Anti-surge control in centrifugal compressors operating with CO2 in supercritical state based on discharge flow measurement

Abstract

The compression device (200) includes a centrifugal compressor (230) configured to operate with CO2 in a supercritical state and includes anti-surge control systems (240, 250, 260) configured to measure (226) the CO2 flow rate at the discharge side (234) of the centrifugal compressor (230) and calculate CO2 suction and exhaust densities based on the temperature and pressure at both the suction side (232) and the discharge side (234), thereby enabling compressor maps to be used for anti-surge control of the centrifugal compressor (230) when CO2 is in a supercritical state at the inlet of the centrifugal compressor (230).

Description

[Technical Field]

[0001] The subject matter disclosed herein relates to anti-surge control in centrifugal compressors operating with CO2 in the supercritical state. [Background technology]

[0002] For certain applications, such as power generation based on closed thermodynamic cycles using CO2 (i.e., carbon dioxide) as the working fluid, it is advantageous to compress the CO2 in supercritical states via centrifugal compressors. Such techniques are currently implemented primarily at the laboratory level, but not at the industrial level, and are not very common.

[0003] The problem of "surge" is a common problem in centrifugal compressors.

[0004] It is known to solve this problem by providing an anti-surge loop configured to fluidly couple the compressor outlet with the compressor inlet, the loop including an anti-surge valve configured to control the flow of working fluid within the anti-surge loop, such that a portion of the working fluid is fed back from the discharge side to the suction side when a risk of compressor surge is determined.

[0005] According to such known solutions, the control unit measures the temperature and pressure of the working fluid on both the suction side and the discharge side of the compressor, as well as the flow rate of the working fluid on the suction side, and based on these measurements and on so-called "compressor maps", the control unit controls and regulates the anti-surge valve.

[0006] However, measuring the flow rate of the working fluid on the suction side of a centrifugal compressor operating with CO2 in a supercritical state is difficult and results in unreliable measurements because the conditions of the flowing CO2 to be measured are close to its critical point.

[0007] Therefore, it would be desirable to have a method and system for overcoming the problem of surge in centrifugal compressors, especially those operating with CO2 in a supercritical state, in an easy and effective manner. Summary of the Invention

[0008] According to a first aspect, the subject matter disclosed herein relates to a method for performing anti-surge control in a centrifugal compressor operating with CO2 in a supercritical state, the method being performed through an anti-surge loop including an anti-surge valve configured to control CO2 flow in the anti-surge loop, the anti-surge valve being adjusted as a function of a distance of the centrifugal compressor operating point from a surge limit, taking into account a CO2 suction density at a suction inlet of the centrifugal compressor and a CO2 exhaust density at a discharge outlet of the centrifugal compressor. In other words, the method includes providing an anti-surge loop including an anti-surge valve configured to control a CO2 flow in the anti-surge loop; calculating a CO2 suction density at a suction inlet of a centrifugal compressor; calculating a CO2 discharge density at a discharge outlet of the centrifugal compressor; calculating a distance of an operating point of the centrifugal compressor from a surge limit; and adjusting the anti-surge valve taking into account the calculated CO2 suction density and CO2 discharge density as a function of the distance of the operating point of the centrifugal compressor from the surge limit and a parameter related to a CO2 volumetric flow rate at the discharge outlet of the centrifugal compressor or a CO2 volumetric flow rate at the discharge outlet of the centrifugal compressor, wherein the CO2 volumetric flow rate at the discharge is related to the CO2 mass flow rate at the suction inlet.

[0009] According to a second aspect, the subject matter disclosed herein relates to an anti-surge control system for a centrifugal compressor operating with CO2 in a supercritical state, the system being configured to adjust an anti-surge valve as a function of the distance of the centrifugal compressor operating point from a surge limit, taking into account parameters related to the CO2 suction density at the suction inlet and the CO2 discharge density at the discharge outlet of the centrifugal compressor, and the CO2 volumetric flow rate at the discharge outlet of the centrifugal compressor or the CO2 volumetric flow rate at the discharge outlet of the centrifugal compressor, wherein the CO2 volumetric flow rate at the discharge is related to the CO2 mass flow rate at the suction inlet.

