Mathematical modeling of gas desorption from a gas hydrate

In gas-gashydrate reservoirs the gas is in the free and bound states. The amount of gas bound in the hydrate depends on the thermodynamic conditions. Therefore, when these conditions are varied it is possible for gas to be released from the hydrate in the desorption regime up to total dissociation of the hydrate into gas and water. Below, the problem of extraction of free and bound gas in the desorption regime is considered.Ufa. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 118–125, September–October, 1996.     

Effect of liquid phase mobility on gas hydrate dissociation in reservoirs

Boundary conditions on the dissociation surface that take the motion of the liquid phase into account are derived. An analytic solution of the problem is obtained for small deviations from the initial state. The integral characteristic of the phase transitions in the extended zone is introduced and represented analytically. It is shown that for high initial values of the hydrate and water saturations the mobility of the liquid phase must be taken into account. For media with high permeability the amount of gas hydrate dissociated in the volume phase transition zone exceeds by several orders the amount of hydrate decomposed in the total dissociation zone.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 105–114, July–August, 1991.     

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.     

Analytical solution of the nonlinear problem of gas hydrate dissociation in a formation

The problem of methane hydrate dissociation in a formation at high pressure gradients, when the flow in the near-well region is described by a nonlinear equation, is considered. In the quasistationary approximation, an analytical solution of the problem representable in the form of an implicit function is obtained. It is shown that during dissociation at high pressure gradients ice may be formed at fairly high initial temperatures. A critical diagram of hydrate dissociation regimes is plotted.     

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.     

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).     

Mathematical model of axisymmetric quasi-steady-state heat and mass transfer in a gas hydrate reservoir

Two problems of axisymmetric gas (gas and water) flow through a reservoir which contains a heterogeneous mixture, namely, gas hydrate, ice (water), and gas, are considered. The exact solutions to the corresponding steady-state and quasi-steady-state nonlinear problems are found. The critical diagrams are constructed for various flow regimes. The characteristic distributions of the gas hydrate, ice (water), and gas saturations are shown for various values of the parameters.     

The simulation of gas production from oceanic gas hydrate reservoir by the combination of ocean surface warm water flooding with depressurization

A new method is proposed to produce gas from oceanic gas hydrate reservoir by combining the ocean surface warm water flooding with depressurization which can efficiently utilize the synthetic effects of thermal, salt and depressurization on gas hydrate dissociation. The method has the advantage of high efficiency, low cost and enhanced safety. Based on the proposed conceptual method, the physical and mathematical models are established, in which the effects of the flow of multiphase fluid, the kinetic process of hydrate dissociation, the endothermic process of hydrate dissociation, ice-water phase equilibrium, salt inhibition, dispersion, convection and conduction on the hydrate dissociation and gas and water production are considered. The gas and water rates, formation pressure for the combination method are compared with that of the single depressurization, which is referred to the method in which only depressurization is used. The results show that the combination method can remedy the deficiency of individual producing methods. It has the advantage of longer stable period of high gas rate than the single depressurization. It can also reduce the geologic hazard caused by the formation deformation due to the maintaining of the formation pressure by injected ocean warm water.     

Formation of the impermeable layer in the process of methane hydrate dissociation in porous media

The problem of decomposition of methane hydrate coexisting with water in a highpermeability reservoir is considered. The asymptotic solution is obtained for the decomposition regime in the negative temperature domain. Energy estimates presented show that an impermeable layer saturated with a hydrate-icemixture can be formed in reservoirs with initial positive temperature. The mathematical model of the process of hydrate decomposition is formulated under the assumption on the presence of such a layer in a high-permeability reservoir. In this case the problem is reduced to a purely thermal problem with two unknown moving boundaries. The water-ice phase transition takes place on the leading boundary, while hydrate dissociates at negative temperatures on the slower boundary. The conditions of existence of the layer saturated with a hydrate-ice mixture which is implemented in reservoirs with the high hydrate content are investigated.     

Theoretical study of the limiting regimes of hydrate formation during contact of gas and water

This paper presents a mathematical model and analytical solutions of the problem of the growth of a hydrate layer during contact of gas and water for two limiting regimes of gas hydrate formation determined by mass transfer and heat transfer. Critical values are obtained for thermal parameters and parameters that determine the flow properties of the hydrate layer (diffusion coefficient and permeability), on which the hydrate formation regime depends.     

Fluid-solid coupling model for studying wellbore instability in drilling of gas hydrate bearing sediments

As the oil or gas exploration and development activities in deep and ultra- deep waters become more and more, encountering gas hydrate bearing sediments （HBS） is almost inevitable. The variation in temperature and pressure can destabilize gas hydrate in nearby formation around the borehole, which may reduce the strength of the formation and result in wellbore instability. A non-isothermal, transient, two-phase, and fluid-solid coupling mathematical model is proposed to simulate the complex stability performance of a wellbore drilled in HBS. In the model, the phase transition of hydrate dissociation, the heat exchange between drilling fluid and formation, the change of mechanical and petrophysical properties, the gas-water two-phase seepage, and its interaction with rock deformation are considered. A finite element simulator is developed, and the impact of drilling mud on wellbore instability in HBS is simulated. Results indicate that the re- duction in pressure and the increase in temperature of the drilling fluid can accelerate hydrate decomposition and lead to mechanical properties getting worse tremendously. The cohesion decreases by 25% when the hydrate totally dissociates in HBS. This easily causes the wellbore instability accordingly. In the first two hours after the formation is drilled, the regions of hydrate dissociation and wellbore instability extend quickly. Then, with the soaking time of drilling fluid increasing, the regions enlarge little. Choosing the low temperature drilling fluid and increasing the drilling mud pressure appropriately can benefit the wellbore stability of HBS. The established model turns out to be an efficient tool in numerical studies of the hydrate dissociation behavior and wellbore stability of HBS.     

