Environmental Engineering Reference
In-Depth Information
steel pipe. Each module is made of a non-conductive PVC cylinder machined to
support a stainless steel ring electrode. The conductivity value of each consecutive
pair of electrodes (conductivity cell) is sequentially measured. Once all conductivity
cells have been scanned, the conductance values are processed by an algorithm that
searches for the largest change in the conductance profile (“largest slope”); then the
interface position is assigned to the middle position of the cell generating the largest
slope. The accuracy of this “largest slope” algorithm is strongly related to the sepa-
ration between electrodes. It has been reported though, that the largest conductivity
change gives not one but two possible cells containing the interface [21].
The accuracy problem of the largest slope method was tackled by Uribe-Salas
et al.
[22], by using a “fairly linear relationship” between conductance and the in-
terface position, enabling data interpolation to increase the accuracy of interface
detection. Although good results were obtained using this technique, its major draw-
back is the extensive experimentation required to obtain the linear relation between
cells' conductance and actual interface position, which obviously has to be known.
To describe the nonlinear conductivity profile across the interface (rotated S-shape),
Perez
et al.
[23] proposed the use of an artificial neural network (ANN). Although
this method provides excellent estimates, it is not suited for practical application be-
cause it requires extensive experimentation for the ANN training, where measuring
the interface position by an independent method (
e.g.
, visual observation of trans-
parent laboratory columns or a properly calibrated probe in industrial columns) is
a must. In order to avoid the determination of linear equations in each conductivity
cell of the probe or the extensive experimentation associated with ANN training,
Gregoire proposed a semi-analytical method in which the cell containing the inter-
face is represented as a series of two electrical resistances, corresponding to its two
components: froth and pulp [21]. If the conductivity of the adjacent cells (above and
below) and the cell containing the interface are known, then these two conductiv-
ities (froth and pulp) can be estimated, and the exact interface position, X, within
that cell can be calculated.
As previously mentioned, the detection of the cell containing the interface is fun-
damental to the success of this approach. This is done through an iterative procedure
where the first step is to detect the location of the largest change in the conductance
profile. Extensive experimental work has shown that this cell does not necessarily
correspond to the interface position, as is currently supposed. Gregoire's method can
then be applied, assuming that the interface is indeed located in this cell and then
assuming that it is located in the cell immediately above. If the first assumption was
true, then the calculation made under the second assumption would lead to a negli-
gible value for the pulp level X within the interface cell. On the other hand, if the
second assumption was true, then the calculation made based on the first assump-
tion would result in an extremely high value of X (larger than the actual electrode
separation). A conditional selection algorithm (IF-ELSE clause) is implemented to
deal with this decision.
It was observed though, that near the electrodes, Gregoire's method leads to es-
timate pulp level discontinuities, in the form of a series of sudden jumps, as a result
of the conditional selection algorithm. Although a maximum variation of 5 cm can
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