Compressible fluids Calculation

The structure of the form is as shown in Figure 2.21. The calculation can be done for two correlations (1) Beggs and Brill and (2) Mukherjee and Brill. The existing calculation method uses only the vapor density as entered by the designer. The program does not calculate vapor density from the user input, as is the case for compressible fluid calculations. Therefore, the data entered in the cells inlet temperature, and vapor molecular weight will not be used for the calculation, and the designer may omit these cells. 

The following analysis enables one to calculate the diameter of a pipeline transporting any compressible fluid. The required inputs are volumetric flow rate, the specific gravity of the gas relative to air, flow conditions, compressibility factor Z where Z is defined by nZRT = PV, the pressure at the point of origin and the destination, the pipe length, and pipe constants such as effective roughness. The working equations have been obtained from the literature. Since the friction factor... 

All flowing gases and vapors (compressible fluids) including steam (w hich is a vapor) are limited or approach a maximum in mass flow velocity or rate, i.e., Ibs/sec or Ibs/hr through a pipe depending upon the specific upstream or starting pressure. This maximum rate of flow cannot be exceeded regardless of how much the dow nstream pressure is further reduced [3]. To determine the actual velocity in a pipe, calculate by... 

Relative roughness, pipe, 132 Friction losses, 181 also see Chapter 2 Friction, head loss, 68 Compressible fluids, 101 Factor, 68 Vacuum lines, 131 Gas constants, R, 378 Gravity settlers, 228 Head, 180-200 Calculations, 183, 184, 185 Discharge, 180, 187 Friction, 183 Liquid, 183... 

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 ... 

These asymptotic forms may be useful for conceptual studies, but the real design calculations must be based on the full Ergun equation. Turning to the case of compressible fluids, scaleup using geometric similarity with Sr = Sl = S is generally infeasible. Simply stated, the reactors are just too long and have too much inventory. 

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... 

The phenomenon of critical flow is well known for the case of single-phase compressible flow through nozzles or orifices. When the differential pressure over the restriction is increased beyond a certain critical value, the mass flow rate ceases to increase. At that point it has reached its maximum possible value, called the critical flow rate, and the flow is characterized by the attainment of the critical state of the fluid at the throat of the restriction. This state is readily calculable for an isen-tropic expansion from gas dynamics. Since a two-phase gas-liquid mixture is a compressible fluid, a similar phenomenon may be expected to occur for such flows. In fact, two-phase critical flows have been observed, but they are more complicated than single-phase flows because of the liquid flashing as the pressure decreases along the flow path. The phase change may cause the flow pattern transition, and departure from phase equilibrium can be anticipated when the expansion is rapid. Interest in critical two-phase flow arises from the importance of predicting dis-... 

When a compressible fluid, ie a gas, flows from a region of high pressure to one of low pressure it expands and its density decreases. It is necessary to take this variation of density into account in compressible flow calculations. In a pipe of constant cross-sectional area, the falling density requires that the fluid accelerate to maintain the same mass flow rate. Consequently, the fluid s kinetic energy increases. 

It is found convenient to base compressible flow calculations on an energy balance per unit mass of fluid and to work in terms of the fluid s specific volume V rather than the density p. The specific volume is the volume per unit mass of fluid and is simply the reciprocal of the density ... 

For the delivery of atomization gas, different types of nozzles have been employed, such as straight, converging, and converging-diverging nozzles. Two major types of atomizers, i.e., free-fall and close-coupled atomizers, have been used, in which gas flows may be subsonic, sonic, or supersonic, depending on process parameters and gas nozzle designs. In sonic or supersonic flows, the mass flow rate of atomization gas can be calculated with the following equation based on the compressible fluid dynamics ... 

Of course, for reactive flow calculations a new model would have to be constructed based on these techniques which used instead the equations governing compressible fluids and which contained the added chemical reactions and diffusive transport effects. 

When Eq. (11) is applied in design calculations, information must be available for determining the change in enthalpy over the range of temperature and pressure involved. The following illustrative examples show how Eq. (11) can be used to calculate pumping power when compressible fluids are involved. 

Flows are typically considered compressible when the density varies by more than 5 to 10 percent. In practice compressible flows are normally limited to gases, supercritical fluids, and multiphase flows containing gases. Liquid flows are normally considered incompressible, except for certain calculations involved in hydraulic transient analysis (see following) where compressibility effects are important even for nearly incompressible liquids with extremely small density variations. Textbooks on compressible gas flow include Shapiro Dynamics and Thermodynamics of Compressible Fluid Flow, vol. 1 and 11, Ronald Press, New York [1953]) and Zucrow and Hofmann (Gas Dynamics, vol. I and II, Wiley, New York [1976]). 

In all compressible fluid pressure drop calculations it is usually justifiable to evaluate the friction factor at the inlet conditions and to assume it constant. The variation because of the effect of temperature change on the viscosity and hence on the Reynolds number, at the usual high Reynolds numbers, is rarely appreciable. 

The excesses (deficits) were calculated with eqn (13). The KBIs for binary Lennard-Jones fluids were found in literature." The partial molar volumes and the isothermal compressibility were calculated using the Kirkwood-Buff... 

Gas phase viscosity data, iTq, are used in the design of compressible fluid flow and unit operations. For example, the viscosity of a gas is required to determine the maximum permissible flow through a given process pipe size. Alternatively, the pressure loss of a given flowrate can be calculated. Viscosity data are needed for the design of process equipment involving heat, momentum, and mass transfer operations. The gas viscosity of mixtures is obtained from data for the individual components in the mixture. 

COMPRESSIBLE FLUID FLOW CALCULATIONS IN A PIPE LINE ... 

THIS PROGRAM CALCULATES THE MAXIMUM COMPRESSIBLE FLUID RATE FOR A GIVEN PRESSURE LOSS AND FLUID SYSTEM CHARACTERISTICS. 

FORMAT (///,10X, COMPRESSIBLE FLUID FLOW CALCULATIONS IN A A) WRITE (1, 110)... 

C THIS PROGRAM CALCULATES THE PRESSURE DROP OF A COMPRESSIBLE FLUID... 

Interestingly, the activity of C. thermocellum in SCF ethane, SCF CO2, liquid propane, and gaseous propane does not follow the log P trends seen with liquid solvents. Thus, log P may be of limited value when applied to the correlation of metabolic activity in compressed solvents. The traditional definition of log P (25 °C and 0.1 MPa) was extended to our incubation conditions (60 °C and 7 MPa) using the group contribution associating equation of state (GCA-EOS) (48,49) to calculate the mole fraction of the dissolved compressed fluids in octanol and water. Log P logio(x,- /x,- )] correlated well with the total metabolic activity (ratio of total products formed in the treatment to the total products formed in the control) in liquid hydrocarbon solvents (Fig. 2) (37). 

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