Numerical modeling of fluid flow and solute transport in rock fractures

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.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.QC 20161010</p

Characterization of effective transmissivity for cement grout flow in rock fractures

Cement grouting has been widely used in rock engineering. Proper characterization of the effective transmissivity for cement grout flow in rock fractures is primarily important for the design of rock grouting. In practice, the hydraulic transmissivity of groundwater flow in rock fractures characterized by hydraulic tests, i.e., pumping or slug test, is often used for the design of rock grouting. However, cement grouts used in rock grouting practice are typical non-Newtonian fluids contain yield stress, which has different effective transmissivity from the Newtonian groundwater. Therefore, using the groundwater transmissivity characterized by hydraulic tests may cause significant uncertainty in modeling and design of cement rock grouting. In this study, we focus on the effective transmissivity of non-Newtonian cement grout flow in a single fracture, aiming to illustrate the difference between the effective transmissivity of non-Newtonian cement grouts and the hydraulic transmissivity of the Newtonian groundwater. The cement grout is assumed as a Bingham fluid. The theoretical solution for the effective transmissivity of Bingham grout for homogeneous fractures is presented. This solution is compared with the theoretical hydraulic transmissivity, i.e., the cubic law. The results generally illustrate the significant differences between the effective transmissivity of non-Newtonian cement grouts and the hydraulic transmissivity of groundwater. The effective transmissivity of non-Newtonian cement grout is nonlinear which a function of injection pressure. Using the hydraulic transmissivity for rock grouting may underestimate the propagation length of the cement grout in rock fractures. The obtained result is helpful for rock grouting design in practice to reduce the potential uncertainties caused by using the hydraulic transmissivity.Part of proceedings: ISBN 978-951758648-1QC 20190917</p

Modeling of solute transport in a 3D rough-walled fracture-matrix system

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.QC 20161010</p

Cement grout propagation in 2D fracture networks : impact of rheology

Cement grouts propagation into a two-dimensional water-saturated fracture networks with different values of rheological properties are simulated by using an extended two-phase flow model. The cement grouts are typical non-Newtonian fluids that contain yield stress, which are often assumed as Bingham fluids. The aim of this study is to investigate the impact of Bingham rheological properties, i.e. yield stress and plastic viscosity, on cement gouts propagation in two-dimensional fracture networks. The results generally show that the rheological properties of cement grouts, i.e. yield stress and plastic viscosity, significantly affect cement grouts propagation in the fracture network. The propagation rate in the fracture networks reduces with the increase of the yield stress and the plastic viscosity of the cement grouts.QC 20190930</p

Characterization of effective transmissivity for cement grout flow in rock fractures

Cement grouting has been widely used in rock engineering. Proper characterization of the effective transmissivity for cement grout flow in rock fractures is primarily important for the design of rock grouting. In practice, the hydraulic transmissivity of groundwater flow in rock fractures characterized by hydraulic tests, i.e., pumping or slug test, is often used for the design of rock grouting. However, cement grouts used in rock grouting practice are typical non-Newtonian fluids contain yield stress, which has different effective transmissivity from the Newtonian groundwater. Therefore, using the groundwater transmissivity characterized by hydraulic tests may cause significant uncertainty in modeling and design of cement rock grouting. In this study, we focus on the effective transmissivity of non-Newtonian cement grout flow in a single fracture, aiming to illustrate the difference between the effective transmissivity of non-Newtonian cement grouts and the hydraulic transmissivity of the Newtonian groundwater. The cement grout is assumed as a Bingham fluid. The theoretical solution for the effective transmissivity of Bingham grout for homogeneous fractures is presented. This solution is compared with the theoretical hydraulic transmissivity, i.e., the cubic law. The results generally illustrate the significant differences between the effective transmissivity of non-Newtonian cement grouts and the hydraulic transmissivity of groundwater. The effective transmissivity of non-Newtonian cement grout is nonlinear which a function of injection pressure. Using the hydraulic transmissivity for rock grouting may underestimate the propagation length of the cement grout in rock fractures. The obtained result is helpful for rock grouting design in practice to reduce the potential uncertainties caused by using the hydraulic transmissivity.QC 20190917</p

