Ideal gas compression

For an ideal gas compression, the corresponding temperature rise is given by (see Appendix B) ... 

Equations B.49 and B.47 minimize the overall compression power for an A-stage compression. However, the basis is for adiabatic ideal gas compression and therefore not strictly valid for real gas compression (see Appendix B). It is also assumed that intermediate cooling is back to initial conditions, which might not be the case with real intercoolers. The power for the corresponding expression for a poly tropic compression is given by ... 

Note that the volume changes for the last two processes are identical. We note also that for the liquid phases at room temperature k1t is much smaller than 1 atm-1 (e.g., for water at 0°C, kTxT 1 cm3 mol-1, AV 20 cm3 mol-1, and kT / atm w2x 104cm3 mol-1). Similarly, in equation (7.73) k1t < i P-1 (the limit of an ideal-gas phase). Thus, the volume change for the three standard processes is dominated by the terms which originate from the ideal-gas compressibility. Because of this undesirable feature, it is common to abandon these processes when studying the volume of solvation. Almost all researchers who study the solvation phenomena apply one of these standard processes for quantities like the Gibbs energy, entropy and enthalpy of... 

Therefore, this physically based compressibility index n = l/xad lies between n = 0, i.e. incompressible stiff bulk material and n = 1, i.e. ideal gas compressibility, see Fig. 4 above. Considering the predominant plastic and viscous particle contact deformation and rearrangement in the stochastic homogeneous packing of a cohesive powder, following values of compressibility index are to be suggested, see Table 2. 

Determine the fraction of throughput energy required to compress hydrogen gas from 0.1 to 70 MPa assuming an isothermal, ideal gas compression process. How would nonideal gas effects affect the result ... 

The above equation is valid at low pressures where the assumptions hold. However, at typical reservoir temperatures and pressures, the assumptions are no longer valid, and the behaviour of hydrocarbon reservoir gases deviate from the ideal gas law. In practice, it is convenient to represent the behaviour of these real gases by introducing a correction factor known as the gas deviation factor, (also called the dimensionless compressibility factor, or z-factor) into the ideal gas law ... 

It suffices to carry out one such experiment, such as the expansion or compression of a gas, to establish that there are states inaccessible by adiabatic reversible paths, indeed even by any adiabatic irreversible path. For example, if one takes one mole of N2 gas in a volume of 24 litres at a pressure of 1.00 atm (i.e. at 25 °C), there is no combination of adiabatic reversible paths that can bring the system to a final state with the same volume and a different temperature. A higher temperature (on the ideal-gas scale Oj ) can be reached by an adiabatic irreversible path, e.g. by doing electrical work on the system, but a state with the same volume and a lower temperature Oj is inaccessible by any adiabatic path. 

The first tenn in the compressibility equation is the ideal gas temi and the second temi, the integral of g r)- ... 

Calculation of Actual Work of Compression For simplicity, the work of compression is calciilated by the equation for an ideal gas in a three-stage reciprocating machine with complete intercoohng and with isentropic compression in each stage. The work so calculated is assumed to represent 80 percent of the actual work. The following equation may be found in any number of textbooks on thermodynamics ... 

Isothermal Gas Flow in Pipes and Channels Isothermal compressible flow is often encountered in long transport lines, where there is sufficient heat transfer to maintain constant temperature. Velocities and Mach numbers are usually small, yet compressibihty effects are important when the total pressure drop is a large fraction of the absolute pressure. For an ideal gas with p = pM. JKT, integration of the differential form of the momentum or mechanical energy balance equations, assuming a constant fric tion factor/over a length L of a channel of constant cross section and hydraulic diameter D, yields,... 

With flashes carried out along the appropriate thermodynamic paths, the formalism of Eqs. (6-139) through (6-143) applies to all homogeneous equihbrium compressible flows, including, for example, flashing flow, ideal gas flow, and nonideal gas flow. Equation (6-118), for example, is a special case of Eq. (6-141) where the quahty x = and the vapor phase is a perfect gas. 

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... 

Compressibility of Natural Gas All gases deviate from the perfect gas law at some combinations of temperature and pressure, the extent depending on the gas. This behavior is described by a dimensionless compressibility factor Z that corrects the perfect gas law for real-gas behavior, FV = ZRT. Any consistent units may be used. Z is unity for an ideal gas, but for a real gas, Z has values ranging from less than 1 to greater than 1, depending on temperature and pressure. The compressibihty faclor is described further in Secs. 2 and 4 of this handbook. 

