Flow pattern

One should beware of vendors claiming they can supply mass flow bins with no consideration of the hopper wall material or stored bulk solid. The term mass flow is often misused. 

Jenike (1964) presented a series of graphs defining the limits of hopper angle within which mass flow can develop. The major variables that determine these limits are  

Monolith multiphase chemical reactors are another example of microfluidic multiphase flow applications. The slug flow pattern enhances the mass transfer in the liquid-solid process. There is also low-pressure drop for a given specific contact area. Machado et al (1999) have patented the use of monolith reactors for fast and highly exothermic nitroaromatic hydrogenation. In this process, the product is recycled through the reactors several hundreds of times, and the low-pressure-drop monolith reactor is therefore preferred. 

Broekhuis et al (2004) used monolith reactor for the production of sorbitol. Guenther et al (2004) developed a gas-liquid separator downstream the reaction zone of microfabricated integrated system. Khan et al (2004) used the plug flow characteristic for the production of colloidal silica. 

Film flow. In film flow (downflow only), liquid flows downward on the walls of the channel, and the gas flows through the center, either upward or downward. This takes place typically at low superficial velocities. 

Bubbly flow In bubbly flow, gas flows as small bubbles dispersed in the continuous wetting fluid. This flow pattern is observed at moderate velocities for low gas frictions, where coalescence is minimal. 

Annular flow In annular flow, a thin wavy liquid film flows along the wall with a mist of gas and entrained liquid in the core. This flow pattern is observed at high velocities and low liquid fraction. 

The latest two-phase flow research and design studies have broadened the interpretation of some of the earlier flow patterns and refined some design accuracy for selected situations. The method presented here serves as a fundamental reference source for further studies. It is suggested that the designer compare several design concept results and interpret which best encompasses the design problem under consideration. Some of the latest references are included in the Reference Section. No one reference has a solution to all two-phase flow problems. 

If two-phase flow situations are not recognized, pressure drop problems may develop which can prevent systems from operating. It requires very little percentage of vapor, generally above 7% to 8%, to establish volumes and flow velocities that must be solved by two-phase flow analysis. The discharge flow through a pressure relief valve on a process reactor is often an important example where two-phase flow exists, and must be recognized for its back pressure impact. 

0 The Ekato intermig impeller has reverse pitch on the inner and outer blades and they are almost always used with multiple impellers. They are used at high D/T and promote a more uniform axial flow pattern than other turbine impellers. They are advertised to be very effective for solids suspension, blending, and heat transfer in the medium viscosity range. Lower Nrc limit not given by Ekato (9), perhaps 5. 

3(a)) much swirl and vortexing is produced, resulting in poor 

Consideration will now be given in turn to three particular aspects of gas-liquid flow which are of practical importance (i) flow patterns or regimes (ii) holdup, and (iii) frictional pressme gradient. 

For two-phase cocurrent gas-liquid flow, there is the wide variety of possible flow patterns which are governed principally by the physical properties (density, surface tension, viscosity of gas, rheology of liquid), input fluxes of the two phases and the size and the orientation of the pipe. Since the mechanisms responsible for holdup and momentum transfer (or frictional pressure drop) vary from one flow pattern to another, it is essential to have a method of predicting the conditions under which each flow pattern may occm. Before developing suitable methods for the prediction of flow pattern, it is important briefly to define the flow patterns generally encountered in gas-liquid flows. Horizontal and vertical flows will be discussed separately as there are inherent differences in the two cases. 

This type of flow, sometimes referred to as dispersed bubble flow, is characterised by a train of discrete gas bubbles moving mainly close to the upper wall of the pipe, at almost the same velocity as the liquid. As the liquid flowrate is increased, the bubbles become more evenly distributed over the cross-section of the pipe. 

At increased gas throughput, bubbles interact and coalesce to give rise to large bullet shaped plugs occupying most of the pipe cross-section, except for a thin liquid film at the wall of the pipe which is thicker towards the bottom of the pipe. 

In this mode of flow, the gravitational forces dominate and the gas phase flows in the upper part of the pipe. At relatively low flowrates, the gas-liquid interface is smooth, but becomes ripply or wavy at higher gas rates thereby giving rise to the so-called wavy flow . As the distinction between the smooth and wavy interface is often ill-defined, it is usual to refer to both flow patterns as stratified-wavy flow. 

The distribution of gas between spout and annulus is important in assessing the effectiveness of gas-solids contact. Qualitatively the flo v pattern in a spouted bed is obvious the gas jet flares out as it travels upward, causing the gas flow rate in the spout to decrease, and the flow rate in the annulus to increase, with increasing distance from the inlet orifice. Attempts to quantify this pattern and to relate it to the variables of the system have been made, both theoretically and experimentally. 

