Systematic Comparison of ORC and s-CO₂ Combined Heat and Power Plants for Energy Harvesting in Industrial Gas Turbines

Abstract

Gas turbine power plants are widely employed with constrained efficiency in the industrial field, where they often work under variable load conditions caused by variations in demand, leading to fluctuating exhaust gas temperatures. Suitable energy harvesting solutions can be identified in bottoming cycles, such as the conventional Organic Rankine Cycles (ORC) or the innovative supercritical CO₂ (s-CO₂) systems. This paper presents a detailed comparison of the potential of ORC and s-CO₂ as bottomers of industrial gas turbines in a Combined Heat and Power (CHP) configuration. Different gas turbine models, covering the typical industrial size range, are taken into account and both full- and part-load operations are considered. Performance, component dimensions, and operating costs are investigated, considering ORC and s-CO₂ systems specifics in line with the current state-of-the-art products, experience, and technological limits. Results of the study show that the s-CO₂ could be more appropriate for CHP applications. Both the electric and thermal efficiency of s-CO₂ bottoming cycle show higher values compared with ORC, also due to the fact that in the examined s-CO₂ solution, the cycle pressure ratio is not affected by the thermal user temperature. At part-load operation, the gas turbine regulation strategy affects the energy harvesting performance in a CHP arrangement. The estimated total plant investment cost results to be higher for the s-CO₂, caused by the higher size of the heat recovery heat exchanger but also by the high specific investment cost still associated to this component. This point seems to make the s-CO₂ not profitable as the ORC solution for industrial gas turbine heat recovery applications. Nevertheless, a crucial parameter determining the feasibility of the investment is the prospective carbon tax application.

1. Introduction

The availability of natural gas at relatively low cost and the intensification of environmental regulations on air pollutants and CO₂ emissions have resulted in a shift toward gas-based power generation [1] which, in turn, is leading to the growth in Gas Turbine (GT) market. Nowadays, GTs represent one of the most widely diffused prime mover technologies for power generation in the industry thanks also to their simplicity and flexibility. Indeed, simple cycle GTs have the valuable advantages of (i) limited space requirements and reduced specific costs for moderately sized units; (ii) being placed online within minutes for fast start-up and by remote automation, so that only occasional on-site supervision is needed. As a consequence, GT engines are particularly suitable to operate under part-load conditions, to sustain those industrial processes characterized by fluctuating energy demand and also in isolated locations. For instance, GT units are usually employed in the oil and gas sector, in on-shore and off-shore installations, where they are incorporated into the oil refining process or into natural gas compressor stations for pumping natural gas through pipelines [2]. In addition, GT systems find application also in other areas: industries such as cement, glass, drying, pulp, and paper mills; chemicals production; and tertiary buildings.

The reduction of energy consumption in industry, with the implementation of new and more efficient power generation technologies, are fundamental aspects to meet the new global emission targets and cut process costs [3]. Industries employing simple cycle GTs as prime movers still offer great potential margin for low-cost energy savings and carbon reductions through energy efficiency improvements. Indeed, basic industrial GT engines have limited size, ranging up to 50 MW, with low inherent efficiency, typically not above 40%. A significant amount of fuel energy input is rejected as hot exhaust at relatively high temperatures (400–600 °C) [2]. Figure 1 shows estimated data of heat rejected by many commercial GT units (database of commercial GTs available in Thermoflex software [4] is used) covering the range of size of industrial machines.

This wasted energy could be profitably used as a secondary thermal resource in order to increase the efficiency of fuel usage and to mitigate environmental drawbacks. Wasted heat can be firstly utilized to generate additional electric energy to support the industrial process or to be sold to the grid. Moreover, Combined Heat and Power (CHP) solutions, providing steam or hot water for industrial processes, can further improve primary energy utilization, playing a significant role in achieving economic and environmental benefits [5,6,7].

A well proven Waste Heat Recovery (WHR) solution for large size power plants consists in a steam power plant as the bottomer of the GT. However, small/mid-size industrial GT cannot be always compatible with the traditional steam bottoming cycle featuring complex architecture, especially in industrial applications for which the GT operating conditions often vary following the site demand. More appropriate alternatives might consist in more flexible bottoming cycles, which allow simpler generation of the vapor, thanks to lower critical temperatures of the working fluid. Suitable solutions for the considered operating range are identified in the Organic Rankine Cycle (ORC) and the innovative CO₂ Brayton cycle, or supercritical CO₂ cycle (s-CO₂) [8]; Figure 2 compares the different operating range of heat to power conversion technologies based on bottoming thermodynamic cycles for WHR applications.

The use of an organic fluid as working fluid, in place of water, introduces several advantages over conventional steam plants for low- to mid-temperature applications [9]: lower fluid specific volume resulting in smaller, more compact, and cheaper equipment; higher condensing pressures (being equal the condensing temperature), reducing turbine size requirements and air-in leakage potential; and dry turbine expansion, avoiding moisture droplets that can cause erosion damage of the turbine blades. More specifically, s-CO₂ technology is competitive with the ORC solution, thanks to its other exclusive features, including high density fluid similar to liquid water throughout the cycle; non-toxic, inexpensive, nonflammable working fluid; and abundant working fluid, possibly provided by greenhouse gas emission sequesters [10].

ORCs are quite diffused in the market and commonly used to generate power in different industrial heat recovery applications with more than 340 MW of installed capacity in the world [11,12]. Many of these applications are WHR from gas turbines, mostly installed on compressor stations along gas pipeline. Important WHR opportunities also come from the cement, metal, and glass industries; nevertheless the ORC installed capacity in these sectors is still scarce compared to its potential [13,14,15,16]. The barriers that prevent the growth of this market are, in particular, the lack of green incentives and the long-term paybacks, which determine a high risk on the investment. In addition, industrial capital budgets are limited, and industries usually prefer to give priority to safer investments closer to the company’s core business [17].

