Computational modelling of iron-ore mineralisation with stratigraphic permeability anisotropy

This study develops a computational framework to model fluid transport in sedimentary basins, targeting iron ore deposit formation. It offers a simplified flow model, accounting for geological features and permeability anisotropy as driving factors. A new finite element method lessens computational effort, facilitating robust predictions and cost-effective exploration. This methodology, applicable to other mineral commodities, enhances understanding of genetic models, supporting the search for new mineral deposits amid the global energy transition

Probabilistic Gradients for Fast Calibration of Differential Equation Models

Calibration of large-scale differential equation models to observational or experimental data is a widespread challenge throughout applied sciences and engineering. A crucial bottleneck in state-of-the art calibration methods is the calculation of local sensitivities, i.e. derivatives of the loss function with respect to the estimated parameters, which often necessitates several numerical solves of the underlying system of partial or ordinary differential equations. In this paper we present a new probabilistic approach to computing local sensitivities. The proposed method has several advantages over classical methods. Firstly, it operates within a constrained computational budget and provides a probabilistic quantification of uncertainty incurred in the sensitivities from this constraint. Secondly, information from previous sensitivity estimates can be recycled in subsequent computations, reducing the overall computational effort for iterative gradient-based calibration methods. The methodology presented is applied to two challenging test problems and compared against classical methods

Automated Design of a High-Velocity Channel

Engineering design is a decision-making process. Optimization techniques can be used to insure that better decisions are made. One design of great interest to engineers is that of high-velocity channels used for routing floodwater out of urban areas. In the design of these channels it is very important to avoid such hydraulic phenomena as standing waves, hydraulic jumps, and shocks. These will require higher wall heights and more expense. These channels can be modeled with physical models, but they are expensive and time consuming. To minimize the cost of building and changing the physical models and the time required to perform the study, an automated numerical model can be used to test a range of designs before construction of the physical model. The resulting design can be used as an initial design, which is close to the desired design requiring fewer changes to the physical model, saving time and money

Gemischte und nicht-standard Finite-Elemente-Methoden mit Anwendungen

Mixed and non-conforming finite element methods form a general mathematical framework for the spatial discretisation of partial differential equations, mainly applied to elliptic equations of second order and are becoming increasingly important for the solution of nonlinear problems. These methods are under active discussion in the mathematical and the engineering community and aim of the workshop was to provide a joint forum for the current state of research

Schnelle Löser für partielle Differentialgleichungen

[no abstract available

Development of a generalised compositional multiphase model for flow and transport in porous media

PhD ThesisFresh water is one of the most important natural resources. However, like other natural resources, the usable water is limited while the demand for water increases as industrialization proceeds and the population grows. What makes matters worse is that water resources are being reduced by pollution. Groundwater is an important water resource. However, in many countries, it has not been fully developed yet, either because of sufficient surface water sources, technical problems, or geographical conditions. Generally groundwater is relatively clean and is better protected from pollutants than surface water. Thus groundwater is an important subject for water engineers and scientists who have focused on its development and protection. In both cases, research into the movement of pollutants plays an important role in the effective exploitation of groundwater. Recently hydrologists concerned with groundwater pollution have studied multiphase flows in the subsurface because many pollution problems are characterized by multiphase contamination. The simplest multiphase pollution problem is solute transport in the unsaturated zone. More complex multiphase pollution problems involve organic matter such as petroleum products discharged to use oil. Since many of organic products are essential to our normal life and industry, the potential for groundwater pollution by them is significant unless they are controlled properly. In multiphase problems, the organic compounds may form their own flows that are distinct from the subsurface water flow but partly dissolve with the water phase and cause low concentration long term pollution of the water phase. There have been many efforts dedicated to predicting the movement of pollutants. A lot of mathematical and numerical models have been developed with the aid of laboratory and field works. However almost all models have been developed to solve a few restricted scenarios. Model users are obliged to invest considerable time in understanding the various models; their numerical accuracy and coding.The purpose of this study is to categorize the pollution patterns in the subsurface and to develop a numerical model that can be applicable to a wide variety of subsurface contamination. The general primary variables and generalizing procedures are employed to make the numerical model applicable to various pollution patterns. Many kinds of tracers can be used to know the behaviors of fluid phases in the subsurface. Because the model is able to describe partitioning of mass of a component among fluid phases, tracer problems also can be simulated by the model

Hierarchical Modeling for the Planning and Management of a Total Regional Water Resource System : Joint Consideration of the Supply and Quality of Ground and Surface Water Resources