Mamuro and Hattori (M6) extended their analysis of the balance of forces acting on the spout-annulus interface (Fig. 10) to derive an expression which enables estimation of gas distribution between the annulus and the spout at various levels in the bed. Substitution of Eqs. (19) and (20) into Eq. (18) gives 

Differentiating Eq. (30) with respect to z and combining the result with Eq. (21) gives the differential equation 

Assuming that the gas velocity at the top of the annulus is sufficient to fluidize the solids (i.e., that the bed is at the maximum spoutable depth /fm), Eq. (32) together with Eqs. (30) and (20) gives rise to 

Therefore Ct = —Hm- On substituting this result in Eq. (34), with the boimdary condition f7, = Umt tz = Hm, 

Restrictions which may exist for the choice of a commercial reactor need not be imposed at the development stage. In some cases, a reactor of one type may be best for acquiring data in model characterisation, whereas a reactor of another type might be more suitable for full-scale production. (The cautions expressed in Sect. 4 must be taken into account.) Continuous flow back-mixed reactors can be very useful for kinetic studies because the absence of concentration gradients can reduce uncertainties in concentration measurements. When these reactors have attained a steady state, many of the problems associated with stiffness (see above) can be avoided. 

In order to improve the relative yield of a product from complex reactions, a manufacturer may vary the operational procedure for the chosen reactor. In some cases, this amounts to changing the flow pattern. When more than one reactant is used, it may sometimes be advantageous to use more than one entry point for a tubular-flow reactor (see Fig. 6). Delbridge and Dyson [53] showed that, for the case where reaction (8) was accompanied by 

If a tubular-flow reactor is equipped with a recycle arrangement, as shown in Fig. 7, the mixing pattern is somewhere between the two ideal limits of plug flow and ideal back-mixing. Such a system can be useful for controlling product distribution from a complex reaction. Consider the simultaneous occurrence of reactions (17) and (105) where reaction (105) is second-order and B is the desired product. The discussion above would suggest that plug flow would enhance the relative yield of B but back- 

Ridelhoover and Seagrave [57] studied the behaviour of these same reactions in a semi-batch reactor. Here, feed is pumped into the reactor while chemical reaction is occurring. After the reactor is filled, the reaction mixture is assumed to remain at constant volume for a period of time the reactor is then emptied to a specified level and the cycle of operation is repeated. In some respects, this can be regarded as providing mixing effects similcir to those obtained with a recycle reactor. Circumstances could be chosen so that the operational procedure could be characterised by two independent parameters the rate coefficients were specified separately. It was found that, with certain combinations of operational variables, it was possible to obtain yields of B higher than those expected from the ideal reactor types. It was necessary to use numerical procedures to solve the equations derived from material balances. 

Imposing oscillations in the feed concentrations for a continuous back-mixed reactor can also result in beneficial changes of reaction selectivity [58]. Such changes are likely to be more significant with intermediates in consecutive reactions than with products from simultaneous reactions in parallel [59]. 

As already noted, the exact term of a mortgage-backed bond cannot be stated with assurance at the time of issue because of the uncertainty connected with the speed of mortgage prepayments. As a result, it is not 

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Figure A.2 shows the cash-flow pattern for a typical project. The cash flow is a cumulative cash flow. Consider curve 1 in Fig. A.2. From the start of the project at A, cash is spent without any...

Figure A.2 Cash-flow pattern for a typical project. (From Allen, IChemE, 1980 reproduced by permission of the Institution of Chemical Engineers.)...

If these assumptions are satisfied then the ideas developed earlier about the mean free path can be used to provide qualitative but useful estimates of the transport properties of a dilute gas. While many varied and complicated processes can take place in fluid systems, such as turbulent flow, pattern fonnation, and so on, the principles on which these flows are analysed are remarkably simple. The description of both simple and complicated flows m fluids is based on five hydrodynamic equations, die Navier-Stokes equations. These equations, in trim, are based upon the mechanical laws of conservation of particles, momentum and energy in a fluid, together with a set of phenomenological equations, such as Fourier s law of themial conduction and Newton s law of fluid friction. When these phenomenological laws are used in combination with the conservation equations, one obtains the Navier-Stokes equations. Our goal here is to derive the phenomenological laws from elementary mean free path considerations, and to obtain estimates of the associated transport coefficients. Flere we will consider themial conduction and viscous flow as examples. 

Flow models Flow number FLOWPACK Flow patterns Flow-sheet models FlowSorb 2300 FLOWIRAN... 

