Saltwater Intrusion Problem Research Articles

Motion of Two Compressible Fluids With Interface in a Porous Reservoir

This paper describes the development of a physical model of a reservoir involving two compressible fluids, typically gas over water. The reservoir is assumed to be of constant thickness, but its height varies with position, leading to an undulating topography. Withdrawal of the upper fluid begins and proceeds at a constant rate. Topics of interest are the distribution of fluxes throughout the reservoir, the pressure field as a function of time and space, and the movement of the interface between the fluids. The problem is formulated using a version of the two‐fluid layer concept. One of the space variables is eliminated by vertical integration, assuming that the fluid velocity vector is almost parallel to the upper and lower confining boundaries (Boussinesq reservoir). The resulting equation of motion for the horizontal components of the flow resembles that for a horizontal reservoir, but terms involving the gradient of the undulating reservoir modify the vertical pressure gradient. The problem is solved in two space dimensions and time. The difficulty presented by intersections of the fluid‐fluid interface with one or other of the confining boundaries is resolved by introducing a mathematical continuation of the fluids and their interface through and past the boundary. This is particularly appropriate for “leaky” aquifers; in the case of impermeable boundaries, a concern of the present paper, approximate solutions may be obtained by assuming a virtual porosity and permeability which are extremely small. The method resembles that of Wilson and Sa da Costa (1982). Some useful results have been obtained for Boussinesq reservoirs of fairly arbitrary geometry. Approximate numerical solutions are presented for two‐dimensional flow in a rectangular reservoir, the outer part of which is completely submerged, and for axisymmetric and three‐dimensional flows in a circular quadrant. A constriction upon the gas flow due to a “dip” in the reservoir is found to produce enhanced horizontal water flow due to the increase in horizontal pressure gradient. Downstream of the dip the interface develops an elevation, while a depression appears upstream. The establishment of stable flow of gas through a “neck” between two gas reservoirs is demonstrated, and it is proposed that a similar type of. flow can be developed as a result of gas fingering through an initially submerged neck. Further applications of the technique could be to reservoirs containing steam over water (geothermal) or to the coastal saltwater intrusion problem, but these are not considered in the present paper.

Control of spurious oscillations in the salt water intrusion problem

AbstractThis paper shows that the ‘streamline upwinding’ proposed by Hughes and Brooks1 is particularly simple to implement with the coupled nonlinear equations of the problem of salt water intrusion in a coastal aquifer. Because the mechanical dispersion effect is far larger than the molecular diffusion, the notorious spurious oscillations can be controlled by limiting the ratio of grid size to the streamline mixing length. The method is demonstrated on an example of a typical aquifer by giving the diagnostic variation of concentration and various salt profiles for different values of the key parameter.

Boundary integral equation solutions to moving interface between two fluids in porous media

The boundary integral equation method is formulated for and applied to problems concerning a moving interface between two fluids in porous media. The mixing between two fluids is assumed to be insignificant; a sharp interface exists between them. Numerical and experimental results are presented for the tilting of a vertical interface in a Hele‐Shaw cell. During the initial stage of the interfacial movement, nonlinear effects are clearly demonstrated. The BIEM results are also compared to experimental results for a transient salt water intrusion problem.

Unconfined seepage and salt water intrusion problems solved by the boundary integral method

Unconfined seepage and salt water intrusion problems solved by the boundary integral method

MODEL STUDIES OF SALT WATER INTRUSION1

ABSTRACTModel studies were and are still being used to verify certain theories in ground‐water flow systems in general. In complex cases, the model studies may be extremely useful especially when a theoretical rigorous analysis does not exist. The models cannot be considered entirely satisfactory due to the several drawbacks in each type in addition to the normal human errors in experimentation. This paper is concerned only with the viscous flow models. However, a brief summary of the other types of models, which may possibly be used in connection with salt water intrusion problems is given. It should be noted that some of such experiments are not directly related to the field of salt water intrusion. Two main types lie within this category: The gravity flow systems which are analogous to some phases of salt intrusion problems and problems in oil fields which bear general similarities to sea water intrusion zones. In oil fields, gas cycling studies give valuable information to sea water problems. Model studies are used by hydraulic engineers, geologists, petroleum engineers, physicists, foundation engineers and several other professional groups.