Basic Thermodynamics and System Analysis for Fuel Cells

2 nd Joint European Summer School on Fuel Cell and Hydrogen Technology Crete, 17 th 28 th Sept. 2012 Basic Thermodynamics and System Analysis for Fuel Cells Prof. Dr. Robert Steinberger-Wilckens Centre for Hydogen & Fuel Cell Research University of Birmingham

Overview Basics of Thermodynamics Thermodynamics applied to fuel cells and electrolysis System analysis Thermodynamics & System Analysis Slide 2/61

A very brief Introduction to Thermodynamics Thermodynamics & System Analysis Slide 3/61

The Model Thermodynamic World Consider a volume and ist boundary: U Q, W T, p, V, m system variables: T temperature p pressure V volume m mass It has a given state of being, quantified by the inner energy state U. It exchanges activities with the surroundings by transporting mass and energy across the boundary. Thermodynamics & System Analysis Slide 4/61

Example Representation U Q, W T, p, V, m system variables: T temperature p pressure V volume m mass intake/release valves piston Ideal gas law: p V = n R T V Thermodynamics & System Analysis Slide 5/61

The 4 Laws of Thermodynamics 1. Existance of temperature ( 0 th Law) 2. Conservation of energy (1 st Law) 3. Definition of Entropy (2 nd Law) 4. Entropy at T = 0 (3 rd Law) Thermodynamics & System Analysis Slide 6/61

1 st Law of Thermodynamics Any change of inner energy U is balanced by the exchange of heat Q and work W U = Q + W or rather du = dq + dw Consequences: - conservation of energy, d U = 0 in isolated system - impossibility of perpetuum mobile of the first kind (delivering work) Thermodynamics & System Analysis Slide 7/61

Steady State and Transitions Strictly speaking, all thermodynamic laws are only valid in the steady state (equilibrium). A transition from one state to another must therefore be calculated in infinitesimal steps. These are assumed to be in balance. Between two states at times t 1 and t 2 going through a transition, a process takes place. If the process can be reversed and the state at t 1 be achieved again, the process is reversible. Thermodynamics & System Analysis Slide 8/61

2 nd Law of Thermodynamics Every system possesses a property S (entropy) that can be calculated from d S = d Q / T In irreversible processes d S d Q / T Consequences: - creation of entropy, - impossibility of perpetuum mobile of the second kind (converting heat to work) Thermodynamics & System Analysis Slide 9/61

1 st + 2 nd Law of Thermodynamics Combining we get d U = d W + d S T or d W = d U - d S T or ΔH = ΔG + T ΔS ΔG = ΔH - T ΔS with H. enthalpy G. free enthalpy or Gibb s energy Thermodynamics & System Analysis Slide 10/61

Thermodynamic Machines The relevant thermodynamic processes can mostly be considered as circular processes or machines. p A S A D B D B C C V T Thermodynamics & System Analysis Slide 11/61

The Carnot Machine: Volume Reaction 1. isothermal compression 2. adiabatic compression 3. isothermal expansion 4. adiabatic expansion Thermodynamics & System Analysis Slide 12/61

The Carnot Machine (2) heat source T 1 Q 1 Q 2 heat sink T 2 work efficiency: η c = W / Q 1 from Q 1 - Q 2 - W = 0 (1 st Law) and ds = dq / T (2 nd Law) it follows that η c = 1- T 2 / T 1 Thermodynamics & System Analysis Slide 13/61

Fuel Cell Principle: Surface Reaction Surplus fuel Surplus air + H 2 O Electrolyte H + O 2 (air) H 2 porous anode porous cathode Thermodynamics & System Analysis Slide 14/61

Hydrogen Production: Electrolysis Splitting of water by electric current Cathode side 2H 2 O + 2e - H 2 + 2OH - Anode side 2OH - 1/2 O 2 + H 2 O + 2e - Overall reaction H 2 O H 2 + 1/2 O 2 F... Faraday constant = 96.587 C/mol 2F Question: Definition of cathode and anode? Thermodynamics & System Analysis Slide 15/61

