Energy Conversion System

Abstract

The embodiment relates to an energy conversion system having: a Solid Oxide Fuel Cell (SOFC) unit (A) having an anode and a cathode side, for receiving a fuel (1) and a steam of oxidant (4) and for converting a fraction of chemical power of the fuel (1) into electric power; a combustor unit (B) to receive unconverted fuel (5) and unconverted oxidant (6), configured for converting the unconverted fuel (5) and the unconverted oxidant (6) into product gas (10); an expander unit (C) to receive the product gas (10) and configured for expanding said product gas (10) into flue gas (12); a cooler unit (E) in thermal relationship with a heat sink (27) and configured for cooling said flue gas (12); a separator (F) for removing condensed species (15) from the cooled gas (14) exiting the cooler unit (E); and a first compression unit (K) for increasing the pressure of said oxidant (26, 4, 8) to a value suitable for the SOFC unit (A) and the combustor unit (B).

Claims

1. An energy conversion system comprising: a Solid Oxide Fuel Cell (SOFC) unit (A) having an anode and a cathode side, configured for receiving a fuel (1) and a stream of oxidant (4) and for converting a fraction of chemical power of the fuel (1) directly into electric power through one or more electrochemical reactions occurring on the anode and the cathode side of the SOFC unit (A) involving said fuel (1) and said oxidant (4), parts of the fuel (1) and of the stream of oxidant (4) being maintained unconverted following said electrochemical reactions; a combustor unit (B) arranged to receive the unconverted fuel (5) and the unconverted oxidant (6) from the SOFC unit (A), configured for the combustion of the unconverted fuel (5) using the unconverted oxidant (6), thereby converting the unconverted fuel (5) and the unconverted oxidant (6) into product gas (10); an expander unit (C) arranged to receive the product gas (10) exiting the combustor (B) and configured for expanding said product gas (10) exiting the combustor (B) into flue gas (12); a cooler unit (E) in thermal relationship with a heat sink (27) and configured for cooling said flue gas (12) exiting the expander unit (C); a separator (F) for removing condensed species (15) from the cooled gas (14) exiting the cooler unit (E), thereby obtaining a recycled stream (18); and a first compression unit (K) configured for increasing the pressure of said oxidant (26, 4, 8) to a value suitable for the SOFC unit (A) and the combustor unit (B).

2. The energy conversion system according to claim 1, wherein the SOFC unit (A) is configured to work with an oxidant stream (4) composed of a mixture of CO.sub.2 and oxygen.

3. The energy conversion system according to claim 1, wherein the SOFC unit (A) is configured to work at pressures comprised in the range between 5 and 500 bar.

4. The energy conversion system according to the claim 3, wherein the SOFC unit (A) is configured to work at pressures comprised in the range between 250 and 360 bar.

5. The energy conversion system according to claim 1, wherein the SOFC unit (A) is configured to work at temperatures comprised in the range between 650 and 850° C.

6. The energy conversion system according to claim 1, wherein the expander unit (C) is configured such that the flue gas outlet pressure is between 1 and 50 bar.

7. The energy conversion system according to the claim 6, wherein the expander unit (C) is configured such that the flue gas outlet pressure is between 10 and 30 bar.

8. The energy conversion system according to claim 1, wherein the combustor unit (B) is configured for combusting additional fuel (7) and/or an additional oxidant (8) in addition to said unconverted fuel (5) and to said unconverted oxidant (6) exiting from the SOFC unit (A).

9. The energy conversion system according to claim 1, wherein the SOFC unit (A) is configured to run with an internal reforming process.

10. The energy conversion system according to claim 1, wherein the SOFC unit (A) is configured to run with a pre-reforming process (R).

11. The energy conversion system according to claim 1, wherein the combustor unit (B) is a catalytic combustion unit.

12. The energy conversion system according to claim 1, further comprising a heat exchanger unit (D) for preheating at least one of the streams entering the SOFC (A) and/or the combustor (B), wherein said heat exchanger unit (D) is in thermal relationship with the expander (C) exhaust gas and/or with other hot streams of the energy conversion system itself and/or with one or more further plants.