The s-CO₂ cycle has also long been known, but despite the extensive research carried out in the field, the technology is still at an early stage and not yet ready to be introduced in the market. Current challenges in the s-CO₂ design concern: (i) the development of compact high pressure heat exchangers at reasonable cost, (ii) the reduction of leakage and mechanical losses in turbomachines, and (iii) the optimal regulation and safe operating conditions of the compressor close to the CO₂ critical point [13]. Nowadays, different research programs are being carried out by both industrial and academic research institutes, to develop prototypes of s-CO₂ and study how to overcome these issues. Among them must be mentioned the “EPS100”, proposed by Echogen as the first megawatt topping-class commercial-scale supercritical s-CO₂ heat engine, in the phase of validation testing [18], specifically designed for small-scale gas turbines combined cycle (~30 MW total output) applications.

The literature on ORC for industrial WHR applications is extensive; in particular, a detailed investigation of ORC potential as bottomer in an industrial application, comparing several GT models also at part-load operation, is proposed by Bianchi et al. [19]. However, the same does not apply for s-CO₂. The research is still scarce regarding the medium-to-low temperature CO₂ power cycles applications, especially considering industrial GTs as topper cycle. It can be cited the study proposed by Zhou et al. [20], analyzing complex combined cycle system for off-shore GT WHR, involving s-CO₂ plus a transcritical CO₂ cycle. The analysis is applied to the commercial GT model “Solar TITAN 130”, demonstrating promising performance and economic gains for s-CO₂ application in the oil and gas sector.

At present, only few studies are dedicated to comparing ORC and s-CO₂ as industrial WHR solutions. The study of Astolfi et al. [21] compares CO₂ power cycles and ORC, providing thermodynamic performance maps as a function of different heat sources’ maximum temperature (200–600 °C) and cooling grades. The authors demonstrated that the most convenient choice sensibly depends on the actual boundary conditions. Yoon et al. [22] compared the off-design performance of ORC and transcritical CO₂ cycle, as the bottoming cycle of a micro gas turbine. They highlight how a CO₂ recuperated cycle can be more performant at part-load operations than a simple ORC. In particular, the CO₂ recuperated cycle exhibits a more efficient heat exchange process at the heat recovery unit, due to the presence of the recuperator. However, a more comprehensive analysis could be performed also including an ORC recuperated configuration.

Except for a few works, the literature lacks studies regarding applications of CO₂-based WHR, in industrial likely operating conditions and specific comparison with its main competitor, the ORC. In a previous work of the authors [23], a preliminary analysis has been performed, comparing s-CO₂ and ORC pure electric and CHP configurations as bottomer of different GT models in design conditions. The additional novel contribution of this work relies on a more systematic investigation on ORC and s-CO₂ potential as energy harvesting technologies inside an industrial facility, employing GT at both full and part-load operation. The performance of ORC and s-CO₂ systems are evaluated as bottoming of selected industrial GT models in CHP configuration. For this purpose, Thermoflex commercial software, providing the GT PRO gas turbine library, has been used for the simulations. The ORC and s-CO₂ systems specifics and costs assumptions have been chosen in line with industrial products and state-of-the-art research experience. A comprehensive analysis has been carried out discussing energy results in terms of electric and thermal power additional production, efficiency, primary energy savings, but also components dimensions, costs, and feasibility. The performance of the whole power plant is evaluated both in design and in part-load operating conditions to account for a realistic load profile.

In comparison to the existing publications, it is the aim of the present work to offer an original contribution in the following aspects:

• The s-CO₂ supercritical cycle is systematically evaluated as bottomer of different GT models for industrial applications, considering realistic operating conditions and part-load operation.
• A comparison between ORC and s-CO₂ power systems performance as industrial WHR solutions is performed. The analysis accounts not only for the thermodynamic cycle but also for the systems specifics and technological limits determined by the state of the art of the technologies.
• An investment cost assessment is proposed for a comprehensive comparison between ORC and s-CO₂ power systems. The influence of the design aspects affecting the investment cost are discussed in detail, highlighting the difference between the compared systems.

The paper is organized as follows: Section 2 describes the analyzed power plant configurations, its specifics, and assumptions made for the simulations; Section 3 explains the adopted modeling approach; Section 4 presents the performance results both in design and at part-load conditions; in Section 5, considerations about component size and investment costs are made; in Section 6, the economic assessment of the bottoming cycles based on the yearly operation is evaluated; and finally Section 7 presents the main conclusions.

2. Power Plant Specifics and Operating Conditions

In this section, the assumptions in terms of analyzed power plant architectures, operating conditions, and imposed technological limits are described. First of all, the whole plant configuration is presented, then the gas turbines, the s-CO₂, and the bottomer cycle selected specifics are discussed in more detail in the dedicated subsections.

2.1. Plant Architecture

The combined heat and power plant comprises the topper gas turbine unit and the bottomer cycle, generating electricity to sustain the electric user and the hot water circuit supplying heat to the thermal user (as schematized in Figure 3). In the considered configuration, the gas turbine exhaust gas is directly conveyed into the heat recovery heat exchanger, here named “GAS HX”.

The considered s-CO₂ system, represented in Figure 3a, is based on the closed Brayton thermodynamic cycle. In this cycle, the CO₂ circulates through the plant being heated into the heat recovery heat exchanger (“GAS HX”), expanded into the turbine, cooled (into the “COOL HX1”), and pressurized by means of a compressor. A simple recuperated cycle is considered as a basic compact and flexible setup. Thus, the efficiency of the s-CO₂ is enhanced using an internal heat recuperator (“REC HX”). A generator (GEN) converts the shaft mechanical power into electric power to supply to the electric user. Two heat exchangers employed for cogenerative purpose are present into the plant, named “COOL HX1” and “COOL HX2”, recovering heat respectively from the CO₂ cooling heat exchanger and from the exhaust gas, downstream of the GAS HX, to supply thermal power to the thermal user hot water circuit.

