PROBABILISTIC DYNAMICS OF TWO-LAYER GEOPHYSICAL FLOWS

The problem addressed here is the challenge of determining the best production strategy for multilayer reservoirs which varies from field to field as well as from well to well. Commingled production strategy is one of the most commonly used for several multilayer wells. However, there are some limitations to this method. Mostly, when very complex multilayer wells which contain different types of fluid in each productive layer are identified, the selection process of production approach is basically trial and error and later found to be a poor choice. One attempted solution to choosing the optimal production strategy is using numerical reservoir simulation. In this study, we used reservoir simulation to compare the performance of four different production strategies for different combinations of types of fluid present in a two-layer system. Strategy 1 in which the fluid is produced from two layers simultaneously is the best production approach when oil is present in the top and bottom layers. Strategy 2 in which the fluid is produced from one layer at a time starting with the bottom layer is the best production approach when reservoir fluid at the top layer is gas while fluids present in the bottom layer can vary from oil, gas&oil, gas&water and oil&water. Strategy 3 produces fluid from one layer at a time, starting with the bottom layer. When the production rate decreases to half of the original rate, the two zones are produced in a commingled fashion. Similar to strategy 1, strategy 3 is also the best production approach when oil is present in the top and bottom layers. Strategy 4 is similar to strategy 3 but starting with the top layer. This strategy is the best production approach when oil is present in the top layer and gas&water in the bottom layer. This approach can delay water production and sustain reservoir pressure.

Heat and concentration analysis of two-layered muco-ciliary third grade fluid flow in human airways

In the present paper, we endeavor to accomplish a diagram, which demarcates the validity ranges for interfacial wave theories in a two-layer system, to meet the needs of design in ocean engineering. On the basis of the available solutions of periodic and solitary waves, we propose a guideline as principle to identify the validity regions of the interfacial wave theories in terms of wave period T, wave height H, upper layer thickness d 1, and lower layer thickness d 2, instead of only one parameter–water depth d as in the water surface wave circumstance. The diagram proposed here happens to be Le Méhauté’s plot for free surface waves if water depth ratio r = d 1/d 2 approaches to infinity and the upper layer water density ρ 1 to zero. On the contrary, the diagram for water surface waves can be used for two-layer interfacial waves if gravity acceleration g in it is replaced by the reduced gravity defined in this study under the condition of σ = (ρ 2 − ρ 1)/ρ 2 → 1.0 and r > 1.0. In the end, several figures of the validity ranges for various interfacial wave theories in the two-layer fluid are given and compared with the results for surface waves.

The process of eddy detachment from a strong, eastward-flowing oceanic jet, which is modeled after the Gulf Stream, is studied using a two-layer quasi-geostrophic model. Numerical calculations are performed, in which an initial perturbation having a small amplitude is superimposed on a basic flow consisting of the eastward jet in the upper layer. The initial perturbation is located in the western part of the jet and consists of one wavelength of meanders. The initial perturbation propagates eastward and grows rapidly, for the most part because of a baroclinic instability. The extremes of large-amplitude meanders are forced to go along the edges of recirculating gyres which are generated on both sides of the jet in the western part, and as a result the meanders are cut off and form eddies. In some cases, meander interactions—by which an upstream meander overtakes the nearest downstream meander—precedes the detachment. The meander growth, which is the basic condition for the detachment, is highly dependent on the lower layer velocity of the basic jet, i.e., the fast eddy is detached later and farther downstream as the velocity increases from zero. The meander whose wavelength is ∼1.2 times as long as that of the fastest growing linear solution is the major source of the detached eddies, because nonlinearity has the stronger stabilizing effects on the shorter wavelength meanders and reduces group velocity of the longer wavelength meanders to a greater extent. A comparison of solutions on a β plane with ones on an f plane further reveals that the beta-effect assists detachment. The spatially growing solutions, which have larger amplitude in the eastern part, are more analogous to Gulf Stream meanders from which eddies are detached than are the spatially periodic, temporally growing solutions. The numerical results are applied to infrared images made from the NOAA-4 satellite of the Gulf Stream in which eddies are detached from meanders.

Structures are commonly founded on layered soil deposits. In this study, settlement due to a circular load on a two-layer soil system overlying a rock stratum or a stiff soil deposit is estimated and compared with the values obtained using Steinbrenner’s and Finite element approaches. Design tables are proposed for settlements due to uniform circular loading (of radius equal to a) applied on two-layer soil system for top-layer thickness H 1 = 0.2a–6.0a, bottom-layer thickness H 2 = 1.0a–6.0a, moduli ratio of top and bottom layers E 1 /E 2 = 0.01–100 and Poisson’s ratio v = 0.2–0.5. The settlement factors from the study were also compared with the Ueshita and Meyerhof’s values for a finite top layer overlying a semi-infinite bottom layer. Results were compared with the observed settlement of a structure resting on a layered soil profile overlying a rock stratum. Proposed settlement of the two-layer system shows good agreement with these studies.

