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"Mathias, Simon A"
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Groundwater modelling in arid and semi-arid areas
\"Arid and semi-arid regions face major challenges in the management of scarce freshwater resources under pressures of population, economic development, climate change, pollution and over-abstraction. Groundwater is commonly the most important water resource in these areas. Groundwater models are widely used globally to understand groundwater systems and to guide decisions on management. However, the hydrology of arid and semi-arid areas is very different from that of humid regions, and there is little guidance on the special challenges of groundwater modelling for these areas. This book brings together the experience of internationally-leading experts to fill a gap in the scientific and technical literature. It introduces state-of-the-art methods for modelling groundwater resources, illustrated with a wide-ranging set of illustrative examples from around the world. The book is valuable for researchers, practitioners in developed and developing countries, and graduate students in hydrology, hydrogeology, water resources management, environmental engineering and geography\"-- Provided by publisher.
Book
Heat transport and pressure buildup during carbon dioxide injection into depleted gas reservoirs
In this article, a two-layer vertical equilibrium model for the injection of carbon dioxide into a low-pressure porous reservoir containing methane and water is developed. The dependent variables solved for include pressure, temperature and
$\\def \\xmlpi #1{}\\def \\mathsfbi #1{\\boldsymbol {\\mathsf {#1}}}\\let \\le =\\leqslant \\let \\leq =\\leqslant \\let \\ge =\\geqslant \\let \\geq =\\geqslant \\def \\Pr {\\mathit {Pr}}\\def \\Fr {\\mathit {Fr}}\\def \\Rey {\\mathit {Re}}{\\mathrm{CO}}_2$
–
${\\mathrm{CH}}_4$
interface height. In contrast to previous two-layer vertical equilibrium models in this context, the compressibility of all material components is fully accounted for. Non-Darcy effects are also considered using the Forchheimer equation. The results show that, for a given injection scenario, as the initial pressure in the reservoir decreases, both the pressure buildup and temperature change increase. A comparison was conducted between a fully coupled non-isothermal numerical model and a simplified model where fluid properties are held constant with temperature. This simplified model was found to provide an excellent approximation when using the injection fluid temperature for calculating fluid properties, even when the injection fluid was as much as
$\\pm 15\\, ^\\circ \\mathrm{C}$
of the initial reservoir temperature. The implications are that isothermal models can be expected to provide useful estimates of pressure buildup in this context. Despite the low viscosity of
${\\mathrm{CO}}_2$
at the low pressures studied, non-Darcy effects were found to be of negligible concern throughout the sensitivity analysis undertaken. This is because the
${\\mathrm{CO}}_2$
density is also low in this context. Based on these findings, simplified analytic solutions are derived, which accurately calculate both the pressure buildup and temperature decline during the injection period.
Journal Article
Two Film Approach to Continuum Scale Mixing and Dispersion with Equilibrium Bimolecular Reaction
Reliable reactive transport models require careful separation of mixing and dispersion processes. Here we treat displacing and displaced fluids as two separate fluid phases and invoke Whitman’s classical two-film theory to model mass transfer between the two phases. We use experimental data from Gramling’s bimolecular reaction experiment to assess model performance. Gramling’s original model involved just three coupled PDEs. In this context, our new formulation leads to a set of seven coupled PDEs but only requires the specification of two extra parameters, associated with the mass transfer coefficient and its dependence on time. The two film mass transfer model provides a simple and theoretically based method for separating mixing from dispersion in Eulerian continuum-scale methods. The advantage of this approach over existing methods is that it enables the simulation of equilibrium chemical reactions without having to invoke unrealistically small reaction rate coefficients. The comparison with Gramling’s experimental data confirms that our proposed method is suitable for simulating realistic and complicated bimolecular reaction behaviour. However, further work is needed to explore alternative methods for avoiding the need of a time-dependent mass transfer rate coefficient.
