A new mathematical model for horizontal wells with variable density perforation completion in bottom water reservoirs

Horizontal wells are commonly used in bottom water reservoirs,which can increase contact area between wellbores and reservoirs.There are many completion methods used to control cresting,among which variable density perforation is an effective one.It is difficult to evaluate well productivity and to analyze inflow profiles of horizontal wells with quantities of unevenly distributed perforations,which are characterized by different parameters.In this paper,fluid flow in each wellbore perforation,as well as the reservoir,was analyzed.A comprehensive model,coupling the fluid flow in the reservoir and the wellbore pressure drawdown,was developed based on potential functions and solved using the numerical discrete method.Then,a bottom water cresting model was established on the basis of the piston-like displacement principle.Finally,bottom water cresting parameters and factors influencing inflow profile were analyzed.A more systematic optimization method was proposed by introducing the concept of cumulative free-water production,which could maintain a balance（or then a balance is achieved）between stabilizing oil production and controlling bottom water cresting.Results show that the inflow profile is affected by the perforation distribution.Wells with denser perforation density at the toe end and thinner density at the heel end may obtain low production,but the water breakthrough time is delayed.Taking cumulative free-water production as a parameter to evaluate perforation strategies is advisable in bottom water reservoirs.

DISAPPEARANCE OF INTERFACES FOR DEGENERATE PARABOLIC EQUATIONS WITH VARIABLE DENSITY AND ABSORPTION

In this article, the authors deal with the Cauchy problem of a nonlinear parabolic equation with variable density and absorption. By using energy methods, the authors prove that the interfaces can disappear in finite time under some assumptions on the density functions.

Properties of Solutions of Kolmogorov-Fisher Type Biological Population Task with Variable Density

In this paper, we discussed population model of two competing populations with non-linear double diffusion and variable density which described by nonlinear system of competing individuals. We identify new properties, such as finite speed of propagation, and localization of the outbreaks in a specific area.

A High-Order Direct Discontinuous Galerkin Method for Variable Density Incompressible Flows

In this work,we develop a novel high-order discontinuous Galerkin(DG)method for solving the incompressible Navier-Stokes equations with variable density.The incompressibility constraint at cell interfaces is relaxed by an artificial compressibility term.Then,since the hyperbolic nature of the governing equations is recovered,the simple and robust Harten-Lax-van Leer(HLL)flux is applied to discrete the inviscid term of the variable density incompressible Navier-Stokes equations.The viscous term is discretized by the direct DG(DDG)method,the construction of which was initially inspired by the weak solution of a scalar diffusion equation.In addition,in order to eliminate the spurious oscillations around sharp density gradients,a local slope limiting operator is also applied during the highly stratified flow simulations.The convergence property and performance of the present high-order DDG method are well demonstrated by several benchmark and challenging numerical test cases.Due to its advantages of simplicity and robustness in implementation,the present method offers an effective approach for simulating the variable density incompressible flows.

Stability of stratified shear flows in channels with variable cross sections

For the instability problem of density stratified shear flows in sea straits with variable cross sections, a new semielliptical instability region is found. Rurthermore, the instability of the bounded shear layer is studied in two cases： （i） the density which takes two different constant values in two layers and （ii） the density which takes three different constant values in three layers. In both cases, the dispersion relation is found to be a quartic equation in the complex phase velocity. It is found that there are two unstable modes in a range of the wave numbers in the first case, whereas there is only one unstable mode in the second case.

Cylindrical effects in weakly nonlinear Rayleigh Taylor instability

The classical Rayleigh–Taylor instability（RTI） at the interface between two variable density fluids in the cylindrical geometry is explicitly investigated by the formal perturbation method up to the second order. Two styles of RTI, convergent（i.e., gravity pointing inward） and divergent（i.e., gravity pointing outwards） configurations, compared with RTI in Cartesian geometry, are taken into account. Our explicit results show that the interface function in the cylindrical geometry consists of two parts： oscillatory part similar to the result of the Cartesian geometry, and non-oscillatory one contributing nothing to the result of the Cartesian geometry. The velocity resulting only from the non-oscillatory term is followed with interest in this paper. It is found that both the convergent and the divergent configurations have the same zeroth-order velocity, whose magnitude increases with the Atwood number, while decreases with the initial radius of the interface or mode number. The occurrence of non-oscillation terms is an essential character of the RTI in the cylindrical geometry different from Cartesian one.

