scholarly journals Analytical Modeling of Particle Tracking for Dynamic Pumping Conditions

Water ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 2469
Author(s):  
Yuan Gao ◽  
Thomas Sale
Keyword(s):  
Analytical Solution ◽  
Analytical Modeling ◽  
Water Levels ◽  
Subsurface Water ◽  
Particle Movement ◽  
Simple Method ◽  
Capture Zones ◽  
Fluid Particles ◽  
Theis Solution ◽  
Well Data

Movement of fluid particles about historic subsurface releases and through well fields is often governed by dynamic subsurface water levels. Motivations for tracking the movement of fluid particles include tracking the fate of subsurface contaminants and resolving the fate of water stored in subsurface aquifers. Based on superposition of the Theis solution in both space and time, this research explores an analytical solution based on the Theis equation using dynamic pumping well data to resolve how fluid particles move around wells under dynamic pumping conditions. The results provide relatively uniform capture zones for a pumping well. Further, the results show that even under continuous pumping and injection conditions, groundwater will not flow far from the well. Accordingly, groundwater positions can be evaluated based on the research for dynamic pumping. Using the assumptions proposed by the Theis solution, the analytical solution developed in this study provides a simple method to evaluate particle movement in wells used to both store and recover water.

scholarly journals Particle Tracking Using Dynamic Water-Level Data

Water ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 2063
Author(s):  
Yuan Gao
Keyword(s):  
Groundwater Flow ◽  
Water Level ◽  
Water Table ◽  
Flow Direction ◽  
Water Levels ◽  
Subsurface Water ◽  
Pressure Transducers ◽  
Level Data ◽  
Water Level Data ◽  
Fluid Particles

The movement of fluid particles about historic subsurface releases is often governed by dynamic subsurface water levels. Motivations for tracking the movement of fluid particles include tracking the fate of subsurface contaminants and resolving the fate of water stored in subsurface aquifers. This study provides a novel method for predicting the movement of subsurface particles relying on dynamic water-level data derived from continuously recording pressure transducers. At least three wells are needed to measure water levels which are used to determine the plain of the water table. Based on Darcy’s law, particle flow pathlines at the study site are obtained using the slope of the water table. The results show that hydrologic conditions, e.g., seasonal transpiration and precipitation, influence local groundwater flow. The changes of water level in short periods caused by the hydrologic variations made the hydraulic gradient diversify considerably, thus altering the direction of groundwater flow. Although a range of groundwater flow direction and gradient with time can be observed by an initial review of water levels in rose charts, the net groundwater flow at all field sites is largely constant in one direction which is driven by the gradients with higher magnitude.

scholarly journals Transient flow between aquifers and surface water: analytically derived field-scale hydraulic heads and fluxes

2012 ◽  
Vol 16 (3) ◽  
pp. 649-669 ◽  
Author(s):  
G. H. de Rooij
Keyword(s):  
Surface Water ◽  
Transient Flow ◽  
Hydrological Cycle ◽  
Realistic Model ◽  
Water Levels ◽  
Subsurface Water ◽  
Water Model ◽  
Infinite Strip ◽  
Catchment Scale ◽  
Basin Scale

Abstract. The increasing importance of catchment-scale and basin-scale models of the hydrological cycle makes it desirable to have a simple, yet physically realistic model for lateral subsurface water flow. As a first building block towards such a model, analytical solutions are presented for horizontal groundwater flow to surface waters held at prescribed water levels for aquifers with parallel and radial flow. The solutions are valid for a wide array of initial and boundary conditions and additions or withdrawals of water, and can handle discharge into as well as lateral infiltration from the surface water. Expressions for the average hydraulic head, the flux to or from the surface water, and the aquifer-scale hydraulic conductivity are developed to provide output at the scale of the modelled system rather than just point-scale values. The upscaled conductivity is time-variant. It does not depend on the magnitude of the flux but is determined by medium properties as well as the external forcings that drive the flow. For the systems studied, with lateral travel distances not exceeding 10 m, the circular aquifers respond very differently from the infinite-strip aquifers. The modelled fluxes are sensitive to the magnitude of the storage coefficient. For phreatic aquifers a value of 0.2 is argued to be representative, but considerable variations are likely. The effect of varying distributions over the day of recharge damps out rapidly; a soil water model that can provide accurate daily totals is preferable over a less accurate model hat correctly estimates the timing of recharge peaks.