Journal Article
Probabilistic longevity estimate for the Lusi mud volcano, East Java
A new method for estimating the duration of a mud volcano eruption is applied to the Lusi mud volcano in East Java. The estimate is based upon carbonates at depths in the range 2500-3500 m being the water source, with an estimated area of 100-600 km2, thickness of 0.2-1.0 km, porosity of 0.15-0.25, an initial pressure between 13.9 and 17.6 MPa, and a separate, shallower source of mud (c. 1200-1800 m depth). The resulting 50 percentile for the time it takes for flow to decline to <0.1 Ml day-1 is 26 years. By analogy with natural mud volcanoes it can be expected to continue to flow at lower rates for thousands of years. Assuming subsidence rates of between 1 and 5 cm day-1, land surface subsidence of between c. 95 and c. 475 m can be expected to develop within the 26 year time period.
Journal Article
Impact of land cover, rainfall and topography on flood risk in West Java
Flooding represents around 32% of total disasters in Indonesia and disproportionately affects the poorest of communities. The objective of this study was to determine significant statistical differences, in terms of river catchment characteristics, between regions in West Java that reported suffering from flood disasters and those that did not. Catchment characteristics considered included various statistical measures of topography, land-use, soil-type, meteorology and river flow rates. West Java comprises 154 level 9 HydroSHEDS sub-basin regions. We split these regions into those where flood disasters were reported and those where they were not, for the period of 2009 to 2013. Rainfall statistics were derived using the CHIRPS gridded precipitation data package. Statistical estimates of river flow rates, applicable to ungauged catchments, were derived from regionalisation relationships obtained by stepwise linear regression with river flow data from 70 West Javanese gauging stations. We used Kolmogorov–Smirnov tests to identify catchment characteristics that exhibit significant statistical differences between the two sets of regions. Median annual maximum river flow rate (AMRFR) was found to be positively correlated with plantation cover. Reducing plantation land cover from 20 to 10% was found to lead to a modelled 38% reduction in median AMRFR. AMRFR with return periods greater than 10 years were found to be negatively correlated with wetland farming land cover, suggesting that rice paddies play an important role in attenuating extreme river flow events. Nevertheless, the Kolmogorov–Smirnov tests revealed that built land cover is the most important factor defining whether or not an area is likely to report flood disasters in West Java. This is presumably because the more built land cover, the more people available to experience and report flood disasters. Our findings also suggest that more research is needed to understand the important role of plantation cover in aggravating median annual maximum river flow rates and wetland farming cover in mitigating extreme river flow events.
Journal Article
Capillary processes increase salt precipitation during CO2 injection in saline formations
An important attraction of saline formations for CO2 storage is that their high salinity renders their associated brine unlikely to be identified as a potential water resource in the future. However, high salinity can lead to dissolved salt precipitating around injection wells, resulting in loss of injectivity and well deterioration. Earlier numerical simulations have revealed that salt precipitation becomes more problematic at lower injection rates. This article presents a new similarity solution, which is used to study the relationship between capillary pressure and salt precipitation around CO2 injection wells in saline formations. Mathematical analysis reveals that the process is strongly controlled by a dimensionless capillary number, which represents the ratio of the CO2 injection rate to the product of the CO2 mobility and air-entry pressure of the porous medium. Low injection rates lead to low capillary numbers, which in turn are found to lead to large volume fractions of precipitated salt around the injection well. For one example studied, reducing the CO2 injection rate by 94 % led to a tenfold increase in the volume fraction of precipitated salt around the injection well.
Journal Article
Gas Diffusion in Coal Powders is a Multi-rate Process
Gas migration in coal is strongly controlled by surface diffusion of adsorbed gas within the coal matrix. Surface diffusion coefficients are obtained by inverse modelling of transient gas desorption data from powdered coals. The diffusion coefficient is frequently considered to be dependent on time and initial pressure. In this article, it is shown that the pressure dependence can be eliminated by performing a joint inversion of both the diffusion coefficient and adsorption isotherm. A study of the log–log slope of desorbed gas production rate against time reveals that diffusion within the individual coal particles is a multi-rate process. The application of a power-law probability density function of diffusion rates enables the determination of a single gas diffusion coefficient that is constant in both time and initial pressure.
