Darcy Flux Research Articles

Dynamic changes in dissolved organic matter during transport of landfill leachate in porous medium.

The dynamic changes in dissolved organic matter (DOM) during the transport of landfill leachate (LL) in porous medium should be explored, considering the high levels of DOM in the LL of municipal solid waste. Column experiments were carried out at 25°C at a Darcy's flux of 0.29cm/h for 2722h to compare the transport of Cl-, ultraviolet absorbance at 254nm (UV254), chemical oxygen demand (COD), and dissolved organic carbon (DOC) in the simulated porous medium by using the CXTFIT2.1 code. Results showed that the convection-dispersion equation (CDE) could describe Cl- transport well. The high levels of λ and D could be highly correlated with the physicochemical properties of the porous medium. The transport of the studied DOM with evident aromatic character could be described appropriately by the CDE model with the first-order reaction assumption, considering the similar variation trends of UV254, COD, and DOC in the effluent during experiments. Specifically, the values of retardation factor (R) were in the following order: DOC > UV254 > COD, whereas the low values of the first-order decay coefficient (k1) for DOC and COD were still higher than that for UV254. High contents of humic-like substances in the DOM with complex toxic components resulted in the natural low removal efficiencies of COD, DOC, and UV254 (≤ 23%), which could be confirmed by the variations of fluorescence index (FI) and humification index (HIX) in the effluent. The results should be helpful in evaluating the environmental risk induced by the LL leakage in a landfill site.

Estimate of groundwater flow and salinity contribution to the Great Salt Lake using groundwater levels and spatial analysis

Groundwater discharge to Great Salt Lake (GSL) is difficult to quantify but represents a potentially significant source of water and salinity to the lake’s overall water budget and chemistry, respectively. Understanding groundwater and its role in the overall health of GSL is critical due to the current and historically low lake levels. We compiled existing groundwater level data in basin-fill wells around GSL and used spatial analysis methods to 1) create potentiometric-surface maps in the areas adjoining GSL, 2) calculate groundwater contributions to GSL, and 3) estimate salinity inputs from groundwater to GSL. We observed groundwater-level declines in most of the basin-fill wells from the 1980s to 2010s. These declines are consistent with historical groundwater-level trends in the Salt Lake, Tooele, Curlew, and Weber Valleys and are a consequence of aquifer overdraft associated with less than average precipitation in the basin and increased groundwater withdrawals in the GSL watershed. Using the Darcy flux equation, we calculated a groundwater flux to GSL of 313,500 acre-feet per year, substantially greater than previous estimates derived from water balance studies but consistent with estimates derived from geochemical modeling of GSL water chemistry. We calculated a salt contribution from groundwater to GSL of 1.18 million metric tons per year, which represents about 10% of the solutes derived from surface flows to GSL in 2013.

Mechanisms of Non-Fresh Groundwater Presence at Water Tables in Highly Permeable Coastal Aquifers.

Coastal aquifers with high hydraulic conductivities on the order of 10-2 m s-1 have unconventional salinity distributions with the presence of non-fresh groundwater at the water table over a wide swath near the coast. This study aims to unravel the mechanisms underlying the phenomenon via numerical simulations for variably saturated, density-driven flow and solute transport in porous media. The simulation results indicate that the existence of non-fresh groundwater at the water table is attributed to the upward mass flux in the saturated zone near the coast, which transports solute from deeper groundwater toward the water table. With high hydraulic conductivity, the upward mass flux becomes prominent at shallower elevations because of the high Darcy flux and the shallow saline groundwater. The upward mass flux has two main drivers, upward advection by the upward flow component and transverse dispersion by the seaward flow component. The advective mass flux dominates over the transverse dispersion in the deep part of the saturated zone where only groundwater with sea water salinity exists. In contrast, the transverse dispersion becomes more pronounced than the upward advection in the shallow saturated zone just beneath the water table and in the unsaturated zone immediately above the water table. Our findings help interpret the unconventional salinity distributions observed and elucidate the unique dynamics of groundwater flow and solute transport in highly permeable coastal aquifers.

