Analysis and Preliminary Design of a Possible CO₂ Compression System for Decarbonized Coal-Fired Power Plants

Abstract

Carbon capture, utilization, and storage (CCUS) is a key technology for decarbonizing existing or newly designed fossil fuel power plants, which in the short to medium term remains essential to offset the variability of nonprogrammable renewable sources in power generation. In this paper, the authors focus on the CO₂ compression phase of CCUS systems, integrated with power plants, and propose, according to the technical literature, a plant layout aimed at minimizing energy consumption; then, they carry out the preliminary design of all compressors, identifying compact and efficient configurations. The case study concerns an advanced ultra-supercritical steam plant (RDK8 Rheinhafen-Dampfkraftwerk in Karlsruhe, Germany) with a nominal net thermal efficiency of 47.5% and an electrical output of 919 MW. The main results obtained can be summarized as follows. The overall compression in the IGC configuration requires only six stages and each compressor is single-stage, while in the inline configuration, ten stages are needed; the diameters in the IGC solution, also due to a higher rotational speed, are smaller, despite the in-line solution being multistage. An interesting further investigation could be related to modifications of the plant scheme, especially to test whether CO₂ liquefaction at an intermediate stage of compression could result in reductions in energy consumption, as well as even more compact design solutions.

1. Introduction

In recent decades, challenges related to climate change have become a worldwide priority. To address these challenges, the most widely adopted strategies have focused on the reduction in emissions and electrification of processes using renewable energy sources. However, to achieve the goal of “net zero emissions” established by the Paris Agreement (2015, [1]), it is crucial to extend these actions, including CO₂ capture (combined with storage and utilization) [2]. In this scenario, carbon capture, utilization and storage (CCUS) emerges as a key solution to decarbonize several plants, such as existing or newly designed fossil fuel power plants, the cement industry, etc. [3]. According to the International Energy Agency’s (IEA) Sustainable Development Scenario, CCUS is expected to contribute nearly 15% of the global cumulative reduction in CO₂ emissions when compared to the Stated Policies Scenario [4]. As technological advancements drive cost reductions and more cost-effective abatement alternatives are fully utilized, the role of CCUS in mitigating emissions is projected to expand further over time [4]. The deployment of CCUS technologies plays a pivotal role in advancing sustainability by facilitating the transition towards a low-carbon economy while ensuring industrial competitiveness. By capturing and repurposing CO₂ emissions, CCUS directly supports climate change mitigation and aligns with circular economy principles, thereby enhancing resource efficiency. Furthermore, the integration of CCUS within energy-intensive sectors fosters long-term environmental and socio-economic benefits, reducing reliance on fossil fuels and promoting green innovation. In addition to mitigating climate risks, CCUS stimulates job creation, drives technological advancements, and supports regional economic development, particularly in industrial hubs undergoing decarbonization. As global policies and investment frameworks increasingly emphasize sustainable carbon management, CCUS emerges as a crucial enabler of carbon-neutral pathways. Recognizing its strategic importance, international policies increasingly prioritize the development of efficient CCU(S) systems as a key objective in the short to medium term. For instance, the Danish government has established a dedicated funding initiative to advance CCU(S) technologies, underpinned by substantial economic and technological investments that benefit industries nationwide [5]. Similarly, large-scale projects such as HyNet in the Northwest of England demonstrate the growing momentum behind CCUS deployment. HyNet’s initial CO₂ capture capacity is estimated at 4.5 Mtpa, with potential expansion up to 10 Mtpa beyond 2030 [6]. The increasing global commitment towards CCUS is further reflected in the rise of operational facilities. According to a 2021 report by the Global CCS Institute, the number of commercial CCUS facilities worldwide had reached 135 (27 are operational, 4 under construction, 58 in advanced development, 44 in early development, and 2 suspended operations), with a total average CO₂ capture capacity of 149.3 Mtpa [7]. This represents a significant increase compared to previous years, but, despite this progress, by 2030, only one known CCUS project is expected to meet near-zero emissions criteria—assuming the captured CO₂ is permanently stored. This project, the 3D initiative by ArcelorMittal, applies carbon capture technology to a blast furnace in France and has an estimated annual capture capacity of 1 Mt of CO₂ [8].

The term CCUS refers to a group of technologies that enable the capture of CO₂ from a source (such as, for instance, the exhaust gas of fossil fuel power plants), and the compression, the transport, and finally, the storage (CCS) or the utilization in secondary processes (CCU) [2,9]. Two fundamental features characterize these systems; they are energy-intensive and require large spaces and volumes for their installations. Therefore, the energy aspect requires exploring layout and plant solutions that can mitigate energy demands; however, these solutions must simultaneously ensure compactness and minimized spatial requirements. Balancing these two demands has significant economic implications that must be carefully considered.

Regarding the capture of CO₂, which represents the initial phase, there are various methods, such as oxyfuel combustion, pre-combustion and post-combustion [10]. Regardless of the technology used in the capture phase, it is then necessary to compress the fluid to make it transport-ready, that is, at high pressures and moderate temperatures (supercritical conditions—pressures greater than 73 bar (in the range of 100–200 bar)—or liquid conditions, with a temperature below the critical temperature of CO₂, thus below 31 °C). According to the literature, the transportation of relevant amounts of CO₂ (under supercritical conditions), through pipelines over medium distances (less than 1000 km), currently represents the most viable solution [11,12].

In the context of carbon capture and utilization (CCU), CO₂ can be repurposed in various industrial processes. A particularly promising application involves the production of e-fuels [13], which utilize CO₂ captured from industrial emissions or directly from the atmosphere [14]. An example of this approach is the CCU initiative by Celanese Corporation (NYSE: CE), a global leader in specialty materials and chemicals. In collaboration with Mitsui & Co., Ltd., Celanese has launched a CCU project at its Clear Lake, Texas, facility as part of the Fairway Methanol joint venture. This project aims to capture approximately 180,000 metric tons of CO₂ annually, repurposing it to produce 130,000 metric tons of low-carbon methanol [15].

