(12) United States Patent
`Guinot et al.
`
`I 1111111111111111 11111 111111111111111 lllll lllll lllll 111111111111111 11111111
`US006283214Bl
`US 6,283,214 Bl
`Sep.4,2001
`
`(10) Patent No.:
`(45) Date of Patent:
`
`(54) OPTIMUM PERFORATION DESIGN AND
`TECHNIQUE TO MINIMIZE SAND
`INTRUSION
`
`5,792,977
`5,797,464
`
`8/1998 Chawla .
`8/1998 Pratt et al ..
`
`OTHER PUBLICAfIONS
`
`(75)
`
`Inventors: Frederic J. Guinot, Houston; Simon
`G. James, Stafford; Brenden M.
`Grove, Missouri City, all of TX (US);
`Panos Papanastasiou, Hardwick (GB)
`
`(73) Assignee: Schlumberger Technology Corp.,
`Sugar Land, TX (US)
`
`( * ) Notice:
`
`Subject to any disclaimer, the term of this
`patent is extended or adjusted under 35
`U.S.C. 154(b) by O days.
`
`(21) Appl. No.: 09/321,040
`
`(22) Filed:
`
`May 27, 1999
`
`(51)
`(52)
`
`(58)
`
`(56)
`
`Int. Cl.7
`.................................................... E21B 43/117
`U.S. Cl. ........................ 166/297; 166/55.2; 175/4.51;
`175/4.6; 102/313
`Field of Search ............................ 166/297, 55, 55.2;
`175/4.51, 4.6; 102/306, 313
`
`References Cited
`
`U.S. PATENT DOCUMENTS
`3,242,987 *
`4,071,096 *
`5,386,875
`5,633,475 *
`
`3/1966 LeBourg ........................... 175/4.6 X
`1/1978 Dines .................................... 175/4.6
`2/1995 Venditto et al. .
`5/1997 Chawla ................................ 102/306
`
`SPE 38939 "Coupling Reservoir and Geomechanics to Inter(cid:173)
`pret Tidal Effects in a Well II Test" Pinilla, et al, Oct. 1997.
`SPE 36457 "Fracturing, Frac-Packing and Formation Fail(cid:173)
`ure Control: Can Screenless Completions Prevent Sand
`Production?" Morita, et al, Oct. 1996.
`SPE 51187 (Re,ised from SPE 36457) "Fracturing,
`Frac-Packing and Formation Failure Control: Can Screen(cid:173)
`less Completions Prevent Sand Production?" , Morita, et al,
`Mar. 1998.
`* cited by examiner
`Primary Examiner~oger Schoeppel
`(74) Attorney, Agent, or Firm-Trop, Pruner & Hu & P.C.
`ABSTRACT
`
`(57)
`
`The present Invention relates to novel devices and methods
`to minimize the production of sand in subterranean envi(cid:173)
`ronments; in particular, in poorly consolidated formations,
`sand is often co-produced along with the desired fluid (e.g.,
`oil); sand production is undesirable, hence in the present
`Invention, elliptically shaped perforations of a particular
`orientation are created in the casing ( or directly into the
`formation in the case of an uncased wellbore) that lines
`wellbore drilled through the formation, to improve near(cid:173)
`wellbore stability of the formation, hence minimizing sand
`intrusion.
