Development of Total Capital Investment Estimation Module for Waste Heat Power Plant

Power plants with waste heat collection and utilization have gained increasing interest in the high energy-consuming industries, such as steel-making and cement manufacturing, due to its energy efficiency. Waste heat power plants possess some intrinsic characteristics, for instance, the main equipment and the working fluids. However, at the time of this research, we could not find an economic analysis suitable to address the specialized aspects of waste heat power plant, making it difficult to measure the total capital investment needed for the business feasibility assessment. In this paper, we introduced our total capital investment estimation module developed for a waste heat power plant by considering its intrinsic features. We followed a systems engineering approach in designing and developing our module. We performed a requirements analysis of the stakeholders related to the waste heat power plant. Simultaneously, we consider the technical aspects by exploring the working fluids and main equipment implemented in the plant. Then, we developed the cost models for each equipment and used them as the basis of the proposed total capital investment estimation module. The performance verification showed that our proposed method achieved the initial accuracy target of a 5.78% error range when compared to the real data from the reference case study.


Introduction
Renewable energy sources are expected to become the substitute for the absolutely insufficient fossil energy sources. However, in reality, it is difficult to replace fossil fuels completely, thus, the need to efficiently utilize energy sources remains high [1]. This condition triggers competition between companies in searching for strategies to improve the efficient use of energy [2]. For a long time, the industries with high-energy consumption, such as steel-making, cement, and petrochemical industries, have been utilizing the waste heat for an electric power generation system as an effort to increase their energy efficiency [3]. In fact, around 52% of the total consumed energy is thrown away as waste heat, and the recovery and reutilization of waste heat has been proven to save considerable costs [4]. The cost reduction resulting from waste heat-fueled electric power generation plays a significant role in the rapid development of its market.
However, despite the rapid growth of the waste heat power plant, there is no specialized economic analysis solution for it, thus it is difficult to accurately assess the plant's economic feasibility. The previously existing economic analysis solutions such as COMFAR III V3.3, ENetOPT V3.6 cannot be applied directly to the waste heat power plant because its various working fluid and distinct main equipment are not considered in the existing cost model, causing errors in the analysis [5,6]. The waste heat power plant industry requires a solution to accurately evaluate the economic feasibility by considering the characteristics of the waste heat power plant such as the working fluid, cycle configuration, equipment type, and equipment cost model.
The objective of this research is to cope with the previously described problems by developing a module to estimate the total capital investment (TCI) design especially for a waste heat power plant. We developed the TCI module by considering the power application of the waste heat generated in the plant industries such as a power plant, steel-making plant, and refinery plant, and the power ranges of more than 10 kW, the most common thermal capacity in the industries. In order to develop such a module, we need to survey and select the working fluids of the waste heat power plant to determine the main equipment that operates with those fluids, and to develop the cost model of that equipment. Furthermore, to develop a TCI estimation module that can be practically used by the industry, we have to address the requirements in the industrial world. Thus, in this paper, we developed the final system that addresses the stakeholders' requirements systematically by applying systems engineering approaches.
The systems engineering approach used in this research have three main processes [7,8]. The first process is the stakeholder identification and definition process that identifies the stakeholders and their needs associated with the TCI estimation module. A stakeholder's needs are then transformed into a formal set of stakeholder requirements. The second process is the system requirements definition process that transforms stakeholder requirements into system requirements with technical specifications. Finally, the third process, the functional architecture design process, defines the functions of the TCI estimation module to meet defined system requirements. Thus, our work stands out from the existing knowledge in terms of: (1) The development of a various equipment cost model by using real world cost data and their verifications against openly available reference data, and (2) the application of a systems engineering approach that emphasizes the importance of requirements elicitation and analysis, and architecture modeling.
The rest of the paper is organized as follows. In Section 2, a power plant implementing waste heat is introduced and the theoretical background, including the basic concept, of economic feasibility analysis is explained. The related stakeholders are identified and their requirements are extracted by adopting systems engineering approaches in Section 3. In the same section we also described the design of the TCI estimation module from the system architecture and cost model that corresponds with the extracted requirements. In Section 4, we realized and applied the designed module and we verified its performance by comparing the target accuracy and the actual accuracy of the TCI estimation module. Lastly, we completed this paper by presenting the conclusions and future works in Section 5.

