Parallel-plate Fracture Research Articles

Migration and sedimentation of proppant and its influencing factors in a visual plate fracture model

Hydraulic fracturing technology is the main method used to form high-conductivity fracture networks in unconventional oil and gas reservoirs, and the effective filling of quartz sand proppant in the fracture network is key to its successful implementation. Conventional experiments on the evaluation of sand carrying migration are mainly based on the migration and sedimentation law of a single-mesh proppant in the main fracture; the results obtained are inconsistent with the field observations. To improve our understanding of the migration and sedimentation law of the proppant in the main and branch fractures, in this study, the influences of injection time, injection rate, fracturing fluid viscosity, and proppant combination type on the migration and sedimentation law of a proppant in single and branch fractures were analyzed based on the injection parameters of the sand-carrying fracturing fluid obtained using a similarity criterion through a visual large-scale parallel-plate fracture model system built indoors. The results showed that the rapid accumulation stage of the proppant in the fracture is during the injection time of 5–10 min; the injection rate affected the accumulation area and height of the proppant to a certain extent but had little effect on the final sand dike morphology. A low viscosity of the fracturing fluid was not conducive to the sedimentation of the proppant in the branch fractures; an excessively high fracturing fluid viscosity was not conducive to the sedimentation of the proppant in both the main and branch fractures. When the fracture morphology is single, the viscosity of the fracturing fluid is recommended to be between 30 and 60 mPa·s. When the fracture morphology is complex, the recommended value is between 40 and 50 mPa s. Taking the migration and sedimentation laws of the proppant in the main fracture as an example, the flow of fracturing fluid in the fracture after the formation of a stable sand dike could be divided into five regions: ① inlet scour zone; ② buffer zone; ③ sand dike stable transition zone; ④ sand dike stability zone; and ⑤ outlet scour zone. The higher the large mesh proppant ratio used in the fracturing fluid, the lower the total area ratio of the corresponding sand dike; however, the proppant sedimentation ratio in the branch fracture increases. This study enriches and improves the relevant theoretical research on the migration and sedimentation of proppants and has a certain effect on improving the success rate of the hydraulic fracturing technology applied to unconventional oil and gas reservoirs.

Three‐dimensional visualization experimental study on proppant transportation and placement in the Hi‐way channel hydraulic fracturing technique

AbstractThe pattern of placement of the proppant in the fracture determines the stimulation and success of the surgery. Using a three‐dimensional visual parallel plate fracture model capable of simulating fracture height, length, and variable fracture width, we experimentally investigate the impact of fiber loading, fracture fluid viscosity, sand concentration, pulse time, perforation pattern, and injection rate on proppant transport, placement pattern, and access rate. Experimentally and visually, the migration process and the morphology of the proppant placement in the fracture were assessed. The formation laws of stable support columns and well‐shaped high conductivity fracture channels in fractures have been elucidated. Experimental results show that increasing the fiber concentration improves the channel rate and the proppant mass is large and stable. The channel rate increases with the viscosity of the fracturing fluid, and it is difficult to form a perfect channel when the viscosity is small. If the constructive displacement is too slight or too large, it will not favor the formation of a Hi‐way channel in the fracture. The optimal design displacement is 4.5 m3/min. When the proppant concentration is low, the passage rate is large, but the stability of proppant mass is poor under the scour of large displacement, the conductivity is low under the high closure pressure, the proppant concentration is too high, the suspension is difficult, the settlement rate is large, and it is difficult to form a large passage. The current column and the passage rate are larger for pulse times of 15–20 s. Cluster perforations are better than large continuous perforations. The higher the number of clusters in the same number of holes, the higher the channel rate. The formation laws of stable support pillars and well‐shaped high conductivity fracture channels in fractures have been elucidated, which can be useful for efficient stimulation of oil and gas reservoirs.