`
`31 Claims, 11 Drawing Sheets
`
`1.0
`22g CHARGE
`ELLIPSE 3
`JET & HOLE PROFILE
`
`DynaEnergetics Europe GmbH
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`U.S. Patent
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`Sep.4,2001
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`Sheet 1 of 11
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`US 6,283,214 Bl
`
`CIRCLE
`0 '-----l.---'--~-...,____i,_-.;;t::;:,_...J__.1...--__,l
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`
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`U.S. Patent
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`Sep.4,2001
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`Sheet 2 of 11
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`US 6,283,214 Bl
`
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`

`U.S. Patent
`
`Sep.4,2001
`
`Sheet 4 of 11
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`US 6,283,214 Bl
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`U.S. Patent
`
`Sep.4,2001
`
`Sheet S of 11
`
`US 6,283,214 Bl
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`
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`U.S. Patent
`
`Sep.4,2001
`
`Sheet 6 of 11
`
`US 6,283,214 Bl
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`DynaEnergetics Europe GmbH
`Ex.1010
`Page 8 of 19
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`DynaEnergetics Europe GmbH
`Ex.1010
`Page 9 of 19
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`DynaEnergetics Europe GmbH
`Ex.1010
`Page 10 of 19
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`Sep.4,2001
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`Sheet 10 of 11
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`US 6,283,214 Bl
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`

`

`U.S. Patent
`
`Sep.4,2001
`
`Sheet 11 of 11
`
`US 6,283,214 Bl
`
`FIG. 18
`
`110
`
`FIG. 19A
`
`FIG. 198
`
`FIG. 19C
`
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`
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`

`US 6,283,214 Bl
`
`1
`OPTIMUM PERFORATION DESIGN AND
`TECHNIQUE TO MINIMIZE SAND
`INTRUSION
`
`BACKGROUND
`
`1. Technical Field of this Invention
`The present Invention relates to novel devices and meth(cid:173)
`ods to minimize the production of sand in subterranean
`environments. In particular, in poorly consolidated
`formations, for instance, sand is co-produced along with the
`desired fluid ( e.g., oil); sand production is undesirable,
`hence in the present Invention, elliptically shaped perfora(cid:173)
`tions of a particular orientation (in preferred embodiments)
`are created through the casing that lines the wellbore (as well
`as created in an uncased formation) and that penetrate the
`formation rock, to improve the stability of the perforation
`tunnel, and therefore minimizing sand intrusion (or the
`intrusion of disaggregated formation particles generally, in
`the ca'Se of, e.g., carbonate formations).
`2. Prior Art
`In the production of oil and gas from a subterranean
`reservoir, one persistent problem in certain types of reser(cid:173)
`voirs is that sand is also produced along with the hydrocar(cid:173)
`bon. The present Invention is directed to novel techniques to
`control the coproduction of sand with hydrocarbons (i.e.,
`"sand control"). Obviously, the goal in oil and gas produc(cid:173)
`tion is to move the hydrocarbon from the underground
`formation where it resides, to a wellbore drilled in the earth,
`and eventually to the surface, for transportation and eventual
`refining. Many hydrocarbon-bearing formations are
`sandstone, and many of those are poorly consolidated
`sandstone, which means that the sand grains that comprise
`the geologic formation are loosely held together. In certain
`formations, sand flows from the formation along with the
`oil-this may occur initially, or later in the life of the well.
`This "sand production" is highly undesirable. For one thing,
`sand is a harsh abrasive and so abrades just about everything
`it comes in contact with-production string (generally steel
`tubing) lining the wellbore, aboveground pipelines, and so
`forth. If enough sand is co-produced with the oil then it is not
`even suitable for processing, or only at substantial additional
`expense.
`Therefore, numerous techniques have evolved to deal
`with the problem; they are roughly divisible into two cat(cid:173)
`egories: mechanical and non-mechanical. The primary
`mechanical technique is known as "gravel packing." A
`particularly sophisticated type of gravel packing is AllPAC,
`a patented technology jointly developed by Mobil and
`Schlumberger and exclusively licensed to Schlumberger. 50
`(See, e.g., L. G. Jones,Alternate-Path Gravel Packing, SPE
`22796 (1991)). The idea behind gravel packing is to place a
`permeable screen inside the wellbore between the casing (if
`there is one) and the wellbore, next the annulus formed by
`the screen and casing/wellbore is filled with gravel.