13. The energy conversion system according to claim 1, further comprising one or more heater and/or one or more cooler (P,Q,T,U,W,Y) for modifying the temperatures of the streams entering and/or exiting the SOFC to desired values.

14. The energy conversion system according to claim 1, further comprising a second compressor unit (H) for compressing said recycled stream (18), thereby obtaining a compressed recycled stream (19).

15. The energy conversion system according to the claim 14, further comprising a third compressor unit (L) for compressing at least a portion (23) of said compressed recycled stream (19) to a pressure suitable for the combustor (B).

16. The energy conversion system according to claim 1, wherein the SOFC unit is configured for further receiving a stream of steam (3).

17. The energy conversion system according to claim 1, further comprising at least a second SOFC unit (AF) and/or at least a second combustor unit (AG) after the expander unit.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to better comprehend the invention and appreciate the advantages thereof, some exemplifying non-limiting embodiments will be described in the following with reference to the attached figures, illustrating an energy conversion system according to possible embodiments of the invention.

[0018] FIG. 1 is a process flow diagram of the present energy conversion system according to a first embodiment of the invention. The system according to the first embodiment comprises: [0019] A SOFC unit A, partially converting fuel 1 and oxidant 4 directly into electricity via electrochemical reactions; [0020] A combustor B, performing the combustion of the unconverted fuel 5 and unconverted oxidant 6 discharged from the SOFC unit A with the optional injection of a recycled CO.sub.2-rich stream 9 and/or additional fuel 7 and/or additional oxidant 8; [0021] An expander C, expanding the combustor outlet gases 10 to generate mechanical power. [0022] An optional heat exchanger D, recovering the heat of the hot flue gases 12 to preheat the oxidant stream 24,26, the recycle stream used as temperature moderator 25,9, the optional turbine coolant 11, and the optional water/steam for the SOFC 2,3; [0023] A cooler E, cooling down the exhaust gases 13 and transferring the heat to the environment (for example to a stream of water 27,28) taken from a river, lake, sea, or to the air) or to another process/system; [0024] A flash-drum separator F, separating the condensed species 15 (mainly water) from the cooled stream 14 of CO.sub.2-rich exhaust gases; [0025] A splitter G, dividing the stream to be extracted 17 from the one 16 exiting the flash drum F; [0026] An optional compressor train H, comprising one or more compressor units with optional intercoolers to pressurize the recycled stream (18) to a suitable pressure to be mixed with the oxygen stream 21; [0027] A splitter I, separating the recycle stream 19 in the temperature moderator of the combustor 23 and a CO.sub.2-rich stream 20 to dilute the oxygen 21; [0028] A mixer J, producing the oxidant mixture 22; [0029] A compressor train K, comprising one or more compressor units with optional intercoolers to pressurize the oxidant stream 22,24 to the pressure level required by the SOFC A and combustor B; [0030] An optional compressor train L, comprising one or more compressor units with optional intercoolers to pressurize the recycle stream 23,25 to the pressure level required by the SOFC A and combustor B; [0031] An optional splitter M, dividing the oxidant stream 26 in two flows, the first one 4 used in the SOFC unit A and the second one 8 (optional) used in the combustor B.

