Question 5 of 8: Thermal comfort, chilled-water reset and campus cogeneration

Question 5: Thermal comfort, chilled-water reset and campus cogeneration (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. Three discussion topics; parts (b) and (c) are argued quantitatively, so each carries a short data statement of its own.

Find. An explanation of the comfort chart and of how comfort is perceived; a judgement on raising chilled-water temperature, with the consequences for humidity control; and an account of cogeneration applied to a university campus, with the assumptions stated.

Part (a) — the ASHRAE comfort chart and the perception of comfort. Thermal comfort is defined in ASHRAE Standard 55 as "that condition of mind which expresses satisfaction with the thermal environment", and the definition is deliberately psychological: comfort is a judgement made by an occupant, not a property of the air. What the standard supplies is a statistical map of the conditions under which at least 80 % of ordinary occupants will report satisfaction. The comfort chart is that map, drawn on psychrometric axes — operative temperature along the bottom, humidity ratio up the side — with two shaded envelopes, one for winter clothing of about 1.0 clo and one for summer clothing of about 0.5 clo.

Six variables control the heat balance of the body, and the chart is a two-dimensional slice through them. Four are environmental — air temperature, mean radiant temperature, air speed and humidity — and two personal, the metabolic rate and the clothing insulation. Air temperature and mean radiant temperature are combined into the operative temperature, roughly their average at the low air speeds found indoors, which is why a room with a cold window wall feels cold even when the thermostat reads $22^{\circ}\text{C}$: the radiant term is doing the damage, and the fix is better glazing or a perimeter heater rather than more warm air. Fanger's predicted mean vote (PMV) model, on which the envelopes are based, evaluates the body's heat balance and returns a vote on a seven-point scale from cold through neutral to hot; the predicted percentage dissatisfied (PPD) follows from it, and is never below 5 % — there is no set of conditions that satisfies everybody.

Two features of the chart repay attention. The zone is wide in temperature but bounded in humidity, because the body is a good regulator of sensible heat loss and a poor one of evaporative loss: at high humidity, sweat cannot evaporate and skin wetness rises; at low humidity, mucous membranes dry and the perception of stuffiness increases even though the temperature is correct. And the zone shifts with clothing and activity, which is why the chart is drawn for 1.1 met, roughly seated office work — a workshop at 2 met needs conditions two or three degrees cooler. Standard 55 also allows the zone to be extended by elevated air speed, up to about $0.8\ \text{m/s}$ under occupant control, worth roughly $3^{\circ}\text{C}$ of apparent cooling, and permits an adaptive envelope for naturally-ventilated buildings in which the acceptable indoor temperature tracks the running mean outdoor temperature. Both extensions matter in Canadian practice, where the swing between January and July design conditions is severe and rigidly holding one set point year-round is neither comfortable nor economical.

Part (b) — raising the chilled-water temperature. Given. The plant of Problem 2 as a worked example: a space at $25^{\circ}\text{C}$ and 50 % relative humidity, so $W_{R}=10.02$ g/kg and the room dew point is $14.07^{\circ}\text{C}$; a coil designed for an apparatus dew point near $9^{\circ}\text{C}$ on $6^{\circ}\text{C}$ chilled water, and the proposal to raise the supply water to about $10^{\circ}\text{C}$. Find. Whether the saving is real, and what it does to comfort.

The attraction is genuine and easy to quantify: a chiller's efficiency improves by roughly 2 to 3 % for each kelvin of evaporating-temperature rise, so a 4 K increase in chilled-water supply temperature is worth something like 10 % on chiller energy, and it also widens the hours during which a water-side economiser or a cooling tower alone can carry the load. Against that stands the dehumidification, and the arithmetic is unforgiving. The latent capacity of a coil is proportional to the moisture difference between the room air and the coil surface. Raising the apparatus dew point from $9^{\circ}\text{C}$ (where saturated air holds 7.13 g/kg) to $13^{\circ}\text{C}$ (9.33 g/kg) changes the driving potential from $10.02-7.13=2.89$ g/kg to $10.02-9.33=0.69$ g/kg — a fall to 24 % of the design latent capacity. At $14^{\circ}\text{C}$ surface temperature, essentially at the room dew point, the coil stops dehumidifying altogether and becomes a sensible cooler.

The consequence is that the space humidity floats up until the latent gains are balanced by the ventilation air and by whatever residual condensation the coil manages. Relative humidity in the 60 to 70 % band follows, and with it a chain of real problems: the occupants report the space as "close" even at the correct dry-bulb temperature, because skin wetness is what the body notices; mould and dust-mite activity rise sharply above 60 % relative humidity; and the return-air path, ductwork and any cool surface in the building become condensation risks. Since the room dew point is $14.07^{\circ}\text{C}$, any surface below that will wet, and chilled beams or radiant panels — precisely the systems that make high chilled-water temperatures attractive — are exactly the surfaces at risk.