The effect of different directional magnetic fields on critical temperature differences of oscillatory thermocapillary convection in a rectangular cavity with differentially heated side walls filled with two viscous, immiscible, incompressible fluids is simulated in the absence of gravity. In this two-layer fluid system, the upper layer fluid is the electrically non-conducting encapsulant boron oxide (B2O3), while the lower one is the electrically conducting molten indium phosphide (InP). The interface between the two fluids is assumed to be flat and non-deformable. The computational results show that all the magnetic fields along the x, y and z directions can delay the transition from steady convection to oscillatory convection, and critical temperature differences increase with an increasing Hartmann number. Furthermore, the effect of a magnetic field along the z direction is strongest, followed by that along the y direction, and that along the x direction is the weakest for the same intensity of the magnetic field.

On the radiation of meso-scale energy in the mid-ocean

In this chapter, the prediction model proposed by Sassa et al. (in Geotechnique 51(10), 847–857 (2001)) for the wave-induced progressive liquefaction in marine sediment, based on two-layered inviscid fluid system, is re-examined. An alternative approach with a similar framework (Sassa et al. in Geotechnique 51(10), 847–857 (2001)) is developed to correct the inappropriate mechanism of wave components used. Then, a two-layered wave model which includes viscous effects is established and applied to describe the progressive nature of wave-induced liquefaction. A comprehensive comparison shows that the previous model (Sassa et al. in Geotechnique 51(10), 847–857 (2001)) overestimates the maximum liquefaction depth. It is found that the viscosity of liquefied soil cannot be ignored and the solution for an infinite seabed is not suitable for liquefaction analysis of shallow seabed. A parametric study demonstrates the significant influence of numerous wave and soil characteristics on the liquefaction depth.

The quasigeostrophic two-layer model is of superior interest in dynamic meteorology since it is one of the easiest ways to study baroclinic processes in geophysical fluid dynamics. The complete set of point symmetries of the two-layer equations is determined. An optimal set of one- and two-dimensional inequivalent subalgebras of the maximal Lie invariance algebra is constructed. On the basis of these subalgebras, we exhaustively carry out group-invariant reduction and compute various classes of exact solutions. Wherever possible, reference to the physical meaning of the exact solutions is given. In particular, the well-known baroclinic Rossby wave solutions in the two-layer model are rediscovered.

In this paper, the effects of bottom and interfacial friction on localized baroclinic instability are discussed in the weakly nonlinear, long-wave limit. Using a quasigeostrophic two-layer model in which the lower layer is assumed to be deep, we have derived a coupled evolution equation set that consists of a KdV-type equation for the upper layer and a linear long-wave equation for the lower layer. A perturbation theory reveals that there are multiple equilibria in this system, where baroclinic energy conversion and frictional dissipation are in balance; the flow is not forced externally, and multiplicity here refers to the presence or absence of solitary waves propagating steadily on a zonal flow. Further, direct numerical calculations show a rich variety of behavior of solitary waves, including steady, periodic, and complicated interacting evolutions. For a two-layer model to have multiple steady or oscillatory states, both bottom and interfacial friction should be included because if one of th...

A method for estimating the optical properties of two-layered media (such as squamous epithelial tissue) over a range of wavelengths in the ultraviolet-visible spectrum is proposed and tested with Monte Carlo modeling. The method first used a fiber-optic probe with angled illumination and the collection fibers placed at a small separation (<or=300 microm) to restrict the transport of detected light to the top layer. A Monte Carlo-based inverse model for a homogeneous medium was employed to estimate the top layer optical properties from the measured diffuse reflectance spectrum. Then a flat-tip probe with a large source-detector separation (>or=1000 microm) was used to detect diffuse reflectance preferentially from the bottom layer. A second Monte Carlo-based inverse model for a two-layered medium was applied to estimate the bottom layer optical properties, as well as the top layer thickness, given that the top layer optical properties have been estimated. The results of Monte Carlo validation show that this method works well for an epithelial tissue model with a top layer thickness ranging from 200 to 500 microm. For most thicknesses within this range, the absorption coefficients were estimated to within 15% of the true values, the reduced scattering coefficients were estimated to within 20% and the top layer thicknesses were estimated to within 20%. The application of a variance reduction technique to the Monte Carlo modeling proved to be effective in improving the accuracy with which the optical properties are estimated.