Wind-modulated groundwater discharge along a microtidal Arctic coastline

Groundwater discharge transports dissolved constituents to the ocean, affecting coastal carbon budgets and water quality. However, the magnitude and mechanisms of groundwater exchange along rapidly transitioning Arctic coastlines are largely unknown due to limited observations. Here, using first-of-its-kind coastal Arctic groundwater timeseries data, we evaluate the magnitude and drivers of groundwater discharge to Alaska’s Beaufort Sea coast. Darcy flux calculations reveal temporally variable groundwater fluxes, ranging from −6.5 cm d−1 (recharge) to 14.1 cm d−1 (discharge), with fluctuations in groundwater discharge or aquifer recharge over diurnal and multiday timescales during the open-water season. The average flux during the monitoring period of 4.9 cm d−1 is in line with previous estimates, but the maximum discharge exceeds previous estimates by over an order-of-magnitude. While the diurnal fluctuations are small due to the microtidal conditions, multiday variability is large and drives sustained periods of aquifer recharge and groundwater discharge. Results show that wind-driven lagoon water level changes are the dominant mechanism of fluctuations in land–sea hydraulic head gradients and, in turn, groundwater discharge. Given the microtidal conditions, low topographic relief, and limited rainfall along the Beaufort Sea coast, we identify wind as an important forcing mechanism of coastal groundwater discharge and aquifer recharge with implications for nearshore biogeochemistry. This study provides insights into groundwater flux dynamics along this coastline over time and highlights an oft overlooked discharge and circulation mechanism with implications towards refining solute export estimates to coastal Arctic waters.

Influence of site characteristics on the performance of shallow borehole heat exchanger arrays: A sensitivity analysis

Using borehole heat exchangers (BHE) to extract shallow geothermal energy has grown rapidly in recent years. How to maintain a long-term balanced, sustainable operation of the BHE arrays becomes a key issue. Site characteristics, including hydrogeological and geothermal conditions as well as spatial distribution of subsurface physical parameters, are generally idealized or partly neglected in practice. To investigate the consequences of such simplifications, a 3D model, based on data from a planned real site, is established to consider groundwater flow, subsurface heterogeneity, and various hydrogeothermal boundary conditions. After verifying the model, a sensitivity analysis is conducted. Nine factors regarding site characteristics are selected, including Darcy flux in the aquifer, thermal conductivity and volumetric heat capacity of the ground, groundwater depth, thermal and hydraulic heterogeneity, geothermal gradient, heat transfer coefficient on the ground surface and seasonal rainfall. Sensitivity results indicate that the annual total heat production is most sensitive to geothermal gradient, followed by Darcy flux, both of which have positive effects. Groundwater depth and heat transfer coefficient have negative effects on annual heat production. Compared to thermal heterogeneity and rainfall, the influence of hydraulic heterogeneity is higher. Uncertainty of annual heat production due to various Peclet numbers is quantified through regression analysis.

Analytical solutions of fractal and anomalous diffusion models for pressure and rate transient analysis

In this study, we examine the modeling of the naturally fractured reservoirs based on the fractal, Metzler, and Raghavan anomalous diffusion models which are different from Darcy flux law. The governing equations of these models are presented for a vertical well producing at either a constant rate (CR) or constant bottomhole pressure (CBHP) production in an infinite-acting reservoir. New analytical and early- and late-time asymptotic approximate solutions were derived for the finite-wellbore problem for the Raghavan anomalous model. The approximate solutions identify the fractal and anomalous diffusion parameters that influence behaviors of the early- and late-time pressure and rate transient data. The method of Laplace transformation is used to find the solutions in dimensionless forms which are then inverted to the real-time domain using a numerical inversion algorithm. In addition, we compare the solutions for the fractal, Metzler anomalous, and Raghavan anomalous models and delineate the similarities and differences among these solutions. We show the effect of fractal parameters on diffusion models, the relationship between the fractal model, and Raghavan and Metzler anomalous models, in terms of dimensionless pressure and dimensionless pressure derivative responses in the reservoir. We show that the “dimensionless” pressure defined by Raghavan is not a dimensionless quantity unless the Euclidean dimension d=2 (or for a fractal structure with the mass fractal dimension df=2). To the best of our knowledge, in the literature, there exists no study providing a detailed review and comparing the applicability of each diffusion model on real field well-test data as well as providing new analytical solutions and early- and late-time asymptotic approximate solutions for the anomalous diffusion for both the CR and CBHP cases for the finite-wellbore problem. Hence, this study fills this gap. In addition, we apply the three diffusion models to an interference well test data from the Kizildere geothermal reservoir in Turkey by using the ensemble smoother with multiple data assimilation (ES-MDA) method. The results show that the fractal model in terms of the goodness of fit (root-mean-square error – RMSE) best matches the field test data.

