Residence time distribution liquid flow

Economic Pipe Diameter, Laminar Flow Pipehnes for the transport of high-viscosity liquids are seldom designed purely on the basis of economics. More often, the size is dictated oy operability considerations such as available pressure drop, shear rate, or residence time distribution. Peters and Timmerhaus (ibid.. Chap. 10) provide an economic pipe diameter chart for laminar flow. For non-Newtouiau fluids, see SkeUand Non-Newtonian Flow and Heat Transfer, Chap. 7, Wiley, New York, 1967). 

Topics that acquire special importance on the industrial scale are the quality of mixing in tanks and the residence time distribution in vessels where plug flow may be the goal. The information about agitation in tanks described for gas/liquid and slurry reactions is largely apphcable here. The relation between heat transfer and agitation also is discussed elsewhere in this Handbook. Residence time distribution is covered at length under Reactor Efficiency. A special case is that of laminar and related flow distributions characteristic of non-Newtonian fluids, which often occiu s in polymerization reactors. 

Axial Dispersion and the Peclet Number Peclet numbers are measures or deviation from phig flow. They may be calculated from residence time distributions found by tracer tests. Their values in trickle beds are fA to Ve, those of flow of liquid alone at the same Reynolds numbers. A correlation by Michell and Furzer (Chem. Eng. /., 4, 53 [1972]) is... 

Kramers and Alberda (K20) have reported some data in graphical form for the residence-time distribution of water with countercurrent air flow in a column of 15-cm diameter and 66-cm height packed with 10-mm Raschig rings. It was concluded that axial mixing increased with increasing gas flow rate and decreasing liquid flow rate, and that the results were not adequately represented by the diffusion model. 

Lapidus (LI) described liquid residence-time distribution studies for air-water and air-hydrocarbon in cocurrent, downward flow through a column of 2-in. diameter and 3-ft height. Spherical glass beads of 3.5. mm diameter and cobalt molybdate catalyst cylinders of -in. diameter were used as packing materials. 

Glaser and Lichtenstein (G3) measured the liquid residence-time distribution for cocurrent downward flow of gas and liquid in columns of -in., 2-in., and 1-ft diameter packed with porous or nonporous -pg-in. or -in. cylindrical packings. The fluid media were an aqueous calcium chloride solution and air in one series of experiments and kerosene and hydrogen in another. Pulses of radioactive tracer (carbon-12, phosphorous-32, or rubi-dium-86) were injected outside the column, and the effluent concentration measured by Geiger counter. Axial dispersion was characterized by variability (defined as the standard deviation of residence time divided by the average residence time), and corrections for end effects were included in the analysis. The experiments indicate no effect of bed diameter upon variability. For a packed bed of porous particles, variability was found to consist of three components (1) Variability due to bulk flow through the bed... 

Glaser and Litt (G4) have proposed, in an extension of the above study, a model for gas-liquid flow through a b d of porous particles. The bed is assumed to consist of two basic structures which influence the fluid flow patterns (1) Void channels external to the packing, with which are associated dead-ended pockets that can hold stagnant pools of liquid and (2) pore channels and pockets, i.e., continuous and dead-ended pockets in the interior of the particles. On this basis, a theoretical model of liquid-phase dispersion in mixed-phase flow is developed. The model uses three bed parameters for the description of axial dispersion (1) Dispersion due to the mixing of streams from various channels of different residence times (2) dispersion from axial diffusion in the void channels and (3) dispersion from diffusion into the pores. The model is not applicable to turbulent flow nor to such low flow rates that molecular diffusion is comparable to Taylor diffusion. The latter region is unlikely to be of practical interest. The model predicts that the reciprocal Peclet number should be directly proportional to nominal liquid velocity, a prediction that has been confirmed by a few determinations of residence-time distribution for a wax desulfurization pilot reactor of 1-in. diameter packed with 10-14 mesh particles. 

Ross (R2) measured liquid-phase holdup and residence-time distribution by a tracer-pulse technique. Experiments were carried out for cocurrent flow in model columns of 2- and 4-in. diameter with air and water as fluid media, as well as in pilot-scale and industrial-scale reactors of 2-in. and 6.5-ft diameters used for the catalytic hydrogenation of petroleum fractions. The columns were packed with commercial cylindrical catalyst pellets of -in. diameter and length. The liquid holdup was from 40 to 50% of total bed volume for nominal liquid velocities from 8 to 200 ft/hr in the model reactors, from 26 to 32% of volume for nominal liquid velocities from 6 to 10.5 ft/hr in the pilot unit, and from 20 to 27 % for nominal liquid velocities from 27.9 to 68.6 ft/hr in the industrial unit. In that work, a few sets of results of residence-time distribution experiments are reported in graphical form, as tracer-response curves. 

Hoogendoorn and Lips (H10) carried out residence-time distribution experiments for countercurrent trickle flow in a column of 1.33-ft diameter and 5- and 10-ft height packed with -in. porcelain Raschig rings. The fluid media were air and water, and ammonium chloride was used as tracer. The total liquid holdup was calculated from the mean residence time as found... 

Schoenemann (S4) reported qualitatively that the liquid residence-time distribution for cocurrent upward bubble flow was narrower than that observed in trickle-flow operation. 

Liquid residence-time distributions in mechanically stirred gas-liquid-solid operations have apparently not been studied as such. It seems a safe assumption that these systems under normal operating conditions may be considered as perfectly mixed vessels. Van de Vusse (V3) have discussed some aspects of liquid flow in stirred slurry reactors. 

