Plug-flow estimations

Example 8 Calculation of Rate-Based Distillation The separation of 655 lb mol/h of a bubble-point mixture of 16 mol % toluene, 9.5 mol % methanol, 53.3 mol % styrene, and 21.2 mol % ethylbenzene is to be earned out in a 9.84-ft diameter sieve-tray column having 40 sieve trays with 2-inch high weirs and on 24-inch tray spacing. The column is equipped with a total condenser and a partial reboiler. The feed wiU enter the column on the 21st tray from the top, where the column pressure will be 93 kPa, The bottom-tray pressure is 101 kPa and the top-tray pressure is 86 kPa. The distillate rate wiU be set at 167 lb mol/h in an attempt to obtain a sharp separation between toluene-methanol, which will tend to accumulate in the distillate, and styrene and ethylbenzene. A reflux ratio of 4.8 wiU be used. Plug flow of vapor and complete mixing of liquid wiU be assumed on each tray. K values will be computed from the UNIFAC activity-coefficient method and the Chan-Fair correlation will be used to estimate mass-transfer coefficients. Predict, with a rate-based model, the separation that will be achieved and back-calciilate from the computed tray compositions, the component vapor-phase Miirphree-tray efficiencies. 

Foam Drainage and Overflow The rate of foam overflow on a gas-free basis (i.e., the total volumetric foamate rate Q) can be estimated from a detailed theoiy for foam drainage [Leonard and Lemlich, Am. Jn.st. Chem. Eng. J., 11, 18 (1965)]. From the resulting relationship for overflow [Fanlo and Lemlich, Am. Jn.st. Chem. Eng. Symp. Ser, 9, 75, 35 (1965)], Eq. (22-55) can be employed as a convenient approximation to the theory so as to avoid tri and error over the usual range of interest for foam of low hquid content ascending in plug flow ... 

A pilot scale UASB reactor was simulated by the dispersed plug flow model with Monod kinetic parameters for the hypothetical influent composition for the three VPA ccmiponents. As a result, the COD removal efflciency for the propionic acid is smallest because its decomposition rate is cptite slow compared with other substrate components their COD removal eflSciencies are in order as, acetic acid 0.765 > butyric acid 0.705 > propionic acid 0.138. And the estimated value of the total COD removal efficiency is 0.561. This means that flie inclusion of large amount of propionic acid will lead to a significant reduction in the total VFA removal efficiency. 

Estimate the space velocity needed to ensure that the conversion does not exceed say a 5% conversion at the exit of the plug flow reactor. 

We now want to estimate the CO coverage when the catalyst is located in a plug-flow reactor with a partial pressure of Pqq = 0-01 bar at T= 1000 K. The desorption energy is estimated to be 147 kj mol and the pre-exponential factor is set to the usual 10 s , while the sticking coefScient is estimated to be 0.2 and independent of temperature. For simplicity we assume that each Ni atom can adsorb a CO molecule. 

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... 

A Peclet number of zero indicates perfect mixing and a value of oo indicates plug flow. For bubble-cap and sieve plates the eddy diffusivity can be estimated from the equation ... 

From this illustration we can see that the added detail of the radial temperature profile near the wall that could be provided by CFD simulations does not help in obtaining better estimates for the standard heat transfer parameters. It also implies that experimental efforts to measure temperatures closer to the wall are, in fact, counter-productive. Finally, it is clear that the standard model with plug flow and constant effective transport parameters does not fit satisfactorily to temperature profiles in low-Abeds. These considerations have led us to look for improved approaches to near-wall heat transfer. 

Conversion in segregated flow is less than in plug flow and somewhat greater than in a CSTR battery with the same variance or RTD. Thus the variance does not guarantee the segregated conversion, but it often gives an acceptable estimate. 

The results confirm that the adsorption of ammonia is very fast and that ammonia is strongly adsorbed on the catalyst surface. The data were analyzed by a dynamic isothermal plug flow reactor model and estimates of the relevant kinetic parameters were obtained by global nonlinear regression over the entire set of runs. The influences of both intra-particle and external mass transfer limitations were estimated to be negligible, on the basis of theoretical diagnostic criteria. 

Regarding reactor sizes, a comparison of Eqs. 5.4 and 5.19 for a given duty and for s = 0 shows that an element of fluid reacts for the same length of time in the batch and in the plug flow reactor. Thus, the same volume of these reactors is needed to do a given job. Of course, on a long-term production basis we must correct the size requirement estimate to account for the shutdown time between batches. Still, it is easy to relate the performance capabilities of the batch reactor with the plug flow reactor. 

An injected slug of tracer material flows with its carrier fluid down a long, straight pipe in dispersed plug flow. At point A in the pipe the spread of tracer is 16 m. At point B, 1 kilometer downstream from A, its spread is 32 m. What do you estimate its spread to be at a point C, which is 2 kilometers downstream from point A ... 

Calculations show that the conversion in bubbling beds may vary from plug flow to well below mixed flow, see Fig. 20.6, and for many years the perplexing and embarrassing thing about this was that often we could not reliably estimate... 

In general, the material balances and the corresponding solutions for trickle and bubble bed reactors are the same, under the assumption that the plug-flow condition holds for both phases. Of course, the appropriate correlations should be used for the estimation of mass transfer coefficients. However, in packed bubble bed reactors, the liquid-phase is frequently found in a complete mixed state, and thus some adjustments have to be made to the aforementioned models. Two special cases will be presented here. 

As has been analyzed, the basic model for bubble column assumes complete mixed flow for the liquid phase and plug flow for the gas phase. The Deckwer el al. correlation (3.202) for the liquid phase and the Field and Davidson equation (3.206) for the gas phase can be used for the estimation of the dispersion coefficient. The resulting coefficients are Dll = 0.09 m2/s and DLG = 0.49 m2/s. 

Estimate the height of the bed to achieve the same performance of the reactor by using the appropriate simplified model, assuming that the liquid phase remains saturated with 02 throughout the reactor length, plug-flow conditions exist, and the external wetting of the catalyst particle is complete. 

In order to estimate the rate parameters of the kinetic expressions derived in the fundamental study, the kinetic runs performed over the powdered catalyst are typically analyzed according to a heterogeneous ID plug-flow dynamic... 

If the flow of the medium in the holding section were an ideal plug flow, the degree of sterilization could be estimated from the average residence time in the holding section by Equation 10.6 ... 

The values of k a for CO, desorption in a stirred-tank fermentor, calculated from the experimental data on physically dissolved CO, concentration (obtained by the above-mentioned method) and the CO2 partial pressure in the gas phase, agreed well with the k a values estimated from the k a for O, absorption in the same fermentor, but corrected for any differences in the liquid-phase diffusivities [11]. Perfect mixing in the liquid phase can be assumed when calculating the mean driving potential. In the case of large industrial fermentors, it can practically be assumed that the CO, partial pressure in the exit gas is in equilibrium with the concentration of CO, that is physically dissolved in the broth. The assumption of either a plug flow or perfect mixing in the gas phase does not have any major effect... 

The Peclet numbers are useful for estimating the relative contributions of convection and diffusion to mass and heat transfer. If Pe is large (>10), convection dominates, and a plug-flow model may be appropriate for simple reactor computations. When Pe is small (<<1), diffusion dominates, and the system behaves like a well-stirred reactor. Thus, Pe may be used to estimate whether downstream impurities can diffuse into the deposition zone. 

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