ANALYSIS OF A GASIFICATION PLANT FED BY WOODCHIPS INTEGRATED WITH SOFC AND STEAM CYCLE

Transcription

1 ANALYSIS OF A GASIFICATION PLANT FED BY WOODCHIPS INTEGRATED WITH SOFC AND STEAM CYCLE Leonardo Pierobon M. Sc. Student s August 2010 DTU- University of Denmark Thermal Energy System Università degli Studi di Padova, Italy - Laurea Magistrale in Ingegneria Energetica 1

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3 Whenever a theory appears to you as the only possible one, take this as a sign that you have neither understood the theory nor the problem which it was intended to solve Karl Popper 3

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5 Preface The present work has been developed at DTU (Department of Mechanical Engineering, Kongens Lyngby, Denmark) under the supervision of Professor Masoud Rokni and Professor Alberto Mirandola (Dipartimento di Ingegneria Meccanica, Padova, Italy). I am grateful to my family that gave me the great opportunity to study in Denmark and to experience life and work with people from all over the world. I show to Professor Masoud Rokni and to the staff of Mechanical Engineering Department my gratitude for helping and supporting me to carry out my Master Thesis. Thanks also to all the friends I met in Denmark for all the great moments we had together. Kongens Lyngby 8 th of August 2010 Leonardo Pierobon 5

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7 Abstract Conventional biomass plants for electric power generation are not effective in terms of system performance. A gasification plant integrated with SOFC and steam cycle has been studied; calculations have proved a significant increase of plant efficiency. Simulations have been run by means of DNA (Dynamic Network Analysis) a componentbased simulation tool for energy systems analysis developed at the Thermal Energy Systems department (DTU). Two different plant configurations have been studied. In the first no hybrid recuperation is considered; efficiency is 47.74%. Second configuration (hybrid recuperation) shows a significant increase in terms of performance (53.09%). Optimized system is also analyzed; efficiency is up to 57%. Alternatively steam cycle is replaced by a Kalina cycle; ammonia-water mixture has been added as a new fluid inside DNA library. Plant efficiency for optimized system is 52.53%. It has been concluded that better solution is to integrate woodchips gasification and SOFC with a steam cycle (higher efficiency). This solution has also been investigated by means of thermoeconomic analysis; simulations have been run with EES (Engineering Equations Solver). Equations allow also to calculate plant exergy losses; major sources of inefficiency are: gasifier, cathode preheater and burner. An exergetic efficiency of 50% is calculated. With a woodchips price of 165 [ /ton], a price of electricity of 0.40 [ /kwh] is obtained. Future price of SOFC is supposed to decrease by lowering SOFC operating temperature: with a purchase cost of 300 [ /kw] price of electricity is around 0.19 [ /kwh]. The analyzed plant is proved to be theoretically feasible by an energetic and thermoeconomic point of view. 7

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9 Nomenclature HHV LHV LHV 0 U r high heat value [kj/kg] low heat value [kj/kg] dried biomass low heat value [kj/kg] moisture content [kg H2O /kg] water heat of vaporization [kj/kg] η efficiency [-] T P ΔG W R temperature [K] absolute pressure [Pa] change in the Gibbs free energy [kj/kg] work [kj/kg] universal gas constant [kj/(kg K)] U f utilization factor [-] P q h s power [kw] heat flow [kw] enthalpy [kj/kg] entropy [kj/(kg K)] entropy [kw] irreversible entropy contribution [kw] x Φ Ā ammonia fraction [kg NH3 /kg] reduced Helmholtz free energy [kj/kmol] Helmholtz free energy [kj/kmol] 9

10 molar volume [m 3 /kmol] δ reduced volume [-] τ reduced temperature [-] U Z internal energy [kj/kg] quality [kg vap /kg] ζ Regula Falsi increment [-] X Regula Falsi unknown [-] Ċ Ż ċ Ė cost rate [ /h] component cost rate [ /h] specific cost rate [ /kwh] exergy flow [kw] power [kw] y woodchips price [ /ton] I investment cost [ ] m mass flow [kg/s] A surface area [m 2 ] K overall heat transfer coefficient [kw/(m 2 K)] r c compression ratio [-] int interest rate [%] ri rate of inflection [%] qi interest factor [-] f annuity factor [-] n equipment lifespan [years] 10

11 M maintenance factor [-] CP construction period [years] Hr operating hours [hours/year] Δr cost difference factor [%] f exergoeconomic factor [%] ε relative exergy destruction [%] Abbreviations DNA EES SOFC ORC LHV HHV Dynamic Network Analysis Engineering Equations Solver Solid Oxide Fuel Cell Organic Rankine Cycle Low Heat Value High Heat Value HRSG Heat Recovery Steam Generator VLE TEC O&M PEC DC IC LPT HPT PV Vapor-Liquid Equilibrium Theory of the Exergetic Cost Operating and Maintenance Purchase Equipment Cost Direct Cost Indirect Cost Low Pressure Turbine High Pressure Turbine Photovoltaic 11

12 Superscripts 0 reference state or ideal part r CI residual part investment cost OM operating and maintenance cost TOT total Subscripts 0 dried biomass or ideal part irr el irreversible electric max maximum f factor GEN1 generator 1 GEN2 generator 2 amb mean ambient thermodynamic mean temperature 01 water 02 ammonia m n l molar reduced or iteration number liquid 12

13 v k P F vapor kth component product fuel power q i e IN heat flow inlet exit input OUT output L D lost destroyed 13

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15 TABLE OF CONTENTS Preface... 5 Abstract... 7 Nomenclature Biomass energy Ligno-cellulosic biomasses Price of ligno-cellulosic biomasses Woodchips General plant overview Block scheme of the plant Gasification technology Gasification process Viking gasification plant Upscale of the two-stage gasification plant Introduction to Solid Oxide Fuel Cells (SOFC) General features and fuel cells types Solid Oxide Fuel Cells Bottoming cycle Rankine cycle (or steam cycle) Kalina cycle Size of the plant Integrating a gasification plant with SOFC and steam cycle Plant layout Gasification plant General features Main data input SOFC plant General features Main data input Steam cycle General features

16 3.4.2 Main data input Results analysis Efficiency of the plant Steam heat recovery SOFC air preheating Woodchips low heat utilization Steam pressure simulations Hybrid recuperation Plant scheme Main input Results Gasification temperature Wood moisture content SOFC operating temperature Steam cycle pressure Optimized system Integrating a gasification plant with SOFC and Kalina cycle Ammonia-water properties The Fundamental Equation of State Superheated vapor and subcooled liquid Saturated liquid and vapor Vapor-liquid equilibrium (VLE) VLE calculation accuracy Adding the model inside DNA Temperature-pressure Enthalpy-pressure Entropy-pressure Quality-pressure Plant layout Kalina cycle General features Main data input Results analysis

17 4.5.1 Efficiency of the plant Ammonia-water heat recovery Ammonia-water condensation SOFC air preheating Kalina cycle pressure simulations Hybrid recuperation Plant scheme Main input Results Parameters analysis Optimized system Comparing Kalina and steam cycle solutions Thermoeconomic analysis Thermoeconomic theory Components equations Dryer Gasifier Gas cleaner Heat exchangers Blowers Pumps Turbine Electric generator Mixer SOFC Burner Splitter Condenser Other auxiliary equations Cost rate calculation Estimation of total capital investment and calculation Results of thermoeconomic analysis

18 5.4.1 Linear equation system Thermoeconomic parameters Exergetic analysis of the plant Price of electricity Price of woodchips influence on electricity price Plant thermoeconomic parameters Future scenario Conclusions Reference APPENDIX I APPENDIX II APPENDIX III APPENDIX IV

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21 1 Biomass energy Biomass is biological material derived from living, or recently living organisms. It is regarded as a renewable energy source: the carbon, utilized to construct it, is absorbed from the atmosphere as carbon dioxide (CO 2 ). The energy required for biomass growth is obtained from the sun; therefore it can be seen as a sophisticated form of solar energy storage. Biomasses can be used to produce a wide range of solid fuels (chips, pellets), liquid (ethanol, biodiesel), and gaseous (biogas). Those fuels can be used to produce electric or thermal energy or as a fuel in transport. Main benefits are: reduction of greenhouse gas emissions and less waste to be sent to landfills. Another advantage in comparison to renewable sources is that biomasses do not suffer of reliability problems that penalize solar, wind and hydroelectric plants. In order to have a global energetic and environmental point of view, primary energy consumption and emissions due to harvesting, transport, and conversion processes must be considered. 1.1 Ligno-cellulosic biomasses Ligno-cellulosic biomasses are mostly utilized to feed boilers or steam generators in place of conventional fuels (oil, gas, coal, etc.). The use of biomasses in gasification and pyrolysis processes allow to construct large or medium size fuel cells plant with high electric efficiency. Biomasses conversion for electricity production is essentially done by external combustion plants (steam plants, Stirling engines or organic Rankine cycles) or internal combustion plants (gas turbine and gas engines). For large size systems (starting from 10 MW) the main available technology is the traditional steam plant. Organic Rankine cycles (ORC) are utilized with medium size systems and for small size plants (10-50 kw) some Stirling engines are marketed. Production chain of electric energy is basically composed by the phases shown in Figure

22 Figure 1.1.1: production chain of electric power with ligno-cellulosic biomass. Figure 1.1.2: biomass plant classification for electric production. As shown in Figure 1.1.2, maximum size of a biomass plant is of about 5-50 MW. A 10 MW plant with an annual efficiency of 25% fed by woodchips with a low calorific value of 10 MJ/kg requires ton/year of wood. With an annual productivity of about 35 ton/ha the plant requires a cultivation area of about 2900 ha (29 km 2 ). Taking in account street and other crops, needed land is of about 5800 ha (58 km 2 ). It immediately appears 22

23 difficult to build up a 100 MW size plant since it requires a land of about ha (580 km 2 ). Larger size also results in a higher transport and stocking costs and therefore higher greenhouse emissions and price of biomass itself. 1.2 Price of ligno-cellulosic biomasses The price of ligno-cellulosic biomass is very difficult to predict because many situations can be met. Basically three main items can be distinguished: - cultivation and biomass collection cost; - transportation cost; - storage cost. Storage cost is very difficult to determinate because it strongly depends from the biomass material: different ligno-cellulosic biomasses may have different collection periods and therefore different storage volumes. In the Table are shown values (ref. [1]) for each item; Cultivation and collection Transportation TOT (no storage cost is considered) Storage [ /ton] 6 15 [ /ton] [ /ton] Unpredictable Table 1.2.1: main values for each biomass cost items. 1.3 Woodchips Woodchips are a type of ligno-cellulosic biomass commonly utilized as a solid fuel for buildings heating or in energy plants for electric power generation. Main woodchips properties are: - calorific value; - moisture content; - ash content; - chlorine, sulphur, nitrogen content; - specific volume. High ash content results in high cost of ash disposal and problems with fouling, corrosion and erosion of boilers or gasifiers. 23