The liquid residence-time distribution is close to plug flow in trickle-flow operation and corresponds to perfect mixing in the stirred-slurry operation, whereas the other types of bubble-flow operation are characterized by residence-time distributions between these extremes. 

In the absence of diffusion, all hydrodynamic models show infinite variances. This is a consequence of the zero-slip condition of hydrodynamics that forces Vz = 0 at the walls of a vessel. In real systems, molecular diffusion will ultimately remove molecules from the stagnant regions near walls. For real systems, W t) will asymptotically approach an exponential distribution and will have finite moments of all orders. However, molecular diffusivities are low for liquids, and may be large indeed. This fact suggests the general inappropriateness of using to characterize the residence time distribution in a laminar flow system. Turbulent flow is less of a problem due to eddy diffusion that typically results in an exponentially decreasing tail at fairly low multiples of the mean residence time. 

This study investigates the hydrodynamic behaviour of an aimular bubble column reactor with continuous liquid and gas flow using an Eulerian-Eulerian computational fluid dynamics approach. The residence time distribution is completed using a numerical scalar technique which compares favourably to the corresponding experimental data. It is shown that liquid mixing performance and residence time are strong functions of flowrate and direction. 

An investigation into the applicability of numerical residence time distribution was carried out on a pilot-scale annular bubble column reactor. Validation of the results was determined experimentally with a good degree of correlation. The liquid phase showed to be heavily dependent on the liquid flow, as expected, but also with the direction of travel. Significantly larger man residence times were observed in the cocurrent flow mode, with the counter-current mode exhibiting more chaimeling within the system, which appears to be contributed to by the gas phase. 

Glaser, M. B., and Lichtenstein, I. Interrelation of packing and mixed phase flow parameters with liquid residence time distribution. AJ.Ch.E. Journal 9, 30 (1963). (II,E)... 

Figure 12-12 Sketches of possible flow patterns of bubbles rising through a liquid phase in a bubble column. Stirring of the continuous phase will cause the residence time distribution to be broadened, and coalescence and breakup of drops will cause mixing between bubbles. Both of these effects cause the residence time distribution in the bubble phase to approach that of a CSTR. For falling drops in a spray tower, the situation is similar but now the drops fall instead of rising in the reactor.

The study of nonideal flow and liquid holdup can be done by residence time distribution (RTD) experiments (tracing techniques) or by use of correlations derived from literature. Dining this step, physical mechanisms that are sensitive to size are investigated separately from chemical (kinetic or equilibrium) studies (Trambouze, 1990). Here, the fixed bed is... 

The following equations are written for absorption (of any gas) in a continuous-flow stirred tank reactor (CFSTR) under the assumption that the gas and liquid phases are ideally mixed (Figure B 1-2). The assumption of an ideally mixed phase can be checked by determining the residence time distribution in the reactor (e. g. Levenspiel, 1972 Lin and Peng, 1997 Huang et al., 1998). 

In this section, several cases where there is a spread in drop size distribution will be calculated first for an ideal piston flow reactor in which all liquid parts have the same residence time distribution, and, finally, also the case of a CSTR in which there is a spread in drop size will be calculated, but only for the case of zero-order drop conversion. 

One of the key parameters in reactive processing is the distribution of residence times and temperatures for all particles in the liquid, because their reactivity depends on temperature, and the degree of conversion is determined by the dwell time inside the mold. Since the fountain effect changes residence time distribution from that in the hypothetical case of steady unidimensional flow, this factor becomes especially important in chemical (reactive) processing, more so than in standard injection molding of thermoplastic materials.284... 

Many studies on the flow distribution in random packed beds have been reported in the literature. Mercandelli et al. [8] published a short review of the flow distribution work in random packed trickle bed, which includes the list of various techniques used to determine and quantify the flow distribution. Conventional methods include, for example, collecting liquid at the bottom of the column from different zones while advanced methods include tomographic techniques. Mercandelli et al. [8] used several techniques to quantify liquid distribution in columns of diameters up to 30 cm with three different distributor designs. They used global pressure drop measurements, global residence time distribution (RTD) of the liquid, local heat transfer probes, capacitance tomography and a collector at the bottom of the column. 

The local aspects of liquid-liquid two-phase flow in RE has been the focus of CFD analysis by different research groups (123-126). In principle, all aspects concerning single-phase flow phenomena (residence time distribution, impeller discharge flow rate, etc.) can be tackled, even with complex geometries. However, the two-phase CFD is still a challenge, and the droplet interactions (breakup and coalescence) and mass transfer are not implemented in commercially available codes. Thus these issues constitute an open area for further research and development (127). 

An important advantage of the use of EOF to pump liquids in a micro-channel network is that the velocity over the microchannel cross section is constant, in contrast to pressure-driven (Poisseuille) flow, which exhibits a parabolic velocity profile. EOF-based microreactors therefore are nearly ideal plug-flow reactors, with corresponding narrow residence time distribution, which improves reaction selectivity. 

Clear-liquor advance is used for two purposes (1) to reduce the quantity of liquor that must be processed by the solid-liquid separation equipment (e.g., filter or centrifuge) that follows the crystallizer, and (2) to separate the residence time distributions of crystals and liquor. The reduction in liquor flow through the separation equipment can allow the use of smaller equipment for a fixed production rate or increased production through fixed equipment. Separating the residence time distributions of crystals and liquor means that crystals will have an average residence time longer than that of the liquor. This should, in principle, lead to the production of larger crystals, but because the crystallizer is otherwise well mixed, the crystal population density will have the same form as that for the MSMPR crystallizer (Eq. (54)). 

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