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Transcript
Electrical Resistance Tomography
Quak Foo Lee
Department of Chemical and Biological Engineering
The University of British Columbia
Learning Objectives

By the end of this presentation, you should be able
to:
Describe the basic concept and applications of ERT
Design the electrodes for ERT system
Understanding different basic measurement strategies
and image reconstruction
Analyze the ERT data through different numerical and
Statistical data analyses
Outline








Background
Applications and Examples
Operating Principle
Electrode Geometry and Construction
Measurement Strategies
Image Reconstruction
Data Analyses
Summary
Background to ERT

A measurement technique for obtaining information
about the contents of process vessels and pipelines.

Multiple electrodes are arranged around the boundary
of the vessel at fixed location.

The electrodes make electrical contact with the fluid
inside the vessel BUT do not affect the flow or
movement of materials.
Application

A typical application is real time monitoring of
multicomponent flows within process engineering
units.

Use in any process where the main continuous
phase is at least slightly conducting and the other
phases and components have different values of
conductivity.
Examples







Solid/liquid and liquid/gas mixing
Hydrocyclones
Packed columns
Flotation columns
Precipitation processes
Liquid-liquid extraction
Hydraulic conveying
Operating Principles

An ERT system produces a cross-sectional image
showing the distribution of electrical conductivity of
the contents of a process vessel or pipeline from
measurements taking at the boundary of the vessel.

The P2000 system injects a current between a pair
of electrodes and measures the resultant voltage
difference between remaining electrode pairs
according to a pre-defined measurements protocol.
Operating Principles (…cont)

This interrogates an entire “slice” through the
measurement zone – analogous to a “body-scan” in
medical imaging.

A single measurement set consists of over 100
voltage measurements – the exact number depends
on the pre-defined measurement protocol.
Electrode Geometry &
Construction
Electrodes arranged at equal intervals
around the boundary of a circular vessel.
Electrode Arrangements
1.
At equal intervals around the boundary of a
circular vessel
2.
Around a square cross-section
3.
A vertical series of electrodes
Electrode Geometry &
Construction

The electrodes are connected to the data
acquisition system by co-axial cable which assists
in reducing the effect of extraneous environmental
noise and interference.

The outer sheath of the co-axial cable is coupled to
the feedback path of a voltage buffer to provide
further noise immunity and the inner core is
capacitively coupled to the input of the voltage
buffer.
Electrode Geometry &
Construction

The material of electrode should be more conductive
than the fluids being imaged to prevent problems
due to contact impedance.

Typically the electrode material is stainless steel,
brass or silver palladium alloy.
Electrode Geometry & Construction

The dimensions of the electrodes are a function of
the vessel diameter, range of conductivity to be
measured, velocity of materials and the required
imaging speed.

A spare electrode, referred to as the ground
electrode, positioned away from the measurement
electrodes BUT in electrical contact with the internal
fluid is required to ensure all voltage measurements
are fixed against a common ground source.
Electrode Design
2.5
Electrode Diameter
-------------------------- = 0.4
Inter-Electrode Gap
Electrode Diameter (cm)
Electrode
Diameter
2.0
1.5
Inter-Electrode
Gap
y = 0.0777x + 0.0028
R2 = 0.9995
1.0
0.5
0.0
0.0
5.0
10.0
15.0
20.0
Column Diameter (cm)
25.0
30.0
Data Acquisition System

Responsible for obtaining the quantitative data
 Describing the state of the conductivity
distribution inside the pipeline

The data must be collected quickly and accurately
in order to track small changes of conductivity in
real-time
 Allowing the image reconstruction algorithm to
provide an accurate measurement of the true
conductivity distribution.
Measurement Strategies (MS)
MS: Normal Adjacent

Recommended measurement strategy for
sensors with insulating boundaries with 16
electrodes arranged at equal intervals around
the periphery of the sensor.
MS: Normal Adjacent
1.
Current is applied through two neighboring electrodes (e.g.
electrodes 1 and 2),
2.
The voltages are measured from the remaining pairs of
neighboring electrodes (e.g. electrodes 3 and 4),
3.
Current is then applied through the next
pair of electrodes and the voltage
measurements are repeated.
4.
The procedure is repeated until all the
independent measurements have been
made.
MS: Normal Adjacent



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Yields N2 measurements, where N is the number of
electrodes.
Of these only N(N-1)/2 are independent.
To avoid electrode/electrolyte contact impedance
problems, the voltage is not measured at a current
injecting electrode and the total number of
independent measurements M is reduced to
N(N-3)/2.
A 16-electrode sensor gives 104 independent
measurements.
MS: Fast Adjacent

Only suitable for fast data collection when no online image processing is performed.

The principles are the same as those described
for the normal adjacent strategy.
MS: Linear

Used when a vertical series of
electrodes mounted either on a
linear rod or fixed along the
inside of a vessel.
MS: Conducting Boundary



Applied to pipelines and vessels with conducting
boundaries, e.g., stainless steel pipes.
The relatively large surface area of the conducting
boundary is employed as the current sink to
reduce the common-mode voltage across the
voltage across the measurement electrodes.
The earthed conducting boundary also acts as a
shield, reducing the effects of electromagnetic
interference.
Image Reconstruction




For an ERT system the reconstructed image will
contain information on the cross-sectional
distribution of the electrical conductivity of the
contents within the measurement plane.
A square grid with 20 × 20 = 400 pixels represents
the vessel interior cross-section.
Some of these pixels will lie outside the vessel
circumference.
The circular image is constructed using 316 pixels
from the 400 pixel square grid.
Image Reconstruction Grid
The Forward Problem – Sensitivity Map



Forward? Because σ(x,y) is known everywhere
inside the sensor.
The task is to find the boundary voltage
measurements, given the injection current I applied
to the electrode s and the conductivity distribution
σ(x,y) at all points.
Solve the forward problem by calculation of a
sensitivity map which describes the behavior of the
sensor.
The Inverse Problem



To determine the conductivity distribution σ(x,y)
from a finite number of boundary voltage
measurements.
The linear back-projection algorithm back projects
the voltage measurements to conductivity values
within the pixels.
The image is reconstructed via a matrix/vector
multiplication.
Linear Backprojection Algorithm

The potential difference is calculated by the
forward solver, between two equipotentials on
the boundary was back-projected to a resistivity
value in the area enclosed by the two lines for all
possible injection/measurement combinations.
Linear Backprojection Algorithm


Gives the relative difference between the
conductivity distribution in the test set and that of
a single reference set.
The algorithm assumes that no sharp conductivity
differences exist in the measurement plane, and
smoothes interfaces where severe conductivity
gradients exist.
Numerical and Statistical Data Analyses
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Voltage Measurements and Graphs
Conductivity Tomogram
Pixel Range
Resistivity (raw)
Mean Pixel Conductivity
Pixel Trace
Mixing Statistics
Concentration
Scatter Plots
Average Across Frames
Limitations of ERT System




A time lag between measurements made in
planes one and eight.
A resolution of 5 to 10% of the vessel diameter.
Greater image sensitivity at the periphery of the
vessel.
The tomograms in the upper-most and lowest
plane show distortions due to end effects related
to the three-dimensional nature of the electric
field not accounted for during the twodimensional reconstruction of the planar image.