Hele-Shaw Model Research Articles

MODELING OF THE WATER BUDGET SYSTEM IN RECLAIMED MAN-MADE ISLAND

The movement of groundwater and the water budget in a reclaimed, man-made island was studied experimentally and theoretically. A set of experiments were carried out using a Hele-Shaw model that incorporated a rainfall simulator and a tidal generator. The analysis of free surface and the salt/fresh water interface was done through the Boundary Integral Equation Method (BIEM). The results showed that the volume of fresh water in the island increases when the rainfall intensity increases, and the propagation velocity and volume decrease along the free surface and at the salt/fresh water interface depending on the characteristics of tidal oscillation as well as rainfall intensity. An application of the BIEM to groundwater analysis in the reclaimed island was proved.

Convergence of the Cahn-Hilliard equation to the Hele-Shaw model

We prove that level surfaces of solutions to the Cahn-Hilliard equation tend to solutions of the Hele-Shaw problem under the assumption that classical solutions of the latter exist. The method is based on a new matched asymptotic expansion for solutions, a spectral analysis for linearizd operators, and an estimate for the difference between the true solutions and certain approximate ones.

Hele–Shaw flows with a free boundary produced by multipoles

We study Hele–Shaw flows with a moving boundary and multipole singularities. We find that such flows can be defined only on a finite time interval. Using a complex variable approach, we construct a family of explicit solutions for a single multipole. These solutions turn out to have the maximal possible lifetime in a certain class of solutions.We also discuss the generalized Hele-Shaw model in which surface tension at the moving boundary is considered, and develop a method of finding steady shapes. This method yields new one-parameter families of stationary solutions. In the Appendix we discuss a connection between these solutions and a variational problem of potential theory.

The Dynamics of a Conserved Phase Field System: Stefan-like, Hele-Shaw, and Cahn-Hilliard Models as Asymptotic Limits

The dynamics of a conserved phase field system for a free boundary, that is, u t +1/2lφ t =KΔu, −τφ t =ξ 2 Δ[ξ 2 Δφ+f(φ)/a+2u], are studied asymptotically. Many of the major macroscopic free-boundary problems arise as limits in various scalings

Infiltration and Leaching of Chlorinated Organic Compounds and Mechanism of Groundwater Contamination

Organochlorines have been widely detected in the groundwater in Japan. In order to resolve the mechanism of groundwater pollution, migration and leaching of the undiluted organochlorines were examined in water and porous media. It proves that undiluted trichloroethylene (TCE) readily infiltrated in unsaturated zone due to the physical properties, greater in density and less in surface tension and viscosity than water. In saturated zone TCE migrated and remained stagnant as isolated in pore space of the media. These phenomena reappeared in the Hele-Shaw model. Leachate concentration of TCE due to the rainfall infiltration and groundwater flow amounts to several thousands times as much as the tentative standard for drinking water. Besides, a new monitoring method by analysing the gaseous contents in the surface soil has been developed and was applied to the field observation in the waste landfill site.

Graded-Viscosity-Bank Design With Pseudoplastic Fluids

Summary A method for the design of graded viscosity banks of pseudoplastic fluids in five-spot patterns of a single homogeneous layer is presented. This method is based on the extension of Koval’s work on unstable miscible displacements to multiple slugs in radial systems and then to five-spots, with corrections made for pseudoplastic viscous-fingering behavior. Experiments were performed in a Hele-Shaw model to determine the qualitative nature of the various displacements that occur and to determine the parameters used in the equations.

