US10385656B2 - Methods and systems for determining manufacturing and operating parameters for a deviated downhole well component - Google Patents
Methods and systems for determining manufacturing and operating parameters for a deviated downhole well component Download PDFInfo
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- US10385656B2 US10385656B2 US14/895,165 US201414895165A US10385656B2 US 10385656 B2 US10385656 B2 US 10385656B2 US 201414895165 A US201414895165 A US 201414895165A US 10385656 B2 US10385656 B2 US 10385656B2
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- 238000000034 method Methods 0.000 title claims abstract description 38
- 238000004519 manufacturing process Methods 0.000 title claims abstract description 23
- 239000013598 vector Substances 0.000 claims abstract description 55
- 238000012546 transfer Methods 0.000 claims abstract description 34
- 239000000203 mixture Substances 0.000 claims abstract description 8
- 239000003381 stabilizer Substances 0.000 claims abstract description 7
- 239000011159 matrix material Substances 0.000 claims description 29
- 230000008859 change Effects 0.000 claims description 8
- 238000005452 bending Methods 0.000 claims description 3
- 230000009467 reduction Effects 0.000 description 10
- 238000003860 storage Methods 0.000 description 8
- 239000012530 fluid Substances 0.000 description 7
- 230000001186 cumulative effect Effects 0.000 description 5
- 230000015572 biosynthetic process Effects 0.000 description 4
- 238000005553 drilling Methods 0.000 description 4
- 229910000831 Steel Inorganic materials 0.000 description 3
- 238000013461 design Methods 0.000 description 3
- 238000012986 modification Methods 0.000 description 3
- 230000004048 modification Effects 0.000 description 3
- 230000002093 peripheral effect Effects 0.000 description 3
- 230000008569 process Effects 0.000 description 3
- 238000004088 simulation Methods 0.000 description 3
- 239000010959 steel Substances 0.000 description 3
- 238000009795 derivation Methods 0.000 description 2
- 238000002955 isolation Methods 0.000 description 2
- 239000000463 material Substances 0.000 description 2
- 150000003839 salts Chemical class 0.000 description 2
- 230000003068 static effect Effects 0.000 description 2
- 238000004458 analytical method Methods 0.000 description 1
- 238000013459 approach Methods 0.000 description 1
- 238000005094 computer simulation Methods 0.000 description 1
- 238000009826 distribution Methods 0.000 description 1
- 230000014759 maintenance of location Effects 0.000 description 1
- 230000003287 optical effect Effects 0.000 description 1
- 238000012545 processing Methods 0.000 description 1
- 230000032258 transport Effects 0.000 description 1
Images
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
- E21B41/00—Equipment or details not covered by groups E21B15/00 - E21B40/00
-
- 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
- E21B17/00—Drilling rods or pipes; Flexible drill strings; Kellies; Drill collars; Sucker rods; Cables; Casings; Tubings
-
- 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
- E21B7/00—Special methods or apparatus for drilling
- E21B7/04—Directional drilling
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
Definitions
- a well casing is a tubular structure generally made of a steel pipe surrounded by a concrete layer that secures the steel pipe to the surrounding formation, thus defining the outside wall of the well.
- the concrete provides support to the steel pipe, as well as additional isolation layer between the formation and fluids flowing within the casing.
- engineers frequently perform computer simulations to model various casing configurations under simulated downhole conditions. The simulations provide the engineer with information regarding the various loads and stresses to which the casing might be subjected, and enable potential designs to be evaluated.
- casing designs are only as good as the underlying simulation model. While simulations of single section casings in vertical wells are generally well understood and produce accurate results, tapered casings, deviated casings and casings with fluid flow restrictions represent indeterminate complex mechanical systems that can be very difficult or impractical to model using existing techniques. While methods do exist wherein these more complex systems are modeled as simpler single-section vertical wells with the results being adjusted to include additional safety margins, such methods can incur a significant risk, given the lack of quantifiable data to support the selected margins.
- FIG. 1 shows an illustrative downhole well with a well casing modeled using the disclosed systems and methods.
- FIG. 2 shows the various parameters describing the forces operating on an illustrative well casing string segment.
- FIG. 3 shows an illustrative computer system suitable for performing the disclosed methods.
- FIG. 4 shows an illustrative example of the disclosed methods.
- Well casing string 14 also curves to conform to the shape of the deviated well shown.
- a shoe 16 is located at the end of well casing string 14 , wherein shoe 16 and stabilizers 18 fix and mechanically constrain the lower end of well casing string 14 within borehole 30 .
