Fracture Flow Velocities Research Articles

Influence of inertial and centrifugal forces on rate and flow patterns in natural fracture networks

Fluid production from fractured rock masses readily induces fracture flow velocities of meters per second. Yet, most discrete fracture flow models treat flow as laminar creeping flow or account for inertia effects only by single-fracture constitutive relationships.This numeric simulation study investigates water flow patterns and spatial velocity variations in a natural fracture network with mm-wide open fractures, studying the transition from laminar creeping to turbulent flow. After verification with a fracture intersection model, a Reynolds-time-averaged Navier Stokes solver serves to analyse flow regimes and velocity distribution. Our results show that for fracture flow velocities greater than ∼1-cm/s, fluid inertia begins to markedly alter flow patterns and the overall velocity distribution in the network. The pressure-gradient-flow relationship therefore becomes non-linear long before the flow in straight fractures enters the weak inertia regime. This prominence of inertia effects highlights the need to improve fracture network flow models.

Thermo‐Hydro‐Chemical Simulation of Mid‐Ocean Ridge Hydrothermal Systems: Static 2D Models and Effects of Paleo‐Seawater Chemistry

AbstractDecades of research have resulted in characterization of the ocean floor manifestations of mid‐ocean ridge (MOR) hydrothermal systems, yet numerical models accounting for the connections between heat transfer, hydrology and geochemistry have been slow to develop. The Thermo‐hydro‐chemical code ToughReact can be used to describe the coupled effects of fluid flow, heat transfer, and fluid‐rock chemical interactions that occur in MOR systems. We describe the results of 2‐dimensional simulations of steady state flow in fractured diabase with mineral‐fluid chemical reactions. Basal heating and specified permeability yield maximum temperature of 400°C. Total fluid flux and high fracture flow velocities are in accord with observations. Fluid chemistry, mineralogical changes and 87Sr/86Sr ratios can be compared to observations to assess and calibrate models. Simulated high temperature fracture fluids have Mg and SO4 near zero, elevated Ca and 87Sr/86Sr of about 0.7040. Total alteration is 10%–50% for simple models of spreading. Anhydrite forms mainly near the base of the upwelling zone and results in substantial local fracture porosity reduction. A calibrated model is used to predict how Sr isotopes and other features of altered oceanic crust would be different in the Cretaceous (95 Ma) early Proterozoic (1,800 Ma) and Archean (3,800 Ma), when seawater may have had high Ca and Sr concentrations, lower pH, higher temperature, and lower Na, Mg, and SO4. The simulations are offered as a start on what ultimately may require a longer‐term community effort to better understand the role of MOR thermo‐hydro‐chemical systems in Earth evolution.

Analysis of thermal dilution experiments with distributed temperature sensing for fractured rock characterization

Thermal dilution experiments with Fiber-Optic Distributed Temperature Sensing (FO-DTS) were conducted at the In-situ Stimulation and Circulation (ISC) rock laboratory, at the Grimsel Test Site (GTS) in Switzerland. The experiment consists in replacing the total volume of a borehole with a warmer water and monitoring the rate of temperature increase and decrease during the heating and cooling periods, respectively. The changes in temperature monitored in depth and time under various hydraulic conditions and in different boreholes, are used to investigate the information provided by thermal dilution experiments in terms of groundwater flow and thermal properties in low-permeable fractured crystalline rock. The data analysis, and the use of analytical and numerical solutions for reproducing this data in the context of pure diffusion and advection–diffusion scenarios, lead to the following improvements and conclusions. (i) The formation thermal conductivity is estimated along the borehole by inverting the data collected under ambient conditions with a simple analytical solution. The estimated values are consistent with laboratory estimates. The method presents the advantage of requiring much shorter experiments than existing methods based on standard active-line-source (ALS) experiments, i.e., several hours versus the traditional 1–2 days. (ii) Hydraulically active fractures connecting boreholes are detected from experiments conducted under cross-borehole forced hydraulic conditions. (iii) The formation thermal conductivity and fracture flow velocity have a distinguished impact on the temperature anomalies for some ranges of these property values, implying that both properties can be estimated from well-parametrized experiments.

Laboratory experiments and dual‐domain modeling of infiltration dynamics in partially saturated fractured porous media

AbstractMany studies have shown that fracture networks can provide rapid pathways for water infiltration and time‐dependent recharge in the vadose zone of consolidated fractured rock formations. To investigate the control of fracture networks and fracture–matrix interaction on preferential flow and infiltration dynamics, we constructed a simple network system consisting of m × 2 sandstone blocks placed in between two glass plates. Water was injected from a point source directly into the fracture system with a constant flow rate of 1.5 g min−1. We used a dual‐porosity non‐equilibrium model to model the discharge dynamics and the internal fracture–matrix mass exchange and observed strong deviations from the laboratory results when the original parameterization was used. This specifically concerns the matrix–fracture volume ratio κ and the fracture flow velocity v that require modifications in terms of their definition and underlying process description. Although the original model assumes a perfectly coupled fracture and matrix domain, in the experiments the discrete nature of the fracture network led to a much stronger dominance of the rapid flow domain and hence to a reduction of κ. The newly introduced parameter κ* includes additional effects and processes related to the time‐dependent evolution and smaller size of the fracture–matrix interface. Furthermore, experiments of varying total vertical system size reveal convergence toward a unique parameter set and the existence of a representative elementary volume (REV) for the chosen setup. Though it performs less well for very small systems below REV scale, the unique parameter set describes discharge dynamics in sufficiently large systems with high accuracy.