`(Alternatively, a screen without gravel is sometimes used;
`also, sometimes "pre-packed" screens are used, in which the
`gravel is placed in the screen before it is placed in the
`wellbore ). The purpose of the screen is to hold the gravel in
`place, and the purpose of the gravel (and screen) is to
`remove the sand, yet allow the oil ( or gas) to migrate through
`the gravel pack, into the wellbore and eventually to the
`surface.
`Although gravel packing is a venerable sand control
`technique, still widely relied upon, it has numerous very
`substantial disadvantages. First, screens are very expensive;
`this expense is naturally exacerbated in horizontal wells,
`
`10
`
`2
`where the amount of screen needed frequently exceeds a
`thousand feet. Moreover, placing a screen in a horizontal
`section is time-consuming and expensive. Second, a rig or
`mast must be used to place screen in a wellbore; rig rates are
`5 quite often very high, particularly offshore ( e.g., in the North
`Sea, they can exceed Sl00,000/day). Third, whatever
`benefit-in reduced sand production-is derived from the
`gravel pack, the fact remains that it is a choke on production,
`often substantially reducing potential production rates.
`Related to this, screens can become plugged-e.g., by fines
`(very small grain sands) may become affixed to the screen
`face where they form a "filter cake," which can severely
`inhibit, or even halt production.
`The second major category of sand control techniques
`relates not to impeding the flow of sand via a filter (gravel
`15 pack) but instead relates to improving the near-wellbore
`integrity of the formation so that less sand flows into the
`wellbore. For the most part, these techniques involve some(cid:173)
`how consolidating the sandstone around the wellbore-i.e.,
`cementing the sand grains together so that they do not flow
`20 along with the oil, into the wellbore. To do this requires
`some sort of cementing material, such as a furan resin or
`epoxy resin. For instance, U.S. Pat. No. 5,551,514, assigned
`to Schlumberger, discloses and claims, e.g., a method of
`controlling sand production by consolidating the near-
`2s wellbore formation by injecting a resin into that region of the
`formation. Next, that portion of the formation is hydrauli(cid:173)
`cally fractured-i.e., sufficient fluid is pumped into the
`formation to cause it to split. The idea is that formation
`consolidation is achieved (via the resin) but not at the
`30 expense of reduced hydrocarbon production (since the for(cid:173)
`mation is actually stimulated by the fracture).
`These non-mechanical (or chemical) sand control tech(cid:173)
`niques suffer predictably, from reduced permeability in the
`region of the formation where the consolidation is placed. In
`35 other words, while the idea behind these types of treatments
`is to cement the contiguous sand grains together, but not
`leave the resin in the pore spaces (where the oil must flow),
`most treatments rarely approach this ideal. Indeed, to
`remove the resin from the pore spaces requires that still more
`40 chemicals be pumped into the reservoir to "flush" the resin
`from the pore spaces; still more chemicals are required in
`some cases, to "pre-treat" the sand grains so that the resin
`sticks to the sand grains preferentially (hence resists the
`flushing step) but is readily removable from the (un-pre-
`45 treated) pore spaces.
`The present Invention is also directed to sand control, but
`fits in neither of these categories. That is, it is neither
`mechanical nor chemical. The present Invention shall be
`explained below with reference to certain prior art.
`One of the first steps in oil and gas production is drilling
`a wellbore into the hydrocarbon-bearing formation. Next, a
`casing (liner), generally steel, is inserted into the wellbore,
`and forms a gap between the casing and wellbore, typically
`referred to as the annulus. Once the casing is inserted into
`55 the wellbore, it is then cemented in place, by pumping
`cement into the annulus. The reasons for doing this are
`many, but essentially, a liner helps ensure the integrity of the
`wellbore, i.e., so that it does not collapse; another reason for
`the wellbore liner is to isolate different geologic zones, e.g.,
`60 an oil-bearing zone from an (undesirable water-bearing
`zone). By placing a liner in the wellbore and cementing the
`liner to the wellbore, then selectively placing holes in a liner
`cemented to the wellbore, one can effectively isolate certain
`portions of the subsurface, for instance to avoid the
`65 co-production of water along with oil.
