(70bw) A Model to Predict Radial Solids Concentration and Liquid Velocity Distributions in Liquid-Solid Circulating Fluidized Beds

Liquid-Solid Circulating Fluidized Bed (LSCFB) offers potential applications in catalytic and non-catalytic liquid-solid reactions, bio-chemical processes, protein purification processes and in the treatment of radioactive liquid waste.  They offer improved contact between the phases for enhanced heat and mass transfer rates, high liquid-solids volume ratio and control of solids circulation rate and solids holdup through a choice of solids and liquid flow rates.

The present study is addressed to the study of axial and radial particle concentration profiles, and radial liquid profiles in liquid solid circulating fluidized beds.  The liquid-solid fluidized bed is treated as homogeneous in conventional fluidization. However it has been reported in the earlier studies that the radial non-uniformities exist in solids holdup and liquid velocity. The non-uniformities cause non-uniform residence time distributions for the phases giving non-uniform product quality. Information on radial flow structure is thus crucial to reactor design and process optimization.

            The earlier work relating to the study of the axial and radial particle concentration distributions in LSCFB was due to Zheng et. al.(2002) and Liang et. al. (1996) the axial particle distribution in the riser was reported uniform while the radial particle concentration was reported higher at the wall and decreasing gradually to be minimum at the center of the riser.  The liquid velocity and particle velocity were reported higher at the center of the riser and lower near the wall.

It is attempted in the present study to provide a quantitative description of radial fluid velocity and solids concentration distributions based on the experimental conditions.  It is assumed that the radial particle concentration distribution follows power law relationship and the radial liquid velocity distribution follows an exponential relationship.  Thus

                                                  --- (1)

                                                    --- (2)

The distribution parameter defined as (Zuber & Findlay 1965)

--- (3)

is given by

             --- (4)

The distribution parameter, C_o represents an empirical factor correcting the one-dimensional homogeneous theory to account for the fact that the particle volume fraction and the liquid velocity distribution across the riser cross-section can vary independently of one another. The exponents m and n are evaluated using the data reported in literature and are satisfactorily related in the present study to the superficial liquid and solids flow rates in the riser of LSCFB.  From the analysis of about 250 data points the radial particle concentration distribution is related to the solids holdup as

                         --- (5)

where   d =   1.6 for 0 <
< 0.08,    and        d = 2 for
>0.08

Fig 1 is a typical comparison of experimental radial solids distribution and liquid velocity distribution with the distributions predicted using equations (5) and (1) respectively.

Experimental work in the present study covers a wide range in the flow rates of the phases as well as solids size and density (Table 1).  The riser of the LSCFB is of 94 mm i.d. and 2400 mm high, and is provided with a dual liquid feed at the base an auxiliary feed to facilitate solids into the riser and a primary feed to control the solids circulation rate.  Solids are separated from the liquid at the top of the riser and are recirculated to its base.  The distribution parameter, C_o is evaluated from the experimental data by plotting the weighted mean particle velocity, [<U_s>/<
>] against the average volumetric flux density [<j >].  C_o thus obtained is satisfactorily compared with C_o predicted using Equation (4) (Table 1).

Table1: comparison of experimental and predicted C_o for the different experimental conditions of the present study.

Fig 1 Typical comparison of experimental radial solids holdup (Experimental data: fig 3 of Zheng et. al. 2002) and liquid velocity (Experimental data:Fig 3 of Liang et. al. 1997) with the prediction using equations 5 and 1.

Acknowledgement

Guidance received from Prof.Y.B.G. Varma, Professor of Chemical Engineering (Retd.), Indian Institute of Technology, Madras,
India is gratefully acknowledged.

Notation:

A         riser cross-section, (m²)

C_o        distribution parameter, (-)

j           average volume flux density of the phases, (m/s)

r           radial position, (m)

R         riser radius, (m)

m, n    exponents in equations 1 & 2

U_a        auxiliary liquid velocity, (m/s)

U_f           primary liquid velocity, (m/s)

U_s        solids circulation rate, (m/s)

ε          bed voidage

          cross-sectional average solids holdup

ε_sc          solids concentration at the center of the riser

ε_sw          solids concentration near the wall of the riser

d          exponent to ε_s in equation 5

<>        cross-sectional average quantity

References:

1.       Liang, W.G.,  Jing-Xu Zhu, Yong Jin, Zhiqing Yu, Z-W Wang and J.Zhou (1996), ?Radial Non-uniformity of flow structure in a liquid solid circulating fluidized bed?, Chemical Engineering Science, 50, p.2001-2010.

2.       Liang, W.G,  and Jing-Xu Zhu (1997), ?A core-annulus model for the radial flow structure in a liquid solid circulating fluidized bed (LSCFB)?, Chemical Engineering Journal, 68, p.51-62

3.       Zheng, Y., Zhu, J-X.
Marwaha, N.S., Bassi, A.S., (2002) ?Radial Solids flow structure in a liquid-solids circulating fluidized bed?, Chemical Engineering journal, 88, 141-150.

4.       Zuber, N and
Findlay, J.A. (1965), ?Average volumetric concentration in two phase flow system?, Trans. of ASME, Jl. of Heat Transfer, 87. 453-468.