scholarly journals Analytical assessment of subsidence due to Aquifer Storage and Recovery (ASR) applications to multi-aquifer systems

2000 ◽  
Vol 21 ◽  
Author(s):  
J. Li
Keyword(s):  
Analytical Solution ◽  
Land Subsidence ◽  
Potential Risk ◽  
Aquifer Storage And Recovery ◽  
One Dimensional ◽  
Aquifer System ◽  
Aquifer Storage ◽  
Aquifer Systems ◽  
The One ◽  
Development And Management

The present paper emphasises concerns of land subsidence or compression of clay confining beds caused by periodic withdrawal and injection of water from or into the adjacent aquifers. An analytical solution for a one-dimensional case based on a sandwich model is found so that analysis of potential risk of aquifer system deformation due to the technology of Aquifer Storage and Recovery (ASR) can be conducted. A governing equation expressed directly in terms of displacement is employed to describe the one-dimensional subsidence. For simplicity, saturated aquifer systems are assumed to behave like poroelastic material. A cyclic loading function with a triangle pattern is assumed at boundaries to simulate effective stress induced by changes in hydraulic head at boundaries. The both compression and swelling of clay due to the periodic and linear loads at the boundaries are considered in this model. The two aquifers (one above the confining bed and the other beneath) can be pumped independently of each other. The results from the analytical solution are applied to estimate and predict potential risk of land subsidence due to ASR activity and to provide a first-estimate type of guideline for city or regional development and management of water resources.

Using an analytical solution to estimate the subsidence risk caused by ASR applications

2001 ◽  
Vol 7 (1) ◽  
pp. 67-79 ◽  
Author(s):  
J. Li ◽  
D. C. Helm
Keyword(s):  
Land Subsidence ◽  
Potential Risk ◽  
Analytic Solution ◽  
Vertical Displacement ◽  
Water Withdrawal ◽  
Aquifer System ◽  
Aquifer Storage ◽  
City And Regional Planning ◽  
Poroelastic Material ◽  
The One

Abstract Land subsidence, due to the net compression of one or more semi-pervious clay beds, can be induced by the application of aquifer storage and recovery (ASR) technology. ASR technology involves periodically pumping and injecting water from or into adjacent aquifers for various purposes. In order to estimate the potential risk of aquifer system deformation in response to an injecting-pumping scheme, an analytic solution for the one-dimensional case (a sandwich model) is solved. The solution is analyzed for a unit column of an idealized compressible semipervious layer. A governing equation is invoked that is expressed directly in terms of the vertical displacement of the skeletal frame (Helm, 1987). For simplicity, the saturated aquifer system is assumed to behave like poroelastic material (both recoverable and nonrecoverable). The two idealized aquifers (one above the modeled semi-confining bed and the other beneath) can be pumped independently of each other. Analytical solutions are found for subsidence in response to selected stress/pumping patterns. Results from the analytic solution are applied in order to estimate and predict the potential risk of land subsidence due to ground-water withdrawal and injection, and to provide a first-estimate type of guideline for city and regional planning and the exploration of water resources.

scholarly journals Analytical Solution of Tidal Loading Effect in a Submarine Leaky Confined Aquifer System

Geofluids ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Zongzhong Song ◽  
Hailong Li ◽  
Qian Ma ◽  
Chunmiao Zheng ◽  
Jiu Jimmy Jiao ◽  
...  
Keyword(s):  
Analytical Solution ◽  
Confined Aquifer ◽  
One Dimensional ◽  
Aquifer System ◽  
Groundwater Level Fluctuations ◽  
Groundwater Head ◽  
Aquifer Systems ◽  
Groundwater Fluctuation ◽  
Loading Effects ◽  
Tidal Loading

Although there are many existing analytical studies of tidal groundwater level fluctuations in coastal aquifer systems, few of them focus on an offshore submarine aquifer. Here, we consider tidal groundwater head fluctuations in a submarine leaky confined aquifer overlain by a semipermeable seabed. Both the seabed and the confined aquifer are assumed to extend horizontally infinitely. A one-dimensional mathematical model is established to describe the problem, and the analytical solution is derived. The impacts of the tidal loading efficiency, hydraulic conductivity and elastic storage of the semipermeable layer and aquifer on the groundwater head fluctuations in the aquifer system are analyzed and discussed. Solution analyses indicated that tidal loading effects tend to enhance the amplitude of the tidal groundwater fluctuation in the confined aquifer system and to reduce the phase shift between the groundwater head and the sea tide fluctuations.

