Bubble migration 233 pressure

Discovery pressure, also called initial reservoir pressure, will not be below the bubble-point pressure of the reservoir oil. If reservoir pressure were below the bubble-point pressure of the liquid, gas would have formed and migrated to the top of the reservoir. 

The set time should correspond closely with the end of the reaction of aluminium to form hydrogen. Otherwise, if the set is delayed, too many of the hydrogen bubbles migrate to the surface causing the cake to subside, and, in extreme cases, to collapse. Conversely, if the set occurs too early, the ongoing evolution of hydrogen produces internal pressures which can cause cracks within the mix and a consequent loss of strength. 

A volatile oil contains a relatively large fraction of lighter and intermediate oomponents which vaporise easily. With a small drop in pressure below the bubble point, the relative amount of liquid to gas in the two-phase mixture drops rapidly, as shown in the phase diagram by the wide spacing of the iso-vol lines. At reservoir pressures below the bubble point, gas is released In the reservoir, and Is known as solution gas, since above the bubble point this gas was contained in solution. Some of this liberated gas will flow towards the producing wells, while some will remain in the reservoir and migrate towards the crest of the structure to form a secondary gas cap. 

If, however, the reservoir pressure drops below the bubble point, then gas will be liberated in the reservoir. This liberated gas may flow either towards the producing wells under the hydrodynamic force imposed by the lower pressure at the well, or it may migrate... 

Resistance functions have been evaluated in numerical compu-tations15831 for low Reynolds number flows past spherical particles, droplets and bubbles in cylindrical tubes. The undisturbed fluid may be at rest or subject to a pressure-driven flow. A spectral boundary element method was employed to calculate the resistance force for torque-free bodies in three cases (a) rigid solids, (b) fluid droplets with viscosity ratio of unity, and (c) bubbles with viscosity ratio of zero. A lubrication theory was developed to predict the limiting resistance of bodies near contact with the cylinder walls. Compact algebraic expressions were derived to accurately represent the numerical data over the entire range of particle positions in a tube for all particle diameters ranging from nearly zero up to almost the tube diameter. The resistance functions formulated are consistent with known analytical results and are presented in a form suitable for further studies of particle migration in cylindrical vessels. 

Near the top of the hydrocyclone there will be some short-circuiting of the flow between the inlet and the overflow, although the effects are reduced as a result of the formation of circulating eddies, often referred to as the mantle, which tend to act as a barrier. Within the secondary vortex the pressure is low and there is a depression in the liquid surface in the region of the axis. Frequently a gas core is formed, and any gas dispersed in the form of fine bubbles, or coming out of solution, tends to migrate to this core. In pressurised systems, the gas core may be very much reduced in size, and sometimes completely eliminated. 

These observations about the bubble motion are the basis of all the bubble theories which lead to numerical predictions of bubble radius, migration and period. It is a common characteristic of such theories that changes in density of the water surrounding the bubble are neglected (the noncompressive approximation), and it is further assumed that the bubble retains a spherical form thruout its motion. From what has been said, it is evident that both these assumptions are plausible as far as the expanded phase of the motion is concerned. They must, however, be increasingly poor as the bubble approaches its minimum radius for which very much larger pressures and acceleration are involved... 

Most of the features of the theoretical treatment of bubble motion are present in the treatment that considers the water incompressible and neglects gravity effects. We quote from Cole (Ref 1, Chapt 8) The simplest approximation to the true motion of the bas bubble is the one in which it is assumed that the motion of the surrounding water is entirely radial and there is no vertical migration. In this approximation, which has been discussed by a number of writers, the hydrostatic buoyance resulting from differences in hydrostatic pressure at different depths is neglected. It is thus assumed that at an infinite distance from the bubble in any direction the pressure has the same value as the initial hydrostatic pressure P0 at the depth of the charge... 

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