Quantifying seasonal, depression focused recharge in the context of public supply well vulnerability

AbstractDepression focused recharge (DFR) may be a hydrologically important process that impacts the vulnerability of public supply wells, specifically related to pathogenic contaminants. The nature of DFR in glacial moraine environments, such as those located in northern latitudes within North America and Europe, is less well established than in other regions such as the Prairie Pothole Region (Northern United States, Western Canada) and the High Plains Aquifer (Central United States). The objectives of this study were to quantify seasonal infiltration flux beneath a topographically‐closed depression within 50 m of a public supply well and to interpret the impact of this DFR process on well vulnerability. Field instruments including groundwater monitoring wells, pressure transducers, soil moisture sensors and temperature sensors were installed in vertical clusters to capture the dynamics of infiltration, drainage and recharge within the depression feature. Continuous weather data were recorded by a meteorological station at the site. Transient infiltration was quantified during two contrasting hydrological events. The first event (~2 days) was an intense rainfall (>50 mm) on a melting snowpack during the fall season when the soils were unfrozen. The second was a longer (35 day) period during the spring freshet when the surficial soils were initially frozen and subject to diurnal freezing and thawing and occasional precipitation events. The water table fluctuation method augmented by Darcy flux contributions, in addition to numerical modelling using the HYDRUS‐1D model, were used to quantify recharge rates beneath the depression. Numerical DFR estimates and analytical results differed by ±8%. Results indicate that recharge rates on the order of the annual regional average can occur beneath localized features in response to extreme events associated with snowmelt and intense rainfall. Such events may represent a microbial threat to groundwater quality if public supply wells are located nearby.

An equivalent line element approach for free surface flow through two-dimensional rock mass including fracture networks

In this paper, an equivalent line element method is established to analyze seepage problems with free surface through two-dimensional rock mass, including fracture networks. Low-permeablity rock matrix is characterized by the line elements as well as the high-permeablity fracture networks. Unlike the conventional equivalent continuum model, water flow in a rock mass is restricted to the line elements, and the equivalent hydraulic conductivity is determined according to Darcy's law and flux equivalence principle. As a result, uniform expressions of governing equations and boundary conditions are formulated, and the corresponding numerical procedure is developed by introducing the local coordinate and continuous Heaviside function. Satisfactory agreements with the existing test and numerical data verify this proposed line element method. The numerical solutions on the fractured slope indicate that the geological features of fractures have a substantial effect on locating the free surface. In addition, the proposed line element method can efficiently achieve accurate results with less computing time, iteration, and storage.

A multipoint stress-flux mixed finite element method for the Stokes-Biot model

In this paper we present and analyze a fully-mixed formulation for the coupled problem arising in the interaction between a free fluid and a poroelastic medium. The flows in the free fluid and poroelastic regions are governed by the Stokes and Biot equations, respectively, and the transmission conditions are given by mass conservation, balance of stresses, and the Beavers-Joseph-Saffman law. We apply dual-mixed formulations in both domains, where the symmetry of the Stokes and poroelastic stress tensors is imposed by setting the vorticity and structure rotation tensors as auxiliary unknowns. In turn, since the transmission conditions become essential, they are imposed weakly by introducing the traces of the fluid velocity, structure velocity, and the poroelastic media pressure on the interface as the associated Lagrange multipliers. The existence and uniqueness of a solution are established for the continuous weak formulation, as well as a semidiscrete continuous-in-time formulation with non-matching grids, together with the corresponding stability bounds. In addition, we develop a new multipoint stress-flux mixed finite element method by involving the vertex quadrature rule, which allows for local elimination of the stresses, rotations, and Darcy fluxes. Well-posedness and error analysis with corresponding rates of convergence for the fully-discrete scheme are complemented by several numerical experiments.

