  We propose a dynamical systems approach to show how multizone models in
buildings can be simplified upon recognising the existence of fast and slow
modes of response. The study is motivated by extensive observations from an
instrumented classroom equipped with 70 computers used heterogeneously in time
and space, a living computer laboratory, that is mechanically-ventilated. We
develop an analytical model for the CO2 evolution that accounts for air
exchange between the classroom and ceiling plenum by parametrising the mixing
of air within the sub-spaces, which is a feature that is often neglected in
zonal models but shown to be essential for a realistic dynamical
representation. We demonstrate how the model and interpretation of the data can
be simplified by projecting the system onto a lower-dimensional subspace that
describes the slow dynamics. This ability to reduce models based on a physical
understanding is particularly valuable in the development of robust data-driven
approaches. A comparison with the observational data demonstrates that the
model is reasonably accurate in predicting CO2 concentrations in zones of
ventilated spaces. Our laboratory offers a unique dataset to generate insights
into the physics of realistic spaces containing non-uniform and time-varying
heat sources, such as offices and classrooms. Observations show a remarkable
seasonal change in mixing within the space, emphasising the importance mixing
and temperature play in CO2 concentration.