The ORC subcritical recuperated architecture, represented in Figure 3b, is chosen as comparative bottoming system according to the current state of the art of waste heat recovery applications [8]. In this cycle, an organic fluid circulates through the plant being evaporated and superheated into the heat recovery heat exchanger (“GAS HX”), expanded into the turbine, condensed (into the “COOL HX”), and pressurized by means of a pump. An internal heat recuperator (“REC HX”) is used also in this case to improve the cycle efficiency, without over complicating the plant. A generator (GEN) converts the shaft mechanical power into electric power to supply to the electric user, whilst the condenser of the ORC serves as heat exchanger for cogenerative purpose, to supply thermal power to the thermal user hot water circuit.

Before discussing the single systems specifics, some boundary operating conditions concerning the whole power plant operation, are here introduced. These conditions regard: (i) the hot water temperature requested by the thermal user and its return temperature, assumed equal to 90 °C and 25 °C, respectively; (ii) the minimum temperature of the gas turbine exhaust gases at the exhaust stack, limited at 125 °C to avoid the cold-end corrosion issues in the exhaust stack.

Related to these assumptions is the choice of considering two gas heat exchangers for the s-CO₂ configuration, instead of one (see heat exchangers GAS HX and COOL HX2, in Figure 3a). COOL HX2, placed downstream GAS HX, allows to maximize the gas residual heat recovery, by further cooling down the gas until the minimum stack temperature. Indeed, in the s-CO₂ case, it has been observed that a single heat exchanger would not allow to discharge the gas below 250 °C, causing just a partial heat recovery [23]. On the contrary, the GAS HX of the ORC solution has proved to be more performant, as discussed in more detail in the results section.

2.2. Industrial Gas Turbines Specifics

A variety of gas turbine models with different size are employed in industrial applications. Small and mid-size machines (MW size range) are used in flexible multiple arrangements, installed on board of small production facilities, usually operating at part-load conditions, e.g., in off-shore plants. Larger power rating units (ranging up to tens of MW), both heavy-duty and aeroderivative machines, are preferred instead on larger facilities requiring higher power needs and working under more stable conditions. Thus, to perform a systematic analysis, four different types of commercial gas turbines, in terms of size and regulation strategy, are investigated; in particular, gas turbine models often used in the oil and gas sector are considered [19,24].

The design data of selected GT units are summarized in

Table 1. Selected gas turbines nominal data.

	Kawasaki GPB15 (GT1)	GE5 (GT2)	Solar Titan 130 (GT3)	Siemens GT 700 (GT4)
Output power (MW)	1.5	5.5	15	30
Turbine inlet temperature (°C)	991	1232	1093	1260
Pressure ratio (-)	9.4	14.8	15.7	17.6
Efficiency (%)	24.2	30.6	33.3	36
Exhaust flow rate (kg/s)	8	19	49	89
Exhaust temperature (°C)	520	574	474	518
Regulation strategy	VTIT	VIGV	VTIT	VSS

. These gas turbine models are characterized by sizes ranging between 1 and 30 MW, with efficiency values increasing with the size, from 24% for Kawasaki GPB15 up to 36% for Siemens GT 700 machine. Important variables to also consider are the temperature and the flow rate of the exhaust gases, which affect the amount of energy that can be recovered by the bottomer power cycle. In particular, exhaust gas mass flow rate raises with the gas turbine size and it ranges between 8 and 89 kg/s for the selected gas turbines. Exhaust gas temperature is centered around 500–550 °C, varying between 474 and 574 °C.

These values can significantly vary at part-load conditions, strongly influencing the bottoming cycle performance.

Figure 4 reports manufacturer data provided by the GT PRO gas turbine library [4], showing how the exhaust flow rates and temperatures values vary with the gas turbine load for the different models; it can be observed that different gas turbine regulation strategies determine different trends. Three kinds of regulation strategies can be distinguished, here named VTIT (variable turbine inlet temperature), VIGV (variable inlet guide vanes), and VSS (variable shaft speed), which consist of:

• VTIT—variable amount of fuel injected in the combustor into a constant air mass flow rate; hence, regulating the air–fuel ratio and so the turbine inlet temperature. This leads to exhaust temperatures, which decrease as the gas turbine load (GT load) decrease, whilst the exhaust flow rate remains almost constant. GT1 and GT3 are examples of gas turbines regulated by means of the VTIT control.
• VIGV—variable compressor geometry resulting in a variable air mass flow. This kind of regulation strategy allows to work at part-load conditions without decreasing the operating temperatures, whilst the mass flow rate decreases with the load. GT2 is an example of gas turbine regulated by means of the VIGV control.
• VSS—variable shaft speed at the gas generator in multi-shaft engines. This is the strategy that allows for the most limited reduction in shaft efficiency at part-load conditions, compared to the other strategies. A decrease in both the exhaust temperature and flow rate occurs in this case. GT4 is an example of gas turbine regulated with the VSS control strategy.

2.3. Supercritical CO₂ Cycle and ORC Specifics

The choice of the s-CO₂ component specifics and boundary operating conditions, as shown in

Table 2. Bottomer cycles design specifics.

	s-CO2		ORC
Size	<3 MW	>3 MW	<3 MW	>3 MW
Fluid	Carbon Dioxide		MM	Cyclopentane
Low pressure	75 bar		0.9 bar	3.7 bar
High pressure upper limit	300 bar		17 bar	40 bar
Turbine isentropic efficiency	85%	90%	80%	85%
Op. machine isentropic efficiency	70%	80%	60%
Recuperator thermal effectiveness	80%
Pressure drop across heat exchangers	1%
Heat exchangers normalized heat loss	1%
Heat exchangers minimum pinch point	5 °C
Other limits	Min. temperature = 35 °C		Max. temperature = 280 °C
	(supercritical threshold)		(stability limit)

, are derived from a literature survey based on different studies and experimental data [20,22,25,26]. The compressor minimum inlet temperature and pressure are imposed respectively equal to 35 °C and 75 bar. This choice grants maintaining supercritical conditions all along the cycle, given CO₂ temperature equal to 31 °C and critical pressure equal to 74 bar. In line with the current research data, the cycle maximum pressure is limited to 300 bar because of technological limits. The turbine and the compressor isentropic efficiencies values are considered different for s-CO₂ power plant size lower or higher than 3 MW to account for the machine size-effect over the performance. The recuperator thermal effectiveness minimum pinch point assumed for the heat exchangers, pressure drops, and heat loss values are also reported in Table 2, and are chosen equal for the ORC and the s-CO₂ systems for a fair comparison between the two systems.

