BA 4510
9.2 Basics of using potentiometric ZrO2 solid electrolyte sensors in optimal
combustion processes
Many technological processes require optimising and reproducible combustion processes (e.g. production of glass or ceramic
fibres, firing porcelain, generating energy or crude gas from solid or liquid fuels, etc.) for consistent product quality and use of
resources. Quality assurance standards such as ISO 9000 require acquisition and documentation of process-related data for en-
sure product quality. Monitoring and controlling these systems requires variables which are preferably acquired in real time
within a wide gas composition range and are clearly assigned to fully balanced gases.
In practice, these measured values are generally acquired using potentiometric ZrO
2
solid electrolyte sensors. These (unheated
or electrically heated) probes can be short or very long, which are used in various types of combustion systems, technical fur-
naces or in flames in situ, and supply the required signals. There further are devices with electrically heated sensors to analyse
external premixed fuel-air mixtures or flue gases.
The following outlines the chemical, thermodynamic and electrochemical bases for using potentiometric solid electrolyte
sensors (= galvanic solid electrolyte cells) in combustion processes.
Oxygen concentration and air number lambda
The exchange of gaseous, liquid or solid fuels with air is best described using the air number lambda. These parameters specify
the ratio of air supplied during combustion and the air required for the stoichiometric conversion of the fuel used. Air can be
specified in volumes, masses or quantities (which are proportional according to the ideal gas law, as commonly known) (units
such as m
3
, kg or mol will be reduced when determining the ratio). With volumes, v is
λ
= v(supplied air volume) / v(stoichiometric air volume required).
If too much air is supplied (excess air),
λ
> 1, when not supply enough air (lack of air),
λ
< 1. In the case of exact stoichiometric
combustion
λ
= 1.
(Only automotive engineering uses a different definition, as engine test stations weigh the amount of fuel used and convert the
supplied air volume into mass. Dividing the air mass by the fuel mass, e.g. with pure octane at exact, stoichiometric conversion,
then equals 15.3.)
The combustion of hydrocarbon (in engine fuel, natural gas, liquid gas) using a molecular formula of C
n
H
m
, with full combustion
at excess oxygen,
λ
then provides the reaction equation
C
n
H
m
+
λ
(n + m/4) O
2
=> n CO
2
+ m/
2
H
2
+ (
λ
- 1) ∙ (n + m/4) O
2
.
In combustion with a lack of air (oxygen shortage), if the temperature is high enough and, if necessary, using catalysts to pro-
duce total gas balance, all organic substances will essentially turn into a mixture of nitrogen and hydrogen, water vapour, car-
bon monoxide and carbon dioxide, the so-called water gas (which can be produced from carbon and water). The reaction equa-
tion for conversions under oxygen shortage can not only be formulated with
λ
, n and m. Rather,
C
n
H
m
+ [(1-a/2) ∙ n + (1-b) ∙ m/4] O
2
=> (1-a) ∙ n CO
2
+ a ∙ n CO + (1-b) ∙ m/2 H
2
O + b ∙ m/2 H
2
,
with a and b divided by
ʎ
and the state of the temperature-sensitive water gas balance
CO + H
2
O = CO
2
+ H
2
being specific quantities.
Gas potentiometry with solid electrolyte cells first only provides the oxygen concentration
φ
(O
2
) in the respective sample gases.
However, the goal is often to determine
λ
. This can be calculated based on the following equations:
λ
m
=
1+
φ(O
2
)
1+2
V
λ
φ (
)
O
2
φ(O
2
)
Air
1
=
f
1
1
1+2
V
V
1+
φ (O
2
)
K
0.5
c
+
φ (O
2
)
0.5
1+
K
1
H
These equations for some hydrocarbons with
λ
> 1 (lean) and with
λ
< 1 (rich) include the carbon/hydrogen ratio of the hydrocar-
bon, V = 2 n/m, and the thermodynamic equilibrium constants for the reactions
CO
2
= CO + 1/2 O
2
lg K
C
= 4.505 - 14700 K / T,
H
2
O = H
2
+ 1/2 O
2
lg KH = 2.947 - 13008 K / T.
Practice, however, usually sees mixtures of different hydrocarbons, fuel gases can further contain hydrogen, carbon monoxide
and nitrogen, and the humidity and carbon dioxide content of the air used contributes to the gas equilibriums. Equations modi-
fied accordingly must use average V. Thinning with nitrogen slightly affects
ʎ
in the lean range, but not in rich, as the balance
between the water gas components is not affected by pressure, thus the water gas concentration.
23
Bühler Technologies GmbH
BE550013 ◦ 09/2018
