Equivalent Hydraulic Aperture Research Articles

Correlations Developed for Estimation of Hydraulic Parameters of Rough Fractures Through the Simulation of JRC Flow Channels

The hydro-mechanical response of fractured rock masses is complex, due partly to the presence of fractures at different scales. Surface morphology has a significant influence on fluid flow behaviour of a fracture. Different empirical correlations and statistical models have been proposed to estimate the equivalent hydraulic aperture and determine the pressure drop along a fracture. However, the existing models suffer from not being adequately generalised to be applicable to a wide range of real fracture surfaces. To incorporate the effect of profile roughness in the hydro-mechanical behaviour of fractured rock masses, the joint roughness coefficient (JRC) is the most widely used empirical approach. However, the average JRC of two fracture walls in fluid flow analysis, as is a common practice, appears to be inappropriate. It will be shown how different combinations of pairs of JRCs could lead to a similar JRC value. Also, changing the position of the top and bottom walls of a fracture can significantly change the hydraulic response of the fracture while the average JRC is identical in both cases. In this paper, correlations are developed which are based on the simulation of JRCs using estimated fluid flow parameters of 2D fractures can be estimated. In order to widen the application range of the correlations, JRC flow channels were generated: these are 2D channels with their top and bottom walls being made from two of the JRC profiles. To estimate the JRC of linear profiles, a correlation developed between JRC and a newly developed Riemannian roughness parameter, D R1, is proposed. Considering ten JRC profiles, a total of 100 JRC flow channels were generated. In order to only investigate the effect of surface roughness on fluid flow, the minimum closure between the top and bottom walls of JRC flow channels were considered to be constant. Three cases with minimum closures of 0.01, 0.05 and 0.10 cm were considered in this study. All JRC flow channels were subjected to fluid analysis using FLUENT software. Based on these results, correlations were developed between the geometrical and hydraulic properties of flow channels. Analysis of several real fractures demonstrated the applicability of these correlations.

Dissolved and Colloidal Transport of Cesium in Natural Discrete Fractures

Transport of cesium (Cs) was investigated in a saturated natural chalk fracture with an average equivalent hydraulic aperture of 129 microm. The results show that Cs (inflow concentration of 0.22 mmol L(-1)) can be transported in its dissolved form and in association with montmorillonite. Humic acid (HA) did not sorb Cs but enhanced colloid-associated Cs transport by 12.5% in terms of breakthrough curve (BTC) recovery. The BTCs clearly showed desorption of Cs from the fracture walls during the artificial rainwater (ARW)-injection period. Cesium transport associated with montmorillonite colloids was significant, with a maximum colloid-associated Cs C/C(0) (outflow-to-inflow concentration ratio) value of 16.6 +/- 1.1% during the tracer (colloids and LiBr)-injection period. However, the relative contribution of colloid-associated Cs transport to total Cs transport was relatively low, amounting to 10.3 +/- 0.7% and 14.5 +/- 0.7% with montmorillonite (500 mg L(-1)) and the montmorillonite-HA (10 mg L(-1)) mixture, respectively. Readsorption of Cs onto the colloids occurred immediately on switching from the tracer suspension to the background solution of ARW. The significant colloid-associated Cs transport, the stripping effect of Cs from colloids, and the slow desorption of Cs from fracture walls reported in this study have important implications for risk assessments of Cs mobility in fractured carbonatic rocks.

Hydrogeological and geochemical control of the variations of 222Rn concentrations in a hard rock aquifer: Insights into the possible role of fracture-matrix exchanges