- the forces acting on the above-described well casing string are modeled by dividing the system into a series of N subsystems that each only interact with adjacent subsystems, and then determining the forces acting on each subsystem in sequence.
- FIG. 2 shows an illustrative well casing string subsystem identified as segment 202 that is defined by two nodes 204 and 206 .
- Each node is described by a state vector that includes information regarding the location of the node relative to a reference node, and also includes information describing the forces present at the node.
- u i is the true vertical depth (TVD) of node i relative to the reference node;
- v i is the horizontal distance of node i from the reference node
- ⁇ i is the inclination angle of the casing segment at node i
- F hi is the horizontal force present at node i.
- the reference node of the illustrative example is located at the casing hanger and is designated as node 0, and the node at the opposite end of the well casing string and furthest away from node 0 is designated as node N.
- Equation (3) expresses the state vector V 1 as a set of constrained linear equations for the well casing segment that can be solved to determine the unknown forces present at node 1.
- the cross product of the node's transfer matrix and the reference node's state vector is combined with prior cross products for nodes 1 through i ⁇ 1 to determine the state vector for node i, thus determining the unknown forces at each node i (i.e., F xi , F hi and/or M i ).
- a transfer matrix method (TMM) is used to perform the combination of cross products.
- TMM transfer matrix method
- the transfer matrix is not limited to the specific embodiment of equation (2).
- plugs such as cementing plugs present within the casing string and reductions in the cross-sectional area of the casing such as reduction 15 of FIG. 1 may be represented by much simpler transfer matrices.
- such plugs and reductions located at a node i are represented as,
- Computer system 300 operates in accordance with software (which may be stored on non-transitory information storage media 340 ) and enables a user to interact with the system via keyboard 334 , pointing device 335 (e.g., a mouse) and display 336 to configure, control and monitor the execution of the matrix-based well casing string modeling.
- software which may be stored on non-transitory information storage media 340
- pointing device 335 e.g., a mouse
- a display interface 352 Located within processing subsystem 330 of computer system 300 is a display interface 352 , a processor 356 , a peripheral interface 358 , an information storage device 360 , a network interface 362 and a memory 370 .
- Bus 364 couples each of these elements to each other and transports their communications.
- Network interface 362 enables communications with other systems (e.g., via the Internet with a central database server housing additional modeling parameters and suitable for saving the results of the modeling).
- processor 356 processes input from the user and applies it to the well casing string data to perform the disclosed methods and present the results to the user.
- Storage device 360 may be implemented using any number of known non-transitory information storage media, including but not limited to magnetic disks, solid-state storage devices and optical storage disks.
- FIG. 4 shows an illustrative method that implements the above-described matrix-based modeling, at least part of which may be implemented by software executing on computer system 300 .
- FIG. 3 shows various software modules executing on computer system 300 , in other illustrative embodiments some or all of the modules may execute on two or more computers within a networked and/or distributed system.
- the state vector for the reference node (node 0) at the start of a casing string is defined (block 402 ; vector definition module 374 ), either via user input (user interface module 372 ) or using previously stored data (e.g., data stored on information storage device 360 ).
- Node index i is incremented from 0 to 1 and the total product is initialized to zero (block 402 ; TMM module 382 ).
- a state vector for the current i th node (here node 1) is defined in a manner similar to that used for the reference node (block 404 ; vector definition module 374 ), but with at least one unknown state vector element.
- the transfer matrix is defined in terms of one or more forces present at the restriction (block 408 ; matrix definition module 376 ). If the segment associated with the current node is a well casing string, the transfer matrix is defined in terms of the reference node's state vector, the previous node's state vector and/or the known elements of the current node's state vector (block 410 ; matrix definition module 376 ).
- node index i is incremented and the current node's state vector becomes the prior node's state vector (block 416 ; TMM module 380 ).
- the above-described process is then repeated for the next segment and node along the well casing string (blocks 404 through 418 ). If there are no additional well casing string segments (block 418 ; TMM module 380 ), the previously unknown and now calculated elements of each state vector are subsequently used as a basis for determining casing manufacturing parameters such as dimensions and composition, or as a basis for locating centralizers to position the casing within a borehole (block 420 , parameter derivation module 382 ).
- the resulting manufacturing parameters or centralizer position are respectively provided as composition and/or dimensional specifications to manufacturing personnel, or as a position for a centralizer or stabilizer to well operators/component installers (block 422 , presentation module 384 ), ending the method (block 424 ).
- the calculated forces at each node along a casing string are indicated on a graphical representation of the well casing string.
