Dependency of flow and transport properties on aperture distributions and compression states

Fluid conductivity and elastic properties in fractures depend on the aperture geometry – in particular, the roughness of fracture surfaces. In this study, we have characterized the surface roughness with a log-normal distribution and investigated the transport and flow behaviour of the fractures with varying roughness characteristics. Numerical flow and transport simulations have been performed on a single two-dimensional fracture surface, whose aperture geometry changes with different variances and correlation lengths in each realization. We have found that conventional measurement of hydraulic conductivity alone is insufficient to determine these two parameters. Transient transport measurements, such as the particle breakthrough time, provide additional constraints to the aperture distribution. Nonetheless, a unique solution to the fracture aperture distribution is still under-determined with both hydraulic conductivity and transport measurements. From numerical simulations at different compression states, we have found that the flow and transport measurements exhibit different rates of changes with respect to changes in compression. Therefore, the fracture aperture distribution could be further constrained by considering the flow and transport properties under various compression states.     

Eddy correlations for water flow in a single fracture with abruptly changing aperture

Fluid flow in single fractures with non‐uniform apertures is an important research subject in many disciplines. The abruptly changing aperture is a special case of such non‐uniformity. This paper simulates water flow in a single fracture with abruptly changing aperture (SF‐ACA) using the Lattice Boltzmann Method (LBM) and the Finite Volume Method (FVM). The flow occurs with the Reynolds number (Re) ranging from 5 to 900 and a ratio of aperture change (E) of 3 (E = D/d, where D and d are the larger and smaller apertures, respectively). For Re values between 5 and 100, both LBM and FVM can successfully simulate the eddy development in the expansion regime of an SF‐ACA. Flow with high Re values (up to 900) is simulated by FVM, which appears to be numerically more stable than LBM for high‐Re flow problems studied here. The flow symmetry in the expansion regime breaks at the Re value between 400 and 500. Our simulation result shows a linear relationship between l₁/d and Re at low Re (5–100) or higher Re (110–900) values, where defined as the length from the location of abrupt expansion to the right edge of the first eddy along the flow direction. If considering the simulation results for the entire simulated range of Re (5–900), the l₁/d–Re relationship is better described by a non‐linear logarithmical function. The l₁/d approaches an asymptotic constant at large Re. Copyright © 2011 John Wiley & Sons, Ltd.     

The effect of microporosity on transport properties in porous media

Sizeable amounts of connected microporosity with various origins can have a profound effect on important petrophysical properties of a porous medium such as (absolute/relative) permeability and capillary pressure relationships. We construct pore-throat networks that incorporate both intergranular porosity and microporosity. The latter originates from two separate mechanisms: partial dissolution of grains and pore fillings (e.g. clay). We then use the reconstructed network models to estimate the medium flow properties. In this work, we develop unique network construction algorithms and simulate capillary pressure–saturation and relative permeability–saturation curves for cases with inhomogeneous distributions of pores and micropores. Furthermore, we provide a modeling framework for variable amounts of cement and connectivity of the intergranular porosity and quantifying the conditions under which microporosity dominates transport properties. In the extreme case of a disconnected inter-granular network due to cementation a range of saturations within which neither fluid phase is capable of flowing emerges. To our knowledge, this is the first flexible pore scale model, from first principles, to successfully approach this behavior observed in tight reservoirs.     

The role of overland flow and subsurface flow on the spatial distribution of soil moisture in the topsoil

Many investigations show relationships between topographical factors and the spatial distribution of soil moisture in catchments. However, few quantitative analyses have been carried out to elucidate the role of different hydrological processes in the spatial distribution of topsoil moisture in catchments. A spatially distributed rainfall—runoff model was used to investigate contributions of subsurface matric flow, macropore flow and surface runoff to the spatial distribution of soil moisture in a cultivated catchment. The model results show that lateral subsurface flow in the soil matrix or in macropores has a minor effect on the spatial distribution of soil moisture. Only when a perched groundwater table is maintained long enough, which is only possible if the subsurface is completely impermeable, may a spatial distribution in moisture content occur along the slope. Surface runoff, producing accumulations of soil moisture in flat flow paths of agricultural origin (field boundaries), was demonstrated to cause significant spatial variations in soil moisture within a short period after rainfall (<2 days). When significant amounts of surface runoff are produced, wetter moisture conditions will be generated at locations with larger upstream contributing areas. Copyright © 2001 John Wiley & Sons, Ltd.     