[0010] According to a third aspect, the subject matter disclosed herein is a compression device including a centrifugal compressor operating with CO2 in a supercritical state, the device configured to adjust an anti-surge valve taking into account parameters related to the CO2 suction density at the suction inlet and the CO2 discharge density at the discharge outlet of the centrifugal compressor as a function of distance of the centrifugal compressor operating point from a surge limit, and the CO2 volumetric flow rate at the discharge outlet of the centrifugal compressor or the CO2 volumetric flow rate at the discharge outlet of the centrifugal compressor, wherein the CO2 volumetric flow rate at the discharge is related to the CO2 mass flow rate at the suction inlet. [Brief explanation of the drawings]

[0011] A more complete understanding of the disclosed embodiments of this invention and many of the attendant advantages thereof will be readily obtained as the same become better understood by reference to the following detailed description when considered in connection with the accompanying drawings. [Figure 1] A diagram showing the supercritical state of CO2 is shown. [Figure 2] 1 illustrates an embodiment of a compressor configured to operate with CO2 in a supercritical state. [Figure 3] 3 shows a compressor map that may be used, for example, in the compression system of FIG. 2. [Figure 4] 3 shows a flow diagram of one embodiment of an anti-surge control method that may be used, for example, in the compressor of FIG. 2. DETAILED DESCRIPTION OF THE INVENTION

[0012] According to the subject matter disclosed herein, the problem of surge in a centrifugal compressor operating with CO2 in a supercritical state is solved by an anti-surge loop including an anti-surge valve configured to control the flow of CO2 within the anti-surge loop. The anti-surge valve is controlled via an innovative control unit configured to control the flow of CO2 based on a CO2 flow measurement at the discharge side. In fact, measuring the CO2 flow rate at the discharge side of a centrifugal compressor operating with CO2 in a supercritical state becomes less difficult and more reliable as the CO2 moves away from its critical point. However, according to the subject matter disclosed herein, using such different measurements means calculating the CO2 intake density and the CO2 exhaust density.

[0013] Figure 1 shows a diagram illustrating the supercritical state of CO2, i.e., temperatures above about 31°C and pressures above about 7.38 MPa. According to the subject matter disclosed herein and certain embodiments, operating a supercritical state SCC of CO2 can be considered to be in the temperature range of about 31°C to about 300°C (or higher) and the pressure range of about 7.38 MPa to about 30 MPa (or higher). The critical point CP of CO2 is about 31°C and about 7.38 MPa.

[0014] A centrifugal compressor according to the subject matter disclosed herein is designed to receive a CO2 stream at its suction inlet at conditions IC close to the critical point CP, e.g., a temperature range of about 33°C to about 50°C and a pressure range of about 7.5 MPa to about 10 MPa. Higher pressures, and usually higher temperatures, are expected at the discharge outlet when the compressor is operating, especially after starting the compressor and before shutting it down.

[0015] 2 shows an embodiment of a compressor 200 configured to operate with CO in a supercritical state. It basically includes a centrifugal compressor 230 for compressing the CO, a control unit 260 for avoiding surges in the compressor 230, and a control valve 250, i.e., a so-called "anti-surge valve." The valve 250 is coupled, typically electrically coupled, to the control unit 260 and controlled by the control unit 220. The compressor 230 and the control unit 260 are coupled, typically electrically coupled, to each other.

[0016] The apparatus 200 has a suction inlet 210 for receiving an inlet flow of CO at inlet conditions near the critical point of CO, and a discharge outlet 220 for delivering an outlet flow of CO at outlet conditions that are supercritical. The outlet conditions differ from the inlet conditions at least in that the outlet pressure is higher than the inlet pressure. Typically, the outlet temperature is higher than the inlet temperature.

