ML20024B542
| ML20024B542 | |
| Person / Time | |
|---|---|
| Issue date: | 06/16/1983 |
| From: | Logsdon M NRC OFFICE OF NUCLEAR MATERIAL SAFETY & SAFEGUARDS (NMSS) |
| To: | Justus P NRC OFFICE OF NUCLEAR MATERIAL SAFETY & SAFEGUARDS (NMSS) |
| References | |
| REF-WM-1 NUDOCS 8307090103 | |
| Download: ML20024B542 (17) | |
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DISTRIBUTION:
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001.5/ML/83/06/08/0 3001J WHT r/f NP.SS r/f JUN 1649@
CF WHT:
3001.5 Browning MMeH MEMORANDUM FOR:
Philip S. Justus, Section Leader PAltomare Siting Section High-Level Waste Technical hogsdon&r#_
Development Branch
'g p Division of Waste Management FROM:
Mark Logsdon High-Level Waste Technical Development Branch Division of Waste Management
SUBJECT:
TRIP REPORT FOR SHORT COURSE ON CONTAMINANT HYDR 0GE0 LOGY, UNIVERSITY OF WATERLOO, MAY 30 - JUNE 3, 1983 I attended a short course on Contaminant Hydrogeology at the University of Waterloo, May 30 - June 3, 1983.
The course was divided between lectures on physical, chemical and mathematical principles and theory and illustrations of basic processes and common problems using case studies.
Ir,all instances, the instructors emphasized processes that are indicated by laboratory and field evidence and pointed out discrepancies between theoretical formulations and practical experience.
Also, the instructors emphasized the practical aspects of measuring hydraulic and geochemical parameters needed for the prediction.
The course outline is attached.
The course was attended by about 50 hydrogeologists, representing federal and state (provincial) agencies in the U.S. and Canada, national laboratories, private industry, and consulting firms.
A list of attendees is attached.
Numerous lectures and background readings were of significant interest to the high-level waste program.
Among the more important topics were the following:
1)
Difficulties in applying the classical advective-dispersive theory for contaminant transport to field studies because of the scale-dependence of dispersivity (Cherry and Frind).
2)
The use of stream functions to characterize flow and transport in long, thin aquifers under low hydraulic gradients (Frind).
3)
Theoretical difficulties in applying Kd's to transport problems in dynamic systems (Gillham and Reardon).
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Th:euseofenvironmentalisotopesinthecharacterizationof crystalline roc'ks for waste disposal (Fritz).
3)
-Natrix riif fusion as a retardation' process in fractured porous media (Cherry and Frind).
_j Lecture notes, handouts and reprints on these and other topics are part of the short course package and are available to WMHT and WMHL staff on request.
Because it is a potentially significant process that is receiving considerable attention in the technical community, and because it is a-matter that we raised in Chapter 3 and Appendix F of the DSCA, I am attaching abstracts of three papers on matrix diffusion.
The first paper, by Tang et al., discusses the potential significance of matrix diffusion and presents an analytical solution for matrix diffusion from a single fracture.
The second paper, by Feenstra et al., applies the Tang solution to a low-level radioactive waste problem. ~The third paper, by Sudicky and Frind, extends the Tang solution to multiple fractures.
The conclusion to be drawn frorr the series of papers'is that while matrix diffusion is a process which can be eNpected'to retard radionuclides, it probably will be very difficult to apply quantitatively to potential high-level waste disposal sites because of the difficulty of describing the gecmetry of fractures (and therefore of setting boundary conditions).
Copies of the full texts of the three papers are being circulated to the memt ers of the geochemistry team.
Onageneralbasis,themostimportant[informationinthecoursedealt with predictive modeling of contaminant transport.
It was the position of the entire team of instructors that stati-of-the-art modeling of contaminant. transport cannot be used to produce reliable predictions, even for relatively simple hydrogeologic envjronments, such as glacial outwash sands and gravels that the Waterloc' group has studied.
The problem arises because of difficulties in both the dispersion and chemical reaction, tercs'of the generalized transport equation.
