Flow two-phase

Two-phase flow pressure drop for tube bundles may be calculated using the equation  

APlo is the pressure drop for the total mass flowing as liquid X is the mass fraction vapor 

0 for vertical up-and-down flow B = 0.75 for horizontal flow other than stratified flow B = 0.25 for horizontal stratified flow 

Pns is the no-slip density defined in Chapter 26 B = 2/(K - 1) for horizontal flow 

The frictional pressure drop for shellside condensation can be calculated  

Operation of packed trickle-bed catalytic reactors is with liquid and gas flow downward together, and of packed mass transfer equipment with gas flow upward and liquid flow down. 

Liquid holdup was correlated in this work for both nonfoaming and foaming liquids. 

For our purposes, a rough estimate for general two-phase situations can be achieved with the Lockhart and Martinelli correlation. Perry s has a writeup on this correlation. To apply the method, each phase s pressure drop is calculated as though it alone was in the line. Then the following parameter is calculated  

The X factor is then related to either Yl or Yq. Whichever one is chosen is multiplied by its companion pressure drop to obtain the total pressure drop. The following equation is based on points taken from the Yl and Yq curves in Perry s for both phases in turbulent flow (the most common case)  

For fog or spray type flow, Ludwig cites Baker s suggestion of multiplying Lockhart and Martinelli by two. 

For the frequent case of flashing steam-condensate lines, Ruskan supplies the handy graph shown above. 

Ludwig, E. E., Applied Process Design For Chemical and Petrochemical Plants, Vol. 1, Gulf Publishing Co. 2nd Edition., 1977. 

Saturated 600 psig condensate flashed to 200 psig IV2 in line, sch. 80 (ID = 1.500 in) 

GPSA Data Book, Vol. II, Gas Processors Suppliers Association, 10th Ed., 1987. 

There are no precise formulas for calculating orifice area for two-phase flow. The common convention is to calculate the area required for the gas flow as if there were no liquid present and the area required for the liquid flow as if there were no gas present. The two areas are then added to approximate the area required for two-phase flow. 

In the highly turbulent range the disagreement is substantial. TWO-PHASE FLOW 

The pressure gradients for the liquid and vapor phases are calculated on the assumption of their individual flows through the bed, with the correlations of Eqs. (6.108)-(6.112). 

The fraction hL of the void space occupied by liquid also is of interest. In Sato s work this is given by 

Additional data are included in the friction correlation of Specchia and Baldi [Chem. Eng. Sci. 32, 515-523 (1977)], which is represented by  

The decisive flow mechanism in solvent extractors is the motion of swarms of droplets that is in close relation to the motion of single droplets. In liquid-liquid systems, drops reach their terminal velocity after a very short distance of fiee motion since the density difference between the drop and the continuous phase is 

Present knowledge of the terminal velocity of drops in liquids is very high. Small droplets often move a little bit faster than equivalent rigid spheres due to the mobility of the drop surface. Large drops, however, move significantly slower since they lose their spherical shape. Experimental data of the terminal velocity of some organic drops in water are shown in Fig. 6.4-1. The dimensionless terminal velocity is plotted vs. the dimensionless drop diameter. For comparison, the terminal velocity of equivalent rigid spheres is also shown. 

A generalized diagram of the terminal velocity of drops is shown in Fig. 3.6-3. From this diagram, the terminal velocity of drops can be predicted as a function of drop size and system properties. For large drops the velocity is nearly independent of drop size. Their velocity is (see Sect. 3.6.1) 

The rrraximrrm size of drops in free motion is (see Sect 3.6.1) 

4-2 Experimental results on the retardation of drops by the internals of different extractor designs (Garthe 2006). PSE pulsed sieve tray column, RDC rotating disc contactor, PPC pulsed packed column 

Typically, the calculations for two-phase pressure drop are too complicated for hand calculations. It is recommended that the design engineer use one of the available programs specifically designed for such calculations. In addition, an excellent review of two-phase flow is presented in Govier and Aziz (1972). 

In E-E, the bubbles are treated as particles and their paths are followed using Newton s laws, that is, the internal flow of the gas inside the bubble is ignored. This way, the position of all bubbles is known at all times. However, this is not literally true the motion of the water phase is, due to the scale of the fermenters or other multiphase bioreactors, turbulent. Consequently, as with single phase, the flow of the water phase cannot be solved in all its details. Some of the smaller scales have to be modeled. This automatically means that also the motion of the bubbles is captured only in an averaged sense. Having said that, even if we are satisfied with this approach, it is in most industrial cases not feasible. The computational effort is phenomenal, and results cannot be obtained in a reasonable time frame. 

