Non conventional forms of energy and batteries

A fuel cell is an electrochemical device that converts the chemical energy of a fuel (hydrogen) and an oxidant (oxygen from air) directly into electricity, with water and heat as by-products. It works continuously while fuel is supplied, unlike a battery that stores its reactants.

PEM fuel cell

   H2 -->|anode |  PEM   |cathode|<-- O2/air
         |  Pt  |  H+ -> |  Pt   |
         |      |        |       |
   e- <--+------+        +-------+--> e-
            external load (current)
   unused H2 out         H2O + heat out

Reactions

• Anode: $H_2 \rightarrow 2H^+ + 2e^-$
• Cathode: $\tfrac{1}{2}O_2 + 2H^+ + 2e^- \rightarrow H_2O$
• Overall: $H_2 + \tfrac{1}{2}O_2 \rightarrow H_2O$

Hydrogen is split on the platinum catalyst at the anode. The proton exchange membrane (Nafion) passes only H⁺ ions to the cathode, so electrons travel through the external circuit and do useful work. At the cathode, protons, electrons and oxygen form water. Typical cell voltage is 0.6–0.8 V under load, so cells are stacked in series. The operating temperature is 60–80 °C.

Advantages

High efficiency (40–60 %), silent, no moving parts, near-zero emission at the point of use, quick start and modular size.

Types of fuel cells

(a) Reversible voltage and efficiency

Two electrons are transferred per H₂ molecule ($n = 2$).

$$E_{rev} = \frac{-\Delta G}{nF} = \frac{237\,200}{2(96\,485)} = 1.229\ \text{V}$$ $$\eta_{th,max} = \frac{\Delta G}{\Delta H} = \frac{237.2}{285.8} = 0.830 \;(83\ \%)$$

(b) Stack power and voltage efficiency

$$V_{stack} = 50 \times 0.65 = 32.5\ \text{V}, \qquad P = V I = 32.5 \times 40 = 1300\ \text{W}$$ $$\eta_V = \frac{0.65}{1.229} = 0.529 \;(52.9\ \%)$$

Efficiency on the basis of the HHV: $\eta = \dfrac{0.65}{285\,800/(2 \times 96\,485)} = \dfrac{0.65}{1.481} = 43.9\ \%$.

(c) Hydrogen consumption (Faraday's law)

$$\dot n_{H_2} = \frac{N I}{nF} = \frac{50 \times 40}{2 \times 96\,485} = 0.01036\ \text{mol/s}$$ $$\dot m = 0.01036 \times 2.016 = 0.02090\ \text{g/s} = 75.2\ \text{g/h} = 0.0752\ \text{kg/h}$$

(d) Heat generated

Total energy released at the HHV voltage 1.481 V per cell:

$$Q = N I (1.481 - 0.65) = 50 \times 40 \times 0.831 = 1662\ \text{W}$$

Answer: $E_{rev} = 1.229$ V, $\eta_{max} = 83\ \%$; $P = 1.30$ kW, $\eta_V = 52.9\ \%$ (43.9 % on HHV); H₂ use $= 0.0752$ kg/h; heat $\approx 1.66$ kW.

Hydrogen is not free in nature; it is an energy carrier made from water or hydrocarbons, so its cleanliness depends on the source of energy used.

1. Steam methane reforming (SMR)

Natural gas reacts with steam over a nickel catalyst at 700–900 °C, 3–25 bar:

$$CH_4 + H_2O \rightarrow CO + 3H_2 \quad (\text{endothermic})$$

Then the water-gas shift reaction at 200–400 °C: $CO + H_2O \rightarrow CO_2 + H_2$. Pressure swing adsorption purifies H₂. About 95 % of industrial hydrogen is made this way (efficiency 70–80 %), with CO₂ emission of about 9–10 kg per kg H₂ ("grey hydrogen"; with carbon capture it is "blue").

2. Water electrolysis

Direct current splits water:

• Cathode: $2H_2O + 2e^- \rightarrow H_2 + 2OH^-$
• Anode: $2OH^- \rightarrow \tfrac{1}{2}O_2 + H_2O + 2e^-$
• Overall: $H_2O \rightarrow H_2 + \tfrac{1}{2}O_2$

Types: alkaline, PEM and solid oxide electrolysers. Needs about 50–55 kWh of electricity per kg of H₂. With electricity from hydro, solar or wind the product is "green hydrogen" of very high purity (above 99.9 %).

3. Gasification

Coal or biomass is heated with limited oxygen and steam at 800–1500 °C to form syngas (CO + H₂), which is shifted and purified. Suitable where coal or biomass is cheap; coal gasification gives high CO₂ emissions.

Comparison

Other methods

Thermochemical cycles (sulphur-iodine) with high-temperature nuclear or solar heat, photo-electrochemical and biological (algae) production are under development.

Hydrogen has a high energy per kg (120 MJ/kg lower heating value) but a very low density (0.084 kg/m³ at normal conditions), so storage is the main difficulty.

Storage methods

Infrastructure

• Production: electrolysers with renewable power, SMR or gasification units; water supply; purification.
• Compression and storage: compressors, high-pressure tanks, cryogenic tanks, cavern storage.
• Transport: tube trailers, liquid tankers, dedicated pipelines or blending into natural gas pipes (limit about 10–20 %).
• Utilisation: refuelling stations for fuel cell vehicles, fuel cell power systems, hydrogen burners, industry (ammonia, refining, steel).
• Standards: codes, trained staff, leak detectors.

Safety

Hydrogen is colourless and odourless, leaks easily through small gaps, has a wide flammable range (4–75 % in air), very low ignition energy (0.02 mJ) and burns with an invisible flame; it also embrittles steels. So good ventilation, hydrogen sensors, flame detectors and approved materials are required.

(a) Battery fundamentals

• Primary cell: chemical reaction is irreversible; used once and thrown away (zinc-carbon, alkaline).
• Secondary cell: reaction can be reversed by passing charging current; rechargeable (lead-acid, Ni-Cd, Ni-MH, Li-ion).

Terms

• Capacity (Ah): charge a battery can deliver at a specified rate from full to cut-off voltage. Energy = capacity × voltage (Wh).
• C-rate: discharge current expressed as a multiple of capacity; 1C for a 100 Ah battery is 100 A, 0.1C is 10 A.
• Depth of discharge (DoD): percentage of capacity used. Deeper discharge shortens life.
• Energy density: energy stored per unit mass (Wh/kg) or volume (Wh/L).

(b) Battery bank sizing

Energy to be stored (autonomy): $1.2 \times 2 = 2.4$ kWh = 2400 Wh.

$$C = \frac{E \times \text{days}}{DoD \times \eta \times V} = \frac{1200 \times 2}{0.50 \times 0.85 \times 12} = \frac{2400}{5.1} = 470.6\ \text{Ah}$$

Answer: about 471 Ah at 12 V, so a bank of 500 Ah (for example, five 100 Ah, 12 V batteries in parallel) is selected.