Two-phase flow properties of a horizontal fracture: The effect of aperture distribution

A systematic numerical method has been presented to investigate the constitutive relationships between two-phase flow properties of horizontal fractures and aperture distributions. Based on fractal geometry, single rough-walled fractures are generated numerically by modified successive random addition (SRA) method and then aperture distributions with truncated Gaussian distribution are formed by shear displacement between lower and upper surfaces. (The truncated Gaussian distribution is used to describe aperture evolution under different normal stresses.) According to the assumption of two-dimensional porous media and local parallel plate model, invasion percolation approach is employed to model the two-phase flow displacement (imbibition) in generated horizontal fractures, in which capillary forces are dominant over viscous and gravity forces. For truncated Gaussian distributions, constitutive relationships from numerical simulation are compared to closed-form relationships and a good agreement is obtained. The simulation results indicate strong phase interference with the sum of two phase relative permeability values being less than one in the intermediate saturations. It is found that fracture properties related to residual saturations depend on spatial correlation of aperture distributions. Based on the simulation results, we proposed an empirical relationship between the fracture residual-saturation-rated parameters and the corresponding aperture distributions.     

The effect of expansion ratio on the critical Reynolds number in single fracture flow with sudden expansion

Flow in a single fracture (SF) is an important research subject in groundwater hydrology, hydraulic engineering, radioactive nuclear waste repository and geotechnical engineering. An abruptly changing aperture is a unique type of SF. This study discusses the relation between the values of the critical Reynolds number (Re_c) for the onset of symmetry breaking of flow and the expansion ratio (E) of SF, which is defined as the ratio between the outlet (D) and inlet (d) apertures. This study also investigates the effect of inlet aperture d on Re_c for flow in an SF with abruptly changing apertures (SF‐ACA) using the finite volume method. Earlier numerical and experimental results showed that flow is symmetric in respect to the central plane of the SF‐ACA at small Reynolds number (Re) but becomes asymmetric when Re is sufficiently large. Our simulations show that the value of Re_c decreases with the increasing E, and the relationship between the logarithm of Re_c and E can be described accurately using either a quadratic polynomial function or a logarithmic function. However, the relationship of Re_c and d for a given E value is vague, and Re_c becomes even less sensitive to d when E increases. This study also reveals that the hydraulic gradient (J) and flow velocity (v) follow a super‐linear relationship that can be fitted almost perfectly by the Forchheimer equation. The inertial component (J_i) of J increases monotonically with Re, whereas the viscous component (J_v) of J decreases monotonically with Re. The Re value corresponding to equal inertial and viscous components of J (named as the transitional point Re) decreases when E increases, and such a transitional point Re should be closely related to the critical Reynolds number Re_c, although a rigorous theoretical proof is not yet available. Copyright © 2015 John Wiley & Sons, Ltd.     

Contaminant transport in a fracture with spatially variable aperture in the presence of monodisperse and polydisperse colloids

A quasi-three-dimensional particle tracking model is developed to characterize the spatial and temporal effects of advection, molecular diffusion, Taylor dispersion, fracture wall deposition, matrix diffusion, and co-transport processes on two discrete plumes (suspended monodisperse or polydisperse colloids and dissolved contaminants) flowing through a variable aperture fracture situated in a porous medium. Contaminants travel by advection and diffusion and may sorb onto fracture walls and colloid particles, as well as diffuse into and sorb onto the surrounding porous rock matrix. A kinetic isotherm describes contaminant sorption onto colloids and sorbed contaminants assume the unique transport properties of colloids. Sorption of the contaminants that have diffused into the matrix is governed by a first-order kinetic reaction. Colloids travel by advection and diffusion and may attach onto fracture walls; however, they do not penetrate the rock matrix. A probabilistic form of the Boltzmann law describes filtration of both colloids and contaminants on fracture walls. Ensemble-averaged breakthrough curves of many fracture realizations are used to compare arrival times of colloid and contaminant plumes at the fracture outlet. Results show that the presence of colloids enhances contaminant transport (decreased residence times) while matrix diffusion and sorption onto fracture walls retard the transport of contaminants. Model simulations with the polydisperse colloids show increased effects of co-transport processes.     