[0032] FIG. 2 is a possible scheme configuration for the SOFC unit of the energy conversion system in FIG. 1. The system comprises: [0033] A compressor train N, comprising one or more compressor units with optional intercoolers to pressurize the fuel 1 to the pressure level required by the SOFC A and combustor B; [0034] An optional mixer O, which can be used also as an ejector to compress an optional stream recycled from the anode outlet 40 and/or to mix the fuel 29 with a steam flow 3 to obtain a suitable chemical composition of the stream 30 to be fed at the anode side of the SOFC unit S; [0035] An optional heater P, recovering heat from the SOFC S outlet streams and/or from hot process streams to heat up the anode mixture 30 to the temperature level required by the SOFC S or by the optional pre-reformer R; [0036] An optional heater 0, recovering heat from the SOFC S outlet streams and/or from another process/system to heat up the cathode mixture 4 to the temperature level required by the SOFC S; [0037] An optional external pre-reformer R, which can recover heat directly from the electrochemical reaction occurring within the SOFC unit S and/or from another process/system, converting the anode mixture 31 to obtain a suitable chemical composition to operate the SOFC unit S; [0038] A SOFC unit S, converting the chemical energy of the anode mixture 32 in direct electrical current using the oxygen provided by the cathode mixture 33; [0039] An optional cooler T, transferring heat from the stream at the anode outlet 34 to another process/system and/or to the ambient and obtaining a stream 36 at the temperature required by combustor; [0040] An optional cooler U, transferring heat from the stream at the cathode outlet 35 to another process/system and/or to the environment (e.g., cooling water) and obtaining a stream 6 at the temperature required by combustor; [0041] An optional splitter V, dividing the unconverted fuel 36 to a stream to be fed to the combustor 5 and a recycled flow 37 to be mixed with the fuel 29; [0042] An optional cooler W, transferring heat from the (optional) recycled unconverted fuel 37 to another process/system and/or to the environment and obtaining a stream 38 at the temperature required by compressor train X; [0043] An optional compressor train X, pressurizing the recycled unconverted fuel 38 to overcome the pressure drops across the anode side; [0044] An optional heater Y, recovering heat from the hot streams exiting the SOFC unit S and/or the optional cooler W and/or from another process/system to preheat the recycled unconverted fuel 39;

[0045] FIG. 3 is a process flow diagram of the claimed energy conversion system according to a second embodiment of the invention. The system comprises: [0046] A SOFC unit Z, partially converting fuel 41 and oxidant 44 directly into electricity via electrochemical reactions; [0047] A combustor AA, performing the combustion of the unconverted fuel 45 and unconverted oxidant 46 discharged from the SOFC unit Z with the optional injection of a recycled CO.sub.2-rich stream 49 and/or additional fuel 47 and/or additional oxidant 48; [0048] An expander AB, expanding the combustor outlet gases 50 to generate mechanical power (cooling flows 51 may be required depending on the turbine inlet temperature); [0049] A splitter AC, dividing the expanded gasses 53 in two streams, the first one 53 used to be mixed with an oxygen stream 54 and the second one 63 to be used as temperature moderator in the second combustor AG; [0050] A mixer AD, producing the oxidant mixture 55; [0051] A splitter AE, dividing the oxidant stream 55 in two flows, the first one 56 used in the second SOFC unit AF and the second one 62 (optional) used in the second combustor AG; [0052] An optional second SOFC unit AF, converting fuel 58 and oxidant 56 directly into electricity via electrochemical reactions; [0053] A second combustor AG, performing the combustion of the unconverted fuel 60 and unconverted oxidant 69 discharged from the SOFC unit AF with the injection of the first turbine AB exhaust stream 63 and/or additional fuel 61 and/or additional oxidant 62; [0054] A second expander AH, expanding the combustor outlet gases 64 to generate mechanical power (cooling flows 65 may be required depending on the turbine inlet temperature); [0055] An optional heat exchanger AI, recovering the heat of the hot flue gases 66 to preheat the oxidant stream 78,80, the recycle stream used as temperature moderator 79,49, optional water/steam for the SOFCs 42,41 and optional turbine coolant 51,65; [0056] A cooler AJ, cooling down the exhaust gases 68 and transferring the heat to the environment (for example to a stream of water 81,82 taken from a river, lake, sea, or to the air) or to another process/system; [0057] A flash drum separator AK, separating the condensed species 69 (mainly water) from the cooled stream 68 of CO.sub.2-rich exhaust gases; [0058] A splitter AL, dividing the stream to be extracted 71 from the one 70 exiting the flash-drum AK; [0059] An optional compressor train AM, comprising one or more compressor units with optional intercoolers to pressurize the recycled stream 72 to a suitable pressure to be mixed with the oxygen stream 75; [0060] A splitter AN, separating the recycle stream 73 in the temperature moderator of the combustor 77 and a CO.sub.2-rich stream 74 to dilute the oxygen 75; [0061] A mixer AO, producing the oxidant mixture 76; [0062] A compressor train AP, comprising one or more compressor units with optional intercoolers to pressurize the oxidant stream 76,78 to the pressure level required by the SOFC Z and combustor AA; [0063] A compressor train AQ, comprising one or more compressor units with optional intercoolers to pressurize the recycle stream 77,79 to the pressure level required by the SOFC Z and combustor AA; [0064] A splitter AR, dividing the oxidant stream 80 in two flows, the first one 44 used in the SOFC unit Z and the second one 48 (optional) used in the combustor AA; [0065] A splitter AS, dividing the optional water/steam 41 in two flows, the first one 43 used in the SOFC unit Z and the second one 57 used in the second SOFC unit AF.