Simulation of Solute Transport Through Fractured Rock: A Higher-Order Accurate Finite-Element Finite-Volume Method Permitting Large Time Steps

Discrete-fracture and rock matrix (DFM) modelling necessitates a physically realistic discretisation of the large aspect ratio fractures and the dissected material domains. Using unstructured spatially adaptively refined finite-element meshes, we find that the fast- est flow often occurs in the smallest elements. Flow velocity and element size vary over many orders of magnitude, disqualifying global Courant number (CFL)-dependent transport schemes because too many time steps would be necessary to investigate displacements of interest. Here, we present a higher-order accurate implicit pressure-(semi)-implicit trans- port scheme for the advection-diffusion equation that overcomes this CFL limitation for DFM models. Using operator splitting, we solve the pressure and the transport equations on finite-element, node-centred finite-volume meshes, respectively, using algebraic multigrid methods. We apply this approach to field data-based DFM models where the fracture flow velocity and mesh refinement is 2-4 orders of magnitude greater than that of the matrix. For a global CFL of ≤10,000, this implies sub-CFL, second-order accurate behaviour in the matrix, and super-CFL, at least first-order accurate, transports in fast-flowing fractures. Their greater refinement, however, largely offsets this numerical dispersion, promoting a

Fracture-Flow-Enhanced Matrix Diffusion in Solute Transport Through Fractured Porous Media

Over the past few decades, significant progress of assessing chemical transport in fractured rocks has been made in laboratory and field investigations as well as in mathematic modeling. In most of these studies, however, matrix diffusion on fracture–matrix surfaces is considered as a process of molecular diffusion only. Mathematical modeling based on this traditional concept often had problems in explaining or predicting tracer transport in fractured rock. In this article, we propose a new conceptual model of fracture-flow-enhanced matrix diffusion, which correlates with fracture-flow velocity. The proposed model incorporates an additional matrix-diffusion process, induced by rapid fluid flow along fractures. According to the boundary-layer theory, fracture-flow-enhanced matrix diffusion may dominate mass-transfer processes at fracture–matrix interfaces, where rapid flow occurs through fractures. The new conceptual model can be easily integrated with analytical solutions, as demonstrated in this article, and numerical models, as we foresee. The new conceptual model is preliminarily validated using laboratory experimental results from a series of tracer breakthrough tests with different velocities in a simple fracture system. Validating of the new model with field experiments in complicated fracture systems and numerical modeling will be explored in future research.

Influence of flow rate on transport of bacteriophage in shale saprolite.

The objective of this study was to investigate the influence of flow rate on transport and retention of bacteriophage tracers in a fractured shale saprolite, which is a highly weathered, fine-grained subsoil that retains much of the fabric of the parent bedrock. Synthetic ground water containing PRD-1, MS-2, and bromide was passed through a saturated column of undisturbed shale saprolite at rates ranging from 0.0075 to 0.96 m d '. First arrival of the bacteriophage tracers in effluent samples in each of the experiments occurred within 0.01 to 0.04 pore volumes (PV) of the start of injection, indicating that bacteriophage were advectively transported mainly through fractures or macropores. Bacteriophage transport velocities, based on first arrival in the effluent, were very similar to fracture flow velocities calculated using the cubic law for flow in a fractured material. For MS-2, maximum concentration and mass of tracer recovered both increased steadily as flow rate increased. For PRD-1, these values initially increased, but were nearly constant at flow rates above 0.039 m d(-1), indicating that approximately 50% of the observed losses were independent of flow rate. Evaluation of the data indicates that physical straining and electrostatic or hydrophobic attachment to fracture or macropore walls were the dominant retention processes. Inactivation and gravitational settling playing secondary roles, except at the slowest flow rates. The study suggests that microbial contamination from sources such as septic fields and sewage ponds may pose a threat to the quality of ground water and surface water in areas with saprolitic subsoils.

