Effect of decomposition of a gas hydrate on the gas recovery from a reservoir containing hydrate and gas in the free state

The problem of gas recovery in the process of methane hydrate dissociation in a reservoir saturated with gas-hydrate mixture is considered. The mathematical model of hydrate decomposition into gas and water is generalized to include the negative temperature interval and takes ice formation into account. The solution of the problem is represented in the self-similar approximation. It is shown that there exists a transition hydrate decomposition regime in which water and ice are formed simultaneously. A comparative analysis of the recovery is carried out on the basis of relations derived for the masses of recovered gas in different hydrate dissociation regimes. It is shown that an anomalous increase in the recovered gas volumes is observed in the transition hydrate dissociation regime.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, 2005, pp. 132–142. Original Russian Text Copyright © 2005 by Tsypkin.     

Numerical investigation of the decomposition of gas hydrates coexisting with gas in natural reservoirs

The problem of methane hydrate decomposition in a reservoir saturated with a gas and hydrate mixture is investigated numerically. The results of the numerical simulation and an analytic solution obtained in the linear approximation are compared. It is shown that for high-permeability rocks the convective heat transfer in the near-well space of the reservoir predominates over the conductive transfer. This makes the use of intra-well heaters ineffective. It is found that an increase in the reservoir and well pressures and a decrease in the permeability suppress the formation of an extended hydrate dissociation region. Critical diagrams of existence of the frontal decomposition regime are constructed.     

Front Regime of Heat and Mass Transfer in a Gas Hydrate Reservoir under the Negative Temperature Conditions

The analytical self-similar solution to the nonlinear problem of the front regime of heatand- mass transfer in a gas hydrate reservoir under the negative temperature conditions is obtained. In the initial state the reservoir is assumed to be saturated with a heterogeneous gas hydrate–ice–gas mixture. In particular cases there may be no ice or/and gas. The ice and gas are formed behind the gas hydrate dissociation front. The calculations are presented for a stable hydrate–gas system. The critical curves are constructed in the well-pressure–reservoir-permeability plane. These curves separate the domains of the front regime and the regime of volume gas hydrate dissociation ahead of the front. The velocity of the gas hydrate dissociation front is investigated as a function of various problem parameters. The characteristic temperature and pressure distributions corresponding to various regimes on the diagram are investigated.     

Injection of carbon dioxide into a reservoir saturated with methane and water

This paper presents a mathematical model for the injection of carbon dioxide into a natural gas reservoir saturated with methane and water accompanied by the formation of carbon dioxide hydrate in an extended region. The dependence of the coordinates of the boundaries of the region of phase transitions on the pressure of the injected gas and the initial parameters of the reservoir are investigated. It is established that the velocity of the near boundary of the region of hydrate formation decreases with increasing water saturation and initial temperature of the reservoir and the velocity of the far boundary of the region of phase transitions increases with increasing pressure of the injected gas and reservoir permeability. It is shown that at high initial temperatures of the reservoir, a regime is possible in which replacement of methane by carbon dioxide without hydrate formation occurs at the far interface, and at the near interface, water is completely incorporated into gas hydrate.     

Injection of A Hydrate-Forming Gas into A Snow Layer Saturated with the Same Gas

The problem of injection of a hydrate-forming gas (methane) into a snow layer whose pores are initially saturated with the same gas is solved. Self-similar solutions describing the temperature and pressure fields and the snow, hydrate, and gas distributions in the layer are constructed. It is shown that, depending on the initial thermobaric state of the snow–methane system and the rate of gas injection, three characteristic zones can be distinguished in the filtration region: a near zone, in which snow is completely converted into hydrate and, consequently, the hydrate layer is saturated with gas; an intermediate zone, in which gas, snow, and hydrate are in phase equilibrium; far zone filled with gas and snow. It is shown that the length of the heated zone decreases with increasing initial snow content in the layer and with decreasing injected gas pressure. It is also shown that the length of the region of hydrate formation increases with increasing permeability. It is noted that the heating of the intermediate zone occurs more rapidly.     

Modeling of Gas Hydrate Formation Upon Injection of Carbon Dioxide Gas into A Natural Reservoir

This paper presents the results of numerical modeling of gas hydrate formation upon injection of carbon dioxide into a finite-length reservoir saturated with methane and water. It is shown that at different stages, hydrate formation can occur on both the frontal surface and in a reservoir region of finite length. The effects of pressure at the reservoir boundaries and the effects of the permeability and initial water saturation of the reservoir on the hydrate formation process were studied. The dependences of the time of the complete conversion of water into gas hydrate in the entire reservoir on the injection pressure and reservoir permeability were obtained.     

Mathematical model of the dissociation of gas hydrates coexisting with ice in natural reservoirs

The dissociation of gas hydrate coexisting with ice in a low-temperature natural reservoir is investigated. A mathematical model of the process consisting of a generalization of the Stefan problem and containing two unknown moving phase transition boundaries — the hydrate dissociation and ice melting fronts — is constructed. It is shown that in high-permeability reservoirs the velocity of the dissociation surface is higher than that of the ice melting surface. As the permeability decreases, the fronts change places. The problem is solved in the self-similar approximation.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 84–92, March–April, 1993.     