Vertical migration of chlorinated organic compounds in porous media

The migration behavior of trichloroethylene through porous media made of glass beads of 5, 3 and 1 mm dia is described. Experiments were carried out in three hydraulic conditions: (1) unsaturated (completely dry), (2) saturated and (3) two layers (the upper portion of the porous media being unsaturated and the lower portion being saturated). In the case of the dry condition (1) trichloroethylene easily flows through the porous media regardless of the size of the glass beads, while it remains in the pore space in the saturated medium in the saturated condition (2). The stagnation of test liquid in the saturated medium increases with decreasing glass bead diameter. With 5 mm glass beads, in the case of condition (3), all the liquid coming from the upper portion moved into the saturated zone, whereas with 3 and 1 mm glass beads, the liquid seemed to stagnate on the surface of the saturated zone. With 1 mm glass beads, especially, almost all the liquid remained stagnant in the boundary region between the unsaturated and the saturated zone. The difference of the trichloroethylene behavior in the capillary zone can be qualitatively explained from the results of the visualized testing by means of the Hele-Shaw model.

Analytical Transient Equations for Drains in Artesian Areas

ABSTRACT Atransient solution for a falUng water above drains in irrigated areas subject to artesian conditions was developed. The solution determines the water table height midway between the drains, the corresponding drain discharge and the fraction of drain discharge originating from the aquifer. The transient solution for the falling water table was verified against experimental results obtained from a Hele-Shaw model. Satisfactory agreement between analytical and experimental results was found over a reasonable and practical range of flow conditions. The rate of water table drawdown strongly depends on the piezometric head in the aquifer and the depth of the soil layer between the drains and the aquifer. It also depends on the soil layer hydraulic conductivity and drainable porosity. The water table drawdown slightly depends on the drain size.

PREDICTION OF SEA WATER INTRUSION TO UNDERGROUND CAVERNS BY MEANS OF BOUNDARY INTEGRAL EQUATION METHOD IN COASTAL ROCK MASS

The encroachment and intrusion of the sea water wedge toward the underground caverns in coastal rock mass are investigated experimentally and theoretically. The theoretical analysis was done by using the boundary integral equation method. The experiments are conducted in the Hele-Shaw model with two different densities of fluids. Comparing theoretical results with experimental ones, the application technique of the boundary integral equation method for analyzing the fresh-sea water interface in coastal rock aquifer was confirmed. In addition, the process of sea water encroachment around caverns was made clear.

Predicting the Orientation of Short Fibers in Thin Compression Moldings

A method is presented for predicting the distribution of orientation of rigid short fibers in thin compression molded parts. The method extends Folgar and Tucker's model for fiber orientation in a concentrated suspension to the case of spatially non-uniform flows and orientation states. A generalized Hele-Shaw model is used to predict flow and defor mation during mold filling. Other assumptions are appropriate for sheet molding com pound : fibers much longer than the part thickness and a cold material molded in a hot mold. The predictions compare favorably to experiments on sheet molding compound and on a model suspension of nylon monofilaments in silicone oil.

Hydraulics of a well pumped with linearly decreasing discharge

Abstract Varying the discharge rate of a well with time makes the Theis and Cooper-Jacob methods inapplicable for determination of the formation constants of an aquifer. Analytical and graphical solutions for variable discharge cases are available for a few empirical or functional relationships. A number of other modes of variation of discharge with time are physically possible. In this paper, a method has been developed with the help of analytical and graphical solutions to determine aquifer constants by pumping the well with linearly decreasing discharge. The linearly decreasing discharge was simulated on a horizontal Hele-Shaw model. The transmissivity and storage coefficient were evaluated by using the type curve developed for a linearly decreasing discharge well. The solution gave fairly satisfactory values of aquifer constants.

The Ill-Posed Hele-Shaw Model and The Stefan Problem for Supercooled Water

The Ill-Posed Hele-Shaw Model and The Stefan Problem for Supercooled Water

The ill-posed Hele-Shaw model and the Stefan problem for supercooled water

The Hele-Shaw flow of a slow viscous fluid between slightly separated plates is analyzed in the ill-posed case when the fluid recedes due to absorption through a core G G . Necessary and sufficient conditions are given on the initial domain occupied by the fluid to ensure the existence of a solution. Regularity of the free boundary is established in certain rather general cases. Similar results are obtained for the analogous parabolic version, which models the one-phase Stefan problem for supercooled water.

