Spectral and numerical analysis for a thermoelastic problem with double porosity and second sound

We study some spectral and numerical properties of the solutions to a thermoelastic problem with double porosity. The model includes Cattaneo-type evolution law for the heat flux to remove the physical paradox of infinite propagation speed of the classical Fourier’s law. Firstly, we prove that the operator determined by the considered problem has compact resolvent and generates a C 0 -semigroup in an appropriate Hilbert space. We also show that there is a sequence of generalized eigenfunctions of the linear operator that forms a Riesz basis. By a detailed spectral analysis, we obtain the expressions of the spectrum and we deduce that the spectrum determined growth condition holds. Therefore we prove that the energy of the considered problem decays exponentially to a rate determined explicitly by the physical parameters. Finally, some numerical simulations based on Chebyshev spectral method for spatial discretization are given to confirm the exponential stability result and to show the distribution of the eigenvalues and the variables of the problem.

Numerical modeling of multiphase mass transfer processes in fractured-porous reservoirs

The paper presents an algorithm for solving the problem of the process of mass transfer of a two-phase fluid in a fractured-porous reservoir in a one-dimensional formulation. The presence of natural fractures in such reservoirs impedes various types of exploration and field development. Fractured-porous reservoirs are characterized by intense exchange fluid flow between fractures and porous blocks. Each system has its own individual set of filtration-capacity parameters, and this fact complicates the problem under consideration. To study the mass transfer of a two-phase fluid in a medium with double porosity, a four-block mathematical model with splitting by physical processes is proposed. The model is described by a system of partial differential equations. The splitting method forms two functional blocks on the water saturation and the piezoconductivity. For the numerical solution of this system, an absolutely stable implicit finite-difference scheme is constructed in the one-dimensional case. On the basis of the proposed difference scheme, pressures and saturations in the fracture system and matrix are obtained.

Homogenization of a stochastic model of a single phase flow in partially fissured media

In this paper, we present new homogenization results of a stochastic model for flow of a single-phase fluid through a partially fissured porous medium. The model is a double-porosity model with two flow fields, one associated with the system of fissures and the other associated with the porous system. This model is mathematically described by a system of nonlinear stochastic partial differential equations defined on perforated domain. The main tools to derive the homogenized stochastic model are the Nguetseng’s two-scale convergence, tightness of constructed probability measures, Prokhorov and Skorokhod compactness process and Minty’s monotonicity method.

Research and application experience of water Huff and Puff technology on low-permeability oil field

Background. This paper presents a study of the applicability and the first results of pilot works of the technology of periodic water injection into production wells with subsequent oil production (Huff and Puff ), which was not previously used in Russia. The oil field of the company “Gazprom Neft” with a terrigenous reservoir of low permeability is considered. Aim. It is planned to use the technology at marginal waterless wells with hydraulic fracturing, which are on the verge of profitability, to increase oil production. Materials and methods. The physical principles of capillary impregnation in a hydrophilic reservoir were presented, which, under given conditions, should lead to an increase in oil production in waterless wells during cyclic water injection and shutdown with subsequent production. Since this technology was not previously used in Russia, a review and analysis of the unsuccessful application in the United States and the successful experience in China in fields with similar properties and wells was carried out. For the design of pilot works, calculations were made on a synthetic hydrodynamic model with double porosity and permeability, according to which a significant increase in oil production in a marginal well was obtained relative to standard operation. Pilot work was carried out on four oil wells of the company’s field, which were previously planned to be transferred to the reservoir pressure maintenance stock. Only two of them managed to meet the required injection and shutdown periods. Results. Pilot work didn’t show significant increase in oil production after the application of the technology. At the same time, there was no decrease in representative wells, which should have occurred due to a decrease in the phase permeability of oil, which indicates the work of the effect of capillary imbibition during water injection. Conclusions. Based on the analysis of the ambiguous results of pilot works, a conclusion is made about the ineffectiveness of the huff and puff technology in the specified modes, the necessity of their optimization and further research.