An analytical solution for describing the transient temperature distribution in an aquifer thermal energy storage system

A mathematical model is developed for predicting the temperature distribution in an aquifer thermal energy storage (ATES) system, which consists of a confined aquifer bounded from above and below by the rocks of different geological properties. The main transfer processes of heat include the conduction and advection in the aquifer and the conduction in the rocks. The semi‐analytical solution in dimensionless form for the model is developed by Laplace transforms and its corresponding time‐domain solution is evaluated by the modified Crump method. Field geothermal property data are used to simulate the temperature distribution in an ATES system. The results show that the heat transfer in the aquifer is fast and has a vast effect on the vicinity of the wellbore. However, the aquifer temperature decreases with increasing radial and vertical distances. The temperature in the aquifer may be overestimated when ignoring the effect of thermal conductivity. The temperature distribution in an ATES system depends on the vertical thermal conduction in the rocks and the horizontal advection and thermal conduction in the aquifer. The present solution is useful in designing and simulating the heat injection facility in the ATES systems. Copyright © 2010 John Wiley & Sons, Ltd.     

A coupled discrete element model for the simulation of soil and water flow through an orifice

Soil erosion around defective underground pipes can cause ground collapses and sinkholes in urban areas. Most of these soil erosion events are caused by fluidization of the surrounding soil with subsequent washing into defective sewer pipes. In this study, this soil erosion process is simplified as the gradual washout of sand particles mixed with water through an orifice. The discrete element method is used to simulate the large deformation behavior of the sand particles, and the Darcy fluid model is coupled with this approach to simulate fluid flow through porous sand media. A coupled 3D discrete element model is developed and implemented based on this scheme. To simulate previous experiments using this coupled model considering the current computing capacity, we incorporated a ‘supply layer’ to study the continuous erosion process. The coupled model can predict the erosion flow rates of sand and water and the shape of erosion void. Thus, the model can be used as an effective and efficient tool to investigate the soil erosion process around defective pipes. Copyright © 2017 John Wiley & Sons, Ltd.     

Geological interpretation of a deep seismic‐reflection transect across the boundary between the Delamerian and Lachlan Orogens,in the vicinity of the Grampians,western Victoria

A deep seismic‐reflection transect in western Victoria was designed to provide insights into the structural relationship between the Lachlan and the Delamerian Orogens. Three seismic lines were acquired to provide images of the subsurface from west of the Grampians Range to east of the Stawell‐Ararat Fault Zone. The boundary between the Delamerian and Lachlan Orogens is now generally considered to be the Moyston Fault. In the vicinity of the seismic survey, this fault is intruded by a near‐surface granite, but at depth the fault dips to the east, confirming recent field mapping. East of the Moyston Fault, the uppermost crust is very weakly reflective, consisting of short, non‐continuous, west‐dipping reflections. These weak reflections represent rocks of the Lachlan Orogen and are typical of the reflective character seen on other seismic images from elsewhere in the Lachlan Orogen. Within the Lachlan Orogen, the Pleasant Creek Fault is also east dipping and approximately parallel to the Moyston Fault in the plane of the seismic section. Rocks of the Delamerian Orogen in the vicinity of the seismic line occur below surficial cover to the west of the Moyston Fault. Generally, the upper crust is only weakly reflective, but subhorizontal reflections at shallow depths (up to 3 km) represent the Grampians Group. The Escondida Fault appears to stop below the Grampians Group, and has an apparent gentle dip to the east. Farther east, the Golton and Mehuse Faults are also east dipping. The middle to lower crust below the Delamerian Orogen is strongly reflective, with several major antiformal structures in the middle crust. The Moho is a slightly undulating horizon at the base of the highly reflective middle to lower crust at 11–12 s TWT (approximately 35 km depth). Tectonically, the western margin of the Lachlan Orogen has been thrust over the Delamerian Orogen for a distance of at least 25 km, and possibly over 40 km.     

An approach to the modeling of viscoelastic damage. Application to the long‐term creep of gypsum rock materials

A three‐dimensional phenomenological model is developed to describe the long‐term creep of gypsum rock materials. The approach is based on the framework of continuum damage mechanics where coupling with viscoelasticity is adopted. Specifically, a local damage model based on the concept of yield surface is proposed and deeply investigated. Among the many possibilities, we choose in this work its coupling with a generalized Kelvin–Voigt rheological model to formulate the whole behavior. Long‐term as well as short‐term relaxation processes can be integrated in the model by means of as many as necessary viscoelastic processes. The numerical discretization is described for an easy integration within a finite element procedure. Finally, a set of numerical simulations is given to show the possibilities of the presented model. It shows good agreement with some experimental results found in the literature. Copyright © 2012 John Wiley & Sons, Ltd.     

Water waves generated by instantaneous disturbances at the bed of a sloping beach

The two-dimensional problem of the generation of water waves due to instantaneous disturbances prescribed at the bed of a beach sloping at an arbitrary angle is studied here. It is formulated in terms of an initial-boundary-value problem for the velocity potential describing the motion in the fluid region assuming the linear theory. Using the Laplace transform in time and the Mellin transform in distance, the problem is reduced to solving a difference equation whose method of solution is of considerable importance in the literature. The form of the free surface is obtained in terms of a multiple infinite integral that is evaluated by the method of steepest-descent. For some prescribed forms of the disturbance at the bed of the beach, the free surface is depicted in a number of figures for different beach angles. It is observed that as the beach angle decreases, the maximum wave height increases, which is plausible.     

