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Numerical modeling of fluid flow and solute transport in rock fractures
KTH, School of Architecture and the Built Environment (ABE), Sustainable development, Environmental science and Engineering, Land and Water Resources Engineering. (Engineering Geology and Geophysics)
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This study focuses on numerical modeling of fluid flow and solute transport in rough-walled rock fractures and fracture-matrix systems, with the main aim to investigate the impacts of fracture surface roughness on flow and transport processes in rock fractures. Both 2D and 3D fracture models were built from laser-scanned surface tomography of a real granite rock sample, to consider realistic features of surface tomography and potential asperity contacts. The flow was simulated by directly solving the Navier-Stokes equations (NSE) and the transport was modeled by solving the advection-dispersion equation (ADE) in the entire domain of fracture-matrix system, including matrix diffusion process. Such direct simulations provided detailed flow and concentration fields for quantitatively analysis of flow and transport behavior. The detailed analysis of surface roughness decomposition, complex flow patterns (i.e., channeling, transverse and eddy flows), effective advective flow apertures, effective transmissivity, effective dispersivity, residence time, transport resistance and specific surface area demonstrated significant impacts of realistic fracture surface roughness on fluid flow and solute transport processes in rock fractures. The results show that the surface roughness and shear displacement caused asperity contacts significantly enhance nonlinearity and complexity of flow and transport processes in rough-walled fractures and fracture-matrix systems. The surface roughness also causes invasion flows in intersected fractures which enhance solute mixing at fracture intersections. Therefore, the fracture surface roughness is an important source of uncertainty in application of such simplified models like cubic law (CL) for fluid flow and analytical solutions for solute transport in rock fractures. The research conducted advances our understanding of realistic flow and transport processes in natural fractured rocks. The results are useful for model validation/extension, uncertainty analysis/quantification and laboratory experiments design in the context of various applications related to fracture flow and transport.

Abstract [sv]

Denna studie fokuserar på numerisk modellering av vätskeflöde och transport av lösta ämnen i frakturer med ojämna väggar samt fraktur-matrissystem, med det huvudsakliga syftet att undersöka effekterna av frakturernas ytjämnhet på flödes- och transportprocesser i bergsfrakturer. Både 2D och 3D modeller skapades utifrån laser skannad tomografi av ett verkligt bergartsprov av granit, för att överväga de realistiska egenskaperna hos ytan och potentiell skrovlighet. Flödet simulerades genom att lösa Navier-Stokes ekvationer (NSE) och transporten modellerades genom att lösa advektion-dispersion ekvation (ADE) i hela domänen av fraktur-matrissystemet, inklusive diffusions process i matrisen. Sådana direkta simuleringar resulterade i detaljerade flödes- och koncentrationsfält för att kvantitativt kunna analysera flödet och transportbeteendet. En detaljerad analys av upplösningen av ytjämnhet, komplexa flödesmönster (dvs kanalisering, tvärgående och virvelströmmar), effektiv advektiv flödesöppning, effektiv transmissivitet, effektiv dispersivitet, uppehållstid, transport motstånd och specifik yta visade signifikanta effekter av realistiska ojämna frakturväggar på vätskeflöde och lösta transportprocesser i bergssprickor. Resultaten visar att ytjämnhet och skjuvningssystemsorsakade asperitetskontakter avsevärt förbättrar olinjäritet och komplexitet av flödes- och transportprocesser i frakturer med ojämna väggar samt fraktur-matrissystem. Ytråheten orsakar också intrång av flöde i tvärgående frakturer vilket ökar blandingen av lösta ämnen i korsningarna. Därför är ytjämnhet av frakturerna en viktig källa till osäkerhet i tillämpningen av sådana förenklade modeller som kubisk lag (CL) för vätskeflöde och analytiska lösningar för transport av lösta ämnen i bergsfrakturer. Studien har ökat förståelsen för realistiska flödes- och transportprocesser i naturligt sprucket berg. Resultaten är användbara för modellvalidering/förlängning, osäkerhetsanalys/kvantifiering och design av laboratorieexperiment i samband med olika tillämpningar av flöde och transport i bergsfrakturer.