24 Chlorine, sulphur, nitrogen traces are capable of forming sulphur and nitrogen compounds (SO x, NO x ) and hydrochloric and sulphuric acid (HCl, H 2 SO 4 ). High specific volumes significantly affect transport and storage costs. Dried woodchips composition assumed in this paper is acquired from ref. [2]. It is shown in Table and Figure No chlorine is present. Carbon (SOLID) 48.8 [%] Oxygen 43.9 [%] Hydrogen 6.2 [%] Sulphide (SOLID) 0.02 [%] Nitrogen 0.17 [%] Ashes 0.91 [%] TOT 100 [%] Table 1.3.1: dried woodchips composition (mass base). Figure 1.3.1: dried woodchips composition (mass base). Other main parameters assumed are listed in Table Moisture (mass base) 33.2 [%] Low heat value (dried woodchips) [MJ/kg] Specific Heat 1.35 [kj/(kg K)] Table 1.3.2: other woodchips parameters. Calorific value and moisture content are strictly connected; low and high heat values expressed in MJ/kg are a linear function of moisture content. The higher is moisture content the lower are both heat values. 24

25 It is demonstrated (ref. [1]) that woodchips low heat value (LHV) can be expressed by the following equation: (1.1). With the low heat value (LHV 0 ) given in Table and a water heat of vaporization (r) of about 2.4 MJ/kg, a LHV value of zero is obtained for moisture (U) of about 88 %. In practice, woodchips combustion can sustain itself with moisture contents up to %. In Figure woodchips LHV and HHV are printed as a function of moisture content with the parameters given upon. Figure 1.3.2: LHV and HHV as a function of moisture content. 25

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27 2 General plant overview Biomass utilization for electric generation is poor in terms of plant efficiency. Rankine cycle plants usually have a net electric power around MW and efficiency around %; lower values are obtained with ORC and Stirling engines. With this plant size, costs of investment must be contained and, therefore, optimized systems can not be constructed. Technologies based on gasification are about to reach the market; this will allow syngas production for fuel cells plants that should be able to achieve higher efficiency. Design and calculations of gasification process are based in the two-stage 70 kw gasifier developed at the Technical University of Denmark (DTU). The two stage gasification process can be modified in order to upscale it for higher powers. SOFC (Solid Oxide Fuel Cells) are considered. Current SOFC research is focused on developing cheaper construction materials and methods and to increase components life. To realize that operative temperatures are decreased (around 800 C). Considering this, two different bottoming cycles are analyzed: Rankine and Kalina cycle. The plant is fed by woodchips. 2.1 Block scheme of the plant A very simple scheme of the plant is presented. It is mainly constituted by the following components: - gasification plant; - SOFC plant; - bottoming cycle (Rankine or Kalina cycle). As depicted in Figure 2.1.1, woodchips are converted into woodgas (mainly hydrogen H 2, nitrogen N 2, carbon monoxide CO and carbon dioxide CO 2 ) inside the gasification plant. Woodgas feeds the SOFC plant producing both electric power and heat. Heat is than recovered in the bottoming cycle. Not all the heat coming from the SOFC plant can be converted into electric power: second law of thermodynamics must be respected. For this reason in the bottoming cycle low temperature heat is released to environment. Other energetic losses are caused by: - Ashes, tar; - Off gases. 27

28 Figure 2.1.1: block scheme of the plant. Energy consumption of auxiliary (blowers, pumps, control systems, etc.) is covered directly by means of the electric power production; therefore the efficiency of such a plant is defined by the following equation: (2.1). Woodchips power input can be calculated as the product of mass flow and low heat value. 2.2 Gasification technology Gasification process Thermochemical gasification is the conversion by partial oxidation at elevated temperature of a carbonaceous feedstock such as biomass or coal into gaseous energy carrier (Bridgewater, 1995). This process is carried out in three main steps: - Drying: moisture inside biomass (woodchips) is reduced down to % before the feedstock enters the gasifier. - Pyrolysis: chemical boundaries are broken to form volatile components at temperature below 600 C. Biomass consists of percent volatile matter 28

29 therefore this step plays an important part in the global process. Char, tars and ashes are also present. - Gasification: solid char, pyrolysis tars and gases are oxidized. Temperatures are up to C. Major reactions are: - combustion: C + 1/2O 2 CO; - water-gas reaction: C + H 2 O H 2 + CO; - bounded reaction: C+CO 2 2CO; - water shift reaction: CO + H 2 O CO 2 + H 2 ; - methane reaction: C+2H 2 CH 4. Main parameters influencing gasification process are: - Pressure: it does have a great influence on system design and cost. The higher is the pressure the higher are processing rates. However pressurized gasifiers are more expensive than ambient pressure ones. Pressure has a modest effect on gasification chemistry. - Temperature: it is a crucial parameter since it affects gasification rates and reactor design. Ash disposal is strongly influenced by it. Most biomass gasifiers utilize dry ash removal systems; therefore ash melting temperature ( C) must be avoided. - Type of oxidant: oxygen or air are commonly utilized in gasifiers. Using oxygen produces a better quality gas. Air gasification produces a gas with about half of the calorific value due to the diluting effect of the nitrogen. Steam may be used to increase hydrogen content in the gas Viking gasification plant Modeling of the gasification plant is based on the two-stage biomass gasification process developed at the Technical University of Denmark (DTU). Viking gasifier was established in 2002 and it had during 2003 more than 2000 hours of operation. In Figure (ref. [3]) the following components can be distinguished: - drying and pyrolysis part; - gasification part; - exhaust superheater; - air preheater; - engine. 29

30 Figure : Viking two-stage gasification plant (ref. [3]). Woodchips are entering drying and pyrolysis chamber reaching a temperature of about 600 C. The gaseous mixture along with tars is partially oxidized at 1100 C in the gasification section. Ashes are separated from the woodgas which comes out at C. Drying, air preheating and pyrolysis are carried out by means of the thermal energy inside the woodgas. In the exhaust superheat woodgas is cooled down releasing its energy to warm up exhaust gases coming out from the engine; then exhaust gases feed the drying and pyrolysis chamber. To enable high energy efficiency, air for the oxidation is also preheated by woodgas. After particles are removed, cleaned gas feeds a Diesel engine where electric power is produced. Main features of the Viking plant are (ref. [3]): - gasification at atmospheric pressure; - low tar content in clean gas (<5 [mg/nm 3 ]); - stable unmanned operation; - high coldgas efficiency of the gasification part (>95 %); - low environmental impact (clean condensate, high carbon conversion ratio) Upscale of the two-stage gasification plant Since the Viking gasifier size is of about 70 kw (fuel), an upscale of the plant is needed. Production of 1 MWe and more might be possible in the immediate future. In Figure (ref. [3]) the following differences from Viking plant can be noted: - drying with superheated steam; 30

31 - pyrolysis with superheated steam; - gasification with superheated steam; - stage divided gasification. Figure : upscale of a two-stage gasification process (ref. [3]). In Figure (ref. [3]) the principle of drying with superheated steam is exposed. It involves the use of an external heat source to generate the steam. In Figure this done by means of the engine off gases. Figure : principle of drying with superheated steam (ref. [3]). Advantages offered by this solution are: - Environmental friendly drying (no contamination of condensate); - No fire hazard; - No loss of product; - Improved drying rate. Pyrolysis process requires a certain quantity of moisture (around 10%) inside the feedstock; therefore superheated steam makes gasification process applicable for fuel with high humidity content (up to 60%). Woodchips moisture can be significantly variable during seasons; this makes the solution suitable for this biomass type. 31

32 Higher process rates are achieved when steam is used as gasification agent; temperature can be also lowered. In addition the hydrogen (H 2 ) content is increased this make woodgas composition suitable for fueling a SOFC plant. To conclude main features of the upgraded two-stage biomass gasification process are (ref. [3]): - drying, pyrolysis and gasification with superheated steam; - well suited for fuels with moist content of 40-60%; - no fire hazards in dryer; - low gasification temperature; - higher H 2 content in the clean gas; - higher process rates. 2.3 Introduction to Solid Oxide Fuel Cells (SOFC) General features and fuel cells types Fuel cells working principle is rather simple: as shown in Figure (ref. [4]), at the anode the hydrogen gas ionizes, releasing electrons and creating H + ions (protons). 2H 2 4H + + 4e -. At the cathode, oxygen reacts with electrons taken from the electrode, and H + ions from electrolyte, to form water. O 2 + 4H + + 4e - 2H 2 O. To produce electricity anode and cathode are electrically connected. To complete the circuit H + ions must pass from anode to cathode; therefore between them an ion conductor material (electrolyte) is placed. No electrons should be allowed to pass through the electrolyte. Figure : fuel cells reactions (anode and cathode) (ref. [4]). 32

33 Fuel cell can be distinguished by the electrolyte that is used; the situation now is that six classes of fuel cell have emerged as viable systems for the present and near future. Basic information about these systems is given in Table (ref. [4]). Table : different fuel cell for present and near future (ref. [4]). Fuel cells convert the chemical energy inside the fuel directly into electric power. The maximum work that an electrochemical cell can perform is equal to change in the Gibbs energy as the reactants go to products. Gibbs free energy is a function of temperature and pressure. For hydrogen oxidation the change in the Gibbs energy can be written as (ref. [4]): (2.2); The maximum efficiency of a fuel cell is usually defined as: where LHV is the lower heating value of the fuel. (2.3). (2.4); The higher is the temperature the higher is the theoretic efficiency. Pressure can increase or decrease cell efficiency depending by the number of moles of reactants and products. The electric efficiency (stack efficiency) of a fuel cell is calculated as: (2.5). Real efficiency is influenced by polarization, ohmic and activation losses; therefore, in practice, fuel cells efficiency is higher at higher temperatures. 33

34 For electric efficiency reasons not all the fuel reacts inside the fuel cell. To guarantee the presence of non-oxidized fuel in all anode surface a fraction of fuel input does not take part to the reaction. A utilization factor is therefore defined: Common values for utilization factor are between 0.75 and (2.6) Solid oxide fuel cell The SOFC is a complete solid-state device that uses an oxide ion-conducting ceramic material as the electrolyte. The chemical reaction at the cathode and anode are: cathode: O 2 + 4e - 2O 2- ; anode: 2H 2 + 2O 2-2H 2 O. Until recently, SOFCs have all been based on an electrolyte of zirconia (ZrO 2 ) stabilized with the addition of a small percentage of yttra (Y 2 O 3 ). Typically the state-of-art zirconia based SOFC operates between 800 and 1100 C. Lowering SOFC working temperature should lead to cheaper and more reliable materials. Making electrolytes and electrodes that work well at lower temperature is a major focus of current SOFC research. SOFC can be fed by many different gaseous fuels: methane (CH 4 ), natural gas and woodgas. Operative temperature provides the hydrogen needed at the anode by means of reforming and water-gas shift reaction. The fuel reforming reaction produces hydrogen and carbon monoxide from methane according to the following equation: CH 4 + H 2 O 3H 2 + CO. The water-gas shift reaction provides hydrogen and carbon dioxide from carbon monoxide and water according to the following equation: CO + H 2 O H 2 + CO 2. Figure (ref. [5]) shows the tubular and planar SOFC technology. 34

