Shallow Water Flow Research Articles

Geohazard Investigation On Gas Cloud Distribution At ‘B’ Field (Channel Influence)

Sedimentary rock deposition occur in very fast rates in offshore basin and might cause shallow subsurface geohazards that will incur high risk and increase cost of drilling operations. In general, offshore geohazards consist of a variety of geological features that contribute potential risks to the labour force, offshore amenities including the environment and surrounding areas due to the consequences of long or short period of geological processes. Therefore, further study need to be done properly in terms of geohazards classification that is significant to the offshore oil and gas developments in the Malay Basin (Bujang Field, refer Figure 1); such as shallow gas, gas hydrate, shallow water flow, slumping, landslides, faulting, pockmarks and liquefaction. To mitigate the point of costly drilling and safety risks, several techniques are needed during data gathering to visualize, interpret and identify the potential shallow drilling hazards. Besides, to a geoscientist, data integration and modelling techniques can be used to analyse the structural and physical circumstances of shallow subsurface. At the same time, gas models and geohazards map can be established based on seabed hazard analysis from seismic data to plan secure wells. Several seismic attributes such as instantaneous phase, instantaneous frequency, remove bias and envelope (reflection strength) had been used for channel detection. For gas cloud identification, seismic attributes such as remove bias, instantaneous phase, Chaos and RMS (Root Mean Square) amplitude are used. Besides that, spectral decomposition technique are used to display channel systems and other stratigraphic features in the field. Generally, this paper will explain about the meaning of geohazards in the oil and gas industry, the types of geohazards, general geohazards analysis, and will focuss on the identification of gas cloud through channel structure by applying several seismic attributes on specific parameters. All of this will be related to geohazards perspective and consequently, precautions can be undertaken systematically.

A lattice Boltzmann model for the viscous shallow water equations with source terms

In this paper, a lattice Boltzmann (LB) model is proposed for a class of viscous shallow water equations, in which a second-order moment of the source term is applied to recover the viscosity in the governing equation and eliminate the additional errors generated during the Chapman-Enskog analysis. There are three different schemes based on different treatments of the source term. Through numerical simulations of several classical benchmark problems, we find that the second-order moment of the source term can not only improve the accuracy of the LB model, but also ensure the conservation of the system. In addition, the influence of rainfall intensity on shallow water flow is also taken into account, and the results show that present LB model can also accurately study such problems as overland flows.

A greedy non-intrusive reduced order model for shallow water equations

In this work, we develop Non-Intrusive Reduced Order Models (NIROMs) that combine Proper Orthogonal Decomposition (POD) with a Radial Basis Function (RBF) interpolation method to construct efficient reduced order models for time-dependent problems arising in large scale environmental flow applications. The performance of the POD-RBF NIROM is compared with a traditional nonlinear POD (NPOD) model by evaluating the accuracy and robustness for test problems representative of riverine flows. Different greedy algorithms are studied in order to determine a near-optimal distribution of interpolation points for the RBF approximation. A new power-scaled residual greedy (psr-greedy) algorithm is proposed to address some of the primary drawbacks of the existing greedy approaches. The relative performances of these greedy algorithms are studied with numerical experiments using realistic two-dimensional (2D) shallow water flow applications involving coastal and riverine dynamics.

A new well-balanced finite-volume scheme on unstructured triangular grids for two-dimensional two-layer shallow water flows with wet-dry fronts

In this study, a novel two-dimensional finite-volume method on unstructured triangular meshes for two-layer shallow water flows is developed. First, the one-dimensional relaxation approach developed in Abgrall and Karni (2009) [1] is extended to the currently studied two-dimensional two-layer shallow water equations to build an unconditionally hyperbolic system. Next, a two-dimensional finite-volume HLL scheme on triangular grids for such a non-conservative hyperbolic system is constructed. Special attention is paid to guaranteeing the well-balanced property even in the presence of the wet-dry fronts. To this end, techniques such as spatial reconstruction for the secondary variables, special cell classifications for the two-layer fluid system, and special local reconstruction of auxiliary surface variables are proposed. These special techniques are further combined with new discrete formulas for the nonconservative products and the bed-slope terms, and it thus leads to an exactly well-balanced numerical scheme for the studied two-layer system even in the presence of wet-dry fronts. The developed numerical model is second order accurate and preserves the nonnegative layer depths. The performances of the proposed numerical model are investigated by several numerical experiments.

