Modeling Dewatered Domains in Multilayer Analytic Element Models

This proposed technique allows sensible and numerically stable behavior in multilayer analytic element models when layers dewater. When saturated thickness approaches zero in an unconfined or fresh/salt interface domain, the domain transitions to a very thin confined domain with a minimum saturated thickness M. M is an adjustable input parameter, so you can make the horizontal flow in dewatered domains negligibly small by making the minimum saturated thickness very small. Vertical flows can pass through a dewatered domain, whether it is near the surface or at depth. For example, recharge may pass through a shallow dewatered layer to a deeper layer that is not dewatered. This approach is examined in detail in an example multilayer model of mine dewatering.     

A Hybrid Finite-Difference and Analytic Element Groundwater Model

Regional finite-difference models tend to have large cell sizes, often on the order of 1–2 km on a side. Although the regional flow patterns in deeper formations may be adequately represented by such a model, the intricate surface water and groundwater interactions in the shallower layers are not. Several stream reaches and nearby wells may occur in a single cell, precluding any meaningful modeling of the surface water and groundwater interactions between the individual features. We propose to replace the upper MODFLOW layer or layers, in which the surface water and groundwater interactions occur, by an analytic element model (GFLOW) that does not employ a model grid; instead, it represents wells and surface waters directly by the use of point-sinks and line-sinks. For many practical cases it suffices to provide GFLOW with the vertical leakage rates calculated in the original coarse MODFLOW model in order to obtain a good representation of surface water and groundwater interactions. However, when the combined transmissivities in the deeper (MODFLOW) layers dominate, the accuracy of the GFLOW solution diminishes. For those cases, an iterative coupling procedure, whereby the leakages between the GFLOW and MODFLOW model are updated, appreciably improves the overall solution, albeit at considerable computational cost. The coupled GFLOW–MODFLOW model is applicable to relatively large areas, in many cases to the entire model domain, thus forming an attractive alternative to local grid refinement or inset models.     

Model Calibration Techniques for Use with the Analytic Element Method

The combination of the analytic element method and a nonlinear parameter estimation technique forges a computationally efficient, information-rich, and cost-effective solution to the inverse ground-water flow problem. The recommended model calibration method uses a nonlinear least-squares objective, as quantified by misfitting the measured and modeled heads, and a modified Levenberg-Marquardt algorithm. As detailed and demonstrated by a steady-state regional aquifer model of Bemidji, Minnesota, automated calibration techniques make ground-water modeling feasible for a wider variety of projects where tight budgets and a lack of tools may have previously made such modeling inappropriate.     

Analytic Element Modeling of Steady Interface Flow in Multilayer Aquifers Using AnAqSim

This paper presents the analytic element modeling approach implemented in the software AnAqSim for simulating steady groundwater flow with a sharp fresh‐salt interface in multilayer (three‐dimensional) aquifer systems. Compared with numerical methods for variable‐density interface modeling, this approach allows quick model construction and can yield useful guidance about the three‐dimensional configuration of an interface even at a large scale. The approach employs subdomains and multiple layers as outlined by Fitts (2010) with the addition of discharge potentials for shallow interface flow (Strack 1989). The following simplifying assumptions are made: steady flow, a sharp interface between fresh‐ and salt water, static salt water, and no resistance to vertical flow and hydrostatic heads within each fresh water layer. A key component of this approach is a transition to a thin fixed minimum fresh water thickness mode when the fresh water thickness approaches zero. This allows the solution to converge and determine the steady interface position without a long transient simulation. The approach is checked against the widely used numerical codes SEAWAT and SWI/MODFLOW and a hypothetical application of the method to a coastal wellfield is presented.     

Parallel distributed computing using Python

This work presents two software components aimed to relieve the costs of accessing high-performance parallel computing resources within a Python programming environment: MPI for Python and PETSc for Python.MPI for Python is a general-purpose Python package that provides bindings for the Message Passing Interface (MPI) standard using any back-end MPI implementation. Its facilities allow parallel Python programs to easily exploit multiple processors using the message passing paradigm. PETSc for Python provides access to the Portable, Extensible Toolkit for Scientific Computation (PETSc) libraries. Its facilities allow sequential and parallel Python applications to exploit state of the art algorithms and data structures readily available in PETSc for the solution of large-scale problems in science and engineering.MPI for Python and PETSc for Python are fully integrated to PETSc-FEM, an MPI and PETSc based parallel, multiphysics, finite elements code developed at CIMEC laboratory. This software infrastructure supports research activities related to simulation of fluid flows with applications ranging from the design of microfluidic devices for biochemical analysis to modeling of large-scale stream/aquifer interactions.     

A parallel mesh-free contaminant transport model based on the Analytic Element and Streamline Methods

This paper introduces a new method for simulating large-scale subsurface contaminant transport that combines an Analytic Element Method (AEM) groundwater flow solution with a split-operator Streamline Method for modeling reactive transport. The key feature of the method is the manner in which the vertically integrated AEM flow solution is used to construct three-dimensional particle tracks that define the geometry of the Streamline Method. The inherently parallel nature of the algorithm supports the development of reactive transport models for spatial domains much larger than current grid-based methods. The applicability of the new approach is verified for cases with negligible transverse dispersion through comparisons to analytic solutions and existing numerical solutions, and parallel performance is demonstrated through a realistic test problem based on the regional-scale transport of agricultural contaminants from spatially distributed sources.     