Consider one-dimensional transport through a porous medium with solute-solid interactions:
y ac _ D 32c V ac g ac J5t -
F ax r1 at
-c = concentration of solute in solution phase C = concentration of solute in' solid phase D =.' dispersion coefficient V'= aserage linear pore-water velocity t = tim _e x -(cartesien coordinate in the direction of flow n, OFC :
NAME.:
DATE :83/06/08
001.5/ML/83/06/08/0 JUN 101983 p = bulk mass density of the porous medium q = porosity The first term on the right-hand-side of the equation describes the change in C due to hydrodynamic dispersion.
The second term is the rate of transport of C due to advection.
These two terms describe the flux of C due to physical processes.
The third term describes the loss or gain of solute mass due to chemical reactions and/or radioactive decay.
The problems in applying models based on this equation are:
1)
Dispersion is a scale-dependent phenomenon, but there is no theory currently available to predict the functional relationship between distance (n time) and dispersivity.
In principle, it is possible to derive values of dispersivity at the scale or scales of interest by field tests, though these are likely to be impractical or impossible at the scale of interest to the high-level program.
Field experience indicates that it is not reliable to extrapolate small-scale measurements to significantly large scales (i.e., cm-scale to ten-meter-scale; ten-meter-scale to 100-meter-scale).
Producing conservative, bounding values for dispersivity is problematic. While many researchers assume that dispersivity approaches some asymptotic value, there is no theory to predict that value.
Direct testing to calibrate values for scales of 1-10 km probably is not possible for three reasons:
a)
Travel times under natural gradients are too slow to conduct tracer tests at distances of kilometers in reasonable lengths of time.
b)
Induced gradient tracer tests do not give dispersivities equivalent to natural gradient tests, nor do the dispersivities calculated from induced gradients tests accurately describe plumes that have been monitored over extended period of time.
Typically, dispersivities calculated from induced gradient tests underestimate observed dispersion.
3)
Because the dispersion parameters are not known in advance, it is difficult even at distances of tens of meters to predict the position of sampling points that will intersect the plume.
The alternative is to place a 0FC :
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DATE :83/06/08 1
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- JUN 161983 very high density of monitoring locations, which is very expensive.
2)
In most, if not all, formulations of transport models C the concentration of the solute in the solid phase, is related to C, the concentration of solute in the solution phase, through the use of a distribution functign (Kd) that expresses the functional relationship between C and C.
Typically, it is assumed that the distribution function is a constant.
Distribution functions can be determined from laboratory experiments or field tests.
In general, dynamic field tests yield lower Kd's than batch laboratory tests.
A more significant problem is that the value of the distribution function changes as the concentration in solution changes.
Therefore, the use cf experimentally derived Kd's is justified if and only if the system is chemically at steady state.
In the case of a high-level waste disposal system this condition is unlikely to be met, at least in the near-field.
The Waterloo instructors pointed out that there is active research at Waterloo and elsewhere into ways of resolving both sources of uncertainty.
However, their best advice was to use transport models with great caution and primarily as a qualitative or at best semi quantitative.
scoping tools.
In conclusion, because the instructors stressed the physical and chemical processes of contaminant transport, the course was a valuable exercise in extending my technical expertise in hydrogeology applied to high-level waste mangement, particularly with respect to understanding the assumptions and limitations of state-of-the-art modeling.
_0Rimmu.sggyio my Mark Logsdon High-Level Waste Technical Development Branch Division of Waste Management Attachments:
1.
Short Course on Contaminant Hydrogeology Outline i
2.
List of Attendees 3.
Abstracts Record Note:
l 1.
Draft reviewed by P. S. Justus and H. J. Miller 2.
