Clifford K. Ho and Michael L. Wilson Sandia National Laboratories. P.O. Box Albuquerque, NM

Transcription

1 1 L Calculation of Discrete Fracture Flow Paths in Dual-Continuum Models W + 0 Clifford K. Ho and Michael L. Wilson Sandia National Laboratories P.O. Box 5800 Albuquerque, NM ckho@sandia.gov, mlwilso@sandia.gov L 0 W ---%I Abstract Discrete fracture flow paths, referred to as weeps, have been derived from dual-continuum models of fracture flow. The required parameters include the geometric fracture spacing, an assumed width of each weep, and a scaling factor that accounts for reduced flow between fracture and matrix elements in dual-continuum models. The formulation provides a convenient means to determine discrete weep spacing and flow rates that are mathematically consistent with the dualcontinuum model. Specific applications and examples related to seepage into drifts are also discussed. Introduction Movement of water through fractures plays an important role in performance assessments of the potential high-level nuclear waste repository at Yucca Mountain, Nevada. The magnitude and frequency of water flowing though individual fractures impacts predictions of the near-field environment and waste-package corrosion. However, to date, few models of discrete fracture flow at Yucca Mountain exist. Current models of fracture flow at Yucca Mountain include dualcontinuum models (dual-permeability or dual-porosity) that treat the fractures and matrix as separate continua. Simulated flow in dual-continuum models is typically interpreted as occurring uniformly through each computational grid of the model. Another interpretation, which is presented in this paper, is that the continuum-based flow can be mapped into discrete fracture flow paths, or weeps, for each grid block. T his method is mathematically consistent with the dualdkhuweeps-rpt2. word 1 DRAFT (10/28/97)

2 DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommenduion, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

3 continuum model formulation, and it provides additional information about weep spacing that is required by near-field and waste-package modelers. The remainder of this paper presents a formulation to derive weep spacing, flow rate per weep, and seepage information from dualcontinuum models for use in performance-assessment calculations. Theoretical Formulation Consider a grid block with dimensions L1, L2, and L3 as shown in Figure 1. The objective is to derive a uniform weep spacing, a (m), in the grid block assuming a specified geometric fracture spacing, D (m), and a specified dimensionality of a uniform fracture set (1-D, 2-D, or 3-D). For simplicity, a one-dimensional fracture set is pictured in Figure 1,but the formulation can readily be extended to multiple dimensions. In a standard dual-continuum conceptual model, the total connection area, ADKM(m2),between fractures and matrix in a given primary grid block as shown in Figure 1 is assumed to be equal to the total surface area of all the fractures in the grid block: Number of matrix blocks per grid block A Fracture area per matrix block Equation 1 can be generalized for one-, two-, and three-dimensional uniform fracture sets if the right-hand side of Equation 1 is multiplied by n, where n is the dimensionality of the fracture set being considered (n = 1,2, or 3 for one-, two-, or three-dimensional fracture sets, respectively): For unsaturated flow, the actual wetted area between fractures and matrix is llkely to be less than the total surface area of the fractures due to heterogeneities at various scales that channel liquid flow. Typical dual-continuum models assume ubiquitous sheet flow in all the fractures, but the discrete approach proposed here assumes that the flow occurs in discrete weeps of width w (m) DKM/Weeps_rpQ.word 2 DRAFT (10/28/97)

4 and average uniform spacing a (Figure 1). The reduced wetted area between fractures and matrix, Aweep(m'), can then be expressed as follows for a given grid block: Number of weep blocks per grid block 7 - Area per weep The reduced area can be accommodated in dual-continuum models through the use of a reduction factor,l*2xfm,defined as the ratio of the reduced weep area to the total geometric fracture area: xfm -- Aweep (4) AD,, Assuming that X f m is prescribed in the dual-continuum model,' Equations 2 and 3 can be plugged into Equation 4 to determine the weep spacing, a, as a function of geometric fracture spacing, D,weep width, w,reduction factor, Xfm,and fracture set dimensionality, n: Equation 5 defines an equivalent discrete fracture spacing for flow (weep spacing) at any grid block in a dual-continuum model with a prescribed fracture-matrix reduction factor. The flow rate per weep, Q (m3/s),can be readily obtained by multiplying the continuum percolation flux ( d s ) by the area associated width each weep block (a2). It should be noted that the weep spacing defined in Equation 5 is an average spacing assuming uniformly spaced weeps. Because the actual weep spacing can be highly variable not only within a single fracture but also among multiple fractures, the average weep spacing can be a non-integer multiple of the geometric fracture spacing. In addition, Xfmin Equation 4 can be interpreted as the fracture saturation of the grid block depicted in Figure 1 if the fracture apertures are completely filled with water. However, the value of Xfm can be different from the actual fracture saturation DKMNeeps-rpt2. word 3 DRAFT (10/28/97)

