# Thermal-Economic Modularization of Small, Organic Rankine Cycle Power Plants for Mid-Enthalpy Geothermal Fields

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. System Description and Methodology

**Figure 1.**Diagram of a recuperative small, modular geothermal Organic Rankine Cycle (ORC) with adaptive control.

- Thermodynamic optimization for a given design-point: normal (design) wellhead and ambient temperature. The components will then be sized using optimum thermodynamic parameters.
- Mapping the power plant net-power at operation points from the design conditions. This results from an optimal control strategy that maximizes the net power output.
- Simulation of annual electricity production. Performance is then evaluated using constant exergy input for each off-design condition. The variation of the ambient temperature was examined for three different climate types.
- Steps 1–3 are repeated for each design-point, and finally the optimal design-point is selected using thermo-economic criteria. Cost correlations of each component are implemented to evaluate the component sizes.

## 3. Component Modeling

#### 3.1. Heat Exchangers

_{WTD}is calculated based on heat transfer coefficients and areas of each zone of the exchanger. It is represented by the following equation:

_{fouling}is the thermal resistance associated with fouling in the heat exchanger tubes (R

_{fouling}= 1.3 × 10

^{−4}m

^{2}·K·W

^{−1}, experiment data for geothermal brine [11]). For the evaporator, the heat transfer area dedicated to liquid zone, A

_{l}is computed as the similar equation form is applied for the two-phase and vapor zone. The inner tube was assumed to be a standard stainless-steel with the geometry described in Table 1. Simplified layouts of the heat exchangers are illustrated in Figure 4.

Component | Type | D_{0} [mm] | t [mm] | P_{T} [mm] | N_{tube} | N_{pass} | L [m] | Width [m] |
---|---|---|---|---|---|---|---|---|

Evaporator | shell/tube | 15.875 | 1.651 | 20.64 | variable | 1 | variable | - |

Recuperator | shell/tube | 31.75 | 2.11 | 39.69 | variable | 1 | variable | - |

Condenser (1 cell) | fin/tube | 25.4 | 3.3 | 63.5 | 192 | 3 | 9.14 | 3.05 |

**Figure 4.**(

**a**) Layout of shell/tube exchanger (evaporator and recuperator); (

**b**) Layout of fin/tube exchanger cell (air-cooled condenser).

#### 3.1.1. Evaporator and Recuperator Heat Transfer Coefficients and Pressure Drops

_{p}and F

_{bundle}were calculated using equations found in the literature [12]. The pressure drops are calculated using the Prandtl-Karman equation as follows:

^{2}is approximated with the Grant correlation, for two-phase flow crossing tube-bundles [13].

#### 3.1.2. Air Condenser

_{fouling}= 1.7 × 10

^{−4}(GPSA assumption). Heat transfer and pressure drop on the air-side are also approximated based on a GPSA correlation [15]:

#### 3.2. Feed-Pump

_{0}= 0.8:

#### 3.3. Turbine

_{in}/p

_{out}is the pressure ratio and μ

_{T}is the turbine nozzle position. The turbine constant C

_{T}can be thought of as an equivalent area and has the unit square meters. In off-design operation, the equivalent area was adapted by varying μ

_{T}using variable inlet nozzle guide-vane. The guide vanes are moved in such a way that the flow area between the vanes changes. Thus, the inlet flow area is changed.

_{o}, ratio of radial velocity to spouting velocity. Spouting velocity, ${c}_{o}=\sqrt{2\cdot \Delta {h}_{\text{is}}}$, is defined as that velocity has an associated kinetic energy equal to isentropic enthalpy drop. At the best efficiency point the value of u/c

_{o}is found at 0.7 [17]. The second correction factor was associated with the variation of the volumetric flow rate from the design value. The two correction factors were then observed in Figure 5b, which is typical for radial turbine characteristics. The design point was pointed at a velocity ratio of 0.7 and volumetric flow rate of 100%.

