Enzyme mass transfer coefficient in aqueous two-phase systems: Modified spray extraction columns

The fractional dispersed phase hold-up and mass transfer coefficients were measured in modified spray columns of 50 mm i.d. using an aqueous two phase system of polyethylene glycol (PEG 4000)-sodium sulphate-buffer. The mass transfer coefficients were measured for amyloglucosidase and β-galactosidase. Both co-current and countercurrent modes of operation were investigated. The dispersed phase hold-up (?_D) and the dispersed phase and the continuous phase mass transfer coefficients (k_Da, k_Ca) increased with increasing dispersed phase velocity. An increase in the phase concentration of sodium sulphate and PEG was found to reduce ?_D, k_Da, and k_Ca. The performance of the modified spray column is compared with the conventional spray column. The modifications resulted into about a ten-fold enhancement in the throughput and about a five-fold reduction in the value of the height of a transfer unit (HTU ). It has been shown that the value of HTU of the order of 1 m can be obtained. Empirical correlations for ?_D and k_Da, k_Ca have been proposed.     

Maximaler Wärmeübergang in Apparaten mit dispersen Zweiphasensystemen

Maximum heat transfer in apparatus containing dispersed two phase systems . The structure of dispersed systems such as fluidized beds, bubble columns, and liquid/liquid spray columns in process apparatus can be either homogeneous or heterogeneous. When calculating heat transfer coefficients between such systems and vertical heat transfer areas it is necessary to know the structure of the bed. In homogeneous systems (for instance fixed beds) a relationship between the heat transfer and a Reynolds number was found. This Reynolds number embodies the volumetric flux density and a suitable hydraulic diameter. In gas fluidized beds with a heterogeneous structure the heat transfer depends on a Péclet number. The characteristic time of this number can be obtained by deviding the particle diameter by the mean rising velocity of gas bubbles. Maximum heat transfer coefficients for homogeneous and heterogeneous and heterogeneous systems can be described in a general way by plotting a Nusselt number versus the product Ar_p · Pr_c of the Archimedes number and the Prandtl number. Maximum coefficients are calculable without knowledge of the volumetric flux density. For low values of the product Ar_p · Pr_c there is a significant difference between homogeneous and heterogeneous beds.     

Simultaneous heat and mass transfer in spouted beds

The results of a fluid-particle heat and mass transfer study in air spouted beds of silica gel and activated coal particles, using a 9 cm I.D. column with a 30° and 90° conical base, are reported. The effects of gas velocity, particle size, bed depth and cone angle on the heat and mass transfer coefficients are discussed. Equations correlating heat and mass transfer coefficients have been established. The ratio (jn)_s/(j_D)₈ has been found to be dependent on the Reynolds number and the system of spouting.     

Heat Transfer from Immersed Vertical Cylinders in Gas‐Liquid and Gas‐Liquid‐Solid Fluidized Beds

The heat transfer coefficient, h, was measured using a cylindrical heater vertically immersed in liquid‐solid and gas‐liquid‐solid fluidized beds. The gas used was air and the liquids used were water and 0.7 and 1.5 wt‐% carboxymethylcellulose (CMC) aqueous solutions. The fluidized particles were sieved glass beads with 0.25, 0.5, 1.1, 2.6, and 5.2 mm average diameters. We tried to obtain unified dimensionless correlations for the cylinder surface‐to‐liquid heat transfer coefficients in the liquid‐solid and gas‐liquid‐solid fluidized beds. In the first approach, the heat transfer coefficients were successfully correlated in a unified formula in terms of a modified j_H‐factor and the modified liquid Reynolds number considering the effect of spatial expansion for the fluidized bed within an error of 36.1 %. In the second approach, the heat transfer coefficients were also correlated in a unified formula in terms of the dimensionless quantities, Nu/Pr^1/3, and the specific power group including energy dissipation rate per unit mass of liquid, E^1/3D^4/3/ν_l, within a smaller error of 24.7 %. It is also confirmed that a good analogy exists between the surface‐to‐liquid heat transfer and mass transfer on the immersed cylinder in the liquid‐solid and gas‐liquid‐solid fluidization systems.     