The relation between the Mindanao Current and Mindanao Undercurrent on seasonal scale

The ocean general circulation model for the earth simulator（OFES） products is applied to estimate the transports of the Mindanao Current（MC） and the Mindanao undercurrent（MUC） and explore the relation between them on seasonal scale. In general, the MUC is composed of the lower part of the Southern Pacific Tropical Water（SPTW）and Antarctic Intermediate Water（AAIW）. While the deep northward core below 1 500 m is regarded as a portion of MUC. Both salinity and potential density restrictions become more reasonable to estimate the transports of MC/MUC as the properties of water mass having been taken into consideration. The climatological annual mean transport of MC is（37.4±5.81）×10~6 m^3/s while that of MUC is（23.92±6.47）×10~6 m^3/s integrated between 26.5 σ_θ and 27.7 σ_θ, and（17.53±5.45）×10~6 m^3/s integrated between 26.5 σ_θ and 27.5 σ_θ in the OFES. The variations of MC and MUC have good positive correlation with each other on the seasonal scale： The MC is stronger in spring and weaker in fall, which corresponds well with the MUC, and the correlation coefficient of them is 0.67 in the OFES.The same variations are also appeared in hybrid coordinate ocean model（HYCOM） results. Two sensitive experiments based on HYCOM are conducted to explore the relation between MC and MUC. The MUC（26.5〈σ_θ〈27.7） is strengthening as the MC increases with the enhancement of zonal wind field. It is shown,however, that the main part of the increasement is the deeper northward high potential density water（HPDW）,while the AAIW almost remains stable, SPTW decreases, and vice versa.

Prediction of Gas Chromatographic Retention Indices of Organophosphates by DFT and VSMP Method

Polychlorinated dibenzothiophenes（PCDTs） are a group of important persistent organic pollutants.In the present study,geometrical optimization and electrostatic potential calculations have been performed for all 135 PCDTs congeners at the B3LYP/6-31G＊ level of theory.By means of the VSMP（variable selection and modeling based on prediction） program,one optimal descriptor（molecular polarizability,α） was selected to develop a QSRR model for the prediction of gas chromatographic retention indices（GC-RI） of PCDTs.The estimated correlation coefficients（r2） and LOO-validated correlation coefficients（q2）,all more than 0.99,were built by multiple linear regression,which shows a good estimation ability and stability of the models.A prediction power for the external samples was validated by the model built from the training set with 17 polychlorinated dibenzothiophenes.

Efficient Variable-Coefficient Finite-Volume Stokes Solvers

We investigate several robust preconditioners for solving the saddle-point linear systems that arise from spatial discretization of unsteady and steady variablecoefficient Stokes equations on a uniform staggered grid.Building on the success of using the classical projection method as a preconditioner for the coupled velocitypressure system[B.E.Griffith,J.Comp.Phys.,228(2009),pp.7565–7595],as well as established techniques for steady and unsteady Stokes flow in the finite-element literature,we construct preconditioners that employ independent generalized Helmholtz and Poisson solvers for the velocity and pressure subproblems.We demonstrate that only a single cycle of a standard geometric multigrid algorithm serves as an effective inexact solver for each of these subproblems.Contrary to traditional wisdom,we find that the Stokes problem can be solved nearly as efficiently as the independent pressure and velocity subproblems,making the overall cost of solving the Stokes system comparable to the cost of classical projection or fractional step methods for incompressible flow,even for steady flow and in the presence of large density and viscosity contrasts.Two of the five preconditioners considered here are found to be robust to GMRES restarts and to increasing problem size,making them suitable for large-scale problems.Our work opens many possibilities for constructing novel unsplit temporal integrators for finite-volume spatial discretizations of the equations of low Mach and incompressible flow dynamics.

