Modeling flow in fractured medium. Uncertainty analysis with stochastic continuum approach: Dissertation

Auli Niemi

Research output: ThesisDissertationMonograph


For modeling groundwater flow in formation-scale fractured media, no general method exists for scaling the highly hete- rogeneous hydraulic conductivity data to model parameters. The deterministic approach is limited in representing the heterogeneity of a medium and the application of fracture network models has both conceptual and practical limitations as far as site-scale studies are concerned. This study investigates the applicability of stochastic continuum modeling at the scale of data support. No scaling of the field data is involved, and the original variability is preserved throughout the modeling. Contributions of various aspects to the total uncertainty in the modeling prediction can also be determined with this approach. Data from five crystalline rock sites in Finland are analyzed. The issues considered include stochastic versus deterministic nature of the data, statistical similarities and differences between various data sets, types of theoretical distributions, distribution parameters and their confidence limits, spatial trends and autocorrelation structures, role of measuring equipment detection limit in these analyses, and needs for ergodicity assumptions. A stochastic treatment is applied for data from which significant fracture zones are excluded. With the statistical properties determined, groundwater flow in selected regions is modeled by Monte Carlo simulation to obtain estimates of uncertainties in the flow computations, given the amount and location of hydrological data available. For each problem several hundred permeability realizations are generated, for which the flow equation is solved. Theoretical verification simulations comparing the results with analytically derived expressions demonstrate the insignificant role of numerical inaccuracies. Simulations describing realistic bedrock cross-sections are carried out both with and without spatial correlation. Uncertainty in the head prediction is higher, and more widely spread, when autocorrelation is taken into account. Predicted flow rates through a two-dimensional example cross-section can vary over three orders of magnitude. Conditioning with borehole data in the middle of this section reduces the uncertainty by one order of magnitude. This effect is significant compared to the corresponding reduction achieved by increasing the data base with no regard to the location of this data. The effect of the formula used for interpreting the original well test is also found to be a significant factor in the total analysis.
Original languageEnglish
QualificationDoctor Degree
Awarding Institution
  • Helsinki University of Technology
Award date17 Jun 1994
Place of PublicationEspoo
Print ISBNs951-38-4622-9
Publication statusPublished - 1994
MoE publication typeG4 Doctoral dissertation (monograph)


  • ground water
  • flow
  • models
  • simulation
  • fractures
  • mathematical models
  • numerical methods
  • probability theory
  • analyzing
  • stochastic processes
  • Monte Carlo method
  • numerical analysis
  • computation
  • hydrology
  • permeability
  • crystalline rocks
  • heterogeneity
  • radioactive wastes


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