**Figure 5.**(

**a**) Stodola’s cone rule as a function of nozzle position; (

**b**) Typical turbine efficiency characteristics [18].

## 4. Results

- D
_{shell,ev}, D_{shell,re}, L_{ev}, L_{re}: diameter and length of the shell-and-tube heat exchangers (i.e., evaporator and recuperator). - N
_{cell}, P_{F}: cell numbers and fan capacity for air-cooled condensers. These parameters are a function of the condenser load and the air-outlet temperatures. - C
_{T}, Δh_{is0}, ${\dot{V}}_{\text{5,design}}$: inlet area constant, isentropic enthalpy drop, and outlet-volumetric flow rate at the design-point. The two latter parameters were used to define the pitch diameter. - $\Delta {p}_{\dot{V}=0}$, ${\dot{V}}_{\text{P0}}$: the shut-off pressure head when the flow is zero which is typically 1.25 times of the design-head, design volumetric flow rate.

_{g0}) and ambient temperature (T

_{a0}). The 11 design variables then were a product of the sizing for the design-point (T

_{g0}-T

_{a0}).

#### 4.1. Component Sizing for Normal-Design: Thermodynamic Optimization

T_{g0} | 120 | 130 | 140 | 150 | 160 | 170 |
---|---|---|---|---|---|---|

Evaporation temperature (sat.) (°C) | 80–87 | 85–93 | 91–101 | 99–111 | 111–122 | 115–121 * |

Condensation temperature (°C) | 4–54 | 4–54 | 4–54 | 4–54 | 4–54 | 4–54 |

Geofluid mass flow rate (kg·s^{−1}) | 31.3–95.7 | 24.8–68.8 | 20.2–51.1 | 16.7–38.7 | 12.9–28.1 | 10.3–21.8 |

Isobutane mass flow rate (kg·s^{−1}) | 15.6–50.2 | 14.8–43 | 13.9–37.4 | 13–32.8 | 12.5–27.1 | 12.8–27.1 |

Gross power (kW) | 1000 | 1000 | 1000 | 1000 | 1000 | 1000 |

Net efficiency (%) | 5.1–13.9 | 5.9–14.5 | 6.7–15.2 | 7.6–16 | 8.8–18.1 | 8.8–20.6 |

*****The pinch-point was adjusted to set the geofluid after the evaporator to 70 °C.

- Evaporator: Evaporation was realized using two parallel evaporators, with one shell/one tube pass configuration. During very low load (<50%) operation, one of the evaporators was fully closed. Both evaporators were sized by determining the shell diameter, and the number of tubes was calculated using “tube counts” based on standardized design parameters described in Table 1. The baffle-spacing was constrained below the shell diameter and maximum-spacing in order to avoid instability caused by vibration. After calculating overall heat transfer coefficients and the total heat transfer area, tube length was computed. By setting the allowable pressure drop on the shell side, the optimum design (or equivalently, shell diameter) with smallest area was selected. This design procedure was also applied to the recuperator.
- Condenser: An important preliminary step in the condenser design process is outlet air temperature. This parameter has a major effect on exchanger economics [12]. Increasing the outlet air temperature reduces the amount of air required, which reduces the fan power and, therefore, operating cost. However, it also reduces the air-side heat-transfer coefficient and the mean temperature difference in the exchanger, which increases the size of the unit and, therefore, the capital cost. Consequently, optimization with respect to outlet air temperature (or equivalently, air flow rate) was considered an important aspect of air-cooled condenser design.

_{cd}and fan investment cost C

_{F}are described in Table 3. The annualization factor, CRF (Capital Recovery Factor) is defined as:

^{−1}, as recommended in the literature [12]. The maintenance cost was assumed to be 1% of the fin/tube heat exchangers cost and 3% of fan-motor cost [22]. CF (capacity Factor) of 0.7, y of 30 years, i of 12%, and electricity price C

_{el}of 0.15 $·kWh

^{−1}were assumed.