[0017] Compressor 230 has a suction inlet 232 and a discharge outlet 234. Inlet 232 is fluidly coupled to inlet 210. In the embodiment of FIG. 2, between inlet 210 and inlet 232 are, for example, a temperature sensor 212 and a pressure sensor 214. These sensors are preferably selected to introduce little or no condition fluctuations into the CO2 flow. Outlet 234 is fluidly coupled to outlet 220. In the embodiment of FIG. 2, between outlet 220 and outlet 234 are, for example, a temperature sensor 222 and a pressure sensor 224, and a flow sensor 226 (e.g., an orifice). These sensors are preferably selected to introduce little or no condition fluctuations into the CO2 flow.

[0018] An anti-surge loop 240 including an anti-surge control valve 250 is provided in the apparatus 200 of Figure 1. Typically, the loop is fluidly coupled between the discharge outlet of the compressor or apparatus and the suction inlet of the compressor or apparatus, and the anti-surge valve is positioned along the loop to control the flow of CO2 within the loop. According to the embodiment of Figure 2, there is essentially no difference between the two inlets and the two outlets, since they are nearly directly coupled.

[0019] In the embodiment of FIG. 2, control unit 260 receives input signals from sensors 212 , 214 , 222 , 224 and 226 and an output signal to valve 250 .

[0020] According to the embodiment of FIG. 2, the control unit 260 includes three blocks electrically coupled together: a controller block 270, a first calculator block 280, and a second calculator block 290. The controller block 270 is specifically designed to determine and output a control signal for the anti-surge valve 250 to avoid surges in the compressor 230. The calculator block 280 is specifically designed to calculate the compression factor of CO2 at the suction condition. According to an alternative embodiment, the block 280 outputs the density of CO2 at the suction condition. The calculator block 290 is specifically designed to calculate the compression factor of CO2 at the discharge condition. According to an alternative embodiment, the block 290 outputs the density of CO2 at the discharge condition.

[0021] The calculations of block 280 are based on the temperature values ​​detected by sensor 212 and the pressure values ​​detected by sensor 214. The calculations of block 290 are based on the temperature values ​​detected by sensor 222 and the pressure values ​​detected by sensor 224. The determinations of block 270 are based on the temperature values ​​detected by sensor 212, the pressure values ​​detected by sensor 214, the temperature values ​​detected by sensor 222, the pressure values ​​detected by sensor 224, the parameter values ​​detected by sensor 226, and input values ​​from blocks 280 and 290, particularly the compression factor.

[0022] It should be noted that the determination of the controller block (e.g., block 270) (and thus the output, i.e., control signal, to the antisurge valve) implements an antisurge control strategy based on a compressor map associated with a particular compressor (e.g., compressor 230) within a given compression system (e.g., system 200). Many different antisurge control strategies are possible. Such compressor maps may be stored in the controller block, e.g., in internal data tables.

[0023] It should be noted that the controller block may also need to know other parameters, such as the rotational speed of the compressor and / or the position of the IGVs (= inlet guide vanes), if present. Under certain conditions, the controller block may assume a predetermined rotational speed of the compressor when performing anti-surge control. For example, anti-surge may be enabled and performed when the compressor is at or close to its rated rotational speed.

[0024] As an alternative to FIG. 2, calculator blocks 280 and 290 may be integrated into controller block 270.

[0025] FIG. 3 shows an example of a compressor map for compressor 230 in apparatus 200 of FIG. 1. Three curves are plotted representing the relationship between the compression ratio CR and the so-called "equivalent flow rate" F at the compressor suction inlet for three different rotational speeds N1, N2, and N3 of the compressor rotor. The "equivalent flow rate" is a variable related to the volumetric flow rate that is independent of the gas conditions (e.g., pressure and temperature) at the suction inlet. It should be noted that similar curves can be plotted considering the volumetric flow rate at suction, i.e., at the compressor suction inlet, for various gas conditions, and can be used to perform anti-surge control.