All comments resolved i
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Distribution List David Brooks, WMHT 1
Seth Coplan, WMHT I
Julia Corrado, WMHT Lawrence Doyle, ESBR
- ~
Matthew Gordon, WMHL j
John Greeves, WMHT Robert Johnson, WMHT 1
I Malcolm Knapp, WMHL Peter Ornstein, WMHL John Starmer, WMHT Tilak Verma, WMHT Michael Weber, WMHL Robert Wright, WMHT I
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CONTAMINANT HYDROGE0 LOGY SHORT COURSE o
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8:00 MONDAY
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REGISTRATION 8:30 TUESDAY WEDNESDAY THURSDAY FRIDAY
^I I
INTRODUCTION Transport of Field Aspects Environmental Field Studies Reactive solutes of Fractured Isotope of Organic pe o a
Types of problems Media Hydrogeology Contaminant Geologic Transport features 10:00 - 10:30 BREAK A2 B3 C4 F1 A6 Hydrostratigraphy Transport tiedia Predictability Organic f5e Piezometers/
and Groundwater Modelling Contaminant Q5 Multilevel Flow Techniques A4 Advection and dis-Occurrence and Field Aspects of Transport Eb 3
persion in granula Diffusion Controlled SE
."9 deposit Media o2 ques 12:00 - 13:00 LdNCH B1 C2 B4 D2 Principles of Flow and Modellinq:
Geochemical Groundwater Transport in Case Studies e
9 of Flow Unsaturated Media Contaminant Transport 14:30 - 15:00 BREAK B2 C3 D1 l A5 4 &h 1
'J- % F Principles of Geochemistry Field examples E Y'M Non-reactive Transport as above of Inorganic of Inorganic Id2 Contaminants Contaminant N
Attenuation
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N A Cherry, J.A.
B Frind, E.O.
C Gillham, R.W.
D Reardon, E.
E Fritz, P.
F Barker, J.F.
S
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i s
A List of Participants
~
" Contaminant Hydrogeology" Short Course May 30 to June 3,1983 did 4 b " h Mr. Rober Bacha Rockwel Hanford Corporation P.O. B 800 Richl d, Washington, 99352 Mr. Ron G. Barsi Saskatchewan Environment Mines Pollution Control Branch Box 3003, McIntosh Mall Prince Albert, Saskatchewan S6V 6G1 Mr. Philip Bedell Golder Associates 500 Nottinghill Road London, Ontario N6K 3P1 Mr. Jonathan Bridge Whitman and Howard 45 William Street
[..
6, Wellesley, Massachusetts, 02181 Mr. Dan Brown Ontario Ministry of the Environment 985 Adelaide Street South London, Ontario N6E lV3 Mr. R.W. dryce Rockwel Hanford Operations g/g{ ftv[
A P.O. B 800 Richl d, Washington, 99352 Mr. Brian Buck Getty Mining Company Box 7900 Salt Lake City, Utah,84107 Mr. Larry Chamney Atomic Energy Controi Board P.O. Box 1046 Ottawa, Ontario KlP 559 Mr. John Clerici Golder Associates SlES Peachtree Road
'l Atlanta, Georgia, 30341
'Mr. Neil Crow Lawrence Livermore Laboratories Livermore. California, 94550
'- Mr. Paul Davis Sandia National Labs s
r' Albuquerque, New Mexico, 87185
' N-
' Ms. Maxine Dunkelman U.S. Nuclear Regulatory Commission Washington, D.C.
20555 Ms. Karen Endarle Standard Oil of Ohio 4440 Warrensvilie Center Road Cleveland, Ohio 44128 Mr. James Everhart IBM Corporation Box 950, South Road D/771 B/928 Poughkeepsie, New York, 12602 Mr. Wayne Fox U.S. Army Environmental Hygiene Agency HSHB - ES - G/Mr. Fox Aberdeen Proving Ground, Maryland, 21010 Mr. Robert Galbraith I.T. Enviro-Science 1815 Arnold Drive Martinez, California, 94553
('
,y Mr. Everett Glover Soil & Material Engineers, Inc.
3109 Spring Forest Road Raleigh, North Carolina, 27658 Mr. Tim Harrington Canonie Environmental Services Corp.,
1408 N. Tremont Road Chesterton, Indiana, 45304 Mr. W.F. Heinrich AECL Whiteshell Nuclear Research EstablisNnent Pinawa, Manitoba ROE ILO Mr. Thomas Holm Chalmers University of Technology Department of Geology S-41296 Gothenburg, Sweden Mr. Rudolph Hoagberg R.K. Hoagberg Associates Inc.
1409 Willow Street, Room 304 Minneapolis, Minnesota, 55403 N'
,V v,
Mr. Wayne Jackman Ontario Ministry of the Environment
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Ontario Government Building P.O. Box 2112
'19 King Street West,12th Floor hamilton, Ontario L8N 3Z9
- Mr. Peter Kearl Bendix Field Engineering P.O. Box 1569 Grand Junction, Colorado, 81502 Ms. Susan Keith Water Resources Consultant 2748 E. 9th Street Tucson, Arizona, 85716
'Mr. Dave Kent Clifton Associates Ltd.