Introduction of Waste Heat Power Plant
Input energy is required to operate the industrial process, however some portion of the energy might not be used, being discharged to the external environment. The discharged energy is called the waste heat [9,10]. Waste heat has various forms. Typically, waste heat takes form as emission gas or waste hot water discharged to the external environment as a result of fuel combustion or high-temperature equipment's cooling residue, respectively [11]. In a waste heat power plant, the emission gas or waste hot water are taken as fuel, instead of being released to the external environment. The emission gas or waste hot water still has some amount of remaining heat, and it is sent to a heat exchanger to heat the working fluid. After that, the heated working fluid is used to operate turbines and generate electricity for the second time.
The amount of energy released as waste heat is varied based on the type of the industrial equipment. For example, boilers discharge 8-20% of its energy as waste heat, whereas driers and heating/air-conditioning equipment discharge 10-50% and 30-50%, respectively [12,13]. Therefore, various companies are adopting waste heat power plant to utilize those abundant waste heat, which causes continuous development in the scale of this industry. In fact, the worldwide market scale of a waste heat power plant will exceed USD 30 billion by 2024 [14].
The waste heat power plant can be designed in many ways, depending on the type of the working fluid. Most of related industries apply a steam Rankine cycle that uses steam as the working fluid, because it leads to a steady operation and it has been verified to improve the energy efficiency by more than 20% [15][16][17]. Thus, steel-making plant, cement manufacturing, shipbuilding, and other industries requiring power generation are widely applying a steam Rankine cycle [18]. Recently, in order to further increase the energy efficiency, organic Rankine cycle (ORC) that uses organic, high molecular mass refrigerant as the working fluid in biomass power and heat plants [19,20] and supercritical CO 2 Brayton cycle (sCO 2 BC) that uses carbon dioxide in the supercritical state as the working fluid and other similar methods are being developed, adding to the various methods to design the waste heat power plant [21][22][23].

Basic Concept of the Economic Analysis
The waste heat power plant requires long-term and large-scale investment, thus to avoid unnecessary costs and support efficient investment, the economic feasibility analysis should be performed by considering the overall stages from the business plan until the construction through multiple point-of-views. The representative metric of economic feasibility analysis is the total capital investment (TCI), and in our case of a waste heat power plant, we can use this metric to estimate the investment cost for the construction and operation stages [24], defined as follows: where FCI is the fixed capital investment, OO is other outlays, DC is the direct costs, and IC is the indirect costs. As shown in Equation (1), TCI is the summation of FCI and the other outlays, whereas the FCI is composed of DC and IC [25]. Direct costs include the cost of the equipment contained in the power plant, the installation cost of the corresponding equipment, the cost of pipes providing the utilities, the cost of the land for constructing the power plant, and so on [26][27][28]. Indirect costs include engineering, supervision, construction, and contingency cost. The other outlays are commissioning cost, working capital, licenses cost, research and development cost, and Allowance for Funds Used During Construction (AFUDC) [29,30]. From the above mentioned costs, the equipment cost occupies the largest part of the TCI, which is about 19.89% of the TCI [31]. Hence, accurate estimation of the equipment cost is the essential to improve reliability of the TCI estimation.
Generally, there are two methods to estimate equipment cost. The first method is the vendor quotation-based calculation approach, where the quotations from vendors that manufacture the equipment are collected and used to predict the equipment cost in a straightforward manner [32,33]. This approach considers various specifications, material quality, etc. with highly accurate price prediction. However, when the specifications are changed, it is difficult to predict the cost fluctuation without getting new quotations from the vendors. The second method is the cost model-based calculation approach, that uses previously sold price data as the bases to develop the cost model that contains the correlation between the equipment cost and its specifications/size [34,35]. The cost model is used to predict equipment cost. In the cost model-based calculation approach, the prediction accuracy depends on the amount of the collected equipment specification/size and cost data from the plant construction. In the case of an accurate cost model is used, whenever equipment specification changes, we can estimate the cost immediately. On the other hand, if an inaccurate cost model is used, differences between the estimated cost and the real cost provided by the manufacturing vendors may occur. The comparisons of the two equipment cost estimation methods are shown in Table 1.