[0026] FIG. 3 also shows two other exemplary curves SL and SC, where curve SL is the so-called "surge limit" line and curve SC is the so-called "surge control" line. When the compressor's operating point is, for example, point P0 shown in FIG. 3, there is no risk of surge. When the operating point moves to the left during compressor operation and reaches point P1, the risk of surge begins and increases as the compressor moves further to the left. When the operating point moves to the left during compressor operation and reaches point P2, surge occurs and becomes a risk as the compressor moves further to the left. Typically, curve SL is determined experimentally, and curve SC is derived from curve SL using a specific percentage margin, for example, 5% to 15%, typically 10%.

[0027] 3 also shows other indications, namely, the distance DC between the operating point and the surge control line, and the distance DL between the operating point and the surge limit line, both of which indicate how close or far the compressor is to the risk of surge.

[0028] The controller block may determine either or each of these distances with the aim of limiting the risk of surge in the compressor, and in general should absolutely avoid the compressor entering the region to the left of curve SL. To this end, the control block detects when the compressor reaches curve SC (starting in the region to the right of curve SC), or equivalently when it is at a certain distance from curve SL, and then opens the anti-surge valve appropriately.

[0029] As is clear from the above, surge risk is determined via compressor maps that consider the flow on the suction side of the compressor. However, in devices according to the subject matter disclosed herein, the flow is measured on the discharge side of the compressor. Even considering that the mass flow rates at suction and discharge are equal, the calculation of the volumetric flow rate at suction starting from the volumetric flow rate at discharge requires knowledge of the following: -CO2 suction density (or equivalently CO2 suction compression factor) at the compressor suction inlet. -CO2 emission density (or equivalently CO2 emission compression factor) at the compressor discharge outlet.

[0030] Generally, the density of a gas is a function of its pressure, its temperature, its molecular weight, and its compressibility factor, which is usually considered to be constant. In this case, because CO2 is in a supercritical state, its compressibility factor cannot be considered constant throughout the supercritical zone (unless one is prepared to allow for significant calculation error and, as a result, some uncontrolled surge risk). For example, the compressibility factor can vary from 0.2 to 0.9.

[0031] Thus, in accordance with the subject matter disclosed herein, the anti-surge valve is adjusted as a function of the distance of the CO2 compressor operating point from the surge limit, taking into account at least the following (i.e., the valve is physically opened and closed, and the degree or level of opening and closing is varied on demand as needed for anti-surge control, including fully open, fully closed, or any degree or level of partial opening / closing therebetween). -CO2 suction density at the suction inlet of the CO2 compressor -CO2 emission density at the outlet of the CO2 compressor

[0032] More specifically, as will become apparent from the following description, the anti-surge valve may be adjusted (i.e., its degree or level of opening varies as described above) as a function of the distance of the CO2 compressor operating point from the surge limit, taking into account at least the ratio between: -CO2 suction density -CO2 emission density

[0033] As will be seen below, starting from the density values, the compression factor values ​​can be derived.

[0034] As already partly anticipated when describing Figure 3, the anti-surge valve directly considers a parameter related to the CO2 volumetric flow rate at the suction outlet of the compressor or the CO2 volumetric flow rate at the suction outlet of the CO2 compressor, but indirectly (specific to the subject matter disclosed herein) considers a parameter related to the CO2 volumetric flow rate at the discharge outlet of the compressor or the CO2 volumetric flow rate at the discharge outlet of the CO2 compressor (in particular the pressure drop across the orifice), and is adjusted as a function of the distance of the compressor operating point from the surge limit (i.e., its degree or level of opening varies as described above). The CO2 volumetric flow rate is advantageously measured via a flow sensor at the discharge outlet of the centrifugal compressor.

[0035] Referring to exemplary FIG. 3, the distance of an operating point from the surge limit of operating point P0 can be calculated by considering a constant compression ratio CR, i.e., moving along a horizontal line to the left from point P0, and evaluating the reduction in the "reduced flow" F (at suction) that causes surge.