Concerning carbon capture and storage (CCS), it is now well established that CO₂ can be injected directly into the subsurface both offshore and onshore, using porous rocks, depleted oil and gas fields, and various geological cavities [16]. A significant CCS initiative is the ‘Ravenna CCS project’ [17], set to become one of the largest CO₂ storage hubs in the world and the main facility in the Mediterranean, with Phase 2 expected to store up to 4 million tons of CO₂ annually by 2030, and the potential to increase storage capacity to over 16 million tons per year thereafter.

Due to the high pressure that must be achieved, the use of multistage compressors is necessary; in particular, the state of the art is represented by centrifugal compressors, which can be divided into two main categories [18]:

• single-shaft centrifugals (inline);
• multi-shaft integrally geared centrifugals (IGCs).

The adoption of the IGC configuration leads to some advantages, such as:

• high performance: optimal impeller flow coefficient due to the ability to vary rotational speed, reduced pressure losses in intercooling, etc. [9];
• reduced space requirement: few stages required, pinions arranged around the central bull-gear, and the ability to be driven directly by one or more electric motors, either synchronous or asynchronous, via the central bull-gear, or by a turbine through the integrated transmission pinion [19].

The leading compressor manufacturers have gained extensive experience in this field over the years. To name a few, (i) Siemens Energy has been refining the design and production of integrally geared compressors since 1948, with installations worldwide across various industries and applications, including air separation [11]; (ii) Atlas Copco Gas and Process has over 50 years of expertise in designing integrally geared compressors (IGCs), particularly for the liquefied natural gas (LNG) market [20]; (iii) Mitsubishi proposes integrally geared fuel gas compressors; these solutions are fully standardized to be suitable for low–medium-pressure fuel gas conditions (up to 60 bars) and to minimize installation work [21].

The key challenge is to integrate extensive cross-sector knowledge and expertise into CCUS applications systematically.

Moving the focus now to CO₂ emissions at the European level [22], the results are clear in 2022, 43% of the emissions came from the transport sector, 20% from electricity and heat producers, and 25% from industrial sectors, including also the energy industries. Excluding the transport sector, it is evident that a significant decarbonization potential can be realized by targeting the remaining two sectors. The power generation sector has been extensively investigated by the authors, who have dedicated much of their research to assessing the performance of power plants equipped with CO₂ emission reduction systems, analyzing both conventional and innovative cycles [23,24,25]. The main conclusions confirmed the possibility of achieving drastic CO₂ reductions, with increased electricity production costs depending on the decarbonization technology adopted [26]. In these studies, the CO₂ capture and compression sections have been analyzed as a black box. However, it is extremely important to analyze the compression/liquefaction section in detail, given the energetic weight this phase imposes on the overall energy performance of the plant and the requirement for specific spaces for the installation of these systems.

Considering these aspects, this paper focuses on the CO₂ compression phase within CCUS systems and, based on technical literature, proposes a plant layout designed to minimize energy consumption. A preliminary design of all compressors is then carried out, aiming to develop compact and efficient solutions. Specifically, two configurations are analyzed: single-shaft (inline) compressors and multi-shaft integrally geared compressors. Both configurations are designed, followed by a comparative analysis in terms of performance and, most importantly, spatial footprint. The study presents the key results of the preliminary compressor design to define the kinematics and thermodynamics of the transformations involved, as well as the turbomachinery geometry to quantify the spatial requirements of the proposed solutions. Furthermore, the availability of geometric, kinematic, and thermodynamic data enables the application of specific loss models, allowing for an assessment of the performance of individual compressors (isentropic efficiency) and the overall compression system. Notably, these performance data are not readily available in the existing literature.

The case study accounts for an advanced ultra-supercritical steam plant (RDK8 Rheinhafen-Dampfkraftwerk in Karlsruhe, Germany) with a nominal net thermal efficiency of 47.5% and an electrical output of 919 MW. RDK8 is currently the most efficient coal-fired steam plant in the world [27]. A post-combustion capture, capable of separating 90% of the CO₂ produced, is assumed for this power plant.

Looking at the energy transition context, the proposed application is relevant since it becomes a must to reduce CO₂ emissions in advanced fossil fuel-based solutions (Figure 1).

Although the purity of captured CO₂ is a critical aspect for its compression and, in the technical literature, many studies on this topic are available, as well as guidelines for pipeline transport and storage [28], in the proposed case study, the authors do not go into detail on CO₂ purification systems, as there are different technologies to achieve the right purity of CO₂ for the reference steam plant [28,29] and a small difference in the purity level would not affect the methodology proposed for optimally designing the compressors and the results obtained.

To propose the results, the authors developed dedicated ad hoc codes in the Matlab environment and integrated NIST Refprop sub-routine to establish the thermodynamic properties of process working fluids. The paper is structured as follows. Section 2 first shows the case study together with some thermodynamic considerations, then presents the advantages of the IGC solution and the analyzed plant layout and, finally, describes the procedure for the preliminary design of radial compressors. Section 3 presents the results obtained, first describing the selection of the compressors, then their preliminary design, and finally, the energy balance of the proposed plant scheme.

2. Materials and Methods

2.1. Case Study

As described in the introduction, in this paper, the CO₂ compression system of an advanced ultra-supercritical coal-fired steam plant is analyzed (RDK8 Rheinhafen-Dampfkraftwerk in Karlsruhe, Germany). It should be noted that the technology used to separate CO₂ is the post-combustion capture.

Table 1. RDK8’s performance and operational parameters (adapted from [27]).