Determining effective diffusion coefficients of chlorohydrocarbons in natural clays: Unique results from highly resolved controlled release field experiments

This study aims to precisely determine the effective diffusion coefficients of chlorohydrocarbons in low permeable units under in-situ field conditions. To this end, two controlled release field experiments using TCE and PCE as dense non-aqueous phase liquids (DNAPLs) were conducted in two natural clayey deposits. Several months to years after the controlled DNAPL release, highly resolved concentration profiles were determined for the chlorohydrocarbons that had diffused into the clayey deposits. Effective diffusion coefficients for TCE and PCE were then determined by calibrating a 3D numerical and 1D analytical model, respectively, to the measured high-resolution concentration profiles. The simulations revealed that the effective diffusion coefficients vary by as much as a factor of four within the same low permeability unit being consistent with observed small-scale heterogeneities. The determined chlorohydrocarbon effective diffusion coefficients were further used to determine the equivalent thickness of DNAPL that would completely dissolve in an idealized, parallel-plate fracture by diffusion transport into clayey deposits for the time periods of the controlled release field experiments. The equivalent TCE and PCE DNAPL film thicknesses ranged between 36 and 581 μm, respectively, comparable and exceeding fracture apertures measured in naturally fractured clay rich deposits. Hence, films of DNAPL initially contained within fractures in clay-rich deposits can completely dissolve away within a few months to a few years due to diffusion. This stored contaminant mass poses a risk to adjacent aquifers if it is re-released due to diffusion out of the matrix after source depletion or remediation.

Heat transport by flow through rough rock fractures: a numerical investigation

Fracture surface topography exhibits long-range spatial correlations resulting in a heterogeneous aperture field. This leads to the formation, within fracture planes, of preferential flow channels controlling flow and transport processes. By means of a 3-D heat transport model coupled with a 2-D fracture flow model based on the lubrification approximation (i.e., local cubic law), we investigate how the statistical parameters determining spatial aperture variations in individual fractures control the heat exchange at the fluid/rock interface and heat transport by flow. Ensemble statistics over fracture realizations provide insights into the main hydraulic and geometrical parameters controlling the hydraulic and thermal behaviour of rough fractures. Similarly to the rough fracture’s hydraulic behaviour, we find that its heat transport behaviour deviates from the conventional parallel plate fracture model with increasing fracture closure and/or decreasing correlation length. We demonstrate that the advancement of the thermal front is typically slower in rough fractures compared to smooth fractures having the same mechanical aperture. In contrast with previous studies that neglect temporal and spatial temperature variations in the rock matrix, we find that the thermal behavior of a rough-walled fracture can, under field-relevant conditions, be predicted from a parallel plate model with an aperture equal to the rough fracture’s effective hydraulic aperture. This greatly simplifies the prediction of possible reservoir thermal behavior when using field measurable quantities and hydrological modeling.

Core-scale investigation of convective heat transfer of supercritical pressure CO2 in hot rock fracture with various inclinations

Extracting heat from hot dry rock by injecting working fluids is recognized as an important way of geothermal utilization. In recent years, using CO2 as the working fluid has been paid more attentions since its advantage of saving water, appropriate properties, as well as the potential capacity of large-scale CO2 geological storage. Our previous research has found that the effect of thermal properties variation of CO2 on heat transfer performance in horizontal fracture can’t be ignored when fluid temperature is in the range of Tp,c (pseudo-critical temperature) to 1.2 Tp,c. However, the combine effect of thermal properties variation with different fracture inclinations on heat transfer performance is not clear. In this paper, core-scale experiments and numerical simulations were conducted to investigate laminar convective heat transfer of supercritical pressure CO2 in a vertical smooth parallel-plate fracture and a rough fracture with various inclinations. The convective heat transfer characteristics in smooth horizontal and vertical fractures were compared in terms of velocity distribution, heat transfer coefficient and Nusselt number at different working conditions. It was found that in the vertical fracture, CO2 flow near the pseudo-critical point (Tf,in/Tp,c = 1.1) appeared heat transfer deterioration at low Rein number, followed by recovering to a comparable value with the Nu number in horizontal fracture. While the impact of buoyancy force on the heat transfer away from the pseudo-critical point (Tf,in/Tp,c = 2.9) was comparatively small in this study, especially when Gr/Re2 was smaller than 0.1. The heat transfer performance in a rough fracture was lower than that in the smooth fracture under the same conditions and the effect of the fracture inclination on the heat transfer performance was not significant. A correlation of Nusselt number in a rough rock fracture was proposed with extra considerations of the thermal property variation and fracture inclination. This work would provide a deeper understanding of the influence of fracture inclinations on heat transfer performance in geothermal development.

