Heterogeneous fractured rock properties: implications for unsaturated flow modelling of a high-level nuclear waste repository

Transcription

1 Calibration ami Reliability in Groundwater Modelling: A Few Steps Closer to Reality (Proceedings ol' ModelCARE'2002 (Prague. Czech Republic, June 2002). IAHS Publ. no. 277, Heterogeneous fractured rock properties: implications for unsaturated flow modelling of a high-level nuclear waste repository WALTER A. ILLMAN Department of Geoscience, 121 Trowbridge Hall, University of Iowa, Iowa City, Iowa 52242, USA walter-illman(5),uiowa.edu DEBRA L. HUGHSON National Park Service, 222 East Main Street, Suite 202, Barstow, California 92311, USA Abstract Unsaturated flow through fractured rocks is a concern in the siting and performance of waste disposal facilities. We simulated unsaturated flow through a two-dimensional cross-section of volcanic tuff, using a two-phase flow simulator treating the fractured medium as randomly heterogeneous. Random field simulations revealed preferential flow in the welded units and in the uniformly permeable matrix continua of the nonwelded unit. The magnitude of the variance of water flux through fractures, increased with both the variance of fracture permeability and the infiltration rate, reaching a plateau in the welded units after flowing about 10 correlation scales of the vertical fracture permeability. Calculation of covariances of water flux normal to the layering revealed long range correlations in all units, suggesting that the water flux boundary condition may be important for unsaturated flow in dual continua media. Key words air permeability; fractured rocks; stochastic simulations; unsaturated flow INTRODUCTION Predicting unsaturated flow under various geological conditions is a concern for many environmental and water resource matters. Unsaturated flow through fractured rocks is a concern in the siting and performance of the high-level waste disposal facility planned at Yucca Mountain, Nevada, USA. It is also a concern at some low-level nuclear waste disposal sites, landfills, underground storage tanks, and mine tailings. Predicting unsaturated flow in fractured rocks, however, is complicated by the highly heterogeneous nature of fractured media, interactions between fractures and the rock matrix, and the effect of localized infiltration. Wetting front instability and a poolunderstanding of constitutive relationships for unsaturated fractured rock are additional sources of uncertainty. There is at present no well-established field methodology for characterizing fluid flow and contaminant transport properties of unsaturated fractured rocks. Preferential flow in fractures and gravitational fingering of unstable wetting fronts can cause rapid transport of contaminants through thick vadose zones. Quite often, however, these processes are neglected because of the extensive site characterization and fine grid discretization required to capture this behaviour in numerical models.

2 38 Walter A. Illman & Debra L. Hughson Coarser grids, used to alleviate the computational demands, result in volume-averaging of flow processes and consequent loss of these significant small-scale flow and transport processes. Thus, oversimplification of flow and transport commonly results from efforts to make problems computationally tractable. There is at present, no standard methodology for development of conceptual models that captures important processes of hydrology at all relevant scales of heterogeneity. One reason for this is the difficulty in parameterization of fractured rock properties. The degree to which the rock property under consideration is heterogeneous has a direct bearing on the conceptualization of site hydrogeology. The level to which site hydrogeology is simplified can affect our understanding of unsaturated flow processes, the predictive capabilities of models used, and the propagation of uncertainties in model predictions. To investigate these issues we conducted random field simulations of flow in unsaturated fractured rocks using a two-phase, dual-continuum, non-isothermal flow simulator. Our motivation for constructing the numerical model was not to create a Yucca Mountain site model of unsaturated flow, but instead to investigate the consequences of simplifying the site hydrogeology on unsaturated flow processes in deep, layered, fractured rocks. This modelling study is of national importance because the large three-dimensional site-scale model developed to evaluate the safety of the proposed high-level nuclear waste repository at Yucca Mountain does not consider the variability in fracture permeability within the layers, despite the recognition that fracture permeability varies by several orders of magnitude. Various smaller-scale submodels, such as the one used to predict seepage (Tsang & Li, 2000), do incorporate heterogeneity on a metre-grid size scale but may underestimate seepage because of uniform boundary condition effects. It has been known in the literature that preferential flow can cause rapid fluid flow and solute transport, but to our knowledge no analytical nor numerical study has been undertaken to show the effects of variability in fracture permeability on unsaturated flow in thick, layered fractured rocks using a twophase, dual continuum approach. MODELLING APPROACH A two-dimensional numerical model was constructed to evaluate the effects of heterogeneity in fracture permeability on flow focusing. We employed the numerical model Mass and Energy TRAnsport (METRA, Lichtner et al., 2000) for this purpose. METRA is a two-phase, non-isothermal, dual continuum model based on the integrated finite difference scheme and is analogous to codes such as TOUGH2 (Pruess, 1991) and NUFT (Nitao, 1998). The fractured rock is conceptualized as a dual-continuum porous media with the fracture continuum permeability treated as a spatially correlated random variable. The matrix and fractures constitute two interacting porous media continua, where Darcy's law and the area of the matrixfracture interface open to flow govern the exchange of fluids between the two continua. The fracture-matrix interaction model implemented in the version of METRA used in this study restricts the interface area for liquid flow from fractures to matrix only, by a constant factor. The numerical model considered flow of water and air in three geological units, each having distinct fracture and matrix properties based on the dual continuum concept. The hydrogeological units that we modelled include