35 Figure : tubular and planar SOFC technology (ref. [5]). Planar SOFC technology has a superior stack performance (lower ohmic losses) and a much higher power density. Another advantage is that low-cost fabrication methods such as screen printing and tape casting can be used. One of the major disadvantages is the need for gas-tight sealing around the edge of the cell components. With the tubular design high temperature gas tight seals are eliminated; thermal robustness and SOFC life is increased. SOFCs show an enhanced performance with increasing cell pressure; the improvement is mainly due to the increase in the change of the free Gibbs energy of reactants and products. Operating at higher pressure is advantageous when SOFC is integrated with a gas turbine (ref. [4]). Temperature has a strong influence in the conductivity of materials. Ohmic losses are decreased at high temperature and therefore SOFC efficiency is increased. On the contrary one of the main advantages of operating at lower temperature is the possibility of using cheaper construction materials and methods. 2.4 Bottoming cycle Reasonable values for SOFC stack efficiency are around 45-55%; therefore half of power input is converted into heat. Heat coming out from SOFC can be distinguished in two main categories: - reversible heat; 35

36 - irreversible heat. Reversible heat can be calculated as: (2.7). Irreversible heat is mainly due to ohmic, polarization and activation losses; it can be written as: To recover the heat two solutions can be taken into account: - Electric power generation (Rankine, Kalina, ORC, Brayton cycle); - Heat power generation (district heating, heat for industrial uses). (2.8). As already mentioned, SOFC operating temperature is going to be decreased. Rankine and Kalina cycle seem a good solution for heat recovery since their operating temperatures are around C Rankine cycle (or steam cycle) Steam cycle is a well-known technology for electric power generation. Recently their features have been adjusted to fit combined gas turbine systems. Rankine cycle has different features depending from the plant size; main properties are listed in Table (ref. [6]). Size Small Medium Large Power (MW) >100 Re-superheating no no Yes T max ( C) P max (bar) P cond (bar) η (%) % 30-35% 35-42% Table : steam cycle feature for different plant size. For small sizes power can not go below 0.5 MW (ref. [6]) Kalina cycle Kalina cycle can be seen as a modified Rankine cycle. The most relevant feature is the changing in the working fluid from a pure component to a mixture of ammonia and water. 36

37 An ammonia-water mixture has a varying boiling and condensing temperature. Mixture properties can be changed adjusting mass base composition. In Rankine cycle heat source feeds steam generator with the temperature vs. heat transfer profile shown in Figure (ref. [7]). Figure : exhaust gas recovery with water /steam at 55 kpa (ref. [7]). Exergetic losses are proportional to the area between the two curves; the higher is the area the less the available work is. Ammonia-water varying boiling temperature is able to decrease the area and therefore to decrease heat exchange exergetic losses. Ammonia-water solution is shown in Figure (ref. [7]). 37

38 Figure : exhaust gas recovery with ammonia-water at 3450 kpa (ref. [7]). Ammonia-water should therefore be able to achieve higher efficiency than Rankine cycle for a given exhaust gas temperature profile. In Figure (ref. [7]) a general scheme of Kalina cycle is presented. The following components can be distinguished: - Turbine; - Generator; - Internal recuperator; - Condenser; - Cycle pump. Figure : simple Kalina cycle (ref. [7]). 38

39 Since ammonia-water mixture has a varying condensing temperature, turbine outlet temperature (for a condensing pressure of 550 kpa) is around 110 C. Considering this an internal recuperator is added. Main consequences are: - Lower condenser inlet temperature; - Higher steam generator inlet temperature. Both features can increase Kalina cycle efficiency. The Kalina cycle does not require technological breakthroughs in equipment design. Molar masses of ammonia and water are relatively similar; thus conventional axial flow steam turbine can be used. Turbines in Rankine cycle plants exhaust to a condenser under vacuum, whereas Kalina cycle plants exhaust to a condenser under pressure; no special materials are required. 2.5 Size of the plant Size is a major feature when biomass plant is designed since it influences the cultivation area. Basing on the block scheme presented in Paragraph 2.1, simple calculations have been carried out. Main parameters computed are: - woodchips mass flow; - area of cultivation; - global expected efficiency. Plant efficiency is calculated as a function of components efficiency with the following equation: where η gasification, η SOFC, η bottoming cycle are defined by equations 2.10, 2.11, (2.9); (2.10); (2.11); (2.12). 39

40 For a gasification efficiency of 100%, deriving with respect to bottoming cycle efficiency, the following expression is obtained: (2.13). With a SOFC electric efficiency of 50%, a 1% increase in bottoming cycle efficiency leads to an increment of 0.5% for global plant efficiency. Values assumed for calculations are listed in Table Plant Operating hours 7000 [hours/year] Woodchips LHV (woodchips) 11 [MJ/kg] Woodchips producibility 35 [ton/ha] Gasification plant Gasification efficiency (ash and tar losses) 95 [%] SOFC plant SOFC utilization factor 85 [%] Bottoming cycle Cycle efficiency 30 [%] Table 2.5.1: constant calculation inputs. Bottoming cycle size has been changed according to values listed in Table Plant size [MW] Bottoming cycle size [MW] Table 2.5.2: bottoming cycle size for different plant sizes. Figure and show clearly that the area of cultivation and the woodchips input (kg/s) are a linear function of the plant size. The higher is the plant size the higher are both the cultivation area and woodchips input. 40

41 Figure 2.5.1: cultivation area as a function of plant size. Figure 2.5.2: woodchips input as a function of plant size. Global expected efficiency is about 55% for each plant size. To obtain a reasonable value for the cultivation area (around 20 km 2 ) a size between 5 and 10 MWe is selected. With such a size, suitable value for woodchips input is 1.2 kg/s. 41

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43 3 Integrating a gasification plant with SOFC and steam cycle Simulations and calculations have been carried out by means of DNA (Dynamic Network Analysis), a component-based simulation tool for energy systems analysis developed at the DTU Thermal Energy Systems department. DNA contains models for most of energy system compounds (compressors, pumps, heat exchanger, fuel cells, etc.). Solution is provided solving a system of nonlinear equations with the Newton-Raphson modified algorithm. Viking plant DNA model developed at Thermal Energy Systems department is used to design gasification plant. The sofceq0d_cbm.for file is utilized as SOFC model; main reason is that other available models could not work with nitrogen (N 2 ) a typical woodgas compound. 3.1 Plant layout Plant layout is presented in Figure Three main parts can be distinguished: - gasification plant; - SOFC plant; - steam cycle. 43

44 WOODCHIPS 1 DRYER 2 61 STEAM WOOD GAS CLEANED 64 H.E. 4 H.E. MIXER 63 AIR GASIFIER ASHES 99 STEAM&AIR 74 STEAM BLOWER ANODE PREHEATER CATHODE PREHEATER WOODGAS BLOWER GAS SPLITTER CLEANER HRSG BURNER 49 AIR H 2 S 97 OFF GASES SUPER VAPORIZER ECO WATER GEN 1 HPT 34 STEAM EXTRACTION GEN LPT CONDENSER PUMP 1 DEAERATOR PUMP 2 Figure 3.1.1: plant layout. According to this layout, plant efficiency is defined by equation 3.1. (3.1). 44

45 3.2 Gasification plant General features Gasification plant converts woodchips into woodgas in order to feed fuel cells plant. Inside gasifier both pyrolysis and gasification are performed. Woodgas out of gasifier is cooled down first to preheat the air and than to generate the steam for the drying process. A gas cleaner eliminates Hydrogen Sulfide (H 2 S) from woodgas; ashes are expelled out of gasifier. In Figure the gasification plant scheme is depicted. WOODCHIPS 1 61 STEAM DRYER 2 AIR STEAM BLOWER 72 GASIFIER 64 STEAM&AIR H.E. 3 4 MIXER 73 ASHES H.E GAS SPLITTER CLEANER 55 5 H 2 S 97 Figure : gasification plant Main data input Woodchips compositions and parameters used for simulations are reported in Paragraph

46 Other main gasification inputs are listed in Table Woodchips Temperature 15 [ C] Pressure [bar] Mass flow 1.2 [kg/s] Air Temperature 15 [ C] Dryer T dryer out 150 [ C] Gasifier T gasification 800 [ C] Carbon conversion factor 1.0 Pressure loss [bar] Steam generator T steam generator out 200 [ C] Steam blower Isentropic efficiency 80 [%] Table : gasification plant input. 3.3 SOFC plant General features SOFC plant is fueled by the woodgas produced inside the gasifier. In order to reach the required fuel temperature (650 C) a heat exchanger (anode pre-heater) is introduced; in this component used fuel coming out from fuel cells is cooled down to preheat the woodgas. SOFC air is also blown trough the cathode pre-heater in order to warm it to a convenient temperature (600 C). This is done by mean of the flue gases coming out from SOFC cathode side. Not all the fuel reacts inside the SOFC; a part of the LHV is still inside the used fuel. Therefore used fuel and flue gas are sent to a burner to generate heat. SOFC plant is presented in Figure

47 WOOD GAS CLEANED 5 WOODGAS BLOWER 8 7 ANODE PREHEATER CATHODE PREHEATER AIR BLOWER 49 BURNER AIR 10 Figure : SOFC plant. SOFC stack efficiency is defined, according to Paragraph 2.3.1, by the following expression: (3.2) Main data input Main data input for the SOFC plant are listed in Table Air Temperature 15 [ C] Pressure [bar] Anode pre-heater T anode pre out 650 [ C] Cathode pre-heater T cathode pre out 600 [ C] SOFC Utilization factor 0.85 Operative temperature 780 [ C] 47

48 Current density 300 [ma/cm 2 ] Woodgas blower Isentropic efficiency 90 [%] Air blower Isentropic efficiency 90 [%] Table : SOFC plant data input. 3.4 Steam cycle General features Size of steam cycle is around 1-2 MW; therefore regeneration is done only by means of the deaerator. Steam is generated inside HRSG (heat recovery steam generator). In Figure the steam cycle design is presented. Figure : steam cycle. Steam cycle efficiency is calculated according to the following equation: 48