Diffusion models in chromatographic columns packed with fully and superficially porous particles

Most theoretical analyzes of molecular diffusion in chromatographic columns are based on more or less approximate models. Macroscopic sample diffusion along packed columns results from a complex combination of the local sample diffusivity in the external porosity of the bed (D_m) and in the porous particles (ΩD_m). A further complication arise from the use of the new superficially porous (or core–shell) particles. The obstruction to axial diffusion caused by the presence of their impermeable core has to be quantified.Two original models of longitudinal diffusion in packed beds are derived for these ternary composite materials. They account for the actual 3D micro-structure of the packed column bed. The micro-structure results from the presence of (1) the impermeable spherical cores; (2) the porous shells surrounding these cores; and (3) the eluent within which the particles are randomly dispersed. The theoretical approach is based on the combination of the effective medium theory of Garnett for core–shell spherical inclusions and of the probabilistic theory of Torquato for randomly dispersed spheres in a continuous matrix. The impacts of the core to the shell diameter, ρ, and of the porous shell to the bulk diffusivity, Ω, on the longitudinal diffusion B coefficient of chromatographic columns packed with core–shell particles are analyzed from a theoretical point of view.     

Effects of Chaotic Temperature Fluctuations on the Heat Transfer Coefficient in Liquid‐Liquid‐Solid Fluidized Beds

The effect of chaotic temperature fluctuations on the immersed heater‐to‐bed heat transfer coefficient (h) are investigated in a liquid‐liquid‐solid fluidized bed (0.152 m ID × 2.5 m in height). The time series of temperature fluctuations are measured and analyzed by means of the multidimensional phase space portraits and Kolmogorov entropy (K), in order to characterize the chaotic behavior of heat transfer coefficient fluctuations in the bed. The overall heat transfer coefficient is inversely proportional to the Kolmogorov entropy of temperature fluctuations, as well as the fluctuation range of heat transfer coefficient (Δh_i). The Kolmogorov entropy and fluctuation range of the heat transfer coefficient (Δh_i) increase with increasing dispersed phase velocity, but decrease with increasing particle size. However, they attain their minima with variation of the continuous phase velocity as well as the bed porosity, at which point the flow regime of particles in the beds changes. The overall heat transfer coefficient is directly correlated with the Kolmogorov entropy, as well as the fluctuation range of heat transfer coefficient.     

The plug flow model for mass transfer in three-phase fluidized beds and bubble columns

The plug flow model (PFM), overwhelmingly used to describe mass transfer in bubble columns and three-phase fluidized beds, has never been critically tested. This study analyzes the PFM single parameter, K_La, to quantify mass transfer in the forementioned systems. Particular attention is paid to the mass transfer features of the zone near the distributor (grid zone) largely ignored until now. This study, carried out under the largest gas and liquid flow rates ever published, for similar types of systems, indicates the presence of two well defined mass transfer zones. These features invalidate, for design purposes, the use of the PFM. However, it still can be used as a qualitative mass transfer indicator. This has permitted a comparison between the mass transfer efficiency of bubble columns and three-phase fluidized beds with the conclusion that three-phase fluidized bed of 0.5 cm particles can compete successfully with bubble columns.     