scholarly journals A Simple Method for the Determination of Deposition Coefficient Using the Analytical Solution of Advection-Dispersion-Deposition Equation for Step Input

Water ◽  
2017 ◽  
Vol 9 (6) ◽  
pp. 398
Author(s):  
Nag-Choul Choi ◽  
Jae-Woo Choi ◽  
Kyu-Sang Kwon ◽  
Sang-Gil Lee ◽  
Bong-Ju Kim ◽  
...  
Keyword(s):  
Analytical Solution ◽  
Simple Method ◽  
Step Input ◽  
Advection Dispersion ◽  
Deposition Coefficient

Solution of Free Vibration Equations of Euler-Bernoulli Cracked Beams by Using Differential Transform Method

2011 ◽  
Vol 110-116 ◽  
pp. 4532-4536 ◽  
Author(s):  
K. Torabi ◽  
J. Nafar Dastgerdi ◽  
S. Marzban
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Differential Transform Method ◽  
Beam Model ◽  
Cracked Beam ◽  
Transform Method ◽  
Simple Method ◽  
Differential Transform

In this paper, free vibration differential equations of cracked beam are solved by using differential transform method (DTM) that is one of the numerical methods for ordinary and partial differential equations. The Euler–Bernoulli beam model is proposed to study the frequency factors for bending vibration of cracked beam with ant symmetric boundary conditions (as one end is clamped and the other is simply supported). The beam is modeled as two segments connected by a rotational spring located at the cracked section. This model promotes discontinuities in both vertical displacement and rotational due to bending. The differential equations for the free bending vibrations are established and then solved individually for each segment with the corresponding boundary conditions and the appropriated compatibility conditions at the cracked section by using DTM and analytical solution. The results show that DTM provides simple method for solving equations and the results obtained by DTM converge to the analytical solution with much more accurate for both shallow and deep cracks. This study demonstrates that the differential transform is a feasible tool for obtaining the analytical form solution of free vibration differential equation of cracked beam with simple expression.

scholarly journals Calculating pH from EC and SAR values in salinity models and SAR from soil and bore water pH and EC data.

Soil Research ◽  
1990 ◽  
Vol 28 (6) ◽  
pp. 1001 ◽  
Author(s):  
CW Robbins ◽  
WS Meyer
Keyword(s):  
Soil Ph ◽  
Soil Salinity ◽  
Field Method ◽  
Soil Extract ◽  
Subsurface Water ◽  
Calibration Data ◽  
Exchangeable Sodium ◽  
Solution Ph ◽  
Simple Method ◽  
Water Ph

Currently used soil salinity models do not contain a mechanism for including exchangeable sodium effects on soil pH. A method is needed that allows pH calculation from the sodium adsorption ratio (SAR) or exchangeable sodium percentage (ESP) and electrical conductivity (EC) data. This study developed a simple method for calculating saturated soil paste and aqueous solution pH from SAR (or ESP) and EC data and compared the results with measured values from a number of soils and subsurface waters. The equation pH =A+{B*(SAR)1/2/(1+C*EC)} estimated soil pH from EC and SAR or ESP values. When rewritten as: SAR or ESP={(pH-A)(1 + C*EC)/B)2, the SAR or ESP was estimated from pH and EC data. By using shallow bore (well) water and soil extract data from the Murray Basin, values were determined for the scalar terms A, B and C. These values differed among subsurface water and soil types, however, the range of each scalar was reasonably small. It was found that a range of at least 2.5 pH units in the calibration data was necessary to obtain reliable regression between predicted and measured pH and SAR or ESP values. When these conditions were met, the predicted results were satisfactory. These relationships provide a method for pH calculation in soil salinity models which takes into account soil EC and sodium effects. They also provide a rapid field method to estimate SAR or ESP from easily obtainable EC and pH data. Further research is needed to define the factors that determine the values of A, B and C.