`That process of selectively placing holes in the liner and
`cement so that oil and gas can flow from the formation into
`
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`US 6,283,214 Bl
`
`3
`the wellbore and eventually to the surface is generally
`known as "perforating." One common way to do this is to
`lower a perforating gun into the wellbore using a wireline or
`slickline, to the desired depth, then detonate a shaped charge
`within the gun. The shaped charge creates a hole in the
`adjacent wellbore liner and formation behind the liner. This
`hole is known as a "perforation." Perforating guns are
`comprised of a shaped charge mounted on a base. U.S. Pat.
`No. 5,816,343, assigned to Schlumberger Technology
`Corporation, incorporated by reference in its entirety, dis(cid:173)
`cusses prior art perforating systems ( e.g., col. 1., 1. 17).
`We are aware of one group that has examined the role of
`perforation stability on sand production. See, N. Morita,
`Fracturing, Frac Packing, and Formation Failure Control:
`Can Screenless Completions Prevent Sand Production? SPE
`36457 (1998). For instance, these investigators note that
`"Perforation stability significantly improves if the perfora(cid:173)
`tions are shot in the maximum horizontal in-situ stress
`direction, if the two principal horizontal stresses are signifi(cid:173)
`cantly different, or the perforations can be shot in the ,vell 20
`azimuth direction if the well is highly inclined." Id. at 395.
`Yet this articles neither discloses nor suggests a particular
`perforation geometry (other than circular) and particular
`orientation (since that only has meaning if the perforations
`are non-circular)
`In addition, U.S. Pat. No. 5,386,875, Method for Con(cid:173)
`trolling Sand Production of Relatively Unconsolidated For(cid:173)
`mations ( assigned to Halliburton) is directed to a method for
`controlling sand production by optimizing perforation ori(cid:173)
`entation. This patent differs from the present Invention in 30
`part because the '875 patent neither claims, discloses, nor
`suggest<; optimizing the geometry of the perforations (i.e.,
`their shape), but instead is directed solely to their orientation
`around the well casing.
`The present Invention relates to a method of controlling
`the production of sand, based on optimizing the geometry
`and the orientation of perforations. Hence, this method
`suffers from none of the difficulties which plague conven(cid:173)
`tional sand control techniques---e.g., cost (screens) and 40
`diminished permeability (resin consolidation).
`
`35
`
`SUMMARY OF THE INVENTION
`
`4
`stress, improve the stability of the formation in the region
`near the wellbore, hence minimizing sand intrusion. Par(cid:173)
`ticularly preferred embodiments of this aspect of the Inven(cid:173)
`tion are perforations with an aspect ratio of about 5:1, and
`5 having their principal axis substantially aligned (:t: about
`10°) with the direction of maximum compressive stress.
`Having shown that the benefit of producing such unusu(cid:173)
`ally shaped perforations, another aspect of the present Inven(cid:173)
`tion relates to perforating guns ( or the shaped charges
`10 deployed within the guns) modified to produce such perfo(cid:173)
`rations. In preferred embodiments, the shaped charge is
`modified by making the case exterior more oval-shaped. In
`particularly preferred embodiments, the shaped charge is
`modified by modifying the case exterior and interior in
`15 accordance with the disclosure below.
`As evidenced by our preceding remarks, the present
`Invention has numerous advantages over the state-of-the-art
`sand control techniques. For one thing, all of the significant
`disadvantages associated with screen placement are avoided,
`and for another, no chemicals are pumped in the formation,
`which inevitably lead to a loss in permeability. In addition,
`the sand control measures of the present Invention are not
`exclusive-that is, they can be used to supplement existing
`techniques, e.g., a screen-only completion. Put another way,
`25 all cased wellbores must be perforated-regardless of
`whether they are later gravel packed or resin consolidated,
`etc.