Place, publisher, year, edition, pages
Stockholm: Kungliga Tekniska högskolan, 2016. , 47 p.
Series
TRITA-LWR. PHD, ISSN 1650-8602 ; PhD - 2016:08
Keyword [en]
Rough-walled rock fractures; Nonlinear flow; Solute transport; Navier-Stokes equations; Matrix diffusion; Uncertainty.
National Category
Geophysical Engineering
Research subject
Land and Water Resources Engineering
Identifiers
URN: urn:nbn:se:kth:diva-193666ISBN: 978-91-7729-138-1 (print)OAI: oai:DiVA.org:kth-193666DiVA: diva2:1033548
Public defence
2016-11-03, Kollegiesalen, Brinellvägen 8, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

QC 20161010

Available from: 2016-10-10 Created: 2016-10-07 Last updated: 2016-10-10Bibliographically approved
List of papers
1. Roughness decomposition and nonlinear fluid flow in a single rock fracture
Open this publication in new window or tab >>Roughness decomposition and nonlinear fluid flow in a single rock fracture
2015 (English)In: International Journal of Rock Mechanics And Mining Sciences, ISSN 1365-1609, E-ISSN 1873-4545, Vol. 75, 102-118 p.Article in journal (Refereed) Published
Abstract [en]

The objective of this paper is to investigate the effects of wall surface roughness on fluid flow through rock fractures. A wavelet analysis technique was developed to define a mathematical criterion for decomposing the original wall surface roughness profiles of a fracture into a high-frequency (secondary roughness) profile and a low-frequency (primary roughness) profile, in order to examine their impacts on fluid flow, by solving the Navier-Stokes equations (NSE) without linearization, using a self-developed 2D finite volume method (FVM) code. The results indicate that the high-frequency secondary roughness is the main cause for dynamic evolution of Eddy flow regions in the fracture flow field, besides the Reynolds number (Re). In the original fracture model with the high-frequency secondary roughness, our results show that fluid flow fields are not only generally non-linear, but also with non-stop generation and motions of eddies in the boundary layer regions of rough fractures when the Re = 1000 in this study, which will affect the solute transport processes in fractured rock masses. The complete NSE were solved without removing acceleration and inertial terms, so that the impacts of surface roughness on the nonlinear and dynamic flow behavior of rock fractures were calculated and visualized more accurately, which is important for modeling mass and energy transport processes in fractures and fractured rock masses.

Place, publisher, year, edition, pages
Elsevier, 2015
Keyword
Rock fractures, Roughness decomposition, Wavelet analysis, Navier-Stokes equations, Hydraulic aperture
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-166495 (URN)10.1016/j.ijrmms.2015.01.016 (DOI)000352129700009 ()2-s2.0-84922989675 (Scopus ID)
Note

QC 20150518

Available from: 2015-05-18 Created: 2015-05-11 Last updated: 2017-12-04Bibliographically approved
2. Shear enhanced nonlinear flow in rough-walled rock fractures
Open this publication in new window or tab >>Shear enhanced nonlinear flow in rough-walled rock fractures
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Nonlinear flow in 3D rough-walled rock fracture models are simulated by solving the Navier-Stokes equations in this paper. The emphasis is on the impacts of shear caused aperture changes (variable apertures and asperity contacts) and flow conditions (inertial term) upon nonlinear flow behaviors in 3D rough-walled rock fractures. In order to compare shear effects, two 3D fracture models, with and without shear process, were established with the identical initial rough-walled surfaces tomography of a realistic rock sample. Five groups of simulations with different inflow boundary conditions of flowrates/Reynolds numbers (Re) were conducted to demonstrate shear enhanced nonlinearity of flow fields and limitations of local cubic law (LCL) approach. The flow results clearly show channeling flow along the preferential fluid paths, transverse flow around the contact spots and eddy flows behind contact spots with increasing Re numbers, which cannot be observed in 2D models. The effective transmissivity of the 3D fracture model was calculated from the modeling results of velocity and pressure fields. The results showed that the effective transmissivity is a function of local apertures with important uncertainties even when Re is small (i.e. Re = 0.4 in this study), thus the validity of the transmissivity evaluation using LCL approach for nonlinear flow in 3D rough-walled rock fractures is questionable. The mechanical effects, i.e. stress and shear caused aperture space changes and asperity contacts should be considered for modeling flow and mass/energy transport processes in rough-walled fractures in 3D.

