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  • 1.
    Cvetkovic, Vladimir
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering.
    Frampton, Andrew
    KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering.
    Transport and retention from single to multiple fractures in crystalline rock at Äspö (Sweden): 2. Fracture network simulations and generic retention model.2010In: Water resources research, ISSN 0043-1397, E-ISSN 1944-7973Article in journal (Refereed)
    Abstract [en]

    Hydrogeologic characterization of crystalline rock formations on the field scale is important for many applications but still presents a multitude of challenges [Neuman, 2005]. In this work we use comprehensive hydro-structural information and present a detailed simulation study of flow and advective transport in a discrete fracture network (DFN) that replicates the TRUE Block Scale rock volume at the Äspö Hard Rock Laboratory (Sweden). Simulated water residence time τ and hydrodynamic retention parameter β are used as independent constraints for estimating material retention properties as presented in part 1 of this series [Cvetkovic et al., 2009] whereas simulated mean water residence times are compared with observed values. We find that the DFN simulations reproduce water residence times reasonably well, indicating that the characterization data are sufficient and that the DFN model does capture dominant features of the flow paths analyzed. The empirical quadratic law that relates aperture and transmissivity seems to better reproduce calibrated mean water residence times than the theoretical cubic law, for the five flow paths. The active specific surface area (β/τ) [1/L] as inferred from simulations, is used for defining a generic retention model for the dominant rock type (”Äspö diorite”) that matches fairly well the entire range of calibrated retention parameters of the TRUE tests. The combination of Part 1 and this work provide a general, comprehensive methodology for evaluating tracer test results in crystalline rock where a comparable amount of information is available; critical to this methodology is that tracer tests are carried out using tracers with sufficiently different sorption affinities (of factor 10 to 100).

  • 2. Fiori, Aldo
    et al.
    Boso, Francesca
    de Barros, Felipe P. J.
    De Bartolo, Samuele
    Frampton, Andrew
    KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering (moved 20130630), Water, Sewage and Waste technology.
    Severino, Gerardo
    Suweis, Samir
    Dagan, Gedeon
    An indirect assessment on the impact of connectivity of conductivity classes upon longitudinal asymptotic macrodispersivity2010In: Water resources research, ISSN 0043-1397, E-ISSN 1944-7973, Vol. 46, p. W08601-Article in journal (Refereed)
    Abstract [en]

    Solute transport takes place in heterogeneous porous formations, with the log conductivity, Y = ln K, modeled as a stationary random space function of given univariate normal probability density function (pdf) with mean < Y >, variance sigma(2)(Y), and integral scale I-Y. For weak heterogeneity, the above mentioned quantities completely define the first-order approximation of the longitudinal macrodispersivity sigma(L) = sigma I-2(Y)Y. However, in highly heterogeneous formations, nonlinear effects which depend on the multipoint joint pdf of Y, impact alpha(L). Most of the past numerical simulations assumed a multivariate normal distribution (MVN) of Y values. The main aim of this study is to investigate the impact of deviations from the MVN structure upon alpha(L). This is achieved by using the concept of spatial correlations of different Y classes, the latter being defined as the space domain where Y falls in the generic interval [Y,Y + Delta Y]. The latter is characterized by a length scale lambda(Y), reflecting the degree of connectivity of the domain (the concept is similar to the indicator variograms). We consider both "symmetrical" and "non-symmetrical" structures, for which lambda(Y') = lambda(-Y') (similar to the MVN), and lambda(Y') not equal lambda(-Y'), respectively, where Y' = Y - < Y >. For example, large Y zones may have high spatial correlation, while low Y zones are poorly correlated, or vice versa. The impact of lambda(Y) on alpha(L) is investigated by adopting a structure model which has been used in the past in order to investigate flow and transport in highly heterogeneous media. It is found that the increased correlation in the low conductive zones with respect to the high ones generally leads to a significant increase in alpha(L), for the same global I-Y. The finding is explained by the solute retention occurring in low Y zones, which has a larger effect on solute spreading than high Y zones. Conversely, alpha(L) decreases when the high conductivity zones are more correlated than the low Y ones. Dispersivity is less affected by the shape of lambda(Y) for symmetrical distributions. It is found that the range of validity of the first-order dispersivity, i.e., alpha(L) = I-Y sigma(2)(Y), narrows down for non-symmetrical structures.

