Description
Compute remainingFraction = exp(-airChangesPerHour*hours) and finalConcentration = equilibrium+(initial-equilibrium)*remainingFraction.
Air-change and transfer calculations relate a volume, flow, time and driving force under an assumed model. Nominal air exchange or a well-mixed exponential response differs from measured clearance, spatial mixing and contaminant-specific treatment.
Compute remainingFraction = exp(-airChangesPerHour*hours) and finalConcentration = equilibrium+(initial-equilibrium)*remainingFraction.
When to use this tool
Use Indoor Air Change Exponential Removal Term when checking a supplied ventilation, concentration-decay or oxygen-transfer term.
How to use the tool and how it works
- Enter initial, equilibrium, airChangesPerHour, hours. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read remainingFraction, finalConcentration. Use the output convention below.
Require nonnegative initial, equilibrium, airChangesPerHour and hours. Compute remainingFraction = exp(-airChangesPerHour*hours) and finalConcentration = equilibrium+(initial-equilibrium)*remainingFraction. Concentrations share one unit and time is in hours; remainingFraction is the fraction of the initial departure from equilibrium.1
The well-mixed air-removal model relates concentration ratios exponentially to air changes and time. The zero-equilibrium case here has that form; the supplied equilibrium term is an additional constant-reference assumption.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| initial | Initial | Required. Finite number; minimum 0. |
| equilibrium | Equilibrium | Required. Finite number; minimum 0. |
| airChangesPerHour | Air Changes Per Hour | Required. Finite number; minimum 0. |
| hours | Hours | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| remainingFraction | Fraction of initial departure from equilibrium retained, exp(-ACH*hours). | Required. Finite number. |
| finalConcentration | Final Concentration | Required. Finite number. |
{
"input": {
"initial": 100,
"equilibrium": 10,
"airChangesPerHour": 2,
"hours": 0.5
},
"output": {
"remainingFraction": 0.36787944117144233,
"finalConcentration": 43.10914970542981
}
}Limitations and assumptions
- This assumes constant effective removal rate, constant equilibrium and complete mixing. Concentration rises when initial is below equilibrium; the fraction is not always final/initial. Ongoing variable sources, stagnant zones and infection risk are not modeled.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use measured effective airflow and a suitable mixing or transport model before drawing conclusions about treatment performance or exposure.
References
-
Calculation and input contract: environmental-health/indoor-air-change-exponential-removal-term — tool.io
-
Appendix B: airborne contaminant removal — Centers for Disease Control and Prevention
Similar or alternative tools
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Subtract an explicit compatible air background concentration while preserving negative corrected results.