Hydrodynamic parameters

According to Satterfield (1975), fhe cafalyst wetting efficiency is defined with the following ratio  

The catalyst wetting efficiency in experimental reactors has been reported to be in the range of 0.12-0.6, while for commercial reactors in the range of 0.7-1.0 (Satterfield, 1975 Bhaskar et al., 2004). 

Modeling of Processes and Reactors for Upgrading of Heavy Petroleum 

The following partial wetting model of Bondi (1971), modified by Satterfield (1975), was used to correlate the apparent rate constant, Kpp.nos, with the superficial liquid mass velocity, G p, and the intrinsic rate constant, k HDs  

The model makes use of correlations reported in the open literature in order to calculate the transport and thermophysical properties (Mederos et al 2009). 

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Reviews of concentration polarization have been reported (14,38,39). Because solute wall concentration may not be experimentally measurable, models relating solute and solvent fluxes to hydrodynamic parameters are needed for system design. The Navier-Stokes diffusion—convection equation has been numerically solved to calculate wall concentration, and thus the water flux and permeate quaUty (40). 

Table 1.31 Hydrodynamic parameters relevant to erosion corrosion...

Table 2.1 Corrosion rates from hydrodynamic parameters for pipes and annuli...

The scheme of commercial methane synthesis includes a multistage reaction system and recycle of product gas. Adiabatic reactors connected with waste heat boilers are used to remove the heat in the form of high pressure steam. In designing the pilot plants, major emphasis was placed on the design of the catalytic reactor system. Thermodynamic parameters (composition of feed gas, temperature, temperature rise, pressure, etc.) as well as hydrodynamic parameters (bed depth, linear velocity, catalyst pellet size, etc.) are identical to those in a commercial methana-tion plant. This permits direct upscaling of test results to commercial size reactors because radial gradients are not present in an adiabatic shift reactor. 

Table 4. Gelatin B hydrodynamic parameters, measurement to different temperatures.

For heterogeneous media composed of solvent and fibers, it was proposed to treat the fiber array as an effective medium, where the hydrodynamic drag is characterized by only one parameter, i.e., Darcy s permeability. This hydrodynamic parameter can be experimentally determined or estimated based upon the structural details of the network [297]. Using Brinkman s equation [49] to compute the drag on a sphere, and combining it with Einstein s equation relating the diffusion and friction coefficients, the following expression was obtained ... 

The flow domain of TCP can be described by two dimensionless hydrodynamic parameters, corresponding to the rotational speed of the inner cylinder and the imposed axial flow rate the Taylor number, To, and the axial Reynolds number, Re, respectively ... 

The application of Eqs. (17) requires a detailed knowledge of the two-phase hydrodynamics so that the parameters Ru Wc, U,a, U a, Vd, a, and Qt can be evaluated. The fluid dynamics of annular flows have been investigated experimentally. Russell and Lamb (R4) have studied the flow mechanism of horizontal annular flow Cousins et at. (C8) have dealt with droplet movement in vertical annular flow. Anderson and Russell (A6) have analyzed the interchange of droplets in horizontal systems, and numerous other hydrodynamic studies have been reported in Hewitt et al. (HI). Cichy et al. (C4) have reviewed the methods for evaluating the same hydrodynamic parameters that are also used in mass transfer studies. It is difficult to... 

From the continuity and momentum equations for the fluid and solid phases along with the boundary conditions, the following groups of independent dimensionless parameters are found to control the hydrodynamics, noting our assumption that the particle-particle forces are only dependent on hydrodynamic parameters,... 

Ishii and Murakami (1991) evaluated the CFB scaling relationships of Horio et al. (1989) using two cold CFB models. Solids flux, pressure drop, and optical probe measurements were used to measure a large number of hydrodynamic parameters to serve as the basis for the comparison. Fair to good similarity was obtained between the beds. Dependent hydrodynamic parameters such as the pressure drop and pressure fluctuation characteristics, cluster length and voidage, and the core diameter were compared between the two beds. The gas-to-solid density ratio was not varied between the beds. As seen in Table 7, the dimensionless solids flux decreased as the superficial velocity was increased because the solids flux was held constant. 

Injection mode (e.g., electrokinetic, hydrodynamic), parameters (e.g., voltage, pressure, time)... 