Heat transfer in a 3D rough rock fracture with heterogeneous apertures

A clear understanding of the convective heat transfer characteristics in the three-dimensional (3D) rough rock fracture is important for evaluating heat recovery in fractured reservoirs. A granite sample containing a Brazilian-induced artificial fracture, which was tested at increasing normal compressive stresses, was adopted to build 3D numerical models for rough rock fractures. At each stress level, flow-through simulation tests with different injection velocities were performed to examine the effect of fracture geometrical alterations induced by changing stresses on the heat transfer processes within hot fractured rock samples. Meanwhile, a hypothetical rough fracture and a parallel plate fracture, with an equivalent mechanical aperture to the artificial fracture, were constructed for the same heat transfer simulations as references. The results show that the flow and heat transfer behaviors in three types of fractures are significantly different, and the difference becomes more obvious as the normal stress and flow velocity increase. The alterations in asperity contacts and void spaces due to stress changes increase the heterogeneities of the distributions of streamlines and water temperatures in the artificial fracture. The tortuosity induced by the global fluctuation of the surface roughness in the hypothetical fracture cannot describe the flow and heat transport in the artificial fracture. The heat transfer coefficient in three types of fractures decreases non-linearly as the hydraulic aperture increases. Under the same hydraulic aperture, the heat transfer coefficient is larger in the hypothetical fracture than in the other two fractures. The channeling flow within the artificial fracture under high normal stresses weakens the heat transfer, resulting in the smallest heat transfer coefficient compared to the other two fractures. An empirical model was developed to describe the relationship between the normalized heat transfer coefficient and the hydraulic aperture, and this model was validated well using the published heated flow-through experimental results.

Determination of Dynamic Dispersion Coefficient for Solid Particles Flowing in a Fracture With Consideration of Gravity Effect

Abstract A robust and pragmatic method has been developed and validated to analytically determine dynamic dispersion coefficients for particles flowing in a parallel-plate fracture, in which gravity settling has been considered due to its significant impact on particle flowing behavior. More specifically, a two-dimensional (2D) advection–diffusion equation together with the initial and boundary conditions has been formulated to describe the flow behavior of finite-sized particles on the basis of coupling the Poiseuille flow with vertical settling. Meanwhile, three types of instantaneous source conditions (i.e., point source, uniform line source, and volumetric line source) have been considered. Explicit expressions, which can directly and time-efficiently calculate dynamic dispersion coefficient, have been derived through the moment analysis and the Green’s function method. By performing the simulation based on the random walk particle tracking (RWPT) algorithm, the newly developed model has been verified to determine particle dispersion coefficients agreeing well with those obtained from the RWPT simulations. It is found that the point source is the most sensitive to gravity effect among different source conditions, while the volumetric line source is affected more than the uniform line source. For particle size larger than its critical value, an increased particle size leads to a decreased asymptotical dispersion coefficient for all the source conditions due to the significant gravity effect, while gravity positively affects the dispersion coefficient at early times for the point source condition. In addition, average flow velocity positively affects the dispersion coefficient for all the source conditions, while the associated gravity effect is influenced only at early times for the point source condition.

Dependence of fluid flow on cleat aperture distribution and aperture\u2013length scaling: a case study from Gondwana coal seams of Raniganj Formation, Eastern India

Dimensions and mutual relationships amongst fracture (cleat) parameters such as maximum aperture width, average aperture width, length, spacing etc. control the connectivity within a fracture network and the fluid flow in a coal seam as the matrix permeability, here, is negligible. In this paper, we document cleat size distributions and investigate length–aperture relationships from coals of Raniganj coalfield in Eastern India. This coalfield has a proven extractable reserve of six billion tons of coal and holds immense potential to be one of the largest coal bed methane fields serving India’s growing energy needs. Here, cleat length (L) correlates with corresponding maximum aperture width (Dmax) in a power-law function with an exponent of 0.84 (Dmax α L0.84) instead of the commonly observed exponents of 1 or 0.5 applicable for other natural ‘opening-mode’ fractures. The conventional wisdom pertains that laminar fluid flow (Q) through an isolated, smooth-walled, parallel-plate fracture, embedded in an impermeable matrix, is directly proportional to the cube of its aperture width (b, equivalent to Davg; cubic law: Q α b3). This assumes a linear relationship between length and fracture aperture. However, the modified relationship between cleat length and average aperture width changes the cubic law applicable for Raniganj coal seam and now fluid flow correlates with aperture width in a power-law function with an exponent of 4.25 (Q α b4.25) instead of 3 (cube). Such simplifications will come handy for the modeling and estimation of fluid flow as it will reduce the effort of cleat length measurement which is anyway difficult and can be misleading due to the risk of undersampling.