Land Subsidence and Associated Externalities in the Coastal Area of Texas

1975 ◽  
Vol 7 (1) ◽  
pp. 111-115 ◽  
Author(s):  
John P. Warren ◽  
Lonnie L. Jones
Keyword(s):  
Land Subsidence ◽  
Gulf Coast ◽  
Salt Water ◽  
Water Source ◽  
Economic Effects ◽  
Water Levels ◽  
Subsurface Water ◽  
Texas Gulf Coast ◽  
Property Loss ◽  
Alternative Water

Texas Gulf Coast areas near Houston have been affected to an increasing degree by land subsidence in recent years. Sinking of the surface has reached critical proportions in many areas, and subsidence of as much as nine feet has occurred since 1943. Physical effects have been extensive, affecting over 3,000 square miles, and economic effects have been aggravated by the approximity of much of the area to bay waters. Subsidence has resulted in significant damage and property loss, from both permanent salt water inundation and temporary flooding due to storm-related tides and rains.Industrial, municipal and agricultural demands for water have increased sharply in recent years. Engineers.have linked subsidence to the decline of subsurface water levels due to heavy groundwater withdrawals. An alternative water source, the importation and treatment of surface water, has been introduced, but relatively high prices have slowed its acceptance.

scholarly journals The 2019–2020 Rise in Lake Victoria Monitored from Space: Exploiting the State-of-the-Art GRACE-FO and the Newly Released ERA-5 Reanalysis Products

Sensors ◽  
2021 ◽  
Vol 21 (13) ◽  
pp. 4304
Author(s):  
Mehdi Khaki ◽  
Joseph Awange
Keyword(s):  
Lake Victoria ◽  
Water Discharge ◽  
Water Storage ◽  
The State ◽  
Water Levels ◽  
Subsurface Water ◽  
Surface Model ◽  
The Past ◽  
Short Rainy Season ◽  
Spatial Coverage

During the period 2019–2020, Lake Victoria water levels rose at an alarming rate that has caused various problems in the region. The influence of this phenomena on surface and subsurface water resources has not yet been investigated, largely due to lack of enough in situ measurements compounded by the spatial coverage of the lake’s basin, incomplete/inconsistent hydrometeorological data, and unavailable governmental data. Within the framework of joint data assimilation into a land surface model from multi-mission satellite remote sensing, this study employs the state-of-art Gravity Recovery and Climate Experiment follow-on (GRACE-FO) time-variable terrestrial water storage (TWS), newly released ERA-5 reanalysis, and satellite radar altimetry products to understand the cause of the rise of Lake Victoria on the one hand, and the associated impacts of the rise on the total water storage compartments (surface and groundwater) triggered by the extreme climatic event on the other hand. In addition, the study investigates the impacts of large-scale ocean–atmosphere indices on the water storage changes. The results indicate a considerable increase in water storage over the past two years, with multiple subsequent positive trends mainly induced by the Indian Ocean Dipole (IOD). Significant storage increase is also quantified in various water components such as surface water and water discharge, where the results show the lake’s water level rose by ∼1.4 m, leading to approximately 1750 gigatonne volume increase. Multiple positive trends are observed in the past two years in the lake’s water storage increase with two major events in April–May 2019 and December 2019–January 2020, with the rainfall occurring during the short rainy season of September to November (SON) having had a dominant effect on the lake’s rise.

A new simple method for the analytical solution of Kepler's equation

1985 ◽  
Vol 35 (4) ◽  
pp. 305-316 ◽  
Author(s):  
N. I. Ioakimidis ◽  
K. E. Papadakis
Keyword(s):  
Analytical Solution ◽  
Kepler's Equation ◽  
Simple Method ◽  
Kepler’S Equation
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