Energy, exergy, emergy, and economic evaluation of a novel two-stage solar Rankine power plant

Abstract

This paper studies a solar-powered organic Rankine cycle-integrated cooling and electricity co-generation system. This system consists of a steam cycle, an organic Rankine cycle, the parabolic trough solar collectors’ field, and a gas turbine cycle as well as a cooling heat exchanger for the co-production of power and cooling. The steam generator in this cycle is a dual pressure system that works with the thermal energy received from the solar collectors. The proposed process is analyzed thermodynamically and economically using the novel emergoeconomic approach. Then, to find the optimum operating parameters of the power plant, multi-objective optimization is performed by implementing the novel water cycle algorithm. The objectives of this optimization process are to maximize the system’s efficiency and to minimize the monetary emergy rate of the products. This study shows an increase of 8% in the exergy efficiency (from 40.2 to 48.2%) after the optimization. The production cost decreased by 6.1% from 18.8 to 17.6 USD/GJ, and the emergoeconomic rate decreased by 18.9% from 27.1 to 22 sej/s. Furthermore, the power production in the proposed cycle compared to the base cycle increased by 111.7 MW in the gas cycle and 39.4 MW in the steam cycle.

Appendices

Appendix A

The thermodynamic model of the system has been achieved by considering a control volume around each component. The balance of energy in the control volume can be described as follows (Cengel and Boles 2002):

$${\dot{Q}}_{net,in}-{\dot{W}}_{net,out}=\sum_{out}\dot{m}h-\sum_{in}mh+{\left({m}_{2}{u}_{2}-{m}_{1}{u}_{1}\right)}_{system}$$

(11)

In this equation, the specific enthalpy and the internal energy are represented by h and u, mass flow rate and mass of the control volume are represented by $\dot{m}$ and m, and the net output work rate and heat transfer rate are shown as Ẇ and $\dot{Q}$. Due to their small values, the potential and kinetic terms are neglected to simplify the equation.

The mass balance of each component is considered using the following equation:

$${m}_{2}-{m}_{1}= \sum {\dot{m}}_{in}+\sum {\dot{m}}_{out}$$

(12)

By implementing the above equations, the required correlations for evaluating thermodynamic characteristics in the conventional components can be summarized in Table 10.

Table 10 Energy balance equations of the components used in the cogeneration plant

To model the solar unit, the outlet temperature of the collector, working pressure of the solar cycle, and solar heat exchanger effectiveness are assumed. The enthalpy of the theminol oil, which is used as the heat transfer fluid in the solar cycle, is calculated using the following equation (Abdelhay et al. 2020).

$${h}_{i}\text{=3.172}\times 1{0}^{-7}\times {{\text{T}}_{i}}^{3}\text{+10.99}\times 1{0}^{-4}\times {{\text{T}}_{i}}^{2}\text{+1.571}\times {\text{T}}_{i}\text{-23.85}$$

(13)

In this equation, T is the temperature in Celsius, and h is enthalpy in kJ/kg. The outlet temperature of the solar heat exchanger is calculated as below (Abdelhay et al. 2020):

$${\text{T}}_{23}{= \text{T} }_{24}-{\varepsilon }_{SHX}\times {\text{(T}}_{24}{\text{-T}}_{8}\text{)}$$

(14)

${\varepsilon }_{SHX}$ is the effectiveness of the solar heat exchanger. The following equations can also be used to calculate the heat transfer rate and the useful heat absorbed by the solar collectors.

$${Q}_{SHX}={\dot{m}}_{\text{therminol}}\times ({h}_{1}-{h}_{8})$$

(15)

$${Q}_{STC}={\dot{m}}_{stc}\times ({h}_{24}-{h}_{23})$$

(16)

The following equation is used for calculating the needed area of solar collectors. In this equation, ${\eta }_{STC}$ is the collectors’ efficiency and can be calculated from the below formula (Sharaf Eldean and Soliman 2015).

$${A}_{STC}=\frac{{Q}_{STC}}{{\eta }_{STC}\times G/1000}$$

(17)

$$\begin{array}{c}{\eta }_{STC}=0.75-4.5\times {10}^{-5}\times ({T}_{STC,out}-{T}_{0})-0.039\times \frac{{T}_{STC,out}-{T}_{0}}{G}-\\ {0.0003\times \left(\frac{{\mathrm{T}}_{STC, out}-{T}_{0}}{G}\right)}^{2}\end{array}$$

(18)

In the above equations, G is the solar radiation in W/m2, T₀ is the ambient temperature in C, A_STC is the area of solar collectors in m², η_STC is the collectors’ efficiency, and T_STC,out is the outlet temperature in C.

Appendix B

Table 11 shows the validation results between the proposed mathematical model in MATLAB and the commercial software Thermoflex. It can be seen that the mathematical model shows excellent agreement with the results from the software program.

Table 11 Model validation results