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Heterogeneity-Induced Channelling, Flow-Wetted Surface, and Modelling of Transport in Fractured Rock
Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, LUVAL.
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Heterogeneities in fractured rock are found at all scales; from the scale of individual fractures, to the scale of fracture networks, and to the largest regional scales. These heterogeneities cause challenges for modelling and parameter estimation of flow and solute transport. The heterogeneities in fracture aperture, characterization of the flow channelling they are causing, and implementation of this information into numerical simulation models of the solute transport in fractured media are the subjects of this thesis.

Aperture variability within a fracture causes the flow channelling, where the water flow is focused in a few channels and other areas of the fracture have practically stagnant water. The flow-wetted surface is the area where the flowing water is in contact to the fracture area. Contaminants are transported with the flowing water and therefore the flow-wetted surface is an important parameter that influences the diffusion into the rock matrix and sorption to the fracture rock surface. The specific flow-wetted surface (sFWS) is the flow-wetted surface divided by the total fracture area. The sFWS is systematically analyzed for different fracture aperture distribution characteristics. The local aperture is linked to the local hydraulic conductivity K. Increasing standard deviation of the hydraulic conductivity K field (σln K) leads to decreased sFWS. The sFWS is found to be independent of the correlation length (λ) of the field. An empirical relationship is developed, which describes the sFWS as a function of the σln K. A method is also introduced to determine this key parameter by analysis of the breakthrough curve from a single-well injection-withdrawal (SWIW) test. Further, an approach is presented to incorporate the effect of fracture level heterogeneity into fracture network models and to analyze the effect on sorption and matrix diffusion, by including the sFWS parameter into the transport calculations. The results show that the median transport time is proportional to the square of the sFWS-value. The results also suggest that there are an averaging behaviour in the fracture network, the sFWS-value of each individual fracture is not important for the transport over the domain, but a mean-value can be utilized in the numerical model.

Abstract [sv]

Heterogeniteter i sprickigt berg finns i alla skalor, från millimeterskala till en skala på hundratals kilometer. Dessa heterogeniteter orsakar problem vid beräkning av vattenflöde och ämnestransport. Aperturen i en spricka är öppningen mellan de två omslutande bergsidorna, den varierar både inom och mellan olika sprickor. Ämnet för denna avhandling är heterogeniteter i aperturerna inom enskilda sprickor, karaktärisering av den flödeskanalisering som uppstår på grund av dessa heterogeniteter och hur man kan använda denna information till en numerisk modell.Variabilitet av aperturen i en enskild spricka gör att vattenflödet blir fokuserat i ett fåtal kanaler, medan andra områden av sprickan kan ha praktiskt taget stillastående vatten. Den flödesvätta ytan är det område där det strömmande vattnet kommer i kontakt med sprickytan. Den flödesvätta ytan som påverkar diffusionen in i bergmatrisen och sorptionen till sprickytan är en viktig parameter eftersom föroreningar transporteras med det strömmande vattnet. Den specifika flödesvätta ytan (sFWS) är den flödesvätta ytan dividerad med den totala sprickarean. I avhandlingen analyserades sFWS systematiskt för olika statistik över sprickaperturen. Den lokala aperturen är kopplad till den lokala hydrauliska konduktiviteten K. En ökad standardavvikelse för det hydrauliska konduktivitetsfältet (σln K) ledde till minskad sFWS. sFWS visades vara oberoende av konduktivitetsfältets korrelationslängd (λ). En empirisk relation utvecklades som beskriver sFWS som en funktion av σln K. Ett SWIW-test är en typ av spårämnesförsök, där ett spårämne injiceras i en brunn följt av vatten i en bestämd tidsperiod, innan flödet vänds och en genombrottskurva registreras. Testet används traditionellt för att bestämma bergets diffusions- och sorptionsegenskaper. En metod presenterades för att bestämma den specifika flödesvätta ytan genom analys av genombrottskurvan för ett SWIW-test. Ett tillvägagångssätt introducerades för att analysera effekterna av sorption och matrisdiffusion i heterogena sprickor i en spricknätverksmodell genom att inkludera sFWS-parametern i transportberäkningar. Resultaten visade att medianvärdet för transporttiden är proportionell mot kvadraten på sFWS-värdet. Resultaten visade också att transporten genom spricknätverket inte är beroende av sFWS-värdet i de individuella sprickorna, utan att medelvärdet kan användas för modellering.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2012. , 76 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 971
Keyword [en]
channelling, flow-wetted surface, fractured rock, solute transport, groundwater modelling, groundwater
National Category
Oceanography, Hydrology, Water Resources
Research subject
Hydrology
Identifiers
URN: urn:nbn:se:uu:diva-180409ISBN: 978-91-554-8468-2 (print)OAI: oai:DiVA.org:uu-180409DiVA: diva2:550305
Public defence
2012-10-19, Hambergsalen, Geocentrum, Uppsala Universitet, Villavägen 16, 75236 Uppsala, Uppsala, 13:00 (English)
Opponent
Supervisors
Funder
Formas, 245-2006-1152
Available from: 2012-09-28 Created: 2012-09-06 Last updated: 2013-01-23
List of papers
1. A study of flow-wetted surface area in a single fracture as a function of its hydraulic conductivity distribution
Open this publication in new window or tab >>A study of flow-wetted surface area in a single fracture as a function of its hydraulic conductivity distribution
2012 (English)In: Water resources research, ISSN 0043-1397, E-ISSN 1944-7973, Vol. 48, W01508- p.Article in journal (Refereed) Published
Abstract [en]

