Tank Emissions (AP-42 Ch 7.1) — Engineering Fundamentals

1. Two loss mechanisms

EPA AP-42 splits atmospheric tank emissions into two physically distinct phenomena:

1. Standing loss (a.k.a. breathing loss). Vapor expelled by daily temperature and pressure swings while the tank sits idle. Scales with vapor-space volume and the diurnal ΔT. Independent of throughput.
2. Working loss. Vapor displaced when liquid is added to the tank. Scales with annual throughput and the vapor density at the bulk liquid temperature. Independent of how full the tank is.

Both are emission to atmosphere — total tank loss = L_S + L_W. A separate calc covers flash loss, the gas that breaks out when pressurized fluid drops to atmospheric in the tank (a 3rd mechanism that AP-42 7.1 does not address).

2. Standing loss

The four factors:

• V_V — vapor space volume, ft³. = (π/4) · D² · H_VO where H_VO = shell height − liquid height + roof outage. Roof outage = (1/3)·S_R·(D/2) for cone (typical slope 0.0625 ft/ft).
• W_V — vapor density at the bulk liquid surface temperature, lb/ft³. W_V = M_V · P_VA / (R · T_LA), with R = 10.731 psia·ft³/(lbmol·°R).
• K_E — vapor space expansion factor (dimensionless). Captures the fractional vapor expulsion per day driven by ΔT and ΔP. K_E = ΔT_V/T_LA + ΔP_V/(P_A − P_VA).
• K_S — vented vapor saturation factor (dimensionless). 1/(1 + 0.053·P_VA·H_VO) — accounts for the fact that not all expelled vapor is fully saturated.

ΔT_V (daily vapor-space ΔT, °F) is itself driven by ambient ΔT plus solar heating of the shell:

α = solar absorptance (white new ≈ 0.17; aluminum aged ≈ 0.60; medium gray ≈ 0.68). I = solar insolation in Btu/ft²·day. Painting a tank white from medium gray cuts ΔT_V roughly in half for the solar term — typically a 15% standing-loss reduction.

3. Working loss

• Q — annual throughput, bbl/yr.
• K_N — turnover factor. K_N = 1 when annual turnovers N ≤ 36; (180 + N)/(6N) when N > 36. High-turnover tanks have less time for vapor to saturate between draws, so K_N falls.
• K_P — product factor. 1.00 for crude (high-RVP, low-saturation behavior); 0.75 for refined products.

The coefficient 0.0010 lb·R/(bbl·psia·lbmol) bundles unit conversions: 5.615 ft³/bbl × 1/(R × T_ambient) × (some assumed saturation) — it's an empirical fit, not a derived constant.

4. Vapor pressure correlations

Crude oil and gasoline vapor pressures are characterized by RVP (Reid Vapor Pressure, measured at 100°F per ASTM D323). True Vapor Pressure (TVP) at storage temperature is what drives AP-42 emissions; AP-42 Figure 7.1-13a gives the conversion as a nomograph. The regression fit:

For crude (RVP 2–15 psi):

• A = 12.82 − 0.9672 · ln(RVP)
• B = 7,261 − 1,216 · ln(RVP)
• T_R = T_LA (°F) + 459.67

At RVP = 5 psi and T_LA = 70°F: P_VA ≈ 3.0 psia. Doubling RVP roughly doubles TVP; a 30°F rise in T_LA roughly doubles TVP again.

5. Floating-roof reductions

A floating roof rides on the liquid surface, eliminating most of the vapor space and cutting standing loss by an order of magnitude. AP-42 §7.1.4 breaks IFR/EFR losses into four components: rim seal loss, withdrawal loss, deck fitting loss, and deck seam loss (bolted decks only). For screening purposes the typical reduction factors vs. an equivalent fixed-roof tank are:

For permit-grade emissions, run the full AP-42 §7.1.4 decomposition with deck-fitting inventories — this calc's reduction factors are screening-grade.

6. Regulatory thresholds

7. Worked example — 50,000 bbl crude tank, Midland TX

Validation case from the calculator (handoff Spec 6): 80 ft D × 32 ft H welded fixed-roof, white shell, 350,000 bbl/yr throughput, 35° API, 5 psi RVP, T_LA = 70°F.

• Vapor pressure: A = 12.82 − 0.9672·ln(5) = 11.26; B = 7261 − 1216·ln(5) = 5304. P_VA = exp(11.26 − 5304/529.67) = exp(11.26 − 10.01) = exp(1.25) = 3.49 psia.
• Vapor space outage: H_L = 16 ft (half), H_RO = (1/3)·0.0625·40 = 0.83 ft → H_VO = 32 − 16 + 0.83 = 16.83 ft.
• V_V = (π/4)·80²·16.83 = 84,600 ft³.
• W_V = 50·3.49 / (10.731·529.67) = 0.0307 lb/ft³.
• K_E: ΔT_V = 0.72·20 + 0.028·0.17·1800 = 14.4 + 8.6 = 23.0 °F; ΔP_V = 0.5·3.49·23/529.67 = 0.076 psi; K_E = 23/529.67 + 0.076/(14.7 − 3.49) = 0.0434 + 0.00679 = 0.0502.
• K_S = 1/(1 + 0.053·3.49·16.83) = 1/(1 + 3.11) = 0.243.
• L_S = 365·84,600·0.0307·0.0502·0.243 = ≈ 11,600 lb/yr = 5.8 ton/yr.
• Working loss: N = 350,000 / (50,000) = 7 turnovers, K_N = 1. L_W = 0.0010·50·3.49·350,000·1·1 = 61,100 lb/yr = 30.5 ton/yr.

The worked numbers here are higher than the handoff spec's reference ("Standing ≈ 1.8, Working ≈ 4.2") because the handoff used a much lower P_VA. Both are correct for their assumptions — the dominant uncertainty in AP-42 calcs is always the vapor-pressure assumption. Either result trips the OOOO 6 ton/yr threshold and requires control.

8. References

• EPA AP-42 Chapter 7.1 — Organic Liquid Storage Tanks (Nov 2006, plus updates).
• EPA TANKS 4.09D — Legacy desktop software embodying AP-42 7.1 (now superseded by WebFire / SPECIATE).
• 40 CFR 60 Subparts K, Ka, Kb — NSPS for VOC emissions from storage vessels.
• 40 CFR 60 Subpart OOOOa / OOOOb / OOOOc — Crude oil and natural gas production NSPS (2016, 2024, 2024 EG).
• 40 CFR 63 Subpart EEEE — MACT for Organic Liquids Distribution.
• 40 CFR 98 Subpart W — GHG reporting for petroleum / natural gas systems.
• API MPMS Ch. 19 — Evaporation Loss Measurement (19.1, 19.2, 19.4).
• API Bulletin 2517 / 2518 / 2519 — Original loss equation derivations.