Transient Processes in Multiple Scale Heterogeneous Porous Formations
Dr.ir. Amro M. M. Elfeki
Faculty of Civil Engineering and Geosciences, Section Hydrology and Ecology
(on leave from Civil Engineering Dept., Faculty of Engineering, Mansoura University, Egypt)
The objective of this research is to study the influence of multiple scale variability in time and space on transport mechanisms in subsurface structures. The study will focus on extension of models which have been developed by Elfeki et al. since 1996. These models were mainly looking to a single time scale of the groundwater flow process, while considered various spatial scales. So, in the current research project the study will address the time scales extensively and link both the spatial and temporal variability in an integrated framework.
Introduction
Flow and transport processes in natural formations are complex by the coupling of the aquifer heterogeneity that manifests itself at multitude of spatial scales with geochemical reactions and biochemical transformations that take place at various time scales. Adequate representation of these processes with simulation models requires the use of a plausible characterization of the aquifer heterogeneity at the significant scales of variability, appropriate governing equations, parameter representations, and efficient numerical techniques. In this project we are planning to address various aspects of coupling space and time variabilities in flow and transport in porous formations.
This research project started in April, 2001.
Results in 2001
Identification of Large-Scale Spatial Variability by Coupled Markov Chain (CMC) Model:
Numerical simulations of solute transport are performed in a highly heterogeneous field with a complex geological configuration at the Macrodispersion Experiment (MADE1) site, Columbus Air Force Base in northern Mississippi, USA. The purpose of these simulations is two fold. The first is to illustrate how the coupled Markov chain model (CMC), developed by Elfeki and Dekking [2001], can be applied to delineate the complex geometrical configuration (identification of large-scale trends) at the site. The second is to show how reliable this model is for predicting plume behaviour in a highly heterogeneous subsurface. Although we adopted some assumptions like two-dimensional steady flow in confined aquifers, the results are quit satisfactory. The results emphasized that delineation of the geometrical configuration of the aquifer heterogeneity is the key to obtain accurate prediction of plume evolution in heterogeneous formations. The coupled Markov model is a powerful tool to characterize formation heterogeneity. Some results of this study are presented in Figure 1.
Figure 1: Comparison between numerical flow and transport simulations conditioned on number of boreholes. Right most column is the field data (from Adams and Gelhar [1992]). Left most column is a geological simulation of the aquifer conditioned on 6 boreholes with the corresponding plume evolution at 49, 279 and 594 days respectively. Second and third columns from the left side are similar to left most column but conditioned on 9 and 16 boreholes respectively. The concentration scale is in (mg/L).
Time Scale Variability:
Unsteady groundwater flow model in confined heterogeneous aquifer has been developed to study the influence of transient conditions of groundwater flow behaviour at multiple time scales. In this model, the influence of water level fluctuations in a river, that is feeding an aquifer, (which can be seasonal, daily or even hourly variations) on the hydraulic heads in the aquifer is considered. Figure 2 shows some preliminary calculations which have been performed by the model. The model needs to be verified for analytical solutions under simplified cases. Figure 2 shows the excitation on the river side in a form of two-scale temporal variability (in green). The aquifer response shows smooth out of the fine-scale temporal variability (in black). This needs further investigations with different degrees of temporal variability and different aquifer damping factors.
Figure 2: Aquifer response due to two-scale random excitation on the right aquifer boundary. Green line is the water fluctuations in the river (right boundary) and the black line is the groundwater head response at a point in the middle of the aquifer in a homogeneous isotropic aquifer.
Presentations and poster presentations in 2001
Elfeki, A.M.M.; Transient processes in multiple scale heterogeneous porous formations. Presentation on first meeting on DIOC “Water” mini-symposium on 7th June, 2001. Sport centre, TUDelft, The Netherlands.
Elfeki, A.M.M. Multi-Scale and Multi-Resolution Stochastic Modelling of Subsurface Heterogeneity by Tree-indexed Markov Chains. Presentation on the 20th colloquium on Recent Advances in Hydrology, May 21, 2001 in Room 0.96, Faculty of Civil Engineering and Geosciences, Stevinweg 1, Delft, The Nethelands.
Elfeki, A.M.M., Dekking, F.M., Kraaikamp, C. & Bruining, J. Influence of Fine-Scale Heterogeneity Patterns on Large-Scale Behaviour of Miscible Transport in Porous Media. Poster Presentation on second meeting on DIOC “Water” mini-symposium on 20th December, 2001. Civil Engineering Building, Faculty of Civil Engineering and Geosciences, TUDelft, The Netherlands.
Elfeki, A.M.M. and Rajabiani, H.R. Simulation of Plume Behavior at the Macrodispersion Experiment (MADE1) Site by Applying the Coupled Markov Chain Model for Site Characterization. Poster Presentation on second meeting on DIOC “Water” mini-symposium on 20th December, 2001. Civil Engineering Building, Faculty of Civil Engineering and Geosciences, TU Delft, The Netherlands.
Research plan for 2002
Working on a proposal for extension of the coupled Markov chain model to three-dimensions. It is submitted to NWO for a post-doc position.
Attracting some MSc students to work in some aspects of the project and integrate the final results.
Writing scientific publications.
Publications in 2001
Elfeki, A.M.M., F.M. Dekking; (2001) A Markov chain model for subsurface characterization: theory and applications. Mathematical Geology, Vol. 33, No. 5, pp.569-589.
Elfeki, A.M.M.; (2001) Analysis and numerical simulation of single-well tracer test in homogeneous, layered and slightly tilted formations. Mansoura University Engineering Journal (MEJ), Vol.25, pp. c14-c27.
MSc. Supervision
Rajabiani, H.R.; Characterization of subsurface heterogeneity from boreholes with coupled Markov chain for groundwater transport. MSc. at Section Hydrology and Ecology, TU Delft, Delft, The Netherlands, November 2001.