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.     

Simulation of green water flow on deck using non-linear dam breaking theory

Experiments carried out with models of floating production, storage and offloading platforms (FPSOs) showed that the flow of water over the deck edge, onto the deck resembled a suddenly released wall of water rather than a breaking wave. Therefore green water flow onto the deck was simulated using dam breaking theory, but the theory’s shallow-water assumptions may be limiting. In this paper a non-linear dam breaking problem is formulated. Equations of motion in the Lagrangian form are used and the solution is sought as an infinite series in time. Comparisons with the shallow water approximation are carried out.     

Wave enhancement due to blockage in semi-submersible and TLP structures

An exact analytical method is described to solve the diffraction problem of a group of truncated vertical cylinders. In order to account for the interaction between the cylinders, Kagemoto and Yue's exact algebraic method is utilised (Kagemoto, H., Yue, D.K.P., 1986. Interactions among multiple three-dimensional bodies in water waves: an exact algebraic method. J Fluid Mech, 46, 129–139). The isolated cylinder diffraction potential is obtained using Garret's solution and evanescent mode solutions are derived in a similar manner (Garret, C.J.R., 1971. Wave forces on a circular dock. J Fluid Mech, 46, 129–139).Free surface elevations are calculated for an array of four cylinders and compared with experiments. Comparisons show good agreement.     

Pore pressure profiles in fractured and compliant rocks1

Fluid permeability in fractured rocks is sensitive to pore-pressure changes. This dependence can have large effects on the flow of fluids through rocks. We define the permeability compliance γ= 1/k(k/δp_p)_pc, which is the sensitivity of the permeability k to the pore pressure p_p at a constant confining pressure p_c, and solve the specific problems of constant pressure at the boundary of a half-space, a cylindrical cavity and a spherical cavity. The results show that when the magnitude of permeability compliance is large relative to other compliances, diffusion is masked by a piston-like pressure profile. We expect this phenomenon to occur in highly fractured and compliant rock systems where γ may be large. The pressure profile moves rapidly when fluids are pumped into the rock and very slowly when fluids are pumped out. Consequently, fluid pressure, its history and distribution around injection and production wells may be significantly different from pressures predicted by the linear diffusion equation. The propagation speed of the pressure profile, marked by the point where δp_p/δx is a maximum, decreases with time approximately as and the amplitude of the profile also dissipates with time (or distance). The effect of permeability compliance can be important for fluid injection into and withdrawal from reservoirs. For example, excessive drawdown could cause near-wellbore flow suffocation. Also, estimates of the storage capacity of reservoirs may be greatly modified when γ is large. The large near-wellbore pressure gradients caused during withdrawal by large γ can cause sanding and wellbore collapse due to excessive production rates.     

Scaling procedures for heterogeneous unconfined aquifers

Complex flows in heterogeneous confined and unconfined aquifers is a phenomenon that continues to present difficulties in flow mapping and modelling in the field, laboratory, and through numerical simulations. It is often the case with complicated phenomena that transformative scaling and reduction of the problem through symmetry is of great efficacy in the formation of predictive models in both the laboratory and computational settings. A detailed a study of the application of a broad class of Lie scaling transformations on a set of equations representing the groundwater flows in heterogeneous confined and unconfined aquifers has produced a set of scaling relationships between the spatial variables, hydrologic variables, and parameters. The set of scaling transformations preserve the structure of the equations in the sense that the scaling transformations leave the initial‐boundary value system representing the invariant groundwater flows. This theoretical approach elucidates not only the scaling relationships but also the properties that hydrologic variables and parameters must satisfy in order for calling to be possible. Validation of the theory developed is carried out through a series of four numerical simulations using the USGS modflow ‐2005 software package. The results of these experiments demonstrate that the derived scaling transformations can effectively form predictive models of large‐scale phenomena at small scales with negligible error in many cases. Comments on the limitations of the approach and directions for future research are made in the closing sections. Copyright © 2016 John Wiley & Sons, Ltd.     