RDK8 Steam Power
Power (MW)	P	919.0
Annual net thermal efficiency (%)	${\eta }_{net}$	46.5
Annual boiler efficiency (%)	${\eta }_{boiler}$	92.0
Equivalent operating hours	EOH	7000
Carbon dioxide emission factor (t/TJ) 1	EF	104.55

¹ [30].

presents the parameters for the quantification of CO₂ produced and separated.

Based on these data, the annual amount of CO₂ produced is assessed and, assuming a CO₂ removal efficiency (ε) of 90%, the annual CO₂ captured and the mass flow to be sent to the compression system are evaluated through:

$$m_{CO2,annual}={\displaystyle \frac{P·EOH}{{\eta }_{net}·{\eta }_{boiler}}}·0.0036·EF (\mathrm{M}\mathrm{t}\mathrm{p}\mathrm{a})$$

(1)

$$m_{CO2,annual, captured}=m_{CO2,annual} ·\epsilon (\mathrm{M}\mathrm{t}\mathrm{p}\mathrm{a})$$

(2)

$$m_{CO2}={\displaystyle \frac{P}{{\eta }_{net}·{\eta }_{boiler}}}·0.001·EF (\mathrm{k}\mathrm{g}/\mathrm{s})$$

(3)

$$m_{CO2,captured}=m_{CO2}·\epsilon (\mathrm{k}\mathrm{g}/\mathrm{s})$$

(4)

This results in more than 5 million tons per year (Mtpa) and a flow rate of approximately 200 kg/s that must be sent to the CO₂ compression system. Therefore, for this case study, it is possible to adopt a CO₂ system transport via pipeline; furthermore, due to the volumetric flow rate involved (approximately $370 {\mathrm{k}\mathrm{m}}_{\mathrm{n}}^3/\mathrm{h}$, assuming pure CO₂), the CO₂ compression system will be composed of centrifugal compressors [31].

2.2. Thermodynamic Analysis

For the moment, compression from 1 absolute bar to 150 absolute bars of pure CO₂ with ideal transformation is considered. Given the high compression ratio, intercooled compressions are considered, respectively, in 4 and 6 stages, with equal compression ratios. The minimum temperature (excluding the final) has been set at 35 °C, which falls within the range of supercritical gas [11]. In Figure 2, these transformations are depicted on the most significant thermodynamic charts; it can be observed that the thermophysical properties of CO₂ ensure that the compression, within a certain pressure range, is entirely homogeneous in terms of compression work (Figure 2e,f, first three phases in the four-phase compression and first four phases in the six-phase compression), while, beyond this range, different and lower specific energy consumptions occur.

Considering that under reversible conditions:

$${dW}_{rev}={dh}_{is}=vdp={\displaystyle \frac{dp}{\varrho }}$$

(5)

it turns out that Equation (5) allows us to compute the reversible work as a function of the variation in density with pressure.

Figure 3 reports the density variation with pressure for different temperatures. The fluid behaves as an ideal gas at high temperatures (as shown by the yellow line), demonstrating an almost linear proportionality between density and pressure. However, as the temperature decreases, to be considered the minimum temperature during the intercooled compressions, a significant variation of density around the critical pressure is observed (Figure 3b).

The relevant increase in density causes CO₂, beyond the critical pressure, but at temperatures close to the critical temperature, although it is in supercritical conditions, to show a liquid-like behavior (density over 700 kg/m³ beyond 100 absolute bar). For these reasons, it is crucial to study the entire compression process, properly subdividing it into different phases. In fact, the division of compression allows for both determining the system’s energy requirements and the configuration of the turbomachinery that performs such compression.

Furthermore, it is possible to identify a pressure range (Figure 3a) where, in addition to the limited increase in density with pressure for various reference isotherms (1–50 bar for temperatures between 35 and 100 °C), the saturation temperatures of CO₂ are compatible with refrigeration systems (5–20 °C). Therefore, it would be feasible to consider CO₂ liquefaction at an intermediate pressure (40–50 bar), followed by a single compression in the liquid phase up to the final established pressure.

In this paper, the authors want to focus their attention on the CO₂ compression phase in gaseous-supercritical conditions, because the objective of the analysis is the design of the compression system to make the plant efficient and compact. Therefore, in Section 2.4, the analyzed plant scheme will be introduced. The other proposed scheme (with CO₂ compression in liquid phase) will be analyzed in a future paper.

The thermodynamic analysis conducted here allows for the following considerations to be drawn:

• the ideal intercooled compression in six phases, all with an equal pressure ratio, reduces the energy demand by more than 6% compared to the ideal intercooled compression in four phases (all with an equal pressure ratio);
• the ideal intercooled compression in six phases with two different compression ratios (one for the first four phases and another for the last two) results in a reduction in the energy demand by more than 10% compared to the ideal intercooled compression in four phases with the same compression ratio;
• the six-phase compression with two different compression ratios allows, by appropriately selecting the rotation speed, the use of single-stage turbomachinery (as will be proposed for the IGC solution).

2.3. Integrally Geared Compressors (IGCs)

IGCs consist of a drive shaft and multiple pinion shafts, at the end of which the impellers are installed. The number of pinions can be up to 5, and thus, up to 10 stages of compression can be achieved. The bull gear shaft is connected to an electric motor and generally has a fixed speed (usually runs at 1500–3000 rpm). Specific gears allow the speed of the pinions to be elevated, depending on the gear ratios adopted; as high as 50,000 rpm can be reached in the last stages of compression. The volutes are installed outside the gearbox, so the rotor/stator assembly of each stage is independent, allowing high modularity of the plant solution and ease of maintenance operations [19].