Application of an iterative source localization strategy at a chlorinated solvent site

This study presents an inverse modeling strategy for organic contaminant source localization. The approach infers the hydraulic conductivity field, the dispersivity, and the source zone location. Beginning with initial observed data of contaminant concentration and hydraulic head, the method follows an iterative strategy of adding new observations and revising the source location estimate. Non-linear optimization using the Gauss-Levenberg-Marquardt Algorithm (PEST++) is tested at a real contaminated site. Then a limited number of drilling locations are added, with their positions guided by the Data Worth analysis capabilities of PYEMU. The first phase of PEST++, with PYEMU guidance, followed by addition of monitoring wells provided an initial source location and identified four additional drilling locations. The second phase confirmed the source location, but the estimated hydraulic conductivity field and the Darcy flux were too far from the measured values. The mismatch led to a revised conceptual site model that included two distinct zones, each with a plume emanating from a separate source. A third inverse modelling phase was conducted with the revised site conceptual model. Finally, the source location was compared to results from a Geoprobe@ MiHPT campaign and historical records, confirming both source locations. By merging measurement and modeling in a coupled, iterative framework, two contaminant sources were located through only two drilling campaigns while also reforming the conceptual model of the site.

Evaluating anisotropy ratio of thermal dispersivity affecting geometry of plumes generated by aquifer thermal use

Studies on shallow geothermal applications have demonstrated that mechanical thermal dispersion is an important heat transport mechanism in saturated porous media. However, most previous studies have assumed the thermal dispersivity ratio, which has not been sufficiently examined. This study investigates the validity of the general assumption that the transverse dispersivity is one-tenth of the longitudinal dispersivity. For this purpose, heat transport experiments, specifically designed at the laboratory scale for estimating dispersivity, were conducted using two different heat sources at Darcy fluxes of 4.74 to 37.47 m/d (Reynolds number Re < 0.3). The results from the analytical models showed that the dispersivity ratios differed from the thermal dispersivity assumption, indicating that the ratio can vary depending on the properties of the porous media. Additionally, heat transport modeling was performed to confirm the influence of the dispersivity ratio on the temperature plumes that develop from the thermal use of shallow aquifers, such as groundwater heat pump systems. We found that, under steady-state conditions, the decrease in the dispersivity ratio led to smaller plume dimensions in all directions, owing to the increased heat dissipation in the transverse direction. Transient simulations for flow and heat transport indicated that the effect of the thermal dispersivity ratio was time-dependent and heterogeneous and increased with the injection rate. These results suggest that the thermal dispersivity ratio is crucial for assessing the environmental impacts of aquifer thermal use, especially for long-term and large-scale applications. Therefore, the magnitude and ratio of thermal dispersivity should be evaluated at the design stage for more efficient and sustainable use of shallow geothermal resources.

Strontium adsorption characteristics of natural Zeolites for permeable reactive barrier in Fukushima Daiichi nuclear power station

ABSTRACT Laboratory experiments and model estimates were carried out to evaluate the effectiveness of sorbent for construction of the Permeable Reactive Barrier (PRB) at downstream of H4 tank area in Fukushima-Daiichi Nuclear Power Station in September 2014. Measurement of cation exchange capacity and X-ray diffraction analyses of crystal structures were carried out for natural zeolites. The Sr adsorption isotherms were measured for these zeolites contacted with water containing Sr or the simulated groundwater containing Na, K, Ma, Ca, and Sr. According to these equilibrium characteristics, Akita-Futastui zeolite was selected as candidate. The zeolite was served for the column tests to obtain Sr breakthrough curves with different conditions such as particle size of zeolite, Darcy Flux, Sr concentration in the simulated groundwater, and mixed bed with gravel. From the breakthrough curves, kinetic properties such as the film mass transfer coefficient and the effective intraparticle diffusivity were derived by fitting with adsorption model. Based on these kinetic properties, Sr breakthrough curves were estimated for the simulated groundwater containing 0.3 ppm Sr passed at 10 cm∙day-1 through 1.5 m thick PRB with zeolite and gravel. The breakthrough points for the PRB with 33 wt.% zeolite was evaluated as more than 70 years.

