An overall balance around part of a plant involves three inlets and two outlets

Question

An overall balance around part of a plant involves three inlets and two outlets which only contain water. All streams are flowing at steady-state. The inlets are: 1) liquid at 25 deg C, m(dot)=54 kg/min; 2) steam at 1 MPa, 250 deg C, m(dot)=35 kg/min; 3) wet steam at 0.15 MPa, 90% quality, m(dot)=30 kg/min. The outlets are: 1) saturated steam at 0.8 MPa, m(dot)= 65 kg/min; 2) superheated steam at 0.2 MPa and 300 deg C, m(dot)=54 kg/min. Two kW of work are being added to the portion of the plant to run miscellaneous pumps and other process equipment, and no work is being obtained. What is the heat interaction for this portion of the plant in kW? Is heat being added or removed?

Explanation / Answer

Assume steady-state process Inlet1) sat liquid 25C, hi1=104.75kJ/kg Inlet2) superheated steam 250C 1MPa, hi2=2941.87 kJ/kg Inlet3) wet steam 0.15 MPa x=0.9, hi3=0.9(2693.35-467.18)+467.18=2470.73 kJ/kg Outlet1) sat vapor 0.8 MPa, ho1=2768.87 kJ/kg Outlet2) superheated steam 0.2MPa 300C, ho2=3071.4 kJ/kg First law: Q=-(mi1hi1+mi2hi2+mi3hi3)+(mo1ho1+mo2ho2)+W Q=-[(54/60)(104.75)+(35/60)(2941.87)+(30/60)(2470.73)]+[(65/60)(2768.87)+(54/60)(3071.4)]-2 Q=2716.14 kW (heat being added to the system)

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