The effect of a subsurface barrier on the conservation of freshwater in coastal aquifers

An investigation has been undertaken to study the effect on the water table and the shape of a freshwater/seawater interface produced by an impermeable subsurface barrier partially embedded into an unconfined coastal aquifer. Considerations are restricted to steady flow in an isotropic aquifer. Shape factors describing the distribution of mass density and of the velocity are introduced and their values derived. From the laboratory model study using a vertical plane Hele-Shaw model the velocity shape factor was determined. It was approximately unity for flow without a barrier, and decreased when a barrier was introduced. The barrier depressed the interface considerably and the upconing started with a higher flow rate as compared with the case without a barrier. By introducing the concept of a virtual origin it is shown that the free surface does not approach the seepage face tangentially. This was also confirmed experimentally.

Periodic solutions of a nonlinear diffusion equation used in groundwater flow theory: Examination using a Hele-Shaw model

A Hele-Shaw experiment which models groundwater flow is described. The experiment confirms the Philip prediction that in steady periodic nonlinear diffusion the root mean square of the oscillation, rather than the mean is constant. For the weakly nonlinear case examined, however, it is found that the logarithm of the amplitude of the oscillation still diminishes in proportion to xT − 1 2 , so from a practical viewpoint the hydrological problem could be treated as a linear one provided the displaced mean were taken into account. The anomalous appearance and subsequent decay of harmonics in the initially sinusoidal wave are discussed.

Écoulement non permanent dans un sol drainé par des fossés parallèles

The water movement through soils drained by parallel ditches is in general unsteady and can be described by the nonlinear Boussinesq equation. An analytical solution of this drainage equation subjected to general initial and boundary conditions has not yet been found because of its nonlinearity. Therefore, numerical methods should be used to obtain approximate solutions of the mixed boundary value problems of this equation. In this paper numerical solutions are presented based on implicit computational schemes of the Crank-Nicolson, Laasonen and Douglas types. Experimental data, obtained by a Hele-Shaw model in the Hydraulics Laboratory of the School of Agriculture of the University of Thessaloniki, are in very good agreement with the values computed numerically by these implicit schemes.

Study of Fluid Movements through Causeway

The movements of fluid through the fills of a causeway are examined by a numerical model. In the mathematical formulation, a two-fluid flow system through an inhomogeneous and anisotropic porous medium is assumed. Governing equations are solved iteratively by the finite element method using quadratic isoparametric elements. In the actual computations, the porous medium is considered to be isotropic and homogeneous so that the positions of numerically calculated phreatic surface and the interface could be compared with those of the Hele-Shaw experiment. Both the calculations and the Hele-Shaw model show the existence of a counter-flowing fluids system, and their results are in good agreement. Ratios of the total discharges in each directions are also computed.

A Trapping Hele-Shaw Model for Miscible-Immiscible flooding Studies

It has been noted previously that Hele-Shaw (parallel-plate) models are better than other types of laboratory models to properly scale down miscible displacements from field size to laboratory size. In most miscible flooding processes, however, the miscible displacement is preceded or followed by an immiscible displacement in which oil or gas is trapped by water, or waterflood residual oil is reconnected by a miscible slug. This trapping and reconnection could not be simulated in a conventional parallel-plate model. parallel-plate model. Now, however, a new version of this type of model has been invented that simulates the trapping behavior of porous rock. Instead of trapping by capillary (surface tension) forces, the new model traps light fluids by density difference (Fig. 1). A model of this type can be used to simulate, for example, the tertiary recovery process in which a solvent slug (e.g., CO2) injected in a waterflooded oil field and then followed by another water drive. The particular model devised for this purpose was made of 3-in. thick, 14-in. square plates purpose was made of 3-in. thick, 14-in. square plates of Plexiglas. The top plate contained 596 pairs of 1/40-in.-diameter holes, 112 in. apart at the base, and meeting 3/4 in. deep in the plate. Vent holes 1/16in. in diameter were drilled from the other side of the plate to the junctions of these pairs. The 12- x 12-in. square perforated region was supplied with wells in a nine-spot pattern, and was sealed around the periphery by an O-ring in a rectangular groove. The plates were held a fixed distance apart by shims and bolts outside the O-ring. A typical plate spacing was 0.01 cm. After the model was filled with liquids and air was forced out of the trapping holes, the vent holes were plugged with rods. P. 255