49 (3.3) Main data input Main data input for the steam cycle are listed in Table Low pressure turbine isentropic efficiency has been estimated considering plant size and quality at turbine outlet. High pressure turbine P HPT in 20 [bar] Isentropic efficiency 90 [%] Low pressure turbine P LPT in 2 [bar] P LPT out 0.13 [bar] Isentropic efficiency 70 [%] Economizer ΔT pinch eco 12 [ C] Pressure losses (steam side) 0.04 [bar] Pressure losses (off gases side) 0.01 [bar] Vaporizer ΔT pinch vap 10 [ C] Pressure losses (steam side) 0.03 [bar] Pressure losses (off gases side) 0.01 [bar] Superheater ΔT pinch super 15 [ C] Pressure losses (steam side) 0.02 [bar] Pressure losses (off gases side) 0.01 [bar] Table : steam cycle data input. 3.5 Results analysis Efficiency of the plant Plant efficiency calculation is based on equation 3.1. Efficiency and other main results are listed in Table Working fluid temperature is not constant through HRSG; thus efficiency limit is expressed by mean of the thermodynamic mean temperature (equation 3.4). (3.4). 49

50 Carnot efficiency limit can be expressed as: (3.5). Plant Power biomass input 13.7 [MW] Auxiliary consumption [MW] Electric power 6.72 [MW] Efficiency [%] SOFC plant Electric power 6.05 [MW] Steam cycle Heat power input 2.74 [MW] T mean [ C] T off gases [ C] Electric power [MW] Efficiency 24.6 [%] Table : main simulation results. As shown in Figure plant losses are mainly due to the off gases high temperature. Off gases heat losses can be decreased when their energy content is reutilized in the plant itself. Figure : plant energy losses. 50

51 Auxiliary consumptions are reported in Figure More than half auxiliary energy (128 [kw]) is absorbed by SOFC air blower. Figure : auxiliary consumptions of the plant Steam heat recovery Plant heat recovery is carried out inside the HRSG; main components are: economizer, vaporizer and superheater. Figure shows steam and off gases temperature profile inside the heat exchanger. 51

52 Figure : HRSG temperature profile. Higher steam cycle efficiency can be achieved when area between the two curves is decreased SOFC air preheating SOFC air preheating is realized cooling down the flue gas coming out from the fuel cells. Figure shows temperature profiles inside the anode preheater as a function of the heat exchanged. 52

53 Figure : anode preheater temperature profile Woodchips low heat value utilization Woodchips LHV is utilized inside the plant in order to produce electric power. LHV changing occurs in the following components: - dryer: since moisture is no longer present, LHV is increased; - gasifier: LHV is decreased in order to provide heat for the gasification process; - woodgas cleaner: hydrogen sulfide is removed, LHV is marginally lowered; - SOFC: part of woodgas LHV is converted into electric power; - burner: LHV energy content is entirely converted into heat. Figure shows the heat values for different plant working fluids. 53

54 Figure : LHV for different working fluids of the plant. 3.6 Steam pressure simulations Inlet turbine pressure is changed in order to see how it affects plant efficiency. Main parameters influenced by steam cycle pressure are: off gases outlet temperature and steam thermodynamic mean temperature. The higher is steam pressure the higher are steam cycle thermodynamic mean temperature (Figure 3.6.1) and plant efficiency. Figure 3.6.1: thermodynamics mean temperature as a function of steam cycle pressure. 54

55 On the contrary an increase in the pressure produces a higher off gases outlet temperature (Figure 3.6.2); plant efficiency is therefore decreased. Figure 3.6.2: off gases outlet temperature as a function of steam cycle pressure. Figure shows that maximum plant efficiency is obtained for a steam cycle pressure of 10 bar. 55

56 Figure 3.6.3: plant efficiency as a function of steam cycle pressure. 3.7 Hybrid recuperation About 70% of energy losses are due to the high outlet temperature of the off gases coming out form HRSG. This heat can be used inside the plant in order to increase plant efficiency. Heat inside woodgas is utilized to warm SOFC air before entering inside the cathode preheater. This is done by means of a heat exchanger called hybrid recuperator; process is called hybrid recuperation. Main consequences of adding this component are: - larger available heat for the steam cycle; - higher temperature of the off gases going trough HRSG. Inside cathode preheater less heat must be provided by flue gases; thus more heat can be transferred to the steam cycle. Furthermore flue gases temperature entering the burner is increased; steam thermodynamic mean temperature can be upgraded Plant scheme Plant scheme with hybrid recuperation is shown in Figure Off gases coming out from HRSG are sent to the SOFC plant to preheat the air required by the fuel cells. 56

57 Figure : plant scheme with hybrid recuperation Main input Main inputs are listed in Table , and ; hybrid recuperator features are provided in Table Hybrid recuperator T off gases outlet P off gases outlet Pressure losses (SOFC air side) Pressure losses (off gases side) 90 [ C] [bar] 0.01 [bar] 0.01 [bar] Table : hybrid recuperator data input. 57

58 An off gases outlet temperature of 90 C is selected. Since, at this value, off gases water is in vapor phase, formation of sulfuric acid and corrosion problems are prevented Results Main outputs of the simulation are listed in Table An efficiency of 53 % is obtained; the system shows a significant increase (about 6%) of plant performance. Plant Power biomass input 13.7 [MW] Auxiliary consumption [MW] Electric power 7.66 [MW] Efficiency [%] SOFC plant Electric power 6.05 [MW] Steam cycle Heat power input 6.04 [MW] T mean [ C] Electric power [MW] Efficiency [%] Table : main outputs with hybrid recuperation. A significant increase of electric power produced by the steam cycle is obtained. Cycle efficiency is also higher due to a higher steam thermodynamic mean temperature. As can be seen in Figure , energy losses are mainly due to low temperature heat released by the condenser; auxiliary consumptions are reported in Figure

59 Figure : energetic losses of plant with hybrid recuperation. Figure : auxiliary consumption of plant with hybrid recuperation. Figure shows how off gases heat is utilized inside the plant: 30% is given to warm SOFC air and 70% is provided to the steam cycle. In this way a higher thermodynamic mean temperature can be achieved. 59

60 Figure : off gases heat recovery. Figure shows the two-step SOFC air preheating: hybrid recuperator heats it until C; finally the cathode preheater completes the heating up to 600 C. Figure : SOFC air preheating. 60

61 3.7.4 Gasification temperature Gasification temperature is an important parameter since it affects SOFC fuel composition. An analysis of gasification temperature influence on plant efficiency has been carried out. Other parameters are kept constants. Simulations were performed changing gasification temperature form 700 C up to 850 C, according to the values mentioned in Paragraph Figure shows woodgas composition for different gasification temperatures. Figure : gasification temperature influence on cleaned woodgas composition (mass base). Main consequences of increasing gasification temperature are: - a higher air mass flow is required for oxidation (more nitrogen is diluted inside woodgas); hence SOFC fuel heat value is lowered (Figure ); - chemical equilibrium, modeled on free Gibbs energy minimization, leads to higher CO and lower CO 2, CH 4 and H 2 content; steam mass fraction is also increased. 61

62 Figure : gasification temperature influence on cleaned woodgas low heat value. Plant efficiency is slightly influenced by gasification temperature (Figure ). Figure : plant, SOFC and steam cycle efficiency as a function of gasification temperature. Higher gasification temperature results in lower plant efficiency. This is due to two main reasons: 62

63 - SOFC stack efficiency is decreased: as shown in Figure , hydrogen partial pressure drops down when gasification temperature is increased; - fuel and SOFC air mass flow are increased; thus power consumption of SOFC air blower is higher (Figure ). Figure : hydrogen partial pressure as a function of gasification temperature. Figure : SOFC auxiliary consumption as a function of gasification temperature. 63

64 3.7.5 Wood moisture content Wood moisture content has a major influence on the electric power production of the plant. As explained in Paragraph 1.3, low and high heat values are strongly influenced by this parameter. Simulations were run varying wood moisture content from 10% up to 50%; other parameters are kept constants. The higher is the moisture content the lower is electric power production (Figure ); Figure : plant power as a function of wood moisture (mass base). Electric power appears to be a linear function of wood moisture; anyway, lowering steam cycle power, turbine isentropic efficiency is strongly reduced. For this reason electric power produced may decrease more rapidly. Furthermore, when steam is generated at a constant temperature of 200 C and woodgas humidity is raised, steam generator pinch point is significantly decreased. This is due to a higher steam absorption inside the dryer. Figure shows that a zero pinch point is reached for a moisture of about 46%; woodgas steam generation is not thermodynamically possible for higher moisture content. 64

65 Figure : steam generator pinch point as a function of moisture content SOFC operating temperature SOFC operating temperature has been changed from 720 C to 980 C. Anode and cathode preheater outlet temperatures are adjusted in order to maintain a constant difference with SOFC operating temperature. Figure shows that: - SOFC stack efficiency has a maximum (55%) for an operating temperature of about 900 C; - low temperatures (<720 C) result in a remarkable efficiency drop; - steam cycle efficiency is constant; - plant efficiency follows stack efficiency trend. Low temperature drop is due to high fuel cells ohmic losses; on the contrary very high temperature results in a lower theoretical efficiency. 65

66 Figure : plant, SOFC and steam cycle efficiency as a function of SOFC temperature Steam cycle pressure Steam turbine inlet pressure affects cycle efficiency since it modifies steam thermodynamic mean temperature (Figure ). A pressure increment results in more available work and therefore higher performance. Simulations were run keeping other parameters constants. Figure : steam thermodynamics mean temperature as a function of inlet turbine pressure. 66

67 Since turbine size is relatively low (around 1.5 MW), pressure can not be raised too much in order to avoid high moisture content at turbine outlet (Figure ). Corrosion and low isentropic efficiency problems are prevented when 84% of steam is present at turbine outlet. Figure : outlet turbine quality (mass base) as a function of inlet pressure. Figure proves that plant efficiency can be increased till 55% when steam pressure is upgraded up to 55 bar. Figure : plant and steam cycle efficiency as a function of inlet turbine pressure. 67

68 3.7.8 Optimized system Based on results given by parameters analysis, inputs have been adjusted to obtain the optimized system. Hybrid recuperation raises significantly plant efficiency; further improvements can be obtained increasing SOFC temperature up to 900 C and inlet turbine pressure up to 50 bar. Simulation was run in order to provide plant efficiency; optimized system main data input and output are listed in Table and Table respectively. DNA code and detailed results are reported in APPENDIX I. Woodchips Temperature 15 [ C] Pressure [bar] Mass flow 1.2 [kg/s] Gasification air Temperature 15 [ C] Dryer T dryer out 150 [ C] Gasifier T gasification 800 [ C] Carbon conversion factor 1.0 Pressure loss [bar] Steam generator T steam generator out 200 [ C] Steam blower Isentropic efficiency 80 [%] SOFC air Temperature 15 [ C] Pressure [bar] Anode pre-heater T anode pre out 770 [ C] Hybrid recuperator T off gases outlet 90 [ C] P off gases outlet [bar] Cathode pre-heater T cathode pre out 720 [ C] SOFC Utilization factor 0.85 Operative temperature 900 [ C] Current density 300 [ma/cm 2 ] Woodgas blower Isentropic efficiency 90 [%] Air blower Isentropic efficiency 90 [%] 68