The ORC components specifics and boundary operating conditions are selected as consistent with existing industrial established products [19] (see Table 2). The first design decision concerns the choice of the working fluid. Cyclopentane and hexamethyldisiloxane (MM) (respectively belonging to the hydrocarbon and the siloxane families) are the selected fluids since they are state-of-the-art organic fluid in industrial medium waste heat recovery application [19]. Fluids belonging to the hydrocarbon and siloxane families are demonstrated to be the most suitable fluids for the medium temperature applications, thanks to their quite high critical temperature. Indeed, a value of the critical temperature quite similar or slightly higher than the target evaporation temperature is suggested to simultaneously achieve good thermal matching between fluids and exhaust gas and to avoid excessively low vapor densities, which lead to increasing system cost. Cyclopentane and MM feature similar critical temperature and thermal stability limits, while they appreciably differ in terms of critical pressure and molecular weight. In particular, MM presents a higher molecular weight, which leads to lower speed of sound during the expansion, allowing to design the turbine with a lower number of stages (even only a single stage). This is the main reason why MM is the ideal candidate for small size applications (ORC size < 3 MW), even if, on the other hand, due to its high molecular weight, MM also presents smaller enthalpy drop and expansion specific works if compared to cyclopentane.

The operating conditions bounded by the selection of a working fluid rather than another are the cycle maximum temperature and the evaporating and condensing pressure values. In more detail, the temperature is conservatively limited to 280 °C to not overcome thermal stability limit corresponding to 300 °C. The cycle maximum pressure (corresponding to the evaporating pressure) is limited to the 90% of the critical pressure value (equal to 45.1 bar for the cyclopentane and 19.4 bar for the MM). The condensing pressure instead mainly depends on the cooling medium temperature. Its value can be considered as a first approximation equal to the fluid saturation pressure value at the cooling medium temperature (see Figure 5a). In this case also, the turbine and the pump isentropic efficiencies values are considered different for ORC power plant size lower or higher than 3 MW, to account for the machine size-effect over the performance.

Fluids thermodynamic properties useful for the analysis are reported in Figure 5; where the saturation pressure and density are plotted against temperature.

3. Modeling Approach

Thermoflex commercial software [4] was used to simulate the whole combined power plant, involving both the gas turbine unit and the bottoming cycle, i.e., the s-CO₂ or the ORC system. Thermoflex is software dedicated to designing complex power plants, which relies on a built-in library of components modeled on the base of a lumped parameters approach. By following three consecutive steps, namely “Thermodynamic design”, “Engineering design”, and “Off-design”, the software allows for the simulation of the energy systems performance both in design and off-design operation. In the first step, “Thermodynamic design”, the software solves preliminary energy and mass balances to evaluate the plant thermodynamic performance. In the second step, the “Engineering design”, the size and the geometry details of each components is established, on the basis of the imposed design boundary conditions and components specifics. Finally, in the “Off-design” step, being defined the design characteristics of single components, it is possible to evaluate the plant performance in operating conditions different from the design ones.

The approach used to model the single components of the plant at part-load conditions is described below:

• The gas turbine unit is modeled as a single component by means of a black box approach. This component can simulate a wide choice of commercial gas turbine models that are featured in the GT PRO gas turbine library, accounting for design data and performance maps directly supplied by the manufacturers.
  The bottomer cycle instead is modeled by connecting the single components that constitute it: i.e., the heat exchangers, turbine, condenser, and operating machine. In this case, some inputs defining the components performance must be imposed by the user. Specific component inputs are summarized in Table 2.
• The heat exchangers’ off-design behavior is described by the so called “thermal resistance scaling” method. Following this method, the design point convective heat transfer coefficients ($U{A}_{des}$) of the generic fluid involved in the heat exchange, is scaled as function of the ratio between the actual mass flow rate, $\dot{m}$, and the one calculated in the design point, ${\dot{m}}_{des}$. A scaling exponent equal to 0.8 (which recalls the exponent for the Reynolds number in the Dittus Boelter correlation) is applied to the mass flow rate ratio. This approach is valid since the thermal–hydraulic properties of the fluids do not change much over the range of considered conditions, and the fluid velocity remains the main parameter affecting the heat transfer coefficients.

  $$UA=U{A}_{des}\times {\left(\frac{\dot{m}}{{\dot{m}}_{des}}\right)}^{0.8}$$

  (1)
  It can be pointed out that in conditions of fluid phase change or in proximity of the critical pressure, the program implement a discretization of the heat exchanger for the determination of the heat exchanger’s $UA$, automatically assigning distinct zones for each phase of the fluid, or if the pressure is near the critical pressure, 13 equally weighted zones are assumed.
  Normalized heat loss in the heat exchangers is computed as a percentage, relative to the heat transferred out of the higher temperature fluid. The pressure drops across the heat exchangers, $\Delta p$, is obtained by means of Equation (2), expressing the relationship between the flow resistance coefficient $\mu$ (initialized in the design-point), the pressure drops, the mass flow rate $\dot{m}$, a dimensional constant $C$, and the average specific volume $v$ (mean between the specific volumes at the inlet and at the outlet).