Non-Newtonian grout flow in single rough-walled rock fractures

Modeling of cement grout flow in rock fractures plays an important role in the design of rock grouting. Cement grouts used in rock grouting practice are typical non-Newtonian fluids containing yield stress, and are often assumed as Bingham fluids. Natural rock fractures typically consist of rough surfaces. Therefore, in reality, rock grouting process actually involves non-Newtonian fluid flow in rough-walled fractures, which is rarely studied in the literature. In this work, we focus on the impact of surface roughness and present direct numerical simulations of non-Newtonian grouts flow in single rough-walled fractures, using a regularized method to approximate the yield-stress. The rough-walled rock fracture models are created from a laser-scanned surface of a granite rock sample, to represent realistic features of natural rock fractures. The numerical results generally show nonlinear behaviors of non-Newtonian fluid flow in rough-walled fractures. The surface roughness significantly reduces the effective transmissivity when Reynolds number is relatively large. The obtained result can be used for upscaling analysis in practice, in order to reduce the potential uncertainties caused by the surface roughness of the rock fractures.Modellering av cement-baserade injekteringsmedels strömning i bergsprickor spelar en viktig roll för prediktion och design. De medel som används vid injektering är typiskt icke- Newtonska, med en flytgräns, och antas därför vara av Bingham typ. Naturliga bergsprickor har vanligtvis en rå och ojämn yta. Analyser av injekteringsförlopp borde därför innehålla både icke-Newtonska vätskor och råhet hos sprickorna, vilket oftast inte är fallet i den litteratur som finns tillgänglig idag. I föreliggande arbete fokuseras på inverkan av bergsprickors råhet och numeriska beräkningar redovisas för icke-Newtonska injekteringsmedels strömning i enskilda sprickor, med hjälp av en regulariserad metod för hantering av brukets flytgräns. Sprickytornas råhet modelleras från laser-scannade ytor av granitprover för att erhålla så realistiska förhållanden som möjligt. Resultaten visar på icke-linjära effekter och att de råa sprickytorna har en avgörande inverkan på spricktransmissiviteten och att resultaten kan användas för att minska osäkerheten vid praktisk tillämpning.QC 20190412</p

Non-Newtonian fluid flow in 2D fracture networks

Modeling of non-Newtonian fluid (e.g., drilling fluids and cement grouts) flow in fractured rocks is of interest in many geophysical and industrial practices, such as drilling operations, enhanced oil recovery and rock grouting. In fractured rock masses, the flow paths are dominated by fractures, which are often represented as discrete fracture networks (DFN). In the literature, many studies have been devoted to Newtonian fluid (e.g., groundwater) flow in fractured rock using the DFN concept, but few works are dedicated to non-Newtonian fluids.In this study, a generalized flow equation for common non-Newtonian fluids (such as Bingham, power-law and Herschel-Bulkley) in a single fracture is obtained from the analytical solutions for non-Newtonian fluid discharge between smooth parallel plates. Using Monte Carlo sampling based on site characterization data for the distribution of geometrical features (e.g., density, length, aperture and orientations) in crystalline fractured rock, a two dimensional (2D) DFN model is constructed for generic flow simulations. Due to complex properties of non-Newtonian fluids, the relationship between fluid discharge and the pressure gradient is nonlinear. A Galerkin finite element method solver is developed to iteratively solve the obtained nonlinear governing equations for the 2D DFN model. Using DFN realizations, simulation results for different geometrical distributions of the fracture network and different non-Newtonian fluid properties are presented to illustrate the spatial discharge distributions. The impact of geometrical structures and the fluid properties on the non-Newtonian fluid flow in 2D DFN is examined statistically. The results generally show that modeling non-Newtonian fluid flow in fractured rock as a DFN is feasible, and that the discharge distribution may be significantly affected by the geometrical structures as well as by the fluid constitutive properties.QC 20190930</p

Non-Newtonian fluid flow in 2D fracture networks

Modeling of non-Newtonian fluid (e.g., drilling fluids and cement grouts) flow in fractured rocks is of interest in many geophysical and industrial practices, such as drilling operations, enhanced oil recovery and rock grouting. In fractured rock masses, the flow paths are dominated by fractures, which are often represented as discrete fracture networks (DFN). In the literature, many studies have been devoted to Newtonian fluid (e.g., groundwater) flow in fractured rock using the DFN concept, but few works are dedicated to non-Newtonian fluids.In this study, a generalized flow equation for common non-Newtonian fluids (such as Bingham, power-law and Herschel-Bulkley) in a single fracture is obtained from the analytical solutions for non-Newtonian fluid discharge between smooth parallel plates. Using Monte Carlo sampling based on site characterization data for the distribution of geometrical features (e.g., density, length, aperture and orientations) in crystalline fractured rock, a two dimensional (2D) DFN model is constructed for generic flow simulations. Due to complex properties of non-Newtonian fluids, the relationship between fluid discharge and the pressure gradient is nonlinear. A Galerkin finite element method solver is developed to iteratively solve the obtained nonlinear governing equations for the 2D DFN model. Using DFN realizations, simulation results for different geometrical distributions of the fracture network and different non-Newtonian fluid properties are presented to illustrate the spatial discharge distributions. The impact of geometrical structures and the fluid properties on the non-Newtonian fluid flow in 2D DFN is examined statistically. The results generally show that modeling non-Newtonian fluid flow in fractured rock as a DFN is feasible, and that the discharge distribution may be significantly affected by the geometrical structures as well as by the fluid constitutive properties.QC 20190930</p