DETAILED DESCRIPTION

[0066] For the purpose of the present description and of the appended claims, except where otherwise indicated, all numbers expressing amounts, quantities, percentages, and so forth, are to be understood as being modified in all instances by the term “about”. Also, all ranges include any combination of the maximum and minimum points disclosed and include any intermediate ranges therein, which may or may not be specifically enumerated herein.

[0067] The present disclosure, in at least one of the aforementioned aspects, can be implemented according to one or more of the following embodiments, optionally combined together.

[0068] For the purpose of the present description and of the appended claims, the words “a” or “an” should be read to include one or at least one and the singular also includes the plural unless it is obvious that it is meant otherwise. This is done merely for convenience and to give a general sense of the disclosure.

[0069] FIGS. 1-3 show embodiments of an energy conversion system and parts thereof according to the invention.

[0070] The energy conversion system according to the invention comprises: [0071] 1) One Solid Oxide Fuel Cell (SOFC) unit A having an anode and a cathode side, receiving a fuel 1 and a steam of oxidant 4 for converting a fraction of chemical power of fuel 1 directly into electric power through a plurality of electrochemical reactions occurring on the anode and the cathode side of the SOFC unit A. Parts of the fuel and of the oxidant remain unconverted, i.e. they are not directly converted into electric power by the SOFC; [0072] 2) One combustor unit B for converting unconverted fuel 5 and unconverted oxidant 6 into product gas 10, said combustor unit B being arranged to receive the unconverted fuel 5 and unconverted oxidant 6 from the SOFC unit A; [0073] 3) One expander unit C for expanding the gas exiting the combustor B, said expander unit C being arranged to receive the product gas 10 from the combustor B; [0074] 4) One cooler unit E for reducing the temperature of flue gas 12 exiting from the expander unit C to a temperature close to the one of a heat sink 27 (such as a lake, river, sea, air, cold streams of other plants). The exiting stream 14, which is CO.sub.2-rich, contains condensed species; [0075] 5) One flash drum unit F for removing the condensed species 15 from the CO.sub.2-rich stream 14; and [0076] 6) A first compression unit K for increasing the pressure of the oxidant 22 to the value required by the SOFC unit A and the combustor unit B.

[0077] In a first embodiment (FIG. 1), the energy conversion system comprises a high-pressure Solid Oxide Fuel Cell (SOFC) A with a semi-closed oxy-combustion Brayton cycle using CO.sub.2 as moderator of the combustion temperature. The maximum cycle pressure and the SOFC unit A operating pressure are preferably above the critical pressure of CO.sub.2 (i.e., >73.9 bar). In the above-mentioned conditions, the semi-closed Brayton cycle is a supercritical CO.sub.2 cycle with advantages in terms of efficiency.