3 Heterogeneous fractured rock properties: implications for a nuclear waste repository 39 the welded Tiva Canyon Tuff (TCw), the non-welded Paintbrush Tuff (PTn), and the welded Topopah Spring Tuff (TSw), which is the primary repository horizon. The computational domain consisted of overlapping 99 by 99 elements of 1 m 3 for the matrix and fracture continua. We decided to use cubic grid blocks for the numerical mesh of 1 m dimension, commensurate with the support volume of fractured rock properties estimated from single-hole pneumatic injection tests. This amounted to a total of elements and connections. The top 36 m of the model domain consisted of a single layer of TCw, while the next 33 m comprised the PTn, and the last 30 m consisted of the underlying TSw. We modelled a region deep enough in the unsaturated zone such that évapotranspiration and near surface thermal processes can be neglected. In both cases the water flux was varied between 12.5 and 42.5 mm year" 1. These rates were consistent with the US Department of Energy infiltration model for Yucca Mountain (CRWMS M&O, 2000), which predicts spatial variability of mean annual infiltration to range 0-20 mm year" 1 for modern-day climate conditions and 1-50 mm year" 1 for projected future climate conditions. For all cases, 2.5 mm year" 1 of water flux was applied uniformly to the matrix at the top boundary to reduce numerical difficulties. A mixed boundary condition was specified at the entire top boundary for both cases, in which the gas saturation, temperature and liquid flux were specified. Fluxes were set for both fractures and matrix at the top boundary. The left and right boundaries were specified as no flow boundaries, while at the bottom boundary we specified constant field variables for all cases. Isothermal conditions were maintained by fixing the temperature at the top and bottom boundaries at 20 C. Table 1 lists the dual continuum parameters used in the modelling study. Fracture permeability data were obtained from pneumatic injection tests conducted by the US Department of Energy (Wang et al, 1998) in the major lithological units at Yucca Mountain. For the variance and correlation structure of the log-transformed fracture permeability, we initially chose arbitrary values since geostatistical analyses were not available for experimental data from the Yucca Mountain. We also used geostatistical analysis by Chen et al. (2000), Vesselinov et al. (2001) and Hyun et al. (2002) of unsaturated fractured tuffs at the Yucca Mountain analogue Apache Leap Research Site (ALRS) in central Arizona, USA, to obtain statistical parameters for generation of random fracture permeability fields. Other parameters employed in this study were adapted from the unsaturated zone hydrology model developed for the Total System Performance Assessment-Viability Assessment (TSPA-VA) (CRWMS M&O, 1998). The values listed are averaged values for the subunits of TCw, PTn and TSw hydrogeological units listed in the TSPA-VA. As our primary objective was not to reproduce flow through the subunits, the harmonic mean of the matrix and fracture permeability (k) of the subunits was computed for the composite TCw, PTn, and TSw units. The arithmetic mean of matrix and fracture porosities ((j)), van Genuchten parameters (a, m, S r ), fracture frequency (f), and fracture-matrix connection area (Xf, ) were computed for composite values. The subscripts m and/designate matrix and fracture, respectively. Random fields were generated using a direct Fourier Transform Method (Robin et al, 1993). Ten unconditional simulations were conducted to generate permeability fields with isotropic correlation scales for the TCw, PTn, and TSw units. Random field