A Quasi‐3D Numerical Model for Grout Injection in a Parallel Fracture Based on Finite Volume Method

The purpose of the present work is to develop a quasi‐3D numerical method that can be used to study the diffusion mechanism of grout injection in a rock fracture based on the collocated structured grid of the finite volume method (FVM). Considering the characteristics of fracture in geometry that the aperture is much less than its length and width, the Hele‐Shaw model is introduced to deduce the z-derivatives of velocities u and v at walls, which is a function of the relevant average velocity and the fracture aperture. The traditional difference scheme for the diffusive term is partly substituted with the derived analytical expressions; hence a three‐dimensional problem of grout flow in the parallel fracture can be transformed into a two‐dimensional one that concerns fracture aperture. The new model is validated by the analytical solution and experimental data on three cases of grouting in the parallel‐plate fracture. Compared with the results from ANSYS‐Fluent software, the present model shows better agreement with the analytical solution for the distribution of pressure and velocity. Furthermore, the new model needs less grid unit, spends less time, but achieves greater accuracy. The complexity of the grout flow field in the rock fracture is reduced; thus the computational efficiency can be improved significantly.

Thermal Attenuation and Lag Time in Fractured Rock: Theory and Field Measurements From Joint Heat and Solute Tracer Tests

AbstractThe modeling and prediction of heat transfer in fractured media is particularly challenging as hydraulic and transport properties depend on a multiscale structure that is difficult to resolve. In addition to advection and dispersion, heat transfer is also impacted by thermal attenuation and lag time, which results from fracture‐matrix thermal exchanges. Here we derive analytical expressions for thermal lag time and attenuation coefficient in fractured media, which quantify the effect of fracture geometry on these key factors. We use the developed expressions to interpret the results of single‐well thermal and solute tracer tests performed in a crystalline rock aquifer at the experimental site of Ploemeur (H+ observatory network). Thermal breakthrough was monitored with fiber‐optic distributed temperature sensing (FO‐DTS), which allows temperature monitoring at high spatial and temporal resolution. The observed thermal response departs from the conventional parallel plate fracture model but is consistent with a channel model representing highly channelized fracture flow. These findings, which point to a strong reduction of fracture‐matrix exchange by flow channeling, show the impact of fracture geometry on heat recovery in geothermal systems. This study also highlights the advantages to conduct both thermal and solute tracer tests to infer fracture aperture and geometry.

Dynamic Dispersion Coefficient of Solutes Flowing in a Circular Tube and a Tube-Bundle Model

Mathematical formulations have been proposed and verified to determine dynamic dispersion coefficients for solutes flowing in a circular tube with fully developed laminar flow under different source conditions. Both the moment analysis method and the Green's function are used to derive mathematical formulations, while the three-dimensional (3D) random walk particle tracking (RWPT) algorithm in a Cartesian coordinate system has been modified to describe solute flow behavior. The newly proposed formulations have been verified to determine dynamic dispersion coefficients of solutes by achieving excellent agreements with both the RWPT results and analytical solutions. The differences among transverse average concentration using the Taylor model with and without dynamic dispersion coefficient and center-of-mass velocity are significant at early times but indistinguishable when dimensionless time (tD) approaches 0.5. Furthermore, compared to solutes flowing in a 3D circular tube, dispersion coefficients of solutes flowing in a two-dimensional (2D) parallel-plate fracture are always larger for a uniform planar source; however, this is not always true for a point source. Solute dispersion in porous media represented by the tube-bundle model is greatly affected by pore-size distribution and increases as standard deviation of pore-size distribution (σ) increases across the full-time scale.