`We wish also to note that the present Invention is appli(cid:173)
`cable not just in poorly consolidated formations, but rather
`is a more general system for imparting greater in stability on
`well consolidated formations. For one thing, some of these
`may not produce sand initially, but may much later. In
`addition, the present Invention can be relied upon to stabilize
`formations other than sandstones, for instance carbonate
`formations as well; however, for convenience sake, we shall
`use the shorthand "sand" to refer to particles that disaggre-
`gate from the formation, whether sandstone or carbonate,
`etc. Indeed, not only is the present Invention also suitable for
`other than poorly consolidated sandstone formations
`(subject to immediate sanding) in fact it is best suited to
`other than totally unconsolidated formations. By "totally
`unconsolidated formations" we mean formations subject to
`perforation tunnel collapse shortly after the perforation was
`shot. Obviously, if the formation will not support a perfo-
`45 ration tunnel, then the present Invention is essentially inop(cid:173)
`erable.
`
`We have found that perforations having a particular
`geometry and orientation, impart greater stability to the
`formation surrounding the perforation tunnel. Greater sta(cid:173)
`bility in turn means less disaggregation of the individual
`particles that comprise the formation (i.e., sand in the case
`of a sandstone formation). By "geometry" we mean that the
`perforations are ideally elliptically shaped-when viewed in 50
`cross section perpendicular to an axis defined by the direc(cid:173)
`tion of the perforation tunnel. By "orientation" we mean that
`the perforation ( again defined as the roughly largest cross
`section perpendicular to an axis defined by the perforation
`tunnel): (1) has its major(long) axis substantially parallel to 55
`a plane perpendicular to an axis defined by the perforation
`tunnel; and (2) that major axis is substantially aligned in the
`direction of maximum compressive stress in that plane. In
`other words, item (1) fixes the perforation's orientation
`somewhere in a given plane; item (2) fixes the perforation's 60
`long axis within that plane.
`What we have found is that a particular shape and
`orientation of the perforation minimizes this destabilization,
`hence also minimizes sand production. In particular, and in
`the specific case of a vertical wellbore, for instance, ellip(cid:173)
`tically shaped perforations, having the major axis aligned in
`the direction of maximum principal in situ, or compressive
`
`BRIEF DESCRIPTION OF THE FIGURES
`FIG. la depicts stress concentration ( a) as a function of
`the angle 8 from the x-axis for a circular shaped perforation
`as well as elliptically shaped perforations of different ori(cid:173)
`entations with respect to the principal axis.
`FIGS. lb, le, and ld define what we mean by "perforation
`orientation" (and related terms) as well as illustrate the
`requirement for preferred embodiments that the perforations
`be orientated in a particular way.
`FIG. 2 shows a discretized domain in a stress field for a
`quarter section of a circular perforation.
`FIG. 3 shows contours of shear plastic strain after local(cid:173)
`ization of deformation.
`FIG. 4 shows a displacement field in the vicinity of a
`circular perforation.
`FIG. 5 shows a deformed mesh in the vicinity of a circular
`65 perforation.
`FIG. 6 shows a discretized domain in a stress field
`surrounding a quarter section of an elliptical perforation.
`
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`Page 14 of 19
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`

`

`US 6,283,214 Bl
`
`5
`FIG. 7 shows the change of cross-sectional area with
`applied stress for elliptical and circular perforations having
`the same cross-sectional area.
`FIG. 8 shows contours of shear plastic strain after local(cid:173)
`ization of deformation for an elliptically shaped perforation. 5
`FIG. 9 shows a displacement field in the vicinity of an
`elliptically shaped perforation.
`FIG. 10 shows a deformed mesh in the vicinitv of an
`elliptically shaped perforation.
