Steady-state Groundwater Flow Problem Research Articles

Predictive Assessment of Groundwater Flow Uncertainty in Multiscale Porous Media by Using Truncated Power Variogram Model

The spatial distribution of hydrogeological properties is essentially heterogeneous. Heterogeneity can be characterized quantitatively using geostatistics, which conventionally assumes that the stochastic process is stationary. However, growing evidence indicates that the spatial variability has the multiscale self-similarity characteristics and can be better characterized using non-stationary model but with statistically homogeneous increments. A general framework is developed in this work to conduct the uncertainty quantification analysis by using truncated power variogram model, which can explicitly account for measurement scale, observation scale, and window scale. The effect of the multiscale characteristics of the hydrogeological properties on the uncertainty and the consequential risk associated with the groundwater flow process is investigated. A synthetic two-dimensional saturated steady-state groundwater flow problem is used to evaluate the performance to predict the flow field distribution. For comparative purposes, the evaluation is based on both the truncated power and the traditional variogram models when the underlying porous medium is a random fractal field. The results show that the truncated power variogram model can perform the uncertainty quantification more accurately, and the adoption of traditional variogram model tends to result in a smoother estimation on the flow field and underestimate the uncertainty associated with the hydraulic head prediction. Upscaling is generally inevitable to avoid predictive uncertainty underestimation when the underlying random field exhibits multiscale characteristics.

The method of fundamental solutions for steady-state groundwater flow problems

The method of fundamental solutions is a meshless method. Only boundary collocation points are needed during the whole solution process. It has the merits of mathematical simplicity, ease of programming, high solution accuracy, and others. In this paper, the method of fundamental solutions is applied to simulate 2D steady-state groundwater flow problems. The principle of superposition is used during the whole solution process. Numerical results are compared with the multiquadrics method and the mixed finite element method as well as analytical solutions. It is shown that the method of fundamental solutions is promising in dealing with steady groundwater flow problems.

Integrating Electrical Analogy and Computer Modeling of Groundwater Flow for Teaching Flownet Concepts

Laplace equation is the basic differential equation that governs the steady flow of a fluid through an isotropic and homogeneous porous medium and also the steady flow of current in a conducting medium. Therefore, a steady-state groundwater flow problem can be formulated as an analogous electrical current flow problem. A flow net, set of grids formed by orthogonally intersecting equipotential lines and flow lines, is a graphical solution to the equations of steady groundwater flow. By definition, flownet for the original groundwater problem and the corresponding analogous electrical problem should be similar. This feature allows the possibility of introducing the concepts of flownets to students using the easily demonstrable electrical counterpart of the problem in a laboratory setting. This paper discusses the efforts of the authors to widen the scope of an experiment already included in the Fluid Mechanics laboratory course of a Civil Engineering curriculum and to better teach flownet principles using the electrical analogy of groundwater flow problems. Students used a simple experimental setup to obtain flownets for selected groundwater flow situations with different boundary conditions using the electrical analogy concept. Students also used a groundwater flow computer model to obtain flownets for the same flow situations and compared the results. The laboratory lesson plan consisted of five steps: (i) study and understand the selected physical groundwater problems, (ii) conceptualize the corresponding analogous electrical problems (iii) use the electrical analogy experimental setup to obtain flownets, (iv) study and understand the mathematical formulation of the problems, and (v) compare the analogous results with those obtained from a groundwater flow computer model. Sample results obtained by students are presented. The student feedback indicated that this approach resulted in an effective learning of the concepts involved.

Role of model selection criteria in geostatistical inverse estimation of statistical data‐ and model‐parameters

We analyze theoretically the ability of model quality (sometimes termed information or discrimination) criteria such as the negative log likelihood NLL, Bayesian criteria BIC and KIC and information theoretic criteria AIC, AICc, and HIC to estimate (1) the parameter vector of the variogram of hydraulic log conductivity (Y = ln K), and (2) statistical parameters and proportional to head and log conductivity measurement error variances, respectively, in the context of geostatistical groundwater flow inversion. Our analysis extends the work of Hernandez et al. (2003, 2006) and Riva et al. (2009), who developed nonlinear stochastic inverse algorithms that allow conditioning estimates of steady state and transient hydraulic heads, fluxes and their associated uncertainty on information about conductivity and head data collected in a randomly heterogeneous confined aquifer. Their algorithms are based on recursive numerical approximations of exact nonlocal conditional equations describing the mean and (co)variance of groundwater flow. Log conductivity is parameterized geostatistically based on measured values at discrete locations and unknown values at discrete “pilot points.” Optionally, the maximum likelihood function on which the inverse estimation of Y at pilot points is based may include a regularization term reflecting prior information about Y. The relative weight assigned to this term and its components and , as well as are evaluated separately from other model parameters to avoid bias and instability. This evaluation is done on the basis of criteria such as NLL, KIC, BIC, HIC, AIC, and AICc. We demonstrate theoretically that, whereas all these six criteria make it possible to estimate , KIC alone allows one to estimate validly and (and thus ). We illustrate this discriminatory power of KIC numerically by using a differential evolution genetic search algorithm to minimize it in the context of a two‐dimensional steady state groundwater flow problem. We find that whereas , and the integral scale of Y can be estimated on the basis of a zero‐order mean flow equation, the sill of the Y‐variogram is estimated more accurately by a second‐order approximation of flow. This notwithstanding, KIC prefers the simpler zero‐order moment over the more complex second‐order version.