Factors that influence fluid flow in a single fracture

To investigate the influence of compression, Poisson effect and turbulence on the fluid flow process and the inversion for fracture surface geometries, we simulate two sets of fractures: one with a defined fracture height standard deviation σ constant and a varying autocorrelation length λ and another with a fixed λ and a changing σ. Under compression, the normal stress closes fractures with a large aperture and thus reduces the effective permeability. However, the Poisson effect, which is induced by the compression, has little influence on the fluid flow properties and does not affect the inversion for fracture height standard deviation or the autocorrelation length. When introducing turbulence, we observe a significant difference between the performance of the Navier–Stokes equation and the local cubic law; compared with the Navier–Stokes equation, the local cubic law overestimates the peak value of the breakthrough time curve and effective permeability, thereby underestimating the mean fracture aperture.     

Non-Darcian flow in a single confined vertical fracture toward a well

Non-Darcian flow towards a well which fully penetrates a confined single vertical fracture is presented in this paper on the basis of the Izbash equation. We have obtained semi-analytical solutions for non-Darcian flow by using the Boltzmann transform and developed the non-Darcian flow well functions for cases with and without the effect of wellbore storage. The results show that the non-Darcian flow type curves are more or less deviated from the Darcian flow type curve. The non-linear effect is mainly attributable to the turbulent factor, v, a dimensionless parameter related to the pumping rate, the fracture aperture, the fracture thickness, and two constants k′ and n used in the Izbash power-law. The non-linear effect appears to be less sensitive to the power-law index, n. When excluding wellbore storage, the well function at early times is proportional to v^−1/(n−1)u^−n/(n−1), where u is a dimensionless term inversely proportional to time; whereas the well function at late times is approximated as , where A₀(n) is a finite term depending on n. When considering wellbore storage, drawdowns inside the well with different v values approach the same asymptotic value at small times, and the effect of wellbore storage is only found at the early stage of pumping.     

Marker-and-cell and Chorin finite difference modeling for fluid flow in a single fracture

It is important to set up a detailed dynamic model of the fluid flow through fractures for understanding many fluid processes in Earth sciences. Numerical simulation is a popular tool for exploring these processes. The objective of this study is to understand fluid flow in fractures. Contrary to the conventional macro-scale modeling approach, micro-scale simulation is carried out. The Navior-Stokes equation solver was developed by a staggered marker-and-cell and the Chorin pressure iterating finite difference approach. We analyze the effects of the Reynolds number and the frequency of pressure fluctuations on flow mainly through visualization. A significant result is that the effect of pressure fluctuation-induced fluid flow can be observed in a broader frequency range. The peak velocity shifts along the spatial axis depending upon the frequency of the pressure fluctuation. An effective frequency band of the pressure fluctuation was identified which dominates dynamic behavior of the flow. Another major finding is that there exits a critical frequency of the pressure fluctuation which controls approximately the flow dynamic behavior. We conclude that it is only possible to estimate the flow behavior from pressure fluctuation, if effective frequency range is properly accounted for.     

Effect of NAPL exposure on the wettability and two‐phase flow in a single rock fracture

Surface‐wetting properties are an important cause of changing the groundwater and two‐phase fluid flows. Various factors affecting the surface wettability were investigated in a parallel‐walled glass fracture with non‐aqueous phase liquid (NAPL) (gasoline, diesel, trichloroethylene, and creosote) wetted surfaces. First, the effect of the duration of NAPL exposure on wettability change was considered at pre‐wet fracture surfaces using the various NAPL species, and the result showed that the surface became hydrophobic after the exposure time of NAPL exceeded 2000 min. Second, the initial wetting state of the surface affected the timing when the wettability change begins as well as the extent of the wettability change in an NAPL‐wetted rock fractures. Under the dry condition, the wettability change was completed within a very short time of exposure to NAPL (~5 min), and then it finally reached the intermediate and weakly NAPL wetting (contact angle of 118°). Under the pre‐wet condition, a relatively long time of exposure (~5000 min) was needed to observe the obvious change of the surface wettability, which was changed up to strongly NAPL wetting (contact angle of 142°). Third, the wettability changed by NAPL exposure was stable and maintained for a long time, regardless of water flushing rate and temperature. Finally, the wettability change by the exposure of NAPL on parallel fracture surfaces was evaluated at various groundwater flow velocities. Result showed that groundwater flow velocity has an important impact upon measured contact angle. Although fracture surfaces were exposed to NAPL at the low groundwater flow velocity, the wettability was not changed from hydrophilic to hydrophobic when the contact time between NAPL and mineral surfaces was not sufficient owing to the pulse‐type movement of NAPL. This implies that the variation of exposure pattern due to groundwater flow on the wettability change can be an important factor affecting the wettability change of fracture surface and migration behaviour at natural fractured rock aquifers in case of NAPL spill. Copyright © 2015 John Wiley & Sons, Ltd.     

