Bubble pressure drop

This paragraph will briefly present the most frequently used methods for measuring the surface and interfacial tensions as a function of time the maximum bubble pressure, drop volume, growing bubble/drop, bubble/drop shape, and other methods. 

The interfacial tension, y, in the Gibbs adsorption equation is used for equilibrium conditions as bitumen components are adsorbed. Measurement techniques available are extensive. Some of these methods are duNouy ring, maximum bubble pressure, drop volume, Wilmhelmy plate, sessile drop, spinning drop, pendant drop, capillary rise, oscillating jet, and capillary ripples. These and many others are referenced extensively by Malhotra and Wasan (153). These authors also showed that there is no correlation between emulsion stability and interfacial tension. The nature of the film dominates stability. Some relationships between interfacial tensions and crude oil properties follow. 

Using this mixture as an example, consider starting at pressure A and isothermally reducing the pressure to point D on the diagram. At point A the mixture exists entirely in the liquid phase. When the pressure drops to point B, the first bubble of gas is evolved, and this will be a bubble of the lighter component, ethane. As the pressure continues to drop, the gas phase will acquire more of the heavier component and hence the liquid volume decreases. At point C, the last drop of liquid remaining will be composed of the heavier component, which itself will vaporise as the dew point is crossed, so that below... 

For both volatile oil and blaok oil the initial reservoir temperature is below the critical point, and the fluid is therefore a liquid in the reservoir. As the pressure drops the bubble point is eventually reached, and the first bubble of gas is released from the liquid. The composition of this gas will be made up of the more volatile components of the mixture. Both volatile oils and black oils will liberate gas in the separators, whose conditions of pressure and temperature are well inside the two-phase envelope. 

Black oils are a common category of reservoir fluids, and are similar to volatile oils in behaviour, except that they contain a lower fraction of volatile components and therefore require a much larger pressure drop below the bubble point before significant volumes of gas are released from solution. This is reflected by the position of the iso-vol lines in the phase diagram, where the lines of low liquid percentage are grouped around the dew point line. 

As the reservoir pressure drops from the initial reservoir pressure towards the bubble point pressure (PJ, the oil expands slightly according to its compressibility. However, once the pressure of the oil drops below the bubble point, gas is liberated from the oil, and the remaining oil occupies a smaller volume. The gas dissolved in the oil is called the solution gas, and the ratio of the volume gas dissolved per volume of oil is called the solution gas oil ratio (Rg, measured in scf/stb of sm /stm ). Above the bubble point, Rg is constant and is known as the initial solution gas oil ratio (Rgj), but as the pressure falls below the bubble point and solution gas is liberated, Rg decreases. The volume of gas liberated is (Rg - Rg) scf/stb. 

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... 

Solution gas drive occurs in a reservoir which contains no initial gas cap or underlying active aquifer to support the pressure and therefore oil is produced by the driving force due to the expansion of oil and connate water, plus any compaction drive.. The contribution to drive energy from compaction and connate water is small, so the oil compressibility initially dominates the drive energy. Because the oil compressibility itself is low, pressure drops rapidly as production takes place, until the pressure reaches the bubble point. 

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. 

The basic concepts of a gas-fluidized bed are illustrated in Figure 1. Gas velocity in fluidized beds is normally expressed as a superficial velocity, U, the gas velocity through the vessel assuming that the vessel is empty. At a low gas velocity, the soHds do not move. This constitutes a packed bed. As the gas velocity is increased, the pressure drop increases until the drag plus the buoyancy forces on the particle overcome its weight and any interparticle forces. At this point, the bed is said to be minimally fluidized, and this gas velocity is termed the minimum fluidization velocity, The bed expands slightly at this condition, and the particles are free to move about (Fig. lb). As the velocity is increased further, bubbles can form. The soHds movement is more turbulent, and the bed expands to accommodate the volume of the bubbles. 

Successive reflections of the pressure wave between the pipe inlet and the closed valve result in alternating pressure increases and decreases, which are gradually attenuated by fluid friction and imperfect elasticity of the pipe. Periods of reduced pressure occur while the reflected pressure wave is travehng from inlet to valve. Degassing of the liquid may occur, as may vaporization if the pressure drops below the vapor pressure of the liquid. Gas and vapor bubbles decrease the wave velocity. Vaporization may lead to what is often called liquid column separation subsequent collapse of the vapor pocket can result in pipe rupture. 

Cavitation Loosely regarded as related to water hammer and hydrauhc transients because it may cause similar vibration and equipment damage, cavitation is the phenomenon of collapse of vapor bubbles in flowing liquid. These bubbles may be formed anywhere the local liquid pressure drops below the vapor pressure, or they may be injected into the hquid, as when steam is sparged into water. Local low-pressure zones may be produced by local velocity increases (in accordance with the Bernouhi equation see the preceding Conservation Equations subsection) as in eddies or vortices, or near bound-aiy contours by rapid vibration of a boundaiy by separation of liquid during water hammer or by an overaU reduction in static pressure, as due to pressure drop in the suction line of a pump. 

Bubble-Tube Systems The commonly used bubble-tube system sharply reduces restrictions on the location of the measuring element. In order to ehminate or reduce variations in pressure drop due to the gas flow rate, a constant differential regulator is commonly employed to maintain a constant gas flow rate. Since the flow of gas through the bubble tube prevents entiy of the process liquid into the measuring system, this technique is particularly usefiil with corrosive or viscous liquids, liquids subjec t to freezing, and hquids containing entrained solids. 

The plate thickness of bubble-cap and sieve plates is generally estabhshed by mechanical design factors and has little effect on pressure drop. For a sieve plate, however, the plate is an integral component of the vapor-dispersion system, and its thickness is important. 

Pressure Drop Methods for estimating fluid-dynamic behavior of crossflow plates are analogous, whether the plates be bubble-cap, sieve, or valve. The total pressure drop across a plate is defined by the general equation (see Fig. 14-29)... 

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