5 , simulated in the dual-continuum models if the fractures are only partially filled or if fracture coatings exist. For example, if X f m is less than the simulated saturation, we can conceive that the fractures are nearly filled, but only one surface of the fracture is wetted. Fracture coatings may also prevent some of the weeps from contributing to the available wetted fracture-matrix surface area, causing Xfmto be much smaller than the liquid saturation. On the other hand, if Xfm is greater than the simulated saturation, we can conceive that film flow occurs on both fracture surfaces, which yields a large wetted fracture surface area (and hence, large Xfm) with only a small liquid saturation. Results and Discussion The fracture-matrix reduction factor, X f m, has been implemented in a dual-permeability model that is used to generate flow fields for performance-assessment calculations of the potential repository at Yucca Mountain.3 In the current base-case hydrologic property set, this factor is assumed to be a material-dependent constant and is determined via calibration studies3. Alternative property sets include fracture-matrix reduction factors that are dependent on the hydrologic state of the grid block being considered (e.g., Xfm - relative permeabi1ity)z. Table 1 gives the weep spacing for several units in the vicinity of the potential repository at Yucca Mountain associated with the base-case hydrologic property set assuming a one-dimensional fracture set (n = 1). Two bounding weep widths of 0.01 m and 1 m are used. Note that the weep spacing can be significantly greater than the geometric fracture spacing when the fracture-matrix reduction factor is small and the weep width is large. The information in Table 1 can be used to complement drift-scale models of seepage. The weep spacings given in Table 1 can be used to estimate the amount of water that contacts waste packages assuming negligible capillary-barrier resistance to water flow at the drift surface. The fraction of waste packages contacted by weeps, P, can be estimated as the ratio of the crosssectional area of a waste package to the area associated with a weep block (a2). The amount of DKMIWeeps-rpd. word 4 DRAFT (10/28/97)

6 water contacting each waste package can then be estimated using the flow rate per weep, Q, and the number of weeps contacting a waste package (0 or 1 if P e 1; and P if P > 1). Conclusions Discrete fracture flow paths (weeps) have been derived from dual-continuum flow models. The spacing of discrete weeps can readily be obtained from an assumed weep width and parameters used to define the dud-continuum fracture-matrix connections (see Equation 5). The derived weep spacing can be used to complement drift-scale models of seepage for waste-package and near-field analyses. Acknowledgments This work was supported by the Yucca Mountain Site Characterization Office as part of the Civilian Radioactive Waste Management Program, which is managed by the U.S. Department of Energy, Yucca Mountain Site Characterization Project. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under Contract DE-AC04-94AL References 1. Ho, C.K., 1995, Assessing Alternative Conceptual Models of Fracture Flow, in Proceedings of the TOUGH Workshop '95, LBL-37200, SAND CYLawrence Berkeley National Laboratory, Berkeley, CAYMar , pp Ho, C.K., 1997, Models of Fracture-Matrix Interactions During Multiphase Heat and Mass Flow in Unsaturated Fractured Porous Media, in Proceedings of the Sixth Symposium on Multiphase Transport in Porous Media, 1997 ASME International Mechanical Engineering Congress and Exposition, SAND CYDallas, TX, Nov DKMJWeeps-rpQ. word 5 DRAFT (10/28/97)

7 3. Bodvarsson, G.S., T.M. Bandurraga, and Y.S. Wu, 1997, The Site-Scale Unsaturated Zone Model of Yucca Mountain, Nevada, for the Viability Assessment, LBNL-40376, Lawrence Berkeley National Laboratory, Berkeley, CA. DKh4Weeps-rpt2. word 6 DRAFT (10/28/97)

8 . Table 1. Weep spacings for three stratigraphic units in the vicinity of the potential repository at Yucca Mountain using a reference hydrologic property set3. Geometric Weep Spacing, a (m) Unit Fracture Spacing, D (m) Xfm w=o.olm w=lm tsw ~ tsw ~ tsw ~ DKM/Weeps_rpt2. word 7 DRAFT (10/28/97)

9 I L3 7 Figure 1. Conceptual model of available wetted area between fractures and matrix in a computational grid block.

10 M l l I l lll 1 l lll l 1 Publ. Date (11) Sponsor Code(18) L3OE XF UC Category (1 9) /A c/-9 em//) DDE/EF( DOE