EP4646536A1

EP4646536A1 - Anti-surge control in a centrifugal compressor working with co2 in supercritical conditions based on flow measurement at discharge

Info

Publication number: EP4646536A1
Application number: EP24706929.7A
Authority: EP
Inventors: Alessandro MEO
Original assignee: Nuovo Pignone Technologie SRL
Current assignee: Nuovo Pignone Technologie SRL
Priority date: 2023-02-01
Filing date: 2024-01-31
Publication date: 2025-11-12
Also published as: CN120530268A; IT202300001623A1; WO2024160471A1; AU2024213475A1; JP2026504149A; KR20250138789A

Abstract

The compressor arrangement (200) comprises a centrifugal compressor (230) configured to work with CO2 in supercritical conditions and comprises an anti-surge control system (240, 250, 260); the anti-surge control system (240, 250, 260) is configured to measure (226) CO2 flow at the discharge side (234) of the centrifugal compressor (230) and to calculate CO2 suction density and CO2 discharge density based on temperature and pressure both at suction side (232) and at discharge side (234) so that compressor maps may be used for anti-surge control of the centrifugal compressor (230) when CO2 is in supercritical conditions at an inlet of the centrifugal compressor (230).

Description

TITLE

ANTI-SURGE CONTROL IN A CENTRIFUGAL COMPRESSOR

WORKING WITH CO2 IN SUPERCRITICAL CONDITIONS BASED ON FLOW MEASUREMENT AT DISCHARGE

DESCRIPTION

TECHNICAL FIELD

[0001] The subject matter disclosed herein relates to anti-surge control in a centrifugal compressor working with CO2 in supercritical conditions.

BACKGROUND ART

[0002] For certain applications such as for example electric power generation based on a closed thermodynamic cycle using CO2 (i.e. carbon dioxide) as working fluid, compressing CO2 in supercritical conditions through a centrifugal compressor is advantageous. Such technology is not very common being at present implemented mainly at experimental level and not at industrial level.

[0003] The problem of “surge” is a general problem in centrifugal compressors.

[0004] It is known to solve this problem through an anti-surge loop configured to fluidly couple the outlet of the compressor with the inlet of the compressor. The loop includes an anti-surge valve configured to control working fluid flow in the anti-surge loop: some working fluid is fed back from the discharge side to the suction side when a risk of surge for the compressor is determined.

[0005] According to such known solutions, a control unit measures temperature and pressure of the working fluid both at suction side and at discharge side of the compressor as well as working fluid flow at 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 working fluid flow at suction side in a centrifugal compressor working with CO2 in supercritical conditions is difficult and leads to unreliable measured values due to the conditions of the flowing CO2 to be measured being close to its critical point.

[0007] Therefore, it would be desirable to have methods and systems for overcoming the problem of surge specifically for centrifugal compressors working with CO2 in supercritical conditions in an easy and effective way.

SUMMARY

[0008] According to a first aspect, the subject matter disclosed herein relates to a method for performing anti-surge control in a centrifugal compressor working with CO2 in supercritical conditions; the method is carried out through an anti-surge loop including an anti-surge valve configured to control CO2 flow in the anti-surge loop; the anti-surge valve is regulated as a function of a distance of the centrifugal compressor operating point from surge limit taking into account: a CO2 suction density at a suction inlet of the centrifugal compressor, and a CO2 discharge density at a discharge outlet of the centrifugal compressor. Said in another way, the method comprises: providing an anti-surge loop including an anti-surge valve configured to control CO2 flow in the anti-surge loop; calculating a CO2 suction density at a suction inlet of the centrifugal compressor; calculating a CO2 discharge density at a discharge outlet of the centrifugal compressor; calculating a distance of the centrifugal compressor operating point from a surge limit; and regulating the anti-surge valve as a function of the distance of the centrifugal compressor operating point from the surge limit taking into account the calculated CO2 suction and discharge densities and a CO2 volumetric flow at a discharge outlet of the centrifugal compressor or a parameter related to the CO2 volumetric flow at a discharge outlet of the centrifugal compressor, the CO2 volumetric flow at a discharge being related to a CO2 mass flow at a suction inlet.