Parallel-plate fracture transport experiments of nanoparticulate illite in the ultra-trace concentration range investigated by Laser-Induced Breakdown Detection (LIBD)

This study investigates the appropriateness of monodisperse carboxylated polystyrene spheres as clay colloid analogues. Colloid transport experiments using Na-illite are conducted within a parallel-plate fracture flow cell with an aperture of 0.75mm at pH 5 under low ionic strength (1mM NaCl) and laminar flow (7mL/h) conditions. The effects of collector surface material (Grimsel granodiorite or acrylic glass), fracture orientation and residence time on colloid retention are examined. In order to avoid full surface coverage effects, ultra-trace (30ppb) Na-illite colloid concentrations are used. Laser-induced breakdown detection is applied in order to detect and quantify the Na-illite colloids. The results are directly compared to the experiments of Stoll, et al. [1] who investigated the transport and surface interaction of carboxylated polystyrene spheres (25 and 1000nm diameter) using the same experimental setup and conditions. It is concluded that polystyrene spheres are no ideal analogue to predict the mobility and transport behavior of a polydisperse clay colloid suspension. Despite the higher solid density, the Na-illite colloids show higher mobility compared to the polystyrene spheres without significant impact of surface roughness or gravity. The platelet shape, the non-uniform surface charge distribution and slower sedimentation may account for the observed differences.

Convective heat transfer of supercritical CO2 in a rock fracture for enhanced geothermal systems

Convective heat transfer characteristics of supercritical pressure fluid in a rock fracture are important for building an accurate heat transfer model of enhanced geothermal systems. This paper presents experimental investigations of laminar convection heat transfer of supercritical pressure CO2 in an artificial smooth parallel-plate fracture and a rough and tortuous fracture that was created using the Brazilian technique. Hot rock with a relatively high initial temperature reserves more heat, which can ensure a larger heat extraction rate for a longer time when cold fluid flows through the fracture. Compared with the smooth parallel-plate fracture, CO2 flowing through the rough and tortuous fracture with an equivalent hydraulic aperture extracted less heat from the hot rock due to the less efficient heat exchange in a rough fracture caused by channeling effect. This was illustrated by numerical simulation results of the reconstructed fracture based on micro-computed tomography scan data. The overall Nusselt number obtained from the numerical results was larger in a rough fracture with a larger Reynolds number due to disturbance effect on the boundary layer development. The heat transfer performance in a rough fracture is therefore influenced by interactions of the channeling and disturbance effects caused by the tortuous flow path.

Determination of dynamic dispersion coefficient for particles flowing in a parallel-plate fracture

A robust and pragmatic technique has been developed to determine dynamic dispersion coefficients for particles flowing in a parallel-plate fracture. By using local moment analyses, theoretical equations have been formulated to describe flow behaviour of solid particles flowing in a parallel-plate fracture on the basis of the Poiseuille flow under different source conditions. By using the random walk particle tracking (RWPT) algorithm, newly developed models have been verified to determine solute and particle dispersion coefficients agreeing with those obtained from RWPT simulations. At early times, particle dispersion coefficient is not only controlled by the source condition, but also negatively correlated with the center-of-mass velocity. Compared to a point source, at early times, dispersion coefficients of particles originating from a line source are larger; however, after a critical time, all dispersion coefficients approach the values obtained through the extended Taylor theory. Subsequently, the newly developed models have been extended to match experimental measurements, while particle dispersion coefficients are notably less than those calculated by the extended Taylor theory.

Temperature nanotracers for fractured reservoirs characterization

Abstract Nanoparticle tracers are being investigated as a potential tool to measure temperature distributions in subsurface reservoirs. If the temperature distributions could be measured more precisely, this would greatly enhance the ability to estimate other reservoir properties, which would in turn inform reservoir engineering and field management decisions. Work toward two distinct but parallel objectives are described here. The first is to rank the informativity of various tracer candidates using modeling. The second is to develop temperature sensitive tracers experimentally, such that they would be capable of characterizing fracture properties and temperature distribution. The design of temperature-sensitive tracers is built around the design of the temperature sensing mechanism. In other words, the mechanism by which temperature is measured and the form and resolution of the resulting data, or response, have a profound impact on how informative that tracer can be about thermal breakthrough. Therefore, it is important to model the responses of candidate tracers in the context of an inverse problem to determine their relative informativity. In order to quantify tracer informativity for the simplified case in which the reservoir consists of a single parallel-plate fracture, one-dimensional analytical models were used to calculate the responses of four tracer types: conservative solute tracer, dye-releasing nanotracer, threshold nanoreactor, and temperature–time tracer (TTT). Inverse modeling was performed for various scenarios, and thermal breakthrough curves were calculated for each solution found. Tracers investigated in this study were found to perform very well, with small ranges of uncertainty for both thermal breakthrough forecasting and fracture property estimation. This was because the problem was highly constrained by defining the reservoir as a single fracture. For more realistic reservoir models consisting of complex fracture networks, it is expected that the uncertainty ranges would be larger and that all three temperature-sensitive tracers investigated here will outperform conservative solute tracers because their responses contain information about the temperature distribution. Experiments were performed to evaluate several potential nanosensor candidates for their temperature-sensitivity and to investigate particle mobility through porous and fractured media. Temperature-sensitive particles investigated in this study include the irreversible thermochromic, dye-attached silica and silica-protected DNA particles. A combined heat and flow test confirmed the temperature-sensitivity of the irreversible thermochromic particles by observing the color change. A detectable change in the fluorescent emission spectrum of the dye-attached silica particles upon heating was observed. The processing and detection of silica-encapsulated DNA particles with hydrofluoric acid chemistry was tested. A protocol to release the DNA by dissolving the silica layer without completely destroying the DNA was established. The silica-encapsulated DNA particles were flowed through a porous medium at high temperature. Some dissolution of silica particles was observed, leading to a reduction in their size. This research showed that synthesizing particles to respond to a specific reservoir property such as temperature is feasible. Using particles to measure reservoir properties is advantageous because particles can be transported to areas in the reservoir that would not be accessible by other means and therefore provide measurements deep within the formation.