Network properties of a two-dimensional natural fracture pattern

The influence that fractures exert on the permeability of a fractured rock is, to a large extent, controlled by the nature of the network formed by the fracture system. Here, the network properties of a two-dimensional natural pattern, mapped from the surface of a sandstone layer, are investigated and compared to those of realizations of spatially randomly distributed line segments with similar orientation and length distributions and line segment density (line length per unit area) to the natural pattern. These patterns are composed of clusters of varying size and shape, made up of interconnected fracture traces or line segments. Comparing the natural pattern with the realizations, the natural pattern was found to contain roughly half the number of clusters while the mass (total line length) of the largest cluster is approximately double that of the realizations. The size of the largest cluster controls the connectivity of the patterns, as can be seen by comparing the largest cluster of the natural pattern, which connects all four sides of the region, with those of the realizations, which are unconnected or connect only two sides. Cluster scaling characteristics were found to be similar in the natural pattern and the realizations and show a crossover from a dimension of one (their topological dimension) to two (the dimension of the embedding medium) at a point that corresponds to the fracture spacing. An investigation of the self-similarity dimension, using the box-counting method, showed similar characteristics with a broad transition zone between one- and two-dimensional behaviour at smaller box sizes. The patterns are therefore found to be non-fractal. The effect of the spatial distribution shown by the natural pattern is thus to modify the manner in which fractures are distributed among clusters, increasing connectivity (and permeability in the case of open fractures), but does not affect the cluster scaling characteristics or the self-similarity dimension of the fracture patterns.     

裂隙展布特征对EGS采热影响的理论数值模拟研究

增强型地热系统(EGS)储层的裂隙展布特征决定了热开采的效果.基于EGS储层压裂得到的裂隙网络呈现出较强的非均匀性,本文构建EGS平行多裂隙非均匀展布模型研究裂隙展布特征对EGS采热影响.为表征裂隙展布的非均匀性,创新地引入了优势流动比的概念.研究结果表明:在体积为500 m×600 m×600 m,初始温度200℃,均匀激发热储层7条裂隙展布,流量为30 kg/s时,储层产出温度可保持储层初始温度15年,并在热开采进行50年后仍能保持较高产出温度192.3℃,电功率为2.88～3.10 MW,电功率的降幅仅为7.1%.非均匀激发热储层的采热性能受到裂隙数量和裂隙展布特征的共同影响.产出温度与裂隙数量呈不严格的正相关性,并与优势裂隙比呈负相关性.非均匀压裂的热储层中,通过封堵优势裂隙或增强储层压裂使裂隙宽度均匀化,均可增强系统的采热性能.综合来看,裂隙数目越多,裂隙宽度分布越均匀,流体产出温度越高,采热效果越好.本文对EGS地热田的储层激发,和人工热储层的构建有一定的指导意义.     

The exponential decline in saturated hydraulic conductivity with depth: a novel method for exploring its effect on water flow paths and transit time distribution

The strong vertical gradient in soil and subsoil saturated hydraulic conductivity is characteristic feature of the hydrology of catchments. Despite the potential importance of these strong gradients, they have proven difficult to model using robust physically based schemes. This has hampered the testing of hypotheses about the implications of such vertical gradients for subsurface flow paths, residence times and transit time distribution. Here we present a general semi‐analytical solution for the simulation of 2D steady‐state saturated‐unsaturated flow in hillslopes with saturated hydraulic conductivity that declines exponentially with depth. The grid‐free solution satisfies mass balance exactly over the entire saturated and unsaturated zones. The new method provides continuous solutions for head, flow and velocity in both saturated and unsaturated zones without any interpolation process as is common in discrete numerical schemes. This solution efficiently generates flow pathlines and transit time distributions in hillslopes with the assumption of depth‐varying saturated hydraulic conductivity. The model outputs reveal the pronounced effect that changing the strength of the exponential decline in saturated hydraulic conductivity has on the flow pathlines, residence time and transit time distribution. This new steady‐state model may be useful to others for posing hypotheses about how different depth functions for hydraulic conductivity influence catchment hydrological response. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

Velocity distribution in a gradually accelerating free surface flow

This study investigates the interaction of the vertical velocity v and the streamwise velocity u in a gradually accelerating flow. The analytical result shows that the momentum of uv driven by the mean velocities in a non-uniform flow is not negligible. This additional momentum directly results in the concave profiles of Reynolds shear stress in gradually accelerating flows, a departure from the expected linear profile. Consequently, this momentum causes the maximum velocity to be located below the free surface, i.e., the dip-phenomenon. This paper investigated the interactions of the Reynolds shear stress, non-zero vertical velocity and dip-phenomenon, it is found that the non-zero vertical velocity causes the dip-phenomenon. The approach is tested using the experimental data of Song and others, and good agreements between the predicted and measured velocity profiles have been achieved.     