  $$\mu =\frac{\Delta p}{v\times {\dot{m}}^2\times C}$$

  (2)
• The turbine inlet conditions, in terms of temperature and flow rate, vary at part-load operation depending on the exhaust gas temperature and flow rate values. The turbine inlet temperature, $T$, is kept equal to its maximum possible value, respecting the constraints related to the GAS HX performance and the fluid thermal stability limit. The off-design inlet pressure, $p$, is determined consequently by assuming the “sliding pressure” part-load control. Following this regulation strategy, the pressure at the turbine nozzle inlet vary proportionally to the mass flow rate, $\dot{m}$, in order to keep constant the flow function parameter value, $FF$, assuming chocking conditions.

  $$FF=\frac{\dot{m}\times \sqrt{T}}{p}=\mathrm{const}$$

  (3)
  However, there are situations in which it is not possible to maintain constant the flow function parameter, as happens for example when the fluid temperature at the expander inlet changes significantly. In this case, the turbine isentropic efficiency, ${\eta }_{is}$, is reduced with respect to its full load value, ${\eta }_{is,des}$, based on the flow function, as follow:

  $${\eta }_{is}={\eta }_{is,des}-\frac{{\left(\dot{m}\times \sqrt{v/p}\right)}_{des}}{\dot{m}\times \sqrt{v/p}}$$

  (4)

4. Performance Results

4.1. Design

In this section, the s-CO₂ and the ORC configurations are compared in their design operation as bottoming cycles of the four different selected gas turbines. Indexes analyzed in this section are (as defined in

Table 3. Performance indexes for design performance evaluation.

Index	Equation
Heat recovery effectiveness	$\epsilon =Q_{rec}/Q_{ava }$=$\frac{Q_{GAS HX}}{{\dot{m}}_{ex }\times c_{p,ex }\times (T_{ex}-T_{amb})}$
Bottoming cycle efficiency	${\eta }_{bott}$ = $P_{net,bott}/Q_{GAS HX}{}_{ }$
Relative bottoming power production	$\lambda =P_{net,bott}/P_{GT }$
Bottomer expander power	$P_{exp}$, with $P_{net,bott}=P_{exp}-P_{op. machine}$
Electric efficiency	$\eta =\frac{P_{net,bott}+P_{GT}}{F}$
Thermal efficiency	$\tau =\frac{Q_{cog}}{F}$, with $Q_{cog}=\{\begin{array}{c}{Q}_{COOL HX1}+Q_{COOL HX2 }, if s-C{O}_2\\ Q_{COOL HX} , if ORC\end{array}$
Primary energy saving	$PES=1-\frac{1}{\frac{\eta }{{\eta }_{ref}}+\frac{\tau }{{\tau }_{ref}}}$, with ${\eta }_{ref}$= 52.5% and ${\tau }_{ref}$ = 90% (source [28])

): (i) the heat recovery effectiveness, $\epsilon$, (ii) the bottoming cycle efficiency, ${\eta }_{bott}$, (iii) the relative, $\lambda ,$ and absolute bottoming power production, $P_{net,bott}$, (iv) the plant efficiency,$\eta$ and $\tau$ and primary energy savings, $PES$.

Figure 6a indicates that the ORC system can recover a higher amount of thermal power at the heat recovery heat exchanger (“GAS HX”), showing higher heat recovery efficiency, slightly increasing with the gas turbine size (GT size). The better heat recovery performance of the ORC is also due to the heat transfer coefficients of the MM and cyclopentane compared to the CO₂ cases, especially given by the fluid phase change inside the evaporator. As anticipated in Section 2, because of the better heat recovery performance of the ORC, this configuration is able to fully exploit the exhaust gases’ residual heat by means of a single heat recovery heat exchanger. On the contrary, for the s-CO₂ case, it has been observed that a single heat exchanger would not allow to discharge the gas below 250 °C, causing just a partial heat recovery. From these considerations comes the choice of considering two gas heat exchangers for the s-CO₂ configuration, instead of one (see heat exchangers GAS HX and COOL HX2, in Figure 3a), with the aim of further exploiting the exhaust residual heat to provide additional thermal power to the cogenerative thermal user.

Despite the ORC presenting higher heat recovery efficiency, the s-CO₂ is demonstrated to better exploit the recovered thermal power, showing higher bottoming cycle efficiency, up to the 28% (see Figure 6b). The ORC efficiency instead does not exceed the 18%. In general, the bottoming cycle efficiency increases with the GT size and the thermal power available with the exhaust gas. More specifically, some considerations can be made about the bottoming cycles’ performance in combined heat and power application and the influence of the thermal user requested temperature. It is observed that the ORC expander enthalpy drop (thus, the specific work) can be considerably affected by the condensing temperature, which determine the condensing pressure and the expander pressure ratio, consequently. This is not valid instead for the s-CO₂ pressure ratio, which does not depend on the thermal user requested temperature. This explains the not excellent ORC electric production performance [23].

The bottoming cycle power production depends on both the heat recovery efficiency and the cycle efficiency and, more specifically, the product between the two. Figure 7 presents the bottoming cycle design performance in terms of actual power production, showing that the s-CO₂ is the system that exhibits a higher electric power production under the same topper gas turbine. The s-CO₂ allows generating, on average, 31% of the power produced by topper gas turbine, whilst the ORC, 25% (see Figure 7a). The relative bottoming power production decreases with the gas turbine size, caused by the increase of the gas turbine efficiency, which leads to a decrease of the relative rejected heat.

The absolute net bottomer power production ranges between 578–81,117 kW and 447–6580 kW, for the s-CO₂ and the ORC, respectively (see Figure 7b), increasing with the GT size. An interesting point to take into consideration is the amount of power required by the operating machine to sustain the bottoming cycle, and its weight on the expander power production, equal on average to 40% for the s-CO₂ and to 9% for the ORC. This point indeed may not be determinant on the energetic performance, but it can be when evaluating the economic aspect, as discussed in the economic results section.