Hillslope water tracks in the High Arctic: Seasonal flow dynamics with changing water sources in preferential flow paths

Preferential subsurface flow paths known as water tracks are often the principal hydrological pathways of headwater catchments in permafrost areas, exerting an influence on slope physical and biogeochemical processes. In polar deserts, where water resources depend on snow redistribution, water tracks are mostly found in hydrologically active areas downslope from snowdrifts. Here, we measured the flow through seeping water track networks and at the front of a perennial snowdrift, at Ward Hunt Island in the Canadian High Arctic. We also used stable isotope analysis to determine the origin of this water, which ultimately discharges into Ward Hunt Lake. These measurements of water track hydrology indicated a glacio‐nival run‐off regime, with flow production mechanisms that included saturation overland flow (return flow) in a low sloping area, throughflow or pipe‐like flow in most seepage locations, and infiltration excess overland flow at the front of the snowdrift. Each mechanism delivered varying proportions of snowmelt and ground water, and isotopic compositions evolved during the melting season. Unaltered snowmelt water contributed to >90% of total flow from water track networks early in the season, and these values fell to <5% towards the end of the melting season. In contrast, infiltration excess overland flow from snowdrift consisted of a steady percentage of snowmelt water in July (mean of 69%) and August (71%). The water seeping at locations where no snow was left in August 2015 was isotopically enriched, indicating a contribution of the upper, ice‐rich layer of permafrost to late summer discharge during warmer years. Air temperature was the main driver of snowmelt, but the effect of slope aspect on solar radiation best explained the diurnal discharge variation at all sites. The water tracks in this polar desert are part of a patterned ground network, which increases connectivity between the principal water sources (snowdrifts) and the bottom of the slope. This would reduce soil–water interactions and solute release, thereby favouring the low nutrient status of the lake.     

Unsaturated zone fracture flow contributions to stream flow: evidence for the process in South Africa and its importance

Understanding hydrological processes has always been important to the development and successful application of conceptual hydrological models. It can also contribute to informed water resources management, particularly in the context of understanding the potential impacts of both land use and climate change. Improved conceptual and quantitative understanding of near‐surface hydrological processes emerged through field studies during the 1960s to1980s; however, there remains a degree of ambiguity about the processes that link surface water and groundwater. This is especially the case in South Africa where a great deal of confusion has arisen about the source of the ‘baseflow’ signal in stream flow observations. This paper suggests that fracture flow within the unsaturated zone could have a lateral component and therefore re‐emerge and contribute to stream flow in catchments with relatively steep topography. The implication is that ‘baseflows’ could be made up of groundwater contributions (caused by intersection of the water table with stream channels) as well as an unsaturated zone flow component. Evidence for the existence of the process is presented on the basis of small‐scale observations and interpretations of stream flow observations. The potential importance of the process relates to interpreting different methods of recharge estimation, assessing the impacts of groundwater abstraction on stream flow, as well as the application and interpretation of the results of hydrological models. The conclusions are that the process does exist, but that there is less than conclusive evidence for its importance. There is therefore a need for further studies that can quantify the scale of the process and therefore its importance. Only then will it be possible to develop a consistent understanding of the processes of surface water and groundwater interaction and therefore manage water resources in a truly integrated manner. Copyright © 2009 John Wiley & Sons, Ltd.     

Shear dispersion in a fracture with porous walls

We present an analytical expression for the shear dispersion during solute transport in a coupled fracture–matrix system. The dispersion coefficient is obtained in a fracture with porous walls by taking into account an accurate boundary condition at the interface between the matrix and fracture, and the results were compared with those in a non-coupled system. The analysis presented identifies three regimes: diffusion-dominated, transition, and advection-dominated. The results showed that it is important to consider the exchange of solute between the fracture and matrix in development of the shear dispersion coefficient for the transition and advection-dominated regimes. The new dispersion coefficient is obtained by imposing the continuity of concentrations and mass fluxes along the porous walls. The resulting equivalent transport equation revealed that the effective velocity in a fracture increases while the dispersion coefficient decreases due to mass transfer between the matrix and fracture. A larger effective advection term leads to greater storage of mass in the matrix as compared with the classical double-porosity model with a non-coupled dispersion coefficient. The findings of this study can be used for modeling of tracer tests as well as fate, transport, and remediation of groundwater contaminants in fractured rocks.     

Percolation theory as a tool for imitation of fracture process in rocks

The statistical models of earthquake focal processes covering topological, kinetic, energetic and scaling aspects of the phenomenon are considered on the basis of the percolation and reliability theories. It is shown that these models do not contradict the basic experimental data of physics of fracture and seismology. Some predictive signs are also considered.     

