Логин:
Пароль:
Регистрация
Забыли свой пароль?

Mathematical modeling of fluid migration through impermeable layers

UDK: 622.276.43 «5»
DOI: 10.24887/0028-2448-2018-5-48-51
Key words: fluid migration process, impermeable layers, hydraulic fracturing
Authors: V.A. Baikov (Ufa State Aviation Technical University, RF, Ufa; RN-UfaNIPIneft LLC, RF, Ufa), A.V. Aksakov (RN-UfaNIPIneft LLC, RF, Ufa), О.S. Borschuk (RN-UfaNIPIneft LLC, RF, Ufa)

The problem of reservoir fluid migration through oil- and water- impermeable layers has not been completely resolved yet. A variety of different models is proposed to explain this process of oil migration from oil-source rocks. Migration through the impermeable layers occurs due to two main mechanisms: through the discontinuities of the medium (along fractures and faults) and through the continuous medium itself (multiphase filtration through the pore space). Remarkably enough there are no satisfactory mathematical models that describe these mechanisms of the migration process through the impermeable layers.

The article focuses on the problem of mathematical and numerical description of the fluid migration process through the impermeable layers along the fractures induced by hydraulic fracturing. The mechanism of hydraulic fracture vertical growth due to buoyancy forces is considered as minimum closure stress gradient in the reservoir exceeds pressure gradient of the fluid induced by gravity.

This paper presents the following results. We present a closed integral-differential equation system describing the fluid flow through the impermeable layer (fluid stop) in the presence of fractures. We show that for the typical geological parameters with fracture height over 20 meters, the fluid flow is determined by the buoyancy forces and described by a simple transport equation. We describe the mechanism of fracture break through the permeable layer. It is shown that fracture grows slower in the permeable area. Even if fracture breaks through into an upper impermeable layer, it grows slower than in the absence of a permeable area. This mechanism may describe the transfer of oil from source rock into a series of permeable layers.

The authors believe this mechanism of liquid filtration through impermeable seals along hydraulic fractures may play a major role in oil and gas deposits formation process.

References

1. Tissot B.P., Welte D.H., Petroleum formation and occurrence, Springer-Verlag Telos, 1984, 699 p.

2. Gol'dberg V.M., Skvortsov N.P., Pronitsaemost' i fil'tratsiya v glinakh (The permeability and filtration in clays), Moscow: Nedra Publ., 1986, 160 p.

3. Zheltov YU.P., Khristianovich S.A., On hydraulic fracturing of oil reservoir (In Russ.), Izvestiya Akademii nauk SSSR, 1955, no. 5, pp. 3–41.

4. Nordgren R., Propagation of a vertical hydraulic fracture, SPE 3009-PA, 1972.

5. Jin Z.H., Johnson S., Primary oil migration through buoyancy-driven multiple fracture propagation: Oil velocity and flux, Geophysical Research Letters, 2008, V. 35, L09303, DOI:10.1029/2008GL033645

6. Roper S., Lister J., Buoyancy-driven crack propagation from an over-pressured source, Journal of Fluid Mechanics, 2005, V. 536, pp. 79–98.

7. Economides M., Oligney R., Valko P., Unified fracture design. Bridging the gap between theory and practice, Orsa Press, Alvin, Texas, 2002, 262 p.

8. Watanabe T., Masuyama T., Nagaoka K., Tahara T., Analog experiments on magma-filled cracks: Competition between external stresses and internal pressure, Earth, Planets and Space, 2014, V. 54, pp. 1247–1261

9. Le Corvec N., Menand T., Lindsay J., Interaction of ascending magma with pre‐existing crustal fractures in monogenetic basaltic volcanism: an experimental approach, Journal of Geophysical Research: Solid Earth, 2013, V. 118, no. 3, pp. 968–984.

10. Muskhelishvili N.I., Nekotorye osnovnye zadachi matematicheskoy teorii uprugosti (Some basic problems of the mathematical theory of elasticity), Moscow: Nauka Publ., 1966, 709 p. вЃ  

The problem of reservoir fluid migration through oil- and water- impermeable layers has not been completely resolved yet. A variety of different models is proposed to explain this process of oil migration from oil-source rocks. Migration through the impermeable layers occurs due to two main mechanisms: through the discontinuities of the medium (along fractures and faults) and through the continuous medium itself (multiphase filtration through the pore space). Remarkably enough there are no satisfactory mathematical models that describe these mechanisms of the migration process through the impermeable layers.

The article focuses on the problem of mathematical and numerical description of the fluid migration process through the impermeable layers along the fractures induced by hydraulic fracturing. The mechanism of hydraulic fracture vertical growth due to buoyancy forces is considered as minimum closure stress gradient in the reservoir exceeds pressure gradient of the fluid induced by gravity.

This paper presents the following results. We present a closed integral-differential equation system describing the fluid flow through the impermeable layer (fluid stop) in the presence of fractures. We show that for the typical geological parameters with fracture height over 20 meters, the fluid flow is determined by the buoyancy forces and described by a simple transport equation. We describe the mechanism of fracture break through the permeable layer. It is shown that fracture grows slower in the permeable area. Even if fracture breaks through into an upper impermeable layer, it grows slower than in the absence of a permeable area. This mechanism may describe the transfer of oil from source rock into a series of permeable layers.

The authors believe this mechanism of liquid filtration through impermeable seals along hydraulic fractures may play a major role in oil and gas deposits formation process.

References

1. Tissot B.P., Welte D.H., Petroleum formation and occurrence, Springer-Verlag Telos, 1984, 699 p.

2. Gol'dberg V.M., Skvortsov N.P., Pronitsaemost' i fil'tratsiya v glinakh (The permeability and filtration in clays), Moscow: Nedra Publ., 1986, 160 p.

3. Zheltov YU.P., Khristianovich S.A., On hydraulic fracturing of oil reservoir (In Russ.), Izvestiya Akademii nauk SSSR, 1955, no. 5, pp. 3–41.

4. Nordgren R., Propagation of a vertical hydraulic fracture, SPE 3009-PA, 1972.

5. Jin Z.H., Johnson S., Primary oil migration through buoyancy-driven multiple fracture propagation: Oil velocity and flux, Geophysical Research Letters, 2008, V. 35, L09303, DOI:10.1029/2008GL033645

6. Roper S., Lister J., Buoyancy-driven crack propagation from an over-pressured source, Journal of Fluid Mechanics, 2005, V. 536, pp. 79–98.

7. Economides M., Oligney R., Valko P., Unified fracture design. Bridging the gap between theory and practice, Orsa Press, Alvin, Texas, 2002, 262 p.

8. Watanabe T., Masuyama T., Nagaoka K., Tahara T., Analog experiments on magma-filled cracks: Competition between external stresses and internal pressure, Earth, Planets and Space, 2014, V. 54, pp. 1247–1261

9. Le Corvec N., Menand T., Lindsay J., Interaction of ascending magma with pre‐existing crustal fractures in monogenetic basaltic volcanism: an experimental approach, Journal of Geophysical Research: Solid Earth, 2013, V. 118, no. 3, pp. 968–984.

10. Muskhelishvili N.I., Nekotorye osnovnye zadachi matematicheskoy teorii uprugosti (Some basic problems of the mathematical theory of elasticity), Moscow: Nauka Publ., 1966, 709 p. вЃ  



Attention!
To buy the complete text of article (a format - PDF) or to read the material which is in open access only the authorized visitors of the website can. .

Mobile applications

Read our magazine on mobile devices

Загрузить в Google play

Press Releases

02.12.2020
30.11.2020
19.11.2020