An incomplete factorization technique for fast numerical solution of steady-state groundwater flow problems

Se presenta una técnica nueva iterativa para resolver ecuaciones de diferencias finitas en problemas estables de hidrodinámica subterránea.

Uncertainty analysis of groundwater flow with DRBEM

The reliability of groundwater flow numerical simulation is affected by the quality of input data of aquifer physical parameters. This paper presents an uncertainty analysis based on a first order approximation of covariances. A two-dimensional steady state groundwater flow problem is carried out by coupling the first-order uncertainty analysis with dual reciprocity boundary element method.

Simulation of groundwater flow in complex multiaquifer systems: Performance of a quasi three-dimensional technique in the steady-state case

The ability of the classical quasi three-dimensional formulation to describe steady-state groundwater flow problems in complex multiaquifer environments is examined. In the present formulation, discontinuities in the aquifer and aquitard units can be accommodated along with partial or complete aquifer dewatering and confined or unconfined flow conditions. Some of the main assumptions underlying classical quasi three-dimensional schemes are scrutinized, including the requirement of a two orders of magnitude permeability contrast between aquifers and aquitards. Performance of the numerical scheme is studied through a series of test problems by comparing with results obtained from a conventional finite element model. A high degree of accuracy and flexibility is achieved with the extended quasi three-dimensional technique, yet the numerical efficiency inherent in the classical formulation is maintained. By dividing an aquifer into a series of horizontal sublayers, vertical resolution of the flow field can be achieved without resorting to a numerically intensive fully three-dimensional scheme. Because it is possible to compute a three-dimensional representation of the hydraulic head distribution in individual aquifers with the quasi three-dimensional formulation, even in the absence of layers of contrasting hydraulic conductivity, the technique provides a viable alternative to the much more complex fully three-dimensional schemes for a wide variety of groundwater flow problems. Key words: groundwater flow, multiaquifer, complex stratigraphy, numerical analysis, quasi three-dimensional, steady state.

A Comparison of Several Methods of Solving Nonlinear Regression Groundwater Flow Problems

Computational efficiency and computer memory requirements for four methods of minimizing functions were compared for four test nonlinear‐regression steady state groundwater flow problems. The fastest methods were the Marquardt and quasi‐linearization methods, which required almost identical computer times and numbers of iterations; the next fastest was the quasi‐Newton method, and last was the Fletcher‐Reeves method, which did not converge in 100 iterations for two of the problems. The fastest method per iteration was the Fletcher‐Reeves method, and this was followed closely by the quasi‐Newton method. The Marquardt and quasi‐linearization methods were slower. For all four methods the speed per iteration was directly related to the number of parameters in the model. However, this effect was much more pronounced for the Marquardt and quasi‐linearization methods than for the other two. Hence the quasi‐Newton (and perhaps Fletcher‐Reeves) method might be more efficient than either the Marquardt or quasi‐linearization methods if the number of parameters in a particular model were large, although this remains to be proven. The Marquardt method required somewhat less central memory than the quasi‐linearization metilod for three of the four problems. For all four problems the quasi‐Newton method required roughly two thirds to three quarters of the memory required by the Marquardt method, and the Fletcher‐Reeves method required slightly less memory than the quasi‐Newton method. Memory requirements were not excessive for any of the four methods.

Orthonormalization Applied to Ground-Water Flows

The Gram-Schmidt orthonormalization procedure is presented as a numerical method easily adaptable to digital computation for the solution to steady-state ground-water flow problems. The advantages of this method are: (1) a series solution is attained and (2) arbitrary shaped aquifers with arbitrary boundary conditions can be handled. The method is illustrated by application to a well flow problem in a confined aquifer.