@Cesar Jung-Harada : [@November 21, 2023]: I NEED TO REDO MANY CALCULATION! Please dont use new calculations as reference now (if you need, let me know and I finish this. As I learn more I discover some subtleties that are too important to ignore.
The energy density (volumetric) is NOT the specify heat value (energy released by a chemical reaction like combustion). For instance, *energy density* considers the potential work that the gas does as it expands at a certain pressure.

”There are different types of energy stored in materials, and it takes a particular type of reaction to release each type of energy. In order of the typical magnitude of the energy released, these types of reactions are: nuclear, chemical, electrochemical, and electrical. “. (https://en.wikipedia.org/wiki/Energy_density).

I need to make sure the values used for comparison consider the reactions involved in the combustion processes (for H2 or LPG), that is the **heat value also called energy value (omitting “combustion” hence the confusion with energy density)** and I think I have made some mistakes (also misguided by errors online) using gravimetric energy density sometimes. Fortunately, the previous calculations are ok, because I used heat value for **LPG (46-51 MJ/kg) and H2 (120-142 MJ/kg), **but the new comparison with Natural Gas (pakistan bags) is wrong. I’ll work on this by the end of the week.

# INTRODUCTION (basic thermodynamic notions/definitions)

**Specific energy**or**massic energy**is energy per unit mass. It is also sometimes called**gravimetric energy density**, which is not to be confused with energy density, which is defined as energy per unit volume. It is used to quantify, for example, stored heat and other thermodynamic properties of substances such as specific internal energy, specific enthalpy, specific Gibbs free energy, and specific Helmholtz free energy. It may also be used for the kinetic energy or potential energy of a body. Specific energy is an intensive property, whereas energy and mass are extensive properties.The heat value of a fuel is the amount of heat released during its**Heat Values (useful to compare fuels).****combustion**. Also referred to as energy or calorific value, heat value is a measure of a fuel's energy density, and is expressed in energy (joules) per specified amount (*e.g.*kilograms).

# A) Liquefied Petroleum Gas: basics

Liquefied Petroleum Gas (LPG) is a by-product of natural gas extraction and crude oil refining. LPG is a mixture of hydrocarbon gases, the most common being butane and propane.[1]

“L”PG at atmospheric pressure and temperature is a gas which is 1.5 to 2.0 times heavier than air. It is readily liquefied under moderate pressures. The density of the liquid is approximately half that of water and ranges from 0.525kg/L to 0.580kg/L @ 15 C (0.51kg/L for propane, 0.58kg/L for butane). At room temperature, “L”PG is a colorless and odorless non-toxic gas.

**Under modest pressure or cooler conditions, it transforms into a liquid state. **This process leads to the reduction of the volume to 1/250 of the gaseous aggregate state and allows to store and transport LPG easily in cylinders.

LPG is heavier than air (**propane is one and a half times heavier than air**) and can therefore accumulate above the ground. This may lead to LPG-’lakes’ that potentially can causes explosions. A foul smelling odorant is added to help detect leaks and thus reduce the risk of explosion.

__Density (____liquid____PG):__**500g/L**(1 kg of LPG is 1.96 liters. More precisely, 0.493 g/cm³ or 493g/L).__Heat value (combustion):__**46-51 MJ/kg (12.8-14.2 kWh/kg)**__Volumetric energy density:__**25MJ/L (6.9 kWh/L)**- Liquid propane at room temperature (21° C) has to be held in a tank at a pressure of about
**850 kPa (8.5bars)** - Mostly liquified
**propane and butane** - Liquefaction reduces volume about
**250 times.**

**LPG has a typical specific calorific value (= combustion energy density per kg) of 46.1 MJ/kg compared with 42.5 MJ/kg for fuel oil and 43.5 MJ/kg for premium grade petrol (gasoline). **It can vary depending on its specific composition, but **a common value used for energy content of LPG is around ****46 MJ/kg**** (megajoules per kilogram) or equivalently, 46/3.6 kWh/kg = ****12.8kWh/kg **(1 kWh = 1000J/s*3600s = 3.6MJ). In real-world conditions, the actual usable energy obtained can be lower due to inefficiencies in the combustion process. The efficiency of the appliance or engine that is using the LPG can also have a significant impact on the actual usable energy. For instance, a **heating appliance might be 80-90% efficient, while an internal combustion engine might only be 20-30% efficient**. So, the usable energy from 1 kg of LPG could be considerably less than 46 MJ, depending on the specific conditions and applications.

