22-Mec-B2 Environmental Control in Buildings · May 2013

Question 7 of 8: Carbon-dioxide dilution, the ASHRAE comfort chart and chilled-water reset (20 marks)

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

Paper format. Professional Engineers of Ontario / EGBC annual examination, 07-Mec-B2 (now 22-Mec-B2) Environmental Control in Buildings, May 2013 sitting. Three hours, open book. Eight problems of 20 points each; the candidate is instructed to solve five and to nominate which five are to be graded. Psychrometric charts and a pressure–enthalpy diagram for ammonia (R-717) are appended to the paper, and candidates are expected to bring an environmental-control text and steam tables. Instruction 1 invites the candidate to state any interpretation assumptions with the answer — that latitude is used explicitly below where the printed data are redundant.

All eight problems are worked here. Every psychrometric state has been recomputed from the ASHRAE formulation for saturation vapour pressure rather than scaled off a chart, so the numbers are tighter than a graphical solution would be; chart-quality agreement (about ±0.2 K and ±0.0002 kg/kg) is all that an examiner expects.

Reference texts for this subject.

W. P. Jones, Air Conditioning Engineering, 5th ed., Butterworth-Heinemann — the standard reference for this examination code; Ch. 2–3 (psychrometry), Ch. 6 (cooling loads), Ch. 10 (cooling towers), Ch. 15 (duct design).
McQuiston, Parker & Spitler, Heating, Ventilating and Air Conditioning: Analysis and Design, 6th ed., Wiley — Ch. 3 (moist air), Ch. 8 (energy estimating and degree-day methods), Ch. 12–13 (fluid flow and duct design).
ASHRAE Handbook – Fundamentals (2021) — Ch. 1 (psychrometrics), Ch. 21 (duct design), Ch. 25–27 (heat, air and moisture transfer in the envelope).
Moran, Shapiro, Boettner & Bailey, Fundamentals of Engineering Thermodynamics, 9th ed., Wiley — Ch. 10 (vapour-compression and multistage refrigeration).
ANSI/ASHRAE Standard 55, Thermal Environmental Conditions for Human Occupancy, and ANSI/ASHRAE Standard 62.1, Ventilation for Acceptable Indoor Air Quality.
Canadian frame: National Building Code of Canada 2020, National Energy Code of Canada for Buildings 2020, and Environment and Climate Change Canada Canadian Climate Normals for degree-day data.

Psychrometric relations used throughout. At barometric pressure $p$, with saturation vapour pressure $p_{ws}(t)$ from the ASHRAE correlation,

$$W = 0.6220\,\frac{\phi\,p_{ws}(t)}{p - \phi\,p_{ws}(t)}, \qquad h = 1.006\,t + W\,(2501 + 1.86\,t)$$

in SI (kJ per kg of dry air), and in the inch-pound system $h = 0.240\,t + W\,(1061 + 0.444\,t)$ Btu per lb of dry air. The thermodynamic wet-bulb temperature is obtained from the adiabatic-saturation equation, which is what a chart's constant-wet-bulb lines represent.

Question 7: Carbon-dioxide dilution, the ASHRAE comfort chart and chilled-water reset (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. A ventilated room whose carbon-dioxide concentration is to be held below a ceiling value, served entirely by air of known lower concentration.

Given data (part a)
Quantity	Value
Ceiling room concentration	1000 ppm CO₂
Supply-air concentration	250 ppm CO₂
Supply-air flow	5000 cfm = 2360 L/s
Assumed CO₂ generation per occupant	0.0052 L/s (adult, 1.2 met, sedentary office work)

Find. (a) the permissible occupancy, (b) an explanation of the ASHRAE comfort chart and of how thermal comfort is perceived, and (c) an assessment of raising chilled-water temperature as a summer energy-saving measure.

Approach (part a). Treat the room as a completely mixed, steady-state control volume: at equilibrium the carbon dioxide the occupants exhale must equal the carbon dioxide carried out in the exhaust minus that carried in with the supply.

