Previously, the algorithm for the inverse problem for determining the dynamics of mass flow rate changes in the systems of natural gas production and transportation by measuring the outlet pressure was generalized to the case of hydrate formation in the main gas pipeline and in the well. In this research the new algorithm based on the method of half division (bisection, dichotomy), which has unconditional convergence, is presented. In the process of solving the problem of formation and deposition of gas hydrates on the pipe walls, the dynamics of gas pressure and temperature changes, as well as the flowing section along the length of the well are calculated. Comparison of the calculation results showed that at constant bottomhole pressure the realization of this algorithm, unlike the previously proposed one, leads to an increase in the duration of the process of complete plugging of the well with hydrates and, accordingly, to an increase in the total amount of extracted gas.

The influence of changes of pressure and temperature of the reservoir bed on the process of formation and deposition of natural gas hydrates on the wall of a producing well is investigated in the computational experiment. The problem is summarized to the solution of differential equations describing the non-isothermal flow of real gas in a porous medium and in a well, considering the formation and deposition of gas hydrates, heat propagation in rocks with appropriate conjugation conditions. The gas withdrawal mode with constant wellhead pressure is studied. The algorithm of numerical solution of the inverse problem of determining the dynamics of gas mass flow rate is based on the method of half division. The comparison of the calculation results for cases when the pressure at the well bottom is: 1) changing with time in the process of gas withdrawal; 2) remaining constant. It is indicated that consideration of changes in reservoir conditions leads to a significant increase in the time of complete plugging of the well by gas hydrates and to reduction of accumulated gas production.

The paper gives a brief description of geological section of the Indigirka-Zyryanka trough, promising for oil and gas, and the results of parametric drilling. Possibility study of hydrate formation in reservoir conditions of trough as one of the reasons for obtaining negative well test results was conducted. Performed calculations of the equilibrium conditions of hydrate formation have determined that the hydrate stability zone covers an insignificant interval of deposits 222 m thick below the bottom of permafrost rocks. It is concluded that the main reason for the insignificance of the hydrate formation zone is a relatively high geothermal gradient, which causes sufficiently high reservoir temperatures in the section. It is noted that favorable conditions for the formation of gas hydrates may arise in the presence of heavy differential pressure drawdown on the formation in the vicinity of borehole.

A generalized mathematical model of the non-isothermal filtration of natural gas in a porous medium and a modified quasi-stationary model of gas hydrate formation (deposition) in pipelines are used to solve the conjugate problem for the joint operation of the gas reservoir–well system and predict the changes in temperature, pressure, gas moisture content, and well flow section. It is found that the presence of a thick permafrost layer accelerates hydrate formation in the well. It is shown that when the salinity of stratum water is taken into account, the time of complete plugging of the well with hydrates increases.

Институт физико-технических проблем Севера им.В.П

В работе приведены результаты вычислительного эксперимента, направленного на получение критериев выбора геологических структур для создания подземного хранилища природного газа в гидратном состоянии в подмерзлотных водоносных горизонтах. Преимущества такого способа подземного хранения газа заключаются в большей компактности и стабильности хранилища, т.к. газ в гидратном состоянии занимает гораздо меньший объем, чем в свободном состоянии при тех же температуре и давлении. Представлена математическая модель закачки газа через одиночную скважину в горизонтальный водоносный пласт, в которой учтены все основные физические и термодинамические особенности процесса гидратообразования, в том числе сжимаемость газа, эффект Джоуля-Томсона, адиабатическое расширение, неизотермическая фильтрация воды и газа, массообмен между газом, водой и гидратом. С помощью этой модели оценивается динамика распределения гидратонасыщенности, водонасыщенности, давления и температуры в водоносном пласте при различных значениях интенсивности закачки газа и фильтрационно-емкостных свойств пласта. Кроме пористости и проницаемости выбранный пласт (истощенный газовый или водоносный) характеризуется начальными значениями давления, температуры и водонасыщенности. Варьируемыми параметрами являются пористость пласта и объемный расход нагнетаемого газа. Результаты расчетов показали, что для создания подземных хранилищ газа в гидратном состоянии следует выбирать водоносные горизонты в зависимости от их коллекторских свойств и гидродинамических характеристик. В дальнейших исследованиях необходимо оценить тепловое взаимодействие таких хранилищ с окружающими горными породами. Для этого предложенную математическую модель следует обобщить в двумерной постановке. Полученные результаты и математическая модель могут быть использованы при разработке научных основ технологии подземного хранения не только природного газа, но и попутного нефтяного газа, а также парниковых и токсичных газов в гидратном состоянии