[0078] The energy conversion system can use either a gaseous or a liquid fuel 1. The fuel shall be pressurized, optionally preheated, then is fed to the anode of the SOFC unit A while the oxidant mixture containing CO.sub.2 and O.sub.2 4, preheated in a regenerative heat exchanger D, is fed to the SOFC cathode side.

[0079] The SOFC unit A converts a fraction of the chemical power (e.g., in the range 30-90%, tunable depending on the desired performance) of the fuel directly into electric power through the electrochemical reactions occurring on the anode and cathode sides and involving hydrogen oxidation:

H.sub.2+½ O.sub.2.fwdarw.H.sub.2O+2e.sup.− (anode)   (Eq. 1)

½ O.sub.2+2e.sup.−.fwdarw.O.sup.= (cathode)   (Eq. 2)

[0080] with the addition, although with a slower kinetics, of carbon monoxide oxidation:

CO+½ O.sub.2.fwdarw.CO.sub.2+2e.sup.− (anode)   (Eq. 3)

[0081] The SOFC unit A can be designed to run either with or without internal reforming (e.g., adopting specific catalysts, such as Ni-based materials typically used for commercially available SOFCs), depending on the type of fuel to be used; in the case of natural gas feeding, methane is converted into hydrogen within the cell according to the reactions of steam reforming and water gas shift:

CH.sub.4+H.sub.2O.fwdarw.CO+3 H.sub.2 Δ.sup.H.sup.298K.sup.0=205.9 kJ/mol   (Eq. 4)

CO+H.sub.2O.fwdarw.CO.sub.2+H.sub.2=Δ.sup.H.sup.298K.sup.0=−41.1 kJ/mol   (Eq. 5)

[0082] The reforming reaction, which is highly endothermic, occurs exploiting available heat from the cell losses (thus converting heat into chemical energy, with an advantage for the system electric efficiency) and is driven by the consumption of hydrogen allowed by the electrochemical reactions (Eq. 1,2).

[0083] Steam required for hydrocarbons reforming can be supplied directly stream 3 and/or through recycling a fraction of the stream exiting the anode 40. In the latter case, either an ejector (O) or a fan X capable of withstanding high gas temperatures can provide the pressure head required to sustain the stream recycle.

[0084] The compressed fuel entering the power plant can therefore be mixed with part of the stream recycled from the anode outlet 40 and/or with steam 3 (which can be generated in the heat exchanger D). Then, the stream entering the anode side can be preheated within the SOFC unit A to the final operating temperature (e.g., 700-850° C.) using the thermal power made available by the electrochemical process, through either a dedicated heat exchanger P (e.g., cooling the product streams) or internally in the fuel cell stack.

[0085] Alternatively, and following recent R&D tendencies for new types of intermediate and low temperature SOFC units (e.g. running from 600 to 800° C.), the SOFC can be designed to run directly on natural gas (or other high methane fraction hydrocarbon mixture), developing internally direct oxidation reactions:

CH.sub.4+4O.sup.=.fwdarw.H.sub.2O+CO.sub.2+8e.sup.− (anode)   (Eq. 6)

2O.sub.2+8e.sup.−.fwdarw.4O.sup.= (cathode)   (Eq. 7)

[0086] In this case the SOFC unit can be fed directly with methane without needing a preliminary mixing with steam or recycled anode exhaust.

[0087] The unconverted fuel and oxygen leaving the SOFC unit A are sent to the combustor unit B of the semi-closed cycle. Optionally, to moderate the flame temperature, it is possible to recycle a fraction of the combustion products (stream 23).

[0088] Vice versa, optionally, to increase the flame temperature and/or the combustor unit B outlet temperature, it is possible to inject fuel and/or oxidant directly into the combustor B additional fuel 7 and oxidant 8. To increase the efficiency of the proposed system, as a further option, it is possible to preheat the oxidant 26, the temperature moderator 9 and the other streams of the system (e.g., the turbine cooling flows 11, if these are required) in a multi-flow regenerator D. Optionally, if the concentration of fuel and/or oxygen is too low, a catalytic combustor unit B can also be used.