In treating disturbances in process plants problems like the pressure relief of superheated liquids which evaporate on depressurization have to be dealt with. Then two-phase flow results, i.e. the liquid and vapour phase are discharged together. Most work in the area refers to mixtures of water and steam, which are of special importance in nuclear reactor accidents. The much more complex task to treat flow processes of multi-component two phase mixtures, which are a characteristic of process plants, still requires intense research. 

The basic problem in modelling two-phase flow is the question to what extent equilibrium exists between the phases. In general, there is no equilibrium. Yet, as a rule equilibrium is assumed, since this simplifies the analytical treatment of the problem. Fundamental considerations on two-phase flow can, for example, be encountered in [6]. In what follows the model of Leung [7, 8] is described. The presentation draws upon [8]. 

Leung distinguishes between the following initial states  

For the model the parameter co is important it determines the equation of state  

If N = 1 in Eq. (7.28) we speak of the homogeneous equilibrium model. If the expression for N given above, which was derived in [9], the model is referred to as non-equihbrium. 

Fluid-fluid systems are widely used for chemical transformations. Examples are halogenations, hydrogenations, and hydroformylations for gas-liquid reactions and nitrations, polymerizations, and cyclization for liquid-liquid systems. In addition, two-phase slug flow reactors can be used to get narrow residence time distribution at low liquid Reynolds numbers as demonstrated in chapter 3. Most of the reactions mentioned above are highly exothermic and heat evacuation is an important issue for efficient temperature control. 

Theoretical and experimental studies demonstrated that segmented gas/liquid flow enhances the heat transfer considerably compared to a single flow. Multiphase flow simulations revealed mainly two mechanisms explaining the increase of the Nusselt number, namely the circulation within the liquid slugs and the disturbing and renewing of the fluid layer near the wall by the gas bubbles. Detailed multiphase simulations for cylindrical chaimels by Lakehal et al. [19] lead to the 

The theoretical estimations are confirmed by experimental studies carried out with a squared channel of 500 pm height and width and a length of 25 mm [20]. The authors used water and air as fluids. Segmented flow with recirculating wakes could be generated for Bond numbers oi Bo = p g 3.36 and capillary 

On the basis of a detailed analysis [22], chemical reactions can be classified in different categories depending on their kinetics. Followingthis classification, three types of reactions are identified  

Generally, reactions of type A are considered as instantaneous and the transformation rate is limited by mixing. In this case, the intensity of mixing controls the heat production. 

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Aluminum-containing propellants deflver less than the calculated impulse because of two-phase flow losses in the nozzle caused by aluminum oxide particles. Combustion of the aluminum must occur in the residence time in the chamber to meet impulse expectations. As the residence time increases, the unbumed metal decreases, and the specific impulse increases. The soHd reaction products also show a velocity lag during nozzle expansion, and may fail to attain thermal equiUbrium with the gas exhaust. An overall efficiency loss of 5 to 8% from theoretical may result from these phenomena. However, these losses are more than offset by the increase in energy produced by metal oxidation (85—87). 

The pressure drop for gas—Hquid flow is deterrnined by the Lockhart-MartineUi method. It is assumed that the AP for two-phase flow is proportional to that of the single phase times a function of the single-phase pressure drop ratio P. 

In the macroscopic heat-transfer term of equation 9, the first group in brackets represents the usual Dittus-Boelter equation for heat-transfer coefficients. The second bracket is the ratio of frictional pressure drop per unit length for two-phase flow to that for Hquid phase alone. The Prandd-number function is an empirical correction term. The final bracket is the ratio of the binary macroscopic heat-transfer coefficient to the heat-transfer coefficient that would be calculated for a pure fluid with properties identical to those of the fluid mixture. This term is built on the postulate that mass transfer does not affect the boiling mechanism itself but does affect the driving force. 

Internal Flow. Depending on the atomizer type and operating conditions, the internal fluid flow can involve compHcated phenomena such as flow separation, boundary layer growth, cavitation, turbulence, vortex formation, and two-phase flow. The internal flow regime is often considered one of the most important stages of Hquid a tomiza tion because it determines the initial Hquid disturbances and conditions that affect the subsequent Hquid breakup and droplet dispersion. 