Upscaling Heat Flow in Porous Media With Periodic Surface Temperature Fluctuation Using a One‐Dimensional Subordinated Heat Transfer Equation

AbstractThe one‐dimensional (1‐d), constant‐parameter heat transport equation (HTE) built upon Fourier's law proposed in 1822 has been widely used to model heat transport in soil, where the core question is how to fit the observed temperature time series without detailed geomedium heterogeneity being mapped in the model. To address this question, this study extended the classical HTE by adding one parameter (the time index) using the time subordination approach to capture the impact of random operational times spent by individual heat parcels on heat dynamics. This led to a parsimonious, 1‐d, Subordinated HTE (Sub‐HTE), which assumes the temporally non‐Fourier heat transport and contains the classical HTE as an end member, with analytical solutions aimed at upscaling local heat transport in heterogeneous porous media. To test this approach, temperature time‐series were collected in unsaturated soils built in the laboratory that were subjected to periodic surface temperature fluctuations. Model applications showed that, although the HTE captures the general shape of the observed temperature time series, the Sub‐HTE is a mild improvement of the HTE in characterizing the nuances of temperature amplitude attenuation (likely due to the small operational time at the intermediate/late time stages). Both Eulerian and Lagrangian frameworks were developed to interpret other dynamics in heat flow, including the early time temperature jump and phase advance. Parameter analyses also revealed that the thermal front velocity in the Sub‐HTE is a function of Darcy flux, the time index, and the system's thermal properties, while the thermal diffusivity (the only parameter related to thermal properties in the Sub‐HTE) can be scale independent. Therefore, the 1‐d Sub‐HTE can be a reliable generalization of the classical 1‐d HTE in upscaling heat transport in soil.

Quantifying groundwater flow variability in a poorly cemented fractured sandstone aquifer to inform in situ remediation

This study applies innovative methods to characterize and quantify the magnitude of groundwater flow in a fractured and variably cemented sandstone aquifer to inform an in-situ remediation strategy for trichloroethene (TCE) contamination. A modified active-distributed temperature sensing (A-DTS) approach in which fiber optic cables were permanently grouted in the borehole was used to quantify groundwater flow rates. Two additional tracer tests were conducted: 1) fluorescein tracer injection followed by rock coring and sampling for visual mapping and porewater analysis, and 2) deployment of passive flux meters in conventional monitoring wells to evaluate groundwater velocity and mass flux distributions. Forced gradient injection of fluorescein tracer suggests a dual porosity flow system wherein higher rates of groundwater flow occur within discrete features including highly permeable bedding planes and fractures, with slower flow occurring within the rock matrix. Tracer was observed and detected in the unfractured matrix porewater >1.5 m away from the injection well. Beyond this distance, >6 m radially away from the injection hole, tracer was primarily detected within and adjacent to high transmissivity fractures serving as preferential flow paths. The Darcy flux calculated using active distributed temperature sensing (A-DTS) shows depth-discrete values ranging from 7 to 60 cm/day, with average and median values of 23 and 17 cm/day, respectively. Passive Flux Meters (PFMs) deployed in three conventional monitoring wells with slotted screens and sand filter packs showed groundwater flux values ranging from 2 to 11 cm/day, with an overall average of 4 cm/day and are likely biased low due to spreading in the sand pack. The study results were used to inform an in-situ remediation system design including the proposed injection well spacing and the amendment delivery approach. In addition, the results were used to build confidence in the viability of delivering an oxidant to the rock matrix via advective processes. This is important because 1) the matrix is where the majority of the TCE mass occurs, and 2) it provides insights on processes that directly affect remedial performance expectations given advective delivery to preferential pathways and the matrix overcomes diffusion only conditions.