A New Non-Darcy Flow Model for Low-Velocity Multiphase Flow in Tight Reservoirs

The pore and pore-throat sizes of shale and tight rock formations are on the order of tens of nanometers. The fluid flow in such small pores is significantly affected by walls of pores and pore-throats. This boundary layer effect on fluid flow in tight rocks has been investigated through laboratory work on capillary tubes. It is observed that low permeability is associated with large boundary layer effect on fluid flow. The experimental results from a single capillary tube are extended to a bundle of tubes and finally to porous media of tight formations. A physics-based, non-Darcy low-velocity flow equation is derived to account for the boundary layer effect of tight reservoirs by adding a non-Darcy coefficient term. This non-Darcy equation describes the fluid flow more accurately for tight oil reservoir with low production rate and low pressure gradient. Both analytical and numerical solutions are obtained for the new non-Darcy flow model. First, a Buckley–Leverett-type analytical solution is derived with this non-Darcy flow equation. Then, a numerical model has been developed for implementing this non-Darcy flow model for accurate simulation of multidimensional porous and fractured tight oil reservoirs. Finally, the numerical studies on an actual field example in China demonstrate the non-negligible effect of boundary layer on fluid flow in tight formations.     

天然气水合物降压开采沉积物压缩效应数值模拟研究

深海天然气水合物降压开采过程中,沉积物的压缩会改变储层的物理力学特性,进而对天然气的开采效果产生显著影响.为揭示沉积物压缩效应下井周围储层物理力学特性演化规律,本文建立了考虑沉积物压缩效应的理论模型,通过COMSOL模拟研究了不同初始固有渗透率、初始水合物饱和度和井底压力条件下的降压开采中生产井周围储层的物理力学特性演化规律以及开采效果.结果表明:受沉积物压缩的影响,水合物分解区的渗透率随着与井筒距离的增加先增加后减少;产气与产水速率由零立即上升至峰值,然后迅速下降,并且考虑沉积物压缩时的产气与产水速率比不考虑时低;在水合物完全分解区,渗透率的大小与有效应力成负相关关系,未分解区渗透率的大小与水合物饱和度成负相关关系;井底压力越小,有效应力越大,生产井周围储层的渗透率下降越明显;初始水合物饱和度对产气与产水的影响存在拐点,饱和度拐点位于0.25与0.35之间,高水合物饱和度并不代表储层开采效果好,产气速率的高低还与储层的渗透率有关,高水合物饱和度储层的渗透率较低,产气速率较低;储层初始固有渗透率较高时显著促进了开采效果,但储层变形量较大增加了储层的不稳定性.     

Stability of a water-vapor phase transition interface in geothermal systems

The problem of normal stability of a phase transition interface for vertical flows in a geothermal reservoir with the water layer lying above the vapor layer is solved. The problem is formulated with account for convective energy transfer, which ensures applicability for arbitrary permeability values. Typical examples of variation of the phase transition interface stability parameters in response to changes in permeability are considered for various geothermal reservoirs.     

The Flow Problem of Fluids Flow in a Fractal Reservoir with Double Porosity

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Natural Convection Induced by a Heated Vertical Plate Embedded in a Porous Medium with Transpiration: Local Thermal Non-equilibrium Similarity Solutions

This paper is concerned with the thermal non-equilibrium free convection boundary layer, which is induced by a vertical heated plate embedded in a saturated porous medium. The effect of suction or injection on the free convection boundary layer is also studied. The plate is assumed to have a linear temperature distribution, which yields a boundary layer of constant thickness. On assuming Darcy flow, similarity solutions are obtained for governing the steady laminar boundary layer equations. The reduced Nusselt numbers for both the solid and fluid phases are calculated for a wide range of parameters, and compared with asymptotic analyses.     

考虑二次梯度项及动边界的双重介质低渗透油藏流动分析

在传统试井模型的非线性偏微分方程中根据弱可压缩流体的假设,忽略了二次梯度项,对于低渗透油藏这种方法是有疑问的.低渗透问题一个显著的特点就是流体的流动边界随着时间不断向外扩展.为了更好地研究双重介质低渗透油藏中流体的流动问题,考虑了二次梯度项及活动边界的影响,同时考虑了低渗透油藏的非达西渗流特征,建立了双重介质低渗透油藏流动模型.采用Douglas-Jones预估-校正差分方法获得了无限大地层定产量生产时模型的数值解,分别讨论了不同参数变化时压力的变化规律及活动边界随时间的传播规律,还分析了考虑和忽略二次梯度项影响时模型数值解之间的差异随时间的变化规律,做出了典型压力曲线图版,这些结果可用于实际试井分析.     