Electrolysis Thermodynamics 2F H 2 O -----> H 2 + 1/2 O 2 Free enthalpy It follows that ΔG o = 237 kj/mol (at 25 C, 1 bar = standard conditions) = 2F U o o U o o = 1,23 V which is the voltage necessary for water splitting (ideal case at standard conditions). Thermodynamics & System Analysis Slide 16/61

Electrolysis Overpotential Due to kinetic processes and competition of ion reactions at the electrodes the technically necessary Voltage for electrolysis is considerably higher, generally at the order of 1,7 to 1,9 V. The ideal amount of energy needed per Nm³ H 2 is ΔG o / V N = 237 kj/mol / 22,41 l/mol = 3 kwh/nm³ Standard electrolysers require about 4,2 to 4,8 kwh/nm³ Question: lower or higher heating value? (LHV or HHV) Thermodynamics & System Analysis Slide 17/61

Electrolysis Temperature Dependency Due to the relationship Δ G o = Δ H o - T ΔS The energy for splitting water can also be supplied by heat, not only electricity. Graphics from Winter/Nitsch,1988 Thermodynamics & System Analysis Slide 18/61

Gibbs free energy for H 2 - O 2 reaction Form of water product Temperature [ C] G [kj/mol] Liquid 25-237,2 Liquid 80-228,2 Gas 80-226,1 Gas 100-225,2 Gas 200-220,4 Gas 400-210,3 Gas 1000-177,4 U o [V] 1,23 1,18 1,17 1,14 1,09 0,92 Other fuels Temperature [ C] G [kj/mol] Methanol 25-698,2 Methane 25-802,7 Alkali (battery) 25-277 U o [V] 1,21 1,04 1,44 Thermodynamics & System Analysis Slide 19/61

Generating Entropy? Loosing Energy? T = 0 ΔH = ΔG vibrational energy T > 0 ΔH = ΔG + TΔS consequence: - less energy needed for electrolysis - less energy reclaimed in fuel cell Thermodynamics & System Analysis Slide 20/61

Electrode Definition e - + - e - Where are cathode and anode? Electrolysis 2 H 2 O 1/2 2 OH - H 2 O 2 reverse reaction: Fuel Cell (=battery!) e e - - - + H 2 O 2 OH - H 2 1/2 O 2 Thermodynamics & System Analysis Slide 21/61

Reaction Equilibrium: Fuel Cell Case Cathode side Anode side 1/2 O 2 + H 2 O + 2e - 2 OH - H 2 + 2 OH - 2 H 2 O + 2e - Overall reaction H 2 + 1/2 O 2 H 2 O U o (open circuit) is identical to that of electrolysis (but negative!) ΔG o = 2F U o o = -237 kj/mol (at STP, for H 2 - O 2 cell) U o o = 1,23 V (for convenience, U is not marked as negative) i.e. energy is released. Thermodynamics & System Analysis Slide 22/61

Schematic Voltage Characteristics: Electrolysis and Fuel Cell U [V] electrolysis I * R i internal resistance due to non-ideal conductibility resulting in heat produced a.o. U o o (T) fuel cell I * R i I * R e work delivered to external circuit I [A] Thermodynamics & System Analysis Slide 23/61

Fuel Cell Efficiency 1. Efficiency = useful output / total input η = Q el / - ΔH 2. Ambiguity: HHV or LHV? 3. Maximum possible efficiency (thermodynamic efficiency) η = ΔG / ΔH assuming that all change in Gibbs free energy can be transformed to electricity alternative: η = U / U o o (since U = - ΔH / 2F) Compare to Carnot efficiency (T 1 - T 2 ) / T 1 (T 1,2 in [K]) and Betz efficiency (58%) Thermodynamics & System Analysis Slide 24/61

Maximum Efficiency as Function of Temperature Form of water product Temperature [ C] G [kj/mol] U o [V] η Liquid 25-237,2 Liquid 80-228,2 Gas 80-226,1 Gas 100-225,2 Gas 200-220,4 Gas 400-210,3 Gas 1000-177,4 1,23 83% 1,18 80% 1,17 79% 1,14 77% 1,09 74% 0,92 62% Thermodynamics & System Analysis Slide 25/61