69 High pressure turbine P HPT in 50 [bar] Isentropic efficiency 90 [%] Low pressure turbine P LPT in 2 [bar] P LPT out 0.13 [bar] Isentropic efficiency 70 [%] Economizer ΔT pinch eco 12 [ C] Vaporizer ΔT pinch vap 10 [ C] Superheater ΔT pinch super 15 [ C] Table : data input for the optimized system. Plant Power biomass input 13.7 [MW] Auxiliary consumption [MW] Electric power 8.24 [MW] Efficiency [%] SOFC plant Electric power [MW] Steam cycle Heat power input 5.8 [MW] T mean [ C] Electric power [MW] Efficiency 31.3 [%] Table : optimized system data output. The optimized system has a plant efficiency of 57.54%; more than a half of woodchips energy is converted into electric power. 69

70 70

71 4 Integrating a gasification plant with SOFC and Kalina cycle Plant design has been modified replacing steam cycle with a Kalina cycle. Ammoniawater mixture features should allow to reduce exergy destruction inside HRSG and, therefore, to achieve a better system performance. Since ammonia-water properties were not inside DNA library, a new media has been added. Properties are based on a thermodynamic model incorporating fundamental equation of state for the Helmholtz free energy. Ammonia-water modeling, developed by Tillner and Roth, is reliable in vapor phase for pressure up to 100 bar and in liquid phase for pressure and temperature up to 400 bar and 600 K (ref. [8]). In this paper mixture properties have been extended for vapor phase temperature around 700 K; accuracy is maintained decreasing pressure limit down to 80 bar. Plant analysis is carried out first with a free HRSG off gases outlet temperature and then including hybrid recuperation (T off gases outlet : 90 C). 4.1 Ammonia-water properties Since ammonia-water is widely utilized as working fluid in refrigeration absorption cycle several models have recently been developed. Most of them are applicable only in a restricted range or allow calculation of only limited number of thermodynamic properties. Furthermore models are developed for low temperature usually between K. Tillner-Roth approach allows thermodynamics calculation for all ammonia-water properties with uncertainties in single-phase regions of ± % for density and ±200 J mol -1 for enthalpies (ref. [8]) The Fundamental Equation of State A fundamental equation of state for the Helmholtz free energy (A=U TS) for a binary mixture has been developed by Tillner-Roth (ref. [8]). It is expressed in terms of reduced Helmholtz free energy as: (4.1). Φ is split into an ideal part ϕ o, depending on the dimensionless variables τ o =T o n/t, δ o = /, and ammonia mole fraction x, and a residual part ϕ r depending on τ=t n /T, δ= / and x. Ā is the molar Helmholtz free energy and R m = J mol -1 K -1 is the universal gas constant given by Moldover et al. (ref. [9]). 71

72 Ideal part ϕ o is given by a linear combination of water and ammonia ideal-gas parts ϕ 0 01, ϕ 0 02, adding two terms resulting from entropy of mixing of the ideal mixture. For given T and equation is: Equation for the ideal-gas part ϕ 0 is obtained from ref. [8]. The residual part ϕ r has the form: (4.2). (4.3). Φ r 01 and Φ r 02 are the residual contributions of water and ammonia; full equations are acquired from ref. [10] and [11] respectively. To adjust calculations to experimental data an empirical departure function Δϕ r is added (ref. [8]) Superheated vapor and subcooled liquid Main thermodynamics properties of superheated vapor and subcooled liquid are obtained as a function of residual and ideal part of the Helmholtz free energy (ref. [8]) Saturated liquid and vapor Properties for liquid and vapor on saturation curve are read from an external file provided for different ammonia-water compositions. Data were first acquired from EES and then transferred in a texture file. If a state along the saturation curve is not given, it is computed linearizing between the closest available data. Since data are provided for temperature intervals of 1 K (starting from 245 K), no relevant accuracy drop has been found Vapor-liquid equilibrium (VLE) Vapor-liquid phase changing, for ammonia-water mixture, occurs with a varying temperature. Fugacity coefficients (given in ref. [8]) could be used for VLE calculations. In this paper, to simplify ammonia-water algorithm, VLE properties are linearized with mixture quality Z (mass of vapor inside the fluid). For a given mixture composition and pressure, other parameters are calculated according to the following equations: (4.4); (4.5); 72

73 (4.6); (4.7). Since thermodynamics states for saturated vapor and liquid are known, calculations inside VLE can be easily carried out VLE calculation accuracy Linearization leads to less accurate calculation inside VLE. Centigrade temperature maximum relative errors for different pressures are listed in Table ; an ammonia mass percentage of 70% is chosen. Pressure [bar] Quality [%] Maximum relative error [%] Table : centigrade temperature maximum relative errors for different VLE pressure. Table shows that the lower is the VLE pressure the higher is the maximum relative error. Figure shows the condensing temperature profile of ammonia-water mixture for a pressure of 5.5 bar; saturated liquid temperature is around 20 C. VLE linearization is compared to EES (Engineering Equations Solver) results based on Ibrahim and Klein correlations. Figure : temperature as a function of fluid quality (pressure 5.5 bar). 73

74 For 70% ammonia in the mixture maximum relative error is around 40%; instead of 32.5 C linearization gives a temperature of around 48 C. Attention must be paid when such a condensing profile is utilized for Kalina cycle simulation; especially when a quality of 40% is met. Maintaining a constant saturated liquid temperature of 20 C, centigrade temperature maximum relative errors as a function of ammonia content in the mixture are given in Table Ammonia in the mixture [%] Quality [%] Maximum relative error [%] Table : centigrade temperature maximum relative errors for different ammonia content. As expected higher relative error occurs when mixture is close to pure component (constant condensing temperature). Lowest displacement is met for an ammonia mass fraction of 60%; this composition was selected as the working fluid inside Kalina cycle. Figure shows condensing temperature profile with 60% of ammonia for a pressure of 4.2 bar; saturated liquid temperature is around 20 C. VLE linearization is compared to EES results based on Ibrahim and Klein correlations. Figure : temperature as a function of fluid quality (pressure 4.2 bar). 74

75 As concerns other thermodynamic properties, maximum absolute errors for a pressure of 4.2 bar and an ammonia content in the mixture of 60% are reported in Table Property Quality [%] Maximum absolute error Entropy [kj/(k kg)] Enthalpy [kj/kg] Specific volume [m 3 /kg] Table : entropy, enthalpy specific volume maximum absolute errors (pressure 4.2 bar). Maximum relative errors are reported in Table Property Quality [%] Maximum relative error [%] Entropy Enthalpy Specific volume Table : entropy, enthalpy specific volume maximum relative errors (pressure 4.2 bar). Enthalpy maximum relative error is very high (183.7%); with a quality of 30% it drops down to 20%. Since a quality of 10% is never encountered in DNA simulations of the plant, linearization does not have remarkable effects on results. However it must be known that model is not reliable to know precise thermodynamics properties inside VLE. 4.2 Adding the model inside DNA Based on Tillner-Roth model, ammonia-water mixture has been added as a new media inside DNA library. Fortran file (Ammonia&Water.for) is reported in APPENDIX II. DNA provides the solution of energy system solving a system of non-linear equations (based on mass and energy balances); fluid properties for each node are required in order to get the solution. Gibbs rule asserts that to define ammonia-water state with a given mixture composition two thermodynamics independent variable must be given. DNA works with different pairs of variables; anyway most common combinations are: enthalpy-pressure, entropypressure, temperature-pressure and pressure-quality Temperature-pressure When temperature and pressure are known together with the mixture composition, enthalpy, entropy, internal energy and specific volume can be calculated. Tillner-Roth model provides an explicit equation for the pressure when temperature and specific volume are known. When these three are calculated all the other properties can be computed. 75

76 Compressibility factor equation (ref. [8]) provides the three variable (temperature, pressure and specific volume) function. In Ammonia&Water.for implicit equation is solved by means of Regula Falsi algorithm. Solution is found iteratively according to the following linearization formula: (4.8). To initiate the algorithm two unknowns (X o, X 1 ) must be selected; X 1 is usually determined with equation 4.9. (4.9). where ζ is a quantity small as desired (10-6 ). In this way only one initial value must be specified. In this case (temperature and pressure) specific volume is the unknown and function is given by the expression for compressibility factor. Starting values have been set working on tables of ammonia-water properties given in ref. [8]. As concerns vapor-liquid equilibrium properties, calculations are provided solving the linearized equations given in Paragraph 4.1.4; no iterative method is needed Enthalpy-pressure In DNA, when thermodynamics states are uploaded during iterations, media properties are predominantly asked as a function of enthalpy and pressure. Tillner-Roth equations do not provide a specific formula for this particular case; enthalpy and pressure are both provided as a function of specific volume and temperature. A system of two non-linear equations must be solved. This is enabled by Regula Falsi algorithm; in this case equations are: (4.10); (4.11). Starting values are determined by means of equation 4.9. As concerns vapor-liquid equilibrium properties, calculations are provided solving the linearized equations given in Paragraph 4.1.4; no iterative method is needed. 76

77 4.2.3 Entropy-pressure Entropy and pressure combination is needed since turbine model works with isentropic efficiency. A system of two non-linear equations must be solved; solution is obtained applying Regula Falsi algorithm (equations 4.10, 4.11) Quality-pressure Quality and pressure case is solved by means of the linearized equations (4.4, 4.5, 4.6, and 4.7); explicit formulas are given and no iterative methods are required. 4.3 Plant layout Plant layout is presented in Figure Three main part can be distinguished: - gasification plant; - SOFC plant; - Kalina cycle. 77

78 Figure 4.3.1: plant layout with Kalina cycle. According to this layout, plant efficiency is defined by the following formula: (4.12). 4.4 Kalina cycle General features Ammonia-water mixture is used as working fluid; ammonia percentage (mass base) inside the mixture is 60%. 78

79 Regeneration is done by mean of the high pressure and temperature of exhaust steam coming out from turbine. Since ammonia-water mixture provides a varying condensing temperature, turbine outlet temperatures can be up to 120 C for a condenser outlet of 20 C. Exhaust turbine energy is therefore available to heat up the pumped mixture before entering HRSG; it is noted that, with an inlet turbine pressure of 20.7 bar, HRSG is fed by a partially vaporized fluid. Depending from turbine inlet pressure, the economizer might be needed. Simulations demonstrated that for pressure beyond 40 bar economizer must be added. Kalina cycle layout is presented in Figure Figure : Kalina cycle layout. Kalina cycle efficiency is calculated according to equation (4.13). (4.13). 79