[0036] The CO2 mass flow rate at the compressor discharge outlet may be calculated from the CO2 volumetric flow rate at the compressor discharge outlet using the CO2 suction density and CO2 exhaust density, and equated to the CO2 mass flow rate at the compressor suction inlet assuming negligible mass injection and / or release, or they should be accurately measurable. In other words, mass flow rate at discharge = volumetric flow rate at discharge × density at discharge = mass flow rate at suction = volumetric flow rate at suction × density at suction.

[0037] The density of CO2 can be advantageously calculated by using two different equations of state, namely a first equation of state and a second equation of state, which applies to both the CO2 flow at the suction inlet and the CO2 flow at the exhaust outlet. Advantageously, such calculations are performed for CO2 in both streams.

[0038] In general, the first equation of state should be chosen to be particularly applicable to CO2 in the supercritical state.

[0039] This equation can be expressed as follows: compressibility factor Z as a function of other parameters including density, specifically reduced density and inverse reduced temperature:

[0040]

number

[0041]

number

[0042] In particular, the first equation of state can advantageously be the so-called "GERG2008" equation or the so-called "GERG2004" equation (using specific coefficients applicable to CO2 in the supercritical state). The equation used by GERG (= "Groupe Europeen de Recherches Gazieres") in the 2004 and 2008 publications was actually developed by R. Klimeck in 2000. In general, the use of other equations is not excluded. More information on Klimeck can be found in the article "Dissertation, Fakultat fur Maschinenbau", published in 2000 by R. Klimeck, in a publication by Ruhr-Universitat Bochum.

[0043] In the first equation of state above, the compressibility Z is a function of density, more precisely the reduced density, and also of temperature, more precisely the inverse reduced temperature. In general, other parameters should not be excluded.

[0044] In general, the second equation of state should be chosen to be particularly applicable to CO2 in the supercritical state.

[0045] The second equation of state may advantageously be the so-called "real gas law" which is practically applicable to CO2 in the supercritical state.

[0046] This equation can be expressed as follows: compressibility factor Z as a function of other parameters, including density:

[0047]

number

[0048] In the second equation of state above, the compressibility Z is a function of density, temperature, and pressure (and of the particular substance being considered, i.e., CO2). In general, other parameters should not be excluded.

[0049] The two equations above may be considered equivalent since compressibility should have the same value regardless of the formula used to calculate it, and other parameters may be considered constant in this case, resulting in a single equation containing only one true variable: density.

[0050] For example, this single equation can be:

[0051]

number

[0052] To obtain the unknown density value, this single equation needs to be solved, in other words, the root is searched.

[0053]

number

[0054] Advantageously, this single equation is solved numerically, for example by Newton's method (iterative method).

[0055] The "reduced molar Helmholtz free energy" in the first equation of state can be expressed as follows:

[0056]

number

[0057]

number

[0058] Starting from a density value calculated, for example, by the above equation (e.g., calculated in calculator blocks 280 and 290), a compressibility factor value can be derived (e.g., derived in calculator blocks 280 and 290) to be used, for example, by controller block 270 of FIG. 2 to drive anti-surge valve 250 of FIG. 2.

[0059] FIG. 4 illustrates a flow diagram of one embodiment of an anti-surge control method that may be used, for example, in compressor 200 of FIG.

[0060] The flow begins at start block 410 where the antisurge control begins and ends at stop block 480 where the antisurge control stops.

[0061] After block 410, the flow branches due to certain calculations relating to the suction side of the compressor (reference numbers belonging to such branches end with the letter "S") and other calculations relating to the discharge side of the compressor (reference numbers belonging to such branches end with the letter "D"). The activities of these two branches may be performed in parallel, not necessarily synchronously. According to an alternative embodiment, these activities may be performed sequentially.

[0062] In blocks 420S / 420D, there is an initial guess of the CO2 concentration, which may be done, for example, when or before anti-surge control begins, as will be explained later.

