Pressure drop compressible flow

Compound dynamic instabilities as secondary phenomena. Pressure-drop oscillations are triggered by a static instability phenomenon. They occur in systems that have a compressible volume upsteam of, or within, the heated section. Maul-betsch and Griffith (1965, 1967), in their study of instabilities in subcooled boiling water, found that the instability was associated with operation on the negative-sloping portion of the pressure drop-versus-flow curve. Pressure drop oscillations were predicted by an analysis (discussed in the next section), but because of the... 

In order to determine the viscous and inert through-plane gas permeabilities of diffusion layers at varied compression pressures, Gostick et al. [212] designed a simple method in which a circular specimen was sandwiched between two plates that have orifices in the middle, aligned with the location of the material. Pressurized air entered the upper plate, flowed through the DL, and exited the lower plate. The pressure drop between the inlet and the outlet was recorded for at least ten different flow rates for each sample. The inert and viscous permeabilities were then determined by fitting the Forchheimer equation to the pressure drop versus flow rate data as explained earlier. 

PDOs are categorized as compound dynamic instability and occur as secondary phenomenon triggered by stahc instability. PDO occurs in a system having compressible volume upstream or within the heated section and when the system operates in the negative slope region of the pressure drop versus flow rate curve. 

In the solution gas drive case, once production starts the reservoir pressure drops very quickly, especially above the bubble point, since the compressibility of the system is low. Consequently, the producing wells rapidly lose the potential to flow to surface, and not only is the plateau period short, but the decline is rapid. 

Natural water drive occurs when the underlying aquifer is both large (typically greater than ten times the oil volume) and the water is able to flow Into the oil column, i.e. it has a communication path and sufficient permeability. If these conditions are satisfied, then once production from the oil column creates a pressure drop the aquifer responds by expanding, and water moves into the oil column to replace the voidage created by production. Since the water compressibility is low, the volume of water must be large to make this process effective, hence the need for the large connected aquifer. 

Equation (6-95) is valid for incompressible flow. For compressible flows, see Benedict, Wyler, Dudek, and Gleed (J. E/ig. Power, 98, 327-334 [1976]). For an infinite expansion, A1/A2 = 0, Eq. (6-95) shows that the exit loss from a pipe is 1 velocity head. This result is easily deduced from the mechanic energy balance Eq. (6-90), noting that Pi =pg. This exit loss is due to the dissipation of the discharged jet there is no pressure drop at the exit. 

Isothermal Gas Flow in Pipes and Channels Isothermal compressible flow is often encountered in long transport lines, where there is sufficient heat transfer to maintain constant temperature. Velocities and Mach numbers are usually small, yet compressibihty effects are important when the total pressure drop is a large fraction of the absolute pressure. For an ideal gas with p = pM. JKT, integration of the differential form of the momentum or mechanical energy balance equations, assuming a constant fric tion factor/over a length L of a channel of constant cross section and hydraulic diameter D, yields,... 

The Lapple charts for compressible fluid flow are a good example for this operation. Assumptions of the gas obeying the ideal gas law, a horizontal pipe, and constant friction factor over the pipe length were used. Compressible flow analysis is normally used where pressure drop produces a change in density of more than 10%. 

Loeb used Lapple s compressible flow work, techniques, and reasoning to develop graphs useful for direct calculations between tw o points in a pipe. Lapple s graphs were designed for pressure drop estimations for flow from a large vessel into a length of pipe (having static velocity in the reservoir). 

Permeability is normally determined using linear flow in the incompressible or compressible form, depending on whether a liquid or gas is used as the flowing fluid. The volumetric flowrate Q (or Q ,) is determined at several pressure drops. Q (or Q ,) is plotted versus the average pressure p . The slope of this line will yield the fluid conductivity K or, if the fluid density and viscosity are known, it provides the intrinsic permeability k. For gases, the fluid conductivity depends on pressure, so that... 

When the cake structure is composed of particles that are readily deformed or become rearranged under pressure, the resulting cake is characterized as being compressible. Those that are not readily deformed are referred to as sem-compressible, and those that deform only slightly are considered incompressible. Porosity (defined as the ratio of pore volume to the volume of cake) does not decrease with increasing pressure drop. The porosity of a compressible cake decreases under pressure, and its hydraulic resistance to the flow of the liquid phase increases with an increase in the pressure differential across the filter media. 

Flexible ducts (or tubes) and their pressure drops ar various flow rates both when extended and when compressed connection to metal sheet ducts. 

F = an allowance for interstage pressure drop = 1.00 for single-stage compression 1,08 for two-stage compression 1.10 for three-stage compression Qg = flow rate, MMsefd... 

FIGURE 2.12 Pressure drop as a function of liquid fiow through a packed bed of Superose 6 prep grade packed in a HR 10/30 column. At high velocities of the mobile phase the beads are compressed and the void channels reduced, which leads to a high pressure drop. If this happens, the material can be resuspended and packed at a lower flow rate. [Reproduced from Hagel and Andersson (1984), with permission.]... 

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