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the separator. Therefore, the holdup mass of pentane vapor in the lower part of separator is added to the total holdup mass of pentane in the vaporizer. 2. There is a temperature gradient in the separator along the diameter towards the vertical direction. To approximate it, the upper half of the separator is assumed responsible for the superheating. 3. The holdup mass of pentane in the upper half of the separator is negligible. 4. Heat capacity of the material of the vaporizer/separator is negligible. The Biot number of combined vaporizer and separator is 0.00433 (<0.1) which justifies such assumption (Holman 1992). 5. Heat loss to the environment is negligible. Using the above assumptions, the heat balance equation of the vaporizer in lumped parameter form is given as follows: Figure 4: Simplified cross-sectional view of the vaporizer Sohel et al. d•V• dt(Mlh2a+Mvh2b)=m2h2+Q −m2bh2b (1) Here, Ml is the holdup mass of liquid; h2a is the enthalpy of the holdup liquid; Mv is the holdup mass of vapour; h2b is the enthalpy of the holdup vapour; • is the mass flow of m2 inlet liquid; h2 is the enthalpy of inlet liquid; QV is the heat input in the vaporizer and lower half of theseparator; and • is the mass flow of outlet vapour. m2b Figure 3: Schematic diagram of the vaporizer and separator Figure 5: Simplified cross sectional view of the separator The heat transfer from the brine to the working fluid is calculated from the following equation. QT =UTAT∆tmT (2) Where, UT is the overall heat transfer coefficient, AT is the total effective heat transfer area of the vaporizer and the separator and ∆tmT is the combined log mean temperature deference (LMTD) and calculated as: ∆tmT =(Ti,B −T3)−(To,B −T2a) (3) ln (Ti,B −T3) (To,B −T2a) Unfortunately, it is not possible to calculate the LMTD for the vaporizer and the separator separately. In the ORC cycle, the outlet temperature of the brine from the separator before entering the vaporizer is not known. Therefore, the LMTD for the combined vaporizer and separator was used. The value of the overall heat transfer coefficient for the combined vaporizer and separator is calculated using the following approximated equation as presented by Bai et al. (Bai et al. 2004) taken from experimental results presented by Nakaoka and Uehara (Nakaoka and Uehara 1988). 3PDF Image | Dynamic Modelling and Simulation of an Organic Rankine Cycle Unit of a Geothermal Power Plant
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