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6. Thermodynamics Optimization The performance of the proposed organic Rankine cycle is optimized using a heat exchanger surface area based objective function [7, 10, 13]. The objective function used in this study is defined as the ratio of the total surface area of the heat exchangers to the useful output power as follows: ̇ where At is the total heat transfer surface area of the heat exchangers of the system in m2, and ̇ is the net power in kW. In the optimization process, the objective function is minimized considering the variable metric method with varying the pressure of the condenser and the temperature values at the expander inlet and condenser outlet as the decision variables. Superheating and subcooling are considered. The temperature of the rejected geothermal fluid is arranged to be not less than 80oC [12]. 7. Results and Discussion A complete thermodynamic analysis based on the first and second law is performed on the system shown in Fig. 1. The mass, energy, entropy and exergy balance equations are applied on each of the system components at steady state operation. The optimal designs of the ORC at four different values of the geothermal water inlet temperature are presented in Table 4. The calculations of the mass flow rate of the organic fluid, the corresponding geothermal fluid and cooling water are calculated. The temperature values at the turbine inlet and the amount of subcooling of the condenser outlet are also calculated and presented in Table 4. The results in Table 4 show that the exergy efficiency decreases gradually after increasing the temperature of the geothermal source over 165oC, based on the tested temperature values and the values of the optimal operating parameters. The corresponding T-s diagram of the organic Rankine cycle with the geothermal and cooling water is presented in Fig. 2. This diagram is for the case when geothermal temperature is at 165oC. Figs. 4 and 5 show the temperature profile with the total enthalpy change of the organic fluid for the evaporator and the condenser, respectively. The pinch temperature is shown to be taken at the inlet of the two phase flow section of the organic fluid at the evaporator at the saturated liquid condition, and at the inlet section of the two phase flow at the condenser at the saturated vapor condition of the organic fluid. The results shown in Figs. 5 to 13 represent the optimum performance condition at evaporator pressure of 33 bar and inlet temperature of 165oC for the geothermal water. The effect of the expander inlet temperature on the exergy destruction of the ORC components is demonstrated at Fig. 5. The exergy destruction occurs at the condenser, which represent about 38% of the total exergy destruction in the system, decreases with the increase of the expander inlet temperature. The evaporator exergy destruction increase with the increase of expander inlet temperature till it reach a maximum at about 10oC over the saturation temperature of the evaporator operating pressure and then starts to decrease. The regenerative heat exchanger has a considerable percentage of the total exergy destructions in the system and it increases in a linear form with the increase of the expander inlet temperature. The total exergy destruction in the ORC is also shown. Fig. 6 shows the effect of the evaporator pressure on the exergy destruction that occurs at the ORC 10PDF Image | Exergoeconomic Analyses and Optimization of Geothermal ORC
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