Phase flow

To prepare gas for evacuation it is necessary to separate the gas and liquid phases and extract or inhibit any components in the gas which are likely to cause pipeline corrosion or blockage. Components which can cause difficulties are water vapour (corrosion, hydrates), heavy hydrocarbons (2-phase flow or wax deposition in pipelines), and contaminants such as carbon dioxide (corrosion) and hydrogen sulphide (corrosion, toxicity). In the case of associated gas, if there is no gas market, gas may have to be flared or re-injected. If significant volumes of associated gas are available it may be worthwhile to extract natural gas liquids (NGLs) before flaring or reinjection. Gas may also have to be treated for gas lifting or for use as a fuel. 

Figure 2. Principle of 3 phase flow measurements by the continuous dilution tracer method.

Figure C3.6.2 (a) The (fi2,cf) Poincare surface of a section of the phase flow, taken at ej = 8.5 with cq < 0, for the WR chaotic attractor at k = 0.072. (b) The next-amplitude map constmcted from pairs of intersection coordinates. ..,(c2(n-l-l),C2(n-l-2),C2(n-l-l)),...j. The sequence of horizontal and vertical line segments, each touching the diagonal B and the map, comprise a discrete trajectory. The direction on the first four segments is indicated.

The quasiperiodic route to chaos is historically important. It arises from a succession of Hopf birfurcations. As already noted, a single Hopf bifurcation results in a limit cycle. The next Hopf bifurcation produces a phase flow tliat can be represented on tire surface of a toms (douglmut). This flow is associated witli two frequencies if tire ratio of tliese frequencies is irrational tlien tire toms surface is densely covered by tire phase trajectory, whereas if... 

A convenient and constructive approach to attain symplectic maps is given by the composition of symplectic maps, which yields again a symplectic map. For appropriate Hk, the splittings (6) and (7) are exactly of this form If the Hk are Hamiltonians with respect to the whole system, then the exp rLnk) define the phase flow generated by these Hk- Thus, the exp TL-Hk) are symplectic maps on the whole phase space and the compositions in (6) and (7) are symplectic maps, too. Moreover, in order to allow for a direct numerical realization, we have to find some Hk for which either exp(rL-Kfc) has an analytic solution or a given symplectic integrator. 

In general, the longer a chromatographic column, the better will be the separation of mixture components. In modem gas chromatography, columns are usually made from quartz and tend to be very long (coiled), often 10-50 m, and narrow (0.1-1.0 mm, internal diameter) — hence their common name of capillary columns. The stationary phase is coated very thinly on the whole length of the inside wall of the capillary column. Typically, the mobile gas phase flows over the stationary phase in the column at a rate of about 1-2 ml/min. 

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). 

Motionless inline mixers obtain energy for mixing and dispersion from the pressure drops developed as the phases flow at high velocity through an array of baffles or packing in a tube. Performance data on the Kenics (132) and Sul2er (133) types of motionless mixer have been reported. 

In addition to the reduction in performance, flow maldistribution may result in increased corrosion, erosion, wear, fouling, fatigue, and material failure, particularly for Hquid flows. This problem is even more pronounced for multiphase or phase change flows as compared to single-phase flows. Flow distribution problems exist for almost all types of exchangers and can have a significant impact on energy, environment, material, and cost in most industries. 

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. 

A. M. Nazar and T. W. Clyne in T. N. Vezkoglu, ed.. Proceedings Multi-Phase Flow and Heat Transfer Symposium Hemisphere, Washington, D.C., 1980. 

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. 

Rapid approximate predictions of pressure drop for fully developed, incompressible horizontal gas/fiquid flow may be made using the method of Lockhart and MartineUi (Chem. Eng. Prog., 45, 39 8 [1949]). First, the pressure drops that would be expected for each of the two phases as if flowing alone in single-phase flow are calculated. The LocKhart-Martinelli parameter X is defined in terms of the ratio of these pressure drops ... 

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