“Where is what in the vessel, right now? Is there still a dead zone behind the baffle? Has the changeover front gone past?” Three questions about an opaque volume, whose answer is an image rather than a value.
A question distinct from the ones spectroscopy handles: where is what in the section, right now.
Where you meet it: mixing vessel in cosmetics, dairy line, chromatography column.
The essentials in four points
- Returns a distribution, not a content: the image of the section, at a resolution of roughly 5 % of the sensor diameter.
- No multivariate model is needed for the image: it comes straight out of the physics of the measurement. A few calibration points suffice for a content.
- Two variants, chosen by the medium: ECT for weakly conducting media (powders, granules, oils), ERT for conducting media (aqueous suspensions, brines, culture media).
- Reference texts: none, in pharma or elsewhere: the method is validated against your reference method.
How the measurement works
Electrodes around the wall measure the electrical response of the contents; a reconstruction algorithm turns it into an image of the phases.
Typical applications
Phase distribution
Dead zone, gas pocket, persistent stratification: often the first time the team sees what it suspected.
End of homogenisation
The contrast settles once the blend is done, with no calibration: you follow a convergence.
Columns and interfaces
Packed bed of a column, filling of an opaque container, travel of an interface.
A real case
A continuous process in an opaque volume: dead zones and regime changes made visible.
A product front in a pipe is followed the same way, rather than purging for a flat-rate duration.
Identity card of the technique
| Criterion | ECT and ERT tomography |
|---|---|
| What the measurement sees | A distribution, not a content. Wall electrodes measure the capacitive response of the contents (ECT, poorly conductive media) or their resistive response (ERT, conductive media). |
| Selectivity | It rests on the electrical contrast between phases, not on their chemistry. Two phases of similar permittivity are indistinguishable, however different they are chemically. |
| What interferes | Insufficient electrical contrast closes the measurement. Resolution is about 5 % of the sensor diameter: the same rule gives fine detail on a pipe and coarse detail on a large vessel. And it is not uniform across the section: better near the electrodes, poorer at the centre — adding electrodes even degrades the centre, which is often where a dead zone is sought. |
| Sample presentation | Electrodes built into the wall, or a fitted belt. On a qualified vessel, drilling triggers a requalification, to be costed at scoping. |
| What the model requires | No multivariate model for a distribution — which is rare, and an asset. A few calibration points to turn it into a content. |
| Reference texts | In pharma: no pharmacopoeial chapter covers electrical tomography — we looked: Ph. Eur. 5.24, Chemical imaging, which names OCT, terahertz and X-ray tomography, does not mention it. The method is validated on its own terms, in the sense of ICH Q2(R2). Outside pharma: no text is devoted to it: the method is validated on its own terms, against your laboratory’s reference method. |
ECT or ERT: what separates them
ECT, capacitance tomography
The capacitive response between pairs of electrodes. Suited to weakly conducting media: powders, granules, oils, divided solids.
ERT, resistivity tomography
The resistive response, in alternating current. Suited to conducting media: aqueous suspensions, brines, culture media.
No model to develop or maintain
For the image, there is no chemometric model to develop or maintain. It is the point that sets this family of measurements apart from almost all the others, and it changes the economics of a project. No reference sample campaign, no design of experiments, no model that drifts and whose review frequency has to be decided. When such a frequency exists, it follows from the process — material variability, supplier changes, seasonality — and never from a calendar.
The reason: the quantity comes directly from the physics of the measurement. A difference in permittivity or conductivity is the contrast in the image. A measured property, not a correlation learnt on a population of samples.
The nuance to know: if what you want is not an image but a content, a calibration step is needed. It stays light (a few points, not a campaign) but it exists. See what calibration burden your measurement imposes, and the section on content further down.
The specifications, with the configuration they come from
Here are the orders of magnitude, with what makes them usable: a frame rate is always read with the configuration it comes from. These values are requested case by case.
| Quantity | Value | In which configuration |
|---|---|---|
| Spatial resolution | About 5 % of the sensor diameter | On a 200 mm pipe, structures of the order of a centimetre are separated |
| Frame rate | About 30 images per plane per second | On certain families of device only |
| Acquisition rate | Under one millisecond for a complete set | On two planes of 16 electrodes, on another family of device |
| Electrodes | 8, 16 or 32 per plane | In a 16-electrode configuration: 104 voltage measurements per set, around thirty frames per plane per second |
| Dimensions covered | 5 mm to 2 m in diameter, 5 cm to 4 m in length | The spread between those bounds says this is a family of sensors |
| Explosive atmospheres | ATEX Ex ia IIC T6 certification | IP66 rating on certain enclosures |
A frame rate takes its meaning once it is attached to its number of electrodes and planes. It then becomes a sizing figure.
