One-dimensional Aquifer Research Articles

Estimation of Hydraulic Diffusivity of a Confined Limestone Aquifer at the Xiluodu Dam

Hydraulic diffusivity is a fundamental parameter in studying groundwater flow. An analytical solution for groundwater flow within a finite-length one-dimensional aquifer has been introduced. This analytical solution simplifies the river water level (RWL) by a piecewise linear function, accurately describing the arbitrary variation pattern. An inversion method for hydraulic diffusivity has been provided based on the analytical solution. Then, the method was employed to estimate the hydraulic diffusivity of a limestone aquifer in the Xiluodu reservoir and was verified by the FEFLOW software. The parameter sensitivity increases with the RWL fast increasing and reaches its peak value when the RWL approaches the maximum value. Given the sensitivity analysis, great attention should be paid to the stage when RWL fluctuates drastically for estimating hydraulic diffusivity. The proposed method is flexible to conditions that lack observation data or RWL fluctuating drastically.

Groundwater level response to the Wenchuan earthquake of May 2008

We have comprehensively analysed the co-seismic response of the groundwater levels of 280 wells in mainland China that were associated with the Wenchuan earthquake (Mw 7.9) that occurred on 12 May 2008. The observed co-seismic responses can be classified as step-like changes in 138 wells, variations in 69 wells and non-responses in 73 wells. After a quantitative analysis of spatial distribution, there was no spatially coherent signal found in the step-like changes (positive values indicate a step-like rise, and negative values indicate a step-like fall), even within 300 km of the epicenter. The amplitude and the phase shift of the M2-wave were compared between the pre- and post-earthquake conditions. The phase was forward and was concentrated at , regardless of the proximity of wells to the epicenter; however, the change in amplitude randomly increased or decreased. By computing the post-seismic groundwater recession, the characteristic times of the aquifers were . We concluded that by assuming a first-order approximation, i.e. a one-dimensional aquifer, the causal mechanism of the co-seismic response of the groundwater level was that the seismic waves enhanced rock permeability by clearing the facture-filling materials. The shapes of the co-seismic responses were determined by the well-aquifer system and the proximity of the wells to recharge or discharge areas (). The water level rose if the well was closer to the recharge area, the water level decline if the well was closer to the discharge area, and the water level oscillated if the well was farther from the recharge or discharge areas when the seismic wave was transmitted. The water level remained unchanged if the well did not penetrate any confined aquifer.

Differential Quadrature Solution for One-Dimensional Aquifer Flow

Differential Quadrature Method (DQM) has been applied to the solution of aquifer flow problems. Three examples from of each of the three one-dimensional aquifer flow equation problems, a confined aquifer flow with time dependent boundary conditions, a composite confined aquifer and an unconfined aquifer with seepage, were examined. The results of DQM solution were then compared with the results obtained from analytical solution, the Explicit Finite Differences Method and Implicit Finite Differences Method. Based on the comparison results, it was concluded that the DQM provides similar results but with relatively faster calculation speed, less nodes and memory usage.

Explicit algebraic influence coefficients: two-dimensional aquifer model / Coefficients d'influence algébriques explicites: modèle d'aquifère bidimensionnel

This work extends the algebraic expression of influence coefficients developed for one-dimensional aquifer models to a two-dimensional (2-D) case. First, the partial differential equation governing the flow in a 2-D semi-confined aquifer is discretized using a finite difference scheme. This results in a system of discrete equations presented in the form of water balance equations associated with a network of interconnected compartments centred on the grid nodes. The foregoing system is transformed into a series of uncoupled 1-D equations stated in terms of some generalized hydraulic head for which they are also solved. Second, the original hydraulic head is recovered from the generalized one via an appropriate linear transformation. Whence, the algebraic expression making the hydraulic head explicit versus sources and boundary conditions is derived. This discrete expression, mapped onto its continuous counterpart, helps to deduce an algebraic form of the inter-compartment influence coefficients. Finally, a comparison with the analytical Green function is carried out.

Explicit algebraic influence coefficients: one-dimensional aquifer model

Explicit algebraic expressions of influence coefficients of an aquifer system are addressed. The methodology is straightforwardly exemplified using a one-dimensional (1D) semi-confined homogeneous aquifer model. It consists of the integration of the governing equation from two different viewpoints. On the one hand, the analytical solution to the governing equation is presented under an integral form involving the appropriate Green function. On the other hand, equations resulting from a finite difference discretization are processed to deduce a fully explicit algebraic expression of the nodal hydraulic head. This latter, arranged after the previously developed continuum solution, helps with deriving an explicit algebraic expression of influence coefficients corresponding to the studied aquifer model. Finally, the study is extended to an inhomogeneous aquifer model.

The use of aquifer response rate in the assessment of groundwater resources

In groundwater resources it is frequently necessary to decide how much of the recharge to a groundwater unit is required to maintain the baseflows in the rivers of the unit. Groundwater recharge enters the aquifer in a very irregular way both in terms of seasonal variation and variation between years. As the water is transferred to the rivers some of this variation is smoothed out so that the baseflows exhibit less severe variation. In an idealised one-dimensional aquifer, the ability of the system to smooth this variation is determined by the parameter, aquifer response rate. An analytic solution is used to develop a type curve which allows calculation of the minimum baseflows in the rivers in the annual cycle from the aquifer response rate. The extension of this theory to unconfined aquifers and to real irregular variation in recharge is investigated using a simple finite difference numerical model. A method of calculation of the response rate for real aquifers is proposed and this is applied to three examples of groundwater units. These units contain rivers which are gauged so that the predicted minimum baseflows can be compared with the observed minimum baseflows. The method is intended to have application to real problems of water resources, particularly in catchments where river gauges do not exist.

The response of aquifers to periodic forcing

In the analysis of aquifer behavior, it is common to distinguish between steady-state and dynamic or unsteady behavior. A special case of the latter is periodic behavior, in which an aquifer responds to forcing that varies sinusoidally in time. This paper presents an efficient method for obtaining analytical solutions for periodic aquifer flow, based on the use of complex algebra. It also provides a number of solutions which are simpler in form than those that are currently available. The solutions provide valuable insights into the spatial variations of amplitudes of head fluctuations and of the phase lags between periodic forcing and aquifer response. The classical problem of the response of a one-dimensional aquifer to tidally fluctuating boundary levels is re-examined. A solution is presented for the response of a one-dimensional aquifer to seasonal or diurnal variations in net recharge; interesting results include the amplification of head fluctuations beyond the expected maximum, and an explanation for the 3-month and 6-h lags observed in annual and daily time series, respectively. Other examples include the effects of mixed boundary conditions, and the behavior of radially symmetric flow systems, either with flow inwards towards a pumping well, or flow outwards, as on a circular island. The amplitude and phase of fluxes through boundaries are also examined.

Interpretation of [formula omitted] activity ratios in groundwaters

The quasi-steady variation in 234 U 238 U activity ratio has been determined along an idealised homogeneous one-dimensional aquifer in which the transfer of radionuclides from the aquifer material to solution occurs by both α-recoil and ion exchange. The results highlight the importance of considering these two effects in predicting the variation of 234 U/U activity ratios in a flowing system. In particular, it was shown that such ratios in old waters should achieve the moderate values indicated by measurements.