansion heights (H GLS ) deviated by only ±10% from the experimental measurements for the three-phase AFBR. According to the modeling results, if a three-phase AFBR is loaded into a carrier with low specific gravity (dry density of carrier, ρ md = 1.37 g cm −3 ; wet density of carrier, ρ mw = 1.57 g cm −3 ) and operated at a high superficial liquid velocity (u l = 4.0 cm s −1 ), the ratio of H GLS to H LS at a high superficial gas velocity (u g = 1.5 cm s −1 ) can reach as high as 271%. A higher fluidized-bed height has a greater effect on the bed-expansion behavior because of the decrease in liquid pressure (surrounding gas bubbles) along the fluidized-bed height. From parametric sensitivity analyses, H GLS is most sensitive to the parameter reactor width (X), especially within a small X/X 0 range of ±10%; sensitive to ρ mw , diameter of the carrier, ρ md and total mass of carrier and least sensitive to u l , biofilm thickness and u g .

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“…Differentiating Equation (4b) with respect to j , and then putting j , = 0 results in , (5) where sUl now represents the velocity of a single gas bubble relative to that of the liquid. Substituting Equation (5) into Equation (3), using Equation (2) with j , = 0 = e,, t); = el and vl = j l / e l , gives after some algebraic manipulation Since the Richardson-Zaki index n always exceeds unity, the denominator of Equation (6) is always positive and hence the sign of the numerator alone determines whether expansion or contraction will occur when gas is introduced to a liquid-fluidized bed.…”

Section: ; = Cmentioning

confidence: 99%