Thermodynamic Conditions of Formation of CO<Subscript>2</Subscript> Hydrate in Carbon Dioxide Injection into a Methane Hydrate Reservoir

The mechanism of replacement of methane by carbon dioxide in the hydrate in the process of CO₂ injection into a reservoir with formation of fronts of methane hydrate dissociation and carbon dioxide hydrate generation is investigated. It is found that such a replacement regime can be implemented in both low- and high-permeability reservoirs. It is shown that in the highintensity injection regime the heat flux from the well does not affect propagation of the fronts of methane hydrate dissociation and carbon dioxide hydrate generation. In this case the replacement regime is maintained by only the heat released at formation of carbon dioxide hydrate. An increase in the injection pressure may lead to suppression of methane hydrate dissociation and termination of the replacement reaction. The critical diagrams of existence of the regime of conversion of methane hydrate to carbon dioxide hydrate are constructed.     

Decomposition of gas hydrates in low-temperature reservoirs

The process of dissociation of gas hydrates coexisting with gas and ice in low-temperature reservoirs is considered. A qualitative analysis of the phase transitions which enables possible configurations of the solutions to be predicted is carried out on the basis of the phase diagram for methane hydrate. Mathematical models of hydrate decomposition in reservoirs which take into account the formation of an extended dissociation zone and the presence of two phase transition fronts are proposed. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 101–111, January–February, 1998. The work was carried out with financial support from the Russian Foundation for Fundamental Research (project No. 96-01-00521).     

Numerical modeling of formation of a gas hydrate in a finite-length porous bed purged by a gas

The process of formation of a gas hydrate in a finite-length porous medium partially saturated with water, which is purged by a cold gas, is studied. The influence of the initial parameters of the porous medium and purging conditions on the evolution of hydrate saturation and temperature is examined.     

The Numerical Decomposition of Turbulent Fluctuations in a Compressible Boundary Layer

In many flows the turbulence is weakly compressible even at large Mach number. For example, in a compressible boundary layer Ma<5, the differences relative to an incompressible boundary layer understood as being caused by density variations that accompany variations temperature across the layer. Turbulent fluctuations in a boundary layer are therefore expected to be dominated by the effects nonconstant temperature, and low Mach number theories in which fluctuations are not dominant should be applicable to the fluctuating field. However, the analysis of compressible boundary layer DNS data reveals presence of significant acoustic fluctuations. To distinguish acoustic and thermal effects, a numerical decomposition procedure compressible boundary layer fluctuations is applied to determine the and nonacoustic fluctuations. Except for very near the wall, where decomposition procedure is not valid, it is found that the fluctuations are only weakly coupled to the acoustic fluctuations at numbers as high as 6. Received 13 March 2000 and accepted 21 May 2001     

Mixed Convection in a Darcy–Brinkman Porous Medium with a Constant Convective Thermal Boundary Condition

The characteristics of the boundary layer flow past a plane surface adjacent to a saturated Darcy–Brinkman porous medium are investigated in this paper. The flow is driven by an external free stream moving with constant velocity. The surface is heated with a convective boundary condition with constant heat transfer coefficient. The problem is non-similar and is investigated numerically by a finite difference method. The problem is governed by four non-dimensional parameters, that is, the convective Darcy number, the convective Grashof number, the Prandtl number, and the axial distance along the plate. The influence of these parameters on the results is investigated, and the results are presented in tables and figures. The Darcy term and the Grashof term in the momentum equation contradict each other and this contradiction makes the problem complicated. However, the wall shear stress and the wall temperature increase continuously along the plate and the wall temperature always tends to 1.     

Generation of the mean flow in the fluid layer with a nonuniformly heated wavy boundary

The problem of convection in the horizontal fluid layer with a wavy lower boundary is considered. It is shown that for the periodic temperature distribution with a certain phase shift given on the wavy boundary, in the fluid layer a unidirectional horizontal flow arises. The flow velocity linearly decreases with increase in attitude and depends on the relief distribution wavelength. There is an optimum wavelength (of the order of the layer thickness) at which the velocity reaches its maximum value.     

Influence of spatial modulation of the temperature field on the stability of two-dimensional steady flow in a horizontal layer of fluid

A study is made of the stability of the steady periodic regime that arises in a horizontal layer of fluid in the presence of spatial modulation of of the temperature on the solid bottom boundary. The upper free boundary of the layer is in contact with the atmosphere. The fundamental resonance values of the wave number of the modulation are found; there are five of them. If the temperature of the lower boundary of the layer is constant, and the temperature gradient is not too large, the fluid is in equilibrium. When the temperature gradient passes through the critical value, the equilibrium ceases to be stable, and steady convection develops in the fluid [1]. In the presence of spatial modulation of the temperature on the lower boundary of the layer the fluid cannot be in equilibrium, and a spatially periodic steady regime is established in it. The aim of the present paper is to find the critical values of the temperature gradient at which this fundamental steady regime becomes unstable and a secondary steady regime develops in the fluid. An analogous problem for the case when both boundaries of the layer are free surfaces and without allowance for the influence of the atmosphere has been solved by Vozovoi and Nepomnyashchii [2].