Geophysical granular flows, such as snow avalanches and debris flows, represent a great hazard to man and infrastructures. These natural phenomena are characterized by the rapid flow of a granular solid phase, embedded in an ambient fluid. Since such events occur with little warning, in addition to investigating the triggering conditions, it is of crucial interest to predict their propagation and run-out distances. The main purpose of the present research is to better understand the flow dynamics of dry granular flows, in the presence of no-slip bottom boundary conditions, and predict their propagation by using a depth-averaged approach. In this case, a stratification of different flow regimes, such as quasi-static and dense collisional, occurs and makes the utilization of the classical single layer depth-averaged models insufficient, because of important uncertainties about the velocity and shear stress distributions along the flow depth. In the first part of the present work, an experimental-numerical study on dam-break flows of dry granular material is reported. It has been found that a modification to the formula, proposed in the Savage-Hutter model for calculating the earth-pressure coefficient, leads to an improved agreement with experimental data, in presence of no-slip bottom conditions. In the second part, an experimental study on steady state velocity profiles of dry granular flows is reported. The granular material, used in this experimental research, was Ottawa sand (ASTM C-778 20/30). The velocity profiles at the side walls and free surfaces have been obtained, through granular PIV techniques. The measurements are in accordance with other experimental works on different granular materials and suggest the occurrence of a rheological stratification along the flow depth, in case of no-slip bottom condition. In order to better describe such a complex flow dynamics, a two-layer depth-averaged model has been proposed. The dynamics of the two layers, ideally corresponding to dense-collisional and quasi-static regimes, have been considered independently. As well, mass exchanges between the layers have calculated through a physically based closure equation. The well-known mathematical issue of the hyperbolicity loss in two-layer models has been carefully addressed. In order to overcome it, a local modification of source terms of the original mathematical model has been proposed. Such a treatment consists of introducing an extra resistance at the interface, if necessary, to avoid the hyperbolicity loss. This approach has been found to be robust and yields reasonable results, as long as the asymptotic steady state solution and boundary conditions fulfil the hyperbolicity requirements of the original model. Through comparisons with experimental data, the two-layer approach turns out to be very promising to describe the complex flow dynamics in case of no-slip bottom boundary conditions, although a more detailed description of the basal shear stress seems to be required. In the third part of the present dissertation, the same two-layer approach has been used in order to rewrite the mathematical model in a curvilinear coordinates system, attached to the interface between the two layers. The model equations have been obtained, by using the same approach proposed in Tai and Kuo (2008). In the model derivation, the physically negligible quantities are identified in a more rational way than the previous model, by means of a scaling approximation.

We have investigated a method for solving the inverse problem of determining the optical properties of a two-layer turbid model. The method is based on deducing the optical properties (OPs) of the top layer from the absolute spatially resolved reflectance that results from photon migration within only the top layer by use of a multivariate calibration model. Then the OPs of the bottom layer are deduced from relative frequency-domain (FD) reflectance measurements by use of the two-layer FD diffusion model. The method was validated with Monte Carlo FD reflectance profiles and experimental measurements of two-layer phantoms. The results showed that the method is useful for two-layer models with interface depths of >5 mm; the OPs were estimated, within a relatively short time (<1 min), with a mean error of <10% for the Monte Carlo reflectance profiles and with errors of <25% for the phantom measurements.

The structure of the most unstable baroclinic mode in the presence of elongated topography oriented parallel to the basic state zonal current has been investigated in a number of studies. The topographic modification leads to enhanced baroclinic activity on the southern side of the mountain. The results found in simple quasi-geostrophic models with a ridge were generalized to primitive equations and realistically high and steep isolated topography; the same type of north–south asymmetry apt to explain lee cyclogenesis was observed. In the present study we use a quasi-geostrophic two-layer model with a bottom ridge to investigate the dynamical balance leading to this type of asymmetry. In the case of a purely barotropic Rossby wave, we find that the topographic correction always leads to intensification of the undisturbed wave south of the mountain barrier. In the case of unstable baroclinic waves in the f-plane, a simple criterion holds that determines the conditions favoring lee cyclogenesis in ...

A stability of planetary waves on an infinite beta-plane is investigated in an idealized two-layer fluid system for the large local Rossby numberM. When a primary wave is barotropic, two kinds of barotropic instability modes are found. One of them was previously discussed byGill (1974). When a primary wave is baroclinic, two different kinds of modes that enable barotropic and baroclinic energy transfers are found. The one that has the larger growth rate gains its energy mainly from the mean shear of the primary wave when the internal rotational Froude numberF is smaller than 1/2. WhenF is larger than 1/2, however, the available energy conversion of the primary wave is dominant. This mode has a fairly large part of its energy in the barotropic motion although the primary wave is purely baroclinic.