Pressure drop Compressible fluids

Fig. 5.7(a) Vomeronasal pump (vasomotor activation and control of VN fluid contents) reciprocal compression/relaxation of lumenal and vascular volumes, vi/ve = internal/ external simus vessels, (a) Fluid intake — lumen expanded/vessels relaxed — pressure drops, (b) Fluid expulsion — lumen compressed/vessels expanded — pressure rise (from Schilling, 1970). 

Gas has a much higher compressibility than oil or water, and therefore expands by a relatively large amount for a given pressure drop. As underground fluids are withdrawn (i.e. production occurs), any free gas present expands readily to replace the voidage, with only a small drop in reservoir pressure. If only oil and water were present in the reservoir system, a much greater reduction in reservoir pressure would be experienced for the same amount of production. 

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%. 

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... 

Friction Pressure Drop For Compressible Fluid Flow... 

Simplified Flow Formula For Compressible Fluids Pressure Drop, Rate of Flow and Pipe Sizes ... 

This maximum velocity of a compressible fluid in a pipe is limited by the velocity of propagation of a pressure wave that travels at the speed of sound in the fluid [3]. This speed of sound is specific for each individual gas or vapor or liquid and is a function of the ratio of specific heats of the fluid. The pressure reduces and the velocity increases as the fluid flows downstream through the pipe, wdth the maximum velocity occurring at the downstream end of the pipe. WTien, or if, the pressure drop is great enough, the discharge or exit or outlet velocity will reach the velocity of sound for that fluid. 

If the outlet or discharge pressure is lowered further, the pressure upstream at the origin will not detect it because the pressure w ave can only travel at sonic velocity. Therefore, the change in pressure dow nstream w ill not be detected upstream. The excess pre.ssure drop obtained by lowering the outlet pressure after the maximum discharge has been reached takes place beyond the end of the pipe [3]. This pressure is lost in shock waves and turbulence of the jetting fluid. See References 12, 13, 24, and 15 for further expansion of shock waves and detonadon waves through compressible fluids. 

Scope, 52 Basis, 52 Compressible Flow Vapors and Gases, 54 Factors of Safety for Design Basis, 56 Pipe, Fittings, and Valves, 56 Pipe, 56 Usual Industry Pipe Sizes and Classes Practice, 59 Total Line Pressure Drop, 64 Background Information, 64 Reynolds Number, R,. (Sometimes used Nr ), 67 Friction Factor, f, 68 Pipe—Relative Roughness, 68 Pressure Drop in Fittings, Valves, Connections Incompressible Fluid, 71 Common Denominator for Use of K Factors in a System of Varying Sizes of Internal Dimensions, 72 Validity of K Values,... 

Methods have been given for the calculation of the pressure drop for the flow of an incompressible fluid and for a compressible fluid which behaves as an ideal gas. If the fluid is compressible and deviations from the ideal gas law are appreciable, one of the approximate equations of state, such as van der Waals equation, may be used in place of the law PV = nRT to give the relation between temperature, pressure, and volume. Alternatively, if the enthalpy of the gas is known over a range of temperature and pressure, the energy balance, equation 2.56, which involves a term representing the change in the enthalpy, may be employed ... 

For the flow of a compressible fluid, conditions of sonic velocity may be reached, thus limiting the maximum flowrate for a given upstream pressure. This situation can also occur with two-phase flow, and such critical velocities may sometimes be reached with a drop in pressure of only 30 per cent of the inlet pressure. 

The same result is obtained when the fluid is compressible, as may be seen by substituting Sr = Si = S into Equations (3.40) and (3.41). Thus, using geometric similarity to scale isothermal, laminar flows gives constant pressure drop provided the flow remains laminar upon scaleup. The large and small reactors will have the same inlet pressure if they are operated at the same outlet pressure. The inventory and volume both scale as S. 

As will be outlined below, the computation of compressible flow is significantly more challenging than the corresponding problem for incompressible flow. In order to reduce the computational effort, within a CED model a fluid medium should be treated as incompressible whenever possible. A rule of thumb often found in the literature and used as a criterion for the incompressibility assumption to be valid is based on the Mach number of the flow. The Mach number is defined as the ratio of the local flow velocity and the speed of sound. The rule states that if the Mach number is below 0.3 in the whole flow domain, the flow may be treated as incompressible [84], In practice, this rule has to be supplemented by a few additional criteria [3], Especially for micro flows it is important to consider also the total pressure drop as a criterion for incompressibility. In a long micro channel the Mach number may be well below 0.3, but owing to the small hydraulic diameter of the channel a large pressure drop may be obtained. A pressure drop of a few atmospheres for a gas flow clearly indicates that compressibility effects should be taken into account. 

The pressure drop equations apply to liquids. They also apply to compressible fluids for non-critical flow and AP < 10% Pb... 

S.5.2 Transient two-phase-flow pressure drop. Calculation of transient behavior in a complex flow network containing a compressible fluid in two-phase states was... 

Aladyev et al. (1961) demonstrated that, with a compressible volume connected at the inlet of a test section, the flow oscillates and hence lowers the CHF. Flow fluctuation in the test section also depends on the compressibility of fluid upstream and on the pressure drop through the test section. Because the compressibility of water is approximately a function of temperature alone, the inlet temperature affects the boiling crisis. 

Notice that the superficial mass velocity G is constant throughout the bed, but that p will vary for compressible fluids. When the pressure drop is small compared with the absolute pressure, equation 12.7.4 may be used for gases by employing the arithmetic average of the inlet and... 

The actual vapor heat pump cycle deviates from the ideal cycle primarily because of inefficiency of the compressor, pressure drops associated with fluid flow and heat transfer to or from the surroundings. The vapor entering the compressor must be superheated slightly rather than a saturated vapor. The refrigerant entering the throttling valve is usually compressed liquid rather than a saturated liquid. 

Note that while the fluid density may be a function of the pressure in the bed in a compressible flow, the superficial mass velocity is constant. The Ergun equation in the form given in eq. (3.450) is more convenient when analyzing the effects of pressure drop in the fluid density. 

---