4 40 Walter A. Illman & Debra L. Hughson Table 1 Dual continuum parameters for model simulations. Symbol TCw PTn TSw k,(m 2 ) 9.68 x 10~ x 10" x 10" a,(pa'') 9.83 x 10" x 10" x 10" k f (m 2 ) 1.48 x 10" x 10" x 10~ x 10" x 10' x 10" 4 a/(pa') 1.93 x 10^ x 10" x 10" 5 V Srf Xfm 4.90 x 10" x 10"' 5.76 x 10" 5 k, = matrix permeability; < ), = matrix porosity; a, = Van Genuchten a-parameter for matrix; X, = exponent X in the van Genuchten equation for matrix; S n = residual saturation for matrix; k f = fracture permeability; < )y= fracture porosity; 0C/= Van Genuchten a-parameter for fracture; X f = exponent X in the van Genuchten equation for fracture; S rf = residual saturation for fracture; X fm = fracture-matrix connection area. simulations were conducted for layered, heterogeneous media with varying statistical properties for each layer. Random field simulations were based on the mean value of fracture permeability provided in Table 1 and we used four different variances for the simulations (0.5, 1.0, 1.5, 2.0) to simulate varying degrees of heterogeneity in fracture permeability. We used an arbitrary isotropic correlation length of 2 m and an exponential covariance model as available experimental data from the Yucca Mountain site were insufficient for determining the correlation structure of the fracture permeability field. RESULTS Figures 1(a) and (b) show the steady-state distribution of saturation for a single realization in the fracture and matrix continua, respectively, with an applied water flux of 42.5 mm year" 1 for a 2 = 1.0. Plotted alongside are contour plots of the flux magnitudes in the fracture (Fig. 1(c)) and matrix (Fig. 1(d)) continua. Stream traces are included to indicate flow paths in the fracture and matrix continua. Random field simulations using heterogeneous fracture permeability revealed the development of preferential pathways and focusing of flow, which could have a significant effect on the performance of waste facilities constructed in unsaturated fractured rocks. Preferential flow paths develop despite the uniform application of water at the top boundary and without explicitly building in high permeability pathways or discrete features that represent fractures. The variability in fracture permeability causes the development of preferential flow paths and convergence of flow paths in the fracture continuum for the TCw/TSw units and in the matrix continuum for the PTn unit. The bulk of water flows through those narrow pathways, isolating a large volume of the fracture and matrix continua from gravity-dominated, downward water flow. The development of preferential pathways has been found to

5 Heterogeneous fractured rock properties: implications for a nuclear waste repository 41 (a) (c),--777; 1 ( flux[mm/yf] ' S x[m] x[m] (d) I I x[m] x[m] Fig. 1 Steady-state distribution of: (a) fracture saturation; (b) matrix saturation; (c) fracture water flux; and (d) matrix water flux for a single realization with an applied water flux of 42.5 mm year" 1 for a 2 = 1 (see also Fedors et ai, 2002). increase water saturation locally. This local increase in saturation causes an increase in relative permeability to water along the pathways and reduces the wetted surface area for fracture-matrix interaction. Therefore, many fractures and parts of the matrix remain inactive despite the uniform application water at the top boundary. The degree in heterogeneity has a large effect on the development of preferential flow paths, the magnitude and direction of water flow and its corresponding distribution. To analyse results from the random field simulations from all 10 realizations for various degrees of heterogeneity in fracture permeability and applied water flux, we computed the variance normal to the stratification (Fig. 2). Examination of the figure shows that the computed variances appear to reach a plateau after 10 correlation lengths in the TCw and TSw units. The variance in the PTn decreases exponentially as the water moves from the fracture to the matrix continuum. We also computed the covariances in the same direction as the mean and variance, but calculated separately for each layer. Figure 3 shows results from such a