The main differences between IGCs and traditional inline centrifugal compressors are summarized below:

• In an in-line compressor, all stages are installed on the same shaft and, therefore, have the same rotation speed; in IGCs, on the other hand, a different rotation speed can be chosen for each pinion and, therefore, for the two compression stages installed on that pinion.
• The possibility of adopting different rotation speeds for the individual stages makes it possible to choose compressors in the optimum specific speed range, limiting the number of stages per compression phase.
• In addition, compression stages with optimal specific speeds can achieve high performance (in terms of compression efficiency).
• In IGCs, it is possible to have an intercooler between each stage, minimizing compression work. Of course, heat exchangers introduce pressure losses that must be taken into account.

In mechanical terms, a comparison between an IGC and an inline centrifugal compressor highlights the following aspects:

• In an IGC, a shaft seal is required for each compression stage, whereas in an in-line centrifugal compressor, only two seals are required, regardless of the number of stages, resulting in increased cost and reduced reliability.
• IGCs require much more bearings than in-line compressors.

2.4. Analyzed Plant Layout Scheme

Given the above-mentioned thermodynamic considerations, in this paper, the authors propose a compression system (Figure 4) which divides the overall compression into two ranges:

• an intercooled compression in four phases, with equal partial pressure ratios, from 1 absolute bar to 45 absolute bar;
• an intercooled compression in two phases, with equal partial pressure ratios, from 45 absolute bar to 150 absolute bar.

Although various plant configurations could be considered, this study rigorously examines the selected arrangement to facilitate the comprehensive design of each compressor, offering a comparative analysis between an inline configuration and an integrally geared configuration.

2.5. Selection and Preliminary Design of Radial Compressors

The similarity theory, particularly the Baljè method, allows us to identify the type of turbomachine (axial, radial, mixed flow) with respect to a specific application. In particular, Baljè’s diagrams can be used to derive the specific speed ranges that define each type of turbomachine [32].

Therefore, the choice of the turbomachine type involves the preliminary evaluation of the specific speed based on the available data, which include:

• type of fluid;
• m: mass flow rate (kg/s);
• T_in: inlet temperature of the fluid (°C);
• p_in: inlet pressure of the fluid (bar);
• p_out: outlet pressure of the fluid (bar).

On the basis of such data, it is straightforward to assess the ideal work of the entire machine corresponding to the isentropic enthalpy change within the machine (compressible fluid machines). However, the evaluation of specific speed is not immediate because it also requires knowing the rotational speed (rpm), or the angular velocity (rad/s), and the number of stages z. For compressors, it is indeed found that:

$${\omega }_s=\omega ·{\displaystyle \frac{V_{in}^{1/2}}{{∆h}_{is,stage}^{3/4}}}$$

(6)

where it is necessary to identify a criterion for distributing the reversible work of the entire machine among the individual stages that compose it. After performing this distribution, it is necessary to evaluate the volumetric flow rate at the inlet of each compressor stage. This evaluation can be carried out by calculating the upstream and downstream pressures and temperatures of the individual stages corresponding to the isentropic enthalpy change ${∆h}_{is,stage}$ and consequently the volumetric flow rates. Since, in a compressor, the volumetric flow rate decreases between the inlet and the outlet of the machine, it will be enough to evaluate the specific speed at the first and the last stage (respectively, the maximum and minimum specific speed) and to ensure that both values fall within the optimal specific speed range for each chosen rotational speed. This phase of selecting the turbomachine allows obtaining ranges for n ($n_{min}<n<n_{max}$) and for z ($z_{min}<z<z_{max}$) which serve as input for the subsequent preliminary design phase. This will enable determining precise values of n and z that ensure better performances (in terms of efficiency and/or machine size).

The preliminary design of the centrifugal compressor is carried out stage by stage, following the sequential order below [33]:

• Evaluation of kinematic parameters: The kinematic angles at the rotor inlet and outlet (α₂, β₁, β₂) are determined by setting the following five independent parameters:
  • the flow coefficient, here defined as $\phi =c_{1m}/u_2$;
  • the work coefficient, here defined as $\psi =W/u_2^2$;
  • the rotor meridional velocity ratio: $\xi =c_{2m}/c_{1m}$;
  • the rotor tip diameter ratio: ${\delta }_t=D_{1t}/D_2=u_{1t}/u_2$;
  • the angle ${\alpha }_1$.

Thus, we obtain:

$$\tan {\alpha }_2={\displaystyle \frac{\psi }{\xi \cdot \phi }}+{\displaystyle \frac{{\delta }_t}{\xi }} ·\tan {\alpha }_1$$

(7)

$$\tan {\beta }_1={\displaystyle \frac{{\delta }_t}{\phi }}-\tan {\alpha }_1$$

(8)

$$\tan {\beta }_2={\displaystyle \frac{1}{\xi \cdot \phi }}\cdot \left(1-\psi \right)-{\displaystyle \frac{{\delta }_t}{\xi }}-\tan {\alpha }_1$$

(9)

Therefore, the peripheral velocity $u_2$ can be used to define the stage kinematics fully (Figure 5). To determine $u_2$, in addition to the parameter $\psi$, the initial value of the isentropic efficiency must be assigned (which will be recalculated once the stage is fully defined).

2.

Evaluation of thermodynamic parameters: Given the pressure and temperature at the inlet of the stage and the pressure at the outlet of the stage, it is possible to define thermodynamics at the inlet and outlet of the rotor (thermodynamic parameters, total and total relative quantities, rothalpy [34]) and at the outlet of the stator (thermodynamic parameters and total quantities) if, in addition to the six parameters introduced previously, an initial value of the efficiency of the rotor is assigned (which will be recalculated once the stage is fully defined). The thermodynamics of the stage is effectively depicted in the thermodynamic plane h-s (Figure 6)

3.

