7 Cost modelling and techno-economic optimization
7.1 Cost correlations
7.1.1 Cost component correlations
Even though most of the authors that have studied the techno-economic optimization of ORCs agree on the importance of defining the right cost correlations for the models, the available data has high uncertainty. This is due to the fact that engineering companies (which we can consider the best and most trustful source of information) have strict politics to keep their economic data as concealed as possible. For this reason, three main models have been generalized and defined to keep certain consistency between the different published studies. These models were developed by D.W. Green [56], R. Turton et al. [57] and H. Loth et al. [58].
Green’s model includes only one reference and cost variation exponent, meaning that it is not sufficiently accurate, and calculations may deviate from the real data if the component size is too different from the reference model size. On the other side, Loth’s
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model includes foundations, insulation and instrumentation costs, which are hard to find in the open literature.
Turton’s model is considered the most accurate cost model, since it does not present great deviations when comparing the theoretical cost results with the ones that are found in the market. During the literature review process, it was found that Turton’s model is the most embraced one [3, 24, 46, 59]. For these reasons, Turton’s model is the one that is going to be used to compute the cost of all cycle components in this work.
The cost of each ORC component can be calculated as a function of its most important size factor, also called “Capacity Factor” (CF), which needs to be corrected by taking into consideration a pressure factor and a material factor, as it will be shown next.
Turton’s main correlation is:
log 𝐶( = 𝐾ž+ 𝐾mlogž•(𝐶𝐹) + 𝐾¡ logž•(𝐶𝐹) m 7.1
Where CF depends on the kind of component the correlation is applied to. CF values for each one of the system components can be found in Table 3.
Table 3. Capacity Factors for the different ORC components, [57, 59]
Component Capacity Factor (CF)
PrHE Heat transfer surface, A [m2]
Condenser Heat transfer surface, A [m2]
Turbine Power output, W [kW]
Pump Power consumption, W [kW]
Generator Electrical power, W [kW]
The basic cost (𝐶() needs to be corrected to heed the operating pressure and manufacturing materials. This should be done as follows [46, 59]:
𝐶$% = 𝐶(· 𝐹./ = 𝐶(· 𝐵ž+ 𝐵m· 𝐹/· 𝐹' 7.2
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Where 𝐹/ and 𝐹./ values are extracted from [57] and [46], and they depend on the design of the component.
To define the material factor (𝐹/), carbon steel was selected as the manufacturing material for all components. G. Li stated in [32] that this material is suitable for heat source temperatures up to 290 ºC, and that more advanced manufacturing materials would be needed just in case of operating at higher temperatures. As this temperature level is not going to be exceeded in none of the proposed scenarios, it can be assumed that carbon steel is suitable for avoiding problems related to high thermal stresses in the Rankine cycle components computed in this work10.
Finally, 𝐹' can be calculated as:
log 𝐹' = 𝐶ž+ 𝐶m logž• 𝑝 + 𝐶¡(logž•(𝑝))m 7.3
All constants’ values (𝐾ž, 𝐾m, 𝐾¡, 𝐵ž, 𝐵m, 𝐶ž, 𝐶m and 𝐶¡), which are cost coefficients, are presented in Table 4. In order to select the right values of these coefficients, the following considerations must be taken into account [57]:
- For the primary heat exchanger, in case the evaporation pressure is found between 5 and 140 bar, values for 𝐶ž, 𝐶m and 𝐶¡ must be modified to 0.03881, -0.11272 and 0.08183, respectively.
- For the pump, in case the pressure moves between 10 and 100 bar, 𝐶ž, 𝐶m and 𝐶¡ should take the values -0.3935, 0.3957 and -0.00226, respectively.
10 As it was stated in Section 3.4.2, new plate heat exchangers manufacturing materials allow for operating at considerably high temperatures and pressures. However, Turton’s manual does not include the most advanced materials yet, making it not possible to compute the cost of these components when studying the application of medium- or high-temperature heat sources.
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Table 4. Cost constants values for the different Rankine cycle components [46, 57]
Equipment 𝑲𝟏 𝑲𝟐 𝑲𝟑 𝑪𝟏 𝑪𝟐 𝑪𝟑 𝑩𝟏 𝑩𝟐 𝑭𝒎 𝑭𝒃𝒎
Plate H.E 4.6656 -0.1557 0.1547 0 0 0 0.96 1.21 1.0 - Shell-and-Tube H.E 4.8306 -0.8509 0.3187 0 0 0 1.63 1.66 1.30 -
Turbine 2.2476 1.4965 -0.1618 - - - 3.30
Pump 3.3892 0.0536 0.1538 0 0 0 1.89 1.35 1.5 -
Even though Turton’s correlation is considered to constitute a good approach to the cost modelling of the different Rankine cycle components, defining the right cost correlation for the turbine is not easy, since there are many different parameters that influence its design and, therefore, its cost. For power plants operating at low loads, the expander design is a problem that has not been solved yet [60]. The main difficulty when trying to set the turbine cost is that not all authors agree upon a general nor a specific cost correlation.
Some authors propose to study the turbine cost correlation as a function of its number of stages and size, not taking into consideration the material nor the pressure factor [3].
However, considering that the ORC industry deals with many different solutions and includes a wide range of different types of turbines (some companies are even developing their own models), an agreement with respect to the turbine design does not exist yet. For this reason, Turton’s turbine cost correlation [57] has been chosen to estimate the expander cost, since it does not dig deep into the turbine design. This assumption is also based on different literature research studies, in which we found that most of the authors resort to Turton’s turbine cost correlation, stating that it can be accurate enough when the system is not designed for high power production [24, 31, 46, 59].
The generator is the only one component whose cost correlation is not defined by Turton.
However, it can be easily obtained by means of the following equation [46]:
𝐶',3*• = 60 · 𝑊3*• •.§ 7.4
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Finally, the total investment cost can be calculated as the sum of the cost of all cycle components.
𝐶OMO = 𝐶$%,(7«¬ + 𝐶$%,aM•™+ 𝐶$%,'f/'+ 𝐶$%,Of7.+ 𝐶$%,3*• 7.5
Other factors such as the Capital Recovery Cost (CRC) can also be considered to make the cost analysis more realistic, although they require assuming the interest rate and the plant life time. For this reason, they are not going to be included in the cost modelling.
However, the Chemical Engineering Plant Cost Index (CEPCI) needs to be heeded in order to adjust the system overall cost from 2001 (year of publication of the resource from the one we extracted the cost constants values) to 2018. Therefore, the cost must be corrected as follows [46]:
𝐶OMO,m•ž¦ = 𝐶¸MO,m••ž·𝐶𝐸𝑃𝐶𝐼m•ž¦
𝐶𝐸𝑃𝐶𝐼m••ž 7.6
Where 𝐶𝐸𝑃𝐶𝐼m••ž = 397 [46] and 𝐶𝐸𝑃𝐶𝐼m•ž¦ = 562.1 [61].