Actual compression work

The Carnot cycle plot represents ideal compression work. But we in the process industry have to worry about actual compression work, and the loss of compression efficiency caused by these three problems. 

The area enclosed by the solid line is the total or actual compression work. The area enclosed by the dotted line is ideal or useful compression work. The areas between the dotted line and the solid line represent compression work lost to heat. The area inside the dotted line, divided by the area inside the solid line, is called adiabatic compressor efficiency. 

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 ... 

The isentropic efficiency, r , is defined as the ratio of the isentropic specific work, —Wj, to the actual specific work, — w, associated with compressing the gas from inlet pressure, po, to section outlet pressure, pi. ... 

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

The actual power needed for the compression is the product of the actual specific work and the flow rate... 

We may use equation (17.67) to re-express the actual compression power in terms of isentropic specific work and isentropic efficiency ... 

The expression for the temperature ratio in an actual compression may be found by substituting into equation (17.61) to give the actual specific work ... 

Methods of Testing. ASTM tests for various concrete masonry units are available. These consist of compressive strength and sometimes per cent moisture and rupture modulus tests at a 28-day period. Compressive tests are often made by core-sampling actual construction work during early stages. To avoid waiting, 7-day tests are made and related to 28-day tests as follows ... 

The first step in troubleshooting reciprocating compressors is to quantify the extent of the problem. How much compression work has actually been lost An approximate rule of thumb is ... 

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 ... 

Compression efficiency is the ratio of the work required to adiabatically compress a gas to the work actually done within the compressor cylinder as shown by indicator cards. Figures 12-12 and 12-16. The heat generated during compression adds to the work that must be done in the cylinder. Valves may vary from 50-95% efficient depending on cylinder design and the ratio of compression. Compression efficiency (or sometimes termed volumetric efficiency) is affected by several details of the systems ... 

Horsepower is the work done in a cylinder on the gas by the piston connected to the driver during the complete compression cycle. The theoretical horsepower is that required to isen-tropically (adiabatically) compress a gas through a specified pressure range. The indicated horsepower is the actual work of compression developed in the compressor cylinder(s) as determined from an indicator card. Brake horsepower (bhp) is the actual horsepower input at the crankshaft of the compressor drive. It does not include the losses in the driver itself, but is rather the actual net horsepower that the driver must deliver to the compressor crankshaft. 

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 ... 

Figure 15.5 shows the ideal open cycle for the gas turbine that is based on the Brayton Cycle. By assuming that the chemical energy released on combustion is equivalent to a transfer of heat at constant pressure to a working fluid of constant specific heat, this simplified approach allows the actual process to be compared with the ideal, and is represented in Figure 15.5 by a broken line. The processes for compression 1-2 and expansion 3-4 are irreversible adiabatic and differ, as shown from the ideal isentropic processes between the same pressures P and P2 -... 

The work done in a reversible compression will be considered first because this refers to the ideal condition for which the work of compression is a minimum a reversible compression would have to be carried out at an infinitesimal rate and therefore is not relevant in practice. The actual work done will be greater than that calculated, not only because of irreversibility, but also because of frictional loss and leakage in the compressor. These two factors are difficult to separate and will therefore be allowed for in the overall efficiency of the machine. 

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