Gas Blending Formulas — Dive Team The Fat Flippers

Dalton's Law

Partial Pressure Triangle

Partial pressure (PP), gas fraction (G), and depth (D) are related. Know any two and you can calculate the third. Depth is always expressed in ata; gas fraction always as a decimal (e.g. O₂ in EANx32 = 0.32).

PP — cover PP to get G \times D

G — cover G to get \frac{PP}{D}

D — cover D to get \frac{PP}{G}

PP Partial pressure (e.g. PPO₂ 1.6)

G Gas fraction as a decimal

D Depth in ata (1 ata = surface)

Example: PPO₂ for EANx32 at 27m (3.7 ata) = 0.32 \times 3.7 = \mathbf{1.18}

Trimix

Equivalent Narcotic Depth (END)

Calculates the equivalent air depth in terms of narcotic load. O₂ and N₂ are both considered narcotic. He is not. Depth in ata; narcotic gas fraction as a decimal.

END_{\text{ata}} = D_{\text{ata}} \times f_{\text{narcotic}}

f narcotic = O₂% + N₂% (i.e. 1 - f_{He})

Example: 18/45 Trimix at 60m (7 ata). Narcotic fraction = 1 - 0.45 = 0.55
END = 7 \times 0.55 = 3.85 \text{ ata} = \mathbf{28.5\text{m}}

EANx Blending

Continuous Flow Top-Up

Use this when topping up a partially filled cylinder and you want to hit a different final mix. Calculates the O₂% of the top-up gas required.

SP Starting pressure

EP Ending pressure

SO2 Starting O₂%

EO2 Ending O₂%

SPO2 SP \times SO_2

EPO2 EP \times EO_2

1

Calculate oxygen pressure values:

EPO_2 = EP \times EO_2 \qquad SPO_2 = SP \times SO_2

2

Calculate required top-up mix:

\text{Top-Up } O_2\% = \frac{EPO_2 - SPO_2}{EP - SP}

Example: 50 Bar of EANx32, filling to 200 Bar, target EANx36.
EPO_2 = 200 \times 0.36 = 72 | SPO_2 = 50 \times 0.32 = 16
\frac{72 - 16}{200 - 50} = \frac{56}{150} = 0.37 = \mathbf{EANx37}

EANx Blending

Partial Pressure EANx Blending

For blending EANx using 100% oxygen topped up with air into an empty cylinder. Gives the pressure of oxygen to add first.

O_2 \text{ Fill P} = \frac{O_2\%_{\text{wanted}} - 0.21}{0.79} \times P_{\text{fill}}

Example: EANx36 to 200 Bar.
\frac{0.36 - 0.21}{0.79} \times 200 = \mathbf{38 \text{ Bar } O_2}, then top to 200 Bar with air.

Trimix Blending

Trimix Blending Calculations

Follow steps 1 and 2 when using EANx as a top-up gas. Add step 3 if topping up with air instead (converts the EANx mix to an oxygen fill pressure).

1

Calculate helium fill pressure:

P_{He} = f_{He} \times P_{\text{fill}}

2

Calculate EANx top-up gas (if using EANx):

EANx_{\text{top-up}} = \frac{f_{O_2}}{1 - f_{He}}

3

Convert to O₂ fill pressure (if topping up with air):

O_2 \text{ Fill P} = \frac{EANx\% - 0.21}{0.79} \times (P_{\text{fill}} - P_{He})

Example: Target 21/20 Trimix to 200 Bar.
P_{He} = 0.20 \times 200 = 40 \text{ Bar} | EANx_{\text{top-up}} = \frac{0.21}{1 - 0.20} = EANx26
If using air: \frac{0.26 - 0.21}{0.79} \times (200 - 40) = \mathbf{10 \text{ Bar } O_2}, then 40 Bar He, top to 200 Bar with air.

Transfilling

Transfilling / Decanting Pressure Drop

Determines whether your bank cylinder has enough pressure to decant without a booster pump. If BP2 > required fill pressure, no booster is needed.

BP1 Bank starting pressure

BP2 Bank ending pressure

BV Bank water volume (L)

RP1 Recipient starting pressure

RP2 Recipient ending pressure

RV Recipient water volume (L)

Empty recipient:

BP2 = \frac{(BP1 \times BV) - (RP2 \times RV)}{BV}

Recipient with residual pressure:

BP2 = \frac{(BP1 \times BV) + (RP1 \times RV) - (RP2 \times RV)}{BV}

Example: 50 L He bank at 72 Bar, decanting 40 Bar into empty 22 L twin set.
BP2 = \frac{(72 \times 50) - (40 \times 22)}{50} = \frac{2720}{50} = \mathbf{54.4 \text{ Bar}}
BP2 (54.4) > RP2 (40) — no booster needed.