340 Maxwell Crescent Regina, Saskatchewan S4N SYS Mr. Elmer Klavetter Sandia National Laboratories KAFB Albuquerque, New Mexico
(
Mr'. Y.T. Lin Sandia National Laboratories Division 9762 Box 5800 Albuquerque, New Mexico, 87185
' Mr. Dennis LeNeveu AECL Whiteshell Nuclear Research Establishment Pinawa, Manitoba R0E ILO
' Ms. Marianne Litzinger Crown Zellerbach Corporation Environmental Services 904 N.W. Drake Street Camas, Washington, 98607 Mark Logsdon U.S. Nuclear Regulai.ory Commission Mail Stop 623SS Washington, D.C., 20555 Mr. Thomas Maher Dvirka and Bartilucci
(
6800 Jericho Turnpike v
Syosset, New York, 11791 Mr. John Mateo U.S. Environmental Protection Agency 571 Park Avenue
.Maplewood, New Jersey, 07040 7...
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- =.
Mr. William McConachie
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Lawrence Livermore National Laboratory
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University of California P.O. Box 808 Livermore, California, 94550 Mr. Donald McEdwards Harding Lawson Associates 7655 Redwood Blvd.
Novato, California, 94948 Mr. F.R. McLaren Frederick McLaren Environmental Engineering Inc.
2208-29th Street Sacramento, California, 95817 Mr. Robert Mutch Wehran Engineering Corporation 666 E. Main Street' Middletown, New York, 10940 Mr. Michael Noel Technos Incorporated 3333 N.W. 21st Street Miami, Florida, 33142 Mr. Philip Oberlander r
Battelle Northwest
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P.O. Box 999 Richland, Washington, 99352 Mr. Timothy O'Donnell Stone and Webster Engineering Corp.
P.O. Box 5200 Cherry Hill, New Jersey 08034
' Mr. John Ogle IBM Corporation, Department 559/002 Box 121295 Research Triangle Park, North Carolina, 27709 Ms. Nancy Finlay Sandia National Laboratories Albuquerque, New Mexico, 87185 Mr. Marvin Piwoni R.S. Kerr Environmental Research Laboratory U.S. Environmental Protection Agency P.O. Box 1198 Ada, Oklahoma, 74820 Mr. Greg Powers
-Ontario Ministry of the Environment (E5 985 Adelaide Street South j
London, Ontario N6E IV3 e
Mr. Graham Rawlings
(
Golder Associates 224 West 8th Ave.
Vancouver, B.C.
V5Y IN5 Mr. George Reeves AECL Whiteshell Nuclear Research Establishment Pinaw, Manitoba ROE ILO Mr. Greg Richardson Soil and Material Engineers 3109 Spring Forest Road Raleigh, North Carolina, 27604 Ms. Anne Russell Harding Lawson A es CANCELLED P.O. Bo o, California, 94947 Dr. Marwan Sadat New Jersey Department Environmental Protection Division Waste Management Site Mitigation Administration CN-028,
(
Trenton, New Jersey, 08625
' Ms. Paula Schmittdiel Wyoming Department of Environmental Ouality Land Ouality Division 401 West 19th Street Cheyenne,'dyoming,82002 Mr. Jeffrey Sgambat Geraghty and Miller Inc.