The advantage of single-pass over cross-flow filtration is that it is an easier system to operate and can be cost effective, particularly if the product to be filtered is expensive, because very tittle of the initial fluid is lost during filtration. However, because the flow pattern of the fluid is directly through the filter, filter life maybe too short for the fluid being filtered. The minimum flow rate needed downstream of the filter must also be considered, especially when there are time constraints to the process. In some situations it may be more advantageous to use a cross-flow system where higher flow rates may be easier to obtain. 

Improvements ia membrane technology, vahdation of membrane iategrity, and methods to extend filter usage should further improve the performance of membrane filters ia removal of viral particles. Methods to improve or extead filter life and iacrease flow rates by creating more complex flow patterns could possibly be the focus of the next generation of membrane filters designed to remove viral particles. 

Commercial Extractors. Extractors can be classified according to the methods appHed for interdispersing the phases and producing the countercurrent flow pattern. Eigure 11 summarizes the classification of the principal types of commercial extractors Table 3 summarizes the main characteristics. 

In some cases, however, it is possible, by analysing the equations of motion, to determine the criteria by which one flow pattern becomes unstable in favor of another. The mathematical technique used most often is linearised stabiHty analysis, which starts from a known solution to the equations and then determines whether a small perturbation superimposed on this solution grows or decays as time passes. 

Fig. 15. Flow pattern in rotating Couette flow where and Q2 represent the outer and inner rotational speeds.

Fig. 5. Schematic representation of gas flow pattern in the IMHEX design.

The factors which govern the efficiency of waste destmction iaclude atomi2ation, ie, mean drop si2e, and si2e distribution temperature residence time O2 concentration and flow patterns. 

Computer Models, The actual residence time for waste destmction can be quite different from the superficial value calculated by dividing the chamber volume by the volumetric flow rate. The large activation energies for chemical reaction, and the sensitivity of reaction rates to oxidant concentration, mean that the presence of cold spots or oxidant deficient zones render such subvolumes ineffective. Poor flow patterns, ie, dead zones and bypassing, can also contribute to loss of effective volume. The tools of computational fluid dynamics (qv) are useful in assessing the extent to which the actual profiles of velocity, temperature, and oxidant concentration deviate from the ideal (40). 

Fresh butane mixed with recycled gas encounters freshly oxidized catalyst at the bottom of the transport-bed reactor and is oxidized to maleic anhydride and CO during its passage up the reactor. Catalyst densities (80 160 kg/m ) in the transport-bed reactor are substantially lower than the catalyst density in a typical fluidized-bed reactor (480 640 kg/m ) (109). The gas flow pattern in the riser is nearly plug flow which avoids the negative effect of backmixing on reaction selectivity. Reduced catalyst is separated from the reaction products by cyclones and is further stripped of products and reactants in a separate stripping vessel. The reduced catalyst is reoxidized in a separate fluidized-bed oxidizer where the exothermic heat of reaction is removed by steam cods. The rate of reoxidation of the VPO catalyst is slower than the rate of oxidation of butane, and consequently residence times are longer in the oxidizer than in the transport-bed reactor. 

Macromixing is estabflshed by the mean convective flow pattern. The flow is divided into different circulation loops or zones created by the mean flow field. The material is exchanged between zones, increasing homogeneity. Micromixing, on the other hand, occurs by turbulent diffusion. Each circulation zone is further divided into a series of back-mixed or plug flow cells between which complete intermingling of molecules takes place. 

Fig. 9. Flow patterns with different impeller types, sizes, and liquid viscosity (a) FBT (b) hydrofoil (c) PBT (d) PBT, large diameter (e) PBT, high...

Fig. 22. Bulk flow patterns with increasing N at constant where (a) shows flooding (b) to (d), increasing degrees of dispersion, and (e) complete...

Fig. 25. Flow patterns in jet mixed tanks where represents 2ones that are poody mixed (a) side entry and (b) axial.

Fig. 28. Flow patterns with (a) clustered and (b) distributed mixers.

Wettabihty is defined as the tendency of one fluid to spread on or adhere to a soHd surface (rock) in the presence of other immiscible fluids (5). As many as 50% of all sandstone reservoirs and 80% of all carbonate reservoirs are oil-wet (10). Strongly water-wet reservoirs are quite rare (11). Rock wettabihty can affect fluid injection rates, flow patterns of fluids within the reservoir, and oil displacement efficiency (11). Rock wettabihty can strongly affect its relative permeabihty to water and oil (5,12). When rock is water-wet, water occupies most of the small flow channels and is in contact with most of the rock surfaces as a film. Cmde oil does the same in oil-wet rock. Alteration of rock wettabihty by adsorption of polar materials, such as surfactants and corrosion inhibitors, or by the deposition of polar cmde oil components (13), can strongly alter the behavior of the rock (12). 

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