Room Ventilation Calculator: CO₂, Humidity and Airing Time

The single-zone balances are derived here from conservation. With $k=Q/V$ and a constant concentration source $s$, $dy/dt=s-k(y-y_o)$. For $k>0$, $y(t)=y_o+s/k+(y_0-y_o-s/k)e^{-kt}$; with zero flow, $y=y_0+st$. CO₂ uses volume ppm and $s=10^6G_{CO₂}/V$.

Moisture uses $w=0.62198p_v/(p-p_v)$ (kg water/kg dry air). The reference dry-air inventory is $M_d=(p-p_{v,0})V/(R_dT_i)$, and $s_w=G_w/M_d$. Volumetric flow is interpreted at the room reference state. Vapour pressure is recovered from $p_v=pw/(0.62198+w)$, so RH at room temperature follows from $100p_v/p_{sat}(T_i)$.

Saturation pressure uses the Alduchov–Eskridge Magnus expression $p_{sat}=610.94\exp[17.625T/(243.04+T)]$ Pa, with $T$ in °C; Silicon Labs AN607 Rev. 2.0, Appendix B, PDF p. 26. Its inverse gives dew point. The ideal-gas constants are $R_d=287.055$ and $R_v=461.52$ J/(kg·K).

For one full rectangular aperture on one wall, $Q_w=0.025AU_{ref}$ and $Q_b=C_dA\sqrt{gH|T_i-T_o|/T_{avg}}/3$. Use $Q=\max(Q_w,Q_b)$, as tabulated and experimentally assessed by Gough et al. (2020), Table 1, PDF p. 2. $T_{avg}$ is absolute temperature. This is one-way exchanged flow; do not double it for the outward stream.

Target times are found by inverting the exponential. A target at the asymptote is not reached in finite time. Initially satisfied targets receive time zero. The candidate maximum of individual entry times is checked against both concentrations, preventing a false combined time when one concentration rises while the other falls.

Surface saturation demand is $100p_v/p_{sat}(T_s)$ at a fixed surface temperature. Values above 100% indicate condensation potential before any condensate removal; values around 80% are only a persistent-moisture screen (SMGV guidance, PDF p. 15).

Sensible heating loss is $\dot H=\rho_d(c_{pd}+w_0c_{pv})Q\max(T_i-T_o,0)(1-\eta)$. Integrate over the chosen duration. Engineering approximations $c_{pd}=1006$, $c_{pv}=1860$ J/(kg·K) are constant. Only mechanical mode applies heat recovery; neither CO₂ nor moisture is recovered.

• One well-mixed room, with constant volume, pressure, indoor temperature, outdoor conditions, airflow and sources. No exchange with adjacent rooms.
• Moisture is a dilute ideal-gas mixture with constant reference dry-air density. Material absorption, liquid water, condensation sinks and thermal storage are omitted. Predictions after bulk air reaches saturation are outside the model.
• Room RH means RH after maintaining or restoring the entered indoor temperature. The model does not calculate room or wall cooling during airing.
• A fully open, unobstructed rectangular aperture is assumed for window mode. The default discharge coefficient 0.6 is an engineering assumption. Wind direction, shelter and interactions with buoyancy are not resolved.
• The editable 0.0052 L/s adult CO₂ rate is the historical ASHRAE/ASTM example discussed by Persily and de Jonge (2017), PDF p. 3; it is not a universal physiological rate. Rates must use room conditions. The paper discusses substantial variation and limitations of older estimates.
• The default total moisture source of 100 g/h is a scenario assumption, independent of the people counter. Adjust it when occupancy or activities change.
• Mechanical recovery is sensible only, without moisture transfer, leakage, frost dynamics or fan power. Set effective recovery to the actual operating value. Heating energy is zero when outdoor air is warmer; cooling and latent loads are not calculated.
• CO₂ is treated as a dilute tracer. Results require an interval maximum no greater than 10,000 ppm; concentrated-gas displacement and non-dilute mixture effects are not modelled.

Suitable for preliminary comparisons and short, approximately steady airing events. Input limits are product limits, not a claimed experimental validation envelope. The Magnus water correlation is used within −20 to +40 °C for outdoor air, +5 to +35 °C indoors and 0 to +35 °C at the surface; enhancement factors and ice-surface saturation are omitted. Dew points below −40 °C are extrapolations.

Natural airflow can differ substantially from the estimate, especially in sheltered, leeward, gusty or partly obstructed openings. Use measured outdoor air changes for decisions needing accuracy. At zero wind and equal temperatures the selected correlation gives zero exchange; real turbulence or leakage may still ventilate the room.

The adjustable 1000 ppm default is an operating target, not a health or regulatory limit. CO₂ does not describe all pollutants. The 80% surface screen concerns persistence, substrate and temperature; a short excursion neither proves nor rules out mould. No standard-compliance, exposure or mould-remediation claim is made. Ventilation installation work belongs to a qualified person.

The dilute-CO₂ calculation is limited to 10,000 ppm (1% by volume) throughout the selected interval. This is a conservative modelling cutoff chosen for this tool, not a health or regulatory limit. Because the constant-source transient is monotonic, its maximum is exactly the larger of the initial and final values. Results are blocked if this maximum exceeds the cutoff.