Keywords

1 Introduction

To reduce dependence on fossil fuels, the International Energy Agency (IEA) tries to reduce its consumption from 81.1% registered during 2016 to 68.1% for the year 2030 [1]. Geothermal and solar energy has high potential as a substitute for fossil fuels due to its low carbon emissions and sustainability. In 2014, Zhou [2] investigated a hybrid geothermal-solar plant of parabolic troughs integrated with an organic Rankine cycle (ORC), showing how the output power increases between 22 and 78% depending on the size of the solar field. Astolfi et al. [3], combined an ORC geothermal plant with a concentrating solar plant, obtained a reduction of 54 to 60% in the cost of energy. Mir et al. [4] developed an evaluation model for geothermal-solar systems, achieving a reduction in the consumption of the geothermal resource of approximately 10%. Lentz et al. [5], modeled two strategies for the combination of a flash geothermal system with parabolic collectors in Mexico, increasing the quality of the steam by 10%. This paper evaluates the integration of a double flash plant with a central solar receiver, using specialized software to determine the appropriate size and the optical performance of the solar field for environmental conditions of Baja California, Mexico.

2 System Description

The system consists of a double flash geothermal Rankine cycle based on the configuration proposed by Cardemil et al. [6] integrated with a central solar receiver. The geothermal fluid passes through a flash process, where the saturated vapor is separated from the saturated liquid. The liquid is heated using a heat exchanger to produce an additional percentage of saturated vapor that is again separated and mixed with the vapor coming from the first flash chamber, which is superheated in another heat exchanger before expanding in a high-pressure turbine. The remaining liquid is conducted to a second flashing process. Through an additional heat exchanger, the resulting saturated steam is superheated and mixed with the steam that comes out of the high-pressure turbine to enter a low-pressure turbine Finally, the steam is condensed and cooled before returning to the production well (Fig. 1).

Fig. 1.
figure 1

System layout.

Full size image

The main operating parameters to model the Rankine cycle and the solar field are shown in Table 1, selecting the Valley of Mexicali, Baja California, Mexico as a case study. The mathematical model considers:

  • Components operate under steady state conditions.

  • The pressure drops are negligible in the heat exchangers.

  • Changes in kinetic and potential energy are negligible.

  • The geothermal fluid has the same thermodynamic properties as water.

Table 1. System parameters
Full size table

3 Mathematical Model and Optimization

The thermodynamic and exergetic model of the geothermal Rankine cycle are developed using Engineering Equation Solver (EES®) by applying mass, energy and exergy balances respectively, as:

$$\sum_{i}{\dot{m}}_{i}-\sum_{o}{\dot{m}}_{o}=0 $$
(1)
$$\dot{Q}-\dot{W}+\sum_{i}{\dot{m}}_{i}({h}_{i})-\sum_{o}{\dot{m}}_{o}({h}_{o})=0$$
(2)
$$\sum_{j}{\dot{E}}_{q,j}-\sum_{k}{\dot{E}}_{w,k}\sum_{i}{\dot{m}}_{i}({e}_{i})-\sum_{o}{\dot{m}}_{o}\left({e}_{o}\right)-{\dot{E}}_{d}=0$$
(3)

The cycle was optimized by the genetic algorithm of EES®, establishing as objective function the net power of the plant with limits defined in Table 2, and subject to restrictions established by the balances of mass, energy, and exergy.

$$Max \left[{\dot{W}}_{net}\left(\overrightarrow{x}\right)\right]$$
(4)
$${\dot{W}}_{net}={\dot{W}}_{TAP}+{\dot{W}}_{TBP}$$
(5)
$$\overrightarrow{x}=\left({P}_{sep1},{P}_{sep2}\right)$$
(6)
Table 2. Operating ranges of the design variables.
Full size table

The solar field was optimized by the COBYLA algorithm of Solar Power Tower Integrated Layout and Optimization Tool (SolarPILOT®). The objective function is:

$$Z\left(\overrightarrow{x}\right)=\frac{{C}_{tot}\left(\overrightarrow{x}\right)}{{E}_{an}\left(\overrightarrow{x}\right)}\left(1+\left(1-min\left[\frac{{\dot{q}}_{cs}\left(\overrightarrow{x}\right)}{{\dot{q}}_{cs,dis}\left(\overrightarrow{x}\right)}\right]\right) P\right)$$
(7)

where \(\overrightarrow{x}\) is the set of variables, \({C}_{tot}\) is the total cost of the plant, \({E}_{an}\) is the expected annual energy production of the field, \({\dot{q}}_{cs}\) is the real thermal power of the field, \({\dot{q}}_{cs,dis}\) is the thermal power of the field and \(P\) is a penalty constant.

4 Results

In order to compare the performance of the plant working individually and integrated with the solar receiver, the net power of the plant is maximized based on the separation pressures. The results are shown in Table 3.

Table 3. Rankine Cycle Optimum Values.
Full size table

Figure 2 shows the effect of both separation pressures on the output power, which reaches values of 25734 kW. Since the ranges in the separation pressure of both chambers are different, one of these two will be the one that influences the maximization of the output power; i.e., once the separation pressure in the first chamber is defined, the second separation pressure does not show a significant variation in the output power.

Fig. 2.
figure 2

Exergetic efficiency as a function of separation pressures.

Full size image

Figure 3a shows a comparison between the thermal efficiency and the exergetic efficiency when the plant is working individually and when it is integrated with the solar receiver. It is observed that the thermal efficiency shows similar values for both cases; while the exergetic efficiency is lower when the hybrid system is considered. Figure 3b shows a comparison of the exergy destructions that occur in the main components of each system, with the solar field showing the highest exergy destruction ratio followed by the condenser and the first flashing process. The components with a lower destruction rate are the low-pressure turbines and the second flashing process. In the case of the individual cycle, it does not present the destruction of the field or of the exchangers as they do not have these devices.

Fig. 3.
figure 3

Comparison between a) Thermal and exergetic efficiencies. b) Exergy destruction rates.

Full size image

The results of the optical optimization are shown in Table 4. It is observed that a flux of 555.40 kW/m2 is reached for a tower 44.32 m high, with a receiver 3.90 m high by 4.99 m in diameter and a total of 417 heliostats. With these values, the configuration of the resulting solar field is shown in Fig. 4a, where its annual optical efficiency is observed, reaching an average value of 60.02%, with a maximum value of 87% and a minimum value of 40.1%. One of the most important results in the design of these fields is the flow profile or solar "spot", which is shown in Fig. 4b, and represents the flow distribution that each one of the heliostats projects onto the surface of the receiver, preferring that it be as uniform as possible to concentrate the energy more efficiently.

Table 4. Solar field Optimum Values.
Full size table
Fig. 4.
figure 4

a) Optimum solar field geometry. b) Receiver flux profile

Full size image

5 Conclusions

In this work, the integration of a double flash geothermal Rankine cycle with a central tower solar field was analyzed in order to compare their performance individually and together. The results show that assisting the geothermal system with solar energy to superheat the inlet steam in the turbines can considerably increase power production. Despite the fluctuation of the solar resource, the present work does not contemplate a thermal storage system due to the large additional costs involved, since in this case, the solar resource is used only as an auxiliary to improve performance, but its variation is not significant as the geothermal deposit is the main source of energy. These types of combinations are a viable alternative in the Mexican energy market, due to its high solar incidence, as well as its location in the “Pacific ring of fire”, an area with great geothermal activity.