Dinshaw N. Contractor

Simulated effect of vadose infiltration on water levels in the Northern Guam Lens Aquifer.

Regional-scale hydrology of the fresh water lens in the Northern Guam Lens Aquifer has been simulated in the past using a finite element, sharp interface computer model, SWIG2D. Systematic differences exist between observed and computed water levels. Computed seasonal peak water levels are higher, and the computed seasonal lows are lower than the respective observed levels. It is hypothesized that vadose storage must store a substantial amount of water during the wet season and release it gradually into the lens during the dry season. Flow through the vadose zone was simulated with a one-dimensional finite element, unsaturated flow program, UNSAT1D, in which the van Genuchten model is used to characterize unsaturated diffuse flow through the matrix of the vadose zone. An additional parameter (SINK) was added to the van Genuchten set to account for rapid infiltration down open pathways (fractures) associated with the closed depressions of the karst terrain. A global-optimization technique (Shuffled Complex Evolution or SCE-UA Method) was used to obtain the parameters that minimized the difference between simulated and observed water levels. Simulations incorporating the van Genuchten model were accomplished by combining the two programs, UNSAT1D and SWIG2D, into a single program. The sum-of-squared-errors (SSE) between computed and observed water levels in four observation wells was minimized using SCE-UA, reducing the arithmetically averaged SSE of the four wells by 30% compared with the SSE obtained when the vadose zone was not modeled. These results suggest that vadose storage is significant. On the other hand, the fact that the best fit obtained with an optimum parameter set was able to reduce the SSE by no more than 30% suggests that additional phenomena have yet to be accounted for to more fully explain differences between simulated and observed well water levels.

Simulation of saltwater intrusion in the Northern Guam Lens using a microcomputer

Abstract A two-dimensional (areal) finite element model of saltwater intrusion was modified so that it can run on a microcomputer. The model assumes a sharp interface between fresh water and salt water and simulates the movement of both fresh water and salt water. Linear triangular elements are used to discretize the domain. A preprocessor is used to renumber the nodes of a given network to reduce the bandwidth of the matrix. The model was applied to the Northern Guam aquifer. The hydraulic conductivity in three regions of the aquifer was calibrated using the water-level history for a few observation wells. Field measurements of the depth of the interface indicate that the sharp interface assumption is valid for most of the aquifer. Comparison of the depth of the measured 50% isochlor with the computed depth of the interface shows that the two are equal at most locations. In some cases, the computed depth is less than the measured depth which results in a conservative estimate of the interface depth.

Efficient evaluation of integrals in three-dimensional boundary element method using linear shape functions over plane triangular elements

Abstract The numerical integration of three-dimensional boundary element method kernels involving R -1 and higher negative powers of R is reduced to a line integral by expressing the integrand in terms of shape functions, analytically integrating with respect to one shape function and numerically integrating with respect to the second shape function. This method results in a fully analytical solution of the integral for the singular case, when the source point is at one of the corners of the triangle. Considerable reduction in the computational effort is achieved along with more accurate results than those obtained using the areal Gaussian integration. The method is shown to work well for elements with a large aspect ratio and also for calculations of the basic variable at a source point near the boundary of elements. For points very close to the boundary it requires more integration points compared with some recently proposed schemes but far fewer compared with the standard Gauss integration.

Field application of a finite-element water-quality model to a coal seam with UCG burns

Abstract A two-dimensional finite-element model has been developed to study the flow of water and the transport of water-quality constituents associated with underground coal gastification (UCG) burns in a coal aquifer. The flow model calculates the piezometric head and seepage velocity distributions in the aquifer as a function of time. These outputs are fed into a water-quality model that takes into account the dispersion, decay, and adsorption characteristics of a particular water-quality constituent. These models can be used to study the movement of contaminants within an aquifer. The models have been verified for accuracy by checking their output against analytic solutions that are available for simple aquifer geometries. These programs have been applied to the Hanna UCG burns in Wyoming, U.S.A. Steady-state flows are assumed in the coal seam and the movement of a constituent is studied as a function of time as the five burns were completed. This study illustrates how the model can be used by water-resource managers to understand the environmental impact of UCG burns.

Finite element modeling of flow in a coal seam with underground coal gasification cavities

Abstract A two-dimensional, finite element groundwater flow model was developed to study the movement of water in a coal seam in which large cavities were created by underground coal gasification (UCG) burns. The burns extract natural gas from the coal without any environmental disturbance at the ground level. On completion of the burn, groundwater mixes with the products of combustion in the cavity and the pollutants move into the coal seam. Mathematical modeling is used to study the movement and fate of these pollutants with time. Water quality modeling has to be preceded by flow modeling to determine velocities as a function of time. This paper studies the flow aspects of the problem. A new code was developed because of the unique requirements of the model. The model utilizes linear triangles to discretize the coal seam in plan and takes into account unsteady flow, anisotropic media, internal boundary conditions imposed by the cavities and a time-varying domain of flow in plan. The model was applied to a series of UCG burns in Hanna, Wyoming. Estimates of the time of filling of the five cavities were obtained. Comparisons of measured and computed potential head are presented at different points in the coal seam. Flow modeling can thus be used to predict the movement of water into and out of UCG cavities while the output of velocities is necessary for water quality modeling.

Modelling groundwater changes due to fluctuating dam discharge

Abstract In this contribution, two numerical methods are used to predict the free surface changes in a sand bar due to fluctuations in river stage. One is a fixed-mesh, finite-element seepage formulation including Biots consolidation theory, and the other is a boundary element method solution of the Laplace equation. Both models give overall predictions that are in good agreement with field data recorded at an instrumented sand bar in the Colorado River subjected to stage fluctuations from operation of the Glen Canyon Dam. The boundary element method appears to offer significant advantage in data preparation and computational times over the finite-element method for the problem studied in this paper.

Reduction of pressure surges by minimax optimization

Abstract The control of pressure surges in a pipeline is an important problem in many areas of industry, including hydroelectric power generation, oil refineries and chemical processing plants. This paper deals with the control of pressure surges in a simple system consisting of a single horizontal pipe. The methodology, however, is easily extended to more complex systems and is quite easily implemented. The control problem is formulated as a nonlinear minimax optimization problem. Due to the large-scale nature of such problems, a successive linear programming (LP) method is adopted. The convergence of the method is accelerated by a conjugate gradient type search. Computational results are also provided.

Boundary Element Simulation of Flow Through an Earthen Embankment Subjected to Cyclic Variation of Reservoir Level

The modeling of flow through an earthen embankment is made more complicated by the presence of a seepage surface and the fact that the location of the free surface is not known a priori. There have been many studies involving application of the Boundary Element Method (BEM) to such problems, in both two- and three-dimensions [1,2,3]. Almost all of the applications, though, have been for the cases where the upstream or the downstream water level is either rising or falling monotonically. In this paper, we have developed a BEM code for the simulation of transient two-dimensional (vertical plane) flow through an earthen embankment which is subjected to a cyclic variation of reservoir level on the upstream side. As a result of the periodic rise and fall of the upstream water level, the boundary conditions on the upstream face change from a specified head (Dirichlet boundary condition) during the rising stage to a seepage surface on part of the upstream face during the falling stage. One way of solving this problem is to use one BEM program for the rising stage and another for the falling stage, alternately. This is a cumbersome procedure and this paper presents a new method for changing the boundary conditions within the program. The code accounts for the change in boundary conditions by lumping multiple nodes at the reservoir level during the rising stage and separating them to form the seepage face during the falling stage.