844 West Street Annapolis, Maryland, 21401
' Mr. Jim Shult2 Dames & Moore 6 Connerce Drive Cranford, New Jersey, 07016 Mr. Steven Sneider
'Battelle Northwest P.O. Box 999 Richland, Washington, 99352 Mr. William Thacker NCAS1 Western Michigan University
(
Kalamazoo, Michigan, 49008
..*w.w.m 1
Mr. Greg Welter
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O'Briern and Gere Engineers 8201 Corporate Drive, #1120 Landover, Maryland, 20785 Mr. Wesseling Delft Hydraulics Laboratories P.O. Box 152 8300 AD Entneloord, The Netherlands
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W WATER RESOURCES RESEARCH, VOL 17. NO. 3. PAGES 555-564. JUNE 1981 Contaminant Transport in Fractured Porous Media:
g Analytical Solution for a Single Fracture D. H. TANG' Pnneeton Unnerstry. Pnnceton, New Jersey 08k0 E. O. FRIND AND E. A. SUDICKY U*A'ersxty of Waterloo. Waterloo. Ontario. Canada N2L 3GI A general analyucal soluuon is developed for the problem of contammant transport along a discrete fracture in a porous rock mitnx. The sol:ation takes mio account advecuve transpon in the fracture, ion-gitudinal mecharucal dupersion in ihe fracture. molecular ddusion an the fracture fluid along the frac-ture axis, molecular difusaoa from the fracture into the matnx. adsorpuon onto the face of th adsorpuon within the matnx, and radioacuve decay. Certain assurnprions are made which allow the e matnx, problem to be formulated as two coupled, one-dimensional panial dderenual equauons: one for the fracture and one for the porous matnx in a direcuon perpendicular to the fracture. The soluuon takes the form of an integral which is eva!usted by Gaussian quadrature for each point sa space and ume. The general soluuon is compared to a sampler soluuon which assumes negligible longitudarial dispersion in the fracture. The companson shows that in the tower ranges of groundwater velocines this assumpuon may lead to considerable error. Another companson between the general solution and a numencal solu-tion shows excellent agreement under condtuons of large difusive loss. Since these are also the condi tions under wluch thz formulation of the general soluuon in two orthogonal direcuons is most subject to-quesuon. the resuhs are strongly supporuve of the validaty of the formulation.
INTRODtJCTION tant attenuation mechanism exists in the forto of molecular It is now widely recognized that fractures can play an im*
difusion into the solid matrix [Goluber and Ganbyants,1971].
portant role in the transport of a contaminant m a groundwa-This mechanism acts to reduce contaminant concentrations in
(_
ter system. Because the permeability of a fracture netwod is the fracture and thereby delays the migration of the con-
, onen substantially greater than the permeability of the wst tami: tant.
rock (see, e.g., Wilson and Ihtherspoon 1970; Nelson and In the case of a radioactive contaminant the migration dis-Handin,1977; Gale.1979], continuous fractures or fracture tance is ftnite because of decay. Disusive loss into the matnx networks have the potential for being highly efective path
- further reduces this finite migration distance. The porous ma-ways for the transport of contaminants.
trix in this case may be viewed as a reservoir which holds the The problem of transport in fractured media arises, for ex-contaminant until decay occurs. Provided the source is con-ample, in the case cf a repository for radioactive waste built stant, the distribution of the radionuclide in the system will into a hard rock formation. Ofprime corcern here will be the reach an equilibrium state. The question ofimmediate interest critical path along which any radionuclide's that may have es-is therefore: How far will the contaminant travel before it caped primary confinement can reach the biosphere. This ent-comes to equilibrium, and how long wid it take?
ical path is likely to follow along fractures or fractum net
- A convenient way to study fracture-matrix transport is works that are located near the repository or that form during within the context of a single fracture. This problem is at pres-ita lifetime. Ahbough the exact location of such fractures may ent receiving considerable attention from researchers. One be unknown, worst case predictions of travel time and of con-very recent paper is by Neretnicks [1980], who developed an centrations likely to occur at entical points can be instructive.
analytical solution for transport in a fracture under the as-The problem also arises in the assessment of the protection sumption that dispersicr and difusion along the fracture are that a fractured squitard can provide to a freshwater aquifer negligible. Another recent work is by Grisak and Pickens against contaminatien from the ground surface or the atmo-
[1980] who used the finite element technique to calculate con-sphere. An interesting example is discussed by Day [lM7] and centrations in both the fracture and the matrix. An advantage Cherry et al [1979). The pnme question in this case is con
- of the numencal approach is that it admits any arbitrary cerned with the level of contamination that can be expected at bounaary condition. A disadvantage is that the eEccts of nu-the bottom of an aquitard if a source of contamination is in' merical dispersion are difficuh to nei troduced at its top.