Journal Article
Revisiting Salvucci’s Semi-analytical Solution for Bare Soil Evaporation with New Consideration of Vapour Diffusion and Film Flow
Bare soil evaporation is controlled by a combination of capillary flow, vapour diffusion and film flow. Relevant analytical solutions mostly assume horizontal flow conditions and ignore gravitational effects. Salvucci (
1997
) provided a rare example of a semi-analytical solution for vertical bare soil evaporation. However, they did not explicitly represent vapour diffusion and film flow, which are likely to account for a significant proportion of total flow during vertical evaporation from soils. Vapour diffusion and film flow can be incorporated via Salvucci’s desorptivity parameter, which represents the proportionality constant relating Stage 2 cumulative evaporation to the square root of time under horizontal flow conditions. The objective of this article is to implement vapour diffusion and film flow within Salvucci’s semi-analytical solution and test its performance by comparison with isothermal numerical simulation and relevant experimental data. The following important conclusions are drawn. Analytical solutions that assume horizontal flow conditions are inadequate for understanding vertical evaporation problems because they overestimate evaporation rates and mostly predict vapour diffusion and film flow to be of negligible influence. Salvucci’s semi-analytical solution is effective at predicting the order-of-magnitude reduction in evaporation caused by gravitational effects. However, it is unable to identify the correct importance of vapour diffusion and film flow because these processes can only be represented through its desorptivity parameter.
Journal Article
A simple, efficient, mass-conservative approach to solving Richards' equation (openRE, v1.0)
A simple numerical solution procedure – namely the method of lines combined with an off-the-shelf ordinary differential equation (ODE) solver – was shown in previous work to provide efficient, mass-conservative solutions to the pressure-head form of Richards' equation. We implement such a solution in our model openRE. We developed a novel method to quantify the boundary fluxes that reduce water balance errors without negative impacts on model runtimes – the solver flux output method (SFOM). We compare this solution with alternatives, including the classic modified Picard iteration method and the Hydrus 1D model. We reproduce a set of benchmark solutions with all models. We find that Celia's solution has the best water balance, but it can incur significant truncation errors in the simulated boundary fluxes, depending on the time steps used. Our solution has comparable runtimes to Hydrus and better water balance performance (though both models have excellent water balance closure for all the problems we considered). Our solution can be implemented in an interpreted language, such as MATLAB or Python, making use of off-the-shelf ODE solvers. We evaluated alternative SciPy ODE solvers that are available in Python and make practical recommendations about the best way to implement them for Richards' equation. There are two advantages of our approach: (i) the code is concise, making it ideal for teaching purposes; and (ii) the method can be easily extended to represent alternative properties (e.g., novel ways to parameterize the K(ψ) relationship) and processes (e.g., it is straightforward to couple heat or solute transport), making it ideal for testing alternative hypotheses.
Journal Article
Storage Coefficients and Permeability Functions for Coal-Bed Methane Production Under Uniaxial Strain Conditions
The porosity and permeability of coal change with pore pressure, due to changes in effective stress and matrix swelling due to gas adsorption. Three analytical models to describe porosity and permeability change in this context have been presented in the literature, all of which are based on poroelastic theory and uniaxial strain conditions. However, each of the three models provides different results. Review articles have attributed these differences to the use of stress formulations or strain formulations. In this article, the three aforementioned porosity models are used to derive three associated expressions for the storage coefficient. A single mathematical equation for the storage coefficient in an aquifer under uniaxial strain conditions is well established. The storage coefficient represents the volume of fluid released per unit volume of a porous rock following a unit decline in pore pressure. It is shown that only one of the aforementioned three coal-bed methane porosity models leads to the correct equation for the uniaxial strain storage coefficient in the absence of gas sorption-induced strain.
Journal Article