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

[0010] According to a third aspect, the subject matter disclosed herein relates to a compressor arrangement comprising a centrifugal compressor working with CO2 in supercritical conditions; the arrangement comprises an anti-surge control system configured to regulate the anti-surge valve as a function of a distance of the centrifugal compressor operating point from surge limit taking into account a CO2 suction density at a suction inlet and a CO2 discharge density at a discharge outlet as well as a CO2 volumetric flow at a discharge outlet of the centrifugal compressor or a parameter related to the CO2 volumetric flow at a discharge outlet of the centrifugal compressor, the CO2 volumetric flow at a discharge being related to a CO2 mass flow at a suction inlet.

BRIEF DESCRIPTION OF THE DRAWINGS

[0011] A more complete appreciation of the disclosed embodiments of the invention and many of the attendant advantages thereof will be readily obtained as the same becomes better understood by reference to the following detailed description when considered in connection with the accompanying drawings, wherein:

Fig. 1 shows a diagram wherein CO2 supercritical conditions are represented,

Fig. 2 shows an embodiment of a compressor arrangement configured to work with CO2 in supercritical conditions,

Fig. 3 shows compressor maps that may be used for example in the compressor arrangement of Fig. 2, and

Fig. 4 shows a flow diagram of an embodiment of an anti-surge control method that may be used for example in the compressor arrangement of Fig. 2. DETAILED DESCRIPTION OF EMBODIMENTS

[0012] According to the subject matter disclosed herein, the problem of surge in centrifugal compressors working with CO2 in supercritical conditions is solved through an anti-surge loop including an anti-surge valve configured to control CO2 flow in the anti-surge loop. The anti-surge valve is controlled through an innovative control unit configured to base control on CO2 flow measurement at discharge side. In fact, measuring CO2 flow at discharge side in a centrifugal compressor working with CO2 in supercritical conditions is less difficult and more reliable as CO2 is farther from its critical point. However, according to the subject matter disclosed herein, using such different measurement implies calculating CO2 suction density and CO2 discharge density.

[0013] Fig. 1 shows a diagram wherein CO2 supercritical conditions are represented for CO2, i.e. temperature higher than approximately 31°C and pressure higher than approximately 7.38 MPa. According to the subject matter disclosed herein and a specific embodiment, operating supercritical conditions SCC for CO2 may be considered to be in the temperature range from approximately 31°C to approximately 300°C (or even higher) and in the pressure range from approximately 7.38 MPa to approximately 30 MPa (or even higher). Critical point CP of CO2 is at approximately 31°C and approximately 7.38 MPa.

[0014] Centrifugal compressors according to the subject matter disclosed herein are designed to receive at its suction inlet a flow of CO2 at conditions IC close to the critical point CP, for example in the temperature range from approximately 33 °C to approximately 50°C and in the pressure range from approximately 7.5 MPa to approximately 10 MPa. At the discharge outlet, a higher pressure and, usually, a higher temperature is expected if the compressor is operative, especially after start-up of the compressor and before shut-down.

[0015] Fig. 2 shows an embodiment of a compressor arrangement 200 configured to work with CO2 in supercritical conditions. It includes basically a centrifugal compressor 230 for compressing CO2 and a control unit 260 for avoiding surge in compressor 230 and a controlled valve 250, i.e. a so-called “anti-surge valve”. Valve 250 is coupled to, typically electrically coupled to, and controlled by control unit 260. Compressor 230 and control unit 260 are coupled together, typically electrically coupled.

[0016] Arrangement 200 has a suction inlet 210 for receiving an inlet flow of CO2 at inlet conditions close to the critical point of CO2 and a discharge outlet 220 for delivering an outlet flow of CO2 at outlet conditions being supercritical conditions. The outlet conditions are different from the inlet conditions at least in that outlet pressure is higher than inlet pressure; typically, outlet temperature is higher than 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 there for example is a temperature sensor 212 and a pressure sensor 214; these sensors are preferably chosen so to introduce no or small conditions variations in the CO2 flow. Outlet 234 is fluidly coupled outlet 220; in the embodiment of Fig. 2, between outlet 220 and outlet 234 there for example is a temperature sensor 222 and a pressure sensor 224 and also a flow sensor 226 (for example, an orifice); these sensors are preferably chosen so to introduce no or small conditions variations in the CO2 flow.

[0018] An anti-surge loop 240 is provided in the arrangement 200 in Fig. 1 including the anti-surge controlled valve 250. In general, the loop is fluidly coupled between discharge outlet of the compressor or of the arrangement and suction inlet of the compressor or of the arrangement, and the anti-surge valve is placed along the loop so to control CO2 flow in the loop. According to the embodiment of Fig. 2, there is basically no difference between the two inlets and between the two outlets as they are almost directly coupled.