A system for monitoring a marine well for shallow water flow: Development of early detection

Deepwater basins around the world contain shallow sequences of overpressured, sand-prone sediments that can result in shallow water flow (SWF) events. These events have frequently resulted in wellbore instability and increased man-hour exposure to potential health, safety, security, and environment risks, as well as nonproductive time, and they have sometimes been the cause of the loss of a well while drilling the shallow (riserless) section for oil and gas exploration or development projects. Methods previously established to classify the magnitude of an SWF event have been used with partial success to identify the onset of an SWF event. The need existed to develop a system enabling early prediction, detection, and mitigation of SWF events while drilling. Real-time monitoring of the riserless section of a marine well for SWF requires a system using a plurality of data feeds that we defined as the SYSTEM. The data feeds include seismic data, remotely operated vehicle video, and surface and downhole logging measurements. An SWF surveillance methodology, which we defined as a discharge category model (DCM), has been developed for early detection of an SWF event, prior to the onset of wellbore instability. DCM focuses on baseline discharge categories (ranging from no flow to minor flow) prior to wellbore instability and taking into account the U-tube effects. Real-time monitoring of data feeds coupled with DCM in the context of SYSTEM has helped to mitigate SWF events. There have been no wells lost due to SWF events that have used DCM in the context of SYSTEM in various basins throughout the world. In total, 154 wells have been monitored globally using DCM with 46 SWF events detected and mitigated before reaching a severity level that might compromise well integrity from 2012 to 2019.

Random Walk Particle Tracking for Convection-diffusion Dominated Problems in Shallow Water Flows

This paper deals with a Lagrangian stochastic approach to solve the advection-diffusion equation of a scalar tracer inflow based on random walk particle tracking (RWPT) of a fine number of particles that describe the tracer. The water flow is governed by the shallow water equations that are solved using a finite volume upwinding scheme on a non-structured triangular mesh. Results are presented for two problems, pure advection in a square cavity and pollutant advection in the strait of Gibraltar, that demonstrate the performance, accuracy, and the flexibility of the RWPT method to examine the process of pollutant convection by comparing predictions with those from the Eulerian approach. The Lagrangian approach is shown to have advantages in terms of the high level of simplicity and stability relative to the Eulerian approach.

MPS‐Based Model to Solve One‐Dimensional Shallow Water Equations

AbstractHere, a moving particle simulation method is presented to spatially integrate the cross‐sectional average shallow water equations using a prediction‐correction procedure for the time discretization. A density‐ratio equation is derived for the water depth computation according to the particle number density concept. The newly derived equation does not miscalculate the water depth in case an incorrect searching radius parameter is adopted, unlike the typical volume‐summation formula in meshless shallow water flows. A new one‐dimensional Spiky kernel function is developed to satisfy the unity condition employed in the Newton‐Raphson iteration to calculate the water depth. Dynamic stabilization is adopted to capture shockwave problems, a case‐independent technique based on the inelastic collision with unequal masses. The convective flux term is eliminated under the Lagrangian framework, and so the momentum is adequately conserved without the need for any special treatment. The proposed scheme maintains the exact C‐property, meaning that the water depth gradient and bed slope are hydrostatically well balanced within a discretized solution domain. Compared to analytical solutions and experimental data, the results of this study reveal that the present model is a robust numerical solver without unphysical oscillations. It can capture various shock problems, including steep gradient shock‐front, discontinuous wet bed, transcritical flow regimes, and irregular bed topography. The present model can also simulate the dry‐wet flow transition influenced by friction without experiencing any divisions by zero, negative values, or unphysical perturbations. This advantage is basically due to the water particles' absence and presence for the dry and wet regions, respectively.

