Higher-order compositional modeling with Fickian diffusion in unstructured and anisotropic media

We present advances in compositional modeling of two-phase multi-component flow through highly complex porous media. Higher-order methods are used to approximate both mass transport and the velocity and pressure fields. We employ the Mixed Hybrid Finite Element (MHFE) method to simultaneously solve, to the same order, the pressure equation and Darcy's law for the velocity. The species balance equation is approximated by the discontinuous Galerkin (DG) approach, combined with a slope limiter. In this work we present an improved DG scheme where phase splitting is analyzed at all element vertices in the two-phase regions, rather than only as element averages. This approximation is higher-order than the commonly employed finite volume method and earlier DG approximations. The method reduces numerical dispersion, allowing for an accurate capture of shock fronts and lower dependence on mesh quality and orientation. Further new features are the extension to unstructured grids and support for arbitrary permeability tensors (allowing for both scalar heterogeneity, and shear anisotropy). The most important advancement in this work is the self-consistent modeling of two-phase multi-component Fickian diffusion. We present several numerical examples to illustrate the powerful features of our combined MHFE–dg method with respect to lower-order calculations, ranging from simple two component fluids to more challenging real problems regarding CO₂ injection into a vertical domain saturated with a multi-component petroleum fluid.     

Probabilistic data integration for characterization of spatial distribution of residual LNAPL

The spatial distribution of residual light non-aqueous phase liquid (LNAPL) is an important factor in reactive solute transport modeling studies. There is great uncertainty associated with both the areal limits of LNAPL source zones and smaller scale variability within the areal limits. A statistical approach is proposed to construct a probabilistic model for the spatial distribution of residual NAPL and it is applied to a site characterized by ultra-violet-induced-cone-penetration testing (CPT–UVIF). The uncertainty in areal limits is explicitly addressed by a novel distance function (DF) approach. In modeling the small-scale variability within the areal limits, the CPT–UVIF data are used as primary source of information, while soil texture and distance to water table are treated as secondary data. Two widely used geostatistical techniques are applied for the data integration, namely sequential indicator simulation with locally varying means (SIS–LVM) and Bayesian updating (BU). A close match between the calibrated uncertainty band (UB) and the target probabilities shows the performance of the proposed DF technique in characterization of uncertainty in the areal limits. A cross-validation study also shows that the integration of the secondary data sources substantially improves the prediction of contaminated and uncontaminated locations and that the SIS–LVM algorithm gives a more accurate prediction of residual NAPL contamination. The proposed DF approach is useful in modeling the areal limits of the non-stationary continuous or categorical random variables, and in providing a prior probability map for source zone sizes to be used in Monte Carlo simulations of contaminant transport or Monte Carlo type inverse modeling studies.     

Centrifuge modeling of buried continuous pipelines subjected to normal faulting

Seismic ground faulting is the greatest hazard for continuous buried pipelines.Over the years,researchers have attempted to understand pipeline behavior mostly via numerical modeling such as the finite element method.The lack of well-documented field case histories of pipeline failure from seismic ground faulting and the cost and complicated facilities needed for full-scale experimental simulation mean that a centrifuge-based method to determine the behavior of pipelines subjected to faulting is best to verify numerical approaches.This paper presents results from three centrifuge tests designed to investigate continuous buried steel pipeline behavior subjected to normal faulting.The experimental setup and procedure are described and the recorded axial and bending strains induced in a pipeline are presented and compared to those obtained via analytical methods.The influence of factors such as faulting offset,burial depth and pipe diameter on the axial and bending strains of pipes and on ground soil failure and pipeline deformation patterns are also investigated.Finally,the tensile rupture of a pipeline due to normal faulting is investigated.     

Spatial distribution of cadmium and lead in the sediments of the western Anzali wetlands on the coast of the Caspian Sea (Iran)

Spatial distribution patterns of total cadmium (Cd) and lead (Pb), their bioavailable fractions and total organic matter in sediment from Anzali wetlands are provided. Total sediment Pb was higher than Cd (34.95 versus 0.024 μg/g dry weight). The geoaccumulation index indicated that the sediment was “uncontaminated”, but some stations were categorized as “unpolluted” to “moderately polluted”. Less than 0.01 of Pb existed in exchangeable and carbonate fractions. The sum of exchangeable and carbonate-bound fractions of Cd was 42%, suggesting that Cd poses high risk to the aquatic ecosystems. Total Cd and Pb exhibited positive relationships with total organic matter. Considering spatial distribution maps of total and bioavailable fractions of metals suggested that high concentrations of metals does not necessarily indicate high bioavailable fraction. The methodologies we used in this study can be in more effective management of aquatic ecosystems, as well as ecological risk assessment of metals, and remediation programs.     

