Hund-Der Yeh

A new closed-form solution for a radial two-layer drawdown equation for groundwater under constant-flux pumping in a finite-radius well

A mathematical model is presented for describing the groundwater flow in a radial two-layer confined aquifer system with a constant-flux pumping well that has a wellbore skin and finite well radius. The Laplace-domain solution for the model is first derived by the Laplace transforms; and the time-domain solution in terms of the aquifer drawdown is then obtained form the Laplace inversion using the Bromwich integral method. When neglecting the well radius, our Laplace-domain solution is shown to reduce to a Laplace-domain solution given by Butler [J. Hydrol. 101 (1988) 15]. A unified numerical approach including a root search approach, the Gaussian quadrature, and the Shanks method is employed for evaluating this time-domain solution. The evaluated results of the solution agree well with those of the Laplace-domain solution estimated by the modified Crump algorithm. This new solution can be used either to predict the spatial and temporal drawdown distributions in both the skin and formation zones or to investigate the effects of the skin type, skin thickness and well radius on the drawdown distribution.

Adsorption of precious metals in water by dendrimer modified magnetic nanoparticles

Magnetic nanoparticles modified by third-generation dendrimers (MNP-G3) and MNP-G3 further modified by ethylenediaminetetraacetic acid (EDTA) (MNP-G3-EDTA) were conducted to investigate their ability for recovery of precious metals (Pd(IV), Au(III), Pd(II) and Ag(I)) in water. Experiments were carried out using batch reactors for the studies of adsorption kinetics, adsorption isotherms, competitive adsorption and regeneration. The pseudo second-order model is the best-fit model among others suggesting that the adsorption of precious metals by MNP-G3 in water is a chemisorption process. Three adsorption isotherms namely Langmuir, Freundlich and Dubinin-Radushkevich isotherm were examined and the results showed the similarities and consistency of both linear and nonlinear analyses. Pd(IV) and Au(III) with higher valence exhibited relatively better adsorption efficiency than Pd(II) and Ag(I) with lower valence suggesting that the adsorption of precious metals by MNP-G3 is a function of valence. In the presence of the competing ion Zn(II), the adsorption efficiency of MNP-G3 for all four precious metals was declined significantly. The use of MNP-G3-EDTA revealed an increase in the adsorption efficiency for all four precious metals. However, the low selectivity of MNP-G3 towards precious metals was not enhanced by the modification of EDTA onto the MNP-G3. The regeneration of metal-laden MNP-G3 can be readily performed by using 1.0% HCl solution as a desorbent solution.

Conditional expectation for evaluation of risk groundwater flow and solute transport: one-dimensional analysis

Abstract A one-dimensional groundwater transport equation with two uncertain parameters, groundwater velocity and longitudinal dispersivity, is investigated in this paper. The analytical uncertainty of the predicted contaminant concentration is derived by the first-order mean-centered uncertainty analysis. The risk of the contaminant transport is defined as the probability that the concentration exceeds a maximum acceptable upper limit. Five probability density functions including the normal, lognormal, gamma, Gumbel, and Weibull distributions are chosen as the models for predicting the concentration distribution. The risk for each distribution is derived analytically based on the conditional probability. The mean risk and confidence interval are then computed by Monte Carlo simulation where the groundwater velocity and longitudinal dispersivity are assumed to be lognormally and normally distributed, respectively. Results from the conditional expectation of an assumed damage function show that the unconditional expectation generally underestimates the damage for low risk events. It is found from the sensitivity analysis that the mean longitudinal dispersivity is the most sensitive parameter and the variance of longitudinal dispersivity is the least sensitive one among those distribution models except the gamma and Weibull distributions.

FINITE ELEMENT MODELLING FOR LAND DISPLACEMENTS DUE TO PUMPING

SUMMARY Equations of equilibrium (force balance) and flow in multidimensions were coupled in this paper to describe land displacements due to pressure decline in aquifers. A Galerkin finite element model based on these equations was developed. The saturated/unsaturated behaviour and the isotropic/anisotropic properties of permeability and elasticity were considered when the model was formulated. This model was verified by comparing its simulation results with those of known analytical solutions for simplified cases. The simulation of displacements due to pressure decline in unsaturated media was also performed. Those results demonstrated that the choice of boundary ranges for an aquifer with infinite domain may significantly affect the estimated horizontal and vertical displacements. To obtain a good estimation of land displacements, the boundary ranges should be carefully chosen. The displacements occurring in unconfined aquifers are caused by the drop of the water table and the change in body force in the dewatering zone. Simulation results also indicated that the change in body force should be considered once an unconfined aquifer has been pumped. Otherwise, the horizontal and vertical displacements in unconfined aquifers would be overestimated and underestimated, respectively. The behaviour of land displacements due to pumping was shown to be affected by changes in the total stresses in aquifers.

An analytical solution for tidal fluctuations in unconfined aquifers with a vertical beach

[1] The perturbation technique has been commonly used to develop analytical solutions for simulating the dynamic response of tidal fluctuations in unconfined aquifers. However, the solutions obtained from the perturbation method might result in poor accuracy for the case of the perturbation parameter being not small enough. In this paper, we develop a new analytical model for describing the water table fluctuations in unconfined aquifers, based on Laplace and Fourier transforms. In the new approach, the mean sea level is used as the initial condition and a free surface equation, neglecting the second‐order slope terms, as the upper boundary condition. Numerical results show that the present solution agrees well with the finite different model with the second‐order surface terms. Unlike Teo et al.’s (2003) approximation which restricts on the case of shallow aquifers, the present model can be applied to most of the tidal aquifers except for the very shallow one. In addition, a large‐time solution in terms of sine function is provided and examined graphically with four different tidal periods.