To comprehensively evaluate the electric and thermal performance of the whole power plant, the PES index is plotted on the electric and thermal efficiency cartesian plane in Figure 8. The electrical efficiency increases with the GT size ranging between the 35% and the 45%. It means that the plant electric efficiency increments with respect to the gas turbine efficiency only, on average of 8.7 percentage points with the s-CO₂ and of 7.0 percentage points with the ORC bottoming system. On the other hand, the thermal efficiency generally decreases by increasing the GT size, due to the consequent decreasing relative discharged heat. The thermal efficiency is limited in a narrow range centered around the 36% for the ORC solution, whilst it varies more for the s-CO₂ case, ranging between the 37% and the 44%. The corresponding PES values are increasing with the GT size and largely positive in many cases (up to 22% for GT4 with s-CO₂ cycle). The achievable primary energy savings are attractive in most of the cases. Only in case of GT1 does the ORC bottomer becomes less attractive, showing PES close to 0.

4.2. Part-Loads

In this section the part-load performance of the bottoming cycles is analyzed as a function of the GT load, varying between its technical minimum, assumed equal to 40%, and full load. The trends of the bottoming cycle produced electric and thermal power, normalized on their design values, are reported in Figure 9. The normalized values are useful to immediately compare the effect of the gas turbines regulation strategy on the bottoming cycles’ part-load performance.

Focusing on the electric production (see Figure 9a), it can be observed that the s-CO₂ system maintains higher part-load performance when working with GT1 and GT3 turbines regulated by means of the VTIT strategy; thus, working with almost constant exhaust flow rate (see Figure 4a). On the contrary, the ORC power plant results to be more performant when working with GT2, and following GT4, GT1, and GT3, thus benefitting from working with exhaust temperatures that do not change significantly with respect to the design values (see Figure 4b).

The same considerations apply to the thermal power production at part-load conditions (see Figure 9b). It can be also observed that a higher performance derating occurs for the ORC configuration with respect to the s-CO₂, except for the GT2 case, which is instead in line with the s-CO₂ curves.

5. Components Size and Investment Considerations

Besides performance considerations, it may be also important to take into account some design aspects affecting the investment cost and the system footprint. In this section, different size indexes are introduced as necessary to estimate the component investment costs, by means of chosen cost correlations. Then, the size and investment results are discussed.

5.1. Indexes and Correlations

The size indexes comprise the heat exchangers global heat transfer coefficient, $UA$, and the turbine size parameter, $SP$. The first depends on the heat exchanger exchanged power, $Q$, and its mean logarithmic temperature difference, $\Delta T_{ml}$; see Equation (5). The second is defined as the ratio between the fluid volume flow rate evaluated at the expander outlet pressure, and the isentropic enthalpy drop trough the expander, $\Delta h_{is}$; where the volume flow rate is given by the ratio between the fluid mass flow rate, $\dot{m}$, and its density, ${\rho }_{out,is}$, see Equation (6). Thermodynamic properties of the working fluid are calculated by means of the Refprop thermodynamic library [27].

$$UA=\frac{Q}{\Delta T_{ml}}$$

(5)

$$SP=\frac{{\left(\dot{m}/{\rho }_{out,is}\right)}^{0.5}}{\Delta h_{is}{}^{0.25}}$$

(6)

The generic formula to evaluate the i-th component investment cost, $C_i$, is based on re-scaling a reference cost value, $C_{\mathrm{ref}}$, by the ratio between the actual component size, $siz{e}_i$, and its reference size value, $siz{e}_{\mathrm{ref}}$ [29]. An exponent, $n$, is usually applied to the scaling factor and the effect of some operating conditions can be accounted by applying some correction factors, $corr$, see Equation (7). In this analysis, the correlation parameters (as reported in

Table 4. Cost correlations.

	Component	${\mathit{C}}_{\mathrm{ref}}\mathbf{Value}$	Size Parameter	${\mathrm{Size}}_{\mathrm{ref}}\mathbf{Value}$	$\mathbf{n}$	$\mathrm{corr}$
s-CO2 [30]	Turbine	149,732 EUR *	$P_{exp}$	1 MW	0.5561	/
	Compressor	1,008,600 EUR *	$P_{op. machine}$	1 MW	0.3992	/
	GAS HX	40.55 EUR *	$U{A}_{GAS HX}$	1 W/K	0.7544	/
	REC HX	40.55 EUR *	$U{A}_{REC HX}$	1 W/K	0.7544	/
	COOL HX1,2	26.96 EUR *	$U{A}_{COOL HX}$	1 W/K	0.75	/
ORC [31]	Turbine	1,230,000 EUR	$SP$	0.18 m	1.1	/
	Pump	14,000 EUR	$P_{op. machine}$	200 kW	0.67	/
	GAS HX	1,500,000 EUR	$U{A}_{GAS HX}$	4000 kW/K	0.9	$f\left(p_{max}\right)$
	REC HX	260,000 EUR	$U{A}_{REC HX}$	650 kW/K	0.9	$f\left(p_{max}\right)$
	COOL HX	530,000 EUR	$A_{COOL HX}$	3563 m2	0.9	/

* Values converted from original values in US dollar.