Liquids and Gases For cocurreut flow of liquids and gases in vertical (upflow), horizontal, and inclined pipes, a veiy large literature of experimental and theoretical work has been published, with less work on countercurrent and cocurreut vertical downflow. Much of the effort has been devoted to predicting flow patterns, pressure drop, and volume fractious of the phases, with emphasis on hilly developed flow. In practice, many two-phase flows in process plants are not fully developed. 

The volume fraction, sometimes called holdup, of each phase in two-phase flow is generally not equal to its volumetric flow rate fraction, because of velocity differences, or slip, between the phases. For each phase, denoted by subscript i, the relations among superficial velocity V, in situ velocity Vj, volume fraclion Rj, total volumetric flow rate Qj, and pipe area A are... 

Rhodes, and Scott Can. j. Chem. Eng., 47,445 53 [1969]) and Aka-gawa, Sakaguchi, and Ueda Bull JSME, 14, 564-571 [1971]). Correlations for flow patterns in downflow in vertical pipe are given by Oshinowo and Charles Can. ]. Chem. Eng., 52, 25-35 [1974]) and Barnea, Shoham, and Taitel Chem. Eng. Sci, 37, 741-744 [1982]). Use of drift flux theoiy for void fraction modeling in downflow is presented by Clark anci Flemmer Chem. Eng. Set., 39, 170-173 [1984]). Downward inclined two-phase flow data and modeling are given by Barnea, Shoham, and Taitel Chem. Eng. Set., 37, 735-740 [1982]). Data for downflow in helically coiled tubes are presented by Casper Chem. Ins. Tech., 42, 349-354 [1970]). 

Atomization = Eotvos numher, Eo Two-phase flows, free surface flows Compressible flow, hydraulic transients Cavitation... 

Pressure drop during condensation inside horizontal tubes can be computed by using the correlations for two-phase flow given in Sec. 6 and neglec ting the pressure recoveiy due to deceleration of the flow. 

The same procedure may be applied in principle to design of forced-recirculation reboilers with shell-side vapor generation. Little is known about two-phase flow on the shell side, out a reasonable estimate of the fric tion pressure drop can be made from the data of Diehl and Unruh [Pet Refiner, 36(10), 147 (1957) 37(10), 124 (1958)]. No void-fraction data are available to permit accurate estimation of the hydrostatic or acceleration terms. Tnese may be roughly estimated by assuming homogeneous flow. 

Absorbers These have a two-phase flow system. The absorbing medium is put in film flow during its fall downward on the tubes as it is cooled by a coohng medium outside the tubes. The film absorbs the gas which is introduced into the tubes. This operation can be cocurrent or countercurrent. 

The shape of the coohng and warming curves in coiled-tube heat exchangers is affected by the pressure drop in both the tube and shell-sides of the heat exchanger. This is particularly important for two-phase flows of multicomponent systems. For example, an increase in pressure drop on the shellside causes boiling to occur at a higher temperature, while an increase in pressure drop on the tubeside will cause condensation to occur at a lower temperature. The net result is both a decrease in the effective temperature difference between the two streams and a requirement for additional heat transfer area to compensate for these losses. 

FIG. 23-25 Typ es of industrial gas/Hqiiid reactors, (a) Tray tower, (h) Packed, counter current, (c) Packed, parallel current, (d) Falling liquid film, (e) Spray tower, if) Bubble tower, (g) Venturi mixer, h) Static in line mixer, ( ) Tubular flow, (j) Stirred tank, (A,) Centrifugal pump, (/) Two-phase flow in horizontal tubes. 

Two-phase multiplier, pressure drop for two-phase flow... 

FIG. 26-70 Accuracy in HEM predictions for slightly to moderately siibcooled flashing flow. Comparison with data for water by Sozzi and Sutherland (1975) also ASME Symposium on Non-Equilibrium Two-Phase Flows (1975) (Nozzle type 2). 

For two-phase flow, the phase contraction coefficients Cqc. nd Col relate the area of each phase Ac and A at the vena contracta to the known area of the orifice Ay. Thus ... 

A further generahzation for two-phase flow as suggested by Tan-gren et al. (1949) is to use the generalized value of k as ... 

Design Institute for Emergeney Relief Systems (DIERS) Institute under the auspices of the American Institute of Chemical Engineers founded to study relief requirements for reactive chemical systems and two-phase flow systems. 

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