Understanding of hydraulic properties from configurations of stochastically distributed fracture networks

A systematic investigation of the effect of configurations of stochastically distributed fracture networks on hydraulic behaviour for fractured rock masses could provide either quantitative or qualitative correlation between the structural configuration of the fracture network and its corresponding hydraulic behaviour, and enhance our understanding of appropriate application of groundwater flow and contaminant transport modelling in fractured rock masses. In this study, the effect of block sizes, intersection angles of fracture sets, standard deviations of fracture orientation, and fracture densities on directional block hydraulic conductivity and representative elementary volume is systematically investigated in two dimensions by implementing a numerical discrete fracture fluid flow model and incorporating stochastically distributed fracture configurations. It is shown from this investigation that the configuration of a stochastically distributed fracture network has a significant quantitative or qualitative effect on the hydraulic behaviour of fractured rock masses. Compared with the deterministic fracture configurations that have been extensively dealt with in a previous study, this investigation is expected to be more practical and adequate, since fracture geometry parameters are inherently stochastically distributed in the field. Moreover, the methodology and approach presented in this study may be generally applied to any fracture system in investigating the hydraulic behaviours from configurations of the fracture system while establishing a ‘bridge’ from the discrete fracture network flow modelling to equivalent continuum modelling in fractured rock masses. Copyright © 2007 John Wiley & Sons, Ltd.     

Modeling aggregate size distribution of eroded sediment resulting from rain-splash and raindrop impacted flow processes

Soil susceptibility to detachment and transport sub-processes of erosion is generally controled by the aggregate breakdown mechanism. Measuring particle size and aggregation to the estimate erodibility potential of soils is important under erosive rainfall conditions. The Aggregate Size Distribution (ASD) is one of the most important determinants of soil structure along with soil organic matter content for describing the efficiency of applied, sustainable management strategies. This study aimed to compare the performances of three different aggregate size distribution models to predict the characteristic aggregate size parameter (median diameter, D50) for eroded sediment from interrill erosion processes of Rain- Splash Transport (RST) and Raindrop Impacted Flow Transport (RIFT). The ASDs of 1143 collected sediment samples from the RST and RIFT processes were measured and modeled by the Log-normal, Fractal, and Weibull approaches. The D50 value, as a characteristic parameter for aggregate size distributions, derived from the cumulative ASD curve was compared for soils from different land use types and different slope and rainfall intensity conditions. The performance of each model was evaluated using the Mean Square Error (MSE) and Coefficient of Determination (R^2). The Weibull approach was the most accurate model showing the best fit with the lowest MSE values (0.0002 ≤MSE≤ 0.0048) and having the greatest R2 values (0.936≤ R^2≤ 0.998) when compared with the Log-normal and Fractal models. Herewith, for semi-arid land use and soil, specific shape and scale parameters for the Weibull distribution, the respective ASDs were successfully re-generated for modeling the eroded sediment of the simulated RST and RIFT interill processes.     

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.     

Gas tracer transport through a heterogeneous fracture zone under two phase flow conditions: Model development and parameter sensitivity

Large amounts of gas can result from anaerobic corrosion of metals and from chemical and biological degradation of organic substances in underground repositories for radioactive waste. Gas generation may lead to the formation of a gas phase bubble and to the migration of radioactive gaseous species. Transport occurs in, at least, in two forms: (1) gas bubble, migration is controlled by advection, dispersion and diffusion in the gas phase, and (2) within water pockets, the dissolved species migrate mainly by diffusion. We consider a two-dimensional system representing an isolated heterogeneous fractured zone. A dipole gas flow field is generated and gas tracers are injected. The delay in the breakthrough curves is studied. A simple method is used to solve the gas species transport equations in multiphase conditions. This method is based on a formal analogy between the equations of gas transport in a two phase system and the equations of solute tracer transport in water saturated systems. We perform a sensitivity analysis to quantify the relevance of the various transport mechanisms. We find that gas tracer migration is very sensitive to gas tracer solubility, which affects gas tracer transport of both mobile and immobile zones, and shows high sensitivity to diffusion in the gas phase, to heterogeneity and to gas pressure, but the largest sensitivity was observed with respect to injection borehole properties, i.e. borehole volume and water filled fraction.     

The distribution rule and seepage effect of the fractures in the ultra-low permeability sandstone reservoir in east Gansu Province,Ordos Basin