The Impact of Geology of Recharge Areas on Groundwater Quality: A Case Study of Zhob River Basin,Pakistan

Groundwater is a major source of water supply for domestic and irrigation uses in semiarid, remote but rapidly developing Kilasaifullah district part of Zhob River Basin, located at Pakistan–Afghanistan Border. Zhob River is among few major rivers of perennial nature in Balochistan, which flows from WSW to ENE and falls in Gomal River, a tributary of Indus River. Keeping in view the important geopolitical position and rapid development of the region, this study is primarily focused on groundwater chemistry for contamination sources as well as agriculture development. Water samples from open and tube wells are analyzed and calculated for electrical conductivity (EC), total dissolved solids (TDS), turbidity, pH, K⁺, Na⁺, Ca²⁺, Mg²⁺, HCO, Cl^?, NO, SO, PO, sodium percent (Na%), sodium adsorption ratio (SAR), Kelly's index (KI), and heavy metals (Fe, Cu, Cr, Zn, Pb, and Mn). On the basis of the chemical constituents two zones within the study area are identified and possible causes of the contaminants are pointed out. Two recharge areas were responsible for the different chemical results in groundwater, e.g., zone A was recharged from NNW saline geological formations (Nisai, Khojak, Multana, Bostan formations, and Muslim Bagh ophiolites), which are concentrated with high sodium and chloride. On the other hand Zone B was sourced from SSW from carbonate rich rocks (Alozai, Loralai, Parh formations, and Muslim Bagh ophiolites). The groundwater is classified as C2–S1, C3–S1, C3–S2, C4–S2 on the basis of EC and SAR values which indicate that most of the water of both zones can be used for irrigation safely except the samples plotted in C3–S2 and C4–S2 categories which could be dangerous for soil and crops. Groundwater samples are plotted in good to permissible limits with some samples excellent to good and few samples belong to doubtful category based on sodium percent. Groundwater of zone A is unsuitable for irrigation use due to higher values of KI (more than one) but water of zone B are good for irrigation based on KI. In general, water of both zones is suitable for irrigation but care should be taken during the selection of crops which are sensitive to alkalinity or sodium hazards particularly in zone A.     

Earthquake Stability Analysis of Rock Slopes: a Case Study

Stability analysis of Surabhi landslide in the Dehradun and Tehri districts of Uttaranchal located in Mussoorie, India, has been simulated numerically using the distinct element method focusing on the weak zones (fracture). This is an active landslide on the main road toward the town centre, which was triggered after rainfall in July–August 1998. Understanding the behaviour of this landslide will be helpful for planning and implementing mitigation measures. The first stage of the study includes the total area of the landslide. The area identified as the zone of detachment is considered the most vulnerable part of the landslide. Ingress of water and increased pore pressures result in reduced mobilized effective frictional resistance, causing the top layer of the zone of detachment to start moving. The corresponding total volume of rock mass that is potentially unstable is estimated to 11.58 million m³. The second stage of this study includes a 2D model focussing only on the zone of detachment. The result of the analyses including both static and dynamic loading indicates that most of the total displacement observed in the slide model is due to the zone of detachment. The discontinuum modelling in the present study gives reasonable agreement with actual observations and has improved understanding of the stability of the slide slope.     