Formation of gas hydrate reservoirs in submarine mud volcanos

Transfer mechanisms of the gas dissolved in water are investigated within the framework of the one-dimensional approximation for a submarine mud volcano. The conditions and intensity of transition of the dissolved gas into the hydrate form inside the volcano are determined. Practical recommendations on search for hydrate reservoirs in water areas are given.     

Formation of a gas hydrate due to injection of a cold gas into a porous reservoir partly saturated by water

Specific features of formation of gas hydrates due to injection of a gas into a porous medium initially filled by a gas and water are considered. Self-similar solutions of an axisymmetric problem, which describe the distributions of the basic parameters in the reservoir, are constructed. The existence of solutions is demonstrated, which predict gas hydrate formation both on the frontal surface and in the volume zone. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 137–150, May–June, 2008.     

Formation of hydrate in injection of liquid carbon dioxide into a reservoir saturated with methane andwater

Injection of liquid carbon dioxide into a depleted natural gas field is investigated. A mathematical model of the process which takes into account forming CO₂ hydrate and methane displacement is suggested. An asymptotic solution of the problem is found in the one-dimensional approximation. It is shown that three injection regimes can exist depending on the parameters. In the case of weak injection, liquid carbon dioxide boils up with formation of carbon-dioxide gas. The intense regime is characterized by formation of CO₂ hydrate or a mixture of CO₂ and CH₄ hydrates. Critical diagrams of the process which determine the parameter ranges of the corresponding regimes are plotted.     

Breakdown of under-water gas hydrate deposits

At the floor and upper sediment layers of the submarine volcano Håkon Mosby gas (methane) hydrate deposits have been discovered. Measurements of the water-dissolved methane concentration at different depths near the volcano have shown that its level is higher than the average level in the Ocean. In order to understand the effects observed in concentration distribution, a model is proposed for describing the propagation of methane formed as a result of decomposition of depth and floor hydrate over the hydrosphere. Within the framework of physical modeling the kinetics of methane dissolution and its distribution in the hydrosphere are traced numerically with account for transfer anisotropy in different directions and undercurrents. The dissolution rate and the mass transfer directions are determined and the concentration fields in the floor layers are calculated. It is shown that methane is rapidly dispersed in the hydrosphere and, thus, significant volumes with high methane concentration cannot be formed. Practical recommendations are given for hunting hydrate deposits in water areas. The model proposed is applicable to describing the propagation of any admixture in different anisotropic media.     

Self-similar problem of decomposition of gas hydrates in a porous medium upon depression and heating

We consider the specifics of decomposition of gas hydrates under thermal and depressive action on a porous medium completely filled with a solid hydrate in the initial condition. The existence of volumetric-expansion zones, in which the hydrate coexists in equilibrium with water and gas, is shown to be possible in high-permeable porous media. The self-similar problems of hydrate decomposition upon depression and heating are studied. Ii is shown that there are solutions according to which hydrate decomposition can occur both on the surface of phase transitions and in the volumetric region. We note that, in the first case, decomposition is possible without heat supply to a medium and even with heat removal. Institute of Mechanics of Multiphase Systems, Siberian Division, Russian Academy of Sciences, Tyumen' 625000. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 3, pp. 111–118, May–June, 1998.     

Multiphase flow model developed for simulating gas hydrate transport in horizontal pipe

The hydrate formation or dissociation in deep subsea flow lines is a challenging problem in oil and gas transport systems. The study of multiphase flows is complex while necessary due to the phase changes (i.e., liquid, solid, and gas) that occur with increasing the temperature and decreasing the pressure. A one-dimensional multiphase flow model coupled with a transient hydrate kinetic model is developed to study the characteristics of the multiphase flows for the hydrates formed by the phase changes in the pipes. The multiphase flow model is derived from a multi-fluid model, while has been widely used in modelling multiphase flows. The heat convection between the fluid and the ambient through the pipe wall is considered in the energy balance equation. The developed multiphase flow model is used to simulate the procedure of the hydrate transport. The results show that the formation of the hydrates can cause hold-up oscillations of water and gas.     

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.     

Mathematical model of hydrate formation from microbial methane in marine sediments

A mathematical model of gas hydrate formation from microbial methane in marine sediments is proposed. An analytical solution of the problem is obtained, determining dimensionless parameters are distinguished, and numerical investigation is performed. In the region of main parameters a critical diagram of hydrate existence is plotted. It is shown that at small sediment accumulation rates microbial methane disperses due to diffusion of dissolved gas which does not reach saturation. If the sediment accumulation is intense, the region of possible hydrate formation falls within the region of stable thermodynamic states only at large depths. Correspondingly, in these cases, the probability of formation of hydrate-containing sediment layers is small. The most probable hydrate formation regime is realized at moderate sediment accumulation rates corresponding to Péclet numbers of the order of unity.