A unified conjugate mass transfer model of VOC emission

This paper develops a unified conjugate mass transfer model for VOC (Volatile Organic Compound) emission, which implies conjugate boundary condition for mass transfer at the material-air interface. Thus, no special treatment is needed at the material-air interface and numerical methods for conjugate heat transfer problem can be applied directly. The material-air partition coefficient has been taken into account and its effect is the same as specific heat in the energy equation. The equivalent diffusion coefficient in the material K_maD_m instead of D_m characterizes the rate of mass transfer. The ratioK _ma D _m /D _a indicates whether VOC emission is controlled by the internal diffusion or not. The equivalent air-phase initial concentration C₀/K_ma determines the order of maximum concentration in the air. VOC emission contains two stages: the initial stage and the pseudo-steady stage when the emission rate nearly equals mass rate through the outlet of the air. Diffusion coefficient of VOC in the material has a significant effect on VOC emission in the two stages. The effect of partition coefficient on VOC emission depends on the value of K_maD_m/D_a.     

Flüssigphase-Rückvermischung in gepackten Blasensäulen

Liquid phase backmixing in packed bubble columns . Correlations for the axial liquid phase dispersion coefficient in bubble columns packed with metal Raschig rings and Pall rings are given as Pe_g = f (Ga, Re_g, H/D). The dependencies on physical and operational properties are discussed in detail with the aid of diagrams. Pall rings are not able to completely suppress greater turbulences and backmixing in columns of diameters D > 20 cm. A rule of thumb is also given for the apparent dispersion coefficient in this range. Raschig rings, however, are well suited for suppressing backmixing. The problems of adequate fulfilling of the model and undisturbed measurement of the backmixing behaviour are dealt with in detail.     

Quantifying lateral solids mixing in a fluidized bed by modeling the thermal tracing method

Thermal tracing is a simple method for studying solids mixing in fluidized beds. However, the measurement of temperatures is influenced by both mixing and heat transfer, which limits its usefulness for inferring mixing quantitatively. In this work, a semiempirical model is developed to quantify lateral solids mixing in fluidized beds. The model couples the tracer mass balance, the enthalpy balance of tracers and bed particles, and the response dynamic of thermometers. A series of tests is pezrformed in a lab‐scale fluidized bed, with particle sizes of 0.28–0.45, 0.45–0.6, 0.6–0.8, and 0.8–1.0 mm, and fluidizing velocity from 0.3 to 2.3 m/s. By evaluating the measured transient temperatures using the model, the lateral dispersion coefficient (D_sr) is determined to be between 0.0002 and 0.0024 m²/s. Its reliability is confirmed by bed collapse experiments. Finally, the values of D_sr is compared with a collection of data in the literature. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Analogous description of the hydrodynamics of gas-solid fluidized beds and bubble columns

In this paper we stress analogies in the hydrodynamic behaviour of gassolid fluidized beds and bubble columns. Using published experimental data, it is demonstrated that the analogous hydrodynamic-behaviour is not only qualitative but also quantitative in nature. Specifically, we show the following.(1) The gas holdup in the homogeneous regimes of bubble columns and fluidized beds can be modelled in a unified way using V_slip = υ_∞(1 − ϵ_d)ⁿ⁻¹, where V_slip refers to the slip velocity between the dispersed (bubbles or particles) and continuous phases and ϵ_d the dispersed phase holdup. The Richardson-Zaki exponent n decreases with increasing gas density.(2) The transition from homogeneous to heterogeneous flow regimes in gasliquid bubble columns and gassolid fluid beds is delayed by increasing system pressure. Extrapolation of the influence of increased gas density allows us to consider liquidliquid dispersions and liquidsolid fluid beds as limiting cases.(3) In the heterogeneous flow regime of operation the classic two-phase theory of fluidized beds can be applied with profit to also describe the hydrodynamics of gasliquid bubble columns provided that the “dilute” phase is identified with the fast-rising large bubbles and the “dense” phase is identified with the liquid phase containing entrained “small” bubbles. Tentative analogies can also be drawn for the interphase mass transfer processes.(4) The “dense” phase backmixing can be modelled in a unified manner.(5) The two-phase theory can be extended to describe slurry reactors.It is argued that, because of cross-fertilization of concepts and information, appreciation of analogies can be invaluable tool in scaling up.     