  • 3.
    Frampton, Andrew
    KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering.
    Stochastic analysis of fluid flow and tracer pathways in crystalline fracture networks2010Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Understanding groundwater flow systems and how these control transport is an essential part in assessing the suitability of subsurface environments as hosts for storage of toxic waste. Therefore it is important to be able to integrate knowledge obtained from field characterisation of the subsurface with methods which can be used to evaluate and predict possible impact on surrounding environments.In this thesis I investigate the characteristics of flow and transport in discrete fracture networks by analysing Eulerian and Lagrangian descriptions within a stochastic framework. The analysis is conducted through numerical flow and transport simulations configured according to available field data, combined with independent theoretical analytic and semi-analytic methods which are able to reveal insight to relevant constitutive properties. It is shown that numerical simulations conducted with the discrete fracture network approach can be both conditioned and confirmed against field measurable quantities, and the developed theoretical methods are evaluated against results obtained from simulation. Thereby, a methodology which can provide links between field measurable quantities and tracer discharge is presented, developed and evaluated. It is shown to be robust with respect to underlying assumptions used for flow configurations.In particular, a specific sampling algorithm for obtaining a Lagrangian description of transport based on a Eulerian description of flow is proposed, evaluated and shown to be robust for the cases considered, providing accurate replications. Also a generalisation of both the advection-dispersion solution and the one-sided stable distribution is shown to be able to evaluate advective transport quantities, and combined with a Lagrangian retention model it is shown to be a fairly accurate and robust method for upscaling distributions, enabling predictions of transport in terms of tracer discharge. Evaluation of transport is also conducted against the advective-dispersion assumption, where results indicate advective transport is generally non-Fickian for the fracture networks and domain scales considered, but not necessarily anomalous. Additionally, the impact certain model assumptions have on tracer discharge are analysed. For example, transport is evaluated for assumptions regarding injection mode, fracture network heterogeneity, relationship between aperture and transmissivity, relationship between transmissivity and size, as well as scale and modelling dimension. In relation to hydraulic testing and flow analysis, a method for conditioning fracture transmissivity from field measurements of flow by simulation is developed and evaluated against homogenisation assumptions commonly used in field applications. Results indicate the homogenisation assumption generally fails for current interpretations of field data.

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  • 4.
    Frampton, Andrew
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering.
    Cvetkovic, Vladimir
    KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering.
    Numerical and analytical modelling of advective travel times in realistic three-dimensional fracture networks2011In: Water resources research, ISSN 0043-1397, E-ISSN 1944-7973, Vol. 47, no W02506, p. 16pp-Article in journal (Refereed)
    Abstract [en]

    Travel time distributions obtained from advective transport in multiple realisations of realistic discrete fracture network simulations are analysed using the truncated one-sided stable distribution, which has previously been shown to generalise both the advection-dispersion solution as well as one-sided stable distributions. Using this model it is shown that the Fickian assumption inherent in the advection-dispersion equation generally fails, despite that the first two moments of travel time essentially scale linearly with distance. It is also observed that the equally probable realisations drawn from the ensemble can produce a wide range of behaviour under the current configuration, such that Fickian conditions are almost obtained in some cases for increasing scales. Based on a small-scale calibration against particle breakthrough, the model is then shown to successfully predict limiting bounds of transport for a one order of magnitude increase in scale. Correlation in particle velocity is explicitly shown to be significant for scales close to the characteristic Lagrangian segment length. The network configuration is obtained from extensive site characterisation data at the Laxemar region in Sweden, and represents a block scale domain of reasonably sparse background fractures.

  • 5.
    Frampton, Andrew
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering.
    Cvetkovic, Vladimir
    KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering.
    Significance of injection modes and heterogeneity on spatial and temporal dispersion of advecting particles in two-dimensional discrete fracture networks2009In: Advances in Water Resources, ISSN 0309-1708, E-ISSN 1872-9657, Vol. 32, no 5, p. 649-658Article in journal (Refereed)
    Abstract [en]

    We investigate the impact of injection mode (flux and resident injection) and heterogeneity in hydraulic properties on dispersion of advecting particles in two-dimensional discrete fracture network models, using a Monte Carlo method. We find that the injection mode has a significant effect on dispersion: The resident injection mode exhibits anomalous features of transport whereas the flux injection mode tends to Gaussian transport; this observation is easily understood by considering phase diagrams where a limited number of particles entering low velocity fractures greatly increase macrodispersion. In spite of a sizeable portion of negative longitudinal velocities, it is shown that multiple crossings are negligible when quantifying longitudinal macrodispersion. A simple probabilistic expression of particle mass balance is shown to predict well the spatial distribution of advecting particles.