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

[0020] According to the embodiment of Fig. 2, control unit 260 includes three blocks electrically coupled together: a controller block 270, a first calculator block 280 and a second calculator block 290. Controller block 270 is specifically designed to determine and output control signals for anti-surge valve 250 in order to avoid surge in compressor 230. Calculator block 280 is specifically designed to calculate compressibility factor of CO2 at suction conditions; according to an alternative embodiment, block 280 outputs density of CO2 at suction conditions. Calculator block 290 is specifically designed to calculate compressibility factor of CO2 at discharge conditions; according to an alternative embodiment, block 290 outputs density of CO2 at discharge conditions. [0021] Calculation of block 280 is based on temperature values detected by sensor 212 and on pressure values detected by sensor 214. Calculation of block 290 is based on temperature values detected by sensor 222 and on pressure values detected by sensor 224. Determination of block 270 is based on temperature values detected by sensor 212, pressure values detected by sensor 214, temperature values detected by sensor 222, pressure values detected by sensor 224, the parameter values detected by sensor 226, as well as input values from blocks 280 and 290, in particular compressibility factors.

[0022] It is to be noted that the determination of the controller block (for example block 270) (and therefore also the output, i.e. the control signal, to the anti-surge valve) implements an anti-surge control strategy based on compressor maps relating to the specific compressor (for example compressor 230) in the compressor arrangement of interest (for example arrangement 200); many different anti-surge control strategies are possible. Such compressor maps may be stored in the controller block, for example in an internal data table.

[0023] It is also to be noted that the controller block may need to know also other parameters, for example the rotation speed of the compressor and/or the position of the IGV (= Inlet Guided Vanes) if present. Under certain conditions, the controller block may assume a predetermined rotation speed of the compressor when performing anti-surge control; for example, if anti-surge may be enabled and performed when the compressor is at its rated rotation speed or close thereto.

[0024] Alternatively to Fig. 2, the calculator blocks 280 and 290 may be integrated into controller block 270.

[0025] Fig. 3 shows an example of compressor maps for compressor 230 in arrangement 200 of Fig. 1. Three curves are plotted representing the relation between compression ratio CR and so-called “reduced flow” F at the suction inlet of the compressor at three different rotation speeds Nl, N2, N3 of the rotor of the compressor. The “reduced flow” is a variable related to the volumetric flow that does not depend on the gas conditions (for example pressure and temperature) at the suction inlet It is to be noted that similar curves may be plotted considering the volumetric flow at suction, i.e. at the suction inlet of the compressor, for various gas conditions and that may be used for performing anti-surge control.

[0026] Additionally, Fig. 3 shows other two exemplary curves SL and SC: curve SL is the so-called “Surge Limit” line and curve SC is the so-called “Surge Control” line. If the operating point of the compressor is for example where shown in Fig. 3 at point P0, there is no risk of surge; if during operation of the compressor the operating point moves to the left and reaches point Pl a risk of surge begins and increases moving further to the left; if during operation of the compressor the operating point moves to the left and reaches point P2 surge occurs and becomes words moving further to the left. Typically, curve SL is experimentally determined while curve SC is derived from curve SL using a certain percentage margin, for example from5% to 15% and typically 10%.

[0027] Additionally, Fig. 3 shows other indications: a distance DC between the operating point and the surge control line and a distance DL between the operating point and the surge limit line. Both such distances indicate how close/far is the compressor to/from the risk of surge.

[0028] The controller block aims at limiting the risk of surge in the compressor and may determine any or each of these distances and, in general, should absolutely avoid the compressor entering into the region on the left of curve SL. For this purpose the controller block detects when the compressor has reached curve SC (starting from the region on the right of curve SC) or equivalently is at a certain distance from curve SL, and then appropriately opens the anti-surge valve.

[0029] As it is apparent from above, surge risk is determined through compressor maps that consider the flow of the compressor at its suction side. However, in the arrangement according to the subject matter disclosed herein, the flow is measured at the discharge side of the compressor. Even considering that the mass flow at suction and the mass flow at discharge are equal, calculation of the volumetric flow at suction starting from volumetric flow at discharge requires the knowledge of:

CO2 suction density (or equivalently CO2 suction compressibility factor) at a suction inlet of the compressor,

CO2 discharge density (or equivalently CO2 discharge compressibility factor) at a discharge outlet of the compressor.