Did satellite imagery supersede aerial imagery? A perspective from 3D geopositioning accuracy

In this study, the geometric accuracy comparison of aerial photos and WorldView-2 satellite stereo image data is evaluated with the different number and the distribution of the ground control points (GCPs) on the basis of large scale map production. Also, the current situation of rivalry between airborne and satelliteborne imagery was mentioned. The geometric accuracy of Microsoft UltraCam X 45 cm ground sampling distance (GSD) aerial imagery and WorldView-2 data both with and without GCPs are also separately analyzed. The aerial photos without any GCP by only using global navigation satellite system (GNSS) and inertial measurement unit (IMU) data with tie points give an accuracy of ±1.17 m in planimetry and ±0.71 m in vertical that means nearly two times better accuracy than the rational polynomial coefficient (RPC) of stereo WorldView-2. Using one GCP affects the accuracies of aerial photos and WorldView-2 in different ways. While this situation distorts the aerial photo block, it corrects the shift effect of RPC in WorldView-2 and increases the accuracy. By using four or more GCPs, ½?pixel (～0.23 m) accuracy in aerial photos and 1 pixel (～0.50 m) accuracy in WorldView-2 can be achieved in horizontal. In vertical, aerial photos have 1 pixel (～0.55 m) and WorldView-2 has 1.5 pixels (～0.85 m) accuracy. These results show that Worldview-2 imagery can be used in the production of class I 1:5000 scale maps according to the ASPRS Accuracy Standards for Digital Geospatial Data in terms of geometric accuracy. It is concluded that the rivalry between aerial and satellite imagery will continue for some time in the future.     

Effect of Atmosphere and Temperature Treatment on Leoanardite for Increasing Humic Acid Yield

In this review, the shifts in organic matter (OM) accumulation and C:N ratios in lake sediments to reconstruct paleoclimate and paleo-environmental changes since the early Holocene period are presented. The C:N proxy data of total OM reflect wet climatic conditions during early Holocene (10 to 8.2 kyrs BP) due to enhanced southwest monsoon. This was followed by intermittent arid conditions during the mid and late Holocene period (8.2 to 2.8 kyr BP). Enhanced values of C:N ratio during middle to late Holocene (7.8–2.3 kyrs B.P) indicate periods with lower lake levels and minimum precipitation, while decreased C:N ratio point to stronger SW monsoon and expansion of the lakes. Further, C:N and δ¹³C results from the lake sediments reveal a detailed and continuous paleo-environmental changes in the relative sources of OM (allochthonous vs autochthonous). Proxy records using such natural archives have also been utilized to reconstruct past extreme events and environmental changes around the lake systems, such as causes for lake desiccation, hydrographic changes, alternations between C₃ and C₄ vegetation and historical disturbances in the catchment area since the early-late Holocene period coupled with the Indian summer monsoon.     

‘Filament’ marker beds in the Karababa-A Member (Turonian) of the Arabian platform,SE Turkey: Palaeo-environmental significance,stratigraphy and correlation potential

A ‘filament’ event bed/level corresponds to the occurrence of thin elongate calcitic, shells, or plates of pelagic, bivalve or crinoidal, origin, within pelagic, laminated and organic-matter rich limestones. These organic-rich limestones had been generally deposited under hypoxic/anoxic conditions in an outer-ramp environment. These thin elongate, bivalve shells, or crinoidal plates, are found broken in small pieces, disintegrated, or simply preserved parallel to bedding as almost complete specimens. Such ‘filament’ beds were spotted in SE Turkey in deposits, namely the Karababa-A Member, around the Cenomanian-Turonian boundary (C/TB) and above. On a global scale, these filament event beds illustrate sea-level rise related to eustacy and/or climatic change. The abundance of filaments close to the C/TB is a biological marker of high organic productivity resulting from a climatic change to warmer conditions. The prevailing higher sea-level conditions were then favourable to the accumulation and preservation of organic-rich facies, characteristic of the Oceanic Anoxic Event 2 (OAE2). Using both biostratigraphic and carbon isotopic data, those deposits were dated from the latest Cenomanian-Turonian age. ‘Filament’ event beds were recorded in the same order, except for some small differences. A good number of these bio-events are global. Consequently, on a global scale, they are susceptible to constrain the C/TB, especially the base of the Turonian stage, with a significant degree of confidence.