Objective to TCI Estimation Module
In the current related industry, an economic feasibility analysis optimized for a waste heat power plant is not available. Therefore, TCI estimation, the core of business feasibility assessment, is difficult to perform. In this research, our objective was to develop the TCI estimation module that could be used in the business feasibility assessment stage. For the estimation accuracy, we referred to the economic analysis estimation accuracy indicator proposed by AACE (American Association of Cost Estimators), an international authorized organization in the field of industrial plant's economic feasibility assessment, as shown in Table 2 [36]. Specifically, we were aiming to meet the class 4 accuracy target, as appropriate for feasibility purpose.

Requirements Definition of the TCI Estimation Module
In this research, we defined the requirements of the TCI module by following these processes: (1) Stakeholder identification, (2) stakeholder requirements definition, and (3) system requirements definition [37]. Specifically, in the initial stage of the research, we identified the complete stakeholders related directly and indirectly to the system of interest (waste heat power plant) and defined the stakeholder requirements reflecting their needs. Then, the non-technical contents of the stakeholder requirements were transformed in to a well-defined set of system requirements by considering the development and implementation point-of-view.

Stakeholder Identification
In the first step, we identified the stakeholders related to the TCI estimation module development. Considering the target market, i.e., the waste heat power plant industry, we extracted related stakeholders through the overall industry's value chain analysis. We present samples of the identified stakeholders in Table 3. In general, the stakeholders were categorized as follows: The developers, the users, and the maintainers of the TCI estimation module. Among these stakeholders, the users were divided into five sub-categories: (1) The operating companies who obtain profits by operating the waste heat power plants, (2) the energy demanding companies who need waste heat power plant because of their high energy consumption, (3) the manufacturing companies who produces the main equipment of waste heat power plant, (4) the engineering companies who are responsible for the concept/basic/detailed design of the waste heat power plant, and (5) the constructing companies who perform the waste heat power plant's civil/structural/construction works based on the result of the detailed engineering.

Stakeholder Requirements Definition
In the second step, we elicited requirements of the TCI estimation module based on the identified stakeholders. For each stakeholder group, we performed interviews, surveys and a functional analysis with the practitioners experienced in business feasibility analysis and TCI estimation module. We wrote the requirement statements by following a systems engineering standard on a requirements analysis [38]. The requirements related to TCI estimation module's purposes and usages are presented in Table 4.

System Requirements Definition
In the third step, we performed the translation from the stakeholder requirements defined in the users point of view to the system requirements defined in the developer's point of view. We began with determining the problem domain and solution domain of the TCI estimation module. Next, we defined the technical items that have to be performed in the system level by implementing both the domain experts' decision technique and quality function deployment (QFD) technique [39]. The results of the above are the system requirements shown in Table 5.

Equipment Cost Model Development
As it has been defined in the system requirements of the TCI estimation module, in order to estimate the TCI, cost estimation of the main equipment used in waste heat power plant is highly required. In our research, we discovered that the equipment specifications were frequently changed during the business feasibility analysis. Thus we aimed to develop the cost model for each piece of equipment to assist the business feasibility analysis. The cost model of the main equipment, namely pumps, turbines, and heat exchangers were developed by considering the design factors, manufacture methods, and the correlation between costs.

Pump Cost Model
The pump is a piece of equipment used to compress the liquid in steam Rankine cycle, organic Rankine cycle, and supercritical CO 2 Rankine cycle into a high pressure state [40][41][42]. The components of pumps can be divided into the impeller that compresses the fluid and the motor that drives the impeller, in which the motor costs about 60-80% of the total cost of the pump [43]. In other words, the flow rate and the motor capacity are correlated with the pump cost model. Moreover, the waste heat power plant mostly uses centrifugal water pumps. We surveyed the prices of the centrifugal pumps per the capacity [31,44] and performed a regression analysis. The regression analysis results of a water pump cost model are shown in Figure 1a, for the linear function where the coefficient of determination (R 2 ) equals 0.997. The cost model of the ORC pump and supercritical CO 2 pump generally correlated with the motor capacity, that is, the power consumed by the motor. Similarly, we collected the data about the prices of those pumps based on their capacity [44][45][46][47]. However, in the case of these pumps, the data available to the public is very limited, thus we decided to include the real sales price data of the pumps manufacturing company as well. Based on this data, the results of the regression analysis of the pumps are shown in Figure 1b and 1c, for the linear function where the coefficient of determination (R 2 ) equals 0.994 and 0.998, respectively. We could draw the conclusion that, for all three types of pumps, as the flow rate or the power consumption increases, the cost also linearly increases.