To investigate the possible variations of Rn concentration in crystalline rocks as a function of flow conditions, a field study was carried out of a fractured aquifer in granite. The method is based on the in situ measurement of Rn in groundwater, aquifer tests for the determination of hydraulic characteristics of the aquifer and laboratory measurement of Rn exhalation rate from rocks. A simple crack model that simulates the Rn concentration in waters circulating in a fracture intersecting a borehole was also tested. The Rn concentrations in groundwaters from boreholes of the study site ranged from 192 to 1597 Bq L −1 . The Rn exhalation rates of selected samples of granite and micaschist were determined from laboratory experiments. The results yielded fluxes varying from 0.5 to 1.3 mBq m −2 s −1 in granite and from 0.5 to 0.9 mBq m −2 s −1 in micaschists. Pumping tests were performed in the studied boreholes to estimate the transmissivity and calculate the equivalent hydraulic aperture of the fractures. Transmissivities ranged from 10 −5 to 10 −3 m 2 s −1 . Using the cubic law, hydraulic equivalent fracture apertures were calculated to be in the range of 0.5–2.3 mm. To gain a better insight into the spatial variability of Rn contents in groundwater, theoretical Rn concentrations were calculated from an available simple crack model using results from field and laboratory experiments. This model gave satisfactory results for boreholes characterized by low-flow conditions, in which case, the calculated Rn contents were in the range of Rn concentrations set by the analytical uncertainty of concentrations measured in water. However, for boreholes characterized by high-flow conditions, the model underestimated the Rn concentration in groundwater. The higher the flow in the fracture, the larger the difference between calculated and measured Rn concentrations in water. These observations led to performing pumping tests to obtain a better understanding of the hydrogeological control of Rn content in water. The results clearly show an increase of Rn content in groundwater after the pumping test, which could be explained by the input of Rn-rich waters from the host matrix.

Mechanics of fluid‐driven fracture growth in naturally fractured reservoirs with simple network geometries

A numerical model has been developed for fluid‐driven opening mode fracture growth in a naturally fractured formation. The rock formation contains discrete deformable fractures, which are initially closed but conductive because of their preexisting apertures. Fluid flow that develops along fractures depends on fracture geometry defined by preexisting aperture distribution, offsets along a fracture path, and intersections of two or more fractures. The model couples fluid flow, elastic deformation, and frictional sliding to obtain the solution, which depends on the competition between fractures for permeability enhancement. The fractures can be opened by fluid pressure that exceeds the normal stress acting on them and by interactions with intersecting closed fractures experiencing Coulomb‐type frictional slip. The Newtonian fluid is assumed to flow through the conductive fractures according to a lubrication equation that relates the cube of an equivalent hydraulic aperture to fracture conductivity. The rock material is assumed to be impermeable and elastic. This paper provides the governing equations for the multiple fracture systems and the solution methods used. Flow distribution and fracture growth in conductive fracture sets are simulated for a range of geometric arrangements and hydraulic properties. Numerical results show that elastic interaction between fracture branches plays a controlling role in fluid migration, although initial apertures can give rise to a preferential fluid flow direction during the early stage. In the presence of offsets, fracture segments subject to strong compression are difficult to open hydraulically, and their resulting smaller permeability can increase overall upstream fracture pressure and opening. The patterns of fluid flow become more complicated if fractures intersect each other. A portion of injected fluid is lost into closed empty fractures that cut across the main hydraulic fracture, and this delays the pressure increases required for fracture growth past the crosscutting fracture. The nonlinear fluid loss rate depends on the geometric complexities of the fracture sets and on the fluid viscosity. Sometimes fracture growth can be accelerated by the fast fluid transport along an intersected, relatively conductive natural fracture.

Colloid-facilitated transport of lead in natural discrete fractures

Colloid-facilitated transport of lead (Pb) was explored in a natural chalk fracture with an average equivalent hydraulic aperture of 139 μm. Tracer solution was prepared by adding montmorillonite (100 mg L −1) and/or humic acid (HA) (10 mg L −1) to modified artificial rainwater containing dissolved Pb (21.4 mg Pb L −1), naturally precipitated PbCO 3 particles (16.4 mg Pb L −1) and LiBr (39.0 mg L −1). We found that Pb is only mobile when associated with colloids. PbCO 3 particles were not mobile in the fracture. The addition of HA to the montmorillonite suspension increased the suspension's mobility and therefore promoted the colloid-facilitated transport of Pb. The increases in pH and sodium absorption ratio induced by the chalk-tracer solution interactions appeared to increase the dispersion and mobilization of colloids entering the fracture. The dominant colloid-facilitated transport of Pb reported in this study has significant implications for risk assessment of Pb mobility in fractured rocks.