Field Test of a Hybrid Finite‐Difference and Analytic Element Regional Model

Regional finite‐difference models often have cell sizes that are too large to sufficiently model well‐stream interactions. Here, a steady‐state hybrid model is applied whereby the upper layer or layers of a coarse MODFLOW model are replaced by the analytic element model GFLOW, which represents surface waters and wells as line and point sinks. The two models are coupled by transferring cell‐by‐cell leakage obtained from the original MODFLOW model to the bottom of the GFLOW model. A real‐world test of the hybrid model approach is applied on a subdomain of an existing model of the Lake Michigan Basin. The original (coarse) MODFLOW model consists of six layers, the top four of which are aggregated into GFLOW as a single layer, while the bottom two layers remain part of MODFLOW in the hybrid model. The hybrid model and a refined “benchmark” MODFLOW model simulate similar baseflows. The hybrid and benchmark models also simulate similar baseflow reductions due to nearby pumping when the well is located within the layers represented by GFLOW. However, the benchmark model requires refinement of the model grid in the local area of interest, while the hybrid approach uses a gridless top layer and is thus unaffected by grid discretization errors. The hybrid approach is well suited to facilitate cost‐effective retrofitting of existing coarse grid MODFLOW models commonly used for regional studies because it leverages the strengths of both finite‐difference and analytic element methods for predictions in mildly heterogeneous systems that can be simulated with steady‐state conditions.     

The Analytic Element Method for rectangular gridded domains,benchmark comparisons and application to the High Plains Aquifer

Groundwater studies face computational limitations when providing local detail (such as well drawdown) within regional models. We adapt the Analytic Element Method (AEM) to extend separation of variable solutions for a rectangle to domains composed of multiple interconnected rectangular elements. Each rectangle contains a series solution that satisfies the governing equations and coefficients are adjusted to match boundary conditions at the edge of the domain and continuity conditions across adjacent rectangles. A complete mathematical implementation is presented including matrices to solve boundary and continuity conditions. This approach gathers the mathematical functions associated with head and velocity within a small set of functions for each rectangle, enabling fast computation of these variables. Benchmark studies verify that conservation of mass and energy conditions are accurately satisfied using a method of images solution, and also develop a solution for heterogeneous hydraulic conductivity with log normal distribution. A case study illustrates that the methods are capable of modeling local detail within a large-scale regional model of the High Plains Aquifer in the central USA and reports the numerical costs associated with increasing resolution, where use is made of GIS datasets for thousands of rectangular elements each with unique geologic and hydrologic properties, Methods are applicable to interconnected rectangular domains in other fields of study such as heat conduction, electrical conduction, and unsaturated groundwater flow.     

Visualization of Aqueous Geochemical Data Using Python and WQChartPy

Graphical methods have been widely used for visualization, classification, and interpretation of aqueous geochemical data to obtain a better understanding of surface and subsurface hydrologic systems. This method note presents WQChartPy, an open-source Python package developed to plot a total of 12 diagrams for analysis of aqueous geochemical data. WQChartPy can handle various data formats including Microsoft Excel, comma-separated values (CSV), and general delimited text. The 12 diagrams include eight traditional diagrams (trilinear Piper, Durov, Stiff, Chernoff face, Schoeller, Gibbs, Chadha, and Gaillardet) and four recently proposed diagrams (rectangle Piper, color-coded Piper, contour-filled Piper, and HFE-D) that have not been implemented in existing graphing software. The diagrams generated by WQChartPy can be saved as portable network graphics (PNG), scalable vector graphics (SVG), or portable document format (PDF) files for scientific publications. Jupyter and Google Colab notebooks are available online to illustrate how to use WQChartPy with example datasets. The geochemical diagrams can be generated with several lines of Python codes. Source codes of WQChartPy are publicly available at GitHub ( https://github.com/jyangfsu/WQChartPy ) and PyPI ( https://pypi.org/project/wqchartpy/ ).     

A COMSOL-PHREEQC Coupled Python Framework for Reactive Transport Modeling in Soil and Groundwater

The CPqPy framework coupling COMSOL and PHREEQC based on Python was developed. This framework can achieve the simulation of diversified situations including multi-physics coupling and geochemical reactions of soil and groundwater. The multi-physics coupling models are calculated in COMSOL, whereas PHREEQC was applied to calculate the geochemical models through the Phreeqpy library in Python. Feasibility and accuracy of CPqPy were verified and applied to two cases, including a solute transport model considering equilibrium reaction and ion exchange as well as a reactive transport model of a variable saturation soil considering kinetic reaction. The results show a high degree of credibility of CPqPy. The framework has the advantages of strong portability, and it can be further used in conjunction with multiple Python calculation libraries, which greatly extends the application of the reactive transport model.