Embedded regional/Local-scale model of natural transients in saline groundwater flow. Illustrated using the Beberg Site

The main focus of this report is to develop and test a methodology for performing large simulations of transient variable density flow. Several developments were made to NAMMU to enable such calculations. The following lists the findings of this study: 1) Feasibility: it is numerically feasible to construct large (0.5 million elements) embedded models of transient variable density flow with a relatively fine mesh (about 35m) of the site-scale. 2) Stochastic simulation: performing stochastic realisations of long transients is just possible, although the requirements on CPU and disk to store the results for 100 realisations, say, would be significant. As an indication, about 19 realisations of the current model could be run on a Sun Enterprise 450 (4 x UltraSPARC-II 400MHz) computer in one week if all four processors are fully utilised. 3) Embedded grid: the nesting of a refined site-scale model (35m elements) within a coarser (100m) regional-scale mesh for variable density flow was tested successfully. It was found that grading the refinement around the site-scale to avoid a large step change in element size was beneficial for convergence and stability. This may be less of an issue if a more sophisticated pre conditioner was used. 4) Solver: the most efficient and stable scheme was obtained by decoupling the flow and transport equation at each time-step. GMRES (Generalised Minimum Residual) was the most robust conjugate gradient method for this problem. 5) Boundary conditions: a set of relatively complex non-linear boundary conditions had to be applied for both pressure and salinity on the top and vertical boundaries to give the system sufficient freedom to approximate realistic conditions over a large area and long times. It was important that both flow and a flux of salinity could cross each boundary, and that the direction and magnitude could evolve in time. 6) Calibration on salinity: model predictions of the salinity in the deep boreholes were used to calibrate the model parameters and structural representation. As for the SR 97 regional-scale model the high salinity below Zone 2 could not be reproduced with a highly transmissive zone. A reasonable match could only be achieved if a semi-impermeable band be included in the core of Zone 2, and the position of Zone 2 had to be taken from the detailed geometry defined in Andersson et al. rather than SR 97. 7) Structural model: the calibration demonstrated the important effect that sub-horizontal fracture zones could have on deep groundwater flows, and the importance of having a good structural interpretation of such zones. Aspects such as hydraulic anisotropy, layering, fracture zone truncation and interconnection will be important to characterise in any site either by direct measurement and/or by using modelling to test the ability of different structural models to predict hydraulic and chemical properties in deep boreholes. In fact, this is a good example of how a flow model calibration exercise can augment structural interpretation and help constrain it. 8) Flexible representation: new tools for representing fracture zones and rock volumes allow flexibility in how a structural model is represented e.g. wedge shaped zones and hydraulic anisotropy. 9) Modelling barriers: proved to be non-trivial since approximating the thickness or representation of flow through a thin barrier relative to the grid size can lead to an over-prediction of flow rates through barriers. For standard elements, if only a thin band of elements, one or two thick, is used to model a semi-impermeable barrier, then the flow across the zone may be larger than expected. This is because small flows can 'leak' across element corners because of the lack of localised mass balance. This is not the case with mixed-elements, which motivates more investigation of this element type. 10) Transport statistics: indicate that neither salinity nor release-time has a great effect on statistics of travel times or canister flux. Salinity leads to slightly higher canister flux, but slightly longer travel times and around double the path lengths. Perhaps more important is the structural model for Zone 2. A low permeability core in Zone 2, as used in Case 3-5, leads to slightly longer median travel time, but also much less variance with fewer short paths compared to Case 1 which used the SR 97 representation of Zone 2. These conclusions are very site specific. The Beberg site is located about 15km inland, and hence conclusions on the importance of release time are likely to be different to those for a site nearer the coast. 11) Comparison with previous studies: many of the conclusions from the SR 97 regional model have been shown valid for this more detailed study. For example, the same parameters and structural model were needed to get a calibration on deep salinity profiles. Travel times and exit locations are broadly consistent, and the problem with particles exiting the SR 97 model out of the vertical side has been solved by extending the model northwards. The new model shows that the exit location for these paths is Skaelsjoen. Comparing with the site-scale models of SR 97 travel times are much longer here mainly because of not enhancing the permeability of the rock blocks, but also due to salinity and the structural model for Zone 2. Results are most similar to the SR-97 regional model