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Fractal analysis and drag-resistance modelling of unconsolidated porous media with inclusion of particle surface roughness
Thesis (MSc)--Stellenbosch University, 2025.
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Stellenbosch : Stellenbosch University
2026
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| _version_ | 1867613781955182592 |
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| access_status_str | Open Access |
| author | Van Velden, Rocco Joubert |
| author2 | Fidder, Sonia |
| author_browse | Fidder, Sonia Van Velden, Rocco Joubert |
| author_facet | Fidder, Sonia Van Velden, Rocco Joubert |
| author_sort | Van Velden, Rocco Joubert |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (MSc)--Stellenbosch University, 2025. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/134855 |
| institution | Stellenbosch University (South Africa) |
| last_indexed | 2026-06-10T12:41:36.774Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2026 |
| publishDateRange | 2026 |
| publishDateSort | 2026 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/134855 Fractal analysis and drag-resistance modelling of unconsolidated porous media with inclusion of particle surface roughness Van Velden, Rocco Joubert Fidder, Sonia Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Applied Mathematics Division. Granular materials -- Permeability Porous materials Fluid dynamics Surface roughness Fluid mechanics Thesis (MSc)--Stellenbosch University, 2025. Van Velden, R. J. 2025. Fractal analysis and drag-resistance modelling of unconsolidated porous media with inclusion of particle surface roughness. Unpublished masters thesis. Stellenbosch: Stellenbosch University [online]. Available: https://scholar.sun.ac.za/items/20c310be-a89e-4257-9686-88a7c31f59f5 ENGLISH ABSTRACT: Fluid flow through unconsolidated granular porous media is central to many industrial applications, with biofiltration being particularly important due to its versatility and role in controlling hazardous substances, such as hydrogen sulfide (H2S), in an environmentally friendly manner. Predicting the pressure drop over a biofilter, however, remains a challenging task due to the irregular geometry of the packing material and the complex dynamic flow processes involved. The rectangular Representative Unit Cell (RUC) model, a statistical averaging drag-resistance model, has been applied in a recent study for this purpose, but it lacks the analytical incorporation of particle surface roughness – an important microscopic geometric parameter. A fundamentally different approach, i.e., fractal analysis, has also been applied in prior studies as the primary modelling approach to model fluid flow through unconsolidated granular porous media and to quantify the effects of particle surface roughness. In this study the existing granular RUC model is adapted geometrically and analytically to incorporate particle surface roughness, and thus enhance its predictive accuracy for the pressure drop over a biofilter. The novelty of the proposed adapted RUC model (i.e., rough RUC model) lies in a physically derived roughness factor, incorporated into both the Darcy and Forchheimer flow regimes. This factor depends on the average roughness height, number of roughness elements, porosity, and particle diameter. It is furthermore investigated whether fractal analysis is also a suitable modelling framework to apply to the pressure-drop prediction over a biofilter. Existing fractal permeability and flow resistance models are thus re-derived and assessed, and the incorporation of surface roughness into fractal analysis investigated. The fractal models are validated against experimental data from the literature and compared to the rough RUC model. Their suitability for the application to biofiltration is evaluated based on their user-friendliness and accuracy. Experimental data is provided for a lab-scale biofilter packed with expanded schist, which includes the pressure-drop, porosity, biofilm thickness, and superficial velocity measurements obtained for seven different days of operation. The surface roughness of the schist has also been measured experimentally. For this dataset, fractal analysis is found less suitable for the pressure-drop prediction than the rough RUC model. The rough RUC model accurately predicted the pressure-drop data over the biofilter, and shows satisfactory agreement with a modified Ergun equation. A sensitivity analysis is also performed to investigate the influence of the various input parameters on the model predictions. The proposed rough RUC model is an improvement on the existing models from the literature considered in this study. The findings of this study have the potential to aid in the improvement of optimization in biofiltration systems, and contribute to a deeper understanding