A STUDY OF HYDRAULIC PROPERTIES IN A SINGLE FRACTURE WITH IN-PLANE HETEROGENEITY: AN EVALUATION USING OPTICAL MEASUREMENTS OF A TRANSPARENT REPLICA

Experimental examinations for evaluating fracutres were conducted by using transparent replicas of a single fracture in order to obtain the fracture data to contribute to the methodlogy on how to improve the definitaion of representative parameter values used for a parallel plate fracture model. Quantitative aperture distribution and quantitative tracer concentration data at each point in time were obtained by measuring the attenuation of transmitted light through the fracture in high spatial resolution. the representative aperture values evaluated from the multiple different measurement methods, such as arithmetic mean of aperture distribution measured by the optical method, transport aperture evaluated from the tracer test, and average aperture evaluated from the fracture void volume measurement converged to a unique value that indicates the accuracy of this experimental study. The aperture data was employed for verifying the numerical simulation under the assuption of Local Cubic Law and showed that the calculated flow rate through the fracture is 10%-100% larger than hydraulic test results. The quantitative tracer concentration data is also very valuable for validating existing numerical code for advection dispersion transport in-plane heterogeneous fractures.

Water-soluble gases as partitioning tracers to investigate the pore volume–transmissivity correlation in a fracture

Hydraulically equivalent fractures may show striking differences when a gas-migration experiment is performed because of the different correlations between transmissivity, pore volume and entry pressure. We numerically simulate gas migration between injection and extraction boreholes in a parallel plate fracture with a heterogeneous fault gouge, in a rough-walled fracture filled with homogeneous material, and in a rough-walled empty fracture. The parallel plate model and the empty model clearly show the existence of preferential paths; for high variance of the transmissivity field, gas flow takes place only in few discrete channels separated by water-saturated regions. In contrast, in the fracture filled with homogeneous fault gouge, the gas saturation is continuous and more uniformly distributed. It appears a fundamental issue to be able to discriminate in situ among conceptual models that can yield such a different gas-saturation distribution. As in practice, the saturation distribution cannot be directly observed, tracer experiments are performed to characterize a fracture. For these reasons, we simulate the transport of tracers, which are added to the gas phase as soon as quasi-steady saturation distribution and extraction rate are achieved, and we compare the breakthrough curves obtained assuming different models. Our numerical simulations suggest that discrimination among the models on the basis of single-tracer tests is unlikely. A better tool to investigate fracture properties is provided by a gas-tracer test, in which a cocktail of gases with different water solubility is employed. These gases behave as partitioning tracers and allow us to estimate the gas saturation in the fracture. Indeed, by comparison of the residence-time distributions of different gases, we are able to compute a streamline effective saturation, which is an excellent estimate of fracture saturation. In addition, the streamline effective saturation curve contains information that is useful to identify the conceptual model that more likely applies to the fracture.

