Viktoriya Olegovna Podryga

The work studies the order of approximation of the symbolic tridiagonal matrix algorithm proposed for solving piezoconductivity problems in oil-bearing fractured-porous formations. The symbolic tridiagonal matrix algorithm is a modification of the classical tridiagonal matrix algorithm and consists in finding the values of the sought grid function in a polynomial form. This also entails a polynomial representation of one tridiagonal matrix coefficient and of the residual. The domain decomposition is organized as follows: over the entire oil-bearing formation a macrogrid with a large spatial step is introduced, and in one of its cells a microgrid with a finer spatial step is constructed. The algorithm allows obtaining an exact solution on the microgrid to refine the calculations independently of the function values at the macronodes. The algorithm is verified on problems with a known analytical solution, and the second order of accuracy of the algorithm is obtained in the formulation with nested grids, which corresponds to the accuracy of the stated difference scheme. The algorithm is applied to study the piezoconductivity problem in a fractured-porous reservoir, and pressure distribution patterns in the fracture system are obtained.

1. Natural gas in the shallow crust can exist in either free or hydrate (clathrate) form. Gas hydrates are ice-like, crystalline water-based solids that form under specific temperature and pressure...

The work is devoted to the application of the quasi-gasdynamic (QGD) approach to solving problems of flow around manned descent spacecraft on the final section of the trajectory near the Earth’s surface. The main objective of the work is the numerical analysis of the two-dimensional flow around the descent module at different angles of attack. The feature of the calculations performed is the use of the QGD equations and the finite volume method on an irregular triangular grid as a basic model. Parallel computing based on the OpenMP standard is used to speedup calculations. The gas environment is represented by dry atmospheric air. The QGD system is considered in a one-component formulation and is supplemented by the equations of state of an ideal gas and the dependencies of the kinetic coefficients on temperature and pressure. In numerical experiments, the distributions of density, pressure, temperature and velocity modulus are calculated for several angles of attack. The obtained results are consistent with the calculations in the ANSYS CFD package and confirm the effectiveness of the parallel computing technology used.

Суперкомпьютерное моделирование сверхзвукового течения вокруг тел вращения различной формы

In the Ross Sea region (Antarctica), evidence of warming, ice melt, and high levels of thermogenic gas hydrates indicate that deep-seated hydrocarbons contribute significantly to carbon cycles. The study investigates structural changes in the gas hydrate stability zone as methane moves from the hydrate-free zone to the seabed. A numerical fluid dynamics model is used to study the potential contribution of deep-seated carbon to the Ross Sea ice shelf, taking into account local thermodynamic equilibrium. The results of the calculation support the phenomenon of free gas from deep sediments that filtrates upward through the zone with methane hydrate stability conditions, partially converting into hydrate, while the remaining gas is capable of migrating higher into the water column. The process is accompanied by the formation of a three-phase (gas, hydrate, H ₂ O) hydrate equilibrium zone, replacing the initially two-phase (hydrate, H ₂O) gas hydrate stability zone. The modeling results explain the discrepancy between the radiocarbon dating of the core and the study of the history of the ice sheet in the region.

The work presents new methods for selecting adaptive artificial viscosity (AAV) in iterative algorithms of completely conservative difference schemes (CCDS) used to solve gas dynamics equations in Euler variables. These methods allow to effectively suppress oscillations, including in velocity profiles, as well as computational instabilities in modeling gas-dynamic processes described by hyperbolic equations. The methods can be applied both in explicit and implicit (method of separate sweeps) iterative processes in numerical modeling of gas dynamics in the presence of heat and mass transfer, as well as in solving problems of magnetohydrodynamics and computational astrophysics. In order to avoid loss of solution accuracy on spatially non-uniform grids, in this work an algorithm of grid embeddings is developed, which is applied near transition points between cells of different sizes. The developed algorithms of CCDS using the methods for AAV selection and the algorithm of grid embeddings are implemented for various iterative processes. Calculations are performed for the classical problem of decay of an arbitrary discontinuity (Sod’s problem) and the problem of propagation of two symmetric rarefaction waves in opposite directions (Einfeldt’s problem). In the case of using different methods for selecting the AAV, a comparison of the solutions of the Sod’s problem on uniform and non-uniform grids and a comparison of the solutions of the Einfeldt’s problem on a uniform grid are performed. As a result of the comparative analysis, the applicability of these methods is shown in the spatially one-dimensional case (explicit and implicit iterative processes). The obtained results are compared with the data from the literature. The results coincide with analytical solutions with high accuracy, where the relative error does not exceed 0.1%, which demonstrates the effectiveness of the developed algorithms and methods.

The work considers the problem of gas hydrate dissociation in a porous medium using the two-term Forchheimer law, corresponding to high flow rates of reservoir fluids. Such rates can arise during the decomposition of gas hydrates, since a large amount of gas is released. Intensive emissions of gases from the earth’s interior are observed on the ocean floor. They are also associated with a large number of subvertical geological structures under the ocean floor, coming to the surface in the form of local ring funnels (pockmarks). Many similar objects have also been found on land. Particular interest in this problem is caused by climate threats associated with the release of greenhouse gases. The movement of gas released from the hydrate to the breakthrough channel is similar to the gas inflow to the well (without hydrate), which is usually described by a two-term filtration law. In this work, a mathematical model of gas hydrate dissociation with a nonlinear Forchheimer-type law of motion is developed. The system is split in two blocks by physical processes, taking into account the quadratic correction to the velocity in the filtration law. The first block is responsible for the convective transfer of saturation parameters in the model, water, gas and hydrate saturations are taken into account. The second block corresponds to the equation of dissipative piezoconductivity with a different number of thermodynamic degrees of freedom, taking into account heat and mass transfer in a porous medium. The performed splitting allows using explicit-implicit difference schemes when solving problems and avoiding strong refinement of the step in time and space. For numerical modeling, the support operator method is used, which makes it possible to discretize partial differential equations on irregular grids, which allows taking into account the complex geometry and lithology of the reservoir. A difference scheme based on the support operator method is developed, which, due to the mutually consistent approximation of vector analysis operations (divergence and gradient), allows to take into account the various flux laws between adjacent grid cells, including quadratic corrections to the velocity. Based on the developed numerical algorithms and their program implementations, calculations of gas hydrate dissociation are performed both in a reservoir of simple geometric structure and in a heterogeneous reservoir of complex configuration. The results obtained correspond to the physics of the processes under consideration.