- the axial load e.g., tension
- Casing string parameters such as segment lengths, wall thickness and material compositions may then be determined from the computed axial load. These parameters provide the required casing safety margins at a reduced cost when compared to existing methods that overestimate the required casing string parameters.
- the positions of one or more centralizers are on the casing string's graphical representation.
- the contact points between the casing and borehole wall can be determined from the state vector V i and the well trajectory.
- the computed side force and the contact points are then used to determine a suitable centralizer(s) and the best centralizer position(s), for example, at the contact point(s) between the casing segment and the borehole wall.
- any of a wide variety of well components may be modeled to determine the manufacturing and/or operating parameters of said components.
- These well components include but are not limited to drillstrings, workstrings, production strings and coiled tubing stings.
- Other well components that restrict fluid flow within a running tubular string e.g., packers
- packers are also within the scope of the disclosure. It is intended that the following claims be interpreted to embrace all such modifications, equivalents, and alternatives where applicable.
Abstract
Description
V i=[u i v iαi F xi F hi M i−1]i T (1)
where,
-
- li h is the horizontal distance defined as (vi−vi−1);
- li x is the vertical distance defined as (ui−ui−1);
- Δαi−1 0 is the change in inclination angle at the ith−1 node defined as (αi−1−α0);
- Δαi 0 is the change in inclination angle at the ith node defined as (αi−α0);
- (EI)i is the product of Young's modulus and a moment of inertia of the component at the ith node; and
- (EA)i is the product of Young's modulus and a cross-sectional area of the component at the ith node.
V 1 =T 1 ×V 0 (3).
Equation (3) expresses the state vector V1 as a set of constrained linear equations for the well casing segment that can be solved to determine the unknown forces present at
F αi =F xi×cos(αi)+F hi×sin(αi) (4).
V i=(Π1 i T i)×V 0 (5).
Because each of the prior products of products for each
T acc =T 1 ; V 1 =T acc ×V 0 (6),
T acc =T acc ×T 2 ; V 2 =T acc ×V 0=(T 1 ×T 2)×V 0 (7), and
T acc =T acc ×T 3 ; V 3 =T acc ×V 0=(T 1 ×T 2 ×T 3)×V 0 (8).
-
- Fp x is a vertical force present on a plug or reduction located at the ith node; and
- Fp h is a horizontal force present on the plug or reduction.
Other transfer matrices may include, for example, parameters that describe the load imposed on a casing string by a salt formation (i.e., “salt loading”). A wide variety of transfer matrices suitable for use with the methods described herein will become apparent to those of ordinary skill in the art, and all such variations of transfer matrices are within the scope of the present disclosure.
SideForcei=√{square root over ((F x(i+1) −F xi)2+(F h(i+1) −F hi)2)} (9).
The contact points between the casing and borehole wall can be determined from the state vector Vi and the well trajectory. The computed side force and the contact points are then used to determine a suitable centralizer(s) and the best centralizer position(s), for example, at the contact point(s) between the casing segment and the borehole wall.
Claims (24)
Priority Applications (1)
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US14/895,165 US10385656B2 (en) | 2013-06-21 | 2014-01-17 | Methods and systems for determining manufacturing and operating parameters for a deviated downhole well component |
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US201361837986P | 2013-06-21 | 2013-06-21 | |
US14/895,165 US10385656B2 (en) | 2013-06-21 | 2014-01-17 | Methods and systems for determining manufacturing and operating parameters for a deviated downhole well component |
PCT/US2014/011998 WO2014204521A1 (en) | 2013-06-21 | 2014-01-17 | Methods and systems for determining manufacturing and operating parameters for a deviated downhole well component |
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US20160108704A1 US20160108704A1 (en) | 2016-04-21 |
US10385656B2 true US10385656B2 (en) | 2019-08-20 |
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US14/895,165 Active 2035-09-22 US10385656B2 (en) | 2013-06-21 | 2014-01-17 | Methods and systems for determining manufacturing and operating parameters for a deviated downhole well component |
Country Status (10)
Country | Link |
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US (1) | US10385656B2 (en) |
EP (1) | EP2986819A4 (en) |
