Individual energy saving ideas collected and analyzed

This is a comment of the category "analysis", in the above outlined sense. Comments/corrections are welcome.

This is in a "draft" / "prelim. analysis" status.

EDIT (2022-10-28): Parameters on "showering" were adjusted to give more conservative estimate

of potential saving. Previous values for duration and throughput were 5min and 10 l per minute

respectively. Target temperature previously was 38 deg C.

Computing energy saving potential from reducing private household warm water usage: showering

=========================================

1. Compute amount of warm water used (V_ww) per once showering and the energy equivalent:

Assumptions:

- average shower installation with 10 liter per minute water throughput

- temperature at the output of the local warm water boiler: T_bwo = 60 deg C [1]

- temperature at the input of the shower water mixer: 55 deg C = T_mwi [1]

- temperature of in-house cold water: 12 deg C = T_mci   [avg., est.]

- target temperature of the shower output: 35 deg C = T_tgt

- water throughput at active shower: 8 liter per minute = v

- showering duration: 3 minutes = T_dur

- heat capacity water: c_V = 4.2 kJ/(kg K)   , see [3]

Mixing ratio, expressed by warm water share gamma, from

    T_tgt = gamma T_mwi + (1-gamma) T_mci = T_mci + gamma (T_mwi - T_mci)

    gamma = (T_tgt - T_mci)/(T_mwi - T_mci) = 23/43

In one liter mixer output there is only gamma * 1 liter warm water.

Follows the amount of warm water per once taking a shower is 

    V_ww = T_dur * v * gamma = 24 * 23/43 liters = about 13 liters

To heat that amount of cold water, for simplicity assumed having temperature T_sci = T_mci = 12 deg C,

to T_bwo, require at least the energy

    delta Q = V_ww * \rho * (T_bwo - T_mci) * c_V = 13 kg * 48 K * 4.2 kJ / (kg K) = about 2.62 MJ

This energy is the one without taking into account losses occuring on the way

from power plant to and including the per-house warm water boiler. If we deem

the efficiency of the boiler eta = 80%, then at house boundary the amount of energy

needed is 2.62 MJ / 0.8 = 3.275 MJ. (per once taking a shower)

(To compute the energy demand from this on the "imported-gas" level, the losses 

additionally arising at power plants still need to be incorporated.)

2. The number of persons taking a shower once per day, in an exemplary EU country:

Assume that a share of 65% of the population take a shower daily. In a country of 

80 mn people, the total amount of energy consumed by this share for taking a shower is,

daily: 80 * 10^6 * 0.65 * 3.275 MJ / eta_pp = 170.3 * 10^6 MJ / eta_pp = 170.3 * 10^12 J / eta_pp. 

Per year, this energy share is about 62.2 * 10^15 J / eta_pp =: W_showeringA_DE. 

(Here eta_pp = power plant efficiency)

3. Comparison:

Energy equivalent of gas imported from Russia into EU, yearly, in 2019:

6876 * 10^15 J [4][4b]. Imported into Germany about a third of it, i.e. 2300 * 10^15 J yearly.

Thus: The equivalent of about 2.7% / eta_pp of this imported amount is used (prelim. calculation!!) 

for showering of the mentioned population share.

5. Caveats and comments

- After the edit: The amounts for showering duration and throughput now assume a more 

  resource-aware person, in order to avoid overstating the savings potential.  

- The energy share relative to from-Russia imports looks large. [TODO: cross check] A reason

  likely is that a specific energy type is compared to a consumption from across all primary energy types.

- In the summer period, the cold water temperature will likely be higher than here assumed, reducing the

  computed energy consumption.

- In the Comparison section, it is to be understood that the energy amounts 

  related to each other are numerical values only, irrespective of the actual energy flow.

  For example, saving half of that used energy will not translate into reducing the

  natural gas usage by the same amount. This is due to the heating for, among others, 

  showering is realized at homes from different energy input, further major types being 

  a) electricity (which is generated only according to a certain share from natural 

  gas) and b) oil (whose consumption reduction will only minorly affect gas consumption).

  Thus "equivalent of". Applying suitably researched factors would allow the

  translation into imported gas amounts saved.

6. References

[1] https://www.umweltbundesamt.de/umwelttipps-fuer-den-alltag/haushalt-wohnen/warmwasser#gewusst-wie

[3] https://en.wikipedia.org/wiki/Specific_heat_capacity

[4] https://www.businessinsider.de/wirtschaft/handel/wenn-wir-komplett-auf-russisches-gas-verzichteten-so-viel-muesste-in-der-eu-eingespart-werden-a/

[4b] https://www.fz-juelich.de/iek/iek-3/DE/Home/home_node.html

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