Some Fuel Cell Principal Properties 1. not limited by Carnot efficiency (~ (T 1 -T 2 )/T 1 ), only by electrochemical, kinetic and ohmic losses 2. modular 3. low noise 4. exhaust emission predominantely water (and maybe CO 2 ) 5. no moving parts ergo: efficient and low-emission energy conversion technology Thermodynamics & System Analysis Slide 26/61

Increasing Efficiencies 1 0,9 0,8 eta 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 η c = 1- T 2 / T 1 T 2 = 273 K eta 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 373 573 773 lim T 1 -> 973 1173 T1 [K] 1373 1573 0,1 1773 0 0,6 1973 0,65 0,7 0,75 0,8 0,85 0,9 0,95 1 lim T 2 -> 0 U(jo) lim U -> U o o Thermodynamics & System Analysis Slide 27/61

High Efficiency Electricity Production Efficiency /% 70 SOFC 60 GUD - Power Plant 50 Fuel Cells PAFC 40 Steam Power Plant 30 Diesel Engine Gasturbine 20 Spark-Ignition Engine 10 0 0,1 0,5 1 5 10 50 100 500 1000 Upper Limiting Curve: Future Technology. (Development tendency: GT / GUD: 2000 ; SOFC: 2010). Lower Limiting Curve: Actual Technology. Power Plant Capacity / MW Thermodynamics & System Analysis Slide 28/61

An Introduction to Energy and Efficiency Thermodynamics & System Analysis Slide 29/61

Overview of Indicators Efficiency * of a single process * of a process chain * of energy services Primary energy consumption * direct * cumulative energy Fossil energy consumption Direct emissions Direct & indirect emissions (LCA) Energy payback (harvest factor) Externalities Thermodynamics & System Analysis Slide 30/61

Energy Efficiency Definitions = (desired) energy output / (necessary) energy input conventional: energy input given as lower heating value (LHV) result (example): out of 1 Nm³ of natural gas equivalent to 10 kwh, 1 kwh is disregarded reason: 10% of the combustion energy is contained in the exhaust gas as water vapour and not sensible heat is calculated approx. 10% higher than corresponds to the factual chemical energy content of the fuel Thermodynamics & System Analysis Slide 31/61

Energy Efficiency Definitions /2 correct (but unconventional): energy input given by higher heating value (HHV) corresponds to the factual chemical energy content of the fuel and gives the full picture of the conversion technology = energy output / energy input (HHV) Thermodynamics & System Analysis Slide 32/61

Efficiency and Efficiency Chains Conventional boiler 1 PE CO CO 2 NO x LHV = 0,90 UE (heat) HHV = 0,81 UE (heat) PE primary energy UE useful energy CO combustion Condensing boiler 1 PE CO CO 2 LHV = 1,05 UE (heat) HHV = 0,95 UE (heat) therm = 105 % LHV therm = 95 % HHV Thermodynamics & System Analysis Slide 33/61

Efficiency and Efficiency Chains /2 Coal or Nuclear power plant 1 PE EG 0,33 UE PE primary energy UE useful energy EG electricity generation CO 2 NO x Combined Cycle power plant 1 PE EG 0,42 UE CO 2 NO x Renewable Energy power plant EG 1 UE ( = 1 PE) Thermodynamics & System Analysis Slide 34/61

Efficiency and Efficiency Chains /3 Average German Electricity Grid 1 PE EG 0,33 UE PE primary energy UE useful energy EG electricity generation CO 2 NO x Gas Engine CHP 1 PE CHP CO 2 NO x 0,3 UE electricity reference case 0,6 UE heat 0,7 PE 0,91 PE = 1,61 PE condensing boiler electricity grid Thermodynamics & System Analysis Slide 35/61

Efficiency and Efficiency Chains /4 PE UE FC FP primary energy useful energy fuel cell fuel processing Natural Gas PEFC Residential System 1 PE η = 0,85 FP CO 2 η = 0,87 H 2 O FC 0,34 UE electricity reference case 0,41 UE heat 0,43 PE 1,03 PE = 1,46 PE cond. boiler electricity grid Natural Gas SOFC Residential System 1 PE η = 0,80 FC H 2 O CO 2 0,33 UE heat 0,50 UE electricity reference case 0,35 PE 1,51 PE = 1,86 PE cond. boiler electricity grid Thermodynamics & System Analysis Slide 36/61