Evaluation of geometric parameters: Figure 7 shows the main geometric parameters of a radial stage. The blade angle at the rotor outlet is assessed through the definition of the slip factor [33] and empirical correlations that also take into account the number of blades. Finally, the hydraulic length and diameter of the rotor, which define the equivalent rotor channel, are evaluated. These are crucial for evaluating stage losses [33]. The stator of a radial compressor stage consists of a vaneless and vaned stator. Several experimental correlations are available to define all geometric quantities of the diffuser downstream of the rotor. No additional input is required to define the stage geometry.

4.

Losses and stage efficiency evaluation: The authors have thoroughly illustrated the loss sources and the loss models in any type of turbomachinery [34]. This paper assumes the loss model based on the pressure loss coefficients [33,35,36,37]. After calculating all losses, which naturally depend on kinematics, thermodynamics and geometry, the loss coefficients in the rotor and the stator are used to determine the pressures along the stage (in detail, the total relative pressure downstream of the rotor—$p_{2tr}$—the total pressure downstream the vaneless diffuser—$p_{2St}$—and the vaned diffuser—$p_{3t}$), and consequently, the rotor and stage efficiencies. These values are compared with the initial assumptions, and when their difference is within a specific tolerance, the stage calculation is completed. If the calculated stage efficiency is acceptable, the sizing procedure can be considered complete; otherwise, the input parameters can be adjusted for a new sizing.

If the compressors are multistage, the calculation illustrated here is repeated for each stage; note that between one stage and the next one, a volute is considered where the total enthalpy is constant, as well as the mass flow rate and the angular momentum, assuming friction to be negligible. Under these assumptions, subsequent stages are evaluated by reassigning the six input parameters.

What has been illustrated here very briefly highlights that the calculation of the stages of a radial compressor is based on only six input parameters for each stage, given the type of fluid, mass flow rate, inlet temperature and pressure of the fluid, outlet pressure of the fluid, rotational speed, and number of stages. In [33], the authors have shown that the previously introduced parameters ($\phi , \psi , \xi , {\delta }_t, {\alpha }_1, {\eta }_{is})$ are entirely equivalent to another set (${\psi }_{is}=W_{is}/u_2^2, {\delta }_t, {\alpha }_2, {\eta }_{stage}, {\alpha }_1, {\delta }_h=D_{1h}/D_2)$, referred to as set B. Moreover, in this set B, the first four parameters can be deduced as a function of the specific speed of the stage, while the last two parameters can be assumed to be ${\alpha }_1=0°$ (unless the relative Mach number at the rotor inlet must be reduced) and ${\delta }_h=$ 0.35, as proposed in [38]. Therefore, having established the optimal ranges of the specific speed for high-efficiency radial compressor stages [32], the design procedure for the single stage based on set B requires knowledge of only two input parameters, thus becoming a guided procedure. After the design, it is necessary to conduct a series of checks on the parameters obtained to ensure that they fall within the optimal ranges recommended by the technical literature in the field.

3. Results and Discussion

3.1. Compressor Selection

With reference to the case study presented in Section 2.1 and the plant layout illustrated in Section 2.4, it is now necessary to proceed with the selection and sizing of the compressors. Data at the inlet of each compressor (flow rate, initial pressure and temperature, and final pressure) are reported in

Table 2. Data for each compressor.

	m (kg/s)	pin (bar)	Tin (°C)	pout (bar)
C1	202.1	1.0	35.0	2.670
C2	202.1	2.590	35.0	6.916
C3	202.1	6.708	35.0	17.91
C4	202.1	17.37	35.0	46.39
C5	202.1	45.0	35.0	86.10
C6	202.1	83.52	35.0	159.8

, considering the pressure losses between each compression stage (assumed to be 3%) and assuming a final intercooling temperature of 35 °C.

Then, the turbomachinery selection procedure illustrated in Section 2.5 has been applied. The results are graphically reported in Figure 8. In these figures, the optimal specific speed range for radial compressor stages is highlighted in grey; based on appropriately chosen rotational speeds, the specific speeds of the first and last stages were calculated as the number of stages varied (reported on the x-axis). These charts are essential for selecting the optimal rotational speed and the number of stages for each compression phase.

Based on what was illustrated in Section 2.3, since the IGC solution allows for the installation of two impellers on each pinion, which is characterized by a predetermined rotational speed, it can be seen from Figure 8 that, considering two compression phases at a time, three different rotational speeds can be chosen, ensuring single-stage compressors with the specific speed in the optimal range. Based on various simulations conducted,

Table 3. Data for IGC configuration.

	n (rpm)	z (-)	ωs
C1	3000	1	0.85
C2	3000	1	0.53
C3	8000	1	0.88
C4	8000	1	0.56
C5	12,000	1	0.76
C6	12,000	1	0.65

shows the adopted values of n and z for the subsequent preliminary design of the compressors in the IGC solution. The simulations carried out involve the sizing of compressors and the verification of compliance with a multitude of functional parameters (kinematic, geometric, mechanical parameters, and so on); the data presented here resulted from an in-depth comparative analysis of possible choices. These solutions, therefore, represent an initial possible configuration; this configuration can be further refined by adjusting the individual input parameters of each compressor to verify the potential improvement of the proposed solution. The aim of this paper is to provide a preliminary design of the compressor train in the IGC and inline configuration, and the choice of n and z here fully meets this objective.

