IAP 1999, Presentation 9:

## Frank Ligterink

### APPLICATION OF THE HOETJER EQUATION IN CLIMATE CONTROL STUDIES

ABSTRACT

The Hoetjer equation is often used to explain the dependence of ventilation rates on pollution concentrations when testing emissive sources in chamber experiments. In this talk it is shown how the equation can be derived from basic assumptions. The equation allows a simple analysis of emission chamber data. Nevertheless, it can be anticipated from the fact that the underlying assumptions are in reality not always obeyed, that discrepancies might occur. Further work on this issue is planned.

NOTES FROM SHEETS

How does ventilation influence pollutant concentration levels around emissive sources?

Imagine a chamber with volume V (m3) in which a sample of an emissive material is placed with a total surface A (m2) and a ventilation rate of N (h-1).

The equilibrium concentration, Ceq (µg/m3), is the concentration of pollutant in the air in the chamber at zero ventilation.

The steady state concentration, Cst (µg/m3), is the constant value of the chamber concentration which will set after maintaining a certain fixed ventilation rate.

The ventilation rate, N (h-1), is the ratio of flow over chamber volume, V.

The loading, L (m2/m3), is the ratio of total surface of test material, A, over chamber volume, V.

The emission rate, ER (µg/m2h), is the amount of pollutant emitted from the test material per unit of surface per unit of time.

The emission rate depends on the concentration in the chamber; when the concentration is zero, the emission rate is maximal, when the equilibrium concentration has been reached, the emission rate becomes zero. The linear relationship between emission rate and concentration can be expressed as:

ER = k (Ceq - Cchamber)

Where k is the pollutant transfer coefficient.

Given a material with k and Ceq in a chamber with ventilation rate N, the steady state concentration will be reached when the total mass of pollutant leaving the material equals the total mass of pollutant leaving the chamber. Or:

 ER x A = N x V x Cst or K(Ceq-Cchamber) x A = N x V x Cst thus Cst = Ceq / {1 + (1/k x V/A x N)} or Cst = Ceq / {1 + (N/Lk)} which is known as the Hoetjer Equation.

The Hoetjer equation is useful

1. as a conceptual tool to understand or estimate the effect of ventilation
2. for data reduction (a material is described by 2 parameters, k and Ceq; the showcase also with 2 parameters, L and N)

The Hoetjer equation has limitations though, the model does not take possible 'skin effects' into account. In these cases extraction of k and Ceq from chamber data bears little meaning. Index of presentations at IAP 1999 meeting

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