**However, when doing the comparison with H2 combustion we will assume the same combustion losses, so we can use these numbers as a reference for the energy in an LPG canister.**

# B) Hydrogen energy & storage: basics

of liquid hydrogen:__Energy per kilogram__**120MJ/kg or 33.33kWh/kg**assuming perfect combustion. By comparison, petrol and diesel only hold only about 12 kWh/kg. Hydrogen has an energy-density-per-unit mass that is approximately three times higher than traditional fuel (from**here**and here). Note that this is a kg, so it’s irrelevant if this is liquid or gaseous.

(weight per unit volume):**Density of liquid hydrogen****71g/L**- The density of LPG liquid is 0.493 g/cm³ at 25 °C (77 °F), or
**493g/L (it is much more dense, which explains why despite having a greater heat value, for the same canister****size****, H2 has less energy that LPG)** - Water is 0.997g/cm3 or 997/L, that is about 1kg/L.

Hydrogen turns into a liquid when it is cooled to a temperature below -252,87 °C. At -252.87°C and 1.013 bar. Liquid hydrogen has a density of close to 71 kg/m3 or 71000g/10^6cm3 = 0.071g/cm3 or 71g/L)

For comparison:

**Volumetric energy density**hydrogen (usable assuming perfect combustion):**liquid**- So the energy per liter of liquid hydrogen is 120MJ/14.1L =
**8.57****MJ/L or****2.38kWh/L**(dividing by 3.6) (Also verified here: “*Pressurised hydrogen contains about 0.5 kWh/litre at**200 bar**, 1.1 kWh/litre at 500 bar and 1.4 kWh/litre at 700 bar. The best way of transporting hydrogen in terms of energy density is liquid hydrogen, achieving more than***2.3 kWh/L***”***)**

From the above, 1kg of liquid hydrogen corresponds to 1000g/(71g/L) = 14.1L

__Storing H2 (liquid, cryo-compressed, pressurized, and ambient pressure)__

__1) Liquid and Cold/Cryo compressed hydrogen storage (see above)__

Liquid hydrogen is made possible by cryogenically cooling it to * below its boiling point, -253 ◦C*.

**At atmospheric pressure**(about 1 bar):**it requires cryogenic temperatures, as the boiling point for hydrogen is −252.8°C.**At this pressure, d**ensity is**close to 71 kg/m3.**1 kg of hydrogen can be stored in a 15-liter tank**. In order to maintain liquid hydrogen at this temperature, tanks must be perfectly isolated. Liquid hydrogen tanks typically operate at pressures up to 850 kPa (that is 8.5 bar or 123 psi).**Cryo/Compressed:**Hydrogen (gaseous state) has to be kept under pressure, and at very low temperatures, typically at**350 bar (5,000 psi) and 700 bar (f**rom here). This is**about 690 bar, 10,000 psi, or 69MPa. “***At present time, the most promising hydrogen storage options are compressed hydrogen at 35 MPa (5kpsi) and 70MPa (10kpsi), at the temperature of 20 degrees Kelvin or -253.15 ℃)*” (from here)

**Maintaining cryogenic temperatures is beyond the scope of our project. So this option must be discarded.**

__2) Compressed hydrogen at ambient temperature ____(____this is what we want to do, we are not going to add any cooling system!)__

We plan to produce H2 at atmospheric pressure (sea level), and then compress manually (car tire pump).