To study the impact of the fractures on development in the ultra-low permeability sandstone reservoir of the Yangchang Formation of the Upper Triassic in the Ordos Basin,data on outcrops,cores,slices,well logging and experiments are utilized to analyze the cause of the formation of the fractures,their distribution rules and the control factors and discuss the seepage flow effect of the fractures. In the studied area developed chiefly high-angle tectonic fractures and horizontal bedding fractures,inter-granular fractures and grain boundary fractures as well. Grain boundary fractures and intragranular fractures serve as vital channels linking intragranular pores and intergranular solution pores in the reservoir matrix,thus providing a good connectivity between the pores in the ultra-low perme-ability sandstone reservoir. The formation of fractures and their distribution are influenced by such external and internal factors as the palaeo-tectonic stress field,the reservoir lithological character,the thickness of the rock layer and the anisotropy of a layer. The present-day stress field influences the preservative state of fractures and their seepage flow effect. Under the tec-tonic effect of both the Yanshan and Himalayan periods,in this region four sets of fractures are distributed,respectively assuming the NE-SW,NW-SE,nearly E-W and nearly S-N orientations,but,due to the effect of the rock anisotropy of the rock formation,in some part of it two groups of nearly orthogonal fractures are chiefly distributed. Under the effect of the present-day stress field,the fractures that assume the NE-SW direction have a good connectivity,big apertures,a high permeability and a minimum starting pressure,all of which are main advantages of the seepage fractures in this region. With the development of oilfields,the permeability of the fractures of dif-ferent directions will have a dynamic change.     

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.     

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.     

Efficiency verification of a horizontal flow barrier via flowmeter tests and multilevel sampling

The remediation strategy for an industrial site located in a coastal area involves a pump and treat system and a horizontal flow barrier (HFB) penetrating the main aquifer. To validate the groundwater flow conceptual model and to verify the efficiency of the remediation systems, we carried out piezometric measurements, slug tests, pumping tests, flowmeter tests and multilevel sampling. Flowmeter tests are used to infer vertical groundwater flow directions, and base exchange index is used to infer horizontal flow directions at a metric scale. The selected wells are located both upstream and downstream of the HFB. The installation of the HFB produced constraints to the groundwater flow. A stagnant zone of contaminated freshwater floating over the salt wedge in the upper portion of the aquifer is detected downstream of the HFB. This study confirms that the adopted remediation system is efficiently working in the area upstream of the HFB and even downstream in the bottom part of the aquifer. At the same time, it has also confirmed that hot spots are still present in stagnant zones located downstream of the HFB in the upper part of the aquifer, requiring a different approach to accomplish remediation targets. The integrated approach for flow quantification used in this study allows to discriminate the direction and the magnitude of groundwater fluxes near an HFB in a coastal aquifer. Copyright © 2012 John Wiley & Sons, Ltd.     

Inversion of dynamic production data for permeability: fast streamline-based computation of sensitivity coefficients of fractional flow rate

Generation of permeability field in a reservoir model that matchs historical dynamic production data requires an inverse calculation. A gradient method is typically used to solve the inverse minimization problem and requires sensitivity coefficients of reservoir responses, e.g. fractional flow rate or pressure, with respect to the change in the permeability. This paper presents a novel semi-analytical streamline-based method for computing such sensitivity coefficients under the framework of two-phase (oil-water) flow conditions. This method is shown to be significantly faster and generate permeability fields with lower objective function than the traditional perturbation method. The method decomposes the multiple-dimensional full flow problem into multiple 1D problems along streamlines. The sensitivity of fractional flow rate at the production well is directly related to the sensitivity of time-of-flight (TOF) along each individual streamline and the sensitivity of pressure at grid cells along the streamline. The sensitivity of TOF of a streamline can be obtained analytically. The sensitivity of pressure is obtained as part of a fast single phase flow simulation. The proposed method is implemented in a geostatistically based inverse technique, called the sequential self-calibration (SSC) method. Results for fractional flow rate sensitivities are presented and compared with the traditional perturbation method. This new method can be easily extended to compute sensitivity coefficients of saturation (concentration) data.     

Depth distribution of interrill overland flow and the formation of rills

A Gumbel distribution for maxima is proposed as a model for the depths of interrill overland flow. The model is tested against three sets of field measurements of interrill overland flow depths obtained on shrubland and grassland hillslopes at Walnut Gulch Experimental Watershed, southern Arizona. The model is found to be a satisfactory fit to 81 of the 90 measured distributions. The shape δ and location λ parameters of all fitted distributions are strongly correlated with discharge. However, whereas a common relationship exists between discharge and δ for all depth distributions, the relationships with λ vary systematically downslope. Using the Gumbel distribution as a model for the distribution of overland flow depths, a probabilistic model for the initiation of rills is developed, drawing upon the previous work of Nearing. As an illustration of this approach, we apply this model to the shrubland and grassland hillslopes at Walnut Gulch. It is concluded that the presence of rills on the shrubland, but not on the grassland, is due to the greater runoff coefficient for the shrubland and/or the greater propensity of the shrubland for soil disturbance compared with the grassland. Finally, a generalized conceptual model for rill initiation is proposed. This model takes account of the depth distribution of overland flow, the probability of flow shear stress in excess of local soil shear strength, the spatial variability in soil shear strength and the diffusive effect of soil detachment by raindrops. Copyright © 2005 John Wiley & Sons, Ltd.