Time–space fractional governing equations of transient groundwater flow in confined aquifers: Numerical investigation

In order to model non‐Fickian transport behaviour in groundwater aquifers, various forms of the time–space fractional advection–dispersion equation have been developed and used by several researchers in the last decade. The solute transport in groundwater aquifers in fractional time–space takes place by means of an underlying groundwater flow field. However, the governing equations for such groundwater flow in fractional time–space are yet to be developed in a comprehensive framework. In this study, a finite difference numerical scheme based on Caputo fractional derivative is proposed to investigate the properties of a newly developed time–space fractional governing equations of transient groundwater flow in confined aquifers in terms of the time–space fractional mass conservation equation and the time–space fractional water flux equation. Here, we apply these time–space fractional governing equations numerically to transient groundwater flow in a confined aquifer for different boundary conditions to explore their behaviour in modelling groundwater flow in fractional time–space. The numerical results demonstrate that the proposed time–space fractional governing equation for groundwater flow in confined aquifers may provide a new perspective on modelling groundwater flow and on interpreting the dynamics of groundwater level fluctuations. Additionally, the numerical results may imply that the newly derived fractional groundwater governing equation may help explain the observed heavy‐tailed solute transport behaviour in groundwater flow by incorporating nonlocal or long‐range dependence of the underlying groundwater flow field.     

Developing constitutive models from EPR‐based self‐learning finite element analysis

A constitutive model that captures the material behavior under a wide range of loading conditions is essential for simulating complex boundary value problems. In recent years, some attempts have been made to develop constitutive models for finite element analysis using self‐learning simulation (SelfSim). Self‐learning simulation is an inverse analysis technique that extracts material behavior from some boundary measurements (eg, load and displacement). In the heart of the self‐learning framework is a neural network which is used to train and develop a constitutive model that represents the material behavior. It is generally known that neural networks suffer from a number of drawbacks. This paper utilizes evolutionary polynomial regression (EPR) in the framework of SelfSim within an automation process which is coded in Matlab environment. EPR is a hybrid data mining technique that uses a combination of a genetic algorithm and the least square method to search for mathematical equations to represent the behavior of a system. Two strategies of material modeling have been considered in the SelfSim‐based finite element analysis. These include a total stress‐strain strategy applied to analysis of a truss structure using synthetic measurement data and an incremental stress‐strain strategy applied to simulation of triaxial tests using experimental data. The results show that effective and accurate constitutive models can be developed from the proposed EPR‐based self‐learning finite element method. The EPR‐based self‐learning FEM can provide accurate predictions to engineering problems. The main advantages of using EPR over neural network are highlighted.     

A continuum‐discrete hydromechanical analysis of granular deposit liquefaction

A coupled continuum‐discrete hydromechanical model was employed to analyse the liquefaction of a saturated loose deposit of cohesionless particles when subjected to a dynamic base excitation. The pore fluid flow was idealized using averaged Navier–Stokes equations and the discrete element method was employed to model the solid phase particles. A well established semi‐empirical relationship was utilized to quantify the fluid–particle interactions. The conducted simulations revealed a number of salient micro‐mechanical mechanisms and response patterns associated with the deposit liquefaction. Space and time variation of porosity was a major factor which affected the coupled response of the solid and fluid phases. Pore fluid flow was within Darcy's regime. The predicted response exhibited macroscopic patterns consistent with experimental results and case histories of the liquefaction of granular soil deposits. Copyright © 2004 John Wiley & Sons, Ltd.     

Is the age problem resolved?

The cosmological, astrophysical, and nucleocosmochronological methods for estimating the age of the universe and the corresponding uncertainties are comparatively studied in the present paper. We are led to the conclusion that the new measurements of cosmological parameters, and the recent estimates of the age of globular clusters have led to the gradual disappearance of the age problem from the arena of modern cosmology.     

Source flow expansion of monatomic gas into vacuum under external field of forces

The steady flow expansions of monatomic gases consisting of Maxwellia molecules into a vacuum moving under external forces with a source of spherical symmetry are investigated. The analysis is based on the B-G-K model of the Boltzmann equation with the approximation in hypersonic limit. The kinetic equation is solved by using the moment method. Analytical forms for the density and temperature are obtained for small and large distances from the source. The results show that the temperature in free expansion is less than that in the case of the expansion under the influence of external field of forces.     