- A s
**mall-sized car are usually 30 psi, medium-sized cars are 36 psi, and large cars are 42 psi**. Let’s assume then 35psi (this is 241kPa, or**2.4 atm**or**2.1 bar**

__Note__: Could we produce that underwater? **yes, that would mean in a depth between 10 and 20 meters****. **

** Notes**:

# C) The “3KG LPG” Canister (pic on the right): basics

### a) Physical characteristics

- Diameter: 210mm / Height: 270mm / Volume:
**6.0L total** - Weight:
**3kg total.** - Working pressure:
**18bar**/ Test pressure: 34bar

### b) LPG content

Since 1kg of LPG is 1.96L and steel vessels are filled to 80–85% of their capacity to allow for thermal expansion of the contained liquid, in one canister we have:

**4.8L of LPG**(80% of 6L)**2.45kg of LPG**(4.8/1.96 kg = 2.45 kg).

### c) LPG canister energy content

**Reminder (see A)****: **Energy mass density:** ****46****-51 MJ/kg (****12.8****-14.2 kWh/kg) and ** volumetric energy density: **25MJ/L (6.9**** kWh/L)**

- 2.45kg x 12.8kWh/kg = 31.4kWh or 113MJ
- 4.8L x 6.9kWh/L = 33.1kWh or 119MJ

I will use the average:

**116MJ or 32.25kWh**of energy in one “3kg LPG canister”

A typical LPG cooking system is made up of a steel cylinder filled with LPG, a pressure controller, a tube connecting the cylinder to the pressure controller and the burner, and finally the burner itself.

### d) How many LPG canisters does an average Indonesian household uses per month?

The * average amount* of natural gas

*house is 12.39 m3/*

**per***(here). More practically:*

**month**- Active usage: ~3-4 hours of cooking every day —>
**uses 3-4 of 3kg canisters /month** - Light usage: ~1-2 hours of cooking every day —> 2 of 2kg canisters /month
- Regular household uses 1-2 of 12kg canisters (blue canister /month)

**4 x 3KG LPG canisters**

__ Note:__ How much energy does an average Indonesian household uses per month? (vehicle gas, electricity, gas for cooking)

Indonesia is total consumption is 256.74 billion kWh of electric energy per year. Per capita this is an average of **932 kWh, or 78kWh per month **(from here). Since the * average household* size in Indonesia is 3.8 people, this means 20.5 kWh per household/month (calculated from ).

**By comparision, the EIA aggregates data for the entire U.S. In 2021, the average annual electricity consumption for a U.S. home was 10,632 kilowatt-hours (kWh). Or about**

**886 kWh per month**. But this is not the average household consumption,

*it includes all the industry! Also, we need to consider demographics (the target population are not the richest.)*

### d) Bonus: breakout details (electricity, gas, etc)

** Note**: energy sources

As of 2022, the electricity consumption per capita in Indonesia amounted to around **1,173 kilowatt hours**. In the past few years, the government has been working to steadily increase the electrification rate in Indonesia

I did a google search, but this should be confirmed with locals.

As of 2022, the electricity consumption per capita in Indonesia amounted to around1,173 kilowatt hours.[Statista]

A kilowatt hour is **equivalent to a steady power of one kilowatt running for one hour** and is equivalent to 3.6 MJ (megajoules). Therefore in terms of energy the average consumption per capita is

The calculation for 1173 kilowatt hours is 31173 * 3.6 = **4222.8 MJ**

This means 83.32 canisters of 3kg, each one containing 4.8L. In litters it’s 83*4.8 = 398 L of LIQUIFIED LPG, or if gaseous: 389*250 = 97250L of propane (97.25 cubic meters)

# D) How many H2 canisters are equivalent to one LPG canister? (different pressure/containers)

### a) Example calculation: *mass of H2 contained in a canister of 6 litres, at a pressure of 17.5 bars and temperature of 25C*

Assuming that hydrogen gas behaves as an ideal gas under these conditions, the ideal gas law is a good starting point for this calculation. It relates the pressure, volume, and temperature of a gas to the number of molecules it contains. The ideal gas law is usually stated as:

`PV = nRT`

where P is the pressure, V is the volume, n is the number of moles, R is the ideal, or universal, gas constant, and T is the absolute temperature (in Kelvin).

Here, we want to find the mass of hydrogen gas (H2), so we'll need to convert from moles to grams using the **molar mass of hydrogen gas**.