Performance Comparison between Semi-Lagrangian and Eulerian Numerical Solutions for Two-Dimensional Surface Flows in Basin Irrigation

AbstractTo achieve efficient simulation for surface shallow-water flows in large-scale basin irrigation, a semi-Lagrangian numerical solution for two-dimensional shallow-water equations in unstruct...

A case study of debris flow risk assessment and hazard range prediction based on a neural network algorithm and finite volume shallow water flow model

Due to the need of economic development and energy structure adjustment, China intends to build a number of pumped storage power stations for hydroelectric storage to generate electricity. Pumped storage power stations are generally built in mountainous or hilly areas where sufficient water and height differences will provide the adequate head difference. Geological processes, such as debris flows, often occur in mountainous areas and are one of the main threats to power stations and related projects. In this work, the debris flows in the engineering area of a pumped storage power station in Shangyi County, Hebei Province were selected as a case study. The neural network model was adopted to quantitatively calculate the probability of debris flows. Then, risk zoning was implemented according to the probability values. Finally, the debris flow numerical simulation software SFLOW, which is based on the finite volume shallow water flow model, was used for high-risk gullies. The spatial hazard range of each debris flow was predicted for rainfall frequencies of 20, 50, 100, and 200 years. And the sensitivity of parameters affecting debris flow migration and the advantages of SFLOW compared with FLO-2D software were discussed. In general, the SFLOW model can accurately and efficiently solve the problem of fluid flow on irregular terrain and can be applied to similar engineering projects.

A well-balanced and positivity-preserving SPH method for shallow water flows in open channels

A well-balanced and positivity-preserving meshless method based on smoothed particle hydrodynamics (SPH) is developed to simulate one-dimensional (1D) and two-dimensional (2D) shallow water (SW) flows in open channels with irregular geometries. A new form of the characteristic equations that govern the water-surface level and water velocity is introduced to specify the numerical inflow/outflow boundary conditions. An additional condition, derived from temporal discretization to determine the time-step size, forces the water depth to be positive. A 1D finite volume shallow water (FVSW) model based on the first-order Godunov upwind method is built to conduct a comparison of the 1D meshless-based and mesh-based SW models. Six benchmark cases – still water, single trapezoidal and rectangular and prismatic and non-prismatic channels, and a dendritic channel network – are employed to validate the proposed models and compared with the exact and mesh-based numerical solutions. A real-world case of the Chicago Area Waterways System (CAWS) is investigated to highlight the performance of the proposed 1D model for a practical hydraulic system.

A well-balanced lattice Boltzmann model for the depth-averaged advection–diffusion equation with variable water depth

A well-balanced lattice Boltzmann model for the depth-averaged advection–diffusion equation is developed to solve the solute transport problem in shallow water flows with obvious gradient changes in water depth. The flow field is simulated by the lattice Boltzmann model for shallow water equations with the central moments (CMs) collision operator and D2Q9 lattice pattern. In this model, the diffusion term of the depth-averaged advection–diffusion equation is divided into two parts by the product rule, one part of which is combined into the advection term to produce the pseudo velocity. The relaxation time is independent of the diffusion coefficient, and the remaining value of (3+3)∕6 derived from the Chapmann–Enskog expansion reduces the third-order error. According to the different treatments of the water depth gradient in the equilibrium distribution function, center scheme and linked scheme are developed. Both schemes can ensure the conservation of the solute mass. Numerical tests show that these two schemes give predictions in good agreement, but the linked scheme works better at the breakpoint. Comparisons with the reference indicate that this model is advantageous with respect to both stability and efficiency.