CN (1) | CN105247166A (en) |
AU (1) | AU2014281186B2 (en) |
BR (1) | BR112015029405A2 (en) |
CA (1) | CA2913203C (en) |
MX (1) | MX2015016106A (en) |
RU (1) | RU2015150612A (en) |
SG (1) | SG11201509613UA (en) |
WO (1) | WO2014204521A1 (en) |
Families Citing this family (2)
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MX2015016106A (en) | 2013-06-21 | 2016-08-08 | Landmark Graphics Corp | Methods and systems for determining manufacturing and operating parameters for a deviated downhole well component. |
GB2558824A (en) * | 2015-12-09 | 2018-07-18 | Halliburton Energy Services Inc | Eddy-current responses in nested pipes |
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US6785641B1 (en) * | 2000-10-11 | 2004-08-31 | Smith International, Inc. | Simulating the dynamic response of a drilling tool assembly and its application to drilling tool assembly design optimization and drilling performance optimization |
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WO2014204521A1 (en) | 2013-06-21 | 2014-12-24 | Landmark Graphics Corporation | Methods and systems for determining manufacturing and operating parameters for a deviated downhole well component |
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CN1282818C (en) * | 2001-08-16 | 2006-11-01 | 中海油田服务股份有限公司 | Drill bit advancing direction predicting method, controlling method and controlling system for horizontal well |
CN101826117B (en) * | 2009-03-04 | 2011-12-28 | 中国核电工程有限公司 | Method for manufacturing finite element method mechanical computation model of pipeline system |
US10227857B2 (en) * | 2011-08-29 | 2019-03-12 | Baker Hughes, A Ge Company, Llc | Modeling and simulation of complete drill strings |
US9810213B2 (en) * | 2011-10-28 | 2017-11-07 | Weatherford Technology Holdings, Llc | Calculating downhole pump card with iterations on single damping factor |
-
2014
- 2014-01-17 MX MX2015016106A patent/MX2015016106A/en unknown
- 2014-01-17 WO PCT/US2014/011998 patent/WO2014204521A1/en active Application Filing
- 2014-01-17 EP EP14814632.7A patent/EP2986819A4/en active Pending
- 2014-01-17 RU RU2015150612A patent/RU2015150612A/en not_active Application Discontinuation
- 2014-01-17 SG SG11201509613UA patent/SG11201509613UA/en unknown
- 2014-01-17 CA CA2913203A patent/CA2913203C/en active Active
- 2014-01-17 CN CN201480030508.4A patent/CN105247166A/en active Pending
- 2014-01-17 BR BR112015029405A patent/BR112015029405A2/en not_active IP Right Cessation
- 2014-01-17 AU AU2014281186A patent/AU2014281186B2/en not_active Ceased
- 2014-01-17 US US14/895,165 patent/US10385656B2/en active Active
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US6816082B1 (en) | 1998-11-17 | 2004-11-09 | Schlumberger Technology Corporation | Communications system having redundant channels |
US6785641B1 (en) * | 2000-10-11 | 2004-08-31 | Smith International, Inc. | Simulating the dynamic response of a drilling tool assembly and its application to drilling tool assembly design optimization and drilling performance optimization |
US20110253447A1 (en) | 2004-03-04 | 2011-10-20 | Gleitman Daniel D | Multiple distributed force measurements |
US20070024464A1 (en) | 2004-10-27 | 2007-02-01 | Schlumberger Technology Corporation | Wireless Communications Associated with a Wellbore |
US20100032165A1 (en) | 2007-02-02 | 2010-02-11 | Bailey Jeffrey R | Modeling And Designing of Well Drilling System That Accounts For Vibrations |
US20110320047A1 (en) | 2010-06-24 | 2011-12-29 | Chevron U.S.A. Inc. | Design and control of multiple tubing string well systems |
US20120203515A1 (en) * | 2011-02-08 | 2012-08-09 | Pita Jorge A | Seismic-Scale Reservoir Simulation of Giant Subsurface Reservoirs Using GPU-Accelerated Linear Equation Systems |
WO2014204521A1 (en) | 2013-06-21 | 2014-12-24 | Landmark Graphics Corporation | Methods and systems for determining manufacturing and operating parameters for a deviated downhole well component |
Non-Patent Citations (7)
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Publication number | Publication date |
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MX2015016106A (en) | 2016-08-08 |
CN105247166A (en) | 2016-01-13 |
AU2014281186A1 (en) | 2015-12-10 |
AU2014281186B2 (en) | 2016-09-08 |
US20160108704A1 (en) | 2016-04-21 |
WO2014204521A1 (en) | 2014-12-24 |
CA2913203A1 (en) | 2014-12-24 |
EP2986819A4 (en) | 2017-02-08 |
RU2015150612A (en) | 2017-06-02 |
CA2913203C (en) | 2019-07-16 |
SG11201509613UA (en) | 2015-12-30 |
EP2986819A1 (en) | 2016-02-24 |
BR112015029405A2 (en) | 2017-07-25 |
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