In arctic and subarctic regions the climate change is leading to the melting of permafrost and there is a vital need to assess the timing and extent of the current process. Numerical simulation of the thermal state of permafrost soils is performed in the conditions of the city of Yakutsk. A 1D Stefan problem is solved using climatic data of the general circulation model GFDL CM2.1. The developed model of permafrost accounts for monthly average air temperature, parameters of snow cover (thickness, density, thermal conductivity), radiation balance of the earth surface, wind speed. On the output, profiles of ground temperature and depths of the permafrost top edge are obtained for moderate and aggressive climate warming scenarios up to the year 2100.

Assessment of the natural gas specific humidity is necessary for technological calculations in the production, treatment, and transportation of gas. As well as the knowledge of the dynamics of the natural gas specific humidity allows you to calculate the consumption of hydrate inhibitors before their injection into wells. In this paper, the dynamics of the gas specific humidity in the bottomhole zone and the hole of gas wells depending on the temperature and pressure dynamics have been investigated. The computational experiment was carried out in the framework of non-isothermal filtration models of real gas in a reservoir and formation / dissociation of gas hydrates in the well under conditions of heat exchange with permafrost rocks. It is shown that when sampling with a constant flow rate, the dependence of the moisture fraction in the gas on temperature is most pronounced in the zones, where the Joule-Thomson effect prevails, and in the other zones its value is determined by the pressure dynamics.

The process of formation and deposition of gas hydrates on the walls of a well during its joint operation with reservoir and heat exchange with the environment is modeled. The problem is reduced to solving differential equations describing a non- isothermal flow of an imperfect gas both in a porous medium and in a well, heat propagation in rocks with appropriate coupling conditions. It is shown that for wells with a reservoir temperature significantly exceeding the equilibrium temperature of hydrate formation, at constant values of gas pressure and temperature at the bottom of the well, the hydrate plug formation time is signif- icantly overestimated, in contrast to the case when the reservoir pressure and temperature change over time. For the wells with reservoir temperature approximately equal to the hydrate formation temperature, the time of complete plugging will be slightly longer when the model takes into account the change in temperature and gas pressure at the bottom of the well during the gas extraction process.

МОдЕЛИРОВАНИЕ дЕГРАдАЦИИ МНОГОЛЕТНЕМЕРЗЛЫХПОРОд ПРИ ПОТЕПЛЕНИИ КЛИМАТА В УСЛОВИЯХ ЦЕНТРАЛЬНОй ЯКУТИИ НА БЛИЖАйШИЕ 300 ЛЕТ Иванов В.А., Рожин И

The work focuses on the inverse problem of determining differential equation coefficients for additional information on the behavior of solution. Furthermore, the algorithm for determining parameters of systems of ordinary differential equations on the basis of stomatal pressure measurements is generalized for the model of hydrate formation when the internal well section of changes with time and also has to be determined during the solution of the general problem. The computational experiment has been conducted for wells of Otradninsky gas condensate deposits of the Republic Sakha (Yakutia), the exploitation of which indicates that the complications are most likely caused by formation of gas hydrates both in the bottom-hole and in the well and its plumes. It has been established that the most important influence on the dynamics of hydrate plugs formation in wells is the gas production mode, its equation of state, reservoir and geocryological conditions. Time dependency of mass flow has been determined, which knowledge will make it possible to control the change of flow area of the entire well and, if necessary, to prevent and remove formation of natural gas hydrates

This paper considers the possibility of the underground gas storage facilities creating in a hydrate state on the north-western slope of the Yakut arch of the Vilyui syneclise. For this, the boundaries of the hydrate stability zone were determined for 6 promising areas of the considered geological structure. Equilibrium conditions of the natural gas hydrates formation in the model porous media containing bicarbonate-sodium type water (mineralization 20 g/l), characteristic for the subpermafrost horizons of the Yakut arch, have been studied by the method of differential thermal analysis. On the basis of the obtained results, the boundaries of the natural gas hydrates stability zone were determined. It was shown that the upper boundaries of the hydrate stability zone are located in the thickness of permafrost rocks. It was found that the lower boundaries of the natural gas hydrates stability zone in moist unsalted porous medium lie in the range from 930 to 1120 m. When the samples are saturated with mineralized water, the boundaries are located 80-360 m higher. The obtained experimental results allow us to conclude that in subpermafrost aquifers of the Yakut arch has favorable conditions for the formation of natural gas hydrates. Keywords: natural gas hydrates; aquifers; underground gas storage; hydrate stability zone; geothermal gradient; equilibrium conditions of the hydrate formation; bicarbonate-sodium type water.