A comparison of clay colloid and artificial microsphere transport in natural discrete fractures

Transport of monodispersed buoyant 1-μm latex microspheres, dense 1.34-μm montmorillonite particles, Li + and Br − was investigated in a naturally fractured chalk core with an average equivalent hydraulic aperture of 183 μm. Studied parameters were: tracer arrival time, C / C 0 values, mass recovery, size distribution and the impact of initial concentration. Breakthrough time of both colloidal tracers was faster than that of the soluble tracers. Significantly lower recovery and slightly slower breakthrough time were observed for the clay particles relative to the microspheres, apparently mainly due to the former's higher density, resulting in preferential gravitational settling of the clay particles. However, variable surface charge and nonuniform shape and size of the clay particles may also play a role in the observed differences. From the theoretical scale ratio, the time interval calculation seems to be a major factor in colloid recovery. Clay-particle size fractionation was observed (0.62 vs 1.34 μm at the outflow and inflow, respectively), and there was no significant influence of the initial concentration (100 and 500 mg/L) on transport properties. Our observations indicate that colloid density is a dominant property for their transport in fractures. This work emphasizes the need for caution when the results of studies in which buoyant colloids are used as tracers are extrapolated to natural systems in which clay colloids are present.

Permeability reduction of a natural fracture under net dissolution by hydrothermal fluids

Flow‐through tests are completed on a natural fracture in novaculite at temperatures of 20°C, 80°C, 120°C, and 150°C. Measurements of fluid and dissolved mass fluxes, and concurrent X‐ray CT imaging, are used to constrain the progress of mineral dissolution and its effect on transport properties. Under constant effective stress, fracture permeability decreases monotonically with an increase in temperature. Increases in temperature cause closure of the fracture, although each increment in temperature causes a successively smaller effect. The initial differential fluid pressure‐drop across the fracture increases by two orders of magnitude through the 900 h duration of the test, consistent with a reduction of an equivalent hydraulic aperture by a factor of five. Both the magnitude and rate of aperture reduction is consistent with the dissolution of stressed asperities in contact, as confirmed by the hydraulic and mass efflux data. These observations are confirmed by CT imaging, resolved to 35 microns, and define the potentially substantial influence that benign changes in environmental conditions of stress, temperature, and chemistry may exert on transport properties.

The hydromechanical behaviour of a fracture: an in situ experimental case study

Relationships between flow distributions and mechanical opening in a single natural fracture are investigated in situ through field experiments, at a scale of about 1 m, in a granitic quarry. Experiments have been conducted at various injection flow-rates while the normal stress applied to the fracture was controlled by hydraulic flat jacks. Variations of the collected flow-rate (monitored through contiguous flow collectors distributed along the fracture periphery) with the injection pressure are fully reproducible. They show that the fracture opens only above a threshold pressure which increases with the externally applied stress. This threshold is non-zero with no applied flat jacks pressure which raises questions on the reliability of hydraulic jacking techniques for the measurement of the normal stress on preexisting fractures. It is shown that equivalent hydraulic aperture and mechanical opening are comparable only above a critical mean fracture opening estimated to be around 15–20μm for the tested granite. For mean fracture openings smaller than this value, the standard time scale used for stress measurements distorts the results. It is also shown that channeling effects may control flow away from the injection hole so that the hydraulic jacking stress measurement technique may overestimate the mean normal stress acting on the fracture plane by as much as 4 MPa. It is concluded that hydraulic testing techniques for normal stress measurements should not include results from the fracture opening phase. Moreover, criteria should be established for validating results from the closing phase in order to demonstrate the absence of channelling effects. Finally, it is shown that, because of the elastic response of the rock, water injection in a fracture system decreases the interstitial pressure ahead of the increasing pressure front associated with the water flow.