Mechanical properties of grain contacts in unconsolidated sands

Unconsolidated sands provide zones of high porosity and permeability important for freshwater aquifers, hydrocarbon production, and CO2 sequestration. An understanding of the acoustics of unconsolidated sands enables the characterization of such formations using ultrasonics, borehole acoustics, and seismic methods. Inversion of ultrasonic compressional and shear velocities measured for unloading as a function of confining pressure for room-dry unconsolidated sands allows information on the mechanical properties of the grain contacts to be obtained using an approach based on the divergence theorem. This allows the effective compliance of sand to be written as the sum of the compliance of the pores and of the grain contacts, and it does not assume that the grains are identical spheres, in contrast to previous approaches. Grain contacts are found to be more compliant under shear than under normal compression, and the ratio of the normal-to-shear compliance decreases with decreasing confining pressure, implying that the shear compliance increases faster with decreasing confining pressure than the normal compliance. This is of importance in understanding the role of shear in the failure of unconsolidated sands, such as occurs in shallow water flow, sanding, and failure around injectors, where the change in stress is a function of the normal-to-shear compliance ratio of the grain contacts.

Very high order well-balanced schemes for non-prismatic one-dimensional channels with arbitrary shape

Accurate modelling of shallow water flows in canals for realistic scenarios cannot neglect the variations of the size and shape of the cross-section along the canal. In typical situations, especially in view of applications to flows in networks of canals, a 2D model would be too costly, while the standard 1D Saint-Venant model for a rectangular channel with constant breadth would be too coarse. In this paper we derive efficient, high order accurate and robust numerical schemes for a 1.5D model, in which the canal can have an arbitrary cross-section: the shape can vary along the channel and is described by a depth-dependent breadth function σ(x,z), where x is the coordinate along the channel and z represents the vertical direction. Contrary to all previous schemes for this model, we reformulate the equations in a way that avoids the appearance of the moments of σ and of ∂σ/∂x in the source terms. Our numerical schemes are based on the path-conservative approach for dealing with non-conservative products, are well-balanced on the lake at rest solution and can treat wet-try transitions. They can be implemented with any order of accuracy. Schemes up to third order are explicitly constructed and tested, thanks to the CWENO reconstruction technique. Through a large set of numerical tests we show the performance of the new schemes and compare the results obtained with different orders of accuracy.

Comparing single‐phase, non‐Newtonian approaches with experimental results: Validating flume‐scale mud and debris flow in HEC‐RAS

AbstractPost‐fire debris flows and tailing impoundment failures destroy lives and property. These geologic hazards – and other similar processes – fall on a continuum between classic Newtonian flood analyses and geotechnical stability analyses. The US Army Corps of Engineers (USACE) is developing a non‐Newtonian library (DebrisLib) that includes a suite of rheological and clastic approaches to hyper‐concentrated, mudflow and debris flow dynamics. The Hydrologic Engineering Center (HEC) has implemented these non‐Newtonian methods into the widely used, public‐domain open‐channel hydraulics and morphodynamic software, HEC‐RAS (river analysis system). This work presents part of the verification and validation of these non‐Newtonian approaches, applying several rheological equations to published laboratory results high‐concentration flume experiments.This study tested the linear Bingham model as well as the turbulent and Bagnold quadratic terms of the O'Brien equation. HEC‐RAS also includes the non‐linear Herschel–Bulkley (HB) approach, which quantifies shear‐thickening or shear‐thinning processes. The study used these non‐Newtonian models in HEC‐RAS to simulate 10 of Parsons et al.’s (2001) flume experiments, which measured the snout and plug velocity of fluids with high solid concentrations (Cv = 68–74%) and a broad range of material gradations (d50 = 0.05–1 mm, d15 = 0.006–0.1 mm). The experiments also measured and back‐calculated Bingham and HB parameters of the materials, finding HB powers between 0.45 and 1.25 (i.e. fluids that are dilatant, pseudo‐plastic and visco‐plastic).The rheological models incorporated into DebrisLib and implemented in HEC‐RAS reproduce experimental data well for most experiments. The Bingham model generated a plug velocity root‐mean‐square error (RMSE) of 0.21 m/s using standard flow parameters and Parsons et al.’s calibrated parameters, a substantial improvement over the unmodified shallow water flow equations (RMSE 0.77 m/s). Experiments with strong snout effects tended to generate higher residuals, especially in the snout velocity. The RMSE associated with the O'Brien equation was larger with the Parsons et al. fit parameters, but similar (0.23 m/s) with measured parameters. The turbulent parameter was the largest (often the dominant) parameter in most O'Brien simulations, with the dispersive stress only proving significant for the coarsest material. DebrisLib had to use a modified version of the dispersive term to simulate these concentrations. Both the 2D depth‐averaged shallow water equation (SWE) and diffusion wave equation were used to simulate the experiments. The best results were obtained with the SWE with horizontal mixing.

