Thermodynamics

Chapter 7 | 353Therefore, the error involved in approximating liquid methane as an incompressiblesubstance isError 0 ¢s actual ¢s ideal 0 |0.270 0.303| 0.122 (or 12.2%)¢s actual 0.270Discussion This result is not surprising since the density of liquid methanechanges during this process from 425.8 to 415.2 kg/m 3 (about 3 percent),which makes us question the validity of the incompressible substanceassumption. Still, this assumption enables us to obtain reasonably accurateresults with less effort, which proves to be very convenient in the absence ofcompressed liquid data.EXAMPLE 7–8Economics of Replacing a Valve by a TurbineA cryogenic manufacturing facility handles liquid methane at 115 K and 5MPa at a rate of 0.280 m 3 /s . A process requires dropping the pressure ofliquid methane to 1 MPa, which is done by throttling the liquid methane bypassing it through a flow resistance such as a valve. A recently hired engineerproposes to replace the throttling valve by a turbine in order to producepower while dropping the pressure to 1 MPa. Using data from Table 7–1,determine the maximum amount of power that can be produced by such aturbine. Also, determine how much this turbine will save the facility fromelectricity usage costs per year if the turbine operates continuously (8760h/yr) and the facility pays $0.075/kWh for electricity.Solution Liquid methane is expanded in a turbine to a specified pressureat a specified rate. The maximum power that this turbine can produce andthe amount of money it can save per year are to be determined.Assumptions 1 This is a steady-flow process since there is no change withtime at any point and thus m CV 0, E CV 0, and S CV 0. 2 The turbineis adiabatic and thus there is no heat transfer. 3 The process isreversible. 4 Kinetic and potential energies are negligible.Analysis We take the turbine as the system (Fig. 7–30). This is a controlvolume since mass crosses the system boundary during the process. We notethat there is only one inlet and one exit and thus ṁ 1 ṁ 2 ṁ.The assumptions above are reasonable since a turbine is normally wellinsulated and it must involve no irreversibilities for best performance andthus maximum power production. Therefore, the process through the turbinemust be reversible adiabatic or isentropic. Then, s 2 s 1 andState 1:hP 1 5 MPa 1 232.3 kJ>kgT 1 115 K f s 1 4.9945 kJ>kg # Kr 1 422.15 kg>sFIGURE 7–30A 1.0-MW liquified natural gas (LNG)turbine with 95-cm turbine runnerdiameter being installed in a cryogenictest facility.Courtesy of Ebara International Corporation,Cryodynamics Division, Sparks, Nevada.State 2:P 2 1 MPafhs 2 s 2 222.8 kJ>kg1Also, the mass flow rate of liquid methane ism # r 1 V # 1 1422.15 kg>m 3 210.280 m 3 >s2 118.2 kg>s