_{g0}-T

_{a0}) at air-outlet temperature of 30.4 °C, approximately 10 K above the inlet air temperature (Figure 6b). Once the optimum air-outlet temperature was established, the heat transfer area (or equivalently, number of cells) and fan capacity were determined.

Component | Cost correlation | Reference |
---|---|---|

Evaporator | $13,668+658\cdot {A}^{0.85}$ (Carbon-shell/Stainless-tube) | [22] |

Recuperator | $11,256+579\cdot {A}^{0.8}$ (Carbon-shell/Carbon-tube) | [22] |

Air-cooled condensers | $5.6\cdot A$ | [23] |

Fans | $\left(1887.5+159.95\cdot {D}_{\text{F}}^{2}+3.53\cdot {D}_{\text{F}}+281.25\cdot {P}_{\text{F}}\right)\cdot {N}_{\text{F}}$ | [23] |

Feed-pump | $4900\cdot {\left({P}_{\text{P}}/30\right)}^{0.7}$ | [24] |

Turbine + generator | $\left(91,200\cdot {D}_{pitch}^{2.1}+50,800\cdot {D}_{pitch}^{3}+62,700\cdot {D}_{pitch}^{2}\right)+680,900\cdot {\left({P}_{T}/{10}^{4}\right)}^{0.7}$ | [25] |

Labor | $0.3\times \text{Total component cost}$ | - |

**Figure 6.**Size optimization based on annual cost of condensers at 130-20 (T

_{g0}-T

_{a0}) design-point.

#### 4.2. Off-Design Mapping

_{T}. Second, superheating/turbine inlet temperature was controlled by pump-speed n

_{p}(isobutane mass flow rate), and third, condensation temperature by the fan-speed n

_{F}(air volumetric flow rate). Constant sub-cooling was imposed by making use of the static pressure head between the pump and the liquid hot-well (Figure 1). Using this control strategy for a modular ORC system, the net power output was maximized while keeping the injection temperature above scaling temperature to avoid scaling, which is described as:

_{1}was determined using the three-zone recuperator model, f

_{2}the evaporator model, and f

_{3}the condenser model. Pressure drop in the evaporator was minimized to maintain evaporation temperature drop below 5 K. The equations were solved for given operation parameters to simulate the power-cycle. In order to find the optimum operation parameters for each operating condition, CMA-ES was implemented [27].

_{g,in}= 120 °C, T

_{a,in}= −10 °C for 130-20 (Point A, Figure 7b). While maximum net power output (1025 kW) occurred at T

_{g,in}= 160 °C, T

_{a,in}= −10 °C for 160-20 (Point B, Figure 7b). It can be observed contradictory net power-output trend between the two design points. For 130-20, by increase of geofluid temperature, the net power output decreases, especially at lower ambient temperature. In contrary, for 160-20, the net power output showed an opposite trend. This was affected mainly on the turbine isentropic efficiency characteristic at off-design. The nominal (design) isentropic enthalpy drop was lower and the nominal volumetric flow rate was higher for 130-20. Hence, if the plant was operated at higher wellhead temperature which has higher enthalpy drop and lower flow rate, the turbine isentropic efficiency would steeply deteriorated (see Figure 5b).

_{g,in}at the optimum point, the net power output decreased by 65.1% for 130-20 and 44.5% for 160-20 between −10 °C and 40 °C.