Efficiency and Efficiency Chains /5 PE UE EG FP CH primary energy useful energy electricity generation fuel processing compressed hydrogen 1 PE Hydrogen Fuel cell, grid electricity η = 0,35 EG η = 0,67 ELY η = 0,85 (CH) FP η el = 0,45 FC 0,08 UE CO 2 NO x O 2 H 2 O Hydrogen Fuel cell, wind energy 1 PE η = 0,67 ELY η = 0,85 (CH) FP η el = 0,45 FC 0,27 UE O 2 H 2 O Thermodynamics & System Analysis Slide 37/61

Efficiency and Efficiency Chains /6 Internal combustion motor 1 PE η = 0,9 FP η = 0,15 ICE PE primary energy UE useful energy EG electricity generation ICE internal combustion engine FP fuel processing CH compressed H 2 LH liquid H 2 0,13 UE (propulsion) CO 2 NO x CO H 2 Internal combustion motor, grid electricity 1 PE η = 0,35 EG η = 0,67 ELY η = 0,85 (CH) FP η = 0,15 ICE 0,024 UE CO 2 NO x O 2 H 2 O NO x η = 0,1 (LH) 0,004 UE Thermodynamics & System Analysis Slide 38/61

Efficiency and Efficiency Chains /7 1 PE H 2 FC vehicle, grid electricity η = 0,35 EG η = 0,67 ELY η = 0,85 (CH) FP PE primary energy UE useful energy EG electricity generation FC fuel cell FP fuel processing CH compressed H 2 η = 0,40 FC 0,08 UE CO 2 NO x O 2 H 2 O H 2 FC vehicle, wind energy 1 PE η = 0,67 ELY η = 0,85 (CH) FP η = 0,40 FC 0,23 UE O 2 H 2 O Thermodynamics & System Analysis Slide 39/61

Efficiency and Efficiency Chains Coal or Nuclear power plant + grid 1 PE EG 0,33 UE PE primary energy UE useful energy EG electricity generation FP fuel processing ICE internal combustion engine CO 2 NO x Internal combustion engine 1 PE η = 0,9 FP η = 0,15 ICE 0,13 UE (propulsion) CO 2 NO x CO Thermodynamics & System Analysis Slide 40/61

Combined Heat and Power (CHP) Condensing boiler Electricity grid Water supply Natural gas Hot water storage tank use of waste heat from electricity generation for heating purposes etc. Fuel Cell (CHP) Thermodynamics & System Analysis Slide 41/61

SenerTec Dachs Hot water storage and buffer photographs courtesy SenerTec Thermodynamics & System Analysis Slide 42/61

Micro-CHP Stirling engine insulation gearbox cylinder cooling heater graphics courtesy KWB Thermodynamics & System Analysis Slide 43/61

Efficiency and Efficiency Chains /2 Gas Engine CHP 1 PE CO 2 η = 0,90 CHP NO x 0,3 UE electricity PE primary energy UE useful energy EG electricity generation reference case 0,6 UE heat 0,7 PE 0,91 PE = 1,61 PE condensing boiler electricity grid Natural Gas SOFC Residential System 1 PE η = 0,83 FC H 2 O CO 2 0,33 UE heat 0,50 UE electricity reference case 0,35 PE 1,51 PE = 1,86 PE cond. boiler electricity grid Thermodynamics & System Analysis Slide 44/61

CHP Unit Efficiencies 70% 65% Electrical thermal efficiency 60% 55% 50% 45% 40% 35% 300 MW 30% 25% 0 2 4 6 8 10 12 14 16 Electrical power output [MWe] graph courtesy of RollsRoyce FCS Thermodynamics & System Analysis Slide 45/61

Efficiency and Efficiency Chains /3 1 PE H 2 FC vehicle, grid electricity η = 0,35 EG η = 0,67 ELY η = 0,85 (CH) FP PE primary energy UE useful energy EG electricity generation FC fuel cell FP fuel processing CH compressed H 2 η = 0,40 FC 0,08 UE CO 2 NO x O 2 H 2 O H 2 FC vehicle, wind energy 1 PE η = 0,67 ELY η = 0,85 (CH) FP η = 0,40 FC 0,23 UE O 2 H 2 O Thermodynamics & System Analysis Slide 46/61