В настоящей работе рассматривается возможность создания подземных хранилищ газа в гидратном состоянии на 11 перспективных площадях Вилюйской синеклизы. Для этого были определены границы зоны стабильности гидратов природного газа Средневилюйского газоконденсатного месторождения и метана в пресной воде и в растворе хлорида натрия (минерализация 51,77 г/л). Путем сопоставления мощностей зоны стабильности гидратов природного газа и многолетнемерзлых толщ выбраны наиболее подходящие для создания подземных хранилищ газа площади.

The dual problem of recovery well's thermal interaction with permafrost rocks is considered, which reduces to solving differential equations describing the non-isothermal gas flow in the well and equations of heat distribution in rocks with the certain conjugation conditions. In the case of well pipelines, this task is not conjugate, because hydrate plug can form in a fairly short time. Whereas, in the quasistationary mathematical model of gas hydrate formation in wells and well pipelines, the dependence of the heat transfer coefficient on the gas to the inner wall of the pipe on the passage area that changes with time is taken into account. The dynamics of changes in the temperature and pressure of the gas, as well as the pipe cross-section at various modes of gas extraction in the absence of a hydrate inhibitor, is determined. An analysis of the results showed that the hydrate formation in wells, even at low reservoir temperatures and a thick layer of permafrost, takes a sufficiently long period of time to quickly prevent emergencies in gas production systems. Next, the problem of gas extraction through a single well located in the center of a circular reservoir, in the formulation of which energy transfer due to thermal conductivity is considered negligible compared to convective transfer, is considered. It was found that during selection, the gas temperature will be everywhere below the equilibrium temperature of hydrate formation. Thus, the bottom-hole zone of the wells should be treated with hydrate inhibitors.

The results of a numerical experiment to determine the thermal impact of a gas well cluster on permafrost rocks are given for the conditions of four deposits of Central Yakutiya, Middle-Vilyuy (Srednevilyuiskoe), Middle-Tyung (Srednetyungskoe), Sobolokh–Nidzhili (Sobolokh-Nidzhilinskoe), and Tolon–Mastakh (Tolon-Mastakhskoe). An approximate mathematical problem is solved in a conjugate formulation. In this case, the process of melting of permafrost rocks is described within the framework of a three-dimensional Stefan problem, and the motion of real gas in wells is described within the framework of tubular hydraulics. Use has been made of real data for temperature well logging, formation pressure and temperature, well flow rate, gas composition, and thermophysical properties of rocks. The melting of frozen rock depending on the depth and time has been calculated, and instants of time for linkage of thaw zones of neighboring wells have also been computed.

For the Redlich–Kwong equation of state of real gas, which is widelyused for description of behavior of hydrocarbon mixtures, the inversioncurve, which determines the change in the throttling coefficient sign,is constructed. The reduced pressure and temperature variation rangescorrespond to the characteristic values in natural gas production andtransportation systems.

The current algorithm for calculating mass flow rate in gas production and transportation systems via outlet pressure measurements is generalized to the case when the inner cross section of pipe changes with time and is also to be determined while solving the general problem. The algorithm is recommended for identification of gas hydrate formation in the above-mentioned systems.

A numerical experiment has been carried out to study the influence of the change in the main pipeline cross-section due to hydrate formation on hydraulic resistance and the temperature and pressure dynamics taking into account quasi-stationary heat transfer with permafrost ground. The case where a wet gas is supplied to the pipeline is considered, and the dynamics of hydrate formation is determined along with other parameters. The calculations are carried out until the outlet pressure becomes lower than the standard one. The results of the experiment show that a model assuming a constant hydraulic resistance coefficient leads to a significant underestimation of the allowable pipeline operation time. Consequently, in mathematical modeling of hydrate formation in natural gas pipelines taking into account the relationship between heat transfer and viscous friction is critical.