Characterization of dissolved organic matter derived from coal gangue packed in underground reservoirs of coal mines using fluorescence and absorbance spectroscopy.

Organic and nitrogen pollutants in mine water could be removed effectively during the storage and transport of water in a coal mine underground reservoir packed with coal gangue through various water-rock interactions. However, little is known about the effect of the released dissolved organic matter (DOM) derived from the packed matrix on their removal. Column experiments were performed at a Darcy flux of 1.56 cm·h-1 at 25 °C to investigate the characteristics of DOM derived from Jurassic and Permian coal gangue individually packed in underground reservoirs of Bulianta (BL1) and Baode (BD2) coal mines. Chemical characteristics of the DOM were analyzed by using the ultraviolet and visible (UV-Vis) absorbance and fluorescence spectroscopy techniques. Results showed that the values of dissolved organic carbon (DOC) and electricity (EC) in the outlet of column packed with BL1 were obviously higher than those from BD2 due to the higher permeability of BL1 with more complex mineralogical and chemical compositions. The parallel factor analysis (PARAFAC) indicated that the fluorescence components in the DOM derived from BL1 and BD2 were individually dominated by the humic-like and tryptophan-like substances. Thus, the higher aromaticity, hydrophobicity, and humification indicated by the specific ultraviolet absorbance at 254 nm (SUVA254) and 260 nm (SUVA260) and humification index (HIX) were observed in the DOM from the younger Jurassic BL1, implying that the DOM may contain more plant-derived precursors. Meanwhile, the higher values of fluorescence index (FI) and biological/autochthonous index (BIX) confirmed the stronger autochthonous characterization of DOM originated from the earlier Permian BD2. The observed characterization of DOM will further extend the understanding of purification mechanism of mine water during its storage and transport in coal mine underground reservoirs packed with coal gangue of different geologic ages.

Sediment Bed Borehole Advection Method

This paper introduces and tests the Sediment Bed Borehole Advection Method (SBBAM), a low cost, point-measurement technique which utilizes a push-point probe to quantify the vertical direction and magnitude of Darcy flux at the surface water—groundwater sediment interface. The Darcy flux measurements are derived from the residence-time analysis of tracer arrival calculated from measured tracer concentration time-series data. The technique was evaluated in the laboratory using a sediment bed simulator tank at eight flow rates (1–90 cm/day). Triplicate test runs for each flow rate returned average errors between 4–20 percent; r2 = 0.9977.

A one-dimensional line element model for transient free surface flow in porous media

A simple and physically sound model has been proposed to investigate the transient free surface flow behavior in porous media. Instead of the continuum-based model, the pore space between solid grains is conceptualized as a network of horizontal and vertical flow paths and then the flow paths are characterized by straight line elements. Based on the Darcy's law and flux equivalence between the continuum-based model and line element model, equivalent hydraulic parameters and continuity equation are derived through the control volume. By introducing a local coordinate system, unified governing equations and equivalent boundary conditions of the line element model are obtained in the form of one-dimensional formulations. The two-dimensional transient free surface flow problem is reduced to a one-dimensional problem of line element network and a finite-element algorithm is developed. The proposed one-dimensional line element model is verified by three illustrative examples, which indicate that the numerical results can satisfactorily match the analytical solutions and experimental observations from different sources. It is found that the solution accuracy has weak sensitivity of time-step size but sensitive to the spacing size, while numerical efficiency can be well guaranteed for different time-step sizes and spacing sizes. Based on the numerical results, the proposed model can give better performance for the evolution of free surfaces than the residual flow procedure, and is efficient to model transient surface flow with a complex drainage system.