**Figure 7.**(

**a**) Off-design optimization procedure for a design-point (T

_{g0}-T

_{a0}) and operating condition (${\dot{m}}_{\text{g}}$,T

_{g,in}, T

_{a,in}); (

**b**) Design-point grid; and (

**c**) Off-design grid.

#### 4.3. Annual Simulation and Thermo-Economic Selection

_{F}, N

_{F}, P

_{F}, P

_{T}, and P

_{P}in Table 3 were determined directly from the sizing results. The turbine pitch (average wheel) diameter, D

_{pitch}, was derived from a universal functional relationship, for optimum stage efficiency [30] as:

_{el}and the three later terms are particularly annualized cost of electricity, i.e., investment cost, annual operation and maintenance costs of the overall plant which are assumed to be 4% of the investment cost [31], and well cost. Well cost accounted for the geofluid-pumping and drilling costs, which are arbitrary values dependent on site-specific characteristics. It was assumed a well cost equal to zero since it will only shift the MCF to a lower value, and result in an unchanged optimum design-point. The three climates temperate, tropical and dry—chosen for annual simulation were sampled from existing geothermal sites: Upper-Rhine Graben, Germany (temperate climate), Kamojang, Indonesia (tropical climate), and Birdsville, Australia (dry climate). The temperature distributions of each climate are shown in Table 4.

Temperature [°C] | Temperate climate (
T_{av} = 11.6 °C) | Tropical climate (
T_{av} = 19.9 °C) | Dry climate (
T_{av} = 25.1 °C) | |||
---|---|---|---|---|---|---|

Number of hours | % hours | Number of hours | % hours | Number of hours | % hours | |

−10 | 266 | 3.0 | 0 | 0 | 0 | 0 |

0 | 2438 | 27.8 | 0 | 0 | 17 | 0.2 |

10 | 2926 | 33.4 | 351 | 4.0 | 1195 | 13.6 |

20 | 2159 | 24.6 | 7934 | 90.6 | 3139 | 35.8 |

30 | 726 | 8.3 | 475 | 5.4 | 3154 | 36.0 |

40 | 245 | 2.8 | 0 | 0 | 1254 | 14.3 |

_{a.in}at each site. This calculation only includes cost, which varies significantly according to the component size. The remaining costs, such as piping, instrumentation and working fluid, were excluded.

^{−1}, while MCF maximization yielded 153-10, with a cost value of 761,350 $·year

^{−1}. The SIC and MCF showed large variation, ranging from 1133 $·kW

^{−1}to 5296 $·kW

^{−1}, and 92,224 $·kW

^{−1}to 761,350 $·kW

^{−1}, respectively.

_{g0}of 160 °C across the three climates, and optimum T

_{a0}followed lower temperatures of 6 °C, 10 °C and 10 °C. While in MCF maximization, optimum T

_{g0}was 153 °C, 163 °C and 163 °C, and T

_{a0}followed average temperatures of 10 °C, 22 °C and 23 °C, respectively. Figure 10 shows relative component costs among the three climates.

Sizing | Design-point [°C] | SIC [$·kW^{−1}] | MCF [$·year^{−1}] | |
---|---|---|---|---|

T_{g0} | T_{a0} | |||

Temperate climate | ||||

SIC minimization | 160 | 6 | 1,133 | 745,770 |

MCF maximization | 153 | 10 | 1,198 | 761,350 |

Tropical climate | ||||

SIC minimization | 160 | 10 | 1,303 | 642,070 |

MCF maximization | 163 | 22 | 1,403 | 683,120 |

Dry climate | ||||

SIC minimization | 161 | 10 | 1,520 | 524,230 |

MCF maximization | 163 | 23 | 1,601 | 580,800 |

**Figure 10.**Relative component cost comparison between SIC and MCF optimization under three different climate types.

## 5. Conclusions

- Using the modularization technique described in this paper, design optimization under three different climates (temperate, tropical, and dry) was derived. Using SIC minimization, the normal ambient temperatures were driven by the lower temperature. Using MCF maximization, the normal ambient temperatures were driven by average temperature in each climate region.
- When SIC minimization and MCF maximization were compared, average net-power based on MCF maximization was higher. Although investment cost was slightly higher, the revenue or equivalently, the energy utilization was considerably improved. Consequently, MCF maximization is proposed as an optimization function.
- Concerning the various components analyzed here, the condenser and fan size had the greatest influence on average net power output. The main feature in MCF maximization design was increased size of the cooling-system, which helped maintain low condensation pressure. Using isobutane, the condenser cost amounted to 35%–38% of the investment cost. Enhancing the heat transfer of cooling system technology will reduce the condenser size and, most importantly, the ORC investment cost.