Effectiveness factors for heat transfer in fluidized beds

Rates of heat transfer associated with the evaporation of water from the surface of porous particles into air were measured for both packed and fluidized beds. Direct measurements of the temperature on the surface of these particles permitted the calculation of the heat transfer coefficient, h_g, for both packed and fluidized bed systems. An effectiveness factor, χ, has been introduced to account for the non-plug flow characteristics of fluidized beds. This quantity has been used to define the rate of particle to gas heat transfer as follows where (δt)_m represents the log-mean temperature difference across the bed and h_{g b} is the heat transfer coefficient at the initiation of two phase fluidization defined as the “bubble point”. An analysis of the experimental measurements indicates that where g represents the ratio of the heat transfer factor of the fluidized bed to that corresponding at the bubble point of this bed. This effectiveness factor has also been related to the void fraction ratio as follows where ?_t, and ?_p, are the void fractions of the fluidized bed and its corresponding packed bed arrangement. This equation applies for ?_t/?_p > 1.22.     

Mass transfer characteristics of low H/D bubble columns

The mass transfer characteristics of 0.2, 0.6 and 1.0 m diameter bubble columns having a low height to diameter ratio (0.6 < H/D < 4) and operated at low superficial gas velocities (0.01 < V_G < 0.08 m/s) were investigated. Different types of spargers were used to study their effect on the column performance. The values of effective interfacial area, a , and volumetric mass transfer coefficient, k_L a , were measured by using chemical methods. The values of a and k_L a were found to vary from 40 to 420 m²/m³ of clear liquid volume and from 0.01 to 0.16 s^?1, respectively, in the range of V_G, and V_L covered in this investigation. The value of the liquid-side mass transfer coefficient, k_L, was found to vary from 3 × 10^?4 to 7 × 10⁴ m/s. The effect of the physical properties of the system on the values of a was also investigated. The height to diameter ratio and the column diameter did not have significant effect on the values of gas holdup, a and k_L a . It was found that the sparger design is not of critical importance, provided multipoint/multiorifice gas spargers are used. The comparative performance of bubble columns having low H/D with horizontal sparged contactors and tall bubble columns has been considered.     

Electrochemical wall mass transfer in liquid particulate systems

Ionic mass transfer coefficients between the wall of a 2.081 inch tube and liquid fluidized beds of lead glass, soda glass and lucite spheres have been measured using the diffusion-controlled reduction of ferricyanide ion at a nickel cathode for porosities 0.90 to 0.45 and Schmidt numbers 580 to 2100. The developed fluidization mass transfer coefficient for 41 < D_T/d_p < 105 were correlated by i_D E = 0.274 Re_H^?0.38 for 10 < Re_H <1600 and by J_D E = 0.455 Re_H^?0.44 for 16.7 < D_T/d_p < 27 and 50 < Re_H < 3500. Re_H is the hydraulic Reynolds number = d_H up/μ_E and d_H is D_T E/[1 + (3/2) ((1–E)) (D_T/d_p)). The distinct effect of D_T/d_p ratio is attributed to wall effects and the non-particulate behaviour of the fluidized bed for D_T/d_p < 27. Measurements in the open pipe and packed bed agreed very well with literature values. The packed bed gives highest mass transfer coefficients at given Re_H.     

Gas backmixing in the dense region of a circulating fluidized bed

The gas backmixing characteristics in a circulating fluidized bed (0.1 m-IDx5.3-m high) have been determined. The gas backmixing coefficient (D_ba) from the axial dispersion model in a low velocity fluidization region increases with increasing gas velocity. The effect of gas velocity onD _ba in the bubbling bed is more pronounced compared to that in the Circulating Fluidized Bed (CFB). In the dense region of a CFB, the two-phase model is proposed to calculate D_bc from the two-phase model and mass transfer coefficient (k) between the crowd phase and dispersed phase. The gas backmixing coefficient and the mass transfer coefficient between the two phases increase with increasing the ratio of average particle to gas velocities (U_p/U_g).     