Numerical modeling of two-phase binary fluid mixing using mixed finite elements

Diffusion coefficients of dense gases in liquids can be measured by considering two-phase binary nonequilibrium fluid mixing in a closed cell with a fixed volume. This process is based on convection and diffusion in each phase. Numerical simulation of the mixing often requires accurate algorithms. In this paper, we design two efficient numerical methods for simulating the mixing of two-phase binary fluids in one-dimensional, highly permeable media. Mathematical model for isothermal compositional two-phase flow in porous media is established based on Darcy’s law, material balance, local thermodynamic equilibrium for the phases, and diffusion across the phases. The time-lag and operator-splitting techniques are used to decompose each convection–diffusion equation into two steps: diffusion step and convection step. The Mixed finite element (MFE) method is used for diffusion equation because it can achieve a high-order and stable approximation of both the scalar variable and the diffusive fluxes across grid–cell interfaces. We employ the characteristic finite element method with moving mesh to track the liquid–gas interface. Based on the above schemes, we propose two methods: single-domain and two-domain methods. The main difference between two methods is that the two-domain method utilizes the assumption of sharp interface between two fluid phases, while the single-domain method allows fractional saturation level. Two-domain method treats the gas domain and the liquid domain separately. Because liquid–gas interface moves with time, the two-domain method needs work with a moving mesh. On the other hand, the single-domain method allows the use of a fixed mesh. We derive the formulas to compute the diffusive flux for MFE in both methods. The single-domain method is extended to multiple dimensions. Numerical results indicate that both methods can accurately describe the evolution of the pressure and liquid level.     

A proposed geotechnical-based method for evaluation of liquefaction potential analysis subjected to earthquake provocations (case study: Korzan earth dam, Hamedan province, Iran)

During the earthquakes, a number of earth dams have had severe damages or suffered major displacements as a result of liquefaction, thus modeling by computer codes can provide a reliable tool to predict the response of the dam foundation against earthquakes. These modeling can be used in the design of new dams or safety assessments of existing ones. In this paper, on the basis of the field and laboratory tests and by combination of several software packages a seismic geotechnical-based analysis procedure is proposed and verified by comparison with computer model tests and field and laboratory experiences. Verification or validation of the analyses relies to the ability of the applied computer codes. By using the Silakhor earthquake (2006, M _s 6.1) as a basis in order to check the efficiency of the proposed framework, the procedure is applied to the Korzan earth dam of Iran which is located in Hamedan Province to analyze and estimate the liquefaction and safety factor. Design and development of a computer code by the authors which was named as the ??Abbas Converter?? with graphical user interface which operates as logic connecter function that can compute and model the soil profiles is the critical point of this study. The results confirmed and proved the ability of the generated computer code on the evaluation of soil behavior during earthquake excitations. Also, this code was able to facilitate this study better than previous ones have, taking over the encountered problem.     

A parametric study of stability of geotextile-reinforced soil above an underground cavity

A study based on two-dimensional finite element analyses under plane strain condition was performed by PLAXIS code to investigate the behavior of geotextile-reinforced soil above an underground cavity. The effects of depth of single layer, tensile stiffness, number and length of reinforcement layers, and size of cavity on settlement of ground surface and head of cavity have been investigated. Results indicated that when a single layer of reinforcement is used, there is a critical depth at which settlements are maximum. Maximum settlements reduce with increase in stiffness of reinforcement. Also settlements reduce with increase in number and length of reinforcement but there is a critical value for number and length of geotextile which increase more than this certain value has not significant effect on reduction of settlements. Also for a given load and tensile stiffness, increase in length of reinforcement has more effect for higher diameter of cavity.     

Spectrophotometric Determination of Cationic Surfactants Based on Their Effect on the Complexes of Chrome Azurol S with Be2+ and Al3+ Cations

Simple, rapid, and sensitive spectrophotometric methods have been proposed for the determination of cationic surfactants (CS) as cetyltrimethylammonium bromide (CTAB), dodecyltrimethylammonium (DTAB), and cetylpyridinium bromide (CPB). The methods are based on the effects of CSs on the complexes of Al³⁺ and Be²⁺ with Chrome Azurol S (CAS). The optimum reaction conditions such as CAS concentration, metal ion concentration, and pH have been studied and found to be 2.0 × 10^?4 mol L^?1 CAS, 0.5 mg L^?1 Al³⁺ or 0.4 mg L^?1 Be²⁺ and pH 5.4. The analytical characteristics of the methods such as limit of detections, limit of quantifications, and linear ranges have been obtained. CTAB, CPB, and DTAB could be determined by the Al–CAS complex in the ranges of 0.50–40.00, 0.20–10.00, and 0.40–10.00 µmol L^?1, and for the Be–CAS complex in the ranges of 0.08–5.00, 0.08–3.00, and 0.20–6.00 µmol L^?1, respectively. The limit of the detections of the method for the determination of CTAB, CPB, and DTAB for the Be–CAS complex has been found as 0.025, 0.024, and 0.061 µmol L^?1, respectively. The interfering effect of some anions and cations was also tested. The method was applied to the determination of CS CTAB in conditioner shampoo and water samples.