Analysis of subdiffusion in disordered and fractured media using a Grünwald-Letnikov fractional calculus model

The increasing applications of fractional calculus in simulating the anomalous transport behavior in disordered and fractured heterogeneous porous media has grown rapidly over the past decade. In the present study, a temporal fractional flux relationship is employed as a constitutive equation to relate the volumetric flow rate to the gradient of the pore pressure. The novelty of this paper entails interpreting the time fractional derivative operator in the flux relationship by the Grünwald-Letnikov (G-L) definition as opposed to the Caputo interpretation which has been widely considered. Subsequently, a numerical scheme based on the block-centered finite-difference discretization is formulated to handle the resulting non-linear fractional diffusion model. In addition, a linear stability analysis is successfully performed to establish the stability criterion of the developed numerical scheme. An expression for the modified incremental material balance index was derived to assess the effectiveness of the numerical discretization process. Finally, numerical experiments were performed to provide qualitative insights into the nature of pressure evolution in a hydrocarbon reservoir under the influence subdiffusion. In summary, the results establish that subdiffusion regime results in the development of higher pressure drop in the reservoir. This paper will provide a strong foundation for researchers interested in investigating anomalous diffusion phenomena in porous media.     

Spatial variability of climatic hazards in Bangladesh

Natural Hazards - Climate change is evident with the extreme climatic indices changing all over the world. Bangladesh is one of the most vulnerable countries to climate change. The patterns of...     

Intra‐ and interannual export of nitrogen and phosphorus in the subtropical Richmond River catchment,Australia

Nitrogen and phosphorus concentrations were measured and exports were calculated in the subtropical Richmond River catchment between July 1994 and June 1996. A stratified sampling approach was adopted owing to the extreme and rapid changes in riverine discharge, which varied by up to 10 000 times over the study period. Nutrient concentrations were lowest during baseflow. During storm discharge, dissolve inorganic and organic and particulate nitrogen and phosphorus concentrations increased two‐ to five fold, and followed hysteresis patterns that were attributed to the integration and/or depletion of catchment nutrient sources during an event. Dissolved organic nitrogen and particulate phosphorus were the dominant nutrient forms. Land use and antecedent conditions had a large influence on nutrient concentrations and exports. During the 1995–96 year (slightly above the mean annual discharge) 96% of nitrogen and 98% of phosphorus loads were transported in less than 6% of the time. When averaged across the catchment, monthly riverine nutrient loads varied by up to 1061‐fold during the study and exports were approximately four‐fold greater during the second year relative to the first. The subtropical Richmond River catchment has greater intra‐ and potential interannual variability in nutrient loads and exports when compared with temperate catchments from other parts of the world. It is suggested that in tropical and subtropical Australian catchments with large intra‐ and interannual variation in discharge, the need for parameterizing the antecedent conditions, such as the degree of nutrient storage, may make it difficult to model spatial and temporal (short time‐scale) nutrient exports. Copyright © 2000 John Wiley & Sons, Ltd.     

Is correlation dimension a reliable proxy for the number of dominant influencing variables for modeling risk of arsenic contamination in groundwater?

The correlation dimension (CD) of a time series provides information on the number of dominant variables present in the evolution of the underlying system dynamics. In this study, we explore, using logistic regression (LR), possible physical connections between the CD and the mathematical modeling of risk of arsenic contamination in groundwater. Our database comprises a large-scale arsenic survey conducted in Bangladesh. Following the recommendation by Hossain and Sivakumar (Stoch Environ Res Risk Assess 20(1–2):66–76, 2006), who reported CD values ranging from 8 to 11 for this database, 11 variables are considered herein as indicators of the aquifer’s geochemical regime with potential influence on the arsenic concentration in groundwater. A total of 2,048 possible combinations of influencing variables are considered as candidate LR risk models to delineate the impact of the number of variables on the prediction accuracy of the model. We find that the uncertainty associated with prediction of wells as safe and unsafe by LR risk model declines systematically as the total number of influencing variables increases from 7 to 11. The sensitivity of the mean predictive performance also increases noticeably for this range. The consistent reduction in predictive uncertainty coupled with the increased sensitivity of the mean predictive behavior within the universal sample space exemplify the ability of CD to function as a proxy for the number of dominant influencing variables. Such a rapid proxy, based on non-linear dynamic concepts, appears to have considerable merit for application in current management strategies on arsenic contamination in developing countries, where both time and resources are very limited.     