Referring to an inline solution, all compressors should be installed on the same shaft and thus should be characterized by the same rotational speed. From Figure 8, it can be seen that this solution is not feasible, as it is impossible to define a unique rotational speed that ensures optimal specific speeds in all compression stages while maintaining a technically reasonable number of stages. However, a low-pressure section can be identified, consisting of the first three compressors, which can be assigned a rotational speed of 3000 rpm, and a high-pressure section, consisting of the last three compressors, with a rotational speed of 8000 rpm. However, this choice does not guarantee that all compressors are single-stage;

Table 4. Data for inline configuration.

	n (rpm)	z (-)	ωs
C1	3000	1	0.85
C2	3000	1	0.53
C3	3000	3	0.75–0.66–0.58
C4	8000	1	0.56
C5	8000	2	0.85–0.75
C6	8000	2	0.72–0.69

shows the selected values of n and z for the subsequent sizing of compressors with the inline solution (in the case of multi-stage compressors, the specific speeds are reported for the first and last stages). Again, multiple simulations of compressor sizing and verification of compliance with functional parameters were performed, so the data proposed here are derived from a thorough comparative analysis of possible choices.

Before comparing the two configurations (IGC and inline), it is worth pausing in Figure 8 to note how compressor C6, characterized by an initial pressure (Table 2) above the critical pressure of CO₂, shows a specific speed trend as a function of the number of stages similar to that of an incompressible fluid. This demonstrates that these initial conditions, although in the supercritical phase, are similar to the conditions of the dense phase (for definition, the dense phase is characterized by pressures above the critical pressure and temperatures below the critical temperature). This condition will be reflected in the compressor dimensions (Section 3.2).

3.2. Compressor Preliminary Design

Following the methodology illustrated in Section 2.5 and based on the results discussed in Section 3.1, the sizing of all compressors in the proposed compression system has been carried out. The two configurations, inline and IGC, share three compressors (C1, C2 and C4).

Table 5. Compressors in IGC solution: main results.

		C1	C2	C3_IGC	C4	C5_IGC	C6_IGC
Input f(ωs)
ψis		0.4527	0.5045	0.4474	0.5004	0.4677	0.4864
δt		0.6054	0.5481	0.6114	0.5524	0.5882	0.5674
α2	°	70.44	73.12	70.07	72.97	71.39	72.37
Assumptions
α1M	°	0	0	0	0	0	0
δh		0.35	0.35	0.35	0.35	0.35	0.35
Outputs
Dimensionless coefficients
ψ		0.5080	0.5836	0.5121	0.5902	0.5421	0.5916
φ		0.2879	0.1801	0.2955	0.1911	0.2631	0.2253
Kinematics
ξ		0.6269	0.9831	0.6282	0.9461	0.6936	0.8346
R		0.7955	0.7091	0.7956	0.7082	0.7621	0.7172
β1M	°	58.92	68.14	58.42	67.04	60.71	63.85
β2	°	69.85	66.96	69.17	66.19	68.27	65.28
u2	m/s	374.2	353.1	371.2	341.5	257.2	156.8
Thermodynamics
p2	bar	2.265	5.463	15.26	36.76	75.53	138.6
T2	°C	99.4	94.6	101.7	97.76	78.8	51.3
p3	bar	2.670	6.916	17.91	46.39	86.10	159.8
T3	°C	115.3	117.9	118.0	122.0	91.3	56.3
Geometry
D1t	cm	144.2	123.2	54.2	45.0	24.1	14.2
D2	cm	238.2	224.8	88.6	81.5	40.9	25.0
D3	cm	386.0	355.6	143.9	129.2	65.9	39.8
b1	cm	30.4	22.3	11.6	8.2	4.9	2.7
b2	cm	12.4	5.7	4.7	2.2	2.2	1.3
SF		0.8397	0.8214	0.8383	0.8203	0.8348	0.8361
Dhyd,R	cm	16.5	11.7	6.29	4.4	2.9	1.7
Lhyd,R	cm	194.6	203.1	70.2	70.3	33.8	20.5
Dhyd,vaned	cm	16.2	9.0	6.1	3.5	3.0	1.8
Lhyd,vaned	cm	191.9	126.2	70.9	47.2	31.1	16.1
La	cm	59.4	56.5	21.9	20.5	10.7	6.7
NB,R		15	12	15	12	14	14
NB,S		14	11	14	11	13	13
Dimensionless coefficients
Ma1t		0.919	0.750	0.938	0.765	0.698	0.437
Ma2,S		0.679	0.733	0.690	0.743	0.573	0.300
Re1		3.86 × 106	5.82 × 106	10.1 × 106	15.4 × 106	24.9 × 106	18.9 × 106
Re2,S		5.42 × 106	8.09 × 106	14.0 × 106	20.6 × 106	31.2 × 106	15.6 × 106
Performances
P	MW	14.37	14.70	14.26	13.91	7.25	2.94
ηis	%	0.8910	0.8645	0.8737	0.8479	0.8628	0.8221

therefore reports the main results of the compressor sizing in the IGC configuration (C1, C2, C3_IGC, C4, C5_IGC, C6_IGC);

Table 6. Compressors in inline configuration: main results.