80 4.4.2 Main data input Main data input are listed in Table Turbine isentropic efficiency has been estimated considering plant size and quality of turbine outlet. Turbine P in turbine 20.7 [bar] P out turbine 4.2 [bar] Isentropic efficiency 85 [%] Internal recuperator ΔT pinch rec 10 [ C] Pressure losses (steam side) 0.02 [bar] Pressure losses (off gases side) 0.01 [bar] Vaporizer ΔT pinch vap 10 [ C] Pressure losses (steam side) 0.03 [bar] Pressure losses (off gases side) 0.01 [bar] Superheater ΔT pinch super 15 [ C] Pressure losses (steam side) 0.02 [bar] Pressure losses (off gases side) 0.01 [bar] Economizer No economizer is needed. Working fluid Ammonia 60 [%] Table : main data input. Main data input for gasification and SOFC plant are listed in Paragraphs and (Table and Table ). 4.5 Results analysis Efficiency of the plant Plant efficiency calculation is based on equation 3.1. Efficiency and other parameters are listed in Table Plant Power biomass input 13.7 [MW] Auxiliary consumption 0.25 [MW] Electric power 6.93 [MW] Efficiency [%] 80

81 SOFC plant Electric power 6.05 [MW] Kalina cycle Heat power input 5.27 [MW] T mean [ C] T off gases [ C] Electric power [MW] Efficiency [%] Table : main simulation results. Kalina cycle has a very poor efficiency (16.55%); this is mainly due to a low value of ammonia-water thermodynamic mean temperature (142.4 C); Carnot ideal efficiency is around 30%. As shown in Figure , plant losses are mainly due to the low temperature heat released by condenser. Off gases outlet temperature is around 115 C; only a small amount of heat can be recovered when they are cooled down to 90 C. Figure : plant energy losses. Auxiliary consumptions are reported in Figure More than a half of the auxiliary energy (170 [kw]) is absorbed by SOFC air blower. 81

82 Figure : auxiliary consumptions of the plant Ammonia-water heat recovery Heat recovery is done inside HRSG; for a pressure of 20.7 bar its components are: vaporizer and superheater. Figure shows ammonia-water and off gases temperature profiles inside HRSG Figure : HRSG temperature profile. 82

83 Fluid goes into HRSG with a quality of 26%; vaporization starts inside Kalina internal recuperator Ammonia-water condensation Ammonia-water mixture condenses starting from a temperature of 116 C. As shown in Figure , 35% of the heat is exchanged inside the internal recuperator. 75% is given to the cooling water entering Kalina condenser. Figure : ammonia water condensation (4.2 bar) SOFC air preheating SOFC air preheating is realized cooling the flue gas coming out from the fuel cells. Figure shows temperature profiles inside anode preheater as a function of the heat exchanged. 83

84 Figure : anode preheater temperature profiles Kalina cycle pressure simulations Inlet turbine pressure has been increased from 45 up to 70 bar. Figure shows a slight increase of Kalina cycle efficiency; plant performance is almost constant. Figure : plant and Kalina cycle efficiency as a function of turbine inlet pressure. 84

85 Plant efficiency at 20.7 bar is 48.83%; increasing inlet turbine pressure (from 45 to 70 bar) it does not go beyond 48.64%. This is due to the fact that with higher pressures an economizer is needed; pressure losses are added and pump energy consumption is increased. Economizer features are listed in Table Economizer Pressure losses (steam side) Pressure losses (off gases side) 0.04 [bar] 0.01 [bar] Table : economizer pressure losses. 4.6 Hybrid recuperation DNA plant simulation calculates an off gases outlet temperature of 113 C. Since temperature limit to prevent corrosion inside HRSG is 90 C, further available heat is very low (0.6 MW). Kalina cycle enables to get almost all SOFC exhaust heat. In this case hybrid recuperation can affect plant efficiency only marginally. Only a slight increase of the HRSG available heat and Kalina cycle efficiency is obtained. In order to use completely SOFC exhaust heat, outlet off gases temperature is fixed at 90 C. All other parameters are kept constant Plant scheme Plant layout is adjusted in order to add the hybrid recuperator. As shown in Figure , off gases coming out from HRSG are heating up SOFC air before being released to environment. 85

86 Figure : plant layout with hybrid recuperation Main input Main data input have not been modified; hybrid recuperator characteristics are listed in Table Hybrid recuperator T off gases outlet P off gases outlet Pressure losses (air side) Pressure losses (off gases side) 90 [ C] [bar] 0.01 [bar] 0.01 [bar] Table : hybrid recuperator data input. 86

87 An off gases outlet temperature of 90 C is selected. Since, at this value, off gases water is in vapor phase, formation of sulfuric acid and corrosion problems are prevented Results Results of the simulation are listed in Table An efficiency of 49.6 % is achieved; the system shows only a slight increase (about 0.8%) in plant performance. Plant Power biomass input 13.7 [MW] Auxiliary consumption [MW] Electric power 7.09 [MW] Efficiency [%] SOFC plant Electric power 6.05 [MW] Kalina cycle Heat power input 5.95 [MW] T mean [ C] Electric power [MW] Efficiency [%] Table : results of the simulation with hybrid recuperator. Kalina cycle efficiency is increased of 1% due to a higher ammonia-water thermodynamic mean temperature inside HRSG and to additional heat (about 0.6 MW) given to the bottoming cycle. As can be noted from Figure , off gases energy losses are reduced of about 10%; a large amount of heat input (71 %) is released to the cooling water. Auxiliary consumptions are reported in Figure More than half of the auxiliary energy (211 [kw]) is absorbed by SOFC air blower. 87

88 Figure : energy losses of the plant. Figure : auxiliary energy consumption of the plant. Figure shows off gases temperature profile: 10% of the heat is given to warm SOFC air and 90% is provided to the Kalina cycle. Only a slight increase of the ammonia-water thermodynamic mean temperature can be obtained. 88

89 Figure : off gases heat recovery. Figure shows the two-step SOFC air preheating: hybrid recuperator provides only the 5% of the total heat demand; 95% is given by cathode preheater. Figure : SOFC air preheating. Figure shows ammonia-water condensing profile. Outlet turbine temperature is decreased down to 81 C inside the internal recuperator; the mixture is than cooled in the condenser till 21 C. 89

90 Figure : ammonia water condensation (4.2 bar) Parameters analysis A parameters analysis is carried out varying the following data input: - gasification temperature; - woodchips moisture content; - SOFC operating temperature; - inlet turbine pressure (Kalina cycle). Gasification temperature influence on woodgas composition and SOFC efficiency has been investigated in Paragraph Figure shows a decrease of around 1.5% in system performance when temperature is varied from 700 C to 850 C; this is due to a drop of SOFC stack efficiency and an increase of auxiliary consumptions. Kalina cycle efficiency is not significantly influenced by gasification temperature. 90

91 Figure : gasification temperature influence on SOFC, Kalina cycle and plant efficiency. As explained in Paragraph 3.7.5, moisture has a strong influence on electric power production and on steam generator pinch point. Figure shows that electric power output is linearly decreased from 10 MW down to 5 MW when wood moisture is enhanced from 10% to 50%. Figure : electric power production as a function of woodchips moisture content. 91

92 SOFC operating temperature influence on plant efficiency has already been analyzed in Paragraph Also in this case plant efficiency reaches a maximum (52.32%) for an operating temperature of 900 C. Figure depicts a constant Kalina cycle efficiency of 17.5%. Figure : SOFC operating temperature influence on stack, Kalina cycle and plant efficiency. Inlet turbine pressure of Kalina cycle is varied from 40 bar and 60 bar; with those values an economizer is needed. Main consequences are: - higher ammonia-water thermodynamic mean temperature; - higher Kalina cycle efficiency; - higher plant efficiency; - higher pump electric consumption; - lower steam content at turbine outlet. When pressure is increased, a higher thermodynamics mean temperature is obtained; since Carnot efficiency limit is increased, Kalina cycle performance is improved (Figure ). 92

93 Figure : pressure influence on Kalina cycle and plant efficiency. In order to avoid a high moisture content at turbine outlet, pressure increment can not be too high; as shown in Figure , with 60 bar ammonia-water quality is around 90.6%. Figure : outlet turbine quality as a function of inlet pressure. 93

94 4.6.5 Optimized system Optimized system is obtained by means of the following devices: - Hybrid recuperation; - SOFC operating temperature: 900 C; - Inlet turbine pressure: 60 bar. Simulations were run in order to provide plant efficiency; optimized system main data input and output are listed in Table and Table respectively. DNA code and detailed results are provided in APPENDIX III. Woodchips Temperature 15 [ C] Pressure [bar] Mass flow 1.2 [kg/s] Gasification air Temperature 15 [ C] Dryer T dryer out 150 [ C] Gasifier T gasification 800 [ C] Carbon conversion factor 1.0 Pressure loss [bar] Steam generator T steam generator out 200 [ C] Steam blower Isentropic efficiency 80 [%] SOFC air Temperature 15 [ C] Pressure [bar] Anode pre-heater T anode pre out 770 [ C] Hybrid recuperator T off gases outlet 90 [ C] P off gases outlet [bar] Cathode pre-heater T cathode pre out 720 [ C] SOFC Utilization factor 0.85 Operative temperature 900 [ C] Current density 300 [ma/cm 2 ] Woodgas blower Isentropic efficiency 90 [%] Air blower 94

95 Isentropic efficiency 90 [%] Turbine P in turbine 60 [bar] P out turbine 4.2 [bar] Isentropic efficiency 85 [%] Internal recuperator ΔT pinch rec 10 [ C] Pressure losses (steam side) 0.02 [bar] Pressure losses (off gases side) 0.01 [bar] Vaporizer ΔT pinch vap 10 [ C] Pressure losses (steam side) 0.03 [bar] Pressure losses (off gases side) 0.01 [bar] Superheater ΔT pinch super 15 [ C] Pressure losses (steam side) 0.02 [bar] Pressure losses (off gases side) 0.01 [bar] Economizer Pressure losses (steam side) 0.04 [bar] Pressure losses (off gases side) 0.01 [bar] Working fluid Ammonia 60 [%] Table : optimized data input. Plant Power biomass input 13.7 [MW] Auxiliary consumption [MW] Electric power [MW] Efficiency [%] SOFC plant Electric power [MW] Kalina cycle Heat power input 5.8 [MW] T mean [ C] Electric power [MW] Efficiency 20.1 [%] Table : optimized data output Comparing Kalina and steam cycle solutions Two plants with different bottoming cycles have been analyzed; comparison between the two is based on plant performance and includes the following analysis: 95