It s the purpose of this paper (and its sequels) to develop In the absence oflosses a continuous open fracture would general analytical solutions for the problem of contaminant provide a virtually unobstructed travel path for a con-transport in discrete fractures under consideration o.'all dis-taminant, and the protective cEect of either a rock formation persive and difusive processes. These solutions will be useful or a fractured aquitard would be low. Fortunately, an impor-in the determination of penetration distances and response times. They will also be useful in evaluating the accuracy of
' Now at EXXON Producuan Research Company. lfouston. Texas special case solutions as well as numer L
77001.
THE PHYSICAL SYSTEM Copynght C 1981 by the Amencan Geophysical IJnion.
We will consider the case of a thin rigid fracture situated in Paper number 80W1646.
a saturated porous rock (Figure 1). The groundwater velocity 0043 l.'97/81/000W 1646$01.00 333 w
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MATRIX DIFFUSION EFFECTS ON CCNTAMETANT MIGRATION FRCM AN DiJECTION WELL Di EiACTURED SANDSTCNE l
StanFeenstrg J.A. Cherry 3
E.A.Sudicpy 7.ia Haq
%s 1.
Golder Associates, 3151 Wharton Way, Mississauga, Cntario, LtX 226 2.
Departnent of Earth Sciences, University of Water 10c, Waterloo, Ontario, N2L 301 an>3 Associated Censultant, Golder Associates 3
Departnent of Earth Sciences, University of Waterleo, Wa:erico, Ontario, N2L 3G1 4.
Geology Department, University of Western Ontario, Londen, Cataric, 7
N6A 3K7 To be submitted to GROUND WATER B
May, 1983 h
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AESTRACT During the final stage of dewatering of an open-pit uranium mine in a sandstone region in northern Saskatchewan, there is a possibility that a portion of the groundwater recoved by the dewatering wells areund the pit could beccme centaminated by the oxidation of uranium and arsenic minerals in the orebody.
If this occurs, it would be necessary to provide for the treatment or disposal of the contaminated discharge frem the wells. Deep-well injection of the contaminated water into fractured sandstone is a disposal option. As part of the assessment of potential contaminant migration frem deep well injection, the effect of matrix diffusion was evaluated.
An analytical mathematical model was developed fer the simulation of the radial movement of a contaminant front away from an injection point under steady flow conditions in a planar fracture with uniform properties.
The model includes the effects of advection in the fracture, diffusion of contaminants frem the fracture into the rock matrix and equilibrium adsorption on the fracture surface as well as in the rock matrix.
Effective diffusien coefficients obtained from laboratory experiments on 11 intact core sa=ples varied fren 3.4 x 10 4
2 to 32 x 10 cm /s, which is a narrow range in ecmparisen to the considerable differences in texture and degree of induratien of the samples. Model simulations were made with diffusion coefficient values in this range and with single-fracture injection rates. esti=ated fren
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fracture frequencies in tereholes, and frc= bulk hydraulic conductivity values obtained frem field tests. Because of matrix diffusion, the rate of outward movement of the front of the non-reactive contaminants frem the injection well is =uch slewer than the rate of water flow in the fractures.
After a simulation of one year the relative difference between the position of the centaminant front and the pcsition of the front of the injected fluid was found not to vary with the flow rate.
Simulations of the movement of contaminants that undergo adsorption indicates that even a small distribution coefficient for the rock matrix 1
causes the centaminants to remain very close to the injection well during the one-year period.
The results of this investigation are favorable to the concept of short-term disposal of contaminated water in the sandstone; however, in order to make a definitive assessment of the capability of matrix diffusion and associated matrix adsception to strengly limit the extent of contaminant migration around injection wells, it would be necessary to cenduct field tests such as a preliminary or experimental injection. Although uncertainty persists at present because of the lack of account for the effects of variable fracture apertures and of the spatial distribution of fracture and their interconnectivity, the results of the simplified model demonstrates that matrix diffusien is an important process that cannot be neglected in the I
assessment of a waste disposal scheme located in fractured poreus rock.