[0030] In general, the density of a gas is a function of its pressure, its temperature, its molecular weight as well as its compressibility factor that, however, is usually considered constant. In the present case, as CO2 is in supercritical conditions, its compressibility factor cannot be considered constant throughout the supercritical zone (unless prepared to tolerate a considerable calculation error and consequently some uncontrolled surge risk); for example, it may vary from 0.2 to 0.9.

[0031] Therefore, according to the subject matter disclosed herein, the antisurge valve is regulated (i.e. the valve is physically opened and closed and its degree or level of opening and closing is varied on demand as required including being fully opened, fully closed or any degree or level of partial opening/closing therebetween for anti-surge control) as a function of distance of the CO2 compressor operating point from surge limit taking into account at least: a CO2 suction density at a suction inlet of the CO2 compressor, and a CO2 discharge density at a discharge outlet of the CO2 compressor. [0032] More specifically, as it will be apparent from the following explanation, the anti-surge valve may be regulated (i.e. its opening degree or level is varied as previously indicated) as a function of a distance of the CO2 compressor operating point from surge limit taking into account at least a ratio between: the CO2 suction density, and the CO2 discharge density.

[0033] As it will apparent from the following, starting from density values, compressibility factor values may be derived.

[0034] As already partially anticipated when describing Fig. 3, the anti-surge valve is regulated (i.e. its opening degree or level is varied as previously indicated) as a function of a distance of the compressor operating point from surge limit taking into account also directly a CO2 volumetric flow at a suction outlet of the compressor or a parameter related to the CO2 volumetric flow at a suction outlet of the CO2 compressor but indirectly (which is specific of the subject matter disclosed herein) a CO2 volumetric flow at a discharge outlet of the compressor or a parameter related to the CO2 volumetric flow at a discharge outlet of the CO2 compressor (in particular a pressure drop across an orifice) - the CO2 volumetric flow is advantageously measured through a flow sensor at a discharge outlet of the centrifugal compressor.

[0035] With reference to exemplary Fig. 3, distance of the operating point from surge limit of operating point P0 may be computed considering a constant compression ratio CR, i.e. moving along a horizontal line from point P0 to the left, and evaluating the reduction of “reduced flow” F (at suction) that would cause surge.

[0036] A CO2 mass flow at a discharge outlet of the compressor may be computed starting from the CO2 volumetric flow at a discharge outlet of the compressor using the CO2 suction density and the CO2 discharge density, and is equated to a CO2 mass flow at a suction inlet of the compressor assuming negligible any mass injection and/or ejection; otherwise, they should be precisely measurable. In other words, mass flow at discharge = vol flow at discharge x density at discharge = mass flow at suction = vol flow at suction x density at suction.

[0037] Density of CO2 may be advantageously calculated through the use of two different state equations, namely a first state equation and a second state equation. This applies to both CO2 in the flow at suction inlet and CO2 in the flow at discharge outlet. Advantageously, such calculation is made for CO2 in both flows.

[0038] In general, the first state equation should be chosen so to be specifically applicable to CO2 in supercritical conditions.

[0039] This equation may be expressed as follows, i.e. compressibility factor Z as a function of other parameters including density, specifically as a function of reduced density and inverse reduced temperature: wherein 8 is the “reduced density”, wherein T is the “inverse reduced temperature”, wherein a^r _s is the partial derivative of the “reduced molar Helmholtz free energy”.

[0040] Specifically, the first state equation may be advantageously the so- called “GERG2008” equation or the so-called “GERG2004” equation (using the specific coefficients applicable to CO2 in supercritical conditions). The equation used both by GERG (= “Groupe Europeen de Recherches Gazieres”) in its publications of 2004 and 2008 was actually developed by R. Klimeck in 2000. In general, the use of the other equations is not to be excluded. Detailed information regarding Klimeck may be found in the publication by R. Klimeck entitled “Entwicklung einer Fundamentalgleichung fur Erdgase fur das Gas- und Fliissigkeitsgebiet sowie das Phasengleichgewicht”, Dissertation, Fakultat fur Maschinenbau, Ruhr-Universitat Bochum, published in 2000.

[0041] In the above first state equation, compressibility Z is a function of density, more precisely reduced density, and of temperature, more precisely inverse reduced temperature. In general, other parameters are not to be excluded.

[0042] In general, the second state equation should be chosen so to be specifically applicable to CO2 in supercritical conditions.

[0043] The second state equation may be advantageously the so-called “real gas law” that is indeed applicable to CO2 in supercritical conditions.

