EP3423672A1 - Modèle de puits séquentiel entièrement implicite avec structure de matrice tridiagonale pour simulation de réservoir - Google Patents

Modèle de puits séquentiel entièrement implicite avec structure de matrice tridiagonale pour simulation de réservoir

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Publication number
EP3423672A1
EP3423672A1 EP17711453.5A EP17711453A EP3423672A1 EP 3423672 A1 EP3423672 A1 EP 3423672A1 EP 17711453 A EP17711453 A EP 17711453A EP 3423672 A1 EP3423672 A1 EP 3423672A1
Authority
EP
European Patent Office
Prior art keywords
well
reservoir
model
cells
layers
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Withdrawn
Application number
EP17711453.5A
Other languages
German (de)
English (en)
Inventor
Ali H. Dogru
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Saudi Arabian Oil Co
Original Assignee
Saudi Arabian Oil Co
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Priority claimed from US15/061,572 external-priority patent/US10113400B2/en
Application filed by Saudi Arabian Oil Co filed Critical Saudi Arabian Oil Co
Publication of EP3423672A1 publication Critical patent/EP3423672A1/fr
Withdrawn legal-status Critical Current

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Classifications

    • E—FIXED CONSTRUCTIONS
    • E21—EARTH DRILLING; MINING
    • E21B—EARTH DRILLING, e.g. DEEP DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
    • E21B49/00—Testing the nature of borehole walls; Formation testing; Methods or apparatus for obtaining samples of soil or well fluids, specially adapted to earth drilling or wells

Definitions

  • the instructions stored in the data storage device also include instructions causing the data processor to determine the total rate for the well(s) from the determined completion rates for the layers of the well or wells, and form a record the determined completion rates for the layers and the determined total rate for the well(s).
  • Figures 20A and 20B are schematic diagrams of horizontal well models in a reservoir simulator of multiple subsurface formation layers in the area of a flow barrier in a reservoir, before and after being formed into a reduced horizontal well model according to the present invention.
  • Figure 21 and 22 are functional block diagrams or flow charts of data processing steps for a method and system for a reduced horizontal well model according to the present invention.
  • Reservoir simulation is a mathematical modeling science for reservoir engineering.
  • the fluid flow inside the oil or gas reservoir (porous media) is described by a set of partial differential equations. These equations describe the pressure (energy) distribution, oil, water and gas velocity distribution, fractional volumes (saturations) of oil, water, gas at any point in reservoir at any time during the life of the reservoir which produces oil, gas and water.
  • Fluid flow inside the reservoir is described by tracing the movement of the component of the mixture. Amounts of components such as methane, ethane, CO 2 , nitrogen, 3 ⁇ 4S and water are expressed either in mass unit or moles.
  • Equation (6) the numerator defines the phase relative permeability and the denominator is the phase viscosity.
  • a reduced well model system is formed which yields the same determination of a calculated bottom hole pressure as complex, computationally time consuming prior fully coupled well models.
  • Ax t is the grid block size (cell size) in the x direction for the grid block(cell) number i.
  • z/_y is the grid block size (cell size) in the y direction for the grid block(cell) number /
  • An is the grid block size (cell size) or grid layer thickness in the z direction for the grid block(cell) number i.
  • K Z .J/2 is the vertical permeability at the interface of the cells i and Similarly, is the vertical permeability at the interface of the cells i and i+1. As seen in Figure 6, the cell i is at the center, i + 1/2 interface between the cell i and i + 1.
  • Equation (12) Substituting Equation (12) into Equation (10) for cell i results in
  • PI t is the layer productivity index
  • ⁇ is the specified bottom hole potential( datum corrected pressure)
  • ⁇ is the reservoir grid block pressure where well is going through for grid block(cell)
  • r o i is called Peaceman's well block radius for grid block defined as
  • Equation (26) The coefficient matrix (A RR - A ⁇ ⁇ ⁇ ) of Equation (26) is an (Nz x Nz) full matrix.
  • step 102 the time step is incremented by one, and an iteration counter of the number of non-linear iterations performed during the present time step is set to zero.
  • step 104 a Jacobian matrix of reservoir data is formed.
  • step 106 the resultant linear system of Equation (19) is then solved by iterative methods using sparse preconditioners (Yousef Saad, Iterative Methods for Sparse Linear Systems, Society of Industrial & Applied Mathematics (SIAM) Publication, 2003).
  • simulation begins by reading the reservoir and production data. Reservoir and production data read in during step 200 are of the types discussed above.
  • the reservoir simulator is also initialized during step 200, setting the simulation day and the time step to zero.
  • step 202 the time step is incremented by one, and an iteration counter of the number of non- linear iterations performed during the present time step is set to zero.
  • the well 300 extends horizontally along a longitudinal axis through each of a succession of grid blocks 302 in the y direction. If a known total well rate, q is input into a reservoir simulator, the reservoir simulator calculates for each time step the potential values ⁇ for each grid block 302 shown in Figure 19.
  • step 402 an estimate of well bore potential is formed according to Equation (32) as set forth below:
  • each well 500 is completed in the vertical or z-direction through Nz cells, and the potentials in the adjacent cells:
  • the reservoir simulator calculates for each time step the potential values ⁇ for each grid block 502 shown in Figure 23.
  • Equation 20 The linear system of equations (Equation 20) for the reduced system still has an unstructured coefficient matrix, but with a 50% less number of unknowns.
  • the well model size reduction according to the present invention would be drastic, for example, a reduced well model system model according to the present invention could be 1 percent of size of the full system.
  • the reduced system is solved by a direct solver for the layer potentials and the bottom hole potential. Table 4 presents the results.
  • Results presented in Table 5 are the same as in Table 1 for the fully implicit well model. Difference or error between well rates for the calculated and input well is zero for this case and there no need for an extra iteration. This is because of the fact that the reservoir was homogeneous and no upscaling errors were made while forming the reduced system.
  • Matrix diagonal elements and right hand side are the same as in Figure 14, i.e., lower diagonal solid line represents T uPi i defined by Equation (11), upper diagonal solid line describes the elements called Toown.i described above.
  • the terms PI appear on Equation (17) are the perforation productivity indexes for a square grid is defined by:

Abstract

Cette invention concerne la simulation d'un réservoir souterrain d'hydrocarbures avec des puits horizontaux ou des puits verticaux multiples, par résolution séquentielle d'équations de réservoir et de puits pour simuler l'écoulement de fluide à l'intérieur du réservoir et les taux de production de puits. La résolution séquentielle d'équations de réservoir et de puits traite les puits en tant que puits à pression de fond spécifique. Ceci permet d'éviter la résolution de grandes matrices résultant de la résolution simultanée des équations de réservoir et de puits qui peut être informatiquement très coûteuse pour grand nombre d'inconnues et nécessiter des résolveurs spéciaux par matrice creuse. Une telle résolution séquentielle met en œuvre des résolveurs normaux de système de réservoir complétés par une petite matrice pour la résolution numérique des pressions de fond de puits.
EP17711453.5A 2016-03-04 2017-03-02 Modèle de puits séquentiel entièrement implicite avec structure de matrice tridiagonale pour simulation de réservoir Withdrawn EP3423672A1 (fr)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
US15/061,572 US10113400B2 (en) 2011-02-09 2016-03-04 Sequential fully implicit well model with tridiagonal matrix structure for reservoir simulation
PCT/US2017/020318 WO2017151838A1 (fr) 2016-03-04 2017-03-02 Modèle de puits séquentiel entièrement implicite avec structure de matrice tridiagonale pour simulation de réservoir

Publications (1)

Publication Number Publication Date
EP3423672A1 true EP3423672A1 (fr) 2019-01-09

Family

ID=58347943

Family Applications (1)

Application Number Title Priority Date Filing Date
EP17711453.5A Withdrawn EP3423672A1 (fr) 2016-03-04 2017-03-02 Modèle de puits séquentiel entièrement implicite avec structure de matrice tridiagonale pour simulation de réservoir

Country Status (5)

Country Link
EP (1) EP3423672A1 (fr)
CN (1) CN109072688B (fr)
CA (1) CA3013807C (fr)
SA (1) SA518392200B1 (fr)
WO (1) WO2017151838A1 (fr)

Families Citing this family (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20230351078A1 (en) * 2020-01-20 2023-11-02 Schlumberger Technology Corporation Methods and systems for reservoir simulation
US11613957B1 (en) 2022-01-28 2023-03-28 Saudi Arabian Oil Company Method and system for high shut-in pressure wells
CN116882218B (zh) * 2023-09-07 2023-11-21 北京大学 一种油藏数值模拟方法、装置、计算机设备及存储介质

Family Cites Families (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6980940B1 (en) * 2000-02-22 2005-12-27 Schlumberger Technology Corp. Intergrated reservoir optimization
US8285532B2 (en) * 2008-03-14 2012-10-09 Schlumberger Technology Corporation Providing a simplified subterranean model
US8095349B2 (en) * 2008-05-30 2012-01-10 Kelkar And Associates, Inc. Dynamic updating of simulation models
EP2350915A4 (fr) * 2008-09-30 2013-06-05 Exxonmobil Upstream Res Co Procédé de résolution d'équation matricielle de simulation de réservoir utilisant des factorisations incomplètes à multiples niveaux parallèles
US8589135B2 (en) * 2009-05-07 2013-11-19 Saudi Arabian Oil Company Systems, computer implemented methods, and computer readable program products to compute approximate well drainage pressure for a reservoir simulator
CN102339326B (zh) * 2010-07-16 2014-01-15 中国石油化工股份有限公司 一种分析模拟缝洞型油藏流体流动的方法
US9164191B2 (en) * 2011-02-09 2015-10-20 Saudi Arabian Oil Company Sequential fully implicit well model for reservoir simulation
CN103975341B (zh) * 2011-10-18 2017-03-15 沙特阿拉伯石油公司 基于4d饱和度模型和仿真模型的储层建模
CN104533370B (zh) * 2014-11-06 2017-03-15 中国石油大学(北京) 压裂水平井油藏、裂缝、井筒全耦合模拟方法

Also Published As

Publication number Publication date
CA3013807A1 (fr) 2017-09-08
CN109072688B (zh) 2021-05-11
SA518392200B1 (ar) 2021-09-15
WO2017151838A1 (fr) 2017-09-08
CA3013807C (fr) 2021-11-16
CN109072688A (zh) 2018-12-21

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