Pressure Buildup During Supercritical Carbon Dioxide Injection From a Partially Penetrating Borehole into Gas Reservoirs

Injecting CO2 into a subsurface formation causes a buildup of pressure in the vicinity of the injection well. While a large injection rate can reduce the cost associated with injection, an indefinitely large injection rate can result in excessive formation damage. To obtain an optimal injection rate without exceeding the safe pressure limits, one will like to have some knowledge of the transient pressure buildup characteristics resulting from a particular injection rate. While elaborate numerical simulations can provide reliable pressure buildup predictions, they require extensive knowledge about the formation, which is normally not available at the start of an injection process. To alleviate this problem, using some simplifying assumptions, we have developed a solution to predict the transient buildup of pressure resulting from injection of supercritical carbon dioxide from a partially penetrating well into a gas reservoir. The solution in space and time is first obtained in the Fourier–Laplace transform space, and then inverted back into real space (in cylindrical coordinates) and time. We use the solution to study pressure transient characteristics for different formation permeabilities and anisotropy ratios. Results obtained using the solution compared well with those from numerical simulations.

Applying Hybrid Heuristic Approach to Identify Contaminant Source Information in Transient Groundwater Flow Systems

Simultaneous identification of the source location and release history in aquifers is complicated and time-consuming if the release of groundwater contaminant source varies in time. This paper presents an approach called SATSO-GWT to solve complicated source release problems which contain the unknowns of three location coordinates and several irregular release periods and concentrations. The SATSO-GWT combines with ordinal optimization algorithm (OOA), roulette wheel approach, and a source identification algorithm called SATS-GWT. The SATS-GWT was developed based on simulated annealing, tabu search, and three-dimensional groundwater flow and solute transport model MD2K-GWT. The OOA and roulette wheel method are utilized mainly to reduce the size of feasible solution domain and accelerate the identification of the source information. A hypothetic site with one contaminant source location and two release periods is designed to assess the applicability of the present approach. The results indicate that the performance of SATSO-GWT is superior to that of SATS-GWT. In addition, the present approach works very effectively in dealing with the cases which have different initial guesses of source location and measurement errors in the monitoring points as well as problems with large suspicious areas and several source release periods and concentrations.

A new approximate solution for chlorine concentration decay in pipes.

Biswas et al. (1993. A model for chlorine concentration decay in pipes. Water Res. 27(12), 1715-1724) presented an analytical solution of a two-dimensional (2-D) steady-state chlorine transport equation in a pipe under the turbulent condition and employed fractional error function and regression technique to develop an approximate solution. However, their approximate solution may not give a good result if the wall decay parameter is large. This paper provides a more accurate approximate solution of the 2-D steady-state chlorine transport equation under the turbulent condition. This new approximate solution has advantages of easy evaluation and good accuracy when compared with the approximate solution given by Biswas et al. (1993). In addition, this paper also develops a methodology that combines simulated annealing (SA) with this new approximate solution to determine the wall decay parameter. Two cases are chosen to demonstrate the application of the present approximate solution and methodology. The first case is to use this new approximate solution in simulating chlorine decay in pipes with the experiment-observed data given by Rossman (2006. The effect of advanced treatment on chlorine decay in metallic pipes. Water Res. 40(13), 2493-2502), while the second case presents the determination of the wall consumption at the end of the pipe network.

Transient Flow into a Partially Penetrating Well during the Constant-Head Test in Unconfined Aquifers

This study derives a semianalytical solution for drawdown distribution during a constant-head test at a partially penetrating well in an unconfined aquifer. The constant-head condition is used to describe the boundary along the screen. In addition, a free-surface condition is used to delineate the upper boundary of the unconfined aquifer. The Laplace-domain solution is then derived using separation of variables and Laplace transform. This solution can be used to identify the aquifer parameters from the data of the constant-head test when integrated with an optimization scheme or to investigate the effects of vertical flow caused by the partially penetrating well and free-surface boundary in an unconfined aquifer.

Parameter Estimation/Sensitivity Analysis for an Aquifer Test with Skin Effect

Aquifer information carried by aquifer test data may be affected by the presence of a finite thickness skin around the wellbore. The mathematical treatment for an aquifer accounting for the skin zone can be characterized by five parameters, that is, the outer radius of the skin zone and the transmissivity and storativity for each of the skin and aquifer zones. Sensitivity analysis was performed to examine the ground water flow behavior in the skin and aquifer zones in terms of the constant-head test (CHT) data. The simulated annealing procedure was applied to simultaneously determine the skin and aquifer parameters from the analysis of CHT data. Toward the previously mentioned goals, four suites of CHT data were analyzed in this article. The analyses of wellbore flow rate at the test well and the specific drawdown at the observation well gave accurate estimates for the skin and aquifer parameters, respectively. Only the skin thickness and both the skin and the aquifer diffusivities could be accurately estimated from the analysis of drawdown data in the observation well. The estimates for all skin and aquifer parameters from the composite analysis of flow rate and drawdown data were the most accurate. The results of sensitivity analyses and parameter estimations provide instructive references in the analysis of the skin-affected CHT data.