of surface roughness characterization. AFRIKAANSE OPSOMMING: Vloei deur ongekonsolideerde korrelagtige poreuse media is sentraal tot baie industriële toepassings, met biofiltrasie wat veral belangrik geag word vanweë die veelsydigheid en rol daarvan in die beheer van gevaarlike stowwe, soos waterstofsulfied (H2S), op ’n omgewingsvriendelike wyse. Die voorspelling van die drukval oor ’n biofilter bly egter ’n uitdagende taak as gevolg van die onreëlmatige geometrie van die poreuse verpakkingsmateriaal en die betrokke komplekse dinamiese vloeiprosesse. Die reghoekige “Representative Unit Cell” (RUC) model, ’n statistiese gemiddelde weerstandsmodel, is in ’n onlangse studie vir hierdie doel toegepas, maar skort die analitiese inkorporering van die partikels se oppervlakgrofheid – ’n belangrike mikroskopiese geometriese parameter. ’n Ander fundamentele benadering, d.w.s. fraktale analise, is ook in vorige studies toegepas as die primêre modelleringsbenadering om vloei deur ongekonsolideerde korrelagtige poreuse media te modelleer, en om die effekte van oppervlakgrofheid te kwantifiseer. In hierdie studie word die bestaande korrelagtige RUC model geometries en analities aangepas om oppervlakgrofheid in te sluit, en sodoende die akkuraatheid van voorspellings vir die drukval oor ’n biofilter te verbeter. Die oorspronklikheid van die voorgestelde aangepaste RUC model (d.w.s. growwe RUC model), lê in ’n fisiese afgeleide grofheidsfaktor, wat in beide die Darcy- en Forchheimer-vloeigebiede geïnkorporeer is. Hierdie faktor hang af van die gemiddelde hoogte van grofheidselemente, aantal grofheidselemente, porositeit, en partikel diameter. Verder word daar ondersoek of fraktale analise ook ’n geskikte modelleringsraamwerk is om op die drukvalvoorspelling oor ’n biofilter toe te pas. Bestaande fraktale deurlaatbaarheids- en vloeiweerstandsmodelle word dus herafgelei en beoordeel, en die inkorporering van oppervlakgrofheid in fraktale analise word ondersoek. Die fraktale modelle word geëvalueer teenoor eksperimentele data vanuit die literatuur en vergelyk met die growwe RUC model. Hul geskiktheid vir die toepassing op biofiltrasie word geëvalueer op grond van hul gebruikersvriendelikheid en akkuraatheid. Eksperimentele data is verskaf vir ’n laboratoriumskaal-biofilter gepak met leisteen, insluitend die drukval, porositeit,biofilmdikte en gemiddelde snelheidsmetings, vir sewe verskillende dae van werking. Die oppervlakgrofheid van die leisteen is ook eksperimenteel gemeet. Fraktale analise is minder geskik gevind in vergelyking met die growwe RUC model vir die drukvalvoorspelling van hierdie datastel. Die growwe RUC model het die drukvaldata oor die biofilter akkuraat voorspel en toon bevredigende ooreenstemming met ’n gewysigde Ergun-vergelyking. ’n Sensitiwiteitsanalise is ook uitgevoer om die invloed van die verskillende parameters op die modelvoorspellings te ondersoek. Die voorgestelde growwe RUC model is ’n verbetering op die bestaande modelle wat in hierdie studie vanuit die literatuur oorweeg is. Die bevindinge van hierdie studie het die potensiaal om te help met die verbetering van optimalisering in biofiltrasiestelsels, en by te dra tot ’n dieper begrip van oppervlakgrofheidkarakterisering. Masters 2026-01-13T06:07:15Z 2026-01-13T06:07:15Z 2025-12 Thesis https://scholar.sun.ac.za/handle/10019.1/134855 Stellenbosch University xvii, 105 pages : illustrations application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Granular materials -- Permeability Porous materials Fluid dynamics Surface roughness Fluid mechanics Van Velden, Rocco Joubert Fractal analysis and drag-resistance modelling of unconsolidated porous media with inclusion of particle surface roughness |
| title | Fractal analysis and drag-resistance modelling of unconsolidated porous media with inclusion of particle surface roughness |
| title_full | Fractal analysis and drag-resistance modelling of unconsolidated porous media with inclusion of particle surface roughness |
| title_fullStr | Fractal analysis and drag-resistance modelling of unconsolidated porous media with inclusion of particle surface roughness |
| title_full_unstemmed | Fractal analysis and drag-resistance modelling of unconsolidated porous media with inclusion of particle surface roughness |
| title_short | Fractal analysis and drag-resistance modelling of unconsolidated porous media with inclusion of particle surface roughness |
| title_sort | fractal analysis and drag resistance modelling of unconsolidated porous media with inclusion of particle surface roughness |
| topic | Granular materials -- Permeability Porous materials Fluid dynamics Surface roughness Fluid mechanics |
| url | https://scholar.sun.ac.za/handle/10019.1/134855 |
| work_keys_str_mv | AT vanveldenroccojoubert fractalanalysisanddragresistancemodellingofunconsolidatedporousmediawithinclusionofparticlesurfaceroughness |