Effect of Depth Discontinuity on Interfacial Stability of Tangential-Velocity Discontinuity in Shallow-Water Flow

Effect of Depth Discontinuity on Interfacial Stability of Tangential-Velocity Discontinuity in Shallow-Water Flow

Project and Control Allocation of a 3 DoF Autonomous Surface Vessel With Aerial Azimuth Propulsion System

To gather hydrological measurements is a difficult task for Autonomous Surface Vessels. It is necessary for precise navigation considering underwater obstacles, shallow and fast water flows, and also mitigate misreadings due to disturbs caused by their propulsion system. To deal with those problems, this paper presents a new topology of an Autonomous Surface Vessel (ASV) based on a catamaran boat with an aerial propulsion system with azimuth control. This set generates an over-actuated 3 Degree of Freedom (DoF) ASV, highly maneuverable and able of operating over the above-mentioned situations. To deal with the high computational cost of the over-actuated control allocation (CA) problem, this paper also proposes a Fast CA (FCA) approach. The FCA breaks the initial nonlinear system into partially-dependent linear subsystems. This approach generates smaller connected systems with overlapping solution spaces, generating fast and robust convergence, especially attractive for embedded control devices. Both proposals, i.e., ASV and FCA, are assessed through mathematical simulations and real scenarios.

Estimation of Shallow Water Flow Based on the Extended Kalman Filter FEM Using Water Level Measurements by Image Analysis

Estimation of Shallow Water Flow Based on the Extended Kalman Filter FEM Using Water Level Measurements by Image Analysis

Stochastic Variational Formulations of Fluid Wave\u2013Current Interaction

We are modelling multiscale, multi-physics uncertainty in wave–current interaction (WCI). To model uncertainty in WCI, we introduce stochasticity into the wave dynamics of two classic models of WCI, namely the generalised Lagrangian mean (GLM) model and the Craik–Leibovich (CL) model. The key idea for the GLM approach is the separation of the Lagrangian (fluid) and Eulerian (wave) degrees of freedom in Hamilton’s principle. This is done by coupling an Euler–Poincaré reduced Lagrangian for the current flow and a phase-space Lagrangian for the wave field. WCI in the GLM model involves the nonlinear Doppler shift in frequency of the Hamiltonian wave subsystem, which arises because the waves propagate in the frame of motion of the Lagrangian-mean velocity of the current. In contrast, WCI in the CL model arises because the fluid velocity is defined relative to the frame of motion of the Stokes mean drift velocity, which is usually taken to be prescribed, time independent and driven externally. We compare the GLM and CL theories by placing them both into the general framework of a stochastic Hamilton’s principle for a 3D Euler–Boussinesq (EB) fluid in a rotating frame. In other examples, we also apply the GLM and CL methods to add wave physics and stochasticity to the familiar 1D and 2D shallow water flow models. The differences in the types of stochasticity which arise for GLM and CL models can be seen by comparing the Kelvin circulation theorems for the two models. The GLM model acquires stochasticity in its Lagrangian transport velocity for the currents and also in its group velocity for the waves. However, the CL model is based on defining the Eulerian velocity in the integrand of the Kelvin circulation relative to the Stokes drift velocity induced by waves driven externally. Thus, the Kelvin theorem for the stochastic CL model can accept stochasticity in its both its integrand and in the Lagrangian transport velocity of its circulation loop. In an “Appendix”, we also discuss dynamical systems analogues of WCI.

