Predicting effective thermal conductivity in sands using an artificial neural network with multiscale microstructural parameters

https://doi.org/10.1016/j.ijheatmasstransfer.2021.120997Get rights and content

Highlights

  • Coordination number is weighted by contact area to quantify microstructure.

  • Weighted coordination number (WCN) considers contact number and contact area.

  • WCN well relates to heat flux in irregular sand samples.

  • Multiscale microstructural variables are critically selected as inputs for ANN.

  • ANN can accurately predict the thermal conductivity of sand based on CT images.

Abstract

Accurate and efficient prediction of thermal conductivity of sands is challenging due to the variations in particle size, shape, connectivity and mineral compositions, and external conditions. Artificial Neural Networks (ANN) models have been used to predict the effective thermal conductivity but they have not considered variables related to particle connectivity. This work uses computed tomography (CT) scanned images of four dry sands and network analysis to redress this significant shortcoming. Here sands are represented as networks of nodes (grains) and edges (interparticle contacts or/and small gaps between neighbouring particles) to extract network features that characterise interparticle connectivity. A network feature – weighted coordination number (WCN) capturing both particle connectivity and contact area – was found to be a good predictor of effective thermal conductivity in dry materials. Roundness, sphericity, solid particle thermal conductivity and porosity are other input parameters rigorously selected for an ANN model that predicts well the effective thermal conductivity of sands.

Introduction

Granular materials are engaged in numerous applications such as geothermal engineering [1], petroleum and gas extraction [2], carbon dioxide geological storage [3] and pebble bed reactors [4]. In these projects, heat transfer is one of the processes that dominate project design and capital costs. As effective thermal conductivity (λeff) indicates the ease of heat transfer, its accurate and efficient prediction is essential. However, the prediction is challenging due to the complex microstructure of granular materials and external boundary conditions [5,6]. The microstructure can be characterised at different scales, such as particle size, shape, gradation and minerality at the microscale (particle scale); particle connectivity [7,8] at the mesoscale and porosity at the macroscale. Work by van Antwerpen et al. [9], Abdulagatova et al. [10] and Abyzov et al. [11] investigated a number of λeff models against experimental data and found some models simplify granular materials as packings of spheres, ellipsoids or parallel cylinders (regular geometrical forms), which limited their applicability to natural sands. Moreover, models characterise packing structure using porosity alone are insufficient [9] and microstructural parameters about grain-grain resistance [10] and contact area [11,12] have not been incorporated in λeff models although they are important to λeff prediction [13]. In addition, particle connectivity, i.e., microstructural contact topology related to thermo-mechanical response [14], has rarely been quantified except for using coordination number which is defined as the number of neighbouring particles in contact with a given particle.

Recently, researchers abstracted granular materials as contact networks and thermal networks by creating nodes for particles and edges for interparticle contacts (contact networks), and with the addition of near-contacts which represent the small gaps between neighbouring particles (thermal networks) [15]. Then based on complex network theory [16], contact area or thermal conductance can be added as a weight to each edge in the network to eventually identify a single mesoscale network feature which can characterise both the particle connectivity and contact quality. One such feature from the contact network is the weighted degree, which represents an enhanced version of coordination number that accounts for the contact area of each interparticle contact. Hence, while the coordination number only counts the number of neighbouring particles of a target particle, the weighted coordination number (WCN) quantifies both the contact number (particle connectivity) and contact area (contact quality). The physical meaning of the WCN is the total contact area of a target particle to its neighbours.

Numerical simulation methods such as finite element methods (FEM) [17], discrete element methods (DEM) [18] and lattice Boltzmann methods (LBM) [19] can be used to estimate λeff with a more detailed complex microstructure involved in the process. However, these approaches require solving a system of partial differential equations and the computations are generally time-consuming [14,20]. On the other hand, physical experiments such as thermal needle probe test are commonly undertaken to measure λeff [21], but one of the drawbacks is that accurate measurement needs relatively large undisturbed samples (150 mm long, 50 mm in diameter as a minimum) which may be difficult to obtain. The aim of this paper is to develop a model that can predict λeff accurately and computationally efficiently, even from very small samples.

