Mathematical modeling of the processes in the geothermal circulation system with hot water injection into an oil-saturated reservoir

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NTUU «KPI. Igor Sikorsky»

IPME named after G. Ye. Pukhova NASU

Mathematical modeling of the processes in the geothermal circulation system with hot water injection into an oil-saturated reservoir

Furtat Iryna Eduardivna,

candidate of technical sciences, associate professor, associate professor of the department of heat power engineering, faculty of heat power engineering,

Furtat Yuriy Olehovych,

candidate of technical sciences, senior research fellow, department of modeling of energy processes and systems

Kyiv

Abstract

Mathematical modeling is an effective tool for solving very complex problems of estimating heat reserves, choosing rational exploration schemes, designing and optimizing systems for exploiting geothermal deposits. A characteristic feature of geothermal deposits is a significant variety of natural conditions for their formation and functioning.

Water reservoir systems represent a complex set of groundwater pressure horizons separated by low-permeability layers with certain conditions for creating pressure, movement and discharge. Hydraulically interconnected aquifers form aquifer complexes. The flow of underground waters is involved in a complex threedimensional movement. The movement takes place taking into account the configuration of the areas of supply and discharge, the distribution of the filtration parameters of rocks in the basin.

In the general case, the movement of groundwater is a spatial process and is described by a three-dimensional non-stationary filtration equation.

Hot groundwater can be used for displacement of oil as one of the promising methods for increasing oil recovery. Oil production from oil-water zones is one OF THE problems in the theory of oil field development due to the presence of two zones with sharply different hydrodynamic resistances. The complex effect of heat on all parameters of the reservoir system, especially in the production of high-viscosity oils, allows you to significantly increase the oil recovery factor. When hot water is injected into oil-containing formations, non-isothermal oil displacement occurs, the patterns of which are determined mainly by the effect of temperature on the viscosity of oil and water, as well as changes in molecular surface forces and thermal expansion of the reservoir system.

Keywords: mathematical model, heat transfer, circulation, reservoir.

Анотація

Фуртат Ірина Едуардівна кандидат технічних наук, доцент, доцент кафедри теплоенергетики теплоенергетичного факультету, НТУУ «КПІ ім. Ігоря Сікорського», проспект Перемоги, 37, м. Київ,

Фуртат Юрій Олегович кандидат технічних наук, старший науковий співробітник відділу моделювання енергетичних процесів і систем ІПМЕ ім. Г.Є. Пухова НАНУ, вул. Генерала Наумова, 15, м. Київ,

Математичне моделювання процесів в системі геотермальної циркуляції із закаченням гарячої води в нафтонасичений пласт

Математичне моделювання є ефективним інструментом для вирішення дуже складних завдань оцінки запасів тепла, вибору раціональних схем розвідки, проектування та оптимізації систем розробки геотермальних родовищ. Характерною особливістю геотермальних родовищ є значна різноманітність природних умов їх формування та функціонування.

Водосховища являють собою складну сукупність напірних горизонтів підземних вод, розділених малопроникними шарами з певними умовами для створення тиску, руху та скидання. Гідравлічно пов'язані між собою водоносні горизонти утворюють водоносні комплекси. Потік підземних вод бере участь у складному тривимірному русі. Переміщення відбувається з урахуванням конфігурації ділянок подачі і скидання, розподілу параметрів фільтрації гірських порід у басейні.

У загальному випадку рух підземних вод є просторовим процесом і описується тривимірним нестаціонарним рівнянням фільтрації.

Гарячі підземні води можна використовувати для витіснення нафти як один із перспективних методів підвищення нафтовіддачі. Видобуток нафти з нафто-водних зон є однією З проблем теорії розробки нафтових родовищ через наявність двох зон з різко різними гідродинамічними опорами. Комплексний вплив тепла на всі параметри пластової системи, особливо при видобутку високов'язких нафт, дозволяє значно підвищити коефіцієнт видобутку нафти.

При закачуванні гарячої води в нафтовмісні пласти відбувається неізотермічне витіснення нафти, закономірності якого визначаються в основному впливом температури на в'язкість нафти і води, а також зміною молекулярних поверхневих сил і теплового розширення пластова система.

Ключові слова: математична модель, теплообмін, циркуляція, пласт.

Main part

Problem formulation. On the boundaries of the region under study, it is necessary to set conditions that take into account the influence of the territory adjacent to the region. The area under consideration can be limited by a reservoir with a constant set or with a pressure that depends on time (boundary conditions of the first kind), tectonic faults or clayey strata, impermeable to fluids, semi-permeable layers, the filtration rate through which depends on time (boundary conditions). conditions of the second kind), a zone located in front of an area with a constant head, for example, in front of a supply or zhrem area, in this case, the fluid flow through the boundary depends on the pressure at this boundary (boundary condition of the third kind).

It is also necessary to know the distribution of pressures at the initial moment of time (impudent conditions).

In volcanic regions, water-bearing horizons are characterized by numerous local appearances and heterogeneity. Here, in small areas, there are hydrodynamic unconnected aquifers, each of which has its own area of supply and discharge.

Infiltration feeding is also characteristic of hydrothermal systems. areas of volcanism. At the same time, in these cases, a deep supply of high-temperature coolants through cracks, fault zones or outgoing movement with increased rock permeability can also have a significant effect.

The properties of the initial information are the decisive condition for the possibility of constructing mathematical models; they determine the type of goals, as well as the class of problems solved with the help of such models. Due to incomplete certainty and insufficiency of initial information, significant difficulties often arise in the construction of mathematical models.