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WATER RESOURCES RESEARCH. VOL.18. NO. 6. PAGES 1634-1642. DECEMBER 1982
(
ContaIninant Transport in Fractured Porous Media:
Analytical Solutions for a Systern of Parallel Fractures E. A. SuoicKY AND E. O. Fa:No Department of Earth Sciences. University of Waterloo. Waterloo. Ontario N2L 3GI An exact' analytical solution is developed for the problem of transient contammant transport in discrete parallel fractures situated in a porous rock matrix. The solution takes into account advective transport in the fractures, molecular diffusion and mechanical dispersion along the fracture axes, molecular diffusion from the fracture to the porous matrix, adsorption onto the face of the matrix.
adsorption within the matrix and radioactive decay. The general transient solution is in the form of a double integral that is evaluated using Gauss-Legendre quadrature. A transient solution is also presented for the simpler problem that assumes negligible longitudinal dispersion along the fracture.
This assumption is usually reasonable when the advective dux in a fracture is large. A comparison between two steady state solutions, one with dispersion and one without, permits a criterion to be developed that is useful for assessing the significance oflongitudinal dispersion in terms of the overall system response. Examples of the solutions demonstrate that penetration distances along fractures can be substantially larger through multiple, c!csely spaced fractures than through a sing!c fracture because of the limited capability of the finite matrit to store solute.
INTRODUCTION saturated porous rock. The results presented by Barker are, ne transport of contaminants in fractured porous rock is however, cbtained by numerical inversion of the Laplace an important phenomenon that arises in connection with transform rather than by analytical inversion. Another paper many contemporary groundwater pollution problems. As is by Rasmason and Neretnicks [1981), who present a one-open fractures generally offer the path of least hydraulic dimensional solution for transport in fracted media cm-resistance, direct transport of a contanunant entering a sisting of porous blocks separated by Sssures. In their fractured rock system will be primarily along the fractures. solution, the porous blocks are represented by spheres that
. (
Transport through the rock matrix by advection is usually have a Anite capacity to store a contammant, but they are negligible in comparison because of the relatively low hy-small enough to avoid disturbance of the one-dimensional draulic conductivity of the rock itself.
macroscopic average How held. In an earher paper, Nerer -
Molecular diffusion from the fractures into the porous nicks [1980] presents a solution for one-dimensional trans-matrtx, however, constitutes an attenuation mechanism that port in a single fracaire in the absence of longitudinal can be highly effective in removing coctaminant mass from dispersion. A numerical study of the problem of transport in the primary flow channels and thus in retarding the advance discrete fractures was done by Grisak and Pickens [1980).
of the contanunant in the system. In the case of a radioactive The wod described in this paper is an extension of our contaminant having a constant source strength, the advance Previous work [ Tang et al.,1980]. We will develop exact will eventually cease if the now path is sufReiently long, and analytical solutions for the case of transport in a system of the distribution of the contaminant in the system will stabi-discrete multiple. parallel fractures, and we will again denne lize because the loss by decay of the mass stored in both the the ultimate penetration of a radioactive contaminant in such fractures and the porous matrix will balance the mass input a system. Because the solutions are based a analytical at the source and that due to decay of parent species.
mversion of the Laplace transform, difficulties associated Matrix diffission thus acts as a dynamic storage mecha-with numerical inversion are avoided.
nis:n within the fracture now system. As a result, contami-nant transport in fractured porous rock can be quite different Tus PHYSICAL SYSTEM from contaminant transport in porous granular media in the We will consider the case of a set of identical fractures on sense, where such a mechanism is not general-whose axes are parallel and equally spaced (Figure 1). The In a previouhaper [ Tang et al.,1981] we investigated the I " **"
8" dynamics of transport in a system consisting of a single Bracture within a porous matrix. Transient as well as steady
.prmat anahsh, transport of a
- I
- state analytical solutions were developed in that paper, and 8"
the ultimate penetration distance of a prescribed level of a "I""*
radioactive contammant along a fracture was denned.
fractm and one half of the mtervening porous matrix. He Other researchers have also addressed this problem. A "8
- 8**""
recent paper by Barker (1982] exanunes transport in a and hydraulic propernes of the system [ Tang et al.,1981].
system of equally spaced fractures separated by slabs of
- 1. The width of each fracture is much smaller than its Copynght 1982 by the American Geophysical Union.
l
- 2. Transverse diffusion and dispersion within each frac.
Paper number 2W1437, ture assures complete mixing across its width at all times.
00431397/82/002W.1437505.00
- 3. De permeabdity of the intervening porous matrix is 1634
.,,u
- -