) come from literature works providing data from s-CO₂ and ORC and specific components vendors (respectively [30,31]).

$$C_i=C_{ref}{\left(\frac{siz{e}_i}{siz{e}_{ref}}\right)}^n\times corr$$

(7)

5.2. Results Discussion

The computed values of the heat exchangers global heat transfer coefficients and the turbine size parameter are reported in Figure 10. Figure 10a shows the total heat exchanger size (expressed in terms of $UA$) and its distribution between the different heat exchange sections, “GAS, HX”, “REC, HX”, and “COOL, HX”. From Figure 10a, it can be observed that the total heat exchanger size is similarly divided among the various heat exchange sections, varying the examined gas turbine for a given bottoming cycle solution, whilst the $U{A}_{rec,HX}$ value is similar between the s-CO₂ and the ORC solutions, suggesting similar internal heat recovery conditions, and $U{A}_{gas,HX}$ and $U{A}_{cool,HX}$ can greatly differ. s-CO₂ $U{A}_{gas,HX}$ is on average 9 times the ORC $U{A}_{gas,HX}$, mainly because of the higher convective heat transfer coefficient of cyclopentane/MM into the evaporator, also due to the fluid phase change, which guarantees a more performant heat exchange. Concerning instead “COOL HX” (comprehending both “COOL HX1” and “COOL HX2” for the s-CO₂), $U{A}_{cool,HX}$ values are more similar between the different configurations. However, a slight increase in the size parameter is observed when using the ORC rather than the s-CO₂ solution, indicating worse matching between the working fluid heat exchange profile and that of the cold source. This analysis suggests that higher heat exchanger investment costs can be expected if installing s-CO₂ bottoming cycle rather than ORC, given the higher total heat exchanger size, which can be more than 3 times the ORC configuration’s one.

Opposite conclusions can be drawn from the turbine size parameter analysis. Focusing on Figure 10b, it can be observed that comparing the different bottoming cycle options, the s-CO₂ exhibits lower turbine size parameter values, mainly due to the higher density of the fluid passing through the expander. Indeed, the s-CO₂ cycle works at high pressures, between 300 and 75 bar, corresponding to relatively high CO₂ density values that range between 700 and 60 kg/m³. Cyclopentane and MM, instead, both expand in ORC at lower pressure and lower density (below 10 kg/m³), leading to less compact expander machines (see Figure 5b).

The investment cost results reflect the considerations made about the components size. Figure 11 shows that the s-CO₂ requires significantly higher heat exchanger costs because of the large size of the GAS HX but also the high investment cost still associated to this component, due to the current challenges related to the structure design and the selection of materials compatible with the high cycle pressures and the strong corrosive behavior that CO₂ shows at high temperatures [32]. The s-CO₂ also requires larger size (see Figure 7b) and more expensive operating machines. On the other hand, the ORC operates with larger turbines, which entail higher expander investment costs. In the view of the above, the total investment cost, given by the sum of the single component costs, result in being fairly higher for the s-CO₂ rather than for the ORC, despite the s-CO₂ present both better electric and thermal performance (as discussed in Section 4).

6. Yearly Operation and Economic Assessment

A yearly demand profile of a natural gas compressor station is considered here as reference case study to evaluate the yearly energetic production of the proposed bottoming cycles, namely the s-CO₂ and the ORC, and their feasibility. In first analysis, an average carbon tax value is assumed for the reference case. Then, the investment is evaluated by considering also more favorable economic conditions, i.e., a full load yearly demand profile and a higher carbon tax value.

6.1. Economic Indexes

The return on the investment is estimated by assuming that introducing the bottoming cycle produces a fuel saving as it would cover the energy demand that otherwise should be provided by another energetic system. This primary energy saving, $E_{PES}$, is computed as follows, considering both the electric, $E_{net,bott}$, and the thermal energy production, $E_{cog}$, in a year:

$$E_{PES}=\frac{E_{net,bott}}{{\eta }_{ref}}+\frac{E_{cog}}{{\tau }_{ref}}$$

(8)

The reduction of the fuel consumption is reflected in reduced greenhouse gas emissions and in reduced plant operation costs. The differential net present value has been calculated according to Equation (9), where $C{F}_i$ is the differential cash flow at the i-th year corresponding to the yearly avoided costs,$q$ is the discount rate assumed equal to 6%, I is the total investment, and $PB$ is the payback period considered equal to 20 years.

$$\Delta NPV={\displaystyle \sum }_{i=1}^{PB}\frac{C{F}_i}{{\left(1+q\right)}^i}-I$$

(9)

The avoided costs include the fuel purchasing reduction and the CO₂ emission avoided cost. The cost due to the fuel consumption is function of the fuel saving and its specific cost per unit of primary energy, $C_{fuel}$. The cost due to the CO₂ emissions is computed as the product between the avoided mass and its specific cost, $C_{CO2}$. It is assumed that the avoided CO₂ amount is equal the CO₂ mass that would be produced by the stoichiometric combustion of the fuel saved, assumed to be natural gas (thus, the fraction of carbon, $x_C$, is likely considered equal to 0.75 and the lower heating value, $LHV$, is considered equal to 47 MJ/kg [33]).

$$C{F}_i=E_{PES}\times \left(C_{fuel}+\frac{44}{12}\times \frac{x_C}{LHV}\times C_{CO2}\right)$$

(10)

$C_{fuel}$ is chosen equal to the average natural gas price in Europe in 2019, 26.7 EUR/MWh [34], and a reference carbon tax value is selected equal to 40 EUR/ton, as in line with its average value in some European countries [35].

6.2. Reference Case Results

In the reference case, the gas turbine load profile of a natural gas compressor station [36] is considered. The number of operating hours (on the yearly base) in which the gas turbine works at given GT load are presented in Figure 12. It is shown that the gas turbine works at full load for about half of the operating hours, whilst for the rest of the time, the GT load is almost equally distributed between the 50% and the 90%.

A summary of the design performance results, the yearly energy production and savings, is reported in tabular form (see

Table 5. Results summary.