Turbine Cost Model
Turbine is used to produce electricity from the expansion work of the working fluids [48]. Fundamentally, the turbine's design factors such as expansion ratio, number of stages, and others are determined based on the turbine's electricity generation capacity [49,50]. Those design factors highly influence the cost of turbine. In this research, we surveyed the turbine's cost based on its electricity generation capacity for every working fluid [31,44,51]. Based on this data, the results of the regression analysis of the steam turbine are shown in Figure 2a, for the exponential function where the coefficient of determination (R 2 ) equals 0.998. The results of the regression analysis of the ORC turbine and supercritical CO 2 turbine are shown in Figure 2b,c, for the quadratic function where the coefficient of determination (R 2 ) equals 0.972 and 0.999, respectively. The cost models showed that for the low power turbine, similar with the pump, as the electricity generation capacity increases, the cost also linearly increases, whereas for the high power turbine, as the electricity generation capacity keeps on increasing, the cost differences are decreasing.

Heat Exchanger Cost Model
A heat exchanger is required to absorb the heat from the intermediate/low temperature waste heat to provide energy to the power plant [52], as well as to cool down the working fluid of the power plant by releasing the low heat from the turbine. Generally, the types of heat exchanger used in the waste heat power plant are a shell and tube heat exchanger and a printer circuit based heat exchanger (PCHE) [53]. Both types of heat exchangers have differences in their main design factors and manufacturing methods, making it difficult to create a general heat exchange cost model. Therefore, we developed a cost model for each type of heat exchanger.
The first heat exchanger, the shell and tube heat exchanger, is used widely in the steel, cement, petro chemical, and others industries [54], thus preliminary research about its cost model were available.
Couper proposed a concept to calculate a shell and tube heat exchanger's cost by considering its cost per heat transfer area, material factor, and tube-length correction factor, as shown in Equation (2) [27]: where C P is the cost of the shell and tube heat exchanger, C B is the cost per heat transfer area, F P is the pressure factor, F M is the material factor, and F L is the tube-length correction factor. To apply the previous concept, we have to obtain cost per heat transfer area. Therefore, we surveyed the information regarding shell and tube heat exchangers installed in a power plant by referring to the US Department of Energy and created the heat exchanger's cost based on the heat transfer area [44]. Next, we established the shell and tube heat exchanger cost model with the surface area as the baseline, as shown in Figure 3a.
The second heat exchanger, printed circuit heat exchanger (PCHE), is manufactured by diffused bonding of a metal sheet after it is micro-channel etched using a chemical method [55,56]. However, because cases of PCHE application in industries are not sufficient, preliminary research about the cost model was not available. Therefore, in our research, we surveyed and analyzed the design specification and sales prices of vendors [57][58][59][60][61]. Based on the above analysis, we developed the PCHE cost model, as shown in Figure 3b. In our analysis results, the volume and cost of the heat exchanger showed an exponential relationship. The exponential relationship occurred because as the heat exchanger's volume increased, the amount of metal needed by the heat exchanger also increased exponentially.

