Working equations compression

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 ... 

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... 

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 total work of compression from a pressure P to a pressure Pi is found by integrating equation 8.27. For an ideal gas undergoing an isothermal compression ... 

Thus, for a specified intercooler outlet temperature T2 for the gas and fixed inlet and outlet pressures Pi and P3, Equation B.53 predicts the intermediate pressure for minimum shaft work for compression of an ideal gas. The corresponding expression for a polytropic compression is given by replacing y by n in Equation B.53. Although Equation B.53 changes the intermediate pressure for an intercooler temperature different from the inlet temperature, the effect on the overall shaft work for compression is often insensitive to modest deviations of the intercooler temperature from the inlet temperature. 

From equation 6.12, the shaft work of compression W required to compress unit mass of gas from pressure P to pressure P2 in a reversible frictionless process, in which changes in potential and kinetic energy are negligible, is... 

Equation 6.89 gives the theoretical adiabatic work of compression from pressure P to pressure P2. 

This chapter establishes the basis for the Second Law of Thermodynamics. It is not critical that you read this chapter to be able to understand the more practical chapters on compression that follow. But, for those readers who have technical training, wouldn t it be lovely to actually understand the basis for the Second Law of Thermodynamics. Wouldn t it be grand to really see the beauty and simplicity of the basis for the adiabatic compression work equation ... 

A question that arises in connection with distillation processes is How does a vapor-compression process compare with a multiple-effect evaporation process on the basis solely of energy cost This is readily answered as follows. The work of compression as kilowatt-hours per 1000 gallons is given by a specific form of Equation VIII. 134... 

In Sec. 1.6 we derived an equation for the work of compression or expansion of a gas caused by the differential displacement of a piston in a cylinder ... 

Combining the equation for the work of compression with the isentropic expansion yields ... 

By integrating Equation 5.8 over an isentropic path using Equation (5.9), it can be shown that the work of compression for an ideal gas,... 

Because the work of compression should be a minimum, differentiate Equation 5.24 with respect to P2, and then set the derivative equal to zero. 

Let 0 = (n - l)/n and then differentiate Equation 5.30 with respect to P2. Then, set the derivative equal to zero to obtain the minimum work of compression. Thus. 

Assume one stage of compression, and calculate the polytropic work of compression given by Equation 5.7.1. Because the discharge temperature is un-... 

These equations follow from Eq. (2.3 2) when the small changes m potential and kinetic energy are neglected. The work of compression is simply ... 

Close to the critical conditions, these equations should not be used. The procedure for calculation of polytropic work of compression or expansion close to the critical point is more complex (Shultz, 1962), and it is easiest to make such calculations using process simulation programs. 

To obtain an equation for calculating the work of compression, first apply Bernoulli s equation, Equation 5.1, across the compressor. The first term, the kinetic energy term, is small compared to the other terms in the balance. The second term is the change in potential energy, and it is also small. The last two terms are the work done by the system and the friction loss. First, we consider frictionless flow. Thus, the compressor work,... 

Extensive investigation of the monolayer isotherm behavior at the n-heptane and isooctane/aqueous NaCl interfaces (8) has shown that d r(trans)dr and AA s for each film the heats of transition can be calculated from the two-dimensional Clapeyron equation (3). Based upon the variation observed in the heats calculated in a previous study these heats are not significantly different, even at 3°C. In contrast, however (see both isotherms of Figure 1 and data of Table I), the work of compression from high areas to the area at which phase separation begins depends... 

Combining equations (17.63) and (17.64), the actual specific work of compression is given by ... 

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