Steady-state contaminant balance. For $N$ occupants each generating $G$ of CO₂, with volumetric supply $\dot{V}$ and concentrations expressed as volume fractions, $$N G = \dot{V}\,(C_{room} - C_{supply})$$ which rearranges to the per-person outdoor-air requirement $\dot{V}/N = G/(C_{room} - C_{supply})$.
Convert the supply flow. $$\dot{V} = 5000\ \text{cfm} \times \frac{0.0283168}{60} = 2.360\ \text{m}^{3}/\text{s} = 2360\ \text{L/s}$$
Per-person air requirement. The allowable rise across the room is $1000 - 250 = 750$ ppm, i.e. a volume fraction of $7.50\times10^{-4}$, so $$\frac{\dot{V}}{N} = \frac{0.0052}{7.50\times10^{-4}} = 6.93\ \text{L/s per person} = 14.7\ \text{cfm per person}$$ That result is itself a useful sanity check: ASHRAE 62.1 asks for about 15 cfm per person in an office, which is exactly the flow that holds a 700 to 750 ppm rise over outdoors.
Permissible occupancy. $$N = \frac{2360}{6.93} = \boxed{340\ \text{people}}$$ Rounding down is the right direction: 341 people would put the steady-state concentration marginally over the 1000 ppm ceiling.
Assumptions, as the question requires. (i) Steady state — the room has been occupied long enough for the concentration to plateau, which for a normally proportioned office at this air-change rate takes two to three hours; a transient analysis would allow more people for a short meeting. (ii) Complete mixing, so the exhaust concentration equals the room concentration. (iii) All 5000 cfm is at the stated 250 ppm, i.e. it is outdoor or fully treated air, not recirculated room air. (iv) Occupants are sedentary adults at 1.2 met; at 2.0 met (light industrial work) generation rises to about 0.0087 L/s and the occupancy falls to roughly 200. (v) There are no other carbon-dioxide sources such as unvented combustion. (vi) The 1000 ppm figure is used here as a ventilation-adequacy indicator, not as a health limit; the occupational exposure limit is 5000 ppm.

Final results (part a)
Quantity	Result
Supply air flow	5000 cfm = 2360 L/s
Allowable concentration rise	750 ppm
Outdoor air per person	6.93 L/s = 14.7 cfm
Permissible occupancy	340 people

(b) The ASHRAE comfort chart and the perception of thermal comfort.

The comfort chart of ANSI/ASHRAE Standard 55 is a psychrometric chart on which a pair of comfort zones has been drawn, one for winter clothing (about 1.0 clo) and one for summer clothing (about 0.5 clo). Its axes are operative temperature and humidity, and the zones are bounded on the left and right by lines of constant predicted mean vote (PMV of −0.5 and +0.5, i.e. no more than 10% of occupants dissatisfied on thermal grounds), above by a humidity-ratio limit near 0.012 kg/kg, and below by a limit on dryness. In round numbers the summer zone runs from about 23 to 27 °C operative temperature and the winter zone from about 20 to 24 °C, with an overlap near 23 °C where a single set-point suits both seasons. The zones assume still air (below 0.15 to 0.20 m/s), sedentary activity of 1.0 to 1.3 met, and occupants acclimatised to the local season.

What makes the chart work is that comfort is not a response to air temperature but to the whole heat balance of the body. The six governing variables are air temperature, mean radiant temperature, air speed, humidity, clothing insulation and metabolic rate; the chart collapses the first two into the operative temperature (very nearly their mean for still air), fixes the last two by choosing a clothing and activity level, and plots the remaining humidity axis. That is also why the chart must be used with care: a perimeter office with a cold window in January can be uncomfortable at 22 °C air temperature because the radiant term drags the operative temperature down and because the asymmetry itself causes local discomfort. Humidity has a comparatively weak effect on sensation within the zone — which is why the zone is wide in the vertical direction — but it is limited above for reasons of skin wetness, mould and dust mites, and below because dry air causes eye and mucous-membrane irritation and static discharge. Finally, the standard is explicitly statistical: even at the centre of the zone about 5% of occupants will be dissatisfied, so no single set-point will satisfy everybody, and local discomfort sources (draught, vertical air-temperature difference, radiant asymmetry, warm or cool floors) must be checked separately.

(c) Raising the circulating chilled-water temperature.