scholarly journals Analytical solution of one-dimensional Pennes’ bioheat equation

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 1084-1092
Author(s):  
Hongyun Wang ◽  
Wesley A. Burgei ◽  
Hong Zhou
Keyword(s):  
Analytical Solution ◽  
Radiofrequency Energy ◽  
Bioheat Equation ◽  
Surface Cooling ◽  
One Dimensional ◽  
The Fourier Transform ◽  
The One ◽  
Parameter Values ◽  
Mathematical Derivation ◽  
Effect Of Surface

Abstract Pennes’ bioheat equation is the most widely used thermal model for studying heat transfer in biological systems exposed to radiofrequency energy. In their article, “Effect of Surface Cooling and Blood Flow on the Microwave Heating of Tissue,” Foster et al. published an analytical solution to the one-dimensional (1-D) problem, obtained using the Fourier transform. However, their article did not offer any details of the derivation. In this work, we revisit the 1-D problem and provide a comprehensive mathematical derivation of an analytical solution. Our result corrects an error in Foster’s solution which might be a typo in their article. Unlike Foster et al., we integrate the partial differential equation directly. The expression of solution has several apparent singularities for certain parameter values where the physical problem is not expected to be singular. We show that all these singularities are removable, and we derive alternative non-singular formulas. Finally, we extend our analysis to write out an analytical solution of the 1-D bioheat equation for the case of multiple electromagnetic heating pulses.

Diffusion-Limited Cell Dehydration: Analytical and Numerical Solutions for a Planar Model

1999 ◽  
Author(s):  
Alexander V. Kasharin ◽  
Jens O. M. Karlsson
Keyword(s):  
Analytical Solution ◽  
Numerical Solutions ◽  
Planar System ◽  
One Dimensional ◽  
Diffusion Limited ◽  
Dimensional Diffusion ◽  
Constant Diffusivity ◽  
A Cell ◽  
Cell Dehydration ◽  
The One

Abstract The process of diffusion-limited cell dehydration is modeled for a planar system by writing the one-dimensional diffusion-equation for a cell with moving, semipermeable boundaries. For the simplifying case of isothermal dehydration with constant diffusivity, an approximate analytical solution is obtained by linearizing the governing partial differential equations. The general problem must be solved numerically. The Forward Time Center Space (FTCS) and Crank-Nicholson differencing schemes are implemented, and evaluated by comparison with the analytical solution. Putative stability criteria for the two algorithms are proposed based on numerical experiments, and the Crank-Nicholson method is shown to be accurate for a mesh with as few as six nodes.

scholarly journals Assessment of subsidence risk associated with aquifer storage and recovery in the Coastal Lowlands Aquifer System, Houston, Texas, USA

2020 ◽  
Vol 382 ◽  
pp. 487-491
Author(s):  
Van Kelley ◽  
Michael Turco ◽  
Neil Deeds ◽  
Christina Petersen ◽  
Chris Canonico
Keyword(s):  
Water Supply ◽  
Land Surface ◽  
Future Research ◽  
Aquifer Storage And Recovery ◽  
Aquifer System ◽  
Aquifer Storage ◽  
Alternative Water ◽  
Regulatory Plan ◽  
Insight Into ◽  
Coastal Lowlands