Calculating actual crop evapotranspiration under soil water stress conditions with appropriate numerical methods and time step

Calculation of actual crop evapotranspiration under soil water stress conditions is crucial for hydrological modeling and irrigation water management. Results of actual evapotranspiration depend on the estimation of water stress coefficient from soil water storage in the root zone, which varies with numerical methods and time step used. During soil water depletion periods without irrigation or precipitation, the actual crop evapotranspiration can be calculated by an analytical method and various numerical methods. We compared the results from several commonly used numerical methods, including the explicit, implicit and modified Euler methods, the midpoint method, and the Heun's third‐order method, with results of the analytical method as the bench mark. Results indicate that relative errors of actual crop evapotranspiration calculated with numerical methods in one time step are independent of the initial soil water storage in the range of soil water stress. Absolute values of relative error decrease with the order of numerical methods. They also decrease with the number of time step, which can ensure the numerical stability of successive simulation of soil water balance. Considering the calculation complexity and calculation errors caused by numerical approximation for different time step and maximum crop evapotranspiration, the explicit Euler method is recommended for the time step of 1 day (d) or 2 d for maximum crop evapotranspiration less than 5 mm/d, the midpoint method or the modified Euler method for the time step of up to one week or 10 d for maximum crop evapotranspiration less than 5 mm/d, and the Heun's third‐order method for the time step of up to 15 d. Copyright © 2011 John Wiley & Sons, Ltd.     

Particle manifold method (PMM): A new continuum‐discontinuum numerical model for geomechanics

Particle manifold method (PMM) is a new extension of the numerical manifold method (NMM). PMM uses a mathematical cover system to describe the motion and deformation of a particle‐based physical domain. By introducing the concept of particle into NMM, PMM takes the advantages of easy topological and contact operations with particles. In this article, the methodology, formulations and implementation of the method are presented, together with modelling examples for validation. It is found that good solutions for both continuous and discontinuous problems are obtained by the new developed PMM. Due to the underlying coupled continuum‐discontinuum property of PMM, it has great potential for modelling of geomechanical problems. Copyright © 2012 John Wiley & Sons, Ltd.     

The form of the asymptotic depth-limited wind-wave spectrum: Part III — Directional spreading

The directional spreading of both the wavenumber and frequency spectra of finite-depth wind generated waves at the asymptotic depth limit are examined. The analysis uses the Wavelet Directional Method, removing the need to assume a form for the dispersion relationship. The paper shows that both the wavenumber and frequency forms are narrowest at the spectral peak and broaden at wavenumbers (frequencies) both above and below the peak. The directional spreading of the wavenumber spectrum is bi-modal above the spectral peak. In contrast, the frequency spectrum is uni-modal. This difference is shown to be the result of energy in the wind direction being displaced from the linear dispersion shell. A full parametric relationship for the directional spreading of the wavenumber spectrum is developed. The analysis clearly shows that typical dispersion relationships are questionable at high frequencies and that such effects can be significant. This result supports greater attention being focussed on the routine recording of wavenumber spectra, rather than frequency spectra.     

Coupled finite‐element simulation of injection well testing in unconsolidated oil sands reservoir

This paper presents a finite‐element (FE) model for simulating injection well testing in unconsolidated oil sands reservoir. In injection well testing, the bottom‐hole pressure (BHP) is monitored during the injection and shut‐in period. The flow characteristics of a reservoir can be determined from transient BHP data using conventional reservoir or well‐testing analysis. However, conventional reservoir or well‐testing analysis does not consider geomechanics coupling effects. This simplified assumption has limitations when applied to unconsolidated (uncemented) oil sands reservoirs because oil sands deform and dilate subjected to pressure variation. In addition, hydraulic fracturing may occur in unconsolidated oil sands when high water injection rate is used. This research is motivated in numerical modeling of injection well testing in unconsolidated oil sands reservoir considering the geomechanics coupling effects including hydraulic fracturing. To simulate the strong anisotropy in mechanical and hydraulic behaviour of unconsolidated oil sands induced by fluid injection in injection well testing, a nonlinear stress‐dependent poro‐elasto‐plastic constitutive model together with a strain‐induced anisotropic permeability model are formulated and implemented into a 3D FE simulator. The 3D FE model is used to history match the BHP response measured from an injection well in an oil sands reservoir. Copyright © 2013 John Wiley & Sons, Ltd.     

Analytical and computational procedure for solving the consolidation problem of layered soils

One‐dimensional consolidation analysis of layered soils conventionally entails solving a system of differential equations subject to the flow conditions at the bounding upper and lower surfaces, as well as the continuity conditions at the interface of every pair of contiguous layers. Formidable computational efforts are required to solve the ensuing transcendental equations expressing the matching conditions at the interfaces, using this method. In this paper, the jump discontinuities in the flow parameters upon crossing from one layer to the other have been systematically built into a single partial differential equation governing the space–time variation of the excess pore pressure in the entire composite medium, by the use of the Heaviside distribution. Despite the presence of the discontinuities in the coefficients of the differential equation, a closed‐form solution in the sense of an infinite generalized Fourier series is obtained, in addition to which is the development of a Green's function for the differential problem. The eigenfunctions of the composite medium are the coordinate functions of the series, obtained computationally through the application of the extended equations of Galerkin. The analysis has been illustrated by solving the consolidation problem of a four‐layer composite, and the results obtained agree very well with the results obtained by previous researchers. Copyright © 2013 John Wiley & Sons, Ltd.