The measure is genuinely attractive on the chiller side and genuinely risky on the air side, and the two effects must be weighed together. Raising the chilled-water supply temperature raises the evaporating temperature, which reduces the compressor lift and improves the coefficient of performance by roughly 2 to 3% per kelvin — so moving from 6 °C to 9 °C supply typically buys 6 to 10% off the chiller energy, and it also lets the machine run more hours on free cooling or on a water-side economiser. Where the plant serves loads that are mostly sensible and where the terminal coils have spare surface, that saving is real and is the basis of the widely used chilled-water reset strategy, in which the supply temperature is raised automatically whenever no zone valve is fully open.

The difficulty is that a cooling coil dehumidifies only by operating below the dew point of the entering air. Raising the water temperature raises the coil surface temperature and therefore the apparatus dew point, so the coil's sensible heat ratio rises and its latent capacity falls sharply — and in this question's Problem 1, for example, an apparatus dew point of 5 °C was needed to reach a supply moisture content of 0.0059 kg/kg. If the apparatus dew point rises above the required supply dew point the coil simply cannot deliver the design moisture content, indoor humidity drifts upwards, and the space leaves the top of the Standard 55 comfort zone. Occupants report the room as “clammy” even when the thermostat is satisfied, because high humidity suppresses evaporative heat loss from the skin; and sustained relative humidity above about 60% raises the risk of mould growth and dust-mite activity. There are two secondary penalties: the smaller water-to-air temperature difference reduces each coil's capacity, so either the water flow must rise (more pump energy, which can easily exceed the compressor saving) or coils must be re-selected; and if the chilled water also feeds fan-coil or induction units sized on 6 °C water, their capacity shortfall shows up as an inability to hold set-point on design days.

The engineering conclusion is that the measure is feasible as a reset, not as a fixed change: raise the supply temperature on part-load days, when the latent load is small and coil surface is abundant, and return to the design temperature when the outdoor dew point or the zone humidity rises. It is not feasible as a blanket summer set-point increase in a humid climate, and a building that must control humidity tightly is better served by keeping cold water and decoupling the latent load — a dedicated outdoor-air unit with heat recovery, or a desiccant wheel — so that the chilled-water temperature can be raised for the sensible coils without losing dehumidification.

Topic. Ventilation for contaminant control, thermal comfort, and the coupling between chilled-water temperature and latent capacity.

Key relations. Steady-state dilution: $N G = \dot{V}(C_{room} - C_{supply})$, and its transient form $V\,dC/dt = NG - \dot{V}(C - C_{supply})$ with time constant $V/\dot{V}$. Comfort: operative temperature $t_o \approx (t_a + \bar{t}_r)/2$ for still air; PMV within ±0.5. Chiller: $\text{COP}$ improves as the evaporating temperature rises; coil latent capacity requires an apparatus dew point below the required supply dew point.

Why this works. All three parts are consequences of the same idea — that a building conditions people, not air. Carbon dioxide is not itself the pollutant of interest at these levels; it is a tracer for human bio-effluents, generated in proportion to metabolic rate and therefore a direct measure of whether the ventilation rate matches the occupancy, which is what makes demand-controlled ventilation possible. Comfort likewise depends on the body's heat balance rather than on air temperature alone. And the chilled-water question is the point where the plant's thermodynamics collides with the occupant's physiology: the same higher evaporating temperature that makes the compressor efficient makes the coil unable to wring moisture out of the air.

Common pitfall. In part (a), forgetting that the supply air already contains 250 ppm and dividing by the 1000 ppm ceiling instead of by the 750 ppm rise — that gives 454 people, a 33% over-estimate of the safe occupancy. In part (c), quoting the chiller saving without acknowledging the pump-energy and latent-capacity penalties, which is how apparently attractive reset schedules turn into humidity complaints.

Source. ANSI/ASHRAE Standard 62.1-2022, Normative Appendix and the CO₂ generation data of Persily & de Jonge (2017); ANSI/ASHRAE Standard 55-2020 §5.3 and the graphic comfort zone method; ASHRAE Handbook – Fundamentals (2021), Ch. 9 (thermal comfort) and Ch. 16 (ventilation and infiltration); W. P. Jones, Air Conditioning Engineering, 5th ed., Butterworth-Heinemann, Ch. 4.

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