Oxygen consumption calorimetry

Oxygen consumption calorimetry estimates combustion heat release rate from the rate at which a fire consumes oxygen. Its practical usefulness comes from an approximate regularity: many common combustible materials release roughly $13.1\mathrm{MJ}$ per kilogram of consumed oxygen. The coefficient is an empirical energy equivalent for an applicable class of fuels, not a universal physical constant.^[ref]

Let ${\dot{m}}_{{\mathrm{O}}_2,\mathrm{cons}}$ be the consumed oxygen mass flow rate, obtained from a consistent incoming/outgoing gas balance. A simplified model isFor an illustrative measured consumption rate of $0.001\mathrm{kg}{\mathrm{s}}^{-1}$, this model givesThe observable must include gas throughput: an oxygen fraction by itself cannot determine a consumed mass per unit time.

In an exhaust-collection apparatus, a hood captures combustion products together with entrained air. Measurements of exhaust flow and gas composition allow the consumed oxygen rate to be inferred despite dilution. Gas sampling, mixing and the flow measurement must represent the same stream; gas amounts also need consistent wet/dry conventions and reference temperature and pressure. The NIST National Fire Research Laboratory uses exhaust systems to measure large-fire heat release rate by this principle.^[ref][ref]

A useful experimental check is an independently metered reference burner. Its fuel-consumption-based energy input can be compared with the heat release rate inferred from oxygen depletion; NIST describes natural-gas burners for this mutual confirmation. This tests the measurement chain rather than merely exposing a gas analyzer to a known mixture.^[ref]

Incomplete capture, changing fuel composition, incomplete combustion and analyzer transport delays can all affect the inferred curve. They concern different parts of the inference: lost exhaust biases the gas balance, an inappropriate energy equivalent changes the conversion, and delayed sampling shifts the response in time. A reported heat release rate therefore needs both its conversion assumptions and its measurement conditions.

Heat release rate is the rate at which a process releases energy as heat, commonly used to characterize combustion. It has the dimensions of power and is measured in watts, with $1\mathrm{W}=1\mathrm{J}{\mathrm{s}}^{-1}$. Using $Q_{\mathrm{rel}}(t)$ for cumulative released energy,The heat release rate is the height of the curve; total released energy is its area.

For a synthetic fire whose heat release rate rises linearly from zero to $100\mathrm{kW}$ in $60\mathrm{s}$ and falls linearly to zero over the next $60\mathrm{s}$, the area is a triangle:A second fire with a smaller peak but longer duration can release more total energy. A peak value alone therefore cannot describe the full event.

A fuel-based estimate multiplies fuel mass flow rate by the effective released energy per unit mass, under stated assumptions about composition and combustion. For a deliberately stipulated effective value $20\mathrm{MJ}\mathrm{k}{\mathrm{g}}^{-1}$ and fuel rate $0.02\mathrm{kg}{\mathrm{s}}^{-1}$, the estimate is $400\mathrm{kW}$. In oxygen consumption calorimetry, measured gas flow and oxygen depletion instead provide an estimate of heat release rate. NIST uses independently metered reference burners to compare these two inference routes.^[ref]

A fire's heat release rate differs from the heat transfer received by one nearby surface or from the temperature of its exhaust. Released energy can leave by several paths, while a receiving object can store internal energy as well as lose heat. Even a gas-based calorimeter needs a defined measurement boundary, capture conditions and time response. The NIST National Fire Research Laboratory provides an example of using exhaust collection to quantify large-fire heat release rate.^[ref]