Removal mass transfer calculations

A good biofilter will achieve a high efficiency of pollutant removal by providing the best conditions for the microorganisms it contains. Understanding the microbial needs, the fluid physics, mass transfer calculations, degradation pathways and ways of microbial immobilization will help to utilize the enormous power of the microorganisms in the control of fluid pollution. 

The mass transfer coefficient is calculated for a given diffusivity coefficient and reaction rate constant at the equilibrium concentration of oxygen. When oxygen is continuously transported and removed from the liquid phase we may write ... 

Equation (20-80) requires a mass transfer coefficient k to calculate Cu, and a relation between protein concentration and osmotic pressure. Pure water flux obtained from a plot of flux versus pressure is used to calculate membrane resistance (t ically small). The LMH/psi slope is referred to as the NWP (normal water permeability). The membrane plus fouling resistances are determined after removing the reversible polarization layer through a buffer flush. To illustrate the components of the osmotic flux model. Fig. 20-63 shows flux versus TMP curves corresponding to just the membrane in buffer (Rfouimg = 0, = 0),... 

Assuming plug flow of both phases in the trickle bed, a volumetric mass transfer coefficient, kL a, was calculated from the measurements. The same plug flow model was then used to estimate bed depth necessary for 95% S02 removal from the simulated stack gas. Conversion to sulfuric acid was handled in the same way, by calculating an apparent first-order rate constant and then estimating conversion to acid at the bed depth needed for 95% S02 removal. Pressure drop was predicted for this bed depth by multiplying... 

Equations 14.17 and 14.18 are very simple, but the accuracy of the predictions depends greatly on the realistic estimation of Ca, which varies with time during the operation of the SVE system. For the start of the SVE project and considering that the free organic phase, NAPL, is present in the subsurface, a hrst approximation is to calculate Ca from the vapor pressure data of the contaminants (equation 2 in Table 14.3 or Equation 14.1). The actual concentration, however, will be lower than this value for two main reasons (1) the extracted airstream does not pass only through the contaminated zone and (2) limitations on mass transfer exist. An effectiveness factor q should be considered to take into account the effect of these phenomena on removal rates. The value of this factor can be determined by comparing the calculated concentration with data obtained from the preliminary pilot tests at the site ... 

Step 4 Estimate the effectiveness factor i) for the removal and the cleanup time required to obtain a residual toluene concentration of 150 mg/L. The phase distribution calculations carried out in Step 2 indicate that the equilibrium concentration of toluene in the gas phase is Ca equil = 109 mg/L (see Table 14.4). The concentration measured in the extracted air during the field tests is lower, at Q,flew = 78 mg/L, indicating that the removal effectiveness is limited either as a result of mass transfer phenomena or the existence of uncontaminated zones in the airflow pattern. The corresponding effectiveness factor is T = 78/109 = 0.716. 

Once the initial equilibrium state of the system is known, the model can trace a reaction path. The reaction path is the course followed by the equilibrium system as it responds to changes in composition and temperature (Fig. 2.1). The measure of reaction progress is the variable , which varies from zero to one from the beginning to end of the path. The simplest way to specify mass transfer in a reaction model (Chapter 13) is to set the mass of a reactant to be added or removed over the course of the path. In other words, the reaction rate is expressed in reactant mass per unit . To model the dissolution of feldspar into a stream water, for example, the modeler would specify a mass of feldspar sufficient to saturate the water. At the point of saturation, the water is in equilibrium with the feldspar and no further reaction will occur. The results of the calculation are the fluid chemistry and masses of precipitated minerals at each point from zero to one, as indexed by . 

In a number of refining reactions where bubbles are formed by passing an inert gas through a liquid metal, the removal of impurities from the metal is accomplished by transfer across a boundary layer in the metal to the rising gas bubbles. The mass transfer coefficient can be calculated in this case by the use of the Calderbank equation (1968)... 

With that caveat the design proceeds in essentially the same manner as was outlined for water removal by 4A. We always do the dehydration design first, calculating the bed consumption for handling the water, allowing for a mass transfer zone and then factoring up the bed requirements in view of cyclic stability. 

Nearly all the examples contained are based on real experimental data found in the literature with environmental interest. Most of the examples consider all aspects of operation design—kinetics, hydraulics, and mass transfer. All parameters in the examples are calculated using correlations, figures, and tables provided in the book—thus no parameters just appeal1 in the text. Moreover, some text in the examples is also devoted to provide information about the pollutants removed or heated. 

