Intraparticle Pressure Gradients

Volume changes due to the reaction may become considerable. This may lead to intraparticle pressure gradients, which will influence the effectiveness factor because ... 

Using the dusty gas model [5] analytical solutions are derived to describe the internal pressure gradients and the dependence of the effective diffusion coefficient on the gas composition. Use of the binary flow model (BFM, Chapter 3) would also have yielded almost similar results to those discussed below. After discussion of the dusty gas model, results are then implemented in the Aris numbers. Finally, negligibility criteria are derived, this time for intraparticle pressure gradients. Calculations are given in appendices here we focus on the results. 

Therefore, in this case as well, the number a equals zero and again the intraparticle pressure gradient vanishes. So, no pressure will build up inside the pellet either if there is no volume change due to reaction or if the catalyst pores are very broad. 

Now that we have derived the intraparticle pressure gradients, we can also determine the effective diffusion coefficient as a function of the gas composition. 

Many complex situations have not been addressed, such as simultaneous intraparticle temperature and pressure gradients and nondiluted gases with anisotropic catalyst pellets. Calculations for these and other complex situations proceed along the same line as demonstrated for bimolecular reactions and nondiluted gases. A framework that can be used to investigate the effect of complex situations on the effectiveness factor is given. Also presented are criteria that can be used for a quick estimate as to whether or not certain phenomena are important. 

Intraparticle Pressure Gradients for Nondiluted Gases and Simple Reactions... 

To evaluate the impact of intraparticle convection it is necessary to impose a pressure gradient across the network. Such pressure gradients arise naturally in fixed-bed operation, though the pressure difference across a particle is usually only about I cm H O. By solving the Hagen-Poisenille equation across every pore in the network, the overall flow through the particle (network) is known. 

At low velocities /(A) <= 1 and both equations lead to similar results. However, at high superficial velocities, /(A) <= 3/A and so the last term in Rodrigues equation becomes a constant since the intraparticle convective velocity Vq is proportional to the superficial velocity u. The HETP reaches a plateau that does not depend on the value of the solute diffusivity but only on the particle permeability and pressure gradient (convection-controlled limit). 

The catalyst was presulphured for 10 hours at 350°C and atmospheric pressure in a flowing stream of hydrogen containing 10 (v/v) % of H2S. In order to avoid intraparticle gradients, the catalyst has been crushed at a range of particle size between 53 and 530 pm. To avoid... 

The only instances in which external mass transfer processes can influence observed conversion rates are those in which the intrinsic rate of the chemical reaction is so rapid that an appreciable concentration gradient is established between the external surface of the catalyst and the bulk fluid. The rate at which mass transfer to the external catalyst surface takes place is greater than the rate of molecular diffusion for a given concentration or partial pressure driving force because turbulent mixing or eddy diffusion processes will supplement ordinary molecular diffusion. Consequently, for porous catalysts one does not encounter external mass transfer limitations except in those circumstances in which intraparticle diffusional limitations are also present. 

Fixed- and Ebulliating-Bed Processes Intraparticle Diffusion Limitations in FT Catalysts. In a fixed-bed mode of operation, pressure drop considerations will dictate a minimum particle size, which in general is of the order of one or a few millimetres. Heat removal and minimization of temperature gradients in the bed rely on the effective heat conductivity in the bed, which is favoured by high fluid velocities and large particles. In an ebulliating bed, too, catalyst particles should not be too small lest they be entrained by the fluid as in a slurry reactor. 

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