Examining the utility of continuously quantified Darcy fluxes through the use of periodic temperature time series

Fluxes across the groundwater-surface water interface are spatially and temporally variable, difficult to observe and measure, and play a major role in regulating ecological habitat distributions, water quality, and water quantity. The long-term quantification of these fluxes is difficult as field conditions dictate when data can be collected. Ultimately there is a pressing necessity to quantify these long-term flow regimes, as impacts from a changing climate are altering the timing and extent of key groundwater-surface water interactions. The use of periodic temperature time series data is one method that can be utilized to capture these fluxes over long periods of time. Long term deployment of temperature sensors, continuously logging temperature time series data, can be leveraged into time-varying Darcy fluxes via time series analysis and the advection–dispersion equation. However, as hydrologic boundary conditions change, fluxes transition in both magnitude and direction and these temperature time series-based methods are less capable of accurately quantifying fluxes. Real world data taken from five existing United States Geological Survey paired stream gages and riparian groundwater wells sites were used as boundary conditions to inform a one-dimensional heat and mass transport model, with the simulated temperatures used to quantify Darcy fluxes through time. Comparing the Darcy fluxes found using Darcy's Law and the estimated Darcy fluxes from the use of heat as an environmental tracer, periodic temperature time series derived fluxes accurately matched those derived from Darcy's law at three of the sites. For the remaining two sites, hydrologic conditions resulted in erroneous flux estimates, allowing for the identification of specific conditions where temperature time series methods relying on a periodic signal cannot be applied.

Quantification of the information content of Darcy fluxes associated with hydraulic conductivity fields evaluated at diverse scales

We rest on an Information Theory perspective and assess (i) the average information content and (i) the information shared between Darcy flux fields associated with fields of hydraulic conductivity (K) characterized by differing support (or measurement) scale. We treat hydraulic conductivity as a spatial random field, characterized by a given distribution and correlation structure. The latter is modeled through a truncated power law variogram (TPV), which explicitly takes into account a characteristic length scale of the support volume of K through a lower cutoff scale. We then frame our study in a numerical Monte Carlo context where groundwater flow is evaluated across a collection of realizations of hydraulic conductivity characterized by different values of the TPV parameters and subject to uniform in the mean flow. We quantify information through the Shannon entropy of the probability mass functions of the Darcy flux components as well as the mutual information and the multivariate mutual information respectively shared by pairs and triplets of Darcy flux components related to hydraulic conductivity fields evaluated at diverse scales and associated with various levels of heterogeneity. Partitioning of multivariate mutual information according to unique, redundant and synergetic contributions is also quantified. We found consistent trends (i) in the variation of the average information content with respect to the size of lower cutoff scale and (ii) in the way information is shared between pairs and triplets of Darcy flux components associated with diverse support scales of the underlying conductivities.

Gas slippage in anisotropically-stressed shale: An experimental study

Due to the extensive presence of nanopores, the slippage effect is frequently invoked in shale to enhance gas transport, therefore, causing the more than expected gas production. We conducted laboratory experiments on cubic shale samples (drilled from the Longmaxi Formation in southwestern China) to study the gas slippage effect with respect to anisotropic stresses and low pore pressures. The pore size distribution (PSD) of Longmaxi shale demonstrates that pore sizes mostly lie in the range of 8–400 nm and that gas transport in shale generally exists within the slip flow regime (0.001 < Knudsen number (Kn) < 0.1) given its distribution of pore sizes and pressures. The permeability dependence on effective stress became less significant when the deviatoric stress dropped. As a result of the gas slippage effect, the apparent permeability increased more rapidly as the pore pressure declined and this relationship was more prominent at low pore pressures. Also, shale permeability decreased with increasing stress anisotropy, with this effect dropping gradually. An almost 10- to 50-percent in permeability reduction response can be attributed to the stress anisotropy effect, reflecting a need for paying attention to this effect in permeability predictions. The gas slippage effect became significant with increasing effective stress and it is interesting that decreasing deviatoric stress enhanced the gas slippage effect dramatically. Additionally, we introduced a new relationship between the intrinsic permeability k∞ and gas slippage factor b for shale. The gas slippage factor first increased slightly and then significantly with decreasing intrinsic permeability. Moreover, the simultaneous effects of rising effective stress and diminished pore pressure (as commonly encountered during commercial gas production) both contribute to the deviation of the apparent permeability from that predicted according to Darcy flux. We hypothesize this new insight may be able to shed light upon the more than expected gas production in the petroleum industry, especially for shale gas. Finally, a theoretical model was introduced to describe permeability evolution by combining the stress and gas slippage effects. The model was in good accordance with the experimental results.