Keyword
rough-walled rock fractures; shear; contact spots; nonlinear fracture flow; eddy flow; effective transmissivity.
National Category
Geophysical Engineering
Research subject
Land and Water Resources Engineering
Identifiers
urn:nbn:se:kth:diva-193669 (URN)
Note

QC 20161010

Available from: 2016-10-07 Created: 2016-10-07 Last updated: 2016-10-10Bibliographically approved
3. Assumptions of the analytical solution for solute transport in a fracture-matrix system
Open this publication in new window or tab >>Assumptions of the analytical solution for solute transport in a fracture-matrix system
2016 (English)In: International Journal of Rock Mechanics And Mining Sciences, ISSN 1365-1609, E-ISSN 1873-4545, Vol. 83, 211-217 p.Article in journal (Refereed) Published
Place, publisher, year, edition, pages
Elsevier, 2016
Keyword
Solute transport, Rock fracture-matrix system, Matrix diffusion, Numerical modeling vs. analytical solution
National Category
Mineral and Mine Engineering
Identifiers
urn:nbn:se:kth:diva-183305 (URN)10.1016/j.ijrmms.2016.01.011 (DOI)000369609700021 ()2-s2.0-84954485079 (Scopus ID)
Note

QC 20160309

Available from: 2016-03-09 Created: 2016-03-07 Last updated: 2017-11-30Bibliographically approved
4. Modeling of solute transport in a 3D rough-walled fracture-matrix system
Open this publication in new window or tab >>Modeling of solute transport in a 3D rough-walled fracture-matrix system
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Fluid flow and solute transport in a 3D rough-walled fracture-matrix system was simulated by directly solving the Navier-Stokes equations for fracture flow and solving the transport equation for the whole domain of fracture and matrix with considering matrix diffusion. The rough-walled fracture-matrix model was built from laser-scanned surface tomography of a real rock sample, by considering realistic features of surfaces roughness and asperity contacts. The numerical modeling results were compared with both analytical solutions based on simplified fracture surface geometry and numerical results by particle tracking based on the Reynolds equation. The aim is to investigate impacts of surface roughness on solute transport in natural fracture-matrix systems, and to quantify the uncertainties in application of simplified models. The results show that fracture surface roughness significantly increases heterogeneity of velocity field in the rough-walled fractures, which consequently cause complex transport behavior, especially the dispersive distributions of solute concentration in the fracture and complex concentration profiles in the matrix. Such complex transport behavior caused by surface roughness are important sources of uncertainty that needs to be considered for modeling of solute transport processes in fractured rocks. The presented direct numerical simulations of fluid flow and solute transport serve as efficient numerical experiments that provide reliable results for the analysis of effective transmissivity as well as effective dispersion coefficient in rough-walled fracture-matrix systems. Such analyses are helpful in model verifications, uncertainty quantifications and design of laboratorial experiments.