Vehicle Requirement Profile New European Driving Cycle example source: EU Thermodynamics & System Analysis Slide 47/61

CUTE Results: Total system efficiency source: CUTE Thermodynamics & System Analysis Slide 48/61

Change in On-Board E-Power Generation Today: 100% 20 25%* 50 70% (Generator) 70 90 % (KSG) 10 17% 14 22 % * Average efficiency Future: 100% 35 50% (FC-APU) 35 50% Graph: BMW Thermodynamics & System Analysis Slide 49/61

Cumulative Energy: Definitions b = total chain energy efficiency = (end) energy output / (primary) energy input Energy input includes all input, i.e. not only for operating the system, but also for building it. EF = energy harvest factor = energy output / fossil energy input Thermodynamics & System Analysis Slide 50/61

Cumulative Energy: NG Steam Reforming primary energy b = UE / Σ E input natural gas supply production appliances NatGas steam reforming appliances, transport national distribution source: FfE Thermodynamics & System Analysis Slide 51/61

Cumulative Energy: PV-Hydrogen production PV panels insolation PV Africa appliances, demin water electricity electrolysis appliances appliances, transport pipeline transport national distribution source: FfE Thermodynamics & System Analysis Slide 52/61

LCA Elements Definition of boundaries Thermodynamics & System Analysis Slide 53/61

LCA Procedure Analysis of all process steps involved Cumulation of all specific emission and impact factors, i.e. kg CO 2 / kwh energy kg CO 2 / kg of building material kg SO 2 / kwh energy etc. Detail given by inclusion or omission of secondary, tertiary etc. sources (system boundary). Goal: Comparison of base case with alternative variants Thermodynamics & System Analysis Slide 54/61

Well-to-Wheel Analysis (1) CO 2 equiv. per 100 km 700 600 [kgco2 eq. / 100 km] 500 400 300 200 Fahrzeug Vehicle Treibstoff Fuel 1. MeOH reforming 2. NG reforming 3. Grid electr. 4. Wind energy 5. Green electr. 6. Hydro 100 0 Referenz: Diesel 1. Methanol- Rreformierung 2. Erdgas- Reformierung 3. Netzstrom 4. Wind Energie 5. Grüner Strom 6. Wasserkraft FC vehicle, various hydrogen production paths, base case: Diesel Thermodynamics & System Analysis Slide 55/61

Well-to-Wheel Analysis (2) Fossil fraction of energy Fossiler fossil Anteil fraction Erneuerbarer renewable Anteil fraction 100% 80% 60% 1. MeOH reforming 2. NG reforming 3. Grid electr. 4. Wind energy 5. Green electr. 6. Hydro 40% 20% 0% Referenz: Diesel 1. Methanol- Rreformierung 2. Erdgas- Reformierung 3. Netzstrom 4. Wind Energie 5. Grüner Strom 6. Wasserkraft FC vehicle, various hydrogen production paths, base case: Diesel Thermodynamics & System Analysis Slide 56/61

Total Balance of Conversion: kg CO 2 / kwh alternative biogas X kg CO 2 / kwh NG producing electricity and heat example: natural gas drivenchp unit (engine or fuel cell) reference kg CO 2 / kwh electricity from grid kg CO 2 / kwh balance kg CO 2 / kwh conventional heating Thermodynamics & System Analysis Slide 57/61

Internal versus External Costs examples for vehicle traffic Internal costs: costs of production and delivery of vehicles and fuels taxes and levys market price (as a sum of the above plus company profit) External costs costs caused for the society, but not attributed or attributable to single products or services health services due to environmental pollution health and other services due to noise pollution public services in safety, accident prevention etc. general costs of land use, rain run-off management etc. Thermodynamics & System Analysis Slide 58/61

Including External Costs ext. costs 17,47 Internal costs / market price H 2 3:2 ext. costs 5,12 3:1 Diesel Thermodynamics & System Analysis Slide 59/61

External Costs of Electricity Generation source: DLR Thermodynamics & System Analysis Slide 60/61

Thanks for your Attention! Any Questions? Thermodynamics & System Analysis Slide 61/61