First, let's convert the given values into SI units so we can use R=8.3145J/(mol.K):

- Pressure P: 17.5 bar = 1750000 Pa (since 1 bar = 100000 Pa),
- Volume V: 6 liters = 0.006 m³ (since 1 liter = 0.001 m³),
- Temperature T: 25 degrees Celsius = 298.15 K (since T(K) = T(C) + 273.15),
- Ideal gas constant R: 8.3145 J/(mol·K).

We can rearrange the ideal gas law to solve for n (the number of moles):`n = PV/RT`

Substituting the given values:

`n = (1750000 Pa * 0.006 m³) / (8.3145 J/(mol·K) * 298.15 K)`

≈ 4.24 mol.

The molar mass of H2 is approximately 2 g/mol (**2.016 g/mol)**, so the mass m of the hydrogen gas is:`m = n * molar mass`

. Substituting the values`m = 4.24 mol * 2 g/mol`

**8.48 grams.**

### b) Energy that can be released (assuming perfect combustion) by this quantity of hydrogen?

**Using Enthalpy:**

The energy released in the combustion of hydrogen is given by its heat of combustion. The heat of combustion (also known as the enthalpy of combustion) of hydrogen is about -286 kJ/mol. This value is negative because energy is released (exothermic process) during the combustion.

The heat of combustion (ΔH) is typically given per mole of substance combusted. So, to find the total energy released (E), we multiply the heat of combustion by the number of moles: `E = -ΔH * n`

We have around 4.24 moles of hydrogen in 6L at 25C and 17.5bars. Substituting the values:

`E = -(-286 kJ/mol) * 4.24 mol`

After doing the calculation, we find that E ≈ 1212.64 kJ.

Energy values can be converted from kilojoules (kJ) to kilowatt-hours (kWh) using the following conversion factor (1 kWh = 3600 kJ), so, to convert the energy released E (which we have found to be approximately 1212.64 kJ) to kWh, we divide by 3600: `E_kWh = 1212.64 kJ / 3600`

So, assuming perfect combustion, approximately **1.2MJ** (**0.337 kWh)** of energy can be released by this quantity of hydrogen. Please note that this calculation assumes a perfect combustion process, which may not be completely accurate in the real world due to factors such as heat loss to the surroundings.

**Using heat value in J/kg:**

The energy content of hydrogen per kilogram is **33.33 kWh/kg or 120kJ/kg**

Therefore if m=8.48g, the energy is ≈ 33.33kWh/kg*8.48/1000kg = **0.283kWh**

__ Using volumetric energy density:
__….it depends on the pressure. The values in (C) are for LIQUID hydrogen, so we cannot use this method here.

__the energy in the H2 canister (6L, 17.5bars, 25C) is about__

**Conclusion:****0.3 kWh**or

**1.08MJ**

### c) how many of these hydrogen filled canister (pressurized hydrogen) are needed to match ONE similar canister filled with *liquid* LPG?

- We saw that the energy stored in one such
**LPG canister is****116MJ or 32.25kWh**and an H2 canister at 17.5 bars contains 0.3kWh of energy, therefore:

**107.5 canisters**

__Notes: __

- These canisters should resist more pressure: they are tested and should sustain at least 34bars. At that pressure we need about 23 canisters… but obviously this is not safe.
- However, it is interesting to note that the output of the H2 electrolyser is about 35 bars. This means that LPG canisters are
*almost*good, but at their limit (no margin of security). - Other pressurized tanks can work though, like a scuba tank (see on the right). Assuming a typical tank (see on the right), having a usable volume of 11.1L and resisting well over 35bars (up to 232bars!), the number of tanks needed will be equal to:

107.5 * 17.5/232 * 6/11.1 = **4.38 scuba tanks **(@232bars, from a *typical scuba tank compressor*.)

…or if using the pressurized hydrogen coming from the electrolyser (35bars):

107.5 * 17.5/35 * 6/11.1 = **29 scuba tanks **(@35bars).

Note that this pressure is right at the limit of what the “3kg LPG” canister can withstand). Interestingly, the electrolytic cell we have can produce 15L of compressed hydrogen at 35 bar. That is about one and a half scuba tanks *per day*. In two days, the energy for the month can be produced and stored.