[0044] This equation may be expressed as follows, i.e. compressibility factor Z as a function of other parameters including density:

7 - ^{P Mw} p R T wherein P is the pressure, wherein M_w is the molecular weight, wherein p is the density, wherein R is the universal gas constant, wherein T is the temperature.

[0045] In the above second state equation, compressibility Z is a function of density and of temperature and of pressure (and of the specific substance considered, i.e. CO2). In general, other parameters are not to be excluded.

[0046] The above two equations may be equated as compressibility should have the same value irrespective of the formulas used for calculation, and a single equation results containing only one true variable, namely density, as the other parameters may be considered constant in the present case.

[0047] For example, this single equation may be:

[0048] This single equation needs to be solved in order to obtain the unknown density value; in other words, the root is searched:

/(«) = 0

[0049] Advantageously, this single equation is solved numerically, for example by Newton method (which is an iterative method).

[0050] The “reduced molar Helmholtz free energy” in the first state equation may be expressed as: and its partial derivative (with respect to <5) may be expressed as: da^r

««(<!>, T)

~d8

[0051] Starting from density values calculated for example with the above formulas (for example calculated inside calculator blocks 280 and 290), compressibility factor values may be derived (for example derived inside calculator blocks 280 and 290) to be used for example by controller block 270 in Fig. 2 in order to drive anti-surge valve 250 in Fig. 2.

[0052] Fig. 4 shows a flow diagram of an embodiment of an anti-surge control method that may be used for example in the compressor arrangement 200 of Fig. 2.

[0053] The flow begins with a START block 410 where anti-surge control starts and ends with a STOP block 480 where anti-surge control stops.

[0054] After block 410 the flow branches as there are certain calculation that regards the suction side of the compressor (reference signs belonging to such branch ends with the letter “S”) and other calculation that regards the discharge side of the compressor (reference signs belonging to such branch ends with the letter “D”). The activities of these two branches may be carried out in parallel, not necessarily synchronously. According to alternative embodiments, these activities may be carried out in series.

[0055] At block 420S/420D, there is an initial guess of CO2 density; this may be done for example when anti-surge control starts or even before, as it will be explained afterwards.

[0056] At block 430S/430D, a bias is determined to previously guessed or calculated CO2 density that minimizes the difference between the compressibility factors calculated through the two state equations based on current field measurements. So a current density value is determined.

[0057] Advantageously, as the previously calculated CO2 density (and the previously guessed CO2 density, if it was a good guess) is close to the current CO2 density, a single iteration of the Newton method may be sufficient. However, more iterations are not to be excluded.

[0058] At block 440S/440D, current compressibility factor value is calculated from current density value as just calculated.

[0059] After blocks 440S and 440D, the flow rejoins in a single flow and block 450 follows. It is to be noted that the activities associated to block 450 may be carried out only if the activities associated to blocks 440S and 440D are over.

[0060] At 450 block, reduced mass flow is calculated (for example as explained previously) by combining field measurements (e.g. pressure, temperature and flow) and calculated compressibility at both suction and discharge.

[0061] At 460 block, distance of the operating point from surge limit is calculated at current pressure ratio, current compressor flow (mass flow and volumetric flow at suction and discharge) is calculated, and at block 470 antisurge valve opening or closing level is calculated as a function of the calculated distance.

[0062] According to some embodiments, the anti-surge valve is either (completely) close or (completely) open.

[0063] According to other embodiments, the anti-surge valve is gradually opened/closed.

[0064] The flow diagram of Fig. 4 implements a double loop, in the sense that the calculations of blocks 430-470 are repeated for example periodically during anti-surge control time lapse; at every cycle, the need to open/close the anti-surge valve is accessed.

[0065] Fig. 2 shows an embodiment of an arrangement 200 including an innovative anti-surge control system for a centrifugal compressor 230 designed to work in supercritical conditions. The system includes in particular control unit 260, but may be considered to include also one or more or all of the following components: anti-surge valve 250, anti-surge loop 240 with its conduits,

- temperature sensor 212, - pressure sensor 214,

- temperature sensor 222,

- pressure sensor 224, flow sensor 226 (for example orifice).

[0066] It is not to be excluded that other embodiments may include more components, for example further sensors e.g. a rotation speed sensor, or more connections e.g. an electrical connection to a computer system.

[0067] It is apparent that the embodiment of anti-surge control system in Fig. 2 comprising means, i.e. valve, sensors, electrical connections (e.g. cables) and fluid connections (e.g. pipes), specifically adapted to carry out the method with all the technical features as set above.