Three algorithms, three different uses
The reconstruction is more than an internal detail: it decides what the image shows well, and what it shows coarsely.
Linear back-projection
Fast, usable in real time. Good on concentration gradients: a stratification fading, a blend becoming homogeneous.
Iterative conjugate gradient
Costlier in computation, more faithful. Good on sharp interfaces: a gas pocket, a plug, a clean separation.
Parametric reconstruction
Reserved for processes already modelled: the parameters of a known geometry are sought rather than a free image.
What several planes add
One plane of electrodes gives a section. Two planes or more give something else, and it is more than a prettier image.
- A reconstructed volume. The sections stack into a three-dimensional representation, orientable, usable live or afterwards. On a column or a tall vessel, that is the difference between knowing that an anomaly exists and knowing at what height it sits.
- A velocity, by cross-correlation. The same event crosses plane 1 then plane 2. The time gap and the distance between planes give a flow velocity, with no extra sensor. The ceiling follows the rate: the closer the planes and the slower the acquisition, the lower the maximum correlatable velocity.
- A mixing index between planes, which compares the state of two heights rather than the homogeneity of one section.
Two points the manufacturer’s documentation states itself
Between two planes there is no measurement. The volume displayed is a stack of sections, with an interpolation whose distance is set to match the real physical spacing. What happens between two electrode belts is inferred rather than measured. So the number of planes and their spacing are a design decision rather than a display setting.
Accuracy shifts in multi-plane use. Of the order of ± 1 % on a single plane, ± 3 % in a multi-plane configuration, for background conductivities of the order of 0.1 mS/cm. And three-dimensional rendering during acquisition slows the rate. The manufacturer recommends keeping it for off-line analysis where temporal resolution counts.
What the image gives, and what a content needs in addition
A content, through a correlation
The image gives a distribution rather than 3.2 %. What it measures is an electrical property, and one more step draws a composition from it. That step exists and it is light: a few calibration points are enough where the quantity sought really drives the conductivity of the medium. What is then built is a soft sensor, conductivity and temperature in, content out, rather than a multivariate model on a sample campaign.
That is what the academic literature establishes on milk. On the calibration burden axis, tomography therefore sits away from the calibration-free end as soon as a content is the target. It moves towards the middle of the axis, for a cost that stays unrelated to a full spectroscopic calibration.
Where this stops holding. Where two different compositions give the same conductivity, and where the temperature is unmeasured at the measurement point. An electrolyte sees its conductivity vary by the order of two per cent per degree. With no compensation, the thermal drift reads as a variation in content.
Resolution, the criterion for comparison
The published criterion is the resolution relative to the diameter, about 5 %: that is what two offers are compared on, and what decides whether you will see the structure you care about. The other values are requested case by case.
Temperatures and pressures come from your specification
The admissible temperature and pressure range is defined for each installation, and is requested case by case. A wall sensor is made for a given process: your specification sets the range.
So the service conditions are defined by a requirements document, what is called a user requirements specification. Written before consulting suppliers, it turns a discussion into a technical commitment.
| Section | What goes in it |
|---|---|
| Contacts | Who decides, who operates, who validates, often three different people |
| Process | Continuous or batch, installation arrangement, the aim of the measurement in one sentence |
| Sensor | Wetted material, dimensions, chemicals present, cable length |
| Variable factors | The heart of the document: temperature, pressure, velocity, concentration, conductivity, each with its real range rather than its nominal value |
| Further requirements | Adapters, ATEX requirement, input-output module, expected software |
| Traceability | Requirement → technical answer → solution retained → approval, with the customer’s signature |
That last block matters most and is most often absent. It lets you find, two years later, why a choice was made and who approved it. That is what an auditor asks for, and what a team that has turned over can no longer reconstruct. We write it during the scoping, before any consultation.
Purification columns: seeing the packed bed rather than inferring it
In protein purification and oligonucleotide synthesis, the yield follows the flow conditions in a packed bed, and the resin carries a real cost. Judging the quality of a packing simply is what has been missing: it is inferred from what comes out rather than seen inside. Electrical tomography is one of the few methods that gives access to the state of the bed in situ.
The arrangement is a stack of electrode belts along the column, typically eight planes of sixteen electrodes, sampled several times a second. The contrast comes from conductivity: a buffer change, an elution front, a tracer.
- The elution front is followed plane by plane as it descends. A front that stays flat and symmetrical says the bed is regular. A deformation says otherwise, and says above all where.
- Preferential flow, or channeling, reads as a zone of conductivity ahead of its plane, localised in height. It is the feature that outlet analysis reports late and without an address.
- The quality of the packing and how it evolves. The same column can be re-examined after a number of separations to judge its integrity, rather than being replaced on a calendar.