**Typical scuba tank: **

**Size (Volume)**: The volume of the most commonly used scuba tank for recreational diving is typically around 11.1 liters (or 0.0111 cubic meters). This is the so-called "Aluminum 80" tank, with "80" referring to its capacity in cubic feet under normal atmospheric pressure. It's important to note that this is not the physical volume of the tank, but the volume of air it can hold at atmospheric pressure.**Pressure**: Scuba tanks are also rated for a specific maximum pressure. The Aluminum 80 tanks are typically rated for a maximum pressure of about 200 bar or 20,000 kPa (kilopascal). High-pressure steel tanks can have a maximum pressure of up to 232 bar or 23,200 kPa, or even higher.**Physical Dimensions**: The physical dimensions of an Aluminum 80 scuba tank are typically about 66 cm in height and about 18.4 cm in diameter

# F) SUMMARIZING

Note: some entries are a little absurd (who will use a metal canister for storing gas at 1atm; also, a normal canister cannot sustain pressures>30bars). Only for having a sense of things. The relevant/meaninful entries in the tables are in BLUE

### A) Energy in a 6L (25C) canister depending on it’s content

Energy | Mass | Volume | |

Liquid LPG | 33.15 kWh (1) | 2.59 kg (2) | 4.8L (80% canister) |

Liquid H2 | 12.6 kWh (3) | 377g | 4.8L (80% canister) |

H2 & 1 bar | 0.018 kWh | 0.535g (4) | 6L (full canister) |

Compressed H2 & 17.5 bars | 0.283 kWh | 8.48g | 6L (full canister) |

Compressed H2 & 35 bars | 0.565 kWh | 16.96g | 6L (full canister) |

Compressed H2 & 200 bars | 3.23 kWh | 96.1g | 6L (full canister) |

### B) Quantity H2 canisters/balloons to substitute __one__ LPG canister (6L at 25C) at different pressures:

__Reminder:__ *LPG canister has 33.15 kWh of energy, equivalent to 33.15/33.33kg of hydrogen, or about **1kg of H2 (995 grams). *

Volume (L) | Yoga Ballons ( 221L, 1atm) | Big plastic bags (Pakistan video), V~2000L (2 cubic meters) | Canisters ( 6L) | Scuba tanks ( 11L) | |

Natural Gas (mostly methane*) | 3189 | 14 | 1.5 | 531.6 | 289 |

H2 & 1 bar | 11046 | 50 | 5.5 | 1841 (1) | 1004 |

Compressed H2 & 17.5 bars | 702 | not possible | not possible | 117 | 64 (4) |

Compressed H2 & 35 bars | 351 | not possible | not possible | 58.5 (barely possible) | 32 (5) |

Compressed H2 & 200 bars | 61.2 | not possible | not possible | 10.2 | 5.6 |

(*) Natural Gas is mostly methane. Methane has a slightly higher energy density than propane (and LPG is made of propane and methane mostly). Gravimetric energy density of Methane is ~ 55.5MJ/kg.

From a quick calculation using PV=nRT at ambient pressure (1atm) and temperature (25C), and considering that the mass of methane needed to produce the same usable energy in an LPG 3kg canister is 116MJ is equal to 116/55.5 = 2.09kg, and the molar mass of methane is approximately 16.04 g/mol (12.01 g/mol for carbon and 4.03 g/mol for hydrogen), corresponding to n = 2090g/16.04g = 130.3 moles:

V = nRT/P = 130.3 mol*0.0821 L·atm/(K·mol) * 298.15 K / 1atm = **3189 Liters **(note Avogadro constant in LITERS.atm/(K.mol))

Another way using energy density (volumetric):

- At standard pressure/temperature, Natural Gas has an energy density of 0,0364MJ/L (reminder: gaseous H2 energy density is

**Reminder: **

- Liquid LPG:
**116MJ or 32.25kWh**of energy in one “3kg LPG canister” - Liquid H2:

**(1)**LPG has a typical specific calorific value of

**46.1 MJ/kg or 12.8kWh**

**, but the usable energy is not that; f**or instance, a heating appliance might be 80-90% efficient, while an internal combustion engine might only be 20-30% efficient. If we ASSUME that the conversion efficiency for H2 combustion is similar, then it is ok to use 46.1MH/kg.