		C3_Inline			C5_Inline		C6_Inline
		1	2	3	1	2	1	2
Input f(ωs)
ψis		0.4686	0.4846	0.4974	0.4525	0.4702	0.4738	0.4790
δt		0.5873	0.5694	0.5555	0.6055	0.5855	0.5814	0.5756
α2	°	71.44	72.28	72.85	70.43	71.53	71.73	72.01
Assumptions
α1M	°	0	0	0	0	0	0	0
δh		0.35	0.35	0.35	0.35	0.35	0.35	0.35
	Outputs
Dimensionless coefficients
ψ		0.5245	0.5446	0.5641	0.5207	0.5398	0.5589	0.5649
φ		0.2616	0.2294	0.1990	0.2881	0.2587	0.2518	0.2414
Kinematics
ξ		0.6730	0.7585	0.8753	0.6424	0.6969	0.7326	0.7600
R		0.7735	0.7482	0.7261	0.7865	0.7620	0.7468	0.7394
β1M	°	60.83	63.48	66.28	58.91	61.06	61.60	62.45
β2	°	69.68	69.09	68.22	68.89	68.61	67.31	67.14
u2	m/s	209.4	206.8	205.0	184.9	182.5	112.4	112.0
Thermodynamics
p2	bar	8.863	12.25	16.61	59.15	80.55	111.3	150.0
T2	°C	56.5	83.4	110.1	57.6	84.9	44.1	53.9
p3	bar	9.523	13.20	17.91	62.99	86.10	120.4	159.8
T3	°C	62.7	90.1	117.4	63.3	91.2	46.7	56.2
Geometry
D1t	cm	78.3	75.0	72.5	26.7	25.5	15.6	15.4
D2	cm	133.3	131.7	130.5	44.2	43.6	26.8	26.8
D3	cm	214.4	210.2	207.1	71.5	70.0	43.0	42.8
b1	cm	15.8	14.4	13.4	5.6	5.1	3.1	3.0
b2	cm	8.9	7.2	5.8	3.4	2.9	1.8	1.8
SF		0.8360	0.8299	0.8216	0.8394	0.8354	0.8354	0.8362
Dhyd,R	cm	10.0	9.3	8.6	3.5	3.3	2.1	2.0
Lhyd,R	cm	115.3	118.2	119.8	36.2	37.0	22.4	22.6
Dhyd,vaned	cm	11.1	9.9	8.5	3.9	3.6	2.3	2.3
Lhyd,vaned	cm	102.0	91.5	79.9	34.5	32.6	19.3	18.7
La	cm	36.4	35.6	34.8	12.1	11.9	7.5	7.4
NB,R		14	13	12	15	14	14	14
NB,S		13	12	11	14	13	13	13
Dimensionless coefficients
Ma1t		0.501	0.455	0.418	0.522	0.467	0.325	0.234
Ma2,S		0.419	0.413	0.409	0.413	0.398	0.233	0.196
Re1		8.67 × 106	9.11 × 106	9.50 × 106	21.9 × 106	22.5 × 106	16.8 × 106	15.3 × 106
Re2,S		9.48 × 106	9.90 × 106	10.2 × 106	22.6 × 106	22.8 × 106	19.1 × 106	18.0 × 106
Performances
P	MW	14.15			7.23		2.86
ηis	%	0.8934	0.8897	0.8816	0.8691	0.8710	0.8477	0.8479
ηis,C		0.8806			0.8650		0.8457

reports the main results of the sizing of compressors C3, C5, and C6 in the inline configuration (C1, C2, C3_inline, C4, C5_inline, C6_inline). These tables highlight the input parameters derived from the specific speed and those assumed. Parameters related to work and flow coefficients are also reported for each compressor stage, showing that their values fall within the range required for high-efficiency compressor configurations [33,35]. Other results related to the thermodynamics and kinematics of the stages and the geometry are also provided.

Among the kinematic parameters, it is particularly relevant to analyze the peripheral velocity u₂ (tip speed):

• In the IGC configuration (Table 5), the first four stages show a high tip speed (340–375 m/s), whereas in the last two stages, where CO₂ behaves as a dense fluid, this velocity is significantly lower. Notably, the maximum tip speed remains within the optimal range recommended for such applications [19].
• In the inline configuration (Table 6), the multistage compressors C3 and C5, consisting of three and two stages, respectively, exhibit lower tip speeds.
• The compressors C6_IGC and C6_inline are characterized by much lower tip speeds compared to conventional gas centrifugal compressors, making these turbomachines increasingly resemble pumps.

Regarding the thermodynamic parameters, it is worth examining the stator exit temperature (T₃). It turns out that the compressions occurring in the supercritical phase (C5 and C6 compressors in both configurations) exhibit only modest temperature variations, further highlighting that the fluid behaviour is more similar to that of a liquid rather than an ideal gas. The geometric parameters will subsequently be investigated.

Finally, the performance parameters (power and isentropic efficiency) of each compressor are presented. Both configurations exhibit similar performance and high isentropic efficiencies (both compressors and single stages, ranging from 80 to 90%). Based on the results presented here, the two proposed configurations exhibit very similar energy performance, provided that the intercooler downstream of each compressor can be installed for the inline configuration. However, the compactness of the IGC solution compared to that of the inline solution is undeniable. First, the overall compression in the IGC configuration requires only six stages, meaning each compressor is a single-stage compressor. In the inline configuration, instead, ten stages are needed (more than 40% more); specifically, compressor C3 consists of three stages, and compressors C5 and C6 have two stages each.

Figure 9 shows the rotational speed of the compressors and the final pressure of each stage; it is immediately clear that, given the same outlet pressure of the overall train, the inline solution requires a significant number of stages.

Continuing with the analysis of the results obtained, it is interesting to focus on the geometry and the impact of the impeller dimensions on the proposed solution. In Figure 10, the diameters at the impeller exit are shown; disregarding the common configurations, it emerges that in the different configurations, the diameters in the IGC solution are smaller despite the inline solution being multistage. Therefore, by comparing the C3_IGC compressor with the C3_inline compressor, it can be deduced that each impeller of the multistage compressor has an external diameter approximately 50% larger than that of the single-stage compressor; moreover, these impellers are three in number. A similar observation applies to compressors C5 and C6, where the diameter increases are more contained (less than 10%).

Based on this last consideration, it is worth focusing on compressors C5 and C6, for which the thermodynamic conditions of the process fluid result in very limited volumetric flow variations (see Section 3.3), making these turbomachines similar to pumps.

Finally, in Figure 11, the axial dimensions of the shafts (three pinions in the IGC configuration and two shafts in the inline configuration) required for housing the impellers and volutes are shown (it is assumed that the axial footprint of the volutes downstream of each stage is approximately half that of the impeller). It can be noted that the axial length required by the first shaft in the inline configuration is approximately double that required by the first pinion; in the case of the second shaft, this requirement is 40% greater. Despite the IGC configuration requiring three pinions, the overall axial dimension for housing the compressors in the inline solution is up to 60% larger, highlighting the compactness of the IGC solution compared to the inline one.