`'
`FIG. 11 shows contours of shear plastic strain after 10
`localization of deformation for an elliptically shaped perfo(cid:173)
`ration having an aspect ratio a/b=3, and applied stresses
`aifa2 =1.5.
`FIG. 12 is a three-dimensional computer-drawn picture of
`a conventional shaped charge (22 g HMX deep-penetrating 15
`charge used in a 3 1/s' perforating gun) modified by a small
`change to the case exterior (made more elliptical). FIG. 12a
`is a side view from the widest portion of the charge; FIG.
`12b is a view of the narrow side.
`FIG. 13 is a three-dimensional computer-drawn picture of 20
`a conventional shaped charge (22 g HMX deep-penetrating
`charge used in a 3 %' perforating gun) modified by a
`substantial change to the case interior (made more elliptical).
`FIG. 13a is a side view from the widest portion of the
`charge;
`FIG. 13b is a view of the narrow side.
`FIG. 14 is a three-dimensional computer-drawn picture of
`a conventional shaped charge (22 g HMX deep-penetrating
`charge used in a 3 1/s' perforating gun) modified by small
`changes to the case exterior and interior (made more
`elliptical).
`FIG. 14a is a side view from the widest portion of the
`charge;
`FIG. 14b is a view of the narrow side.
`FIG. 15 is a computer-simulated picture of the collapsing
`liner and jet, viewed parallel with the trajectory. This Figure
`shows the jet produced (at 12.5 microseconds) from the
`modified shaped charge in FIG. 12.
`FIG. 15a (left) shows the jet midsection, and
`15b shows the jet tip.
`FIG. 16 is a computer-simulated picture of the collapsing
`liner and jet, viewed parallel with the trajectory. This Figure
`shows the jet produced (at 12.5 microseconds) from the
`modified shaped charge in FIG. 13.
`FIG. 16a (left) shows the jet midsection, and 16b shows
`the jet tip.
`FIG. 17 is a computer-simulated picture of the collapsing
`liner and jet, viewed parallel with the trajectory. This Figure
`shows the jet produced (at 12.5 microseconds) from the
`modified shaped charge in FIG. 14.
`FIG. 17a (left) shows the jet midsection, and 17b shows
`the jet tip.
`FIG. 18 is a side-view schematic of a conventional shaped
`charge (for convenient comparison with FIG. 19 below)
`showing the primary features of the charge: case, explosive,
`and liner.
`FIG. 19 is a schematic of a shape charge modified in
`accordance with the present Invention; 19a is a side-view;
`19b the corresponding view from the rear of the charge;
`FIGS. 19b and 19c show the identical shaped charge,
`except that the charge has been rotated 90°; 19d shows the
`back view corresponding to FIG. 19c.
`
`35
`
`DETAILED DESCRIPTION OF THE
`PREFERRED EMBODIMENTS
`We have found that perforations having a particular
`geometry and orientation, impart greater stability to the
`
`6
`formation surrounding the perforation tunnel. The term
`"greater stability" means that as oil flows from the
`formation, through the perforation and into the wellbore, it
`has an obvious destabilizing effect on the geologic formation
`near the perforation-i.e., it tends to cause it to break down,
`or to cause the individual sand grains to slough off from the
`formation and migrate towards the wellbore, carried by the
`oil. In other words, breakdov,m of the formation in the region
`near the wellbore ( and hence the perforation) leads to sand
`production (assume that the formation is a loosely consoli(cid:173)
`dated sandstone formation, hence as it weakens, loose sand
`grains disaggregate from the formation).
`Before going further, we wish to define several additional
`terms which are critical to properly understand the present
`Invention. One concept crucial to the present Invention is
`"orientation," another is "perforation." As used here, orien(cid:173)
`tation can refer either to the orientation of the perforation
`tunnel axis or the orientation of the major axis of the
`elliptically shaped perforation. The difference between these
`two meanings of the same term needs to be understood; in
`each instance here, the meaning intended by us is either
`expressly stated or is clear from context.