[0063] In blocks 430S / 430D, a bias is determined relative to the previously estimated or calculated CO concentration that minimizes the difference between the compressibility coefficients calculated through the two equations of state based on the current field measurements, and thus the current density value is determined.

[0064] Advantageously, one iteration of Newton's method may be sufficient since the previously calculated CO concentration (and, if it was a good guess, the previously estimated CO concentration) is close to the current CO concentration, although more iterations are not excluded.

[0065] At blocks 440S / 440D, a current compression factor value is calculated from the current density value just calculated.

[0066] After blocks 440S and 440D, the flows recombine into a single flow, followed by block 450. Note that the activity associated with block 450 can only be performed once the activity associated with blocks 440S and 440D has finished.

[0067] In the 450 block, the reduced mass flow rate is calculated (e.g., as described above) by combining the field measurements (e.g., pressure, temperature, and flow rate) at both the suction and exhaust with the calculated compressibility.

[0068] In block 460, the distance of the operating point from the surge limit is calculated at the current pressure ratio, the current compressor flow rates (mass flow rate and volume flow rate at suction and discharge) are calculated, and in block 470 the opening or closing level of the anti-surge valve is calculated as a function of the calculated distance.

[0069] According to some embodiments, the anti-surge valve is either (fully) closed or (fully) open.

[0070] According to another embodiment, the anti-surge valve opens / closes gradually.

[0071] 4 implements a double loop in the sense that the calculations of blocks 430-470 are repeated periodically, for example, during the antisurge control time course. In each cycle, the need to open / close the antisurge valve is assessed.

[0072] 2 shows an embodiment of an apparatus 200 including an innovative anti-surge control system for a centrifugal compressor 230 designed to operate in supercritical conditions. The system includes, among other things, a control unit 260, but may also be considered to include one or more or all of the following components: -Anti-surge valve 250, -Anti-surge loop 240 and its conduit, temperature sensor 212, pressure sensor 214, temperature sensor 222, pressure sensor 224, A flow sensor 226 (eg, an orifice).

[0073] It is not excluded that other embodiments may include more components, for example more sensors such as rotational speed sensors, or more connections such as electrical connections to a computer system.

[0074] It will be apparent that the embodiment of the anti-surge control system of FIG. 2 includes means, namely valves, sensors, electrical connections (e.g., cables), and fluid connections (e.g., pipes), specially adapted to carry out the method having all the technical features as described above.

[0075] According to a typical possibility, the control unit 260 may be comprised of a single computer system having appropriate software or software for performing the method of the present invention, even if the control unit 260 includes three separate blocks. Such a single computer system may be configured to perform not only anti-surge control but also other functions, such as other control functions. Such a single computer system may be configured to communicate with one or more other computer systems to perform anti-surge control or control functions.

[0076] The innovative anti-surge control system may be configured to perform anti-surge control only when the centrifugal compressor is in a supercritical state at the compressor inlet. This means that, according to some embodiments, the innovative system is only active or fully active when the sensed suction temperature (e.g., via sensor 212) and sensed suction pressure (e.g., via sensor 214) fall within the SCC zone shown in Figure 1. Outside this zone, anti-surge control is not performed, or surge is avoided in a different way, or another (different and separate) anti-surge control system is active.

[0077] For example, the innovative anti-surge control system may be configured to perform anti-surge control only after the end of a start-up period of the centrifugal compressor when CO2 is in a supercritical state at the compressor inlet and / or only before the start of a shut-down period of the centrifugal compressor. During start-up, surges can be avoided, for example, by keeping the anti-surge valve open (e.g., fully open) at a predetermined level. During shut-down, surges can be avoided, for example, by keeping the anti-surge valve open (e.g., fully open) at a predetermined level.

[0078] However, according to some embodiments, the innovative anti-surge control system may be configured to calculate the CO2 intake density and the CO2 exhaust density both before and after the end of the startup period. This is useful because in this way, density values ​​close to the actual values ​​are already available as soon as the innovative anti-surge control system is activated. In particular, if an iterative numerical algorithm is used to calculate the densities, the algorithm may converge in a much shorter time, i.e., with fewer iterations, if it starts from an "initial guess" that is close to the "solution."

