Filtration combustion of a gas in a semiinfinite porous medium

An asymptotic analysis of the combustion of a gas moving in a semiinfinite porous medium is performed for large values of the Zel’dovich parameter. The case of a highly porous medium with high gas permeability is considered. The basic terms of asymptotic expansions of the main parameters of the process for combustion and separation regimes are obtained by the method of joined asymptotic expansions. The effect of the rate of motion of the gas and heat transfer from the surface of the skeleton into the ambient medium on the combustion parameters is analyzed. The critical conditions of failure of stationary combustion at the external surface of the layer and the conditions of transition of the process to the separation and induction regimes are determined. Translated fromFizika Goreniya i Vzryva, Vol. 36, No. 4, pp. 3–14. July–August, 2000. This work was supported by the Russian Foundation for Fundamental Research (Grant No. 98-01-03009).     

Numerical modeling of gas hydrate decomposition in gas injection into a porous medium

The decomposition of gas hydrates during the injection of gas into a porous medium is studied in planar one-dimensional and axisymmetric self-similar formulations. The effect of the parameters of the porous medium and the pressure and temperature of an injected gas on the length of the region of gas hydrate decomposition in a porous stratum is analyzed.     

Stabilized gas combustion wave in an inert porous medium

A stabilized gas combustion wave in an inert porous medium with intense internal interphase heat exchange (at low velocities) is considered to elucidate the mechanism underlying the increase in the burning velocity of the homogeneous gas mixture due to the porous medium. It is shown that the major factor of the increase in the burning velocity is conductive heat recuperation from the postflame zone to the region of the fresh mixture through the solid skeleton of the porous medium. Analytical dependences of the degree of increase in the burning velocity of the mixture in the stabilized wave on the determining parameters are obtained. The possibilities and restrictions of the use of the results to analyze the operation of porous burners are discussed. __________ Translated from Fizika Goreniya i Vzryva, Vol. 44, No. 5, pp. 8–15, September–October, 2008.     

多孔介质中水合物生成与分解的电阻率性质

A new one-dimensional system for resistivity measurement for natural gas hydrate (NGH) exploitation is designed, which is used to study the formation and decomposition processes of NGH.The experimental results verify the feasibility of the measurement method, especially in monitoring the nucleation and growth of the NGH.Isovolumetric formation experiment of NGH is performed at 2 ℃ and 7.8 MPa.Before the NGH formation, the ini-tial resistivity is measured to be 4-7 Ω·m, which declines to the minimum value of 2-3 Ω·m when NGH begins to nucleate after the pressure is reduced to 3.3 MPa.As the NGH grows, the resistivity increases to a great extent, and finally it keeps at 11-13 Ω·m, indicating the completion of the formation process.The NGH decomposition ex-periment is then performed.When the outlet pressure decreases, NGH begins to decompose, accordingly, the resis-tivity declines gradually, and is at 5-9 Ω·m when the decomposition process ends, which is slightly higher than the resistivity value before the formation of NGH.The occurrence and distribution uniformity of NGH are determined by the distribution and magnitude of the resistivity measured on an one-dimensional sand-packed model.This study tackles the accurate estimation for the distribution of NGH in porous medium, and provides an experimental basis for further study on NGH exploitation in the future.     

Some features of the synthesis of gas hydrates by gas injection into a moist porous medium

The formation of gas hydrates during gas injection into a porous medium partially saturated with water is studied in a planar one-dimensional selfsimil ar formulation. The influence of the initial parameters of the porous medium (porosity, permeability, and moisture content), the temperature of the injected gas, and the intensity of the injection on the pattern of the hydrodynamic and temperature fields in the porous medium is analyzed. It is shown that depending on the intensity of the injection of a cold gas into the moist porous medium, the process can occur in several modes with qualitatively different structures of the zones of hydrate formation. Because of the formation of gas hydrates in volumetric regions, the heating of the porous medium by tens of degrees can occur during the injection of the cold gas; thus, the process of hydrate formation can serve as a certain means for increasing the temperature.     

Stagnation-point flows in a porous medium

In this paper, we present non-linear exact and asymptotic solutions to a Navier-Stokes equation of Brinkman type proposed by Joseph et al. (Water Resour. Res. 18(4) (1982) 1049) for the flow in the stagnation-point laminar boundary layer on a cylinder or sphere if fibers of increasing concentration are uniformly added to a porous medium surrounding these blunt bodies. Although one cannot perform a rigorous averaging of the (u·∇)u term, one is able to gain useful insight into the transition in behavior that occurs between the classical solutions of Hiemenz (Dinglers Polytech. J. 326 (1911) 321) and Homann (Z. Angew. Math. Mech. 16 (1936) ; Forsch. Geb. Ingenieurwes. 7 (1936) 1) for the two-dimensional and axisymmetric stagnation-point boundary layers and the local expansion of the Brinkman solution for the flow past a cylinder or sphere in the stagnation regions as the Darcy permeability is decreased. In this analysis, a new fundamental dimensionless parameter emerges, β=υ/KA, where A is the characteristic velocity gradient 4U /D imposed by the external flow, υ is the kinematic viscosity and K, the Darcy permeability. β denotes the ratio of the square of two lengths, the classical boundary layer thickness for a high Reynolds number flow and the fiber-interaction layer thickness K^1/2. The exact solutions of the non-linear Brinkman equation for the stagnation-point flow presented herein show the structure of a new type of boundary layer that evolves as β varies from zero, the classical limit of the Hiemenz and Homann solutions, to β?1, the classical Brinkman limit where inertial effects are negligible. Using asymptotic analysis we shall show that when β?1 the classical boundary layer thickness decreases as β^-1/2. Because of the introduction of the Darcy term, the pressure field differs greatly from the classical stagnation-point flow. The pressure does not increase monotonically along the stagnation streamline, and for β?1 there is a pressure minimum that approaches the origin as β^-1/2.     