[0089] The combustion products 10 are mainly CO.sub.2 and H.sub.2O, and may contain also some amounts of O.sub.2, Ar, N.sub.2 and other chemical species.

[0090] The product gases are expanded in an expander C to a lower pressure, indicatively in the range 1-50 bar. However, such value depends on the other pressures and temperatures of the cycle, and it may not be limited to such range. Depending on the fuel utilization factor (fraction of the inlet fuel oxidized electrochemically within the fuel cell) of the SOFC unit A, its operative temperature, and the mass flow rate of the stream used as temperature moderator in the combustor unit B, the turbine inlet temperature can be higher or lower, requiring to adopt a cooled or uncooled expander C.

[0091] If the expander unit C needs to be cooled (because the gas inlet temperature is above the maximum allowed operating temperature of the turbine materials), the cooling flows 11 can be taken from the stream of recycled CO.sub.2 and can be preheated in the regenerator D. The product gases 10 leaving the turbine are cooled in the regenerator D and then in a cooler E to a temperature approaching that of the heat sink (e.g., lake, river, sea, air, cold streams of other plants). Most of the H.sub.2O of the product gases condenses, and it is separated with a gas-liquid separator F, such as a flash drum. The outlet gas stream leaving the separator 16 is rich in CO.sub.2. A fraction can be recycled 18 to be used as temperature moderator and/or to be mixed with the oxygen stream 21 and/or used as turbine cooling flow 11 while the remaining part 17 can be separated and either vented into the atmosphere or sent to the CO.sub.2 purification and utilization/storage system. When compressing the recycle CO.sub.2-rich stream above the critical pressure, if water condenses, it is possible to use a liquid-liquid separation process to remove further water.

[0092] Depending on the specifications of the final destination of CO.sub.2 (e.g., an injection well for enhanced oil recovery or any other storage or utilization option), it could be necessary to treat the separated CO.sub.2 stream in a CO.sub.2 purification unit (a conventional plant capable of producing nearly pure liquid CO.sub.2).

[0093] It is also possible to recover heat in the regenerator D from the main compressor of the Air Separation Unit (ASU) and/or the intercoolers of the compressors H,K,L and/or from nearby heat sources. This can result in a further improvement of the efficiency of the proposed energy conversion system.

[0094] For systems using natural gas and 99.5% purity O.sub.2 produced by a commercially available cryogenic air separation unit, the best performance of the system is achieved adopting the operating parameters reported in Table 1.

TABLE-US-00001 TABLE 1 indicative ranges of operating pressures and temperatures for the key streams. Operating Type of parameter range Working pressure of the SOFC (A) 5-500 bar and combustor (B) units Expander (C.) outlet pressure 1-50 bar Working temperature of the SOFC unit (A) 600-1000° C. Expander (C.) inlet temperature 800-1500° C. Temperature of the temperature moderator (9) and 400-800° C. oxidant stream (26) leaving the regenerator (D)

[0095] It is worth noting that the system is capable of working with good efficiencies also if the operating conditions are outside the above-specified ranges, even if the SOFC unit A and combustor unit B pressures are below the critical pressure of CO.sub.2.

[0096] In another exemplary embodiment, it also possible to use a second oxidation stage after the expansion (reheating configuration), adding a second SOFC unit AF and/or a second combustor unit AG optionally feeding additional fuel 61 and oxidant 62. Then the working fluid can be further expanded in a second expander AH before entering the regenerator AI (see FIG. 3). This scheme can further increase the power output of the plant and lead to a lower specific investment cost (total plant cost/net electric power), specially for designs featuring one SOFC, two combustors and two expanders. This second embodiment could also feature a wider operational range thanks to the possibility of adjusting the fuel flow rate fed to the different SOFCs and/or combustors.

Simulation and Optimization of a Possible Embodiment of the Energy Conversion System

[0097] The cycle shown in FIG. 1 has been modelled using a process simulation software and its efficiency has been optimized using a systematic optimization algorithm.