**(2)**Density of LPG is typically between 500 to 580 kg/m³ when stored under moderate pressure to keep it in liquid form

**. Let’s take 540g/L (average)**

**(3)** Liquid LPG is much more dense than liquid hydrogen, hence even though the energy density of hydrogen is bigger than LPG, for the same volume, liquid LPG stores slightly more energy. The density of __liquid__ hydrogen is **70.85 g/L**, while the *energy* density of liquid hydrogen is **120MJ/kg or 33.33kWh/kg
****(4) **1 kg of hydrogen gas occupies a volume of approximately 11,207 liters at STP. So in 6L there is a mass of hydrogen = 6L/11207L*1kg = 0.535g

**Energy released by chemical reactions (oxidation):**

### Big plastic bags filled with Natural Gas (in Pakistan):

### C) Quantities to cover a __full month __(average household):

Average number of LPG canisters/month: **4 canisters. **This is 995g x4 =** ****4kg/month of hydrogen **(at STP, this is about 45 cubic meters, the volume contained in a cube 3.6m side).

Multiplying the table values by four:

Quantity Yoga Ballons ( 221L) (*) | Quantity canisters ( 6L) | Quantity scuba tanks ( 11L) | |

Natural Gas (mostly methane*) | |||

H2 & 1 bar | 200 | 7364 (total 45 cubic meters) | n.a. |

Compressed H2 & 17.5 bars | n.a. | 420 | 256 |

Compressed H2 & 35 bars | n.a. | 234 | 128 |

Compressed H2 & 200 bars | n.a. | 40.8 | 22 |

### D) Quantities to cover per day:

An important fact to remember is that the electrolyser we have discussed can produce **1.1kg/24h** when powered at 2.4 kW (see below “Production”). Also, there is no need of having all the storage for the month (unless we are talking about a plant). A household can consume the hydrogen as it is generated, using* much less solar power. *In fact per DAY we need this quantities* divided by 30*:

Quantity canisters ( 6L) | Quantity Yoga Ballons ( 221L) (*) | Quantity scuba tanks ( 11L) | |

H2 & 1 bar | 245 (total 1.5 cubic meters) | 6.7 | n.a. |

Compressed H2 & 17.5 bars | 14 | n.a. | 8.5 |

Compressed H2 & 35 bars | 7.8 | n.a. | 4.3 |

Compressed H2 & 200 bars | 1.4 | n.a. | 0.7 |

# G) PRODUCTION (Solar power + electrolysis)

Can we produce this using solar power and a commercial electrolyser?

- The EL 4.0 electrolyser we plan to use produces
**1.1kg/24h when powered at 2.4 kW**(here). This requires 2.4kW*24 =**57kWh**. Note: as of 2022, more efficient commercial electrolysis requires around 53 kWh of electricity to produce one kg of hydrogen, which holds 33.6 kWh of energy - From consultation with Agung and Dery (company Energyhub, @August 23, 2023 ): taking into account solar intensity variations, and their solar panels (size?), it would be possible to generate an average power of
**2kW**during the day. This is approximately what the EL4.0 electrolyser needs to produce one kg of H2 per day. - Our solar panel system produces
**6kW**, so we can run at least two electrolysers simultaneously, to produce**2.2kg/day.** - In both cases, this is more than the 1.45kg needed for an average household, and this happens in a day or two. Assuming the conservative number 1kg/two day, in a month we could have 15kg.

**10.34 households!**

# H) How much do they pay for it?

- In the USA, hydrogen costs around
**US$16**per kilogram. Currently, renewable hydrogen produced via electrolysis costs between US$3 – US$6/kg, though analysts expect this figure to drop significantly over the next decade (from here) - The 3 kg LPG is subsidized by the government, with the price set by each local government. Prices are officially set at
in Java island (from here)**IDR 16.000 per canister** - From Gender and Fossil Fuel Subsidy Reform: An audit of data on energy subsidies, energy use and gender in Indonesia, Nov. 1, 2017, pp. 9-19:

Note: A volume of around **11 m3** (which is the volume of the trunk of a large utility or commercial vehicle) is needed to store just 1 kg of hydrogen, which is the quantity needed to drive 100 km.