Explosion in a highly porous medium

Moscow. Translated from Fizika Goreniya i Vzryva, Vol. 25, No. 3, pp. 89–96, May–June, 1989.     

Specific features of the formation of gas hydrates during the injection of a cold gas into a porous medium saturated with a gas and water

A mathematical model of the process of the formation of gas hydrates in a porous medium during the injection of a cold gas is presented. The cases where hydrate formation is limited by the kinetics of the process and heat and mass transfer in a porous medium are considered. The influence of the initial parameters of the porous medium and the intensity of the gas injection on the dynamics of the processes of hydrate formation is studied. The critical conditions that separate the different modes of hydrate formation are found.     

Diffusion-thermal stability of gas filtration combustion waves in an inert porous medium

A mathematical model for the filtration gas combustion taking into account thermal conductivity, diffusion, and intense interfacial heat transfer is presented. The temperature dependence of the chemical reaction rate is approximated by a δ-function and the thermal-expansion coefficient of gases behind the combustion front is taken into account. Unsteady combustion regimes are analyzed using the method of small perturbations. The boundaries of the longitudinal and spatial stability for steady regimes of the filtration combustion wave are obtained. The dependence of the Lewis number on the thermal-expansion coefficient of the gas mixture along the boundary of stability is derived, along with other relations.     

Unsteady-state effects upon gas combustion in closed vessels with an inert porous medium

Two groups of unsteady-state effects have been studied. The first group includes the effects that are connected with initial and boundary conditions, i.e., combustion-wave formation and extnction near the walls of a vessel. The size of a combustion zone in a steady-state wave is the spatial scale of these processes. These effects are based on temperature nonequilibrium. between the gas and the porous medium. The second group includes the effects that are caused by both the dynamic change in the parameters of the reacting-gas state upon combustion and the corresponding loss of steady-flame stability which is manifested either in transitions of one combustion regime to another or in flame extinction. Institute of Chemical Kinetics and Combustion, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Fizika Goreniya i Vzryva, Vol. 33, No. 1, pp. 24–32, January–February, 1997.     

Motion of a shaped-charge jet in a porous medium

The problem of the motion of a shaped-charge jet in a porous medium is equivalent to the problem of a blunt cylinder in a hypersonic flow whose velocity at infinity is equal to the jet velocity in the porous medium. The flow pattern of the medium is the same as in the case of propagation of a blast wave generated by a point explosion of a cylindrical charge. The approximate theory of a strong explosion is used to obtain the basic relations for the shock wave and the expanding cavity in the hypersonic flow of a porous medium around the blunt cylinder. A comparison with experiments on the motion of a copper shaped-charge jet in porous aluminum is performed. Translated fromFizika Goreniya i Vzryva, Vol. 35, No. 6, pp. 119–124, November–December 1999.     

Stability of a plane reaction front in a porous medium

Porous media can be dissolved by pumping acids through them. The permeability of the porous material will be raised, and this is used by the petroleum industry to increase the productivity of oil wells. The acid flows preferentially into zones of high permeability which are therefore most rapidly dissolved, leading to a further preferential enhancement of the permeability. Thus the reaction front is unstable. This paper studies a simple model which demonstrates the effect of the Damköhler number and of the Acid Capacity number on the instability of a plane reaction front. Scaling lengths by the depth of the reaction zone, it is found that perturbations with wave number k grow exponentially at a rate σ ∝ log (1 + k) rather than the σ ∝ k which occurs in the Saffman—Taylor instability. Although perturbations with the smallest wavelengths (of the order of the pore size) will grow most rapidly, fingering will be marked for all fingers with wavelengths smaller than, or similar to, the width of the reaction zone. Laboratory experiments reveal negligible fingering in sandstones, and the instability is thought to be mainly associated with the rapid reactions which occur in carbonate rocks. The results obtained here predict that the instabilities in slower reacting sandstones will only become apparent in experiments on a much larger scale.     

The stability of a steam-water front in a porous medium

We present a first order stability analysis of a steam-water front moving through a porous medium. The interplay between gravity, mobility and phase change are investigated. Several new phasical effects are observed in this dynamic study (e.g. oscillatory solutions, multiple solutions, etc.) and a number of specific limiting solutions are also considered.