Abstract. In the Houston, Texas region, groundwater use is regulated by the Harris-Galveston Subsidence District (District) because of historical regional subsidence from groundwater development. The District regulates groundwater production in the Coastal Lowlands Aquifer System (CLAS) to mitigate subsidence through the implementation of District Groundwater Regulatory Plan. The District has successfully reduced groundwater pumping as a percent of demand regionally while controlling subsidence through the implementation of alternative water supplies. Aquifer Storage and Recovery (ASR) is an alternative water supply strategy that provides a means to store water underground and increase water supply more cost effectively than traditional storage expansion strategies. Groundwater users in the District are interested in the many potential benefits of ASR as a water supply strategy. Little is known about the potential effects on compaction and land surface subsidence resulting from ASR operations. Recognizing this, the District funded research on the potential subsidence risk associated with ASR. Two hypothetical, though representative, ASR projects were developed and analysed: (1) an industrial ASR project meant to provide water supply during a drought of record (DOR), and (2) a municipal ASR project designed to provide an annual municipal summer peaking water supply. Simulations of groundwater hydraulics and subsidence were performed at three potential locations within the CLAS to provide insight into variability associated with location and aquifer depth. Theoretical simulations confirmed the potential for subsidence associated with the application of ASR in the CLAS, although operating an ASR for summer peaking needs has less potential risk of subsidence than the DOR scenario in the scenarios simulated. The study simulations provide insight into how an ASR project may be designed and operated to minimize compaction and potential subsidence. Based on this study, ASR operated to address summer peaking showed the greatest potential to reduce additional compaction verses sourcing all water from groundwater. This theoretical study provides a basis for future research on subsidence associated with ASR and provides a framework for consideration for the regulation of ASR within the District.

scholarly journals On sound waves of finite amplitude

1953 ◽  
Vol 216 (1127) ◽  
pp. 539-547 ◽  
Keyword(s):  
Integral Equation ◽  
Analytical Solution ◽  
Arbitrary Function ◽  
Initial Conditions ◽  
Finite Amplitude ◽  
Sound Waves ◽  
One Dimensional ◽  
The One ◽  
Complex Integral ◽  
Gas Cloud

An analytical solution of Riemann’s equations for the one-dimensional propagation of sound waves of finite amplitude in a gas obeying the adiabatic law p = k ρ γ is obtained for any value of the parameter γ. The solution is in the form of a complex integral involving an arbitrary function which is found from the initial conditions by solving a generalization of Abel’s integral equation. The results are applied to the problem of the expansion of a gas cloud into a vacuum.

An Exact Solution to Steady Heat Conduction in a Two-Dimensional Annulus on a One-Dimensional Fin: Application to Frosted Heat Exchangers With Round Tubes

2005 ◽  
Vol 128 (4) ◽  
pp. 397-404 ◽  
Author(s):  
A. D. Sommers ◽  
A. M. Jacobi
Keyword(s):  
Thermal Conductivity ◽  
Analytical Solution ◽  
High Thermal Conductivity ◽  
Two Dimensional ◽  
One Dimensional ◽  
Low Thermal Conductivity ◽  
Fin Efficiency ◽  
Coated Metal ◽  
The One ◽  
Term Approximation

The fin efficiency of a high-thermal-conductivity substrate coated with a low-thermal-conductivity layer is considered, and an analytical solution is presented and compared to alternative approaches for calculating fin efficiency. This model is appropriate for frost formation on a round-tube-and-fin metallic heat exchanger, and the problem can be cast as conduction in a composite two-dimensional circular cylinder on a one-dimensional radial fin. The analytical solution gives rise to an eigenvalue problem with an unusual orthogonality condition. A one-term approximation to this new analytical solution provides fin efficiency calculations of engineering accuracy for a range of conditions, including most frosted-coated metal fins. The series solution and the one-term approximation are of sufficient generality to be useful for other cases of a low-thermal-conductivity coating on a high-thermal-conductivity substrate.

LOCALIZED BREATHER-LIKE EXCITATIONS IN THE HELICOIDAL PEYRARD–BISHOP MODEL OF DNA

2009 ◽  
Vol 02 (04) ◽  
pp. 405-417 ◽  
Author(s):  
CONRAD BERTRAND TABI ◽  
ALIDOU MOHAMADOU ◽  
TIMOLEON CREPIN KOFANE
Keyword(s):  
Analytical Solution ◽  
Continuous Wave ◽  
Exact Analytical Solution ◽  
Modulational Instability ◽  
Elliptic Functions ◽  
Instability Criterion ◽  
Dna Dynamics ◽  
Jacobian Elliptic Functions ◽  
One Dimensional ◽  
The One

We consider the one-dimensional helicoidal Peyrard–Bishop (PB) model of DNA dynamics. By means of a method based on the Jacobian elliptic functions, we obtain the exact analytical solution which describes the modulational instability and the propagation of a bright solitary wave on a continuous wave background. It is shown that these solutions depend on the modulational (or Benjamin-Feir) instability criterion. Numerical simulations of their propagation show these excitations to be long-lived and suggest that they are physically relevant for DNA.

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