Heat transfer between particle beds and submerged surfaces

Theoretical modelling of heat transfer to particle beds comprises two sequential steps: transfer from the heating surface to contacting particles followed by transfer to the interior of the bed. Two different limiting case can be formulated for the second step: unmixed and homogeneously mixed bed. In the case, heat is transferred gradually via a repeated sequence of heat transfer in the gap between adjacent particles and conduction in the particulate material. In the second case, heat is transferred to the interior of the bed by mixing of particles which have previously attained the temperature of the heating surface. On the other hand, the mixing motion maintains a homogeneous lower temperature throughout the bed. Theory predicts a significant and easily measurable difference in the behaviour of heat transfer coefficients for the two regimes at long contact times t: unmixed beds ∝ $$ \sqrt t $$ and homogeneously mixed beds ∝ 1/t. For short times t, both regimes show the same behaviour, namely of t. From a theoretical standpoint, it makes sense to differentiate further between the behaviour patterns of unmixed beds: at long times t, instantaneous heat transfer coefficients are independent of heat transfer form the heating surface to adjacent particles. Comparison with experimental result from literature shows that the derived models, which are consistent, are suitable for describing the heat transfer from submerged surfaces to unmixed and mixed beds of particles.     

Systematic mesh development for 3D CFD simulation of fixed beds: Single sphere study

To develop and validate meshes for computational fluid dynamics (CFD) simulations of transport in fixed beds, a single particle is often used as a test case. We present results for drag coefficient (C_D) and heat transfer Nusselt number (Nu) for flow past a sphere, focusing on high flow rates typical of industrial steam reformers (400 < Re < 20,000). Over this range, good predictions of C_D were obtained using large eddy simulation (LES) to capture vortex shedding and wake dynamics, with a mesh refined downstream from the sphere. The small time-steps and high cell count required make this too expensive for fixed beds. Nu can be accurately calculated using a Reynolds-averaged Navier-Stokes (RANS) method with shear-stress transport (SST) k-ω closure provided the mesh at the particle surface is fine enough and covers most of the boundary layer. Single sphere simulations of heat transfer are more useful for fixed bed mesh development than drag coefficient calculations.     

Fluidization Characteristics in Micro‐Fluidized Beds of Various Inner Diameters

The fluidization characteristics of quartz sand and fluid catalytic crack (FCC) catalyst particles in six micro‐fluidized beds with inner diameters of 4.3, 5.5, 10.5, 15.5, 20.5, and 25.5 mm were investigated. The effects of bed diameter (D_t), static bed height (H_s), particles and gas properties on the pressure drop and minimum fluidization velocity (u_mf) were examined. The results show that the theoretical pressure drops of micro‐fluidized beds deviated from the experimental values under different particles and gas properties. The possible reason is due to an increase in bed voidage under smaller bed diameters. The equations for conventional fluidized beds did not fit for micro‐fluidized beds. u_mf increased with decreasing D_t. When the ratio of H_s to D_t ranged from 1:1 to 3:1, u_mf was characterized by a linear equation with H_s, while the slope of the equation u_mf versus H_s decreased with increasing D_t. In this paper, D_t/d_p and H_s/d_p were defined as dimensionless variables and a new equation was developed to predict u_mf in micro‐fluidized beds under the present experimental conditions.     

Estimation of dispersion coefficients in packed beds

The design and performance of fixed beds are greatly influenced by fluid dispersion. Unfortunately, the existing design data do not provide an accurate picture of this phenomenon. This paper presents an attempt to characterize the dispersive features of packed beds by obtaining reliable estimates of the associated coefficients in the axial (D_L ) and radial (D_R ) directions. Such an objective is achieved by developing a representative two-dimensional pseudo-continuous dispersed flow model which is subsequently employed to compute the desired coefficients using data obtained from a refined experimental approach. The established values have been correlated to allow such coefficients to be reliably predicted under a variety of physical and operating conditions.