Hele-Shaw Model of Long Island Aquifer System

An experimental study, using a vertical Hele-Shaw model, is undertaken to determine fresh and salt ground-water flow for various ground-water development schemes on Long Island, N.Y. To satisfy dynamic similitude, some portions of the model are anisotropic. To simulate stream base flow, a significant hydrologic feature along the south shore of the island, an internal weir is incorporated in the model. Liquid silicones simulate fresh and salt water. Verification of the model is achieved by reproduction of long-term water table profiles, the stream base flow, and the double salt-water wedge structure, i.e., two salt-water wedges separated vertically by fresh water, south of the island. Response of the salt water to hydrologic transients on the island is slow. Recharge is effective in arresting or reversing salt-water movement.

Impact of Perforation Deficiency on a Fluid Injection Project - A Case History

Production logging and testing of selected intervals with straddle Production logging and testing of selected intervals with straddle packers indicated that perforation deficiency contributed to low packers indicated that perforation deficiency contributed to low vertical sweep efficiency. Mulitistage perforation fracture treatment with mud cleanout acid, condensate, and wax beads achieved production of oil from 15 to 30 feet of perforations in previously production of oil from 15 to 30 feet of perforations in previously nonproductive permeable sand. Introduction Sohio Petroleum Co. is the major working-interest owner and operator of a unitized fluid injection project using an improved recovery method. All project using an improved recovery method. All physical aspects of the reservoir rock and fluids, physical aspects of the reservoir rock and fluids, as well as pressure-production performance during primary operation, indicated that conditions were primary operation, indicated that conditions were favorable for "improved" oil recovery over and above that possible by combinations of gas injection, gravity drainage, and waterflooding. Extensive pre-unit reservoir studies utilized a Hele-Shaw (parallel plate) model to analyze the effects of gravity and mobility ratio on areal sweep efficiency. Also, a "one-dimension" 20-layer computer model without cross-flow was used to investigate the effects of these factors on vertical sweep efficiency for various possible recovery techniques. Analysis also considered analogy with actual waterflood performance in an adjacent fault block. A formation dip performance in an adjacent fault block. A formation dip of 25 degrees to 60 degrees and an average core air permeability of 196 md combine to indicate better sweep permeability of 196 md combine to indicate better sweep efficiency for all oil displacement processes than would be obtained in a similar flatter reservoir. During actual operation. breakthrough of injected fluids into wells offsetting input wells occurred much earlier than anticipated. Injected fluids now have encompassed 15 producing wells up to a maximum distance of 3,000 ft from the nearest input wells. This performance is sufficient to confirm that vertical sweep efficiency at breakthrough has been much less than that expected from the pre-unit studies. In an effort to understand and to control this vertical sweep behavior, we conducted extensive subsurface testing of many injection and producing wells. This included using modern production logging techniques in many wells and separately testing seven different intervals in one observation well using straddle packers. We found that the ineffectiveness of well completion with conventional jet perforation through casing was a major contributor to this poorer-than-expected vertical sweep efficiency. Even poorer-than-expected vertical sweep efficiency. Even in this "clean, homogeneous" sand, the path of the fluid flow through the formation tended to be the same as the intervals where the fluids left the input wells and entered the producing wells. The primary purposes of this paper are as follows:To review the production logging of one well that demonstrated the ineffectiveness of perforations.To outline a perforation fracture treatment cleanout technique used to improve the well completion efficiency.To review subsequent production logging and pressure-production testing that confirmed the pressure-production testing that confirmed the improvement in the producing profile. Enough of the additional subsurface testing of other wells is included to demonstrate that reservoir heterogeneity controls the over-all fluid movement in this "clean" sand reservoir, a fact that makes thoroughly effective well completions mandatory. JPT P. 1063