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US-12624615-B2 - Method of simulating fluid flows in an underground formation comprising a fracture network

US12624615B2US 12624615 B2US12624615 B2US 12624615B2US-12624615-B2

Abstract

The present invention is a method of simulating fluid flows in an underground formation comprising a fracture network. A porosity model is constructed, comprising a first medium representative of an unfractured matrix, a second medium representative of fractures oriented in a first direction and a third medium representative of fractures oriented in a second direction orthogonal to the first direction. From at least the porosity model, flow parameters of a grid representation of the formation are determined, which include conduction and convection transmissibilities between two neighboring cells for the second and third media, as well as mass and energy exchanges by convection and conduction between each medium taken two by two for a single cell. Flows in the formation are simulated by f a flow simulator implementing the porosity model.

Inventors

  • Didier Yu DING

Assignees

  • IFP Energies Nouvelles

Dates

Publication Date
20260512
Application Date
20220624
Priority Date
20210701

Claims (19)

  1. 1 . A computer-implemented method of simulating fluid flows in an underground formation comprising a fracture network for exploiting the fluid of the underground formation wherein, from measured properties relative to the formation, a grid representation of the formation is constructed and at least one statistical parameter relative to the fracture network is determined, comprising steps of: A) constructing from the at least one statistical parameter relative to the fracture network, a porosity model for the underground formation comprising the fracture network, the porosity model comprising a first medium representative of an unfractured matrix of the formation, a second medium representative of fractures of the formation oriented in a first direction, and a third medium representative of fractures of the formation oriented in a second direction, the first and second directions being orthogonal to one another; B) determining from at least the measurements of properties relative to the formation, from the at least one statistical parameter relative to the fracture network and from the porosity model flow parameters in each cell of the grid representation, the flow parameters comprising: determining between two neighboring cells in the second direction, a convection transmissibility and a conduction transmissibility of the fluid in the first and second directions in the second medium, the convection and conduction transmissibilities of the fluid being zero in the second direction in the second medium; determining between two neighboring cells in the first direction, a convection transmissibility and a conduction transmissibility of the fluid in the first and second directions in the third medium, the convection and conduction transmissibilities of the fluid being zero in the first direction in the third medium; and determining within a cell of the grid representation, mass exchanges by convection, energy exchanges by conduction between the second and third mediums, between the first and second mediums, and between the first medium and the third medium; and C) simulating from the grid representation and the flow parameters in each cell of the grid, the flows of the fluid in the underground formation comprising the fracture network by use of a flow simulator implementing the porosity model.
  2. 2 . A method as claimed in claim 1 , wherein the mass exchanges F w , i ff by convection between the second and third mediums in one of the cells i of the grid are determined with a formula: F w , i ff = λ i f ⁢ T i ff ( P i fX - P i fY ) wherein T i ff is a convection transmissibility between the second and third mediums of the cell i, P i fX and P i fY correspond to a pressure in the second and third mediums of the cell i respectively, and λ i f is mobility of the fluid between the second and third mediums of the cell i.
  3. 3 . A method as claimed in claim 1 , wherein the energy exchanges F H , i ff by convection between the second and third mediums in one of the cells i of the grid are determined with a formula: F H , i ff = λ i f ⁢ H i f ⁢ T i ff ( P i fX - P i fY ) wherein H i f is a enthalpy of the fluid between the second and third mediums of the cell i, T i ff is the convection transmissibility between the second and third mediums of the cell i, P i fX and P i fY correspond to the pressure in the second and third mediums of the cell i respectively, and λ i f is the mobility of the fluid between the second and third mediums of the cell i.
  4. 4 . A method as claimed in claim 2 , wherein energy exchanges F H , i ff by convection between the second and third mediums in one of the cells i of the grid are determined with a formula: F H , i ff = λ i f ⁢ H i f ⁢ T i ff ( P i fX - P i fY ) wherein H i f is a enthalpy of the fluid between the second and third mediums of the cell i, , T i ff is the convection transmissibility between the second and third mediums of the cell i, P i fX and P i fY correspond to the pressure in the second and third mediums of the cell i respectively, and λ i f is the mobility of the fluid between the second and third mediums of the cell i.
  5. 5 . A method as claimed in claim 2 , wherein the convection transmissibility between the second and third mediums of the cell i is determined with a formula: T i ff = α ⁢ ∑ j ∈ Ω i ⁢ ( T x , ij fX + T y , ij fY ) where α is a multiplier equal to at least 100, Ω i is all cells next to cell i, T x , ij fX corresponds to the convection transmissibility in the first direction in the second medium for the cell i, and T y , ij fY corresponds to the convection transmissibility in the second direction in the third medium for the cell i.