	GT1		GT2		GT3		GT4
	s-CO2	ORC	s-CO2	ORC	s-CO2	ORC	s-CO2	ORC
Bottomer size (MW)	0.58	0.45	1.70	1.30	3.86	3.19	8.11	6.58
Electric power output (MW)	2	1.87	7.02	6.65	16.25	15.66	35.73	34.54
Thermal power (MW)	2.65	2.23	6.94	6.42	15.07	13.49	29.30	28.36
Electric energy (GWh/year)	15.32	14.43	54.36	51.95	124.81	120.69	274.38	266.89
Thermal energy (GWh/year)	21.47	17.12	56.55	52.46	121.52	103.57	233.24	220.31
Fuel saving (GWh/year)	32.19	25.64	87.63	78.45	189.62	161.75	371.16	342.37
Avoided emissions (tonCO2)	1.88	1.50	5.13	4.59	11.09	9.46	21.72	20.03
Economic gain (kEUR/year) *	75.33	60.01	205.09	183.61	443.80	378.57	868.68	801.30

* Reference case results—Figure 12 demand profile and $C_{CO2}$ = 40 EUR/ton

). As discussed in the previous sections, the s-CO₂ configurations exhibit better performance than the ORC, in design operation, both concerning the electric and the thermal production. The yearly energetic results demonstrate that this applies also to the yearly based performance; indeed, the s-CO₂ allows saving, on average, 16% more fuel than the ORC solution and consequently also 16% more CO₂ emissions. The same increase is observed for the yearly economic gain.

Yet, in spite of the significant economic gain expected from the s-CO₂ operation, the net present value of the investment does not seems to always be favorable on this system, as shown in Figure 13 (see “s-CO₂ ref” and “ORC ref” data). This is mainly due to the fact of the still high investment costs associated with this fledgling technology, in particular concerning the recovery heat exchangers. However, given the considerable economic gain, it is not excluded that once the technology becomes established, s-CO₂ may become a very competitive solution for industrial gas turbines’ heat recovery. On the other hand, the current lower investment costs required to install an ORC system make this solution practical and often profitable.

6.3. Costs Parametric Analysis

Factors that can influence the bottoming cycles’ feasibility, and which can considerably vary from application to application, are the user profile demand and the carbon tax value. The profile demand can be more or less shifted to high or low loads, whilst the carbon tax value is variable from country to country can be null or even equal to 108 EUR/ton, as in the case of Sweden [35]. Thus, to complete the economic analysis, the investment is evaluated by considering also more favorable economic conditions, i.e., a full load yearly demand profile (see Figure 13a) and a higher carbon tax value, equal to 108 EUR/ton (see Figure 13b).

These results reveal that among the two analyzed factors, the most decisive one on the return of the investment is surely the carbon tax value. It is observed, indeed, that higher values of the carbon tax reduce the gap between the gain obtained with the ORC and the one obtained with the s-CO₂ (see Figure 13b). This is due to the higher valorization of the avoid emissions, which are the 15% higher for the s-CO₂ than for the ORC (see Table 1). Generally, with higher values of the carbon tax, the s-CO₂ system may become convenient as the bottomer of all the analyzed gas turbines, as well as the ORC, with a net present value more than twice of its reference value.

The return on the investment is instead less sensitive to the variation of the profile demand (see Figure 13a). Working at full load during the entire year does not grant such a significant gain equal to the one obtainable by introducing a high carbon tax. Comparing the case at the reference load profile and the full load profile, the net present value increase of the 17%. However, in some cases, the yearly demand profile can be decisive to have a return on the investment, for example, when the investment is uncertain and the net present value is near to zero. This is the case of the GT1-ORC and the GT3 s-CO₂ configurations, which are not convenient if operating at part-load conditions, but they can become so if working at full load during the entire year.

Other several factors can then affect the return on the investment, among which are the natural gas cost and the discount rate (directly influencing the net present value) and the ambient temperature (influencing the performance and indirectly the net present value). Studies dedicated to the parametric analysis of these factors are already proposed by the authors for what concerns the ORC industrial WHR application (as the reader can find in [19]). Future works are instead under development to focus deeply on investigating these aspects focusing on the s-CO₂ systems only.

7. Conclusions

This paper presents a detailed investigation and comparison of ORC and s-CO₂ potential as bottoming recovery cycles in combined heat and power plant configuration inside industrial facility, comparing several gas turbine models at part-load operation. The findings of this work can be summarized as follows:

• Despite the ORC presenting higher heat recovery efficiency, the s-CO₂ demonstrates better exploitation of the recovered thermal power, showing higher bottoming cycle efficiency, up to the 28%. The ORC efficiency instead does not exceed the 18%. The ORC specific work is considerably affected by the condensing temperature, which determines the condensing pressure and the expander pressure ratio, consequently. This is not valid for the s-CO₂ pressure ratio, which does not depend on the thermal user requested temperature, making the s-CO₂ most suitable for combined heat and power plant applications. The s-CO₂ thermal efficiency is also greater than that of the ORC, with largely positive PES values, up to 22%).
• At part-load operation, an influence of the gas turbine regulation strategy over the bottoming cycles’ performance can be observed. In particular, the s-CO₂ system maintains higher part-load performance when working with turbines regulated by means of the VTIT strategy, thus working with almost constant exhaust flow rate. On the contrary, the ORC power plant benefits from working with exhaust temperatures that do not change significantly with respect to the design values.
• In economic terms, the total plant investment cost results in being conspicuous for the s-CO₂ rather than for the ORC. The s-CO₂ requires very higher heat exchangers costs, because of the large size of the heat recovery heat exchanger, but also to the high specific investment cost still associated to this component. The s-CO₂ also requires larger size and more expensive operating machines. On the other hand, the ORC operates with larger turbines due to the lower densities of the fluid during the expansion process, which entail higher expander investment costs. However, this cost item is not counterbalanced by the previous.
• Considering the analyzed scenarios, the high investment costs still associated with the s-CO₂ technology make it already not practical for industrial gas turbine heat recovery applications (no return on the investment), except in the case where a high value carbon tax value is applied. On the contrary, the current lower ORC investment costs make this solution profitable, granting a return on the investment in most of the cases. However, given the considerable economic gain, it is not excluded that once the technology will be established, the s-CO₂ may become very competitive in this sector. Nowadays, a crucial parameter determining the feasibility of the investment is surely the carbon tax value. The influence of the user profile demand is instead less strong, even if it can be decisive when the investment is uncertain and the net present value close to zero.