Considering the main geometric parameters, it can be concluded that the IGC solution with six stages represents a well-optimized design, being highly compact compared with the inline configuration while maintaining performance fully aligned with that of the inline solution. Furthermore, it is important to emphasize that the IGC configuration, with six impellers distributed across three pinions, inherently facilitates intercooling between stages. In contrast, intercooling in the inline configuration may not always be feasible [19]; as a result, the inline configuration may lead to a significant increase in the power required for compression.

3.3. Energy Balance and Power Required

Table 7. Thermodynamic quantities in sections of the analyzed plant layout scheme (Figure 4).

	p (bar)	T (°C)	h (kJ/kg)	S (kJ/kgK)	ρ (kg/m3)	V (m3/s)
1	1.0	35.0	514.4	2.7675	1.725	117.1
2	2.670	115.3	585.5	2.7877	3.658	55.25
3	2.590	35.0	513.0	2.5846	4.501	44.90
4	6.916	117.9	585.8	2.6102	9.490	21.30
5	6.709	35.0	509.4	2.3964	11.89	17.00
6	17.91	118.0	579.9	2.4195	25.13	8.043
7	17.37	35.0	499.3	2.1932	32.50	6.219
8	46.39	122.0	568.1	2.2200	68.21	2.963
9	45.00	35.0	467.0	1.9345	101.5	1.991
10	86.10	91.3	502.8	1.9481	163.7	1.234
11	83.52	35.0	314.1	1.3683	586.1	0.3448
12	159.8	56.3	328.6	1.3762	669.5	0.3019
13	155.0	35.0	271.6	1.1993	821.3	0.2461

shows the relevant sections of the plant layout proposed in Section 2.4 and the most relevant thermodynamic quantities established through energy balance in each of the plant components, adopting the efficiencies of the compression stages obtained in the compressor sizing in the IGC configuration. The compressors transfer a power of 67.43 MW from the blades to the fluid; the external losses of the compressors as well as the mechanical losses that depend on the chosen configuration must then be counted. The authors are deepening the mechanical analysis of the IGC configuration to define the mechanical losses of such a configuration. Considering that a steam plant equipped with a flue gas treatment system for CO₂ separation has an efficiency loss of approximately 10 pp [23], it becomes clear that the phase of CO₂ compression for its transport is particularly energy-intensive (approximately 10% of net power).

The thermal power for the intercooling of the compression stage amounts to more than 116 MW; all intercoolers involve an outlet temperature of 35 °C, which can be achieved with a cooling fluid available in nature (typically water). The authors are also delving into the aspect of CO₂ cooling in order to be able to determine the intercooling footprint as well.

In addition to such cooling, an additional cooling step is then required to bring CO₂ to typical transport temperatures (typically 15 °C, as shown in the thermodynamic diagrams in Figure 2); such additional cooling must be carried out by dedicated equipment (chillers).

The analysis of the results reported in Table 7, thanks to the integration of fluid properties from NIST [39] in the dedicated ad hoc codes developed by the authors, again confirms how in the last two compressors (C5 and especially C6), the process fluid has a liquid-like behaviour: the volumetric flow rates show little variability between the inlet and outlet of the turbomachinery, and the compressors themselves resemble dynamic pumps (Section 3.2).

4. Conclusions

In this paper, the authors focused on the CO₂ compression phase of CCUS systems and have carried out the preliminary design of each compressor, using a compact and efficient configuration (IGC). The case study concerned an advanced ultra-supercritical steam plant (RDK8 Rheinhafen-Dampfkraftwerk in Karlsruhe, Germany), since today, a great fraction of CO₂ emissions comes from electricity and heat producers where significant decarbonization potential could be realized.

IGCs consist of a drive shaft and multiple pinion shafts at the ends of which the impellers are installed; this configuration has some advantages, such as high performance and a reduced space requirement. Taking into account two compression phases at a time, three different rotational speeds were chosen, ensuring single-stage compressors with specific speeds in the optimal range.

Referring to an inline solution, all compressors should be installed on the same shaft, but this solution was not feasible because it is impossible to define a single rotational speed that ensures optimal specific speeds in all compression stages while maintaining a technically reasonable number of stages. For this reason, a low-pressure section was identified consisting of the first three compressors with a rotational speed of 3000 rpm, and a high-pressure section consisting of the last three compressors, with a rotational speed of 8000 rpm.

The authors performed the sizing of all compressors in the proposed compression system in the two configurations, inline and IGC; these configurations share three compressors (C1, C2, and C4). The main results obtained can be summarized as follows:

• The two proposed configurations exhibit very similar energy performance.
• The IGC solution is more compact than the inline one; the overall compression in the IGC configuration requires only six stages, meaning that each compressor is single-stage, while in the inline configuration, ten stages are needed.
• The diameters in the IGC solution, also due to a higher rotational speed, are smaller despite the inline solution being multistage. For example, comparing the C3_IGC compressor with the C3_inline compressor, we found that each impeller of the multi-stage compressor has an external diameter approximately 50% larger than that of the single-stage compressor; moreover, these impellers are three in number. A similar observation applies to compressors C5 and C6, where the diameter increases are more contained (less than 10%).
• The overall axial dimension for housing the compressors in the inline solution is 60% greater, highlighting the compactness of the IGC solution compared to the inline one.

Future developments in the present work concern the analysis of mechanical losses of IGC solutions and the sizing of heat exchangers for intercooling. Further investigation then merits the modification of the plant layout analyzed to test whether CO₂ liquefaction at an intermediate stage of compression can result in reductions in energy consumption and even more compact design solutions.