Effect of Mass-Transfer Resistance

When the resistance to mass transfer to the external surface of the pellet is significant compared with that within the particle, part of the concentration driving force is required to overcome this external resistance, and the concentration of reacting material at the surface of the pellet Cm is less than that in the bulk of the fluid phase Cao- In Sections 10.7.1-10.7.3, the effect of mass transfer resistance within a porous particle... 

A hydrocarbon is cracked using a silica-alumina catalyst in the form of spherical pellets of mean diameter 2.0 mm. When the reactant concentration is 0.011 kmol/m3, the reaction rate is 8.2 x 10"2 kmol/(m3 catalyst) s. If the reaction is of first-order and the effective diffusivity De is 7.5 x 10 s m2/s, calculate the value of the effectiveness factor r). It may be assumed that the effect of mass transfer resistance in the. fluid external Lo the particles may be neglected. 

The mass transfer coefficient describes the effect of mass transfer resistance of the reactants flowing from the gas phase to the surface of the individual particles in the bed. The mass transfer coefficient can be obtained from a correlation for the Sherwood number (or dimensionless mass transfer coefficient) given by Eq. (7) ... 

It is obvious that to have high conversion, the reaction should be fast enough and the term Zf /wbub should be high. Hence, uhuh should be small or, in other words, t/bub should be small. The effect of mass transfer resistance is shown in Figures 5.20 and 5.21 for the cases of a fast (kvs = 1 s-1) and a slow reaction (kvs = 0.01 s-1), respectively. 

Figure 5.20 The effect of mass transfer resistance for a slow reaction ( vs = 0.01 s r).

The orthogonal collocation polynomial approximation using a single parameter trial function was employed to solve equations (l)-(3), In addition to the solution for time concentration and activity profiles, effectiveness factors representing the combined effect of mass transfer resistance and poisoning in terms of pellet surface conditions were computed according to... 

X. EFFECT OF MASS TRANSFER RESISTANCES IN PREPARATIVE HPLC OF POLYPEPTIDES AND PROTEINS... 

X. Effect of Mass Transfer Resistances in Preparative HPLC of Polypeptides and Proteins 178... 

Related Calculations. In this example, it was stated at the outset that mass-transfer effects were not limiting the process rate. In the general case, however, it is important to calculate the effect of mass-transfer resistance on the reaction rate. 

Bubble column reactors are quite commonly employed in the petrochemical industries for many oxidation and hydrogenation reactions (1 ). This type of reactor is ideal for reactions occurring in the slow reaction regime in which relatively low energy input is required to minimize the effect of mass transfer resistance. Nevertheless, attention has been drawn to the... 

Estimating the effect of mass transfer resistance was done based on the coimection between k and k ... 

Ariga et al. [48] have investigated the behavior of the monolith reactor in which Echerichia coli with P-galactosidase or Saccharomyces cerevisiae was immobilized within a thin film of K-carragcenan gel deposited on the channel wall. The effects of mass transfer resistance and axial dispersion on the conversion were studied. Those authors found that the monolith reactor behaved like the plug-flow reactor. The residence-time distribution in this reactor was comparable to four ideally mixed tanks in series. The influence of gas evolution on liquid film resistance in the monolith reactor was also investigated. It was shown that at low superficial gas velocities, the gas bubble may adhere to the wall, which decreases the effective surface area available for the reaction. The authors concluded that the reactor was very effective in the reaction systems accompanied by gas evolution, such as fermentations. 

If the effect of mass transfer resistance in the HETP equation is very dominant, then Eq. 7.42 can be simplified to... 

A more comprehensive analysis of constant pattern behavior for a binary system has been given by Rhee and Amundson [3]. In this work, these authors have extended to binary systems the analysis of the combined effects of mass transfer resistance and axial dispersion that they had previously made in the case of single-component bands [4]. Rhee and Amundson [3] assumed the solid film linear driving force model, finite axial dispersion, and no particular isotherm model. The system of equations becomes... 

AUgeier S.C., Summers R.S. (1995b), Effect of mass transfer resistance and system recovery on membrane permeation, Proc. AWWA Membrane I echnology Conf., Reno, Nevada, Aug 95, 39-66. 

In an agitated reactor, the effect of mass transfer resistance can be reduced to a minimum by adjusting the stirring speed. The mass transfer coefficient is also a function of the size of suspended particles. From the point of view of reactor design, to maintain the uniformity of the desired product from batch to batch the particle size distribution of the solid reactant should be in a rather narrow range to render the mass transfer resistance unimportant. 

In the analysis of breakthrough curves or chromatographic response peaks, a single response curve can provide reliable information only on the combined effects of mass transfer resistance and axial dispersion. 

If the effects of mass transfer resistance and axial dispersion were linearly additive, as they are for a linear system, then the breakthrough curve plotted in terms of the modified time parameter t would be independent of 6. That this is approximately, though not exactly, true may be seen from Figure 8.22i. However, the deviation from the linear addition rule becomes important only when S is large and the isotherm is highly nonlinear (/3 < 0.5). Even for a highly nonlinear isotherm (= 0.33) the linear addition principle evidently provides a useful approximation except in the extreme case of low mass transfer resistance and large axial dispersion (5 > 5). 

The effect of mass transfer resistance is to broaden the mass transfer zone relative to the profile deduced from equilibrium theory. Where equilibrium theory predicts a shock transition the actual profile will approach constant-pattern form. Since the location of the mass transfer zone and the concentration change over which the transition occurs are not affected by mass transfer resistance, the extension of equilibrium theory is in this case straightforward and requires only the integration of the rate expression, subject to the constant-pattern approximation, to determine the form of the concentration profile. This is in essence the approach of Cooney and Strusi who show that for a Langmuir system with two adsorbable components a simple analytic expression for the concentration profile may be obtained when both mass transfer zones are of constant-pattern form. 

This chapter is divided into two parts In the first, we take up the topic of equilibrium stages in their various configurations and apply them to a number of different mass transfer operations. The second part, which is less extensive, considers the effect of mass transfer resistance expressed through an appropriate stage efficiency. 

Such porous structure can be understood by considering the effect of mass transfer resistances to steam/ /carbon reaction, the different volume increases of each pore type which depends on the actual reactivity of the carbon, and the reaction position within the particle. 

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