- The repeatability of a cyclic process. On a synthesis running to dozens of successive steps, the overall tomographic signal compares from one step to the next and shows the one that moves.
Two points to keep in view. The electrodes are built into the column: that is decided at design, rather than retrofitted onto a column already qualified. And the demonstrated use is a development and characterisation use rather than a release measurement. The literature carries no release use yet, and that is the question to put before going further.
What a published trial establishes, and what it does not
A product changeover trial in a pipe establishes the detectability of the front. Two fluids separated by a very small conductivity gap are separated reliably. That is the result to hold on to.
The same trial quantifies no cycle gain, so we quote no purge reduction percentage, since the source carries none. The gain is costed process by process, from your rinse volumes, your purge durations and your number of changeovers a year. On your data, before any investment.
What is worth preparing on your side
- Access at the wall. Built-in electrodes, or a retrofitted belt. On a qualified vessel, a penetration brings a requalification to be costed at scoping rather than discovered mid-project.
- The real electrical contrast between your phases. Feasibility question number one: two media of identical conductivity read alike. A laboratory trial settles it quickly.
- The real ranges of your variable factors, rather than the set points. That is what the requirements specification asks for, and often the longest part to assemble.
- A definition of what you will do with the image. An image looked at by an operator carries different requirements from an indicator triggering an automatic stop.
Frequently asked questions
Is there really no chemometric model?
For a distribution, that is right: no multivariate model to calibrate, and that is rare. Choices remain: the reconstruction algorithm, the sensor settings. They are not models built on a population of samples, and they do not drift.
For a content, a model comes in. The physical quantity measured is a conductivity, and relating it to a composition calls for a soft sensor, a model correlating conductivity and temperature with the concentration sought. That model is calibrated, validated and maintained like any other. The calibration burden therefore follows the use rather than the technology.
Can it be installed with the vessel unpierced?
In some configurations, yes: the electrodes can be carried on a retrofitted belt rather than built into the wall. It is the first point to establish, because it changes the cost and the lead time of a project on existing equipment.
Is it usable in an explosive atmosphere?
An ATEX Ex ia IIC T6 certification exists, along with an IP66 rating on certain enclosures. As always it covers a precise configuration. It is verified on the declaration of conformity of the equipment retained.
What size of structure can be seen?
The sizing rule is about 5 % of the sensor diameter. On a small pipe that gives a fine resolution in absolute terms. On a large vessel the same rule gives a coarse one. So the question of resolution has an answer once the diameter is known.
How many measurements a second can be expected?
It follows the configuration entirely. Some systems reach about 30 images per plane per second. Others acquire a complete set in under a millisecond on two planes of 16 electrodes. Those two figures describe neither the same device nor the same thing: always ask which configuration the one you are quoted refers to.
Can it be used to release a batch?
Not as it stands. The image alone answers a distribution question rather than a composition specification. A soft sensor returning a content would then be validated like any analytical procedure: accuracy, precision, range, robustness. Where tomography installs most easily is as a contribution to a documented control strategy: proving that homogenisation has been reached. See analytical procedure validation.
And where the electrical contrast is small?
Then another route serves better, and a feasibility trial establishes it rather than an installation. It is a clear case of a founded answer: the physics is what it is, and a setting does not change it.
The instruments we implement
ITS, Industrial Tomography Systems. ECT and ERT systems for vessels, pipes and containers, with electrodes integrable in the wall or on a retrofitted belt.
Measuring a content by tomography: what the literature says
The best documented case is milk. Two works from the University of Auckland establish the approach and its bounds.
- Sharifi and Young, Food and Bioproducts Processing 90(4), 2012, pp. 659-666, estimating total solids and fat content of milk from resistivity tomography and a temperature measurement, with a mean accuracy announced above 96 % at constant temperature.
- Sharifi and Young, Journal of Food Engineering, 2013, correlation between conductivity, temperature and composition to reach total solids, by design of experiments and response surface. Accuracy above 93 %, with a useful observation: a multiple linear regression does better at low concentrations, the response surface at high ones.
What these works establish, and what they leave open. The content is reachable, with a small number of calibration points rather than a campaign, and it goes through a correlative model in which temperature is a variable in its own right. A tomography installed with no associated temperature measurement will return a content that carries the thermal drift with it.
The same reasoning transposes to the continuous monitoring of total solids in any conducting medium. Conductivity carries the composition information, provided it is corrected for temperature and a few reference values are available to set the relation.
The same logic holds outside dairy whenever the conductivity of the medium follows the composition sought. It stops holding as soon as two different compositions give the same conductivity. That is the bound to establish first.
Describe your vessel or your pipe. You will hear whether the contrast is there.
Forty-five minutes is enough: whether your phases separate electrically, what resolution your diameter allows, which wall access would be needed, and what the gain would represent on your real purge volumes.