96 - confrontation with free off gases outlet temperature at a constant inlet turbine pressure (20 bar); - confrontation with a fixed off gases temperature of 90 C (Hybrid recuperation) at a constant inlet turbine pressure (20 bar); - confrontation of the optimized systems. In Table are listed main simulation results with a free off gases outlet temperature for the Kalina and the Rankine cycle solution. Main data input and results are acquired from Tables , RANKINE CYCLE KALINA CYCLE Plant Power biomass input 13.7 [MW] 13.7 [MW] Auxiliary consumption [MW] 0.25 [MW] Electric power 6.72 [MW] 6.93 [MW] Efficiency [%] [%] SOFC plant Electric power 6.05 [MW] 6.05 [MW] Bottoming cycle Heat power input 2.74 [MW] 5.27 [MW] T mean [ C] [ C] T off gases [ C] [ C] Electric power [MW] [MW] Efficiency 24.6 [%] [%] Table : data output with a free off gases temperature. Main parameters affecting plant efficiency are: - off gases temperature: Kalina cycle utilizes almost all the heat (5.27 MW) released by SOFC plant this results in a very low off gases temperature (113.8 C). Rankine cycle wasted heat is very high because of the high off gases temperature (206 C). - thermodynamic mean temperature of working fluid: ammonia-water mixture has a low value for this parameter and therefore cycle efficiency is very poor; - auxiliary consumption: integration with Rankine cycle provides a lower auxiliary power demand; plant efficiency is increased. Figure shows a comparison based on Carnot and cycle efficiency; an ambient temperature of 15 C is assumed. 96

97 Figure : Rankine and Kalina Carnot and cycle efficiency. Even if steam cycle offers a better performance, plant efficiency is higher with Kalina cycle; this is due to a lower off gases temperature, more heat is available. Plant efficiency is 47.7% for Rankine cycle and 48.8% for Kalina cycle In Table are listed main simulation results with a fixed off gases outlet temperature of 90 C; plant is equipped with the hybrid recuperator. An inlet turbine pressure of 20 bar is maintained. Main data input and results are acquired from Tables , RANKINE CYCLE KALINA CYCLE Plant Power biomass input 13.7 [MW] 13.7 [MW] Auxiliary consumption [MW] [MW] Electric power 7.66 [MW] 7.09 [MW] Efficiency [%] [%] SOFC plant Electric power 6.05 [MW] 6.05 [MW] Bottoming cycle Heat power input 6.04 [MW] 5.95 [MW] T mean [ C] [ C] Electric power [MW] [MW] Efficiency [%] [%] Table : data output with a fixed off gases temperature. Hybrid recuperator has a crucial influence on the performance of Rankine cycle plant; around 3.2 MW are recovered from off gases and an increase of steam thermodynamic 97

98 mean temperature is obtained. On the other hand hybrid recuperation has a slight effect on Kalina cycle plant; recovered heat is around 0.7 MW and ammonia-water thermodynamics mean temperature is almost constant. Plant efficiency is 53% for Rankine cycle and 49.6% for Kalina cycle. In ultimate, optimized systems are compared; off gases outlet temperature is fixed (90 C) and inlet turbine pressure are increased maintaining a moisture content of around 90% at turbine outlet. In Table are listed main results of optimized systems simulations. Main data input and results are acquired from Tables , , , RANKINE CYCLE KALINA CYCLE Plant Power biomass input 13.7 [MW] 13.7 [MW] Auxiliary consumption [MW] [MW] Electric power 8.24 [MW] [MW] Efficiency [%] [%] SOFC plant Electric power [MW] [MW] Bottoming cycle Heat power input 5.8 [MW] 5.8 [MW] T mean [ C] [ C] Electric power [MW] [MW] Efficiency 31.3 [%] 20.1 [%] Table : data output for the optimized systems. According to the values given upon, gasification-sofc plant has to be integrated with Rankine cycle; main reason is a higher cycle efficiency and, therefore, higher electric power for a given biomass input. Kalina cycle enables to fit properly low temperature profiles; anyway, since hybrid recuperator increase significantly steam temperature profile inside HRSG, it is concluded that the best solution is to integrate the plant with a Rankine cycle. 98

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101 5 Thermoeconomic analysis Thermoeconomy combines thermodynamic analysis and economic principles to provide information not available through conventional energy approach and economic evaluations but crucial to the design and operation of a cost-effective system. Best solution, regarding plant efficiency, is to integrate the gasification-sofc plant with a steam cycle; in this case optimized system gives a plant efficiency of 57%. Higher efficiencies are usually achieved using new technologies and, therefore, increasing investment cost. Main target is to know the production cost of electricity of the plant in order to acquire information about the economic operability of the system. Since a SOFC market is not yet developed, stack cost is still very high (3000 /kw). Anyway the price is expected to be lowered down to 300 /kw in 2020, especially when operating temperature is decreased. Since SOFC price is the predominant item, as concerns investment cost, a significant decrease of electricity price can be obtained. 5.1 Thermoeconomic theory Analysis is based on the theory of the exergetic cost (TEC) developed by Lozano and Valero. In this approach the cost balance expresses that the cost rate associated with the product of system (Ċ P [ /h]) equals the total rate of expenditures made to generate the product, namely the fuel cost rate (Ċ F [ /h]) and the cost rates associated with capital investment (Ż CI [ /h]) and operating and maintenance (Ż OM [ /h]). For the kth component, operating at steady state, it is formulated as: (5.1). The rates Ż CI and Ż OM are calculated by dividing the annual contribution of capital investment and the annual operating maintenance (O&M) costs, respectively by the number of hours of system operation per year. As exergy measures the true thermodynamic value of energy streams, TEC is based on the exergy costing method. For entering and exiting streams of matter with associated rates of exergy transfer Ė i and Ė e, power, and the exergy transfer rate associated with heat transfer Ė q equations are: 101

102 (5.2); (5.3); (5.4); (5.5). Here c i, c e, c w, and c q denote average costs per unit of exergy or unit costs expressed in /kwh. A single product and fuel for each component of the system must be defined. Thus, a system of equations can be built with a cost-balance equation for each unit (proposition 1), unit cost equations for external flows into the system for which costs are externally defined (proposition 2), and losses for which the unit cost is set equal to zero (proposition 3). In this way a linear system is built up. The solution is possible when auxiliary equations, based on the two following propositions, are added. 1) If definition of fuel of a component includes a stream that goes through another component and is used in it, then the unit cost of stream flowing into and out of the component is the same; 2) if the product of a component is composed of two or more streams then the unit cost of those streams is equal. TEC method requires to know exergy for each node of the plant. Exergetic analysis of the plant is carried out by DNA, fixing a thermodynamic state for environment (T amb : 15 C and P amb : bar). To identify sources of thermodynamic inefficiencies, exergy destruction for the kth component of the plant is calculated. Equation is: (5.6); where Ė k is the flow rate of exergy for the ith material or energy stream at the inlet and outlet of the kth component. When exergies of fuel and product are identified, equation 5.6 can be written as: where Ė L,k represents the exergy loss in the kth component. For each component of the plant the following equations have been set: - investment cost; (5.7); 102

103 - cost-balance; - exergy-balance; - auxiliary equations. Collecting all the those equations, a solvable linear system is created. 5.2 Components equations Dryer Aim of the component is to obtain dried woodchips; fuel is made up by the difference of costs rate of steam coming out and exiting the dryer. Figure : dryer model. Referring to Figure , cost and exergy balance are expressed by the following equations: (5.8); (5.9); (5.10). Two auxiliary equation are needed: as equation 5.11 asserts, price of woodchips in /kwh must be given. (5.11). 103

104 Price of woodchips ( /ton) is acquired from Paragraph 1.2 and converted in /kwh by means of the following equation: Second auxiliary equation equalizes steam unit costs according to equation Dryer purchase cost is assumed to be (ref. [12]). (5.12). (5.13) Gasifier Component products are: woodgas and ashes; fuel is made up by steam-air mixture and dried woodchips. Figure : gasifier model. Referring to Figure , cost and exergy balance are expressed by the following equations: (5.14); (5.15); (5.16). One auxiliary equation is needed: as equation 5.17 asserts, cost of ash disposal in /kwh is set equal to zero. 104

105 (5.17). Atmospheric gasifier purchase cost ($) is given as a function of woodchips mass flow input (ref. [13]). (5.18) Gas cleaner Products of the component are cleaned woodgas and hydrogen sulfide; fuel is the woodgas produced by the gasifier. Figure : gas cleaner model. Referring to Figure , cost and exergy balance are expressed by the following equations: (5.19); (5.20); (5.21). One auxiliary equation is needed: as equation 5.22 asserts, cost of hydrogen sulfide disposal in /kwh is set equal to zero. (5.22). Gas cleaner purchase cost is assumed to be (ref. [14]). 105

106 5.2.4 Heat exchangers Heat exchanger aim is to heat up a cold flow using the heat coming from a hot flow. Heat exchangers, studied with the same set of equations, are: - gasification preheater; - steam generator; - anode preheater; - cathode preheater; - hybrid recuperator - HRSG. Figure : heat exchanger model. Referring to Figure , cost and exergy balance are expressed by the following equations: (5.23); (5.24); (5.25). Since off gases coming out from the hybrid recuperator are released to environment, for this component equation 5.25 must be replaced by equation 5.26 (5.26). Based on TEC method, one auxiliary equation is given: as equation 5.27 asserts, unit costs of hot stream inlet and outlet are equalized. (5.27). Heat exchanger purchase cost ($) is given as a function of exchange surface (ref. [15]) according to equation (5.28). 106

107 Heat exchanger area is calculated by means of equation In the heat exchangers mentioned upon, heat is exchanged between two gases; therefore a K value of 35 W/(m 2 K) is selected. (5.29) Blowers Blowers increase pressure of a working fluid using mechanical energy as fuel. No heat loss is considered. Blowers, studied with the same set of equations, are: - steam blower; - woodgas blower; - air blower. Figure : blower model. Referring to Figure , cost and exergy balance are expressed by the following equations: No auxiliary equation is needed. Blower purchase cost ($) is given by equation 5.33 (ref. [13]). (5.30); (5.31); (5.32). (5.33). 107

108 5.2.6 Pumps Pumps increase pressure of water using mechanical energy as fuel. Pumps, studied with the same set of equations, are: - pump1; - pump2. Figure : pump model. Referring to Figure , cost and exergy balance are expressed by the following equations: No auxiliary equation is needed. Pump purchase cost ($) is given by equation 5.37 (ref. [16]). (5.34); (5.35); (5.36). (5.37) Turbine Turbine produces mechanical power by means of a reduction in the working fluid enthalpy. 108

109 Figure : turbine model. Referring to Figure , cost and exergy balance are expressed by the following equations: (5.38); (5.39); (5.40). One auxiliary equation is needed: unit cost of the turbine inlet and outlet are equalized according to equation Turbine purchase cost ($) is given by equation 5.42 (ref. [16]). (5.41). (5.42) Electric generator Electric generator produces electric power by means of mechanical energy. No heat loss is considered. Equations are applied to generator1 and generator2. Figure : generator model. Referring to Figure , cost and exergy balance are expressed by the following equations: 109