Executive Summary -- Table of Contents -- List of Figures -- List of Tables -- Chapter 1 Introduction -- Chapter 2 Modeling of a Complex System of Surface Water Pollution Control and Management -- Chapter 3 Multiobjective Integrated Planning Model for Surface Water Pollution Control -- Chapter 4 Modeling for a Complex, Large-Scale Groundwater System - The Decomposition and Superposition Approach -- Chapter 5 Identification of Groundwater Parameters in a Multicell System -- Chapter 6 An Optimal Control Analysis for the Management of a Groundwater Aquifer-Stream System -- Chapter 7 Example Problem - A Conjunctive Use of Ground and Surface Water Systems -- Chapter 8 A Tax Quota Model in a Multicell-Multistream System -- Chapter 9 Summary, Conclusions and Recommendations -- Reference

Modeling multiphase flow in porous medium systems at multiple scales

Problems involving multiphase flow and transport in porous media arise in a number of scientific and engineering applications including oil reservoir engineering and groundwater remediation. The inherent complexity of multiphase systems and the marked heterogeneity over multiple spatial scales result in significant challenges to the fundamental understanding of the multiphase flow and transport processes. For many decades, multiphase flow has been modeled using the traditional approach based on mass conservation and the generalized Darcy's law. The traditional approach, however, is subject to model errors and numerical errors. The focus of this dissertation research is to improve models of flow and transport in porous medium systems using numerical modeling approaches for a range of scales including pore scale and continuum scale. A major part of this research examines the deficiency of Darcy's relationship and its extension to multiphase flow using the lattice-Boltzmann (LB) approach. This study investigates the conventional relative permeability saturation relation for systems consisting of water and non-aqueous phase liquid (NAPL). In addition, it also examines the generalized formulation accounting for the interfacial momentum transfer and lends additional support to the hypothesis that interfacial area is a critical variable in multiphase porous medium systems. Another major part of the research involves developing efficient and robust numerical techniques to improve the solution approach for existing models. In particular, a local discontinuous Galerkin (LDG) spatial discretization method is developed in combination with a robust and established variable order, variable step-size temporal integration approach to solve Richards' equation (RE). Effective spatial adaptive LDG methods are also developed to further enhance the efficiency. The resulting simulator with both spatial and temporal adaption has demonstrated good performance for a series of problems modeled by RE

Optimal water resources management model for Ash Sharqiyah region domestic water supply, Oman

Continuously increasing water demand in various sectors is intensifying the water scarcity problem particularly in arid and semi-arid regions like Oman. In many areas of the Sultanate, demand for water far exceeds its current availability. This presents logistical challenges in overcoming this situation or at least keeping the water deficit as low as possible. In Oman, most of the readily accessible fresh groundwater resources have already been extensively developed in order to attempt to meet the increasing demand for water, and any further intensification of groundwater abstraction is therefore not sustainable. Attention has therefore turned to desalination of sea water to supplement the available groundwater resources. Desalination is expensive and energy intensive; hence it cannot realistically be the sole source of drinking water in Oman. Rather, a conjunctive use of groundwater and desalination optimally operated to meet water demands while ensuring the sustainability of the groundwater resources is the best option. Thus, a numerical simulation model of Ash Sharqiyah Sands Aquifer was developed in this study and used to assess the long-term impacts on piezometric heads of supplying the eight Wilayats of Ash Sharqiyah Region with water from the 29 operational wells located in two regional groundwater fields- the Jaalan and the Al Kamil. The simulation results showed that the existing provision from the two wellfields will be inadequate by the 1st of September 2025 to meet domestic water supply needs without creating excessive drawdown and the cessation of flow in some of the existing operational Aflaj, which are artificial, surface channels that tap and convey by gravity groundwater for diversion into various uses along its route. Supplementing the abstraction from the wellfields with the more costly desalinated water of the Sur Desalination Plant offers the prospect for combating the problem; consequently, a constrained optimization problem was formulated to find the least cost blending of groundwater and desalinated water to meet demands while satisfying various constraints including the need to maintain Aflaj flow. The optimisation revealed increasing contribution of desalination to future total water supply for the Region, as desalination water replaces pumping from wells that affect Aflaj flow, with implications for the project cost. However, significant reduction in the long-term total production cost was achieved by increasing up to 50% the existing pump capacity at the Jaalan, made possible because its associated Aflaj are located upstream of the wellfield and are hence only minimally affected by the current abstractions