It follows that the efficiency of the Carnot engine is entirely determined by the temperatures of the two isothermal processes. The Otto cycle, being a real process, does not have ideal isothermal or adiabatic expansion and contraction of the gas phase due to the finite thermal losses of the combustion chamber and resistance to the movement of the piston, and because the product gases are not at tlrermodynamic equilibrium. Furthermore the heat of combustion is mainly evolved during a short time, after the gas has been compressed by the piston. This gives rise to an additional increase in temperature which is not accompanied by a large change in volume due to the constraint applied by tire piston. The efficiency, QE, expressed as a function of the compression ratio (r) can only be assumed therefore to be an approximation to the ideal gas Carnot cycle. 

Ideal gas obeys the equation of state PV = MRT or P/p = MRT, where P denotes the pressure, V the volume, p the density, M the mass, T the temperature of the gas, and R the gas constant per unit mass independent of pressure and temperature. In most cases the ideal gas laws are sufficient to describe the flow within 5% of actual conditions. When the perfect gas laws do not apply, the gas compressibility factor Z can be introduced ... 

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%. 

Since non-ideal gases do not obey the ideal gas law (i.e., PV = nRT), corrections for nonideality must be made using an equation of state such as the Van der Waals or Redlich-Kwong equations. This process involves complex analytical expressions. Another method for a nonideal gas situation is the use of the compressibility factor Z, where Z equals PV/nRT. Of the analytical methods available for calculation of Z, the most compact one is obtained from the Redlich-Kwong equation of state. The working equations are listed below ... 

The pressure vessel under consideration in this subsection is spherical and is located far from surfaces that might reflect the shock wave. Furthermore, it is assumed that the vessel will fracture into many massless fragments, that the energy required to mpture the vessel is negligible, and that the gas inside the vessel behaves as an ideal gas. The first consequence of these assumptions is that the blast wave is perfectly spherical, thus permitting the use of one-dimensional calculations. Second, all energy stored in the compressed gas is available to drive the blast wave. Certain equations can then be derived in combination with the assumption of ideal gas behavior. 

Deviations from Ideal Gas Laws Compressibility See Figures 12-13A-D. 

The ideal gas law or perfect gas law is a combination of Boyle s and Charles laws for any compressible fluid (gas/vapor). 

The solution of the work compression part of the compressor selection problem is quite accurate and easy when a pressure-enthalpy or Mollier diagram of the gas is available (see Figures 12-24A-H). These charts present the actual relationship of the gas properties under all conditions of the diagram and recognize the deviation from the ideal gas laws. In the range in which compressibility of the gas becomes significant, the use of the charts is most helpful and convenient. Because this information is not available for many gas mixtures, it is limited to those rather common or perhaps extremely important gases (or mixtures) where this information has been prepared in chart form. The procedure is as follows ... 

One pound-mole of an ideal gas is compressed at a constant pressure of 1 atm in a piston-like device from an initial volume of 1.5 ft to a final volume of 0.5 ft. The internal energy is known to decrease by 20 Btu. How much heat was transferred to or from the gas ... 

The physical laws of thermodynamics, which define their efficiency and system dynamics, govern compressed-air systems and compressors. This section discusses both the first and second laws of thermodynamics, which apply to all compressors and compressed-air systems. Also applying to these systems are the ideal gas law and the concepts of pressure and compression. 

Compressibility is experimentally derived from data about the actual behavior of a particular gas under pVT changes. The compressibility factor, Z, is a multiplier in the basic formula. It is the ratio of the actual volume at a given pT condition to ideal volume at the same pT condition. The ideal gas equation is therefore modified to ... 

Example 1.4 A volume of an ideal gas in a cylinder and at atmospheric pressure is compressed to half the volume at constant temperature. What is the new pressure ... 

Molecules are much closer to one another in liquids and solids. In the gas state, particles are typically separated by ten molecular diameters or more in liquids or solids, they touch one another. This explains why liquids and solids have densities so much larger than those of gases. At 100°C and 1 atm, H20(/) has a density of 0.95 g/mL that of H20(g) under the same conditions is only 0.00059 g/mL For the same reason, liquids and solids are much less compressible than gases. When the pressure on liquid water is increased from 1 to 2 atm, the volume decreases by 0.0045% the same change in pressure reduces the volume of an ideal gas by 50%. 

Ideal Gases.—The state of unit mass of an ideal gas, undergoing adiabatic compression or expansion, is completely defined by the equations... 

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