[0098] The assumptions at the basis of the process simulation are reported in the following: [0099] No extra-oxidant and no extra-fuel are used in the combustor (i.e., streams 8 and 7 have zero mass flow rate). [0100] The regenerator H is used to preheat the streams of temperature moderator 9, cooling flows 11, oxidant 26 and to evaporate water and superheat steam 3. [0101] Fuel is a natural gas with composition reported in Table 2:

TABLE-US-00002 TABLE 2 Composition of the fuel considered in the simulation example Composition, Type of molar molecule basis CH.sub.4 89.00% C.sub.2H.sub.6  7.00% C.sub.3H.sub.8  1.00% i-C.sub.4H.sub.10  0.05% n-C.sub.4H.sub.10  0.05% i-C.sub.5H.sub.12 0.005% n-C.sub.5H.sub.12 0.005% CO.sub.2  2.00% N.sub.2  0.89% [0102] The oxygen is provided at 120 bar and 15° C., thus compressor H pressurizes stream 19 to 120 bar. [0103] Stream 2 is liquid water at 15° C., 1.013 bar. [0104] An oxygen stream corresponding to 3% of excess with respect to the stoichiometric condition (considering the oxygen already available in the working fluid) is used to produce the oxidant stream. [0105] The GERG-2008 equation of state is used to estimate the thermo-physical properties of the streams (to this regard, see: O. Kunz, and W. Wagner, “The GERG-2008 wide-range equation of state for natural gases and other mixtures: An expansion of GERG-2004”, Journal of Chemical and Engineering Data, vol. 57(11), pp. 3032-3091, 2012, doi: 10.1021/je300655b). [0106] The turbine efficiency and cooling flow requirement are computed according to the model presented in R. Scaccabarozzi, M. Gatti, and E. Martelli, “Thermodynamic analysis and numerical optimization of the NET Power oxy-combustion cycle”, Applied Energy, vol. 178, pp. 505-526, 2016, doi: 10.1016/j.apenergy.2016.06.060, with isentropic efficiency of the expansion steps of 89% and maximum metal temperature allowed by the blade materials of 860° C. [0107] Isentropic efficiencies of 90% and 85% are assumed respectively for the vapor and supercritical compressor stages. [0108] A relative pressure drop of 5% (with respect to the inlet pressure) is considered for the stream exiting the turbine. The value is progressively reduced in the inter-cooled compression as to reach a value of 1% at the cold side of the regenerator. [0109] Two minimum temperature approaches are used in the regenerator: 5° C. is assumed at the cold side to maximize the heat recovery, 20° C. is used at the hot end to limit the required heat transfer area at high temperatures. [0110] A cooling water temperature of 15° C. is assumed. [0111] A minimum approach temperature of 11° C. is assumed for the coolers (exchanging heat with cooling water), leading a minimum temperature of the working fluid in the condenser and intercoolers of 26° C.

[0112] As far as the SOFC unit is concerned, the assumptions are the following: [0113] The optional heaters P, Q, Y and coolers T, U, W are not used. [0114] The recycle stream 37 is used to recycle a fraction of the anode outlet flow (containing useful water and unconverted fuel species) to the anode inlet. [0115] A recycle compressor X with isentropic efficiency 0.7 is used. [0116] The pressurized SOFC unit operates with a ratio between the carbon and oxygen atoms equal to 2.5, chosen to prevent coking on the anode electrode. [0117] A maximum value of power per unit of area of 0.5 W/cm.sup.2 (corresponding to a specific current of around 0.6 A/cm.sup.2) has been assumed to avoid risks of excessive thermal stresses. [0118] The SOFC unit Area-Specific Resistance (ASR) is assumed to be 0.28Ω/cm.sup.2, comprehensive of all the losses affecting the fuel cell stack (e.g., activation, ohmic, concentration), while the alternator converting the direct current to alternate current is assumed to be characterized by an efficiency of 98%. [0119] To avoid concentration losses which would reduce the conversion efficiency, a maximum utilization factor (fraction of the fed fuel oxidized within the SOFC unit, this value is different from the one referred to the fuel cell stack if the recycle at the anode side is not null) of 85% and a minimum concentration of oxygen at the cathode outlet of 10% mol are considered. [0120] The relative pressure drop across the SOFC unit is fixed at 0.5%.