A technique for evaluating flow parameters in water bodies with a highly heterogeneous depth

A method is proposed for calculating the hydrodynamic parameters of flows in water bodies with shallow and deep zones. Calculation of flow parameters in the Sea of Azov is given as an example.Translated from Vodnye Resursy, Vol. 32, No. 1, 2005, pp. 55–60.Original Russian Text Copyright © 2005 by Chikin.     

A new multiscale scheme for computing statistical moments in single phase flow in heterogeneous porous media

In this work we develop a new multiscale procedure to compute numerically the statistical moments of the stochastic variables which govern single phase flow in heterogeneous porous media. The technique explores the properties of the log-normally distributed hydraulic conductivity, characterized by power-law or exponential covariances, which shows invariance in its statistical structure upon a simultaneous change of the scale of observation and strength of heterogeneity. We construct a family of equivalent stochastic hydrodynamic variables satisfying the same flow equations at different scales and strengths of heterogeneity or correlation lengths. Within the new procedure the governing equations are solved in a scaled geology and the numerical results are mapped onto the original medium at coarser scales by a straightforward rescaling. The new procedure is implemented numerically within the Monte Carlo algorithm and also in conjunction with the discretization of the low-order effective equations derived from perturbation analysis. Numerical results obtained by the finite element method show the accuracy of the new procedure to approximated the two first moments of the pressure and velocity along with its potential in reducing drastically the computational cost involved in the numerical modeling of both power-law and exponential covariance functions.     

地下含水层氡浓度和水位实时动态的潮汐现象与数字化单井综合观测

在宁德地震台进行的地下水数字化单井综合观测实验中, 采用“恒流式”单井综合观测方法, 配套相应的技术系统, 实现了对地下含水层氡浓度和水位实时动态的连续综合观测, 而且记录到两者具有与固体潮相对应的同步性半日波微动态。 分析认为, 这一方面为地下水有关测项预报地震力学基础的研究提供了新的观测事实; 另一方面, 为试图通过综合观测以期有利于识别干扰与地震前兆信息研究思路的实践提供了一种新途径。     

Statistical simulation analysis of the correlation between the annual estimated key regions with a certain seismic risk and the earthquakes in China

IntroductionEarthquake prediction is still one of most difficult problems in the world although the researches on it in China have been done for more than 30 years. A lot of experience, however, has been accumulated and some theoretical study on earthquake prediction conducted so that some prediction could be issued prior to earthquakes to obtain real effectiveness of mitigating disasters from these earthquakes to some extent, in China. The annual national consulting convention of earthquake …     

Effect of fracture pressure depletion regimes on the dual-porosity shape factor for flow of compressible fluids in fractured porous media

A precise value of the matrix-fracture transfer shape factor is essential for modeling fluid flow in fractured porous media by a dual-porosity approach. The slightly compressible fluid shape factor has been widely investigated in the literature. In a recent study, we have developed a transfer function for flow of a compressible fluid using a constant fracture pressure boundary condition [Ranjbar E, Hassanzadeh H, Matrix-fracture transfer shape factor for modeling flow of a compressible fluid in dual-porosity media. Adv Water Res 2011;34(5):627-39. doi:10.1016/j.advwatres.2011.02.012]. However, for a compressible fluid, the consequence of a pressure depletion boundary condition on the shape factor has not been investigated in the previous studies. The main purpose of this paper is, therefore, to investigate the effect of the fracture pressure depletion regime on the shape factor for single-phase flow of a compressible fluid. In the current study, a model for evaluation of the shape factor is derived using solutions of a nonlinear diffusivity equation subject to different pressure depletion regimes. A combination of the heat integral method, the method of moments and Duhamel’s theorem is used to solve this nonlinear equation. The developed solution is validated by fine-grid numerical simulations. The presented model can recover the shape factor of slightly compressible fluids reported in the literature. This study demonstrates that in the case of a single-phase flow of compressible fluid, the shape factor is a function of the imposed boundary condition in the fracture and its variability with time. It is shown that such dependence can be described by an exponentially declining fracture pressure with different decline exponents. These findings improve our understanding of fluid flow in fractured porous media.     