Trichloroethene DNAPL flow and mass distribution in naturally fractured clay: Evidence of aperture variability

A cylindrical sample, 0.5 m in diameter and length, was obtained by excavation from 3.7–4.2 m depth below ground surface in a surficial deposit of fractured glaciolacustrine clay. The sample was enclosed in a triaxial cell in a cold room to impose conditions close to field temperature and stress. Hydraulic testing using a hydraulic gradient of 2 provided a saturated hydraulic conductivity of 7 × 10−10 m/s, which is only slightly larger than the matrix hydraulic conductivity. The cubic law provided a mean hydraulic aperture of 5–6 μm for the four continuous vertical fractures in the sample. A column of immiscible‐phase trichloroethene (TCE) imposed incrementally at the top of the sample provided an entry‐pressure‐derived aperture equal to 17 μm for a parallel‐plate fracture. TCE dense nonaqueous phase liquid (DNAPL) that flowed through the sample produced dissolved‐phase diffusion haloes in the matrix that indicated the preferential fracture pathways. These haloes indicated that DNAPL flowed through only 5–15% of the visible, oxidation‐stained fractures; hence natural fractures had variable apertures along their length, and the larger aperture regions provided channels for fluid flow. Using the hydraulic test results and applying the cubic law only to the aperture segments of confirmed DNAPL flow, an equivalent hydraulic aperture of 8–11 μm was obtained, which is greater than the conventional mean hydraulic aperture and smaller than the local aperture determined from the DNAPL entry pressure. These differences are large in the context of fluid flux, which is proportional to the aperture cubed.

Particles’ transport in a single fracture under variable flow regimes

A mathematical model to account for non-laminar terms, during simulated transports in fractured rocks has been developed. The relevant conceptual model consists of a two dimensional grid block equivalent to a variable fracture plane. The block aperture variability is expressed by means of stochastic procedures, based upon some characteristics of fractured media. One of them, e.g. the equivalent hydraulic aperture, may be estimated by means of the results of field tests. The solution of Navier–Stokes and Darcy–Weisbach's equation for steady state flow between two parallel plates with constant aperture allows the systems of equations under respetively, laminar and non-laminar conditions, to be wirtten. The flow model is a standard finite-difference method with a modified version of Darcy's equation to account for non-laminar terms that are important at high water velocity. To simulate solute transports, the particle tracking technique was applied.

222Rn transport in a fractured crystalline rock aquifer: results from numerical simulations

Dissolved 222Rn concentrations in ground water from a small wellfield underlain by fractured Middle Proterozoic Pikes Peak Granite southwest of Denver, Colorado range from 124 to 840 kBq m −3 (3360-22700 pCi L −1). Numerical simulations of flow and transport between two wells show that differences in equivalent hydraulic aperture of transmissive fractures, assuming a simplified two-fracture system and the parallel-plate model, can account for the different 222Rn concentrations in each well under steady-state conditions. Transient flow and transport simulations show that 222Rn concentrations along the fracture profile are influenced by 222Rn concentrations in the adjoining fracture and depend on boundary conditions, proximity of the pumping well to the fracture intersection, transmissivity of the conductive fractures, and pumping rate. Non-homogeneous distribution (point sources) of 222Rn parent radionuclides, uranium and 226Ra, can strongly perturb the dissolved 222Rn concentrations in a fracture system. Without detailed information on the geometry and hydraulic properties of the connected fracture system, it may be impossible to distinguish the influence of factors controlling 222Rn distribution or to determine location of 222Rn point sources in the field in areas where ground water exhibits moderate 222Rn concentrations. Flow and transport simulations of a hypothetical multifracture system consisting of ten connected fractures, each 10 m in length with fracture apertures ranging from 0.1 to 1.0 mm, show that 222Rn concentrations at the pumping well can vary significantly over time. Assuming parallel-plate flow, transmissivities of the hypothetical system vary over four orders of magnitude because transmissivity varies with the cube of fracture aperture. The extreme hydraulic heterogeneity of the simple hypothetical system leads to widely ranging 222Rn values, even assuming homogeneous distribution of uranium and 226Ra along fracture walls. Consequently, it is concluded that 222Rn concentrations vary, not only with the geometric and stress factors noted above, but also according to local fracture aperture distribution, local groundwater residence time, and flux of 222Rn from parent radionuclides along fracture walls.