  6. 6 . A method as claimed in claim 3 , wherein the convection transmissibility between the second and third mediums of the cell i is determined with a formula: T i ff = α ⁢ ∑ j ∈ Ω i ⁢ ( T x , ij fX + T y , ij fY ) where α is a multiplier equal to at least 100, Ω i is all cells next to cell i, T x , ij fX corresponds to the convection transmissibility in the first direction in the second medium for the cell i, and T y , ij fY corresponds to the convection transmissibility in the second direction in the third medium for the cell i.
  7. 7 . A method as claimed in claim 1 , wherein energy exchanges F D , i ff by conduction between the second and third mediums in the cell i are determined with a formula: F D , i ff = G i ff ( Θ i f ⁢ X - Θ i f ⁢ Y ) where G i ff is conduction transmissibility between the second and third mediums for the cell i, Θ i fX and Θ i f ⁢ Y correspond to the temperature in the second and third mediums respectively.
  8. 8 . A method as claimed in claim 2 , wherein energy exchanges F D , i ff by conduction between the second and third mediums in the cell i are determined with a formula: F D , i ff = G i ff ( Θ i f ⁢ X - Θ i f ⁢ Y ) where Θ j ff is conduction transmissibility between the second and third mediums for the cell i, Θ i f ⁢ X and Θ i f ⁢ Y correspond to the temperature in the second and third mediums respectively.
  9. 9 . A method as claimed in claim 3 , wherein energy exchanges F D , i ff by conduction between the second and third mediums in the cell i are determined with a formula: F D , i ff = G i ff ( Θ i fX - Θ i fY ) where G i ff is conduction transmissibility between the second and third mediums for the cell i, Θ i f ⁢ X and Θ i f ⁢ Y respectively correspond to the temperature in the second and third mediums.
  10. 10 . A method as claimed in claim 4 , wherein energy exchanges F D , i ff by conduction between the second and third mediums in the cell i are determined with a formula: F D , i ff = G i ff ( Θ i fX - Θ i fY ) where G i ff is conduction transmissibility between the second and third mediums for the cell i, Θ i f ⁢ X ⁢ and ⁢ Θ i f ⁢ Y respectively correspond to the temperature in the second and third mediums.
  11. 11 . A method as claimed in claim 5 , wherein energy exchanges F D , i ff by conduction between the second and third mediums in the cell i are determined with a formula: F D , i ff = G i ff ( Θ i fX - Θ i fY ) where G i ff is conduction transmissibility between the second and third mediums for the cell i, Θ i fX respectively correspond to the temperature in the second and third mediums.
  12. 12 . A method as claimed in claim 6 , wherein energy exchanges F D , i ff by conduction between the second and third mediums in the cell i are determined with a formula: F D , i ff = G i ff ( Θ i fX - Θ i fY ) where G i ff is conduction transmissibility between the second and third mediums for the cell i, Θ i fX and Θ i fY respectively correspond to the temperature in the second and third mediums.
  13. 13 . A method as claimed in claim 12 , wherein conduction transmissibility between the second and third mediums for the cell i is determined with a formula: G i ff = Λ i ff ⁢ C i ff where Λ i ff is an arithmetic mean of an effective thermal conductivity of the second and third mediums, C i ff is a geometric coefficient depending on the dimensions of the cell i, the dimensions of one of the matrix blocks into which the first medium is broken, and the opening of the fractures of the second and third mediums.
  14. 14 . A method as claimed in claim 8 , wherein the conduction transmissibility between the second and third mediums for the cell i is determined with a formula: G i ff = Λ i ff ⁢ C i ff where Λ i ff is an arithmetic mean of an effective thermal conductivity of the second and third mediums, C i ff is a geometric coefficient depending on the dimensions of the cell i, the dimensions of one of the matrix blocks into which the first medium is broken, and the opening of the fractures of the second and third mediums.
  15. 15 . A method as claimed in claim 9 , wherein conduction transmissibility between the second and third mediums for the cell i is determined with a formula: G i ff = Λ i ff ⁢ C i ff where Λ i ff is an arithmetic mean of an effective thermal conductivity of the second and third mediums, C i ff is a geometric coefficient depending on the dimensions of the cell i, the dimensions of one of the matrix blocks into which the first medium is broken, and the opening of the fractures of the second and third mediums.
  16. 16 . A method as claimed in claim 10 , wherein conduction transmissibility between the second and third mediums for the cell i is determined with a formula: G i ff = Λ i ff ⁢ C i ff where Λ i ff is an arithmetic mean of an effective thermal conductivity of the second and third mediums C i ff is a geometric coefficient depending on the dimensions of the cell i, the dimensions of one of the matrix blocks into which the first medium is broken, and the opening of the fractures of the second and third mediums.
  17. 17 . A method as claimed in claim 11 , wherein the conduction transmissibility between the second and third mediums for the cell i is determined with a formula: G i ff = Λ i ff ⁢ C i ff where Λ i ff is an arithmetic mean of an effective thermal conductivity of the second and third mediums, C i ff is a geometric coefficient depending on the dimensions of the cell i, the dimensions of one of the matrix blocks into which the first medium is broken, and the opening of the fractures of the second and third mediums.
  18. 18 . A method of exploiting a fluid of an underground formation comprising a fracture network, wherein the method as claimed in claim 1 is performed and, from at least simulation of the flows in the underground formation, an exploitation scheme comprising at least one site for at least one of an injection well and at least one production well is determined for the fluid, and the fluid of the underground formation is exploited at least by drilling the wells at the site and by providing wells with exploitation infrastructures.
  19. 19 . A non-transitory computer-readable medium storing a computer program product which, when executed on a computer, implements the method as claimed in claim 1 .