Analys och simulering av cementinjektering i sprickigt berg

Modeling of cement grout propagation in fractured rocks is important for the design, execution and monitoring of rock grouting in practice. In this project, we studied non-Newtonian cement grouts propagation in rock fractures by theoretical analyses and numerical simulations.  The analytical solutions for radial flow of a Bingham fluid, between parallel plates, are analyzed and existing disagreements in the literature regarding the two different analytical solutions that are used for analysis of grouting in rock fractures is investigated. The analyses reveal that the two solutions are both zero-order approximation solutions based on different assumptions, that is with or without consideration of the vertical velocity component across the aperture. The one without considering the vertical velocity yields to a solution with radius-independent plug flow region, which largely simplifies the calculations. By using the solution with radius-independent plug flow region, Bingham grout penetration and flowrate (at the injection borehole) evolution as functions of grouting time are given for the first time. Discrepancies in the two approximation solutions for grout penetration and flowrate evolution are illustrated, showing negligible differences. The clarification of the plug flow region and evaluation of discrepancies in the two solutions presented in this work improves our confidence and simplifies modeling and design of grouting in rock engineering applications.  In reality, rock fracture grouting process involves non-Newtonian fluid flow in fractures with rough surfaces, which is rarely studied in the literature. To investigate the impact of fracture surface roughness on rock fracture grouting, we presented direct numerical simulations of non-Newtonian grouts flow in single rough-walled fractures, using a regularized method (i.e., the Bingham-Papanastasiou model) to approximate the yield-stress. The rough-walled rock fracture models are created from a laser-scanned surface of a granite rock sample, to represent realistic features of natural rock fractures. The numerical results show nonlinear behaviors of non-Newtonian fluid flow in rough-walled fractures caused by non-Newtonian rheological properties and enhanced by the fracture surface roughness. The surface roughness significantly reduces the effective transmissivity (defined as the ratio between the flowrate and the pressure gradient) when Reynolds number (Re) is relatively large, i.e., Re &gt;10. A mathematical model based on the Reynolds flow equation for cement grout propagation in a homogeneous water-saturated rock fracture is presented. The model is based on two-phase flow, i.e., grout as a Bingham fluid and groundwater as a Newtonian fluid, and is used for investigating the importance of the water flow in rock grouting. The modeling results for the two-phase flow generally show the importance of the water phase that can significantly affect the pressure distribution and grout propagation in the fracture, especially under the condition of grout hardening. Such effects depend on the viscosity ratio between the grout and groundwater, which becomes increasingly important for cases with smaller values of the viscosity ratio. Applying an analytical solution based on single-phase flow, i.e., neglecting the impact of groundwater flow, for modeling of rock fracture grouting, will generally overestimate the propagation length. The two-phase flow model for single fractures is extended to simulate non-Newtonian cement grouts propagation in water-saturated fracture networks. We verified the two-phase flow model by comparing numerical simulation results of two-phase flow of cement grouts propagation in fracture networks with the benchmark data in Håkansson (1987). Using this extended model for numerical simulations on the grout propagation the impacts of network geometry, hydraulic aperture distribution and the rheological properties (yield stress and plastic viscosity) are investigated. Cement grout propagation in randomly generated two-dimensional discrete fracture network (2D DFN) are simulated with different cases of hydraulic aperture variability, i.e., constant aperture, uncorrelated and length-correlated heterogeneous apertures following a truncated lognormal distribution. The results indicate that network structure and hydraulic aperture variability significantly affect the grout propagation negatively in 2D DFN systems. The randomized network structure and uncorrelated heterogeneous apertures significantly delay the propagation rate and largely increase the variability range of the penetration volume fraction (the ratio between penetrated volume and total volume of fractures). In contrast, in the case with