Double Scale Method Research Articles

A Double-Scale method for near-well flow in reservoir simulation

Simulation of near-well flow around a single well in reservoirs is normally studied using radial logarithmic grids. A promising method for more complicated, multi-well cases is a combined approach of using a Cartesian and a radial grid. In this paper, a new method of overlapping grids is introduced in which a radial grid is overlapped on a coarse Cartesian grid in the area around a well. Connectivity between the two grids is established using an appropriate boundary condition. Five different algorithms of grids connectivity with internal boundary conditions are presented in which the data are transferred between the grids by interpolation pressure and saturations in each grid. This method is implemented in the open-source Matlab Reservoir Simulation Toolbox (MRST) using the modified black-oil model. The proposed approach is validated by simulation of a reference fine radial grid model on a gas-condensate reservoir. Comparing the results with the reference model indicates that the proposed Double-Scale method using a 21 × 21 coarse Cartesian grid is as accurate as a 1001 × 1001 simple Cartesian fine grid model. Then, a double-layer numerical problem with two production wells was simulated and sensitivity analysis was conducted to investigate the effect of critical condensate saturation and vertical permeability. Finally, the second SPE comparative solution project was simulated to compare the performance of the proposed method with the use of the perpendicular bisector (PEBI) grids around the well. Results showed that the accuracy of the PEBI grid and Double-Scale method are comparable. However, the proposed Double-Scale method is almost 2 times faster in this specific problem. • The new Double-Scale method is implemented in MRST toolbox. • The accuracy of results highly increases by using the Double-Scale method. • This method reduces the CPU time of simulation significantly. • The gravity drainage can be seen by monitoring vertical permeability variation. • The second SPE comparative solution project was simulated by the Double-Scale method.

Asymptotic waves in viscoanelastic media with memory by the double-scale method

In this paper asymptotic dissipative waves in viscoanelastic media with shape and volumetric memory, previously studied by the author in a more classical way, are studied from the point of view of the double-scale method. Then, a physical interpretation is given of a new (fast) variable ξ, related to the family of hypersurfaces S , across which the solutions or/and some of their derivatives vary steeply, whereas their variation is slow along S and related to the old variables x α (called slow variables). The double-scale method is sketched. The thermodynamical model governing in the three-dimensional case the motion of the rheological media under consideration is presented and many results regarding the propagation of a particular solution into a uniform unperturbed state and the approximation of the first order of the wave front of this solution are given in full detail and reviewed by the double-scale method. Other novel results are worked out. The thermodynamic models for viscoanelastic media with memory are applied in rheology and in several technological sectors.

DOUBLE SCALE METHOD OF DISTANCE MEASURING WITH THE USE OF QUADRATURE MULTIPLEXING OF PHASE-SHIFT KEYED SIGNALS

In this article a new method is proposed for building measurement scales for radio-electronic systems using phase-shift keyed signals with quadrature multiplexing. A possibility is reviewed for application thereof in global navigation satellite systems to increase the range of ambiguous measurement range by using the ranging codes. The algorithm is presented for computing the total signal propagation delay time based on the results of measurements on two non-multiple scales.

Wave propagating in multilayers composed of piezo electric and piezo magnetic layers

Abstract In this paper, a study of effective parameters and wave properties of a slab of an artificial material comprised of alternating piezomagnetic and piezoelectric layers is presented. This kind of composite structure features new functionalities including effective magneto-electric coupling nonexistent in either constituent layer. In the first section, the equations of propagation of hybrid elasto-electro-magnetic waves in the equivalent homogeneous medium are derived by using a double scale method based on the periodical homogeneization. The wave length is considered to be much greater than the layer spatial periodicity and electromagnetic retardation is not taken into account. In the second section, dispersion relations for the hybrid waves travelling in a slab with previously established effective parameters are obtained. It was shown that although all three components, mechanic, electric and magnetic, contribute to the overall oscillatory behavior, the wave is predominantly elastic. At the same time, such composite media demonstrate double tunability, electric via the piezoelectric phase and magnetic through the piezomagnetic one, and can be regarded as novel functional materials.

Scaling algorithms for the calculation of solar radiative fluxes

We derived new scaling formulae based on the method of successive orders of scattering to calculate solar radiative flux. In this report, we demonstrate a multiple scaling method, in which we introduce scaling factors for each scattering order independently. The formula of radiative transfer by the method of successive orders of scattering cannot be solved rapidly except in the case of optically thin atmospheres. Then we further derived a double scaling method, which scales the ordinary radiative transfer equation by two scaling factors. We applied the double scaling method to two-stream and four-stream approximations of the discrete ordinates method. Comparing the results of the double scaling method with those of the delta-M method, we found that the double scaling method improved the accuracy of radiative fluxes at large solar zenith angles, especially in the optically thin region, and that in the region where multiple scattering dominates, its accuracy was comparable to that of the delta-M method. Once we determined the scaling factors appropriately, the double scaling method calculated radiative fluxes as rapidly as the delta-M method in the two-stream and four-stream approximations. This method, therefore, is useful for accurate computation of solar radiative fluxes in general circulation models.

Asymptotic waves from the point of view of double-scale method

In this paper the asymptotic waves (smooth solutions of nonlinear hyperbolic partial differential equations (PDEs)) are introduced from the point of view of double scale method, giving a physical interpretation of the new (fast) variable, related to the surface across which the derivatives of the solution vary steeply.

DISCRETE INTEGRABLE SYSTEMS ASSOCIATED WITH THE UNITARY MATRIX MODEL

The orthogonal polynomials on the unit circle associated with the unitary matrix model have various interesting properties, and have been studied in connection with different applications, such as double scaling, Riemann–Hilbert problems and integrable Fredholm operators. In this paper, we study the orthogonal polynomials on the unit circle with the weight function [Formula: see text]. We use the orthogonality of the polynomials to show that the orthogonal polynomials on the unit circle satisfy the linear problems associated with the discrete PainlevéII hierarchy, alternate discrete PainlevéII hierarchy and the discrete MKdV hierarchy. Thus the isomonodromy deformation method can be used to study the unitary matrix model. Typically, we focus on the orthogonal polynomials with the weight function exp {s(z+z-1)}. The recursion formula z(pn+vnpn-1)=pn+1+unpn (derived from Szegö's equation) for the orthogonal polynomials pn(z,s) is proved to be equivalent to the discrete AKNS-ZS system which is the base equation in the linear problem for the discrete equations. The variable xn=pn(0,s) satisfies the discrete PainlevéII equation and the discrete MKdV equation; un, vn satisfy the alternate discrete PainlevéII equation; 1/un-1=-xn-1/xn satisfies the PainlevéIII equation; and [Formula: see text] satisfies the PainlevéV equation. Also, we discuss the continuum limits of the discrete equations by using the double scaling method. Further, we present a procedure for finding the linear equations for the orthogonal polynomials and the consistency conditions of the linear equations by using the orthogonality of the polynomials.