`To best understand these terms, refer to FIGS. lb, le, and
`Id. FIG. le shows an axis 10 defined by the direction of the
`25 perforation tunnel (the direction in \Vhich the jet traveled to
`create the perforation). That is one of the two crucial axes.
`The other is shown in FIG. lb. Again, in preferred embodi(cid:173)
`ments of the present Invention the perforation is an ellipse;
`that ellipse is defined by a cross-section ( cross-section with
`30 respect to the axis shown at 10. Hence, as shown in FIG. lb,
`the term "ellipse," "perforation orientation," and in particu(cid:173)
`lar "perforation," refer to the perforation's cross-section:
`The orientation of that perforation has a major ( or long) axis
`20 and a minor (or short) axis 30.
`FIG. ld shows a perforation shot in a deviated wellbore
`40. (This discussion subsumes the vertical and horizontal
`wellbore cases as well.) As we shall discuss in far more
`detail below, particularly preferred embodiments of the
`present Invention require that the perforation (again defined
`as a cross-section, as shown in FIG. lb): (1) have its major
`axis 20 substantially aligned ("substantially" in this context
`shall be more precisely defined later) in the direction of a
`plant ptrptmlicular lo lht axis formtd by lht ptrforalion
`tunnel (shown at 10); this plane is shown at 50; and (2) this
`major axis is substantially aligned in the direction of the
`formation's maximum compressive stress.
`Having defined crucial terms, we now turn to a discussion
`of the preferred embodiments of the present Invention. We
`50 wish to note that for clarity's sake, the discussion that
`follows is directed to a vertical wellbore, a perforation
`tunnel shot 90° from that wellbore, and the direction of
`maximum compressive stress is vertical.
`Again, conventional methods of sand control are roughly
`55 classifiable into either (1) screens, or (2) chemical consoli(cid:173)
`dation. Chemical consolidation, even if performed properly,
`can lead to diminished permeability of the formation. The
`disadvantages of screens are numerous. See, for instance, N.
`Morita, Fracturing, Frac Packing, and Formation Failure
`60 Control: Can Screenless Completions Prevent Sand Produc(cid:173)
`tion? SPE 36457 (1998). This article is hereby incorporated
`by reference in its entirety. (This article also discusses other
`types of "screenless completions, or means of controlling
`sand production without the use of a screen, not discussed
`65 here.)
`The present Invention is premised upon the insight that
`elliptically shaped perforations, having their major axis
`
`40
`
`45
`
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`

`US 6,283,214 Bl
`
`7
`substantially parallel to the direction of major principal
`compressive stress, is much more stable, than a perforation
`of circular cross-section area having identical flow capacity.
`By "stable" we mean that the perforation, or the formation
`around the perforation, can experience greater drawdown
`and depletion before the production of sand occurs. In other
`words, one particularly preferred set of embodiments of this
`invention relates to methods for controlling sand production,
`comprising shooting elliptically shaped perforations.
`The enabling support for the present Invention is based in
`part upon three separate detailed studies: (1) an elastic stress
`analysis to show enhanced nearwellbore formation stability
`of elliptically shaped perforations; (2) finite element analysis
`to corroborate the (1); and (3) numerical modeling to design
`a shaped charge in a perforating gun that will create ellip(cid:173)
`tically shaped perforations.
`
`EXAMPLE 1
`
`Elastic Stress Analysis
`
`8
`field with respect to the ellipse (i.e., the orientation of the
`ellipse). In particular, FIG. 1 presents modeling results for a
`circular shaped perforation as well as elliptically shaped
`perforations of different orientations v.rith respect to the
`5 principal axis.
`Thus, according to FIG. 1, for a circular perforation, hole
`collapse is expected to occur at a=0 where the stress
`concentration is a,=3aca2 =5a. Hydraulic fracture will
`initiate at a=90, where the stress concentration is min