length-correlated heterogeneous apertures, the propagation rate increases, while the variability range and rate of change of the penetration volume fraction decreases. The rheological properties of cement grouts, i.e., yield stress and plastic viscosity, also significantly affect cement grouts propagation in fracture networks. The propagation rate in the fracture networks reduces with the increase of the yield stress and the plastic viscosity of the cement grouts. The results presented in this report will be helpful in the design and prediction of rock grouting.Modellering av cementbruks spridning i sprickist berg är viktigt för en ökad förståelse vid projektering, utförande och kontroll av injektering i praktiken. I detta projekt studerade vi icke-Newtonsk cementinjektering i bergssprickor genom teoretiska analyser och numeriska simuleringar. De analytiska lösningarna för radiell strömning av en Bingham vätska studeras kritiskt och tvetydigheter i litteraturen beträffande pluggflödet i de två olika lösningar som används, för analys och design av injektering i bergssprickor, studeras. Analyserna baserade på en kraftbalans visar att pluggen vid radiell strömning av en Bingham vätska är oberoende av inträngningslängden. Bingham vätskans inträngning och flöde som funktion av injekteringstiden visas med användning av det konstanta pluggflödet. Skillnader i de två analytiska lösningarna och utveckling av flödet som funktion av tid illustreras. Förklaringen till pluggflödet och utvärderingen av skillnaderna i lösningarna som presenteras förbättrar vår kunskap och förenklar modellering och design av injektering i berg. I praktiken utförs injektering med icke-Newtonska vätskor i råa sprickor, vilket dock sällan studeras. För att undersöka inverkan av en rå sprickyta vid injektering, presenteras numeriska beräkningar av icke-Newtonian strömning i enskilda råa sprickor, med hjälp av en regulariserad metod. De råa sprickmodellerna är skapade från en laserskannad yta av ett granitbergprov, för att representera realistiska egenskaper hos naturliga bergssprickor. De numeriska resultaten visar icke-linjära beteenden för flödet i råa sprickor orsakade av icke-Newtonska reologiska egenskaper förstärkta av sprickornas rånet. Råheten reducerar avsevärt den effektiva transmissiviteten när Reynolds tal (Re) är relativt stort, dvs Re&gt; 10. En matematisk modell baserad på Reynolds flödesekvation för inträngning av cementbruk i en slät, vattenmättad, bergspricka presenteras. Modellen är baserad på ett tvåfasflöde, dvs injektering som en Bingham-vätska och grundvatten som en Newtonsk vätska, vilka används för att undersöka påverkan av vattenfasen vid injektering. Modelleringsresultaten för tvåfasflödet visar i allmänhet på vikten av vattenfaten som väsentligen påverkar tryckfördelningen i sprickan, speciellt under härdning av bruket. Sådana effekter beror på viskositetsförhållandet mellan injekterings. Bruket och grundvattnet, vilka blir allt viktigare för fall en med mindre värden på viskositetsskillnaden. Att tillämpa en analytisk lösning baserad på ett enfasflöde, dvs att försumma påverkan av grundvatten vid modellering av ett injekteringförlopp, kommer att överskatta inträngningslängden. Modellen för tvåfasflöde i enskilda sprickor utvidgas för att simulera icke-Newtonsk strömning i vattenmättade sprick nätverk. Modellen verifieras genom att jämföra simuleringsresultat för utbredningen i spricknät verk med referensdata från Håkansson (1987). Med användning av denna utökade modell undersöktes effekterna på utbredningen av nätverksstruktur och hydraulisk variabilitet, dvs nätgeometri och fördelning av spricköppningar, samt reologiska egenskaper, d.v.s. flytgräns och viskositet. Injekteringens utbredning i slumpmässigt genererat tvådimensionellt diskret spricknätverk (2D DFN) simuleras med olika fall av variabilitet i spricköppning, d.v.s. konstant öppning, baserat på och längdkorrelerad heterogena öppningar, efter en trunkerad lognormal fördelning. Resultaten indikerar att både nätverksstruktur och hydraulisk variation har en stor påverkan för utbredningen i ett 2D DFN-system. Den slumpade nätverksstrukturen och de okorrigerade heterogena öppningarna minskar avsevärt utbredningshastigheten och ökar till stor del variationen i injekterad volym. För längdkorrelerade heterogena öppningar, ökar utbredningshastigheten, medan variabiliteten och förändringen av injekterad volym minskar. De reologiska egenskaperna hos cementbruk, d.v.s. flytgräns och viskositet, påverkar väsentligen utbredningen i ett spricknätverk. Utbredningshastigheten i spricknätverken minskar med en ökning av flyt gräns och viskositet hos cementbruket. Resultaten som presenteras i denna rapport kommer att vara till hjälp vid utformningen och förutsägelsen av bergsprutning.QC 20211220</p