  • 6.
    Frampton, Andrew
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering.
    Cvetkovic, Vladimir
    KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering.
    Upscaling particle transport in discrete fracture networks: 1. Nonreactive tracers2007In: Water resources research, ISSN 0043-1397, E-ISSN 1944-7973, Vol. 43, no 10, p. W10428-Article in journal (Refereed)
    Abstract [en]

    We study tracer transport through discrete fracture networks and develop a methodology for upscaling particle breakthrough curves on the basis of fracture segment data. Our prime interest is to model the early arrival and peak of tracer breakthrough curves, i.e., to capture the bulk of the tracer mass arrival. This study is based on two-dimensional discrete fracture network simulations, combined with a truncated one-sided stable distribution as a model for upscaling particle transitions. Results indicate that this model can accurately capture the bulk mass and peak of the breakthrough distributions for an upscaled distance of at least 1 order of magnitude in terms of transport scale, which for our simulations is about 2 orders of magnitude greater than the mean fracture segment scale. We also introduce an accurate mapping algorithm for transforming Eulerian into Lagrangian flow statistics, without a priori knowledge of network connectivity.

  • 7.
    Frampton, Andrew
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering.
    Cvetkovic, Vladimir
    KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering.
    Upscaling particle transport in discrete fracture networks:  2. Reactive tracers2007In: Water resources research, ISSN 0043-1397, E-ISSN 1944-7973, Vol. 43, no 10, p. W10429-Article in journal (Refereed)
    Abstract [en]

    We study sorbing tracer transport through discrete fracture networks using astochastic Lagrangian framework, combined with the methodology for upscalingparticle breakthrough curves developed in the first part of this article series.Results indicate that this procedure can accurately predict expected normalizedtracer discharge for an upscaled distance of 1 order of magnitude in terms oftransport scale, which for our simulations is about 2 orders of magnitudegreater than the mean fracture segment scale. Specifically, we show theimportance of retaining the correlation between the water residence time τ andthe hydrodynamic control of retention β in order to make accurate tracerdischarge predictions. Also, we show that the extreme tails of τ and β distributions have essentially no impact on tracer discharge. These results areillustrated using the unlimited diffusion model, and for two hypotheticaltracers with properties designed to capture the behavior of many commonlyoccurring natural radionuclides.

  • 8.
    Frampton, Andrew
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering, Water Resources Engineering.
    Vladimir, Cvetkovic
    KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering, Water Resources Engineering.
    Inference of field scale fracture transmissivities in crystalline rock using flow log measurements2010In: Water resources research, ISSN 0043-1397, E-ISSN 1944-7973, Vol. 46, no 11, p. W11502-Article in journal (Refereed)
    Abstract [en]

    Characterization of transmissivity for crystalline rock is conducted through simulation by conditioning against borehole flow rates obtained from high-resolution, in situ field measurements during extraction pumping. Full three-dimensional discrete fracture network simulations are carried out according to specifications obtained from site characterization data in a stochastic Monte Carlo setting. A novel method of conditioning is thereby introduced and applied using nonparametric comparison tests, which provide quantifiable measures of accuracy enabling evaluation of simulated results against field measurements. The assumption of a constitutive relationship ( perfect correlation) between fracture size and transmissivity is adopted. The method is evaluated against both single and multiple realizations, various domain size, and fracture length configurations and shown to be robust for the cases considered. When the introduced method of conditioning is applied, transmissivity parameterization can be inferred to a narrow range with a quantifiable accuracy in terms of a probability value. Results indicate that elementary interpretation of transmissivity based on homogenization of a porous medium will generally underestimate transmissivity. Further implications on advective transport for natural flow conditions are briefly evaluated, indicating advective breakthrough times can be overestimated up to a factor of about 10 in the median.

1 - 8 of 8
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