Evaluation of chloride and pesticide transport in a fractured clayey till using large undisturbed columns and numerical modeling

Saturated groundwater flow and tracer experiments using fluorescent dye, chloride, and the herbicides mecoprop and simazine were carried out in the laboratory using three large‐diameter (0.5 m) undisturbed columns of fractured clayey till. Hydraulic conductivity of the columns ranged from 10−5 m/s in the shallowest column (1 m dept)) to 10−7 m/s in the deepest column (4 m depth) and were similar to field‐measured values for these deposits. Results of the tracer experiments are consistent with a conceptual model of advective transport along the fractures combined with diffusion into the fine‐grained matrix between the fractures. Arrival of the chloride tracer in the effluent was highly retarded relative to fracture flow velocities calculated on the basis of the cubic law and measured values of fracture spacing and hydraulic conductivity. The herbicides were more strongly retarded than the chloride at low flow rates, but at higher flow rates the herbicides arrived with the chloride, indicating the influence of nonequilibrium sorption of the herbicides to fracture walls and the matrix solids. The columns were dismantled following the tracer experiments and mapping under UV light showed that nearly all of the visible, weathered fractures (and the few root holes in the case of the shallowest sample) were active transport pathways, with the dye appearing mainly on the fracture surfaces and as a “rim” in the adjacent matrix. Concentration profiles measured perpendicular to the fracture surfaces showed that the herbicides had also moved into the matrix, apparently by diffusion. Simulations of solute transport with a discrete fracture flow/matrix diffusion model showed that the simulations could be “fit” to the data if all of the visible fractures were hydraulically active, but could not be fit if all or most of the flow was channelled through just the primary fractures (defined by prominent oxidation stains). Simulations with an equivalent porous media (EPM) model could not fit the data using the measured total porosity as the effective porosity. The simulations could likely be fit with a smaller value of effective porosity, but this would limit applicability to field situations because fitted effective porosity is expected to change with physical scale and residence time of the solute in the soil.

Fracture Aperture Measurements and Migration of Solutes, Viruses, and Immiscible Creosote in a Column of Clay‐Rich Till

AbstractA series of ground‐water flow and tracer experiments were performed on an undisturbed column of fractured clay‐rich till, 0.5 m diameter by 0.5 m long, in a pressure‐controlled cell. The measured hydraulic conductivity of the sample was 1.0 to 1.2 × 10–6 m/sec and the average hydraulic gradient during the tracer experiments ranged from 0.45 to 0.49. The experiments clearly show that ground‐water flow and contaminant migration through the sample is primarily controlled by fractures and root holes. Tracer experiments using a solute (chloride), colloid‐sized bacteriophage (PRD‐1 and MS‐2) and uncharged latex microspheres, indicated very fast transport rates of 4 to 360 m/day. These rates are similar to fracture flow velocities calculated on the basis of the measured bulk hydraulic conductivity of the column, and measured fracture spacing, using the cubic law for flow through parallel‐walled fractures. Fracture aperture values calculated from the ground‐water flow data (35 to 56 μxm) are of the same magnitude as values calculated from the breakthrough of tracers (13 to 120 μm). Aperture values calculated for fractures (1 to 94 μm) and root holes (2 to 188 μm), on the basis of measured immiscible creosote entry pressures, are also comparable with these values. The injected creosote, a DNAPL, penetrated most of the visible and a few invisible fractures and root holes, indicating that, for this till, fractures and root holes are important conduits for the transport of DNAPL's.

Analysis of the migration of instantaneously injected cesium in artificial fractures of Lac du Bonnet granite, Manitoba, Canada

Breakthrough curves of 137Cs and tritiated water injected instantaneously into artificial fractures in Lac du Bonnet granite were analyzed using the analytical solution for a single rock-fracture system and assuming the linear sorption isotherm of the solute. Parameters of nuclide diffusion and sorption in rock matrices, obtained by fitting, varied depending on the flow velocity in the fractures. According to theoretical calculations, different fracture flow velocities lead to different diffusion distances of nuclides in matrices at the same injection volume. As microscopic inhomogeneity is considered to exist in the rock matrix, the average diffusion-sorption characteristics of the matrix within the diffusion distance may have varied with the fracture flow velocity. Surface sorption was marked in fractures that had relatively high matrix sorption-diffusion capacities. The phenomenon was interpreted using the theoretical relationships developed between the surface sorption, matrix sorption and pore diffusion coefficient, and the porosity of matrices. The effect of the nonlinear sorption of solute was examined by numerically solving model equations that incorporate the nonlinear isotherm. This incorporation may contribute to the reduction of deviations between theoretical and experimental BTC's.

Analysis of Tracer Movement in Single Fracture in Granite Core (INTRAVAL Case 2).

This paper presents an analysis of INTRAVAL (An International Project to Study Validation of Geosphere Transport Models) test case 2, which is based on laboratory experiments on the tracer movement in a single fracture in granite cores. We have applied two kinds of mathematical models for simulations of tracer experiments; a constant aperture model that aperture of fracture is constant in the fracture plane and a variable aperture channel model that apertures of fracture are varied with a given probability distribution. Calculated breakthrough curves of non-sorbing and sorbing tracers were compared with experimental ones. Analysis of non-sorbing tracer shows that fracture flow velocities do not have linear relationship to injection flow rates, it may be explained by the variable aperture model taking into account of the stagnant water in the fracture. Those of sorbing tracers show that calibrated matrix retardations of the constant aperture model are approximately two times larger than the variable aperture model. This feature indicates that the variable aperture model gives longer travel time of nuclide than the constant aperture model if the retardations are same, and channeling is important phenomenon in safety evaluations of waste disposal.