[0121] Under the above-listed assumption, the proposed system still can be designed and operated in a large variety of conditions due to the possibility of varying (i) the SOFC A unit and combustor B operative pressure, (ii) the expander C outlet pressure, (iii) the fraction of the unconverted fuel 40 recycled back to the anode inlet, (iv) the mass flow rate of the temperature moderator 9 of the combustor, (v) the regenerator outlet temperature of the oxidant 26, temperature moderator 9 and steam 3, (vi) the regenerator outlet temperature of the expander cooling flows 11, and (vii) the fraction of the recycled 20 stream mixed with the oxygen to produce the oxidant flow. To determine the most efficient design and operating conditions, the above listed independent variables have been optimized using a systematic process optimization approach.

[0122] The objective function to be maximized is the net electric efficiency (net electric power output of the integrated system divided the chemical power of the inlet fuel, LHV basis). The optimization constraints considered in this example are summarized in Table 3:

TABLE-US-00003 TABLE 3 Technical constraints considered in the optimization example Parameter Value Concentration of oxygen at the SOFC cathode 10%.sub.mol outlet (35) %.sub.mol (minimum) Concentration of water at the SOFC anode 60%.sub.mol outlet (34) (maximum) Temperature difference within the regenerator  5° C. (D) (minimum) Temperature difference at the hot end of the  20° C. regenerator (D) (minimum) Expander (C.) allowed metal temperature 860° C. (maximum) C/O at the SOFC (A) anode inlet 2.5-

[0123] In the optimization it is assumed that the oxidant, the temperature moderator and the steam for the SOFC unit exit the regenerator at the same temperature. Moreover, it is assumed that the oxidant provides 3% excess of oxygen compared to the stoichiometric condition.

[0124] The optimization problem has been tackled using an optimization algorithm specifically developed for process and energy system optimization purposes.

[0125] The optimization results are reported in Table 4:

TABLE-US-00004 TABLE 4 Key results of the optimization and simulation example. Parameter Value Natural gas flow rate 10.75 kg/s Natural gas LHV 46.49 MJ/kg Oxygen mass flow rate 40.37 kg/s Total recycle mass flow rate 148.2 kg/s Turbine inlet mass flow rate 187.7 kg/s SOFC operating pressure 352.7 bar SOFC operating temperature 800.0° C. Turbine inlet pressure 349.2 bar Turbine inlet temperature 1 025.9° C Turbine outlet pressure 14.5 bar Turbine outlet temperature 521.0° C. Recycle stream temperature 501.0° C. at SOFC inlet SOFC electric power output 340 kW 640 Turbine blade power output 128 kW 193 Compressor blade power 25 kW consumption 597 Air Separation Unit power 56 kW consumption 148 Net power output 377 kW 050 Fuel thermal input (LHV basis) 500.0 MW Net electric efficiency 75.41%

[0126] The SOFC produces 72.7% of the plant gross power output while the turbine accounts for the remaining 27.3%.

[0127] The intercooled compression and the ASU are the two major penalties, consuming 5.5% and 12.0% of the gross power output respectively.

[0128] The compression of the captured CO.sub.2, sent to the storage, account only for 0.8% percent and the remaining auxiliaries for 0.9% of the gross production.

[0129] The resulting net electric efficiency is 76.2% without CO.sub.2 capture (i.e., venting the excess CO.sub.2 not recycled), and 75.4% with CO.sub.2 capture.

[0130] The resulting performance indexes are outstanding compared to state-of-the-art as well as advanced energy systems (with and without CO.sub.2 capture) which feature efficiencies in the range 60-63% for the systems without capture, and 40-46% for the systems with capture.