Effects of pore volume–transmissivity correlation on transport phenomena

The relevant velocity that describes transport phenomena in a porous medium is the pore velocity. For this reason, one needs not only to describe the variability of transmissivity, which fully determines the Darcy velocity field for given source terms and boundary conditions, but also any variability of the pore volume. We demonstrate that hydraulically equivalent media with exactly the same transmissivity field can produce dramatic differences in the displacement of a solute if they have different pore volume distributions. In particular, we demonstrate that correlation between pore volume and transmissivity leads to a much smoother and more homogeneous solute distribution. This was observed in a laboratory experiment performed in artificial fractures made of two plexiglass plates into which a space-dependent aperture distribution was milled. Using visualization by a light transmission technique, we observe that the solute behaviour is much smoother and more regular after the fractures are filled with glass powder, which plays the role of a homogeneous fault gouge material. This is due to a perfect correlation between pore volume and transmissivity that causes pore velocity to be not directly dependent on the transmissivity, but only indirectly through the hydraulic gradient, which is a much smoother function due to the diffusive behaviour of the flow equation acting as a filter. This smoothing property of the pore volume–transmissivity correlation is also supported by numerical simulations of tracer tests in a dipole flow field. Three different conceptual models are used: an empty fracture, a rough-walled fracture filled with a homogeneous material and a parallel-plate fracture with a heterogeneous fault gouge. All three models are hydraulically equivalent, yet they have a different pore volume distribution. Even if piezometric heads and specific flow rates are exactly the same at any point of the domain, the transport process differs dramatically. These differences make it important to discriminate in situ among different conceptual models in order to simulate correctly the transport phenomena. For this reason, we study the solute breakthrough and recovery curves at the extraction wells. Our numerical case studies show that discrimination on the basis of such data might be impossible except under very favourable conditions, i.e. the integral scale of the transmissivity field has to be known and small compared to the dipole size. If the latter conditions are satisfied, discrimination between the rough-walled fracture filled with a homogeneous material and the other two models becomes possible, whereas the parallel-plate fracture with a heterogeneous fault gouge and the empty fracture still show identifiability problems. The latter may be solved by inspection of aperture and pressure testing.

Effects of biofilm growth on flow and transport through a glass parallel plate fracture

The effects of biofilm growth on flow and solute transport through a sandblasted glass parallel plate fracture was investigated. The fracture was inoculated using soil microorganisms. Glucose, oxygen and other nutrients were supplied to support growth. The biomass initially formed discrete clusters attached to the glass surfaces, but over time formed a continuous biofilm. From dye tracer tests conducted during biofilm growth, it was observed that channels and low-permeability zones dominated transport. The hydraulic conductivity of the fracture showed a sigmoidal decrease with time. The hydraulic conductivity was reduced by a factor of 0.033, from 18 to 0.6 cm/s, corresponding to a 72% decrease in the hydraulic aperture, from 500 to 140 μm. In contrast, the mass balance aperture, determined from fluoride tracer tests, remained relatively constant, indicating that the impact of biomass growth on effective fracture porosity was much less than the effect on hydraulic conductivity. Analyses of pre-biofilm tracer tests revealed that both Taylor dispersion and macrodispersion were influencing transport. During biofilm growth, only macrodispersion was dominant. The macrodispersion coefficient α macro was found to increase logarithmically with hydraulic conductivity reduction.

Numerical simulation of two-phase flow in conceptualized fractures

Two-phase flow in fractured rock is an important phenomenon related to a range of practical problems, including non-aqueous phase liquid contamination of groundwater. Although fractured rocks consist of fracture networks, the study of two-phase flow in a single fracture is a pre-requisite. This paper presents a conceptual and numerical model of two-phase flow in a variable fracture. The void space of the fracture is conceptualized as a system of independent channels with position-dependent apertures. Fundamental equations, governing two-phase displacement in each channel, are derived to represent the interface positions and fractional flows in the fracture. For lognormal aperture distributions, simple approximations to fractional flows are obtained in analytical form by assuming void occupancy based on a local capillary allowability criterion. The model is verified by analytical solutions including two-phase flow in a parallel-plate fracture, and used to study the impacts of aperture variation, mobility ratio and fracture orientation on properties of two-phase flow. Illustrative examples indicate that aperture variation may control the distribution of wetting and non-wetting fluids within the fracture plane and hence the ability of the fracture to transmit these fluids. The presence of wetting fluid does little to hinder non-wetting fluid flow in fractures with large aperture variations, whereas a small volume of non-wetting fluid present in the fracture can significantly reduce wetting fluid flow. Large mobility ratios and high fracture slope angles facilitates the migration of non-wetting fluid through fractures.