In the upper layers of the earth's crust, heat is transferred by conduction and convection. If heat transfer by thermal conductivity always takes place in the presence of a temperature horizon, then convective heat transfer can occur only when the coolant moves.

An unambiguous solution to the problem of heat transfer is possible when specific boundary conditions are specified.

In the case of an unsteady regime, the boundary conditions must be specified over the entire time interval under study, and at the initial moment, the temperature distribution is specified over the entire region.

The filtration area under consideration can be limited by a known temperature zone (boundary conditions of the first kind), by a known heat flux (boundary conditions of the second kind) by a zone where the heat flow through the boundary is proportional to the temperature difference at the boundary and in the environment (boundary conditions of the third kind).

Convective transport can be critical, especially in the upper layers of the earth'sfood.

Article purpose - analysis of the processes in the geothermal circulation system involving oil, groundwater and geological strata to build a mathematical model of such processes suitable for implementation in computer systems of mathematical modeling and computation.

Main material. An analysis of the structural characteristics of underground reservoirs of oil, gas and water shows that the underground permeable layer (reservoir) is a porous medium consisting of particles or blocks of rock that, under the action of rock pressure, fit tightly to each other, forming a continuous structure called the reservoir skeleton. [1]

The transfer of heat in the reservoir occurs from particle to particle through the liquid that fills the pores between the rock particles and through the contacts between them, which determines the effective nature of the thermal conductivity of the reservoir.

The following assumptions are usually accepted[2]:

1. The permeable layer and the surrounding rock mass are homogeneous and isotropic.

2. The intensity of heat inflows from the underlying and covering rocks of the mountain range surrounding the formation is the same.

3. The sizes of rock particles and their geometric shape are not changed along the coordinate axis.

4. The fluid evenly flows around all the rock particles and completely fills the pores.

Taking into account these assumptions, the process of heat transfer and filtration will be written as follows:

where T - temperature; Л(Т) - coefficient of thermal conductivity of water - saturated rock; v_x, Vy, V_z - projections of filtration rates on the coordinate axes; t - time; w is the intensity of heat sources; c, c 0 - specific heat capacity of liquid and rock; p, po - density of liquid and rock; p is porosity; m is the thickness of the reservoir; K(T) - filtration coefficient; H - pressure; p - coefficient of elasticity water - saturated rocks. Boundary conditions are determined for a particular problem.

If the reservoir thickness m is a constant, then equations (1) and (2) are rewritten in the form

In practice, a linear dependence is often encountered K = K f + бT and л= л_?+ ЯT from temperature.

In this case, equations (3) and (4) take the form:

When extracting geothermal energy, the temperature difference is usually 5o + 2oo K. In this temperature range, the change in the thermal conductivity can be neglected, i.e. can be considered Л= Лг = const. Heat transfer from rock to reservoir is negligible. The filtration coefficient in this temperature range varies significantly. Its change obeys the linear law K = K f + aT. When extracting geothermal energy, pressure filtration takes place, in which the value л has a value of the order of 10 «⁶ m ^-2. In this regard, the system almost instantly enters the stationary mode. Then in that case the equations (3) and (4) take the form

The process of non-isothermal filtration of two incompressible, immiscible liquids is described by a system of three equations in partial derivatives

Here

Equations (9) - (11) use the following notation: vi is the filtration velocity vector of the i-th phase; m (x, y) - variable layer thickness; K is the absolute permeability tensor; T is temperature; Pi - pressure in the i-th phase; p is porosity; у - water saturation; µ i - viscosity of the i-th phase; л - coefficient of thermal conductivity; ci is the specific heat capacity of the i-th phase; x, y are spatial variables; ф - time. Index «1» refers to the displacing phase, index «2» to the displaced one, index «3» to the surrounding rocks.

To solve system (9) - (11) it is necessary to know the phase velocities v1 and v2, which are expressed in terms of the total filtration rate

mathematical modeling geothermal field

Here Pc is the capillary pressure,

For the case of planned filtration, the system of equations (1) - (3) takes the form

The phase velocities of the filtration in this case are determined by the battles

In these equations, the unknown functions are: pressure in the water phase, water saturation and temperature.

Conclusions. The solution of such a system of equations for an inhomogeneous region arbitrary form is associated with great difficulties. An effective way to overcome the arising difficulties is the combination of numerical methods and analog modeling methods.

References

1. Furtat, I.E., & Furtat, Yu.O. (2022), Eurasian scientific discussions. Proceedings of the 3rd International scientific and practical conference Barca Academy Publishing. Barcelona, Spain. 2022. Pp. 93-94. [in Ukrainian]

2. Prodaivoda, G.T, & Vyzhva, S.A. (1999) Matematychne modeliuvannia geofizychnyh parametriv [Geophysical parameters modeling]. - Kyiv: VC «Kyivskii univesytet» [in Ukrainian].

Література

1. Фуртат І.Е. Підземні циркуляційні системи в геотермальній енергетиці / І.Е. Фуртат, Ю.О. Фуртат // Матеріали конференції «Eurasian Scientific Discussion» (10-12 квітня 2022 року). - Барселона, Іспанія: Barca Academy Publishing, 2022 - С. 93-94.

2. Продайвода Г.Т. Математичне моделювання геофізичних параметрів / Г.Т. Продайвода, С.А. Вижва. - Київ: ВЦ «Київський університет», 1999. - 112 с.

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