Machine learning techniques have enabled substantial advances in data-driven approaches throughout academia and industry. In the material sciences, materials informatics combine machine learning, Bayesian optimisation and Monte Carlo tree searches in an attempt to address the challenge of rapidly finding optimal materials [22]. A limited number of studies have also used machine learning to predict λeff of sphere packings [14,23], equation-based irregular materials [20] and sands [24]. The input parameters for the machine learning models in these works include porosity, particle size, component content, the thermal conductivity of solid and interstitial gas, temperature and loadings. Although these parameters are measurable in a laboratory [25,26], bypassing a detailed understanding of structural arrangements and physical mechanisms may result in the differences observed between calculations and measurements [9,13]. Hence, it is necessary to include particle connectivity parameters and the variables detailed above, in machine learning models that investigate heat transfer.

This work intends to predict λeff accurately and efficiently by developing an ANN model using important and non-redundant inputs. Here we justify the selection of average WCN (WCNave) which quantifies the topological structure in sands and other microstructural variables including particle diameter, three-dimensional sphericity and roundness as input parameters in the ANN model. Computed tomography (CT) scanned images of four dry sands that varied in shape, size and endured external loads are used to calculate these parameters. A recently developed in-house thermal conductance network model (TCNM) computed the λeff acting as the output parameter in the ANN model [27,28] alongside complementary experimental measurements. TCNM mitigates the overestimation of λeff possibly induced by the particle volume effect [29] from threshold segmentation, and the variations of λeff estimation for different particle arrangements without additional disturbance of samples that result from insertion of thermal probes.

Section snippets

Artificial neural network models

Artificial neural network (ANN) is at the core of deep Machine Learning (ML) techniques and has managed to render high accuracy in image classification (e.g., Google Images), voice recognition (e.g., Apple's Siri) and learning (e.g., AlphaGo). The ANN was inspired by the architecture of the human brain and its architecture composites of an input layer, one or more hidden layers and an output layer. Each layer has one or more neurons (units/nodes), with the neurons in different layers connected

Materials

Four sands varying in particle shape were sent to the Australian Synchrotron, Imaging and Medical BeamLine (IMBL) for CT scanning at a pixel size of 13 μm. Fig. 1 shows a selection of the acquired images. Glass beads display the roundest particles while the particles in the Ottawa sand are more irregular but still have round corners. Compared to the particles in the Ottawa sand, particles in the angular sand are even more irregular and have sharp corners. Lastly, particles made from crushing

Results and discussion

In this section, the TCNM is first validated for computing effective thermal conductivity λeff followed by a comprehensive discussion for selecting the important and non-redundant input parameters for the ANN models. Since WCNave is a newly introduced mesoscale parameter, the potential benefits of its inclusion in the prediction of λeff is investigated. Additionally, the relationships between WCNave/ WCN and traditional parameters are analysed for feature reduction.

Conclusions

Microstructure and boundary conditions (e.g., axial loading) in granular materials control λeff, but microstructural parameters are seldomly used in existing λeff models, perhaps with the exceptions of (global) porosity and aspect ratio. The advancement of new techniques such as CT, complex network theory, and new numerical simulation methods enable access to the microstructure of natural sands and promote a need for data-driven approaches, for example with the advancement of machine learning

CRediT authorship contribution statement

Wenbin Fei: Conceptualization, Methodology, Investigation, Software, Validation, Formal analysis, Resources, Data curation, Writing - original draft, Writing - review & editing, Visualization, Project administration, Funding acquisition. Guillermo A. Narsilio: Conceptualization, Methodology, Resources, Writing - review & editing, Supervision, Funding acquisition. Mahdi M. Disfani: Resources, Supervision, Writing - review & editing.

Declaration of Competing Interest

The authors declared that there is no conflict of interest.

Acknowledgements

This research was undertaken in the Imaging and Medical Beam Line (IMBL) at the Australian Synchrotron, Victoria, Australia. The authors would like to acknowledge Dr Anton Maksimenko and the other beam scientists at Australian Synchrotron for their support during our experiments. The authors also thank Dr Tabassom Afshar, Dr Joost van der Linden and Dr Xiuxiu Miao for their support in collecting the CT images and thank Gabrielle E. Abelskamp for proofreading the paper. The ARC DP210100433

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