The professional judgement is therefore that the proposal is feasible only if the latent load is removed somewhere else, and there are three orthodox ways to do that. Split the plant: run a small quantity of low-temperature water to a dedicated outdoor-air unit that dries the ventilation air to a low dew point, and high-temperature water to the sensible-cooling terminals; the ventilation air then carries the whole latent load and the room coils never condense. Use a dedicated outdoor-air system with an enthalpy wheel or a desiccant wheel, which is now the common Canadian answer for schools and offices. Or, cheapest of all, apply chilled-water reset scheduled on load or on outdoor dew point rather than a fixed increase: the water temperature rises only when the humidity does not need controlling, which captures most of the chiller saving on the many mild hours and none of the risk on the design day. A blanket increase in supply temperature, applied to a conventional all-air system in a humid Ontario summer, trades a measurable energy saving for an unmeasurable comfort and building-durability liability, and would not be defensible.

Part (c) — cogeneration on a university campus. Cogeneration, or combined heat and power, is the production of electricity and useful heat from a single fuel input in one plant. A conventional generating station converts about a third of its fuel to electricity and throws the rest away as low-grade heat, because it has no customer for warm water at $90^{\circ}\text{C}$; a campus does. Placing a prime mover on site and capturing its jacket water, oil cooler and exhaust heat therefore raises the fuel utilisation efficiency from about 0.33 to about 0.80, and the whole economic argument rests on that single number.

Given (stated assumptions). A reciprocating gas engine or small gas turbine of the size a campus of 20 000 students would install, taken as 5 MW electrical; electrical efficiency $\eta_{e}=0.35$ and recoverable heat $\eta_{h}=0.45$ of fuel input, so the fuel utilisation efficiency is 0.80; displaced grid generation at $\eta_{grid}=0.33$ including transmission and distribution losses; displaced boilers at $\eta_{b}=0.80$; natural gas fuel; and a campus with a substantial year-round heat demand — space heating in winter, domestic hot water, laboratory and pool loads, and sterilisation and humidification in the research buildings. Find. The primary energy saved, and the conditions under which the scheme is worth building.

1. Fuel to deliver one unit of electricity. On site, $$F_{CHP}=\frac{1}{\eta_{e}}=\frac{1}{0.35}=2.857\ \text{units of fuel}$$ which also yields $2.857\times0.45=1.286$ units of recoverable heat.
2. Fuel for the same outputs, generated separately. $$F_{sep}=\frac{1}{\eta_{grid}}+\frac{1.286}{\eta_{b}} =3.030+1.607=4.637\ \text{units of fuel}$$
3. Primary energy saving. $$\text{saving}=\frac{4.637-2.857}{4.637}=\boxed{38\ \%\ \text{of primary energy}}$$ with a proportionate reduction in carbon emissions wherever the displaced generation is fossil-fired.

The saving is only realised if the heat is used, and that is the whole design problem. A campus is an unusually good host for cogeneration because it is a single owner behind one meter, with a district heating loop already in the ground, a diverse and long-hours load, and staff to operate the plant. The engine is therefore sized on the summer base heat load, not the winter peak — typically 30 to 40 % of the peak thermal demand — and run at full output around the clock, with the existing boilers retained to top up in winter and to provide standby. Sizing it on the winter peak would leave it dumping heat for eight months of the year, which destroys the efficiency argument entirely.

Three refinements make the campus case stronger. Absorption chilling turns the summer heat surplus into cooling: at a single-effect COP of about 0.7, the 1.29 units of recovered heat per unit of electricity yield 0.90 units of chilled-water cooling, which flattens the seasonal profile and is the usual justification for calling the plant trigeneration. Thermal storage, a large stratified tank on the heating loop, decouples the engine from the diurnal load swing and lets it run at steady full output. And the electrical interconnection must be settled early: a campus plant running in parallel with the local distribution utility needs protection to CSA and utility standards, an interconnection agreement, and a decision on whether export is permitted and at what price — in Ontario the value of exported power is usually well below the retail rate, so the plant is sized to the campus's own base electrical demand rather than for export.

Finally, the carbon case must be argued on the actual grid, not the textbook one. Against a coal or gas grid the emissions saving tracks the primary-energy saving. Against Ontario's grid, which is largely nuclear and hydro with a marginal gas fleet, burning gas on campus to displace low-carbon electricity can raise emissions even while it lowers cost and primary fuel use. The honest engineering recommendation for a Canadian campus today is therefore to build the district heating loop and the thermal storage first, because those are useful under any future plant, and to select the prime mover against the local grid's marginal emissions factor — with the heat pump, driven by that same low-carbon electricity, as the direct competitor to the gas engine.