An Introduction to Pneumatic Conveying Data Models and Digital Twins

Pneumatic conveying is well established in the process industries as a method of moving powders and granules distances of a few 10’s of meters to 100’s of meters in a safe and hygienic way.  Conceptually, pneumatic conveying systems are relatively simple, with: an air mover, a solids feeder, an initial mixing region, the transport pipeline and some method to separate the solids from the conveying air at the end.  

Unfortunately, the reality of operating a pneumatic conveying system is much more difficult, due in no small way to the complex flow behaviour of a gas – solds mix travelling along a pipeline typically with a number of horizontal and vertical sections connected by 90 degree bends. 

It is this flow behaviour that needs to be modelled in some way to achieve the potential benefits of control, optimisation and intelligent maintenance promised by Digital Twin technologies and the Industrial Metaverse.  There is continued interpretation of the term Digital Twin but the first sentence of the definition given by the Digital Twin Consortium will be used here [1].

 “A digital twin is a virtual representation of real-world entities and processes, synchronised at a specified frequency and fidelity. “

This gives the basis for conceptualising a digital twin as illustrated by Figure 1 below.

Here data is streamed from sensors in in the real world, processed and utilised in the virtual world and returned to the real world as actionable information.  The question of the frequency and fidelity of the data and information is determined by use case.

In the context of pneumatic conveying, let us consider two use cases; case one using global data to optimise or benchmark system performance based on a specified criterion, and case two using local data to estimate the remaining useful life RUL of a particular component of the system.

Case 1:

The global data referred to here is the relationship between conveying line pressure drop, mass flow rate of particulate solids and the mass flow rate of the conveying gas [usually air].  These data may be grouped together to produce a performance map, alternatively called a conveying characteristic. 

The relationship between the variables depends on: pipeline bore, length and route, number and orientation of bends, pipeline material, and material properties including particle size and size distribution, particle shape and particle density and the conveying characteristic represents a unique behavior for each instance of a pneumatic conveying system.  

The data can be presented in different ways and is commonly shown as a 2D plot of solids mass flow rate vs gas mass flow rate with the line pressure drop indicated by isobars.  However, to be useful in the digital world of the digital twin we require a [mathematical] model of this behaviour. 

We can look for a relevant correlation in the published literature or use software such as Modelica to develop a physics-based model, both of these options have associated large uncertainty scores.  The preferred option would be for a model based on experimental data.  A set of data was collected by a student from an industrial scale test rig at Glasgow Caledonian University. 

Depending on the data, it may be possible to generate a surface fit in 3D space using a moving least squares method as shown in Figure 2.  This approach assumed that the line pressure drop was some function of both solids mass flow rate and air mass flow rate, that is:

dP=fn(m ̇_s)

Where,

dP =   line pressure drop

m ̇_s = solids mass flow rate

m ̇_a = air mass flow rate

Assuming a simple 2^nd order polynomial fit to give an equation of the form:

dP=A+Bm ̇_a+Cm ̇_s+Dm ̇_a^2+Em                  (2)

Where,

A, B, C, D, E and F are constants.

This approach gave R-square: 0.969 and RMSE: 0.06787 values on data with considerable scatter.  This approximates the classic Response Surface Methods of Box and Morton dating from the 1950s and described in the NIST Engineering Statistics Handbook [2]

Alternatively, you can use more advanced methods such as Gaussian Process Regression with a Matern 5/2 kernel, which for this data gives similar results with an R-square: 0.97,  RMSE: 0.06798.  In either case, the model and appropriate boundary values would allow prediction of the effects of changes to one or other of the process variables and could be used for optimisation, benchmarking or system degradation monitoring.

That is all well and good, but so far this is no more than a model that could be used without mention of a digital twin.  Looking back at the definition of the digital twin, there must be some synchronisation between the real world and the virtual world, so any changes in the real conveying system [physical twin] must be reflected in the virtual world [digital twin].

Taking this perspective any changes to the physical system must result in an update to the model, for example, a change to the pipeline route would necessitate a revised model which in this case can be based on established scaling rules available in the published literature or new performance data must be generated and a new model established. 

There are no reliable scaling rules for a change in the product being conveyed and this would require the production of a new model.

Models based on these global data could be used within a digital twin framework for;

• Performance assurance, i.e. to check that any measured deviations from the benchmarked condition of the conveying system does not represent an unacceptable change in overall performance relative to the conveying functional requirement.
• Maintenance scheduling and intelligent maintenance strategies, by mimicking known possible fault conditions, e.g. a drop in air mover performance, in the digital twin to predict the expected measured response from the physical twin and so identify potential system failure criteria.

Case 2:

Developing a model to predict the remaining useful life of a bend in a pneumatic conveying system based on an estimation of erosion effects due to particle wall interaction can be approached in several ways, for example, the one-dimensional erosion model (ODEM) of Uzi et al [3].  

Considered here is the use of engineering simulation to estimate the location and severity of impact erosion based on computational fluid dynamics and Lagrangian particle tracking combined with an appropriate erosion model.  Figure 3 shows the contours of predicted erosion for three conveying conditions by using:

• The Discrete Phase Model in ANSYS Fluent  – (Euler-Lagrange approach).
• The fluid phase is treated as a continuum by solving the Navier-Stokes equations.
• The dispersed phase is solved by tracking a large number of particles, through the calculated flow field.
• The dispersed phase can exchange momentum, mass, and energy with the fluid phase.
• Particle-particle interactions are neglected.
• The dispersed second phase occupies a low volume fraction.
• The particle trajectories are computed individually at specified intervals during the fluid phase calculation.
• The erosion model by Oka et al. [4,5]

It can be seen from Figure 3 that the intensity and location of predicted erosion is dependent on the gas – solids flow behavior entering the pipe bend and such information has the potential to be used to predict overall erosive wear and making conservative assumptions predict bend life. 

The issue for use in the context of a digital twin is that although this approach provides a high-fidelity output, computational speed is a limitation for synchronisation of simulation and system monitoring. 

A potential solution is to use a Reduced Order Model or surrogate model, which is a ‘model of the model’, could be developed from a suitable Design of Experiments treatment to identify a range of high-fidelity simulations to provide the basis for such a model. 

The data from the set of high-fidelity simulations can be developed into such a surrogate model by a range of techniques, for example, Gaussian process regression, or a neural network to develop a multi-dimensional response surface.

References:

1. Digital Twin Consortium
2. NIST/SEMATECH e-Handbook of Statistical Methods
3. Uzi, A., Ben-Ami, Y., Levy, A., Erosion prediction of industrial conveying pipelines, Powder Technology, 309 (2017) 49-60
4. Oka, Y.I., Okamura, K., Yoshida, T., 2005. Practical estimation of erosion damage caused by solid particle impact Part 1: effects of impact parameters on a predictive equation. Wear 259, 95–101.
5. Oka, Y.I., Yoshida, T., 2005. Practical estimation of erosion damage caused by solid particle impact Part 2: mechanical properties of materials directly associated with erosion damage. Wear 259, 102–109.