6 42 Walter A. lllman & Debra L. Hughson computation for 10 realizations with the logarithm of permeability with a variance of 1.0 and an applied flux rate of 42.5 mm year" 1. Symbols are used to show the results from the computed covariances from the random field simulations. The solid and dashed curves are model fits of the computed covariance values using the nonlinear regression routine PEST (Doherty et al, 1994) in which an exponential covariance model was fitted. It reveals that the covariances are highest at the TCw/PTn boundary and decay with depth. Some oscillations are visible for covariances in the TCw and TSw units, while the covariance of the PTn decays monotonically. Calculation of covariances of water flux normal to the layering revealed long range correlations in all units suggesting that the water flux boundary condition may be important for unsaturated flow in dual continuum media. The long-range correlation of fluxes implies that a uniform water flux boundary condition may not be applicable at the top of the seepage model and this assumption may significantly underestimate the distribution and quantity of seepage into drifts. This has a direct bearing on the performance of the repository and may affect subsequent radionuclide transport calculations. We expect an even longer correlation of water fluxes if fracture permeability is assumed to vary in a power law fashion. Such long-range correlation (and absence of correlation lengths and finite variance) in permeabilities has been documented in fractured tuffaceous rocks at the ALRS (Chen et al, 2000; Vesselinov et al., 2001; Hyun et al, 2002). rjtjd z[m] 100 Fig. 2 Variance of water flux in the fracture continuum for all simulations (c 2 = 0.5, 1.0, 1.5, 2.0) normal to the stratification. The applied water flux varies: low flux (LF) = 12.5 mm year" 1, medium flux (MF) = 22.5 mm year" 1 and high flux (HF) = 42.5 mm year" 1 (see also Fedors et al., 2002).

7 Heterogeneous fractured rock properties: implications for a nuclear waste repository * TCw-vlO-HF PTn-v F A TSw-vlO-HF TCw-vlO-HF(fit) PTn-v 10-l-IF (fil) TSw-vlO-HF(lit) 4A.i ' A * * " A A 25 JO Depth [m] Fig. 3 Covariance computed normal to each layer of TCw, PTn, and TSw units for logio fracture permeability with cr = 1.0 for realizations 1 to 10. The applied flux at the top boundary is q a = 42.5 mm year" 1. Symbols are computed values of covariances while the solid and dashed curves are fit using nonlinear regression. CONCLUSIONS Unsaturated flow through fractured rocks is a concern in the siting and performance of waste disposal facilities such as the proposed geological repository at Yucca Mountain, Nevada. The highly heterogeneous properties of fractured media, interactions between the matrix and fractures, and infiltration flux boundary conditions contribute substantially to uncertainty in unsaturated flow through fractured rocks. We simulated a two-dimensional cross-section of welded volcanic tuff, representative of the Yucca Mountain stratigraphy, using randomly heterogeneous fracture permeability fields and uniformly permeable matrix continua representing various degrees of welding. Our motivation for constructing the numerical model was not to create a Yucca Mountain site model of unsaturated flow but instead to investigate the consequences of simplifying the site hydrogeology on unsaturated flow processes in deep, layered, fractured rocks. Ten realizations each of randomly heterogeneous fields were generated by the spectral method independently for the welded Tiva Canyon Tuff (TCw), the nonwelded Paintbrush Tuff (PTn), and the welded Topopah Spring Tuff (TSw), which is the primary repository horizon. Random field simulations were run for steady-state flow at three different uniform flux boundary conditions. Simulations were performed using the dual-continuum simulator METRA, which represent matrix and fractures as dual overlapping continua where liquid flux from fracture to matrix can be restricted by a uniform factor. Heterogeneous fracture permeability fields generated strong