Description

CROSS REFERENCE TO RELATED APPLICATION Reference is made to French Application No. 21/07.120 filed Jul. 1, 2021, which is incorporated herein by reference in its entirety. BACKGROUND OF THE INVENTION Field of the Invention The present invention relates to modelling fluid flows in an underground formation comprising a fracture network. The present invention finds a specific application in the field of geothermal energy, but it can also apply to the field of petroleum exploration and exploitation. Description of the Prior Art Diversification of the different energy sources allows reduction of fossil fuel dependence and thus meeting the challenges of energy transition. In this context, the global market for geothermal power generation is expected to double in the next ten years. The geothermal resource exploits the natural geothermal gradient (temperature increase with depth) of the Earth, which may be very variable depending on the sites. Thus, to capture the geothermal energy, a fluid is circulated in the subsoil, at a greater or lesser depth depending on the desired temperature and according to the local thermal gradient. This fluid may be naturally present in the rock (aquifer) or it may be purposely injected into the subsoil. The fluid heats up upon contact with the subsurface rocks and flows back to the surface laden with calories (thermal energy), which is transmitted in a heat exchanger. The fluid is thereafter reinjected into the medium, once cooled and filtered. Numerical simulation of subsurface flows provides essential information for optimal geothermal energy exploitation. First, such a simulation can be advantageously used prior to building a plant in order to determine the potential of a site considered for geothermal energy exploitation, or to determine the location, the geometry and the depth of injection/production wells. Numerical flow simulation can also be advantageously used for monitoring a geothermal site, notably in order to optimize production while preserving the geothermal potential of this site, or for monitoring interactions with surrounding aquifers. Sites favorable to geothermal energy exploitation are often found in geologically active zones such as volcanic zones. Such zones are most often characterized by fracture networks, which have a very significant impact on fluid flows as fractures can act as drains or barriers to fluid flows. It is therefore important for the numerical flow simulators used to provide realistic modelling of the flows, including in the case of a fractured medium. Now, accurate modelling of flows in a fractured medium would require extremely fine cells for modelling heterogeneities such as faults. In order to limit the computing time, approximate fracture medium models have been proposed in the literature relative to petroleum exploration and exploitation. The following documents are mentioned in the description: Aliyu, M. D., Chen, H. P., Harireche, O. and Hills, C. D. (2017) “Numerical Modelling of Geothermal Reservoirs with Multiple Pore Media”, PROCEEDINGS, 42nd Workshop on Geothermal Reservoir Engineering, Stanford University, California, USA, 13-15 February.Austria, J. and O'Sullivan, M. (2015) “Dual Porosity Models of a Two-phase Geothermal Reservoir” Proceedings World Geothermal Congress 2015, Melbourne, Australia, 19-25 April.Fujii, S., Ishigami, Y. and Kurihara, M. (2018) “Development of Geothermal Reservoir Simulator for Predicting Three-dimensional Water-Steam Flow Behavior Considering Non-equilibrium State and Kazemi/MINC Double Porosity System” GRC Transaction, vol. 42.Omagbon, J., O'Sullivan, M., O'Sullivan, J. and Walker, C. (2016) “Experiences in Developing a Dual Porosity Model of the Leyte Geothermal Production Field” Proceedings of 38th New Zealand Geothermal Workshop, Auckland, New Zealand, 23-25 NovemberWarren, J. E. & Root, P. J. (1963) “The Behavior of Naturally Fractured Reservoirs”, SPE Journal, Volume 3, pp. 245-255.Lemonnier, P. and Bourbiaux, B. (2010) “Simulation of Naturally Fractured Reservoirs. State of the Art Part 2, MatriX-fractures Transfers and Typical Features of Numerical Studies” Oil & Gas Science and Technology, Vol. 65 (2010), No. 2, pp. 263-286. In the petroleum sector, the dual porosity model, notably described in the document (Warren and Root, 1963), is widely used to simulate flows in fractured reservoirs. This approach involves the fractured reservoir being broken into identical parallelepiped blocks, referred to as matrix blocks, delimited by an orthogonal system of continuous uniform fractures oriented in the principal directions of flow. In a dual porosity model (also referred to as dual medium model), the medium to be modelled is broken into a “fracture” medium and a “matrix” medium. With such a model, any elementary volume (reservoir model cell) of the fractured reservoir is associated with a fraction of matrix block(s). Fluid flow at reservoir scale occurs essentially through the fractures, fluid excha