WAVE DISSIPATING PERFORMANCE OF AIR BUBBLE BREAKWATERS WITH DIFFERENT LAYOUTS

The wave dissipating performance of air bubble breakwaters with different layouts is studied by experimental and numerical methods in this article. Based on the assumpation that the mixture of air and water is regarded as a variable density fluid, the mathematical model of the air bubble breakwater is built. The numerical simulation results are compared with the experimental data, which shows that the mathematical model is reasonable for the transmission coefficient Ct m. The influencing factors are studied experimentally and numerically, including the incident wave height H i, the incidentt wave period T , the air amount Qm , the submerged pipe depth D and the single or double air discharging pipe structure. Some valuable conclusions are obtained for further research of the mechanism and practical applications of air bubble breakwaters.

The productivity calculation model of perforated horizontal well and optimization of inflow profile

Aiming at the large error in productivity predication and incomplete consideration in completion parameters design of perforated horizontalwell,a model which coupled the relationship of pressure and flow rate in reservoir seepage,near-wellbore inflow and wellbore flow was established.The impact of near-wellbore heterogeneity,wellbore flow pressure drop and completion parameters on the inflow profile of horizontalwell is analysed.Studies showed that with a stronger near-wellbore heterogeneity,the inflowprofilewouldfluctuatemore seriously.Perforationdensityhada great influence onthe inflow profile and local changes of it would bring a shunt effect.Completion design of variable density perforated horizontalwell with an optimized inflowprofile whichwas close to a standard profilewould improve the horizontal well development effect.The achievement can provide directive meanings to productivity predication and completion parameters design of horizontal wells in oilfield.

SPLITTING SCHEMES FOR A NAVIER-STOKES-CAHN-HILLIARD MODEL FOR TWO FLUIDS WITH DIFFERENT DENSITIES

In this work, we focus on designing efficient numerical schemes to approximate a ther- modynamically consistent Navier-Stokes/Cahn-Hilliard problem given in [3] modeling the mixture of two incompressible fluids with different densities. The model is based on a diffuse-interface phase-field approach that is able to describe topological transitions like droplet coalescense or droplet break-up in a natural way. We present a splitting scheme, decoupling computations of the Navier-Stokes part from the Cahn-Hilliard one, which is unconditionally energy-stable up to the choice of the potential approximation. Some nu- merical experiments are carried out to validate the correctness and the accuracy of the scheme, and to study the sensitivity of the scheme with respect to different physical pa- rameters.

雷诺数和施密特数对激波-气泡相互作用中变密度混合的影响

惯性约束聚变、水动力空化侵蚀和微观尺度激波加速流动中的激波-气泡相互作用(SBI)构型处于高黏度(低雷诺数)或低扩散率(高施密特数)环境中,其混合性能尚不清楚.通过测定宽范围内的粘度和扩散系数,采用高分辨率数值模拟研究了雷诺数Re和施密特数Sc对SBI流动结构和混合行为的影响.次级斜压涡度(SBV)增长明显受雷诺数的影响,表现为斜压涡和黏性耗散之间的生长抑制涡度动力学平衡.混合速率受施密特数的影响,标度为χ^(∗)=β·Sc^(−α),其中系数β∼Re−0.2和标度指数α∼Re−0.385.混合标度表明,较高雷诺数下的SBV拉伸增强导致混合速率对施密特数的依赖性减弱,这可能为实际应用中的混合增强设计开辟新的途径.

Novel Mesh Technique and Its Application in the Wind Field Simulation for Flexible Spatial Structure

In this paper,novel mesh techniques are proposed for wind field simulation of flexible spatial structure.For mesh generation,an interpolation strategy is presented to obtain a mesh system with variable density.Two spatial structure examples are used to examine the efficiency and applicability of this technique.Then based on the structured mesh system generated by the technique,the mesh nodal coordinates are updated to adapt the moving boundary conditions by means of the mapping interpolation functions and some examples are given to verify the effectiveness.Furthermore,the constrained counterforce distribution technique and projection interpolation strategy are developed to implement the data exchange on the interaction surface of wind and structure.Finally,the computational accuracy is numerically validated.