8 44 Walter A. Illman & Debra L. Hughson preferential flow in the welded units and significant preferential flow in the uniformly permeable matrix continua of the PTn. The magnitude of the variance of water flux through fractures, indicating preferential flow pathways, increased with both the variance of fracture permeability and the infiltration boundary condition, reaching a plateau in each of the welded units after flowing about 10 correlation scales of the vertical fracture permeability. Calculation of covariances of water flux normal to the layering revealed long range correlations in all units suggesting that the water flux boundary condition may be important for unsaturated flow in dual continuum media. These results suggest that geometric mean, variance and vertical correlation scales of fracture permeability need careful analysis so that seepage into emplacement drifts is not underestimated and radionuclide transport travel time is not overestimated in performance assessments of Yucca Mountain. Acknowledgements The senior author was supported in part by the 2002 Old Gold Fellowship from the University of Iowa. REFERENCES Chen, G., Illman, W. A., Thompson, D. L., Vesselinov, V. V. & Neuinan, S. P. (2000) Geostatistical, type-curve, and inverse analyses of pneumatic injection tests in unsaturated fractured tuffs at the Apache Leap research site near Superior, Arizona. In: Dynamics of Fluids in Fractured Rocks (ed. by B. Faybishenko, P. A. Witherspoon & S. M. Benson), Geophysical Monograph vol. 122, American Geophysical Union, Washington DC, USA. CRWMS M&O (Civilian Radioactive Waste Management System Management and Operating Contractor) (1998) Chapter 2. Total system performance assessment-viability assessment (TSPA-VA) analyses technical basis document, Unsaturated Zone Hydrology Model. BOOOOOOOO REV 00, Las Vegas, Nevada, USA. CRWMS M&O (Civilian Radioactive Waste Management System Management and Operating Contractor) (2000) Simulation of net infiltration for modern and potential future climates, ANL-NBS-GS , Revision 00, Las Vegas, Nevada, USA. Doherty, J., Brebber, L. & Whyte, P. (1994) PEST: Model Independent Parameter Estimation. Watermark Computing, Brisbane, Australia. Fedors, R. W., Winterle, J. R., Illman, W. A., Dinwiddie, C. L. & Hughson D. L. (2002) Unsaturated Zone Flow at Yucca Mountain, Nevada: Effects of Fracture Heterogeneity and Flow in the Nonwelded Paintbrush Tuff Unit, Center for Nuclear Waste Regulatory Analyses, San Antonio, Texas, draft report prepared for the Nuclear Regulator Commission, Contract NRC , April Hyun, Y., Neuman, S. P., Vesselinov, V. V., Illman, W. A., Tartakovsky, D. M. & Di Federico, V. (2002) Theoretical interpretation of a pronounced permeability scale-effect in unsaturated fractured tuff. Water Résout: Res. 38(6), /2001WR Lichtner, P. C, Seth, M. S. & Painter, S. (2000) MULTIFLO User's Manual. MULTIFLO Version 1.2 (Two-phase nonisothermal coupled thermal-hydrologic-chemical flow simulator). Rev. 2 Change 0, January Center for Nuclear Waste Regulatory Analyses, San Antonio, Texas, USA. Nitao, J. J. (1998) User's Manual for the USNT Module of the NUFT code. Version 2.0 (NP-Phase, NC-Component, Thermal) UCRL-MA Lawrence Livermore National Laboratory, Livermore, California, USA. Pruess, K. ( 1991 ) TOUGH2-A General Purpose Numerical Simulator For Multiphase Fluid And Heat Flow. Lawrence Berkeley Laboratory Report LBL UC-251. Robin, M. J. L., Gutjahr, A. L., Sudicky, E. A. & Wilson, J. L. (1993) Cross-correlated random field generation with the direct Fourier Transform Method. Water Résout: Res. 29(7), Tsang, C. F. & Li, G. (2000) Seepage Model for PA Including Drift Collapse. Office of Civilian Radioactive Waste Management, Analysis Model Report. Las Vegas, Nevada, USA. Vesselinov, V. V., Neuman, S. P. & Illman, W. A. (2001) Three-dimensional numerical inversion of pneumatic cross-hole tests in unsaturated fractured tuff: 2. Equivalent parameters, high-resolution stochastic imaging and scale effects. Water Resour. Res. 37(12), Wang, J. S. Y., Cook, P. J., Trautz, R. C, Salve, R., James, A. L., Finsterle, S., Tokunaga, T. K.., Solbau, R., Clyde,.1., Flint, A. L. & Flint, L. E. (1998) Field Testing and Observation of Flow Paths in Niches: Phase 1 status report of the drift seepage test and niche moisture study. Level 4 milestone SPC314M4 for WBS Yucca Mountain Site Characterization Project, Las Vegas, Nevada, USA.