Shaw- Yang

Groundwater flow to a pumping well in a sloping fault zone unconfined aquifer

This study develops a mathematical model for simulating the hydraulic head distribution in response to pumping in a sloping fault zone aquifer under a water table boundary condition. A two-dimensional equation with a sink term representing the pumping is used for describing the head distribution in the aquifer. In addition, a first-order free surface equation is adopted to represent the change in water table at the outcrop. The analytical solution of the model, derived by the Laplace and finite Fourier cosine transforms, is expressed in terms of a double series. A finite difference solution within a deformable grid framework is developed to assess the solution obtained by specifying the free surface equation at the outcrop. Based on the analytical solution, we have found that the models prediction tends to overestimate drawdown in a late pumping period. The temporal head distribution is independent of the aquifer slope if the water table change is small, and exhibits a double-humped shape due to the effect of the free surface. The temporal drawdown predicted from the analytical solution is further compared with those measured from a pumping test conducted in northern Portugal.

Modeling transient heat transfer in nuclear waste repositories.

The heat of high-level nuclear waste may be generated and released from a canister at final disposal sites. The waste heat may affect the engineering properties of waste canisters, buffers, and backfill material in the emplacement tunnel and the host rock. This study addresses the problem of the heat generated from the waste canister and analyzes the heat distribution between the buffer and the host rock, which is considered as a radial two-layer heat flux problem. A conceptual model is first constructed for the heat conduction in a nuclear waste repository and then mathematical equations are formulated for modeling heat flow distribution at repository sites. The Laplace transforms are employed to develop a solution for the temperature distributions in the buffer and the host rock in the Laplace domain, which is numerically inverted to the time-domain solution using the modified Crump method. The transient temperature distributions for both the single- and multi-borehole cases are simulated in the hypothetical geological repositories of nuclear waste. The results show that the temperature distributions in the thermal field are significantly affected by the decay heat of the waste canister, the thermal properties of the buffer and the host rock, the disposal spacing, and the thickness of the host rock at a nuclear waste repository.

Comment on “Evaluation of the Hantush's M(α, β) function using binomial coefficients” by B. A. Mamedov and A. S. Ekenoğlu

where x = y/a. Equations (2)–(4) are evaluated by directly adding the infinite series; yet, the numerical evaluation is not straightforward and the accuracy of the results are not easy to evaluate because of the fact that the series involves the incomplete Gamma function and has a running sum from zero to infinity. [2] In this comment, we provide a simple and efficient numerical approach as an alternative to evaluate the Hantush’s M function. The Gaussian quadrature is employed to perform the numerical integration of equation (1) piecewise along the y axis from (0, a) to ( 1, 1) where a change of variable has been used. An n-point Gaussian quadrature formula may be written as [Gerald and Wheatley, 1989] Z 1