Keyword
solute transport; fracture surface roughness; fracture-matrix system; matrix diffusion; contact spots.
National Category
Geophysical Engineering
Research subject
Land and Water Resources Engineering
Identifiers
urn:nbn:se:kth:diva-193671 (URN)
Note

QC 20161010

Available from: 2016-10-07 Created: 2016-10-07 Last updated: 2016-10-10Bibliographically approved
5. Modeling of advection-dominated transport in rough-walled rock fractures: a comparison of Reynolds and Navier-Stokes equations
Open this publication in new window or tab >>Modeling of advection-dominated transport in rough-walled rock fractures: a comparison of Reynolds and Navier-Stokes equations
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Statistical analysis of flow-dependent specific surface areas of a 3D rough-walled fracture-matrix system were presented in this paper, based on numerical simulations of fluid flow and advective particle transport. The aim is to investigate the flow-dependent solute transport quantities in natural fracture-matrix systems, and identify the potential uncertainty lie in the common used flow model (i.e., Reynolds equation) by comparing with the more realistic flow model(i.e., Navier-Stokes equations). The rough-walled fracture model was built from laser-scanned surface tomography of a real rock sample, by considering realistic features of surfaces roughness and asperity contacts. Based on the flow fields simulated by solving the Reynolds and Navier-Stokes equations, the advective transport was modeled through Lagrangian particle tracking. The controlling quantities of advective transport in fracture-matrix systems (i.e., residence time, transport resistance and specific surface area) were statistically analyzed and compared. The results generally show that fracture surface roughness and associated spatially variable apertures as well as shear caused asperity contacts significantly increase the heterogeneity of flow field in rough-walled fractures, which consequently affects the flow-dependent transport process. By comparison, the simplified flow model (i.e., Reynolds equation) may cause uncertainty in quantifying of the specific surface area for the realistic rough-walled fracture-matrix systems. To identify such uncertainty, it is important to obtain the more reliable flow fields by solving the NSE. The presented results are helpful in uncertainty quantification and risk assessment of solute transport in natural fractured rocks.

Keyword
Navier-Stokes equations; effective transmissivity; residence time; transport resistance; specific surface area.
National Category
Geophysical Engineering
Research subject
Land and Water Resources Engineering
Identifiers
urn:nbn:se:kth:diva-193677 (URN)
Note

QC 20161010

Available from: 2016-10-07 Created: 2016-10-07 Last updated: 2016-10-10Bibliographically approved
6. Invasion flow enhanced solute mixing at rough-walled rock fracture intersections
Open this publication in new window or tab >>Invasion flow enhanced solute mixing at rough-walled rock fracture intersections
(English)Manuscript (preprint) (Other academic)
Abstract [en]

The processes of fluid flow and solute transport through rock fractures are of primary importance in environmental engineering and geosciences. This study presented numerical modeling results of fluid flow and solute transport in a 3D rock fracture-matrix system with an orthogonal intersection of two rough-walled rock fractures. The rough-walled fracture geometry models were built from laser-scanned data of a real rock surface, for a realistic representation of natural rock fracture surface roughness. The fluid flow in the two intersected fractures and solute transport in the fracture-matrix system were simulated by solving the Navier-Stokes equations (NSE) and transport equation in the entire system. The dependence of mixing on Péclet number (Pe), flow directionality and interaction with matrix diffusion were analyzed. The results showed important invasion flow patterns that significantly enhanced the solute mixing process, which cannot be described by traditional complete mixing and streamline routing models. It also cannot be simulated by simplified 2D geometry models ignoring the surface roughness as widely used in previous published studies. The finding of invasion flow and associated impacts on mixing in this study is particularly important in prediction of solute transport in natural fractured rocks, especially when discrete fracture network (DFN) approach is applied.

Keyword
Rough-walled rock fracture intersection; Navier-Stokes equations; invasion flow; mixing ratio; Péclet number.
National Category
Geophysical Engineering
Research subject
Land and Water Resources Engineering
Identifiers
urn:nbn:se:kth:diva-193672 (URN)
Note

QC 20161010

Available from: 2016-10-07 Created: 2016-10-07 Last updated: 2016-10-10Bibliographically approved

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