[0068] According to a typical possibility, control unit 260 may consists of a single computer system with an appropriate piece of software or appropriate pieces of software for carrying out the innovative method even if control unit 260 contains three distinct blocks. Such single computer system may be configured to perform not only anti-surge control but also other functions, for example other control functions. Such single computer system may be configured to communicate with one or more other computer systems in order to perform anti-surge control or control functions.

[0069] The innovative anti-surge control system may be configured to perform anti-surge control only when the centrifugal compressor is in supercritical conditions at an inlet of the compressor. This means that, according to some embodiments, the innovative system is active or fully active only when the detected suction temperature (e.g. through sensor 212) and the detected suction pressure (e.g. through sensor 214) fall in SCC zone shown in Fig. 1. When outside of this zone, no anti-surge control is performed or surge is avoided through in a different way or another (different and distinct) antisurge control system is active. [0070] For example, the innovative anti-surge control system may be configured to perform anti-surge control only after an end of a start-up period of the centrifugal compressor when CO2 is in supercritical conditions at an inlet of the compressor and/or only before an start of a shut-down period of the centrifugal compressor. During start-up, surge may be avoided for example by keeping the anti-surge valve opened at a predetermined level (e.g. completely open). During shut-down, surge may be avoided for example by keeping the anti-surge valve opened at a predetermined level (e.g. completely open).

[0071] However, according to some embodiments, the innovative anti-surge control system may be configured to calculate the CO2 suction density and the CO2 discharge density both before the end of the start-up period and after the end of the start-up period. This is useful as in this way density values close to the real one are already available as soon as the innovative anti -surge control system is activated. In particular, if an iterative numerical algorithm is used for calculating the densities, the algorithm may converge in a much shorter time, i.e. with less iterations, if starting from an “initial guess” close to the “solution”.

[0072] The embodiment of innovative compressor arrangement 200 in Fig. 2 comprises a centrifugal compressor 230 configured to work with CO2 in supercritical conditions and comprises just an innovative anti-surge control system.

[0073] The innovative anti-surge control system is configured to measure CO2 flow at the discharge side of compressor 230 and to calculate both CO2 suction density and CO2 discharge density based on temperature and pressure both at suction side and at discharge side so that compressor maps (see e.g. Fig. 3) may be used for anti-surge control of compressor 230.

Claims

1. A method for performing anti-surge control in a centrifugal compressor working with CO2 in supercritical conditions, the method comprising: providing an anti-surge loop including an anti-surge valve configured to control CO2 flow in the anti-surge loop; calculating a CO2 suction density at a suction inlet of the centrifugal compressor; calculating a CO2 discharge density at a discharge outlet of the centrifugal compressor; calculating a distance of the centrifugal compressor operating point from a surge limit; and regulating the anti-surge valve as a function of the distance of the centrifugal compressor operating point from the surge limit taking into account: the calculated CO2 suction and discharge densities, and a CO2 volumetric flow at a discharge outlet of the centrifugal compressor or a parameter related to the CO2 volumetric flow at a discharge outlet of the centrifugal compressor, the CO2 volumetric flow at a discharge being related to a CO2 mass flow at a suction inlet.

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

3. The method of claim 1, wherein the anti-surge valve is opened/closed as a function of a distance of the CO2 compressor operating point from surge limit taking into account a ratio between: the C02 suction density, and the CO2 discharge density.

4. The method of claim 2, wherein a CO2 mass flow at a discharge outlet of the centrifugal compressor is computed starting from the CO2 volumetric flow at a discharge outlet of the centrifugal compressor using the CO2 suction density and the CO2 discharge density, and is equated to a CO2 mass flow at a suction inlet of the centrifugal compressor.

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

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

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

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

9. The method of claim 5, wherein the first equation and the second equation are equated and solved, in particularly numerically solved, whereby a density is determined.

10. An anti-surge control system for a centrifugal compressor working with CO2 in supercritical conditions, the system being configured to carry out the method of any of the preceding claims.

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

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

13. The anti-surge control system of claim 12, being configured to calculate CO2 suction density and CO2 discharge density before the end of the start-up period and after the end of the start-up period.

14. The anti-surge control system of claim 13, being configured to calculate CO2 suction density and CO2 discharge density using both a first state equation and a second state equation when the system performs antisurge control.

15. A compressor arrangement comprising a centrifugal compressor working with CO2 in supercritical conditions, the arrangement comprising the anti -surge control system of claim 10.