Sensitivity analysis of a deterministic water temperature model to forest canopy and soil temperature in Catamaran Brook (New Brunswick,Canada)

A coupled deterministic hydrological and water temperature model, CEQUEAU, was modified to include soil temperature and crown closure in its calculation of local advective terms in the heat budget. The modified model was than tested to verify its sensitivity to these modifications. An analysis of the heat budget of a small forested catchment in eastern Canada revealed that the advective term related to interflow plays a significant role in the daily water heat budget, providing on average 28% of the local advective budget (which also includes advective heat terms from surface runoff and groundwater) and nearly 14% of the total heat budget (which includes all radiative terms at the water surface, convection and evaporation, as well as the local advective terms). Relative sensitivity indices (RSIs) were used to verify the impact of the newly introduced parameters and variables. Among them, parameters related to the forest cover (crown closure and leaf area index) have a maximum RSI of ?0·6; i.e. a 100% increase in value produces a 60% decrease in the local advective term. Parameters with the greatest influence are the volume of water contributing to interflow and the amplitude of the net radiative flux at the soil surface, which, if doubled, would double the contribution of the local interflow advective term to the heat budget. Copyright © 2003 John Wiley & Sons, Ltd.     

Screening of polymers on selected Hawaii soils for erosion reduction and particle settling

In recent years, high‐molecular‐weight anionic polyacrylamides (PAMs) have been tested on a variety of soils, primarily in temperate climates. However, little information is available regarding the effectiveness of PAM for preventing soil loss through runoff in tropical settings. Screening tests were performed using three negatively charged PAMs and one positively charged PAM on five Hawaii soils (two Oxisols, one Vertisol, and two Aridisols) to determine erosion loss, sediment settling, and aggregate stability. A laboratory‐scale rainfall simulator was used to apply erosive rainfall at intensities from 5 to 8·5 cm h^?1 at various PAM doses applied in both dry and solution forms. Soil detachment due to splash and runoff, as well as the runoff and percolate water volumes, were measured for initial and successive storms. The impact of PAM on particle settling and aggregate stability was also evaluated for selected soil‐treatment combinations. Among the PAMs, Superfloc A‐836 was most effective, and significantly reduced runoff and splash sediment loss for the Wahiawa Oxisol and Pakini Andisol at rates varying between 10 and 50 kg ha^?1. Reduced runoff and splash sediment loss were also noted for PAM Aerotil‐D when applied in solution form to the Wahiawa Oxisol. Significant reductions in soil loss were not noted for either the Lualualei Vertisol or the Holomua Oxisol. It is believed that the high montmorillonite content of the Lualualei Vertisol and the low cation‐exchange capacity of the Holomua Oxisol diminished the effectiveness of the various PAMs tested. The polymers were also found to enhance sediment settling of all soils and helped improve their aggregate stability. This screening study shows the potential use of PAM for tropical soils for applications such as infiltration enhancement, runoff reduction, and enhanced sedimentation of detention ponds. Copyright © 2005 John Wiley & Sons, Ltd.     

Anhydrite pseudomorphs and the origin of stratiform Cu–Co ores in the Katangan Copperbelt (Democratic Republic of Congo)

The stratiform Cu–Co ore mineralisation in the Katangan Copperbelt consists of dispersed sulphides and sulphides in nodules and lenses, which are often pseudomorphs after evaporites. Two types of pseudomorphs can be distinguished in the nodules and lenses. In type 1 examples, dolomite precipitated first and was subsequently replaced by Cu–Co sulphides and authigenic quartz, whereas in type 2 examples, authigenic quartz and Cu–Co sulphides precipitated prior to dolomite and are coarse-grained. The sulphur isotopic composition of the copper–cobalt sulphides in the type 1 pseudomorphs is between −10.3 and 3.1‰ relative to the Vienna Canyon Diablo Troilite, indicating that the sulphide component was derived from bacterial sulphate reduction (BSR). The generation of during this process caused the precipitation and replacement of anhydrite by dolomite. A second product of BSR is the generation of H₂S, resulting in the precipitation of Cu–Co sulphides from the mineralising fluids. Initial sulphide precipitation occurred along the rim of the pseudomorphs and continued towards the core. Precipitation of authigenic quartz was most likely induced by a pH decrease during sulphide precipitation. Fluid inclusion data from quartz indicate the presence of a high-salinity (8–18 eq. wt.% NaCl) fluid, possibly derived from evaporated seawater which migrated through the deep subsurface. ⁸⁷Sr/⁸⁶Sr ratios of dolomite in type 1 nodules range between 0.71012 and 0.73576, significantly more radiogenic than the strontium isotopic composition of Neoproterozoic marine carbonates (⁸⁷Sr/⁸⁶Sr = 0.7056–0.7087). This suggests intense interaction with siliciclastic sedimentary rocks and/or the granitic basement. The low carbon isotopic composition of the dolomite in the pseudomorphs (−7.02 and −9.93‰ relative to the Vienna Pee Dee Belemnite, V-PDB) compared to the host rock dolomite (−4.90 and +1.31‰ V-PDB) resulted from the oxidation of organic matter during BSR.     

