Liquid residence time distribution

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... 

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. 

Figure 1 Liquid Residence time distribution comparison - Experimental vs Numerical (a) counter-current operation Liquid flowrate l.SLmm (b) counter-current operation Liquid flowrate 3Lmin (c) co-current operation Liquid flowrate 1.5Lmm (d) co-current operation Liquid flowrate 3Lmm ...

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)... 

It is important to study the bubble rise velocity and its radial profile in a gas-liquid system as these are closely related to the hydrodynamics, and mass and heat transfer [25]. Bubble rise velocity and its radial profile have also significant influences on gas and liquid residence time distributions. A suitable bubble rise velocity and radial profile can improve production efficiency. Bubble rise velocities in a... 

Table IV presents some data on liquid residence time distributions measured under conditions of hydrocracking in trickle flow. It can be seen that bed dilution with fine inert particles results in a considerable improvement in the plug-flow character of the reactor, which supports the idea that the dispersion is largely determined by the packing of fine particles. Since in the range of Re numbers of interest the Bodenstein number is approximately a constant (see Figure 4), the Peclet numbers for beds of equal length should be inversely proportional to the particle diameter. Dilution of the 1.5 mm particles with 0.2 mm particles should raise Pe by a factor of about 7, which is approximately in line with the data in Table IV.

Liquid holdup Liquid holdup, mean residence time, and liquid residence time distribution are important in determining conversion and selectivity. Catalyst deactivation Catalyst deactivation is often accounted for during design by use of excess catalyst, and increase in reaction severity by increasing reflux (for increased residence time) or by increasing reaction temperature. 

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... 

Only a few investigations concerned with the measurement of gas holdup and residence-time distribution have been reported. The information regarding liquid holdup, which will be discussed in the following section, is considerably more abundant in some cases, values of gas holdup can be deduced from the reported data on liquid holdup and total voidage. 

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. 

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... 

Kramers et al. (K21) measured gas residence-time distribution in a mechanically agitated gas-liquid contactor of 0.6-m diameter for various gas velocities and agitator speeds. In the region where agitation has an effect on the gas-liquid interfacial area (cf. the study by Westerterp et al. (W5), Section V,D,1), the residence-time distribution was found to resemble closely that of a perfect mixer. 

Holdup and Residence-Time Distribution of Liquid Phase... 

From the assumption that liquid volume elements travel as bubble wakes at velocities higher than the average liquid velocity, it follows that the bubble movement must influence the residence-time distribution of the liquid phase. However, no work on this subject has come to the author s attention. 

Fig. 3. Typical residence-time distribution curves in a gas-liquid dispersion [after Gal-Or and Resnick (G8)].

The overall set of partial differential equations that can be considered as a mathematical characterization of the processing system of gas-liquid dispersions should include such environmental parameters as composition, temperature, and velocity, in addition to the equations of bubble-size and residence-time distributions that describe the dependence of bubble nucleation and growth on the bubble environmental factors. A simultaneous solution of this set of differential equations with the appropriate initial and boundary conditions is needed to evaluate the behavior of the system. Subject to the Curie principle, this set of equations should include the possibilities of coupling effects among the various fluxes involved. In dispersions, the possibilities of couplings between fluxes that differ from each other by an odd tensorial rank exist. (An example is the coupling effect between diffusion of surfactants and the hydrodynamics of bubble velocity as treated in Section III.) As yet no analytical solution of the complete set of equations has been found because of the mathematical difficulties involved. To simplify matters, the pertinent transfer equation is usually solved independently, with some simplifying assumptions. 

Example 14.6 derives a rather remarkable result. Here is a way of gradually shutting down a CSTR while keeping a constant outlet composition. The derivation applies to an arbitrary SI a and can be extended to include multiple reactions and adiabatic reactions. It is been experimentally verified for a polymerization. It can be generalized to shut down a train of CSTRs in series. The reason it works is that the material in the tank always experiences the same mean residence time and residence time distribution as existed during the original steady state. Hence, it is called constant RTD control. It will cease to work in a real vessel when the liquid level drops below the agitator. 

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. 

Gavrilescu, M. and R.Z. Tudose, Residence time distribution of the liquid phase in a concentric-tube airlift reactor. Chemical Engineering and Processing, 1999. 38(3) p. 225-238. 

Chemical Kinetics, Tank and Tubular Reactor Fundamentals, Residence Time Distributions, Multiphase Reaction Systems, Basic Reactor Types, Batch Reactor Dynamics, Semi-batch Reactors, Control and Stability of Nonisotheimal Reactors. Complex Reactions with Feeding Strategies, Liquid Phase Tubular Reactors, Gas Phase Tubular Reactors, Axial Dispersion, Unsteady State Tubular Reactor Models... 

The available models mostly refer to ideal reactors, STR, CSTR, continuous PFR. The extension of these models to real reactors should take into account the hydrodynamics of the vessel, expressed in terms of residence time distribution and mixing state. The deviation of the real behavior from the ideal reactors may strongly affect the performance of the process. Liquid bypass - which is likely to occur in fluidized beds or unevenly packed beds - and reactor dead zones - due to local clogging or non-uniform liquid distribution - may be responsible for the drastic reduction of the expected conversion. The reader may refer to chemical reactor engineering textbooks [51, 57] for additional details. 

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... 

---