Dip and anisotropy effects on flow using a vertically skewed model grid

Revisiting MODFLOW's Capability to Model Flow Through Sedimentary Structures

Sedimentary structures have unique geometries and anisotropic hydraulic conductivity, both of which control groundwater flow. Traditional finite-difference simulators (e.g., MODFLOW) have not been able to correctly represent irregular, dipping and anisotropic structures due their use of a simplified conductivity tensor, causing many modelers to turn toward finite-element codes with their sophisticated meshing capabilities. However, the release of MODFLOW 6 with its flexible discretization and multipoint flux approximation scheme prompts us to revisit its capability to compute flow through complex sedimentary structures. Through the use of a novel benchmark and case study, we show that when versions previous to MODFLOW 6 are applied to dipping structures, modeled fluxes and hence flow through the system, can be significantly over or underestimated. For example, effective conductivity for a 30° dipping layer with a 100:1 conductivity ratio is reduced to only 2% of its inputted value. We show that MODFLOW 6, with its XT3D capability and flexible discretization options is far superior to its predecessors, allowing flow through complex sedimentary structures to be simulated more accurately. However, on vertically offset grids, which have been available in all versions of MODFLOW and are often used in practice, loss of accuracy is still a concern when the vertical offset is large, that is, the dip of the sedimentary layer is steep, particularly if the layer is much more conductive than the surrounding material. The hypothesis that vertically offset grids lack sufficient hydraulic connectivity between adjacent model layers to accurately simulate the steeply dipping, highly heterogeneous case is a topic for further investigation.

A new package in MODFLOW to simulate unconfined groundwater flow in sloping aquifers

The nonhorizontal-model-layer (NHML) grid system is more accurate than the horizontal-model-layer grid system to describe groundwater flow in an unconfined sloping aquifer on the basis of MODFLOW-2000. However, the finite-difference scheme of NHML was based on the Dupuit-Forchheimer assumption that the streamlines were horizontal, which was acceptable for slope less than 0.10. In this study, we presented a new finite-difference scheme of NHML based on the Boussinesq assumption and developed a new package SLOPE which was incorporated into MODFLOW-2000 to become the MODFLOW-SP model. The accuracy of MODFLOW-SP was tested against solution of Mac Cormack (1969). The differences between the solutions of MODFLOW-2000 and MODFLOW-SP were nearly negligible when the slope was less than 0.27, and they were noticeable during the transient flow stage and vanished in steady state when the slope increased above 0.27. We established a model considering the vertical flow using COMSOL Multiphysics to test the robustness of constrains used in MODFLOW-SP. The results showed that streamlines quickly became parallel with the aquifer base except in the narrow regions near the boundaries when the initial flow was not parallel to the aquifer base. MODFLOW-SP can be used to predict the hydraulic head of an unconfined aquifer along the profile perpendicular to the aquifer base when the slope was smaller than 0.50. The errors associated with constrains used in MODFLOW-SP were small but noticeable when the slope increased to 0.75, and became significant for the slope of 1.0.

An investigation of numerical grid effects in parameter estimation

Modern ground water characterization and remediation projects routinely require calibration and inverse analysis of large three-dimensional numerical models of complex hydrogeological systems. Hydrogeologic complexity can be prompted by various aquifer characteristics including complicated spatial hydrostratigraphy and aquifer recharge from infiltration through an unsaturated zone. To keep the numerical models computationally efficient, compromises are frequently made in the model development, particularly, about resolution of the computational grid and numerical representation of the governing flow equation. The compromise is required so that the model can be used in calibration, parameter estimation, performance assessment, and analysis of sensitivity and uncertainty in model predictions. However, grid properties and resolution as well as applied computational schemes can have large effects on forward-model predictions and on inverse parameter estimates. We investigate these effects for a series of one- and two-dimensional synthetic cases representing saturated and variably saturated flow problems. We show that "conformable" grids, despite neglecting terms in the numerical formulation, can lead to accurate solutions of problems with complex hydrostratigraphy. Our analysis also demonstrates that, despite slower computer run times and higher memory requirements for a given problem size, the control volume finite-element method showed an advantage over finite-difference techniques in accuracy of parameter estimation for a given grid resolution for most of the test problems.