Seismic geomorphology and overpressure variation in the shallow-water-flow-prone sand units in the north-central Gulf of Mexico

The north-central Gulf of Mexico area received rapid deposition of a basin-floor fan system consisting of interbedded muds, silts, and sandy turbidite deposits during the Pleistocene. Overpressure occurs at shallow depths when burial rates exceed the dewatering rates of sediment pore fluids. Two stratigraphic sequences in the region contain significant overpressure with elevated shallow-water flow risk within these units. We have used publicly available seismic and well data to identify the geomorphology and overpressure variation of these units. The previously described “Blue Unit” and its lateral extent, thickness, depth below sea level (BSL), and overpressure gradient have been revised. The Blue Unit extends from the northern portion of the Mississippi Canyon (MC) protraction area to as far south as the Atwater Valley (AT) protraction area. For the first time, the Green Unit’s lateral extent, thickness, depth BSL, and pore pressure are defined. The “Green Unit” was found to extend further south than the Blue Unit into the AT protraction area and further east in the Desoto Canyon protraction area. The tops of both units are highly incised by postdepositional erosional systems, whereas the base of each unit is well preserved. The top of the Blue Unit below the mud line (BML) varies from <70 m (<230 ft) in the north to as deep as 701 m (2300 ft) in the south, whereas the top of the Green Unit is as shallow as 300 m (985 ft) in the north to 901 m (2956 ft) in the south. Overpressure in the MC area has been reported just BML. The pore pressure gradient ranges from 0.47 to 0.52 psi/ft at the base of the Blue Unit and increases to 0.60 psi/ft within the Green Unit.

Comparison of digital image analysis methods for morphometric characterization of soil aggregates in thin sections

The purpose of this study was to investigate the applicability of semiautomatic segmentation methods for obtaining and evaluating morphometric parameters of soil aggregates in artificially prepared loose samples in soil thin sections. The object of the research is typical arable Chernozem. The aggregates were separated by wet sieving method from loose sample of upper 10 cm of the plowing horizon after erosion by a model shallow water flow on a large erosion tray. The aggregates, loosely scattered on the glass and fixed with polyester resin, were used to produce the thin sections. Images of the thin sections were taken under a polarizing microscope and then were processed using two methods compared: Adobe Photoshop + CTan and Thixomet Pro. Data on morphometric parameters of aggregates were obtained: the shape factor, the degree of roundness and the coefficient of aggregate surface roughness. The convergence of the results obtained using Photoshop + CTan by three researchers was evaluated by comparing samples using the Student's test and the Mann-Whitney test. The convergence of the averaged results obtained using Photoshop + CTan and the results obtained using Thixomet Pro was evaluated using the Mann - Whitney test. No significant differences were found between the parameters of the same aggregates obtained using a combination of Adobe Photoshop and CTan programs by different researchers. No significant differences were found between the parameters of the same aggregates obtained by the compared methods. So, one can conclude that the reliability of determining the morphometric parameters of soil aggregates using Thixomet Pro is comparable to the reliability of results when working with images of sectionsin CTan after binarization in Adobe Photoshop. The method of obtaining data on morphometric parameters of soil aggregates using Thixomet Pro completely eliminates the possibility of subjective error, shows a high degree of automation, reproducibility and reliability of the results obtained, and is faster.