110 (5.43); (5.44); (5.45). No auxiliary equation is needed. Generator purchase cost ($) is given by equation 5.46 (ref [16]). (5.46) Mixer Mixing of two streams (fuel) requires the definition of a new stream (product). Equations are used to model two plant devices: - deaerator; - gasification mixer. Figure : mixer model. Referring to Figure , cost and exergy balance are expressed by the following equations: No auxiliary equation is needed. (5.47); (5.48); (5.49). Gasification mixer purchase cost is set equal to zero, whereas deaerator purchase cost is computed by means of equation 5.50 (ref. [16]). (5.50). 110

111 SOFC SOFC produces electric power and heat, converting the chemical energy of a fuel. Figure : SOFC. Referring to Figure , cost and exergy balance are expressed by the following equations: Two auxiliary equations are needed. Three cases are considered: (5.51); (5.52); (5.53). A. The exergy difference between the outgoing used fuel and the inlet clean woodgas is considered the fuel. Products are electric power and heat absorbed by the fluegas coming out from the SOFC. Since fluegas and usedfuel are not costless in this case, steam cycle can not be considered a recovery cycle. Auxiliary equations are: (5.54); (5.55). B. The exergy difference between the outgoing used fuel and the inlet clean woodgas is considered the fuel (equation 5.54), while fluegas is considered as a plant wastage; therefore its unit cost is set equal to zero (equation 5.56). With this approach steam cycle fuel is not completely costless; this seems a reasonable assumption since some chemical energy (LHV) is still stored inside the usedfuel. (5.56). 111

112 C. Fluegas and usedfuel are considered as SOFC plant wastage; hence their unit cost is set equal to zero (equations 5.56 and 5.57). In this way steam cycle recovers both fluegas and usedfuel heat both chemical usedfuel energy. SOFC purchase cost ($) is given by equation 5.58 (ref. [14]). (5.57). (5.58) Burner A burner uses chemical energy of a fuel to convert it into heat. Products are off gases coming out at high temperatures. Figure : burner model. Referring to Figure , cost and exergy balance are expressed by the following equations: No auxiliary equation is needed. Burner purchase cost is (ref. [12]). (5.59); (5.60); (5.61). 112

113 Splitter Splitter products are the two stream coming out from the component; fuel is the entering fluid. The same set of equations is utilized to model two plant devices: - steam extraction; - gasification splitter. Figure : splitter model. Referring to Figure , cost and exergy balance are expressed by the following equations: Since two products come out of the component, one auxiliary equation is added. Splitter purchase cost is set equal to zero. (5.62); (5.63); (5.64). (5.65) Condenser Condenser aim is to cool down steam or a mixture of water and steam usually by means of water. Figure : condenser model. 113

114 Referring to Figure , cost and exergy balance are expressed by the following equations: Unit costs of the cooling water are set equal to zero; two auxiliary equations are added. (5.66); (5.67); (5.68). (5.69). Condenser purchase cost ($) is given as a function of steam mass flow (ref. [16]) according to equation (5.70) Other auxiliary equations In order to solve the linear system other auxiliary equations are required. SOFC and gasification air unit costs are set equal to zero according to equations 5.71 and (5.71); (5.72). Unit costs of auxiliary (blowers and pumps) are set equal to the weighted average unit cost of electric power produced by the SOFC plant and the steam turbines (HPT, LPT), according to equation (5.73). 5.3 Cost rate calculation Cost-balance equations require to know the cost rate (Ż k [ /h]) for each component of the plant. As equation 5.1 asserts, cost rate can be divided in two items: - Ż CI k represents the contribute of the component capital investment; - Ż OM k represents the component operating and maintenance cost. 114

115 5.3.1 Estimation of total capital investment In thermoeconomic analysis purchase equipment cost (PEC) is only a small part of the total capital investment of the plant. Cost estimates consist of two major elements: direct and indirect costs (ref. [17]). Direct costs (DC) are the costs of all permanent equipment, materials, labor, and other resources involved in the fabrication, erection, and installation of the permanent facilities. Indirect costs (IC) are required for the orderly completion of the project. No other outlays (startup costs, working capital) are accounted. Table shows main direct and indirect costs considered for calculations. TOTAL CAPITAL INVESTMENT A. DIRECT COSTS 1. Onsite costs a) Purchased - equipment costs (PEC) b) Purchased - equipment installation: 45 %PEC c) Piping: 35 %PEC d) Instrumentation + controls: 20 %PEC e) Electrical equipment + materials: 11 %PEC 2. Offsite costs f) Civil, structural + architectural work: 30 %PEC g) Service facilities: 50 %PEC B. INDIRECT COSTS i) Engineering + supervision: 8 %DC j) Construction costs + constructors 15 %DC profit: k) Contingency: 15 %(of i and j) Table : estimate of total capital investment (ref. [17]). According to the values given in Table , total capital investment of the kth component of the plant is given by the following expression: (5.74). Table lists purchase cost and total capital investment of each component of the plant. When an investment cost is given in dollars, a conversion factor (from $ to ) of 0.83 is considered. Figure demonstrates that most expensive items are SOFC (67%) and gasifier (18.5%). Component PEC [ ] DC [ ] Total investment cost [ ] Dryer Gasifier Gasification Pre-Heater Steam generator

116 Steam blower Gas cleaner Blower (woodg_blower) Anode preheater Blower (air_blower) Hybrid recuperator Cathode preheater SOFC Burner HRSG Turbine (turbine1) Generator (generator1) Turbine (turbine2) Generator (generator2) Condenser Pump (pump1) Deaerator Pump (pump2) TOT Table : purchase, direct and total investment costs for each component of the plant. Total investment cost of the plant is around 138 M ; SOFC total investment cost is around 94.6 M. Figure : total investment cost (%) of relevant components of the plant. 116

117 5.3.2 Ż CI k and Ż OM k calculation Ż CI k is calculated by means of equation Capital investment of the kth component (I k TOT ) is amortized in n-years by means of the annuity factor (f), given in equation 5.77; interest factor (qi) in equation 5.76 is calculated by means of the interest rate (int) and rate of inflation (r). (5.75); (5.76); (5.77). If annual operating hours are assumed, Ż CI k is given by equation Table provides the economic parameters assumed for calculations (ref. [16]). Parameter Quantity Operating hours, Hr 7000 [h/year] Interest rate, int 6 [%] Rate of inflation, ri 2 [%] Equipment lifespan, n 15 [years] Construction period, CP 1 [years] Table : economic parameters. (5.78). Maintenance and operating costs (Ż OM k) are considered by means of a maintenance factor (M), as shown in equation (5.79). A maintenance factor of 1.1 is assumed (ref. [16]). Ż k used in cost-balance equations are listed in Table Component Z [ /h] Dryer 9.52 Gasifier Gasification Pre-Heater 2.85 Steam generator 2.59 Steam blower Gas cleaner Blower (woodg_blower) 0.08 Anode preheater

118 Blower (air_blower) 0.79 Hybrid recuperator Cathode preheater SOFC Burner HRSG Turbine (turbine1) Generator (generator1) 3.35 Turbine (turbine2) Generator (generator2) 1.36 Condenser 0,20 Pump (pump1) 0.19 Deaerator 0.62 Pump (pump2) 2.07 Table : Ż k values for each component of the plant. 5.4 Results of thermoeconomic analysis Linear equation system Based on equations reported in Paragraphs 5.2, a linear system has been built up; solution is provided using EES (Engineering Equation Solver) Thermoeconomic parameters Two major exergoeconomic variables are used to evaluate and to optimize the performances of a component: the relative cost difference factor (Δr) and the exergoeconomic factor (f). The relative cost difference Δr k for the kth component is defined as: (5.80); where c P, k is the unit cost of fuel and c F, k is the unit cost of product for the kth component. Exergoeconomic factor f k for the kth component is defined as: (5.81). 118

119 The total cost rate causing the increase in the unit cost from fuel to product is given by the dominator in equation The exergoeconomic factor expresses as a ratio the contribution of the non-exergy related cost to total cost increase. A low value of this parameter (close to zero) suggest to decrease exergetic losses at the expense of a higher total cost of investment for the component; on the other hand, a high value (close to 1) suggest to decrease purchase equipment cost by enhancing the exergetic losses of the component. Suggested exergoeconomic factors for main components of energy systems are given in Table Component Suggested f k Heat exchangers Lower than 55% Compressors and turbines Between 35% and 75% Pumps Above 70% Table (ref. [17]). When a complex energy system is analyzed, optimization of one component by means of exergoeconomic factor might not lead to a more optimized system. Modifications may reflect negatively on other components; major attention should be paid to components that have high exergetic losses and investment costs Exergetic analysis of the plant Equations provided in Paragraph 5.1 allow to carry out the exergetic analysis of the plant. Exergy in each node of the plant is given by DNA, destructions and losses are provided by EES. Full results are given in APPENDIX IV. Exergetic losses of each component, listed in Table and Figure , are calculated by means of equations 5.82, 5.83, (5.82); (5.83); (5.84). Major losses can be identified in the following equipments: - gasifier and burner: oxidation of a fuel requires the conversion of chemical energy into thermal energy; 119

120 - cathode preheater: difference between fluegas and off gases temperature profiles is high (ΔT in = 182 C, ΔT out = 180 C); since fluegas and SOFC air mass flow is also high, exergy destruction affects more on global losses; - hybrid recuperator: in addition to the exergy destruction, due to the off gases high mass flow and temperature (90 C) other exergy is lost. Component ε D [%] ε L [%] ε D+ ε L [%] Gasifier Cathode preheater Burner Hybrid recuperator HRSG Condenser SOFC Others Table : main components wasted exergy. Figure : main components wasted exergy. Exergetic efficiency of the plant can be calculated by means of equations 5.85 or

121 (5.85); (5.86). Both equations provide an exergetic efficiency of 50% Price of electricity power Linear system solution provides the unit costs of the electric power produced by the SOFC and by the high and low pressure turbine. Simulations were run with a fixed woodchips price of 165 /ton. Three different combinations of SOFC auxiliary equation are considered (Paragraph ). Table asserts that average price of electricity for case A), B) and C) does not vary significantly. Case Component C [ /h] c [ /kwh] Ė [kw] Price of electricity [ /kwh] A) SOFC HPT LPT B) SOFC HPT LPT C) SOFC HPT LPT Table : main results and electricity price for case A), B) and C). Figure shows that case B, C have a lower steam turbines electricity price than case A; on the other hand, in those case, a higher SOFC electricity price is encountered. 121

122 Figure : electricity price of SOFC, HPT and LPT for case A), B) and C). For a woodchips cost of 165 /ton, average price of electricity is around 0.45 /kwh. Further analysis about electricity price has been developed using equations provided by case A). Detailed equations and results are listed in APPENDIX IV (Table 1 and 2) Price of woodchips influence on electricity price If storage costs are neglected, price of woodchips varies from 21 to 165 /ton (Paragraph 1.2). Price of wood has been changed according to that range of values letting other parameters constants. Since this approach is based on the solution of a linear system, a linear correspondence between electricity price and cost of woodchips is expected. Figure confirms the awaited trend. 122