The contact area between flowing water and rock-the flow-wetted surface (FWS)-is a main factor controlling the rock-matrix diffusion and sorption of flowing solute in a rock fracture. Flow channeling, therefore, has a strong effect on the retardation of mass transport due to the resulting lower contact area. This work presents a systematic study of the dependency between fracture aperture statistics and FWS in strongly heterogeneous fractures. Particle tracking is used to determine the transversal width of the particle flow lines, FWS, and beta factor, where beta is a variable that has been proposed as controlling tracer retention. The conductivity distribution over the fracture is assumed to be lognormal with standard deviation (sigma(ln) (K)) ranging from 0.23 to 4.61, with correlation lengths from 2% to 18% of the width of the flow domain. Results show a clear dependency between the specific flow-wetted surface (sFWS), defined as FWS divided by the total fracture area, and the standard deviation of the logarithm of fracture conductivity. The behavior is independent of the correlation length for the range of correlation lengths tested. The results are presented in the form of type curves and an empirical equation that provide a simple way to determine the sFWS as a function of sigma(ln) (K). This information can then be used to adjust the results of large-scale fracture network simulations by taking into account the effect of single fracture heterogeneity, an effect that is in practice infeasible to directly take into account in large-scale fracture network simulations.

National Category
Earth and Related Environmental Sciences
Identifiers
urn:nbn:se:uu:diva-168587 (URN)10.1029/2011WR010686 (DOI)000299183100002 ()
Available from: 2012-02-14 Created: 2012-02-13 Last updated: 2017-12-07Bibliographically approved
2. An observed error in PMPATH particle tracking algorithm for MODFLOW in case of varying porosity and a proposed correction
Open this publication in new window or tab >>An observed error in PMPATH particle tracking algorithm for MODFLOW in case of varying porosity and a proposed correction
2012 (English)In: Computers & Geosciences, ISSN 0098-3004, E-ISSN 1873-7803, Vol. 45, 1-3 p.Article in journal (Refereed) Published
Abstract [en]

MODFLOW (Harbaugh and McDonald, 1996) is a code widely used for groundwater modeling. It has been used for numerous projects and thousands of articles have been published with results of MODFLOW, since the code was first released in 1983. Numerous codes have been developed around MODFLOW, the pre- and post processing code Processing MODFLOW (Chiang, 2005) being one example. This code includes the advective particle tracking code PMPATH (Chiang, 2005), especially convenient and commonly used for stochastic groundwater modeling analyses as it includes an easy-to-use random field generator. The particle tracking code has been regularly used to simulate the advective transport of contaminants and tracers (e.g. Stauffer, 2005; Hefting et al., 2006; Dhiman and Keshari, 2006).

A suspected error in the PMPATH code was found by us, when studying flow and particle transport in a strongly heterogeneous hydraulic conductivity fields with co-varying porosity. It emerged in the form of calculated particle flow paths converging into narrower and narrower channels. After many attempts to understand the results turned out to be unsuccessful, we decided to check into details of the code and discovered a significant but non-obvious error. This error is discussed in this paper and a procedure to obtain the correct flow paths and travel times is proposed. 

