We simulate tracer transport in a two-dimensional porous medium. We provide justification for the use of a fractal scaling law to characterize the spatial variability of rock properties, leading to a fractal rock property model. A methodology based on the fractal model discussed is applied to experimental data to generate a "fracta! porous medium" and to solve the associated flow and tracer transport problems. Tracer breakthrough curves are computed for three different breakthrough distances. An advection-dispersion matrix diffusion model, a channeling model, and a channel-network model are used to assess objectively the relative contributions of Fickian dispersal processes and channeling within simulated tracer transport through the fractal medium. The results reveal early breakthrough is fast-channel dominated, while later breakthrough is predominately Fickian. 4077 Thames, England, April 1992c. Hewett, T. A., Fractal distributions of reservoir heterogeneity and their influence on fluid transport, paper presented at 61st AnnualConference and Exhibition, Soc. of Pet. Eng., New Orleans, La., 1988.Marsily, G. de, Quantitative Hydrology, Academic, San Diego, Calif., 1986. Neretnieks, I., A note on fracture flow dispersion mechanisms in the ground, Water Resour.

Analytical and numerical techniques of bifurcation theory are used to study the influence of aspect ratio and the effects of a (small) sidewall heat transfer on steady two-dimensional free convection in a saturated porous cavity heated from below. The dependence of the bifurcation structure on the Fourier decomposition of the sidewall heat flux is demonstrated using weakly nonlinear analysis and symmetry arguments, and confirmed by singularity theory applied to the bifurcation equations derived by Liapunov-Schmidt reduction. The existence of explicit eigenfunctions and the ( Z , X Z,) equivariance of the governing equations for the perfect problem (no sidewall heat transfer) are exploited in the application of these methods. A numerical study using the finite element approximation in conjunction with bifurcation and continuation methods is carried out to complement the analytical attack and extend the work to fully nonlinear regimes. State diagrams and visualisations are presented for flows in a square cavity with various modes of imperfection.The study shows how the changes in alternative convective flows for different aspect ratios and imperfections can be determined systematically by analytical and numerical bifurcation techniques. As an example, the evolution of the bifurcation structure is predicted as the strength of the sidewall heating increases, and an abrupt transition of preferred mode from uni-to bicellular flow is demonstrated for a square cavity.

Techniques of bifurcation theory are used to analyze the possible forms of steady, two-dimensional, buoyancy-driven flow present during the vertical directional solidification of a dilute binary mixture. Morphological instabilities of the crystal–melt interface are ignored and the interface is assumed to be planar. The focus of the study concerns the effect of lateral confinement on the flow patterns observable in this simple model system. The use of a time-dependent numerical scheme by McFadden and Coriell [Proceedings of the First National Fluid Dynamics Congress, Cincinnati (AIAA, Washington, DC, 1988), p. 1572] to investigate this same problem resulted in gaps in the bifurcation structure, because unstable steady states exist that cannot be computed by their method. The present work extends and completes the description of the possible steady states. In particular, the complex modal exchanges that occur as the separation between the lateral walls varies are elucidated, and stable flow regimes and the sensitivity of the results to the closure condition at the upper boundary are determined.

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Bias is a difference between model and reality. Bias can be introduced at any stage of the modelling process during a site characterisation or performance assessment programme. It is desirable to understand such bias so as to be able to optimally design and interpret a site characterisation programme. The objective of this study was to examine the source and effect of bias due to the assumptions modellers have to make because reality cannot be fully characterised in the prediction of ground-water fluxes. A well-defined synthetic “reality” was therefore constructed for this study. A limited subset of these data were independently interpreted and used to compute groundwater fluxes across specified boundaries in a cross section. The modelling results were compared to the “true” solutions derived using the full dataset. This study clarified and identified the large number of assumptions and judgements which have to be made when modelling a limited site characterisation dataset. It is concluded that bias is introduced at each modelling stage, and that it is not necessarily detectable by the modellers even if multiple runs with varied parameter values are undertaken.