[0079] The embodiment of the innovative compressor 200 of FIG. 2 includes a centrifugal compressor 230 configured to operate with CO2 in a supercritical state and includes only an innovative anti-surge control system.

[0080] The innovative anti-surge control system is configured to measure the CO2 flow rate at the discharge side of the compressor 230 and calculate both the CO2 suction density and the CO2 exhaust density based on the temperature and pressure on both the suction side and the exhaust side so that a compressor map (see, for example, FIG. 3) can be used for anti-surge control of the compressor 230.

Claims

1. 1. A method for performing anti-surge control in a centrifugal compressor operating with CO2 in a supercritical state, comprising: providing an anti-surge loop including an anti-surge valve configured to control CO2 flow within the anti-surge loop; Calculating a CO2 suction density at a suction inlet of the centrifugal compressor; Calculating the CO2 emission density at the discharge outlet of the centrifugal compressor; Calculating the distance of the centrifugal compressor operating point from a surge limit; as a function of the distance of the centrifugal compressor operating point from the surge limit; the calculated CO2 intake and exhaust densities; adjusting the anti-surge valve taking into account a CO2 volumetric flow rate at a discharge outlet of the centrifugal compressor or a parameter related to the CO2 volumetric flow rate at a discharge outlet of the centrifugal compressor, wherein the CO2 volumetric flow rate at the discharge is related to the CO2 mass flow rate at a suction inlet.

2. 2. The method of claim 1, wherein the CO2 volumetric flow rate is measured via a flow sensor (226) at the discharge outlet of the centrifugal compressor.

3. The anti-surge valve may be configured to: - CO2 suction density, The method according to claim 1, wherein the opening / closing is performed taking into account the ratio of -CO2 emission density.

4. 3. The method of claim 2, wherein the CO2 mass flow rate at the discharge outlet of the centrifugal compressor is calculated from the CO2 volumetric flow rate at the discharge outlet of the centrifugal compressor using the CO2 suction density and the CO2 exhaust density, and is equalized with the CO2 mass flow rate at the suction inlet of the centrifugal compressor.

5. the CO2 intake density and the CO2 exhaust density are calculated using both a first equation of state and a second equation of state; the first equation of state and the second equation of state are applicable to CO2 in a supercritical state; The method of claim 1 , wherein the second equation of state is a real gas equation of state.

6. 6. The method of claim 5, wherein the first equation of state corresponds to the GERG2008 equation or the GERG2004 equation for CO2 in a supercritical state.

7. The method of claim 5 , wherein the first equation is formulated as a compressibility ratio that is a function of at least temperature and density.

8. The method of claim 5 , wherein the second equation is formulated as a compressibility ratio that is a function of at least temperature, pressure, and density.

9. 6. The method of claim 5, wherein the first equation and the second equation are equated and solved, in particular solved numerically, thereby determining the density.

10. An anti-surge control system for a centrifugal compressor operating with CO2 in a supercritical state, the anti-surge control system being configured to carry out the method of any one of claims 1 to 9.

11. The anti-surge control system of claim 10, configured to perform anti-surge control only when CO2 is in a supercritical state at the inlet of the centrifugal compressor.

12. 12. The anti-surge control system of claim 11, configured to perform anti-surge control after a start-up period of the centrifugal compressor ends when CO2 is in a supercritical state at the inlet of the centrifugal compressor.

13. The anti-surge control system of claim 12 , configured to calculate a CO 2 intake density and a CO 2 exhaust density before and after the end of the startup period.

14. 14. The anti-surge control system of claim 13, wherein the system is configured to calculate the CO2 intake density and the CO2 exhaust density using both the first state equation and the second state equation when performing anti-surge control.

15. 11. A compressor including a centrifugal compressor operating with CO2 in a supercritical state, the compressor including the anti-surge control system of claim 10.

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