Functional Architecture Design of TCI Estimation Module
To develop the final system based on the previously defined system requirements is not a trivial process. There are cases of a highly complicated system with plenty of requirements, that after the system is completely developed, it is required to be re-designed because it fails to address some essential requirements. In order to avoid such a problem we conducted architecture design and defined the system functions to satisfy the requirements of the TCI estimation module by following a systems engineering approach. Specifically, we performed a functional analysis to define the TCI estimation module's functions that have to be accomplished by the module from the external level to the system level (top, middle, and bottom). Moreover, in the architecture, we created an integrated architecture by linking the detailed functions with their related components. We applied Integrated Definition for Functional Modeling (IDEF0), a modeling approach that is widely used to analyze the functions of complex systems, to perform the above processes systematically. The architecture design of TCI estimation module developed through these processes is explained as follows.
The external level (level 0) of the TCI estimation module architecture is shown in Figure 4a. The level 0 of the architecture shows the information flows between the TCI estimation module and its external modules. The external modules (A1-A3) are the design modules of the main equipment of waste heat power plant, and the TCI estimation module (A0) obtain inputs from those external modules in the form of pumps, turbines, heat exchangers design factors, and specification information. From those inputs, the TCI estimation module internally implements the cost models developed earlier to calculate the equipment cost and produces the TCI value as its output. Figure 4b shows the top level of the system (level 1) of the TCI estimation module, that consists of the 'Set-up General Project Data' function to prepare the required basic information for estimating TCI and the 'Calculate Total Capital Investment' function (A52) to estimate the TCI based on the input information.
From the two functions in the level 1 architecture, the middle level of the system (level 2) architecture of the 'Calculate Total Capital Investment' function is shown in Figure 4c

Development of TCI Estimation Module Prototype
It is necessary to verify the accuracy of the TCI estimation module with the previously designed architecture. Basically, the functional architecture has defined up to the bottom level of the module, namely the unit functions, and we developed them through programming into a prototype. In this research, we use Mathworks Matlab that is optimized in computing formulas, without other separate toolbox.
In Table 6, we presented the source code of the unit function, input variables, output variables, operation principles, and algorithm to calculate the AFUDC, as an intermediate process in order to estimate the TCI. We performed similar processes for each unit function and an integrated module with all unit functions. In the developed TCI estimation module, we anticipated the cost of equipment in future years by allowing the users to input a variable called 'annual inflation rate'. This variable is used to reflect the fluctuations in the cost of equipment, raw material, and labor that finally allow the TCI estimation module to calculate the costs in future years. Table 6. Implementation example of TCI estimation module.

TCI Estimation Module Performance Verification
The most accurate method to verify whether the developed TCI estimation model estimates the TCI value properly is to input the equipment cost of an actual operating waste heat power plant to the TCI estimation model and compare the estimated TCI with the actual TCI occurred during the construction of the plant. In this case, if the difference between real TCI and the TCI estimated by the TCI estimation module falls between the range of −15% to +30%, then it can be regarded that the performance objective in this research is achieved.
However, it is difficult to perform the direct comparison because the equipment cost and TCI occurred during a waste heat power plant construction is not made available to the public due to the corporate's privacy and security issue. Moreover, power plant industries tend to close their information, which makes it difficult to gather related data. Therefore, in this research, we referred to the data provided by the US National Energy Technology Laboratory (NETL) about the Natural Gas Combined Cycle (NGCC) power plant's TCI estimation case study [62]. We compared the TCI proposed in the case study and estimated TCI from our designed TCI estimation module as an alternative approach to verify the performance of the TCI estimation module.

NETL NGCC Case Study
Before we describe the NETL NGCC case study, we would like to briefly explain the NGCC power plant to show the resemblance of it to our system of interest, a waste heat power plant. The NGCC power plant takes natural gas as fuel and uses the resulting high-temperature combustion gas to operate a set of high-pressure gas turbine and generate electricity for the first cycle. After that, the intermediate-temperature discharged gas is once again sent to a heat recovery steam generator (HRSG) unit, where steam is produced by using the remaining heat of the discharged gas. This steam is then passed through a steam turbine to generate more electricity, for the second cycle, thus the term combined cycle. Basically, the NGCC power plant are up to 20% more efficient than the coal-fired power plant because they can also generate additional electricity from waste heat by recovering it [63]. In addition, liquid natural gas (LNG), one of gas fuels, has the advantage of low pollutants such as sulfur oxide (SOx) and nitrogen oxide (NOx). For example, LNG has only 4.4% of SOx and 57% of NOx compared to coal [63,64]. The NGCC power plant has higher thermal efficiency with lower environment pollution compared to single-cycle power plants because of the afore-mentioned operation method, thus it is widely utilized in the power generation industries.
The NETL's NGCC report contains the analysis data about the TCI occurred during the construction of net power 512 MW NGCC in two plants located in the Montana and North Dakota states of the US [62]. For each plant, the report analyzes both the condition with CO 2 separation and without CO 2 separation, thus there are total of four case studies available (S31A, S31B, L31A, and L31B). In our research, we selected the S31A case study (Montana NGCC without CO 2 separation) because it has the most similar equipment configuration of the waste heat power plant. In the S31A case study, the NGCC power plant consists of a combustion turbine and generator, HRSG, steam turbine and generator, condenser, stack, and other auxiliary equipment. The process after the combustion turbine is the process of reusing the waste heat to generate power, which can be considered as the target system in our research, the waste heat power plant. Thus, we decided the boundary of our target system as the remaining equipment of the NGCC power plants excluding the combustion turbine and generator. We represent the block flow diagram (BFD) of the NGCC power plant's general structure and the target equipment in Figure 5.