Simulation of field‐scale water flow and bromide transport in a cracked clay soil

Single domain models may seriously underestimate leaching of nutrients and pesticides to groundwater in clay soils with shrinkage cracks. Various two‐domain models have been developed, either empirical or physically based, which take into account the effects of cracks on water flow and solute transport. This paper presents a model concept that uses the clay shrinkage characteristics to derive crack volume and crack depth under transient field conditions. The concept has been developed to simulate field average behaviour of a field with cracks, rather than flow and transport at a small plot. Water flow and solute transport are described with basic physics, which allow process and scenario analysis. The model concept is part of the more general agrohydrological model SWAP, and is applied to a field experiment on a cracked clay soil, at which water flow and bromide transport were measured during 572 days. A single domain model was not able to mimic the field‐average water flow and solute transport. Incorporation of the crack concept considerably improved the simulation of water content and bromide leaching to the groundwater. Still deviations existed between the measured and simulated bromide concentration profiles. The model did not reproduce the observed bromide retardation in the top layer and the high bromide dispersion resulting from water infiltration at various soil depths. A sensitivity analysis showed that the amounts of bromide leached were especially sensitive to the saturated hydraulic conductivity of the top layer, the solute transfer from the soil matrix to crack water flow and the mean residence time of rapid drainage. The shrinkage characteristic and the soil hydraulic properties of the clay matrix showed a low sensitivity. Copyright © 2000 John Wiley & Sons, Ltd.     

Diagenetic signatures in the deltaic and fluvial-estuarine Messinian sandstone reservoirs in the Nile Delta as a tool for high-resolution stratigraphic correlations

The current study utilizes a range of diagenetic fingerprints to differentiate between sandstone facies deposited in the Nile Delta before and during the Messinian salinity crisis (MSC), which is normally a challenging task considering the complex bio- and lithostratigraphic subdivisions of Messinian rock units. Subaerial exposure of the pre-MSC (Qawasim deltaic sandstone), during drawdown of the Mediterranean Sea at the time of the MSC, triggered pervasive dissolution of unstable rock fragments, kaolinization of feldspar, and meteoric dolomitization of carbonate. This was followed by mesogenetic calcite cementation and kaolinite transformation into dickite in deeply buried Qawasim sandstone. Comparatively, the Abu Madi estuarine facies, deposited during transgression after drawdown related to the MSC, is characterized by eogenetic iron (Fe)-calcite, glauconite, and pyrite (averages of 14.5%, 6%, and 2%, respectively). This facies transition is marked by abundance of mature glauconite (with potassium oxide (K₂O) at about 8%) whose content abates upward from the transgression surface. Moreover, the compositional variability of the Abu Madi sandstone gave rise to multiple diagenetic trajectories that resulted in chlorite formation presumably following smectite and kaolinite. Listed diagenetic variations in the studied Messinian sandstone resulted from a complex interplay between rocks’ compositional, depositional, and burial attributes, ultimately serving as a basis for high-resolution stratigraphic correlation in continental and marginal marine settings with poor biostratigraphic controls.     

Sub‐surface water contribution to recession flow in a mountain headwater stream system based on single monitoring campaign

Discharge in mountain streams may be a mixture of snowmelt, water from surface runoff, and deep return flow through valley bottom alluvia. We used δ¹⁸O and δ²H, solute concentrations, and ²²²Rn to determine water sources of a headwater stream located at the McDonald Creek watershed, Glacier National Park, USA, during summer recession flow period. We analysed minimal water isotope ranges of ?17.6‰ to ?16.5‰ and ?133‰ to ?121‰ for δ¹⁸O and δ²H, respectively, potentially due to dominance of snow‐derived water in the stream. Likewise, solute concentrations measured in the stream through the watershed showed minimal variation with little indication of subsurface water input into the stream. However, we observed ²²²Rn activities in the stream that ranged from 39 to 2646 Bq/m³ with the highest value measured in middle of the watershed associated with channel constriction corresponding to changes in local orientation of underlying rocks. Downstream from this point, ²²²Rn activity decreased from 581 to 117 Bq/m³ in a series of punctuated steps associated with small rapids and waterfalls that we hypothesized to cause radon degassing with a maximum predicted loss of 427 Bq/m³ along a 400 m distance. Based on mass balance calculations using ²²²Rn activity values, streamflow, and channel characteristics, we estimated that groundwater contributed between 0.3% and 29% of total flow. Overall, we estimated a 5.9% of groundwater contribution integrated for stream reach measured at McDonald Creek during recession flow period. Finally, a lower mean hyporheic flux of 14 m³/day was estimated compared to the groundwater flux of 70 710 m³/day. These assessments highlight the potential for radon as a conservative tracer that can be used to estimate subsurface water contribution in mountain streams within a complex geologic setting. Copyright © 2015 John Wiley & Sons, Ltd.