The example is concerned with a batch chlorination process. At the beginning, the fresh toluene charged to the reactor will contain no dissolved chlorine. After bubbling of the chlorine has commenced, a period of time will need to elapse before the concentration of the dissolved chlorine rises to a level that just matches the rate at which it is being removed from the solution by reaction. To avoid such a complication in this example, calculations are carried out for the stage when, after chlorine bubbling has continued at a steady rate, the fractional conversion of the toluene has reached a value of 0.10. It is then assumed that, at any instant in time, the rate of mass transfer of chlorine from the gas phase is just equal to the rate at which it reacts in the bulk of the liquid, i.e. the rate is given by equation 4.17. 

If the DMS inventory in Salt Pond is at steady state in summer (5), production should approximately balance removal. Tidal removal of DMS to Vineyard Sound is minimal. Outflow from Salt Pond is thought to be primarily surface water, and using a maximum tidal range of 0-0.2 m/d and a mean surface water concentration of 10 nmol/L, we calculate an export rate of less than 2 /imol/m2/d. The water-air flux of DMS may be calculated using the two film model of liss and Slater (22 flux = -ki C, ). With the same surface water DMS concentration (C ) and an estimated mass transfer coefficient (ki) for DMS of 1.5 cm/h, the projected flux of DMS from the pond into the atmosphere would be 4 /unol/m2/d. This compares with the range of estimated emissions from the ocean of 5-12 /imol/m2/d (1). 

The removal of the acid components H2S and CO2 from gases by means of alkanolamine solutions is a well-established process. The description of the H2S and CO2 mass transfer fluxes in this process, however, is very complicated due to reversible and, moreover, interactive liquid-phase reactions hence the relevant penetration model based equations cannot be solved analytically [6], Recently we, therefore, developed a numerical technique in order to calculate H2S and CO2 mass transfer rates from the model equations [6]. 

The calculated vapor pressure of vanadic acid is a factor of 30 lower than the equilibrium vapor pressure of vanadic acid over pure V2O5. At this vapor pressure of vanadic acid, the transfer of V to trap is rapid while the removal of V by transpiration is negligible. Approximately 64% would be transferred from catalyst to trap, and about 0.05% removed by transpiration. This is rationalized by noting that the velocity of the vanadic acid vapor (calculated from the kinetic theory of gasesX 4.4 x 10" cm s, is four orders of magnitude higher than the superficial velocity of the fluidizing gas. Equation 3a From these calculations it is clear that mass transfer of vapor phase vanadic acid in a fluid bed is sufficient to account for the transport of vanadium from catalyst to trap. 

Pilot plant smdied have also been performed by Larsen et al. [37], who obtained stable operation and more than 95% SO2 removal from flue gas streams with a gas-side pressure drop of less than 1000 Pa. The importance of the membrane structure on the SO2 removal has been studied by Iversen et al. [6], who calculated the influence of the membrane resistance on the estimated membrane area required for 95% SO2 removal from a coal-fired power plant. Authors performed experiments on different hydrophobic membranes with sodium sulfite as absorbent to measure the SO2 flux and the overall mass-transfer coefficient. The gas mixture contained 1000 ppm of SO2 in N2. For the same thickness, porosity, and pore size, membranes with a structure similar to random spheres (typical of stretched membranes) showed a better performance than those with a closely packed spheres stmcture. 

These very simple calculations give only first indications. A more sophisticated approach would need to take into account the fact that lignin gives rise to higher fractions of char than cellulose. Also, the existence of mass transfer resistances must not be ignored if the primary products are not efficiently removed from the reacting zone, they have more chances to take part in subsequent reactions, with formation of char. 

Figure 2z SO2 removal as a function of the ratio Ca S for CEB ( ) and Ca(OH)2 ( ). Operating conditions ,jf,p=2.75 Nm /hr, C>iir,i=14 Nm /hr, and ir,CEB=2 Nm /hr. The lines presented are theoretical lines calculated for mass transfer controlled conditions for effective particle diameters of 2.5 and 3 pm respectively, whereas the dashed line represents the theoretical limit.

It is the overall mass transfer coefficient, however, that ultimately controls the rate of removal of a substance by air stripping. For example, dichloroethane, which has a lower Henry s constant than trichloroethylene, has been found easier to remove by air stripping, owing to its higher mass transfer coefficient (10). The mass transfer coefficient for a specific substance in a specific air-stripping system may be calculated by (9) ... 

The mass-transfer coefficient is sensitive to several factors, including Henry s constant of the contaminant, the packing factor, and the temperature of the ambient air and water to be treated. An HTU value, calculated at 20°C from Eq. (7), would require a fivefold increase if ambient water and air temperatures of 5°C and -12°C, respectively, were encountered (9). Therefore, the equations presented are recommended for initial design work and evaluation of pilot studies or field data. Data from pilot studies are required to provide dependable values for the mass-transfer coefficient and the effects on removal efficiencies produced by varying system parameters. An analytical program... 

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