TCI Analysis and Comparison
We put the input data from equipment cost of a waste heat power plant used in the NETL S31A case study to our designed TCI estimation module and compared the estimated TCI with the NETL S31A case study's TCI, in order to verify the performance of our TCI estimation module. We used the basic input data and assumptions needed for TCI estimation identical with the NETL S31A case study, as presented in Table 7.
Then, these data were connected with the input variables, output variables, and algorithms of each unit function of the previously described prototype to calculate the detailed design factors for TCI estimation. Based on the above basis and assumption of the NETL S31A, we obtained the estimated TCI from our TCI estimation module as $325,353,306, in which this value has the difference of $17,776,456 compared to the referenced TCI value of NETL S31A, as shown in Table 8. The result, +5.78% errors, showed that the TCI estimation module has achieved the target estimation accuracy class 4 (−15% to +30%), and thus can be used sufficiently for the business feasibility assessment phase.

Conclusions
A waste heat power plant that collects and utilizes unused waste heat to generate electricity has proved its production cost reduction and it is growing rapidly in high energy-consuming industries. However, despite its fast development, the waste heat power plant lacks a specialized total capital investment estimation, which makes it difficult to assess business feasibility accurately. In this research, we aimed to solve the aforementioned problem by developing a total capital investment (TCI) estimation module that could be used during a business feasibility assessment of a waste heat power plant.
In order to achieve our goal, we considered the related industry demands in developing the TCI estimation module. We implemented the systems engineering approach by exploring the stakeholders related to the value chain of the waste heat power plant and extracting requirements from them. Then, based on the requirements, we designed the system architecture of the TCI module, including its functions and detailed information. Simultaneously, we developed the cost models required by each operation of the detailed functions. We also went one step further by creating the prototype of our TCI estimation module based on the designed architecture and by performing the prototype's performance verification to the reference case study of a NETL (National Energy Technology Laboratory) NGCC (Natural Gas Combined Cycle) power plant. From the results of our verification, we have confirmed that our TCI estimation module has met its initial development goal by achieving error range of 5.78%, compared to the real data from the reference case study.
Through systematic processes, we have developed the concept to estimate the total capital of the waste heat power plant that did not exist at the time of our research. However, we are aware of the limitations in our study regarding our performance verification method by comparing the proposed solution with the case study from the reference materials. It will be more helpful to the industry if the proposed TCI estimation module results are to be compared to the real waste heat power plant's TCI value. Thus, we aim to overcome those limitations by performing additional verification of our proposed module and by improving the functions to increase the accuracy. We also plan to expand the scope of the economic analysis for a business feasibility assessment of a waste heat power plant, by providing net present value (NPV), internal rate of return (IRR), levelized cost of energy (LCOE), and other similar analyses. Moreover, the developed TCI estimation module implements the equipment cost models that consider a wide range of specifications. We expect that the TCI estimation module can be applied for small-scale waste heat power plants with quite high accuracy, since we considered low-valued specifications (our cost models start from small/near-zero specification value), however its application might not be suitable for large-scale waste heat power plants, especially when the specification value exceeds the values used during the cost model development. We are planning to analyze the accuracy of our TCI estimation module to a wide range of waste heat power plants in our future works. We also plan to expand our cost model to include more equipment, including an air cooled heat exchanger, plate heat exchanger, and other possible equipment to increase our equipment library and promote the implementation of our TCI estimation module in the real-world industry.