Augmentation of seasonal low stream flows by artificial recharge in the Spokane Valley-Rathdrum Prairie aquifer of Idaho and Washington, USA

Conjunctive management of surface water and groundwater requires sophisticated spatial and temporal analysis. In situations involving multiple jurisdictions such as state boundaries, management problems are magnified due to often conflicting regulations and policies. A transient MODFLOW model of the Spokane Valley-Rathdrum Prairie (SVRP) aquifer/river system mutually accepted by both the states of Idaho and Washington, USA, was used to evaluate regional solutions to potential water shortages through the use of strategically placed infiltration basins or injection wells. Artificial recharge of the SVRP aquifer was simulated using diversions from Lake Pend Oreille during winter periods when flows are high and excess water is available. Alternative locations for potential wells and detention basins were examined. Lag times for the water to impact stream/groundwater interaction areas along the Spokane River were evaluated to assess the potential for augmenting stream flows from July through September. Results indicated that the aquifer could be used to improve low-flow season streamflow values utilizing both infiltration basins and injection wells with winter surface water diversions. Depending on the location, as much as 30% of the winter diversion rate could be lagged to improve summer flows at the Spokane gage. Thus, a regional mitigation strategy is scientifically feasible.     

Stability Analyses of Municipal Solid Waste Landfills with Decomposition

A bioreactor landfill is operated to enhance refuse decomposition, gas production, and waste stabilization. Some of the potential advantages of bioreactor include rapid stabilization of waste, increased landfill gas generation, gain in landfill space, enhanced leachate treatment, and reduced post closure maintenance period. Due to the accelerated decomposition and settlement of solid waste, bioreactor landfills are gaining popularity as an alternative to the conventional Subtitle D landfills. However, the addition of leachate to accelerate the decomposition changes the physical and engineering characteristic of waste and therefore affects the geotechnical characteristics of waste mass. The changes in the physical and mechanical characteristics of solid waste with time and decomposition are expected to affect the shear strength of waste mass. The objective of this paper is to analyze the stability of solid waste slopes within the bioreactor landfills, as a function of time and decomposition. The finite element program PLAXIS is used for numerical modeling of bioreactor landfills. Stability analysis of bioreactor landfills was also performed using limit equilibrium program STABL. Finally the results from finite element program PLAXIS and limit equilibrium program STABL are compared. GSTABL predicted a factor of safety of more than 1 in all the cases analyzed, whereas PLAXIS predicted a factor of safety of less than 1 at advanced stages for a slope of 2:1. However, the interface failures between solid waste and landfill liners have not been considered in this paper.     

New Observations on the Brittle Failure Process of Simulated Crystalline Rocks

A biaxial testing program has been performed to study the process of brittle failure in crystalline rocks. Dental plaster has been selected as a model material, and mixing with different ratios of distilled water, different types of common minerals of crystalline rocks have been simulated in the form of brick-like small elements. These elements have been interlocked together according to four systematic patterns and final specimens with 180 × 180 × 76 mm dimensions have been obtained. Details of different types of cracks observed during loading process, effects of mechanical, geometrical and confining pressure on the cracking intensity, the influence of different types of heterogeneity on the macroscopic properties of a system of interlocked elements, and the sequence of events during the failure process are presented in this paper. Based on these observations, a revised mechanism for brittle failure is proposed.