Pressure discontinuity

If a pressure measuring device were run inside the capillary, an oil gradient would be measured in the oil column. A pressure discontinuity would be apparent across the interface (the difference being the capillary pressure), and a water gradient would be measured below the interface. If the device also measured resistivity, a contact would be determined at this interface, and would be described as the oil-water contact (OWC). Note that if oil and water pressure measurements alone were used to construct a pressure-depth plot, and the gradient intercept technigue was used to determine an interface, it is the free water level which would be determined, not the OWC. 

Explosion A rapid or sudden release of energy that causes a pressure discontinuity or blast wave. 

We will be concerned with the interaction of waves with boundaries and with other waves throughout this text. To determine how these interactions take place, it is important to consider that discontinuities in either pressure or particle velocity cannot be sustained in any material. If a discontinuity in either of these variables is created at some point by impact or wave interaction, the resulting motion will be such that the pressure and particle velocity become continuous across the boundary or point of interaction. Unless the material separates at that point, the motion will consist of one or more waves propagating away from the point of the discontinuity. For pressure discontinuities, it is easy to see that waves must propagate by again considering an... 

Application of this procedure to inadvertently ignited safety valve discharges can involve a special problem. Certain combinations of pressure ratio and length of safety valve riser can result in choked flow, with a pressure discontinuity at the exit. The pressure of the jet then adjusts to atmospheric pressure in a system of shock waves or expansion waves over a distance of a few pipe diameters. These waves can affect the local mixing of the jet with the crosswind. Since the calculation procedure incorporates correlations for subsonic jets, it cannot be expected to be entirely accurate in this case. Nevertheless, since the wave system... 

In flow through a frictionless nozzle, there is a critical pressure ratio, r, which will just cause choking. The critical pressure ratio is the ratio of the downstream back pressure to the upstream pressure, both in absolute pressure units. If the actual back pressure (e.g. atmospheric) is less than the critical pressure at which choking occurs, then there will be a pressure discontinuity at the end of the nozzle the pressure just inside the nozzle will be the critical pressure for choking, and that just outside the nozzle will be the actual back pressure, which is normally atmospheric. See Figure 9.2. -. ... 

No enthalpy change occurs. An isenthalpic. sdepressurisation is irreversible. It is common to. assume that, the pressure drop across the pressure discontinuity at a choke is isenthalpic. 

Discontinuation usually results in resolution of the IH, though other measures may be taken to reduce the intracranial pressure. Discontinuation should also occur if nyctalopia develops. 

These results require further that w, v, R, 0, and Yi be continuous in the first approximation and rely on the assumptions that fi2, and 6 are continuous. The conditions obtained from equations (89), (90), and (93) in effect involve only the longitudinal components of the stress tensor and of the heat-flux vector. The first of the conditions quoted from equations (89) and (90) expresses a pressure discontinuity that balances the discontinuity in the viscous stress tensor, and the second states that the streamwise gradients of the components of velocity tangent to the sheet are continuous. 

In more detail, however, the picture is somewhat different (Fig. 13). The 30/7a-9 and 30/7a-llz wells, drilled in the northernmost part of the field, appear to have different aquifer gradients. Within individual wells, there is no evidence of pressure discontinuities between the Jurassic... 

Fulmar reservoir and the Triassic Joanne and Judy reservoirs. However, the data show a large pressure discontinuity within the petroleum column between the 30/7a-Pl olisthostrome and the in-situ Joanne reservoirs. The in-situ Joanne Sands in 30/7a-Pl are part of the southwesterly pressure regime characterized by the 30j7a.-S and 30/7a-P7 wells, whilst the olisthostrome appears to be in pressure communication with the 30/7a-P3 and 30/7a-P9 wells. 

Hydrocarbon fluids in some of the Magnolia reservoirs are not well mixed. This is most evident in hydrocarbon gas character whose vertical variations are revealed by high resolution mud gas data. From MDT and mud gas data across one of the reservoirs, a vertical methane carbon isotope ((5 Cc,) gradient of as much as 2.5%o per 100 ft can be demonstrated to exist in the absence of a pressure discontinuity. Other fluid properties such as density and saturation pressure are correspondingly variable in this instance in the absence of compartmentalization. Similar, though usually not as abundantly sampled, examples of hydrocarbon compositional heterogeneities occur throughout the field. 

Explosions A release of energy that causes a pressure discontinuity or blast wave. Fireball The atmospheric burning of a fuel-air cloud in which the energy is mostly emitted in the form of radiant heat. The iimer core of the fuel release consists of... 

Fundamental theory also tells us there is an intimate connection. The fluctuation-dissipation (FD) theorem (7) relates dissipative quantities such as viscosity to the ever present fluctuations in equilibrium systems, such as correlations in local velocities. A significant statement about the viscosity can now be made. The dissipative quantity has the same kind of temperature and pressure discontinuities as does the correlation function. Thus, if we have a first-order diermodynamic transition then we expect the viscosity to display first-order character in its T-P behavior. This is the case. Since we predict an... 

There is a pressure discontinuity across a curved interface. Consider the example of an oil droplet (O) in water (W) (Fig. 1.4a). The droplet is spherical, so as to reduce its surface energy. Letting R be the radius, and displacing the 0/W interface through dii, the work done by capillary forces and pressure is given by ... 

Gradients depend on the ratio of time scales of various transport and chemical processes. Diffusion (conduction) time scales can easily be estimated from the square of the corresponding length scale divided by the diffusivity (thermal diffusivity). Temperature usually has a fairly small effect on transport time scales (an exception is surface diffusion that is often activated). On the other hand, the time scale of reaction depends very strongly on the chemistry (process) itself and the temperature (via Arrhenius kinetics) and secondary on species concentrations and pressure. Discontinuity at the walls (e.g. slip, lack of thermal accommodation) may also be encountered, but since these phenomena depend on transverse gradients, which are smaller than in large devices, are by-and-large less important in microdevices (I). 

Before integrating the above two equations, an assumption was made that the pressure, p, remains constant, the same as that of the feed solution throughout the membrane cross-section. The pressure falls from the upstream pressure to the downstream pressure discontinuously at the permeate side of the membrane, as illustrated in Figure 5.5. Therefore, the second term of the right-hand side of Equations 5.206 and 5.207 is ignored, and the flux equations become exactly the same as that of solute species (the second species) in reverse osmosis. 

The basic relationships among the properties of a blast wave having a sharp front at which there is a sudden pressure discontinuity, i.e. a true shock front, are given in Tables 9.2-9.S and Fig. 9.5 respectively. 

Figure 6.2. Propagation of velocity and pressure discontinuity during water hammer phenomenon...

Instead of temperature fields, one can use pressure discontinuities in order to probe charge or polarization distributions in dielectrics. According to the pressure excitation method, one can distinguish three basic configurations (a) the LIPP (laser-induced pressure pulse. Fig. 21) (Sessler et al. 1981) or PWP (pressure wave propagation) technique (Alquie et al. 1981), (b) the piezoelectrically generated pressure step technique (PPS, cf. Fig. 22) (Eisenmenger and Haardt 1982), and (c) the pulsed electroacoustic method (PEA, cf Fig. 23) (Takada et al. 1987). 

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