Finally, it has to be emphasized that both the hydrodynamic parameters and the concentrations of the species involved in the extraction reaction simultaneously determine whether the extraction regime is of kinetic, diffusional, or mixed diffusional-kinetic type. It, therefore, is not surprising that different investigators, who studied the same chemical solvent extraction system in different hydrodynamic and concentration conditions, may have interpreted their results in terms of completely different extraction regimes. 

Dobetti and Pantaleo (38) investigated the influence of hydrodynamic parameters per se on the efficiency of a coacervation process for microcapsule formation. They based their work on that of Armenante and Kirwan (39) who described the size of the smallest eddies or vortices generated in a turbulent regime on a microscopic scale in the vicinity of the agitation source, i.e., microeddies, as... 

The second section presents a review of studies concerning counter-currently and co-currently down-flow conditions in fixed bed gas-liquid-solid reactors operating at elevated pressures. The various consequences induced by the presence of elevated pressures are detailed for Trickle Bed Reactors (TBR). Hydrodynamic parameters including flow regimes, two-phase pressure drop and liquid hold-up are examined. The scarce mass transfer data such gas-liquid interfacial area, liquid-side and gas-side mass transfer coefficients are reported. 

Mean Statistical parameter (%) relative error Hydrodynamic parameter AP/Z fit Deviation AP/Z fit Mean relative error AP/Z Bt Deviation AP/Z fi, ... 

For the TBR design the dynamic liquid hold-up is a basic parameter because it is related to other important hydrodynamic parameters (including the pressure drop, wetting, and mean-residence-time of liquid). 

A.E. Saez and R.G. Carbonnel, Hydrodynamic parameters for gas-liquid cocurrent flow in packed beds, AIChE Journal, 31 (1985) 52-62. 

The physical properties of the carrier liquid, especially density and viscosity, can essentially influence both main hydrodynamic parameters of the mixture flow, i.e. critical velocity VCr and the hydraulic gradient/. 

As an example, the dependence of hydrodynamic parameters of critical regime for the sand-water mixture and sand-glycol (80 % glycol solution in water) mixture is illustrated in Figure 1. The volumetric concentration C of the mixtures varied from 5 to 30 %, a mean diameter of sand was d = 0.25 mm and a pipe diameter was D = 50.4 mm. The values of the critical velocity VCr and critical pressure gradient ICr differ substantially according to the used carrier liquid. 

Small bubbles and flow uniformity are important for gas-liquid and gas-liquid-solid multiphase reactors. A reactor internal was designed and installed in an external-loop airlift reactor (EL-ALR) to enhance bubble breakup and flow redistribution and improve reactor performance. Hydrodynamic parameters, including local gas holdup, bubble rise velocity, bubble Sauter diameter and liquid velocity were measured. A radial maldistribution index was introduced to describe radial non-uniformity in the hydrodynamic parameters. The influence of the internal on this index was studied. Experimental results show that The effect of the internal is to make the radial profiles of the gas holdup, bubble rise velocity and liquid velocity radially uniform. The bubble Sauter diameter decreases and the bubble size distribution is narrower. With increasing distance away from the internal, the radial profiles change back to be similar to those before contact with it. The internal improves the flow behavior up to a distance of 1.4 m. 

L. Mi and S.T. Hwang, Correlation of Concentration Polarization and Hydrodynamic Parameters in Hollow Fiber Modules, J. Membr. Sci. 159, 143 (1999). 

We use SEDNTERP for estimating the values of several hydrodynamic parameters and, therefore, have the software downloaded and installed in the same computer used for analysis. Use SEDNTERP to estimate the density (p) and viscosity (rf) of your experimental solution (buffer and ions) using the list of standard reagents and buffer components. Wherever needed, use 0.53 cm3/g as the partial specific volume (r) and 0.59 as the hydration of an RNA molecule. 

The hydrodynamic parameters that are required for stirred tank design and analysis include phase holdups (gas, liquid, and solid) volumetric gas-liquid mass-transfer coefficient liquid-solid mass-transfer coefficient liquid, gas, and solid mixing and heat-transfer coefficients. The hydrodynamics are driven primarily by the stirrer power input and the stirrer geometry/type, and not by the gas flow. Hence, additional parameters include the power input of the stirrer and the pumping flow rate of the stirrer. 

Hydrodynamic parameters that are required for bubble column design and analysis include phase holdups (gas, liquid, and solid for... 

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