The sandstone-hosted stratiform copper mineralization at Mwitapile and its relation to the mineralization at Lufukwe, Lufilian foreland, Democratic Republic of Congo

The Lufilian foreland is a triangular-shaped area located in the SE of the Democratic Republic of Congo and to the NE of the Lufilian arc, which hosts the well-known Central African Copperbelt. The Lufilian foreland recently became an interesting area with several vein-type (e.g., Dikulushi) and stratiform (e.g., Lufukwe and Mwitapile) copper occurrences. The Lufilian foreland stratiform Cu mineralization is, to date, observed in sandstone rock units belonging to the Nguba and Kundelungu Groups (Katanga Supergroup).The Mwitapile sandstone-hosted stratiform Cu prospect is located in the north eastern part of the Lufilian foreland. The host rock for the Cu mineralization is the Sonta Sandstone of the Ngule Subgroup (Kundelungu Group). A combined remote sensing, petrographic and fluid inclusion microthermometric analysis was performed at Mwitapile and compared with similar analysis previously carried out at Lufukwe to present a metallogenic model for the Mwitapile- and Lufukwe-type stratiform copper deposits. Interpretation of ETM+ satellite images for the Mwitapile prospect and the surrounding areas indicate the absence of NE–SW or ENE–WSW faults, similar to those observed controlling the mineralization at Lufukwe. Faults with these orientations are, however, present to the NW, W, SW and E of the Mwitapile prospect. At Mwitapile, the Sonta Sandstone host rock is intensely compacted, arkosic to calcareous with high silica cementation (first generation of authigenic quartz overgrowths). In the Sonta Sandstone, feldspar and calcite are present in disseminated, banded and nodular forms. Intense dissolution of these minerals caused the presence of disseminated rectangular, pipe-like and nodular dissolution cavities. Sulfide mineralization is mainly concentrated in these cavities. The hypogene sulfide minerals consist of two generations of pyrite, chalcopyrite, bornite and chalcocite, separated by a second generation of authigenic quartz overgrowth. The hypogene sulfide minerals are replaced by supergene digenite and covellite. Fluid inclusion microthermometry on the first authigenic quartz phase indicates silica precipitation from an H₂O–NaCl–CaCl₂ fluid with a minimum temperature between 111 and 182 °C and a salinity between 22.0 and 25.5 wt.% CaCl₂ equiv. Microthermometry on the second authigenic quartz overgrowths and in secondary trails related to the mineralization indicate that the mineralizing fluid is characterized by variable temperatures (Th = 120 to 280 °C) and salinities (2.4 to 19.8 wt.% NaCl equiv.) and by a general trend of increasing temperatures with increasing salinities.Comparison between Mwitapile and Lufukwe indicates that the stratiform Cu mineralization in the two deposits is controlled by similar sedimentary, diagenetic and structural factors and likely formed from a similar mineralizing fluid. A post-orogenic timing is proposed for the mineralization in both deposits. The main mineralization controlling factors are grain size, clay and pyrobitumen content, the amount and degree of feldspar and/or calcite dissolution and the presence of NE–SW to ENE–WSW faults. The data support a post-orogenic fluid-mixing model for the Mwitapile- and Lufukwe-type sandstone-hosted stratiform Cu deposits, in which the mineralization is related to the mixing between a Cu-rich hydrothermal fluid, with a temperature up to 280 °C and a maximum salinity of 19.8 wt.% NaCl equiv., with a colder low salinity reducing fluid present in the sandstone host rock. The mineralizing fluid likely migrated upwards to the sandstone source rocks along NE–SW to ENE–WSW orientated faults. At Lufukwe, the highest copper grades at surface outcrops and boreholes were found along and near to these faults. At Mwitapile, where such faults are 2 to 3 km away, the Cu grades are much lower than at Lufukwe. Copper precipitation was possibly promoted by reduction from pre-existing hydrocarbons and non-copper sulfides and by the decrease in fluid salinity and temperature during mixing. Based on this research, new Cu prospects were proposed at Lufukwe and Mwitapile and a set of recommendations for further Cu exploration in the Lufilian foreland is presented.