Fluid compressible

A static bottom hole pressure survey (SBHP) is useful for determining the reservoir pressure near the well, undisturbed by the effects of production. This often cannot be achieved by simply correcting a surface pressure measurement, because the tubing contents may be unknown, or the tubing contains a compressible fluid whose density varies with pressure (which itself has an unknown profile). 

As already explained the necessity to satisfy the BB stability condition restricts the types of available elements in the modelling of incompressible flow problems by the U-V P method. To eliminate this restriction the continuity equation representing the incompressible flow is replaced by an equation corresponding to slightly compressible fluids, given as... 

Compressible Vlow. The flow of easily compressible fluids, ie, gases, exhibits features not evident in the flow of substantially incompressible fluid, ie, Hquids. These differences arise because of the ease with which gas velocities can be brought to or beyond the speed of sound and the substantial reversible exchange possible between kinetic energy and internal energy. The Mach number, the ratio of the gas velocity to the local speed of sound, plays a central role in describing such flows. 

S. C. Lin, E. L. Reslei, and A. R. Kantiowitz,/. Appl Phjs. 26(1), 83—95 (fan. 1955) H. E. VetscReR, Approach to Equilibrium behind Strong Shock Waves in Argon, Pli.D. dissertation, Cornell University, Ithaca, N.Y., 1955 R. M. Patrick, Magnetohjdrodynamics of a Compressible Fluid, Pli.D. dissertation, Cornell University, Ithaca, N.Y., 1956 R. J. Rosa, EngineeringMagnetohjdrodynamics, Ph.D. dissertation, Cornell University, Ithaca, N.Y., 1956 J. Jukes, Ionic Heat Transfer to the Walls of a Shock Tube, Ph.D. dissertation, Cornell University, Ithaca, N.Y., (1956). 

Erequenfly, the term compressed fluid, a more general expression than supercritical fluid, is used. A compressed fluid can be either a supercritical fluid, a near-critical fluid, an expanded Hquid, or a highly compressed gas, depending on temperature, pressure, and composition. 

Gas AntisolventRecrystallizations. A limitation to the RESS process can be the low solubihty in the supercritical fluid. This is especially evident in polymer—supercritical fluid systems. In a novel process, sometimes termed gas antisolvent (GAS), a compressed fluid such as CO2 can be rapidly added to a solution of a crystalline soHd dissolved in an organic solvent (114). Carbon dioxide and most organic solvents exhibit full miscibility, whereas in this case the soHd solutes had limited solubihty in CO2. Thus, CO2 acts as an antisolvent to precipitate soHd crystals. Using C02 s adjustable solvent strength, the particle size and size distribution of final crystals may be finely controlled. Examples of GAS studies include the formation of monodisperse particles (<1 fiva) of a difficult-to-comminute explosive (114) recrystallization of -carotene and acetaminophen (86) salt nucleation and growth in supercritical water (115) and a study of the molecular thermodynamics of the GAS crystallization process (21). 

D. J. Dixon, "Formation of Polymeric Materials by Precipitation with a Compressed Fluid Antisolvent," Ph.D. Dissertation, University of Texas at Austin, Austin, Tex., 1992. 

J. J. H. Brouwers, On the Motion of a Compressible Fluid in a Rotating Cylinder., Doctoral Dissertation, The Technische Hogeschool, Twente, the Nethedands, June, 1976. 

A key limitation of sizing Eq. (8-109) is the limitation to incompressible flmds. For gases and vapors, density is dependent on pressure. For convenience, compressible fluids are often assumed to follow the ideal-gas-law model. Deviations from ideal behavior are corrected for, to first order, with nommity values of compressibihty factor Z. (See Sec. 2, Thvsical and Chemical Data, for definitions and data for common fluids.) For compressible fluids... 

Critical (or choked) Maxinriim flow condition for compressible fluids... 

For the compressible flow cases. Regimes 1 and 3, and Regime 2 with q, > q, making use of Eq. (26-90), integration of Eq. (26-93) gives Compressible Fluid Orifice Discharge by HEM... 

Discharge Coefficients and Gas Discharge A compressible fluid, upon discharge from an orifice, accelerates from the puncture point and the cross-sec tional area contracts until it forms a minimum at the vena contracta, If flow is choked, the mass flux G, can be found at the vena contrac ta, since it is a maximum at that point, The mass flux at the orifice is related to the mass flux at the vena contracta by the discharge coefficient, which is the area contraction ratio (A at the vena contracta to Ay at the orifice) ... 

Pressure Safety Valve (PSV) A safety valve is a spring loaded valve actuated by static pressure upstream of the valve and characterized by rapid opening or pop action. A safety valve is normally used with compressible fluids. 

Figure 2.3. A rigid piston drives a shock wave into compressible fluid in an imaginary flow tube with unit cross-sectional area. The shock wave moves at velocity U into fluid with initial state 0, which changes discontinuously to state 1 behind the shock wave. Particle velocity u is identical to the piston velocity.

Figure 2.8. An x-t diagram of a piston interacting with a compressible fluid. At the origin, the piston begins moving at constant velocity, generating a shock wave. At tj, the piston stops abruptly, generating rarefaction fan. Snapshots of wave profiles at times t2 and 3 are shown.

Harlow, F.H., Dynamics of Compressible Fluid, Los Alamos Scientific Laboratory, University of California Report No. LA-2412, Los Alamos, NM, 200 pp., November 1960. 

For compressible fluids one must be careful that when sonic or choking velocity is reached, further decreases in downstream pressure do not produce additional flow. This occurs at an upstream to downstream absolute pressure ratio of about 2 1. Critical flow due to sonic velocity has practically no application to liquids. The speed of sound in liquids is very liigh. See Sonic Velocity later in this chapter. 

This will give a conservative relief valve area. For compressible fluids use Ah corresponding to lAPi if head difference is greater than that corresponding to Pi (since sonic velocity occurs). If head difference is below that corresponding to APi use actual Ah. 

For compressible fluids, if the downstream head is less than % the upstream head, use the upstream head as Ah. Otherwise use the actual Ah. 

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%. 

The length of the column is also defined by the Poiseuille equation that describes the flow of a fluid through an open tube in terms of the tube radius, the pressure applied across the tube (column), the viscosity of the fluid and the linear velocity of the fluid. Thus, for a compressible fluid. 

For a compressible fluid that undergoes exansion through a valve or an orifice, the Joule-Thompson coefficient is defined as ... 

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