Place, publisher, year, edition, pages
Elsevier, 2012
Keyword
PMPATH, MODFLOW, Particle tracking, Groundwater, Solute transport, Channeling
National Category
Oceanography, Hydrology, Water Resources
Research subject
Hydrology
Identifiers
urn:nbn:se:uu:diva-180406 (URN)10.1016/j.cageo.2012.03.001 (DOI)000306771100001 ()
Funder
Formas, 245-2006-1152
Available from: 2012-09-06 Created: 2012-09-06 Last updated: 2017-12-07Bibliographically approved
3. A new approach to account for fracture aperture variability when modeling solute transport in fracture networks
Open this publication in new window or tab >>A new approach to account for fracture aperture variability when modeling solute transport in fracture networks
Show others...
2013 (English)In: Water resources research, ISSN 0043-1397, E-ISSN 1944-7973, Vol. 49, no 4, 2241-2252 p.Article in journal (Refereed) Published
Abstract [en]

A simple yet effective method is presented to include the effects of fracture aperture variability into the modeling of solute transport in fracture networks with matrix diffusion and linear sorption. Variable apertures cause different degrees of flow channeling, which in turn influence the contact area available for these retarding processes. Our approach is based on the concept of specific flow-wetted surface (sFWS), which is the fraction of the contact area over the total fracture surface area. Larsson et al. [2012] studied the relationship between sFWS and the standard deviation σln K  of the conductivity distribution over the fracture plane. Here an approach is presented to incorporate this into a fracture network model. With this model, solute transport through fracture networks is then analyzed. The cases of sFWS=0 and sFWS=1 correspond to those of no matrix diffusion and full matrix diffusion respectively. In between, a sFWS break point value can be defined, above which the median solute arrival time is proportional to the square of sFWS. For values below the critical sFWS (more channeled cases), the change is much slower, converging to that of no matrix diffusion. Results also indicate that details of assigning sFWS values for individual fractures in a network are not crucial; results of tracer transport are essentially identical to a case where all fractures have the mean σln K (or corresponding mean sFWS) value. This is obviously due to the averaging effect of the network.

Keyword
flow channeling, groundwater transport, fracture networks, flow-wetted surface
National Category
Oceanography, Hydrology, Water Resources
Research subject
Hydrology
Identifiers
urn:nbn:se:uu:diva-180407 (URN)10.1002/wrcr.20130 (DOI)000319282100035 ()
Funder
Formas, 245-2006-1152
Available from: 2012-09-06 Created: 2012-09-06 Last updated: 2017-12-07Bibliographically approved
4. Understanding the effect of single fracture heterogeneity from single well injection withdrawal (SWIW) tests
Open this publication in new window or tab >>Understanding the effect of single fracture heterogeneity from single well injection withdrawal (SWIW) tests
2013 (English)In: Hydrogeology Journal, ISSN 1431-2174, E-ISSN 1435-0157, Vol. 21, no 8, 1691-1700 p.Article in journal (Refereed) Published
Abstract [en]

The single well injection withdrawal (SWIW) tracer test on a fracture or fracture zone is a method used to estimate its tracer retardation properties.  In this study, the effects of single fracture aperture heterogeneity on SWIW test tracer breakthrough curves are examined by numerical modelling. The effects of the matrix diffusion and sorption is accounted for by using a particle tracking method through the addition of a time delay added to the advective transport time. For a given diffusion and sorption property value (Pm) and for a heterogeneous fracture, the peak concentration is larger compared to a homogeneous fracture. The cumulative breakthrough curve for a heterogeneous fracture is similar to that for a homogeneous fracture and a less sorptive/diffusive tracer. It is demonstrated that the fracture area that meets the flowing water, the so-called specific flow-wetted surface (sFWS) of the fracture, can be determined by comparing the observed breakthrough curve for a heterogeneous fracture with that for a homogeneous fracture. SWIW tests are also simulated with a regional pressure gradient present. The results point to the possibility of distinguishing the effect of the regional pressure gradient from that of diffusion through the use of multiple tracers with different Pm-values. 

Place, publisher, year, edition, pages
New York: Springer-Verlag New York, 2013
Keyword
tracer test, SWIW test, flow channelling, flow-wetted surface, fractured rock, aperture heterogeneity
National Category
Oceanography, Hydrology, Water Resources
Research subject
Hydrology
Identifiers
urn:nbn:se:uu:diva-180408 (URN)10.1007/s10040-013-0988-x (DOI)000327391000002 ()
Funder
Formas, 245-2006-1152
Available from: 2012-09-06 Created: 2012-09-06 Last updated: 2017-12-07Bibliographically approved

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