Model packed bed

Most biochemical reactors operate with dilute reactants so that they are nearly isothermal. This means that the packed-bed model of Section 9.1 is equivalent to piston flow. The axial dispersion model of Section 9.3 can be applied, but the correction to piston flow is usually small and requires a numerical solution if Michaehs-Menten kinetics are assumed. 

Illustration 12.7 indicates how to estimate an effective thermal conductivity for use with two-dimensional, pseudo homogeneous packed bed models. 

Effective thermal conductivities and heat transfer coefficients are given by De Wasch and Froment (1971) for the solid and gas phases in a heterogeneous packed bed model. Representative values for Peclet numbers in a packed bed reactor are given by Carberry (1976) and Mears (1976). Values for Peclet numbers from 0.5 to 200 were used throughout the simulations. 

VIII. Evaluation of Common Physical Simplifications in Packed Bed Modeling... 

Ozawa, Y. (1970) Application of the Legendre transformation to one-dimensional packed bed model. Chem. Engng. Sci. 25, 529-533. 

We want to compare the solution for this continuous packed bed model with our earlier computations of the values of Xj and Yj. For this purpose we first determine the value of Ka = Kg am via quadnonequicol. m. A call of quadnonequicol (6,68,0.72,0.01,720, 7000,0.001,1.4) indicates that we have about 5% removal for our original system data with 6 trays, Ka = 68, and L = 720 ... 

Grootenhuis (Proc. Inst. Mech. Eng. [London], A168, 837—846 [1954]) presents data which indicate that for a series of screens, the total pressure drop equals the number of screens times the pressure drop for one screen, and is not affected by the spacing between screens or their orientation with respect to one another, and presents a correlation for frictional losses across plain square-mesh screens and sintered gauzes. Armour and Cannon (AIChE J., 14,415-420 [1968]) give a correlation based on a packed bed model for plain, twill, and dutch weaves. For losses through monofilament fabrics see Pedersen (Filtr. Sep., 11, 586-589 [1975]). For screens Inclined at an angle 0, use the normal velocity component V ... 

The last ten years have witnessed a number of extensive field tests of underground coal gasification (UCG) in the United States and Europe. Model development is essential to the proper understanding of these test results and to the planning of future experiments. This report will focus upon the steady-state "permeation" or "packed bed" model of in situ gasification (forward combustion mode). In this useful but idealistic model the coal bed is assumed to be uniformly permeable to reactant and product gases. 

An orthogonal collocation method for elliptic partial differential equations is presented and used to solve the equations resulting from a two-phase two-dimensional description of a packed bed. Comparisons are made between the computational results and experimental results obtained from earlier work. Some qualitative discrimination between rival correlations for the two-phase model parameters is possible on the basis of these comparisons. The validity of the numerical method is shown by applying it to a one-phase packed-bed model for which an analytical solution is available problems arising from a discontinuity in the wall boundary condition and from the semi-infinite domain of the differential operator are discussed. 

The use of two-phase homogeneous continuum models in packed bed modelling has often been avoided due to the computational difficulties. Recently, Paspek and Varma (15) have found a two-phase model to be necessary to describe an adiabatic fixed-bed reactor, while Dixon and Cresswell (16) have shown that the effective parameters of the one-phase model may be interpreted in terms of the more fundamental parameters of a two-phase model, thus demonstrating more clearly their qualitative dependencies on the operating and design characteristics of the bed. When two phases and several species are involved, the computational advantages of the cubic Hermite method may be anticipated to be high. 

The packed-bed models in Section 9.1 assume a flat velocity profile and are an exception. For them, the smallest value for Az occurs at the centerline. 

However, if the system is in the dependent range, some modeling of the extent of dependence is necessary to get the properties of the packed bed. Models for particles in the Rayleigh... 

Table C.IO. What conditions will maximize the selectivity for drying oil Sketch concentration profiles for the case when this reaction is run in a packed bed modeled as a PFR. 

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