## Acknowledgments

## Nomenclature

$\dot{W}$ | Output power [kW] | D | Diameter [mm] |

P | Power capacity [kW] | t | Thickness [m] |

T | Temperature [°C] | L | Length [m] |

p | Pressure [kPa] | P_{T} | Pitch [mm] |

Δ p | Pressure drop, head [Pa] | A | Area [m^{2}] |

$\dot{m}$ | Mass flowrate [kg·s^{−1}] | n | Rotational speed [Hz], indices |

$\dot{Q}$ | Heat [kW] | i | Interest rate [%] |

h | Spec. enthalpy [kJ·kg^{−1}] | y | Depreciation time [yr] |

s | Spec. entropy [kJ·kg^{−1}] | N | Number |

$\dot{V}$ | Volume flowrate [m^{3}·s^{−1}] | η | Efficiency |

G | Mass flux [kg·m^{−2}·s^{−1}] | C | Constant, cost [$] |

c_{p} | Spec. heat capacity [kJ·kg^{−1}·K^{−1}] | Re | Reynolds number |

k | thermal conductivity [W·m^{−1}·K^{−1}] | Pr | Prandtl number |

α | Heat transfer coef. [W·m^{−1}·K^{−1}] | f | Fanning friction factor |

U | Overall heat transfer coef. [W·m^{−2}·K^{−1}] | F | Multiplier factor |

Φ^{2} | Two-phase multiplier | μ_{T} | Nozzle position [%] |

X_{tt} | Turbulent Lockhart-Martinelli parameter | SIC | Specific investment cost [$·kW^{−1}] |

u | Wheel tip speed [m·s^{−1}] | MCF | Mean cash flow [$·year^{−1}] |

c_{o} | Spouting-velocity [m·s^{−1}] | CRF | Capital Recovery Factor |

γ | Latent heat [kJ·kg^{−1}] | ITD | Initial temperature difference [K] |

ρ | Density [kg·m^{−3}] |

## Subscripts

0 | Normal (design) | l | Liquid |

1 | Pump inlet | tp | Two-phase |

3 | Evaporator inlet | v | Vapor |

4 | Turbine inlet | ev | Evaporator |

g | Geothermal geofluid | cd | Condenser |

a | Air | re | Recuperator |

wf | Working-fluid | P | Pump |

o | Outer | P | Turbine |

i | Inner | F | Fan |

s | Shell | sat | Saturated |

el | Electrical | WTD | Weighted temperature difference |

pp | Pinch-point | O&M | Operation & Maintenance |

## Author Contributions

## Conflict of Interest

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**MDPI and ACS Style**

Nusiaputra, Y.Y.; Wiemer, H.-J.; Kuhn, D.
Thermal-Economic Modularization of Small, Organic Rankine Cycle Power Plants for Mid-Enthalpy Geothermal Fields. *Energies* **2014**, *7*, 4221-4240.
https://doi.org/10.3390/en7074221

**AMA Style**

Nusiaputra YY, Wiemer H-J, Kuhn D.
Thermal-Economic Modularization of Small, Organic Rankine Cycle Power Plants for Mid-Enthalpy Geothermal Fields. *Energies*. 2014; 7(7):4221-4240.
https://doi.org/10.3390/en7074221

**Chicago/Turabian Style**

Nusiaputra, Yodha Y., Hans-Joachim Wiemer, and Dietmar Kuhn.
2014. "Thermal-Economic Modularization of Small, Organic Rankine Cycle Power Plants for Mid-Enthalpy Geothermal Fields" *Energies* 7, no. 7: 4221-4240.
https://doi.org/10.3390/en7074221