17th International Symposium on Ballistics
`Midrand, South Africa, March 1998
`A HYDROCODE-DESIGNED WELL PERFORATOR
`WITH EXCEPTIONAL PERFORMANCE
`
`David Davison (1) and Dan Pratt (2)
`
`(1) Shock Transients, Inc., PO Box 5357, Hopkins, MN 55343 USA
`(2) Owen Oil Tools, Inc., 8900 Forum Way, Ft. Worth, TX 76140 USA
`
`The objective of the well perforator improvement effort was to increase the jet
`energy and penetration as much as possible while maintaining the same outer
`dimensions of the perforator body and limiting the explosive mass to 39 gm. The
`strategy was to replace the conical liner with a bell-shaped one of variable thickness,
`similar to ones that have shown significant gains in performance in prior studies. The
`outcome was an improved design that produced a jet with 10% more kinetic energy
`than before, with much of the increase at the back of the jet, where it was most
`effective in increasing the penetration depth. The penetration into the concrete target
`increased by 28% relative to the baseline.
`
`The hydrodynamic computer program AUTODYN 2D™* and its thin-shell jetting
`option and the analytical penetration analysis program JEPETA™† were used to
`evaluate the baseline design and candidate alternative designs.
`
`INTRODUCTION
`
`Perforators, shaped charges for penetrating well casings and hydrocarbon-bearing rocks (Figure 1)
`must be low in cost yet effective to be marketable. The most critical component of the perforator is
`the liner, which is often fabricated by the low-cost process of pressing from a metal powder. For
`rocks of low porosity, the best perforations are ones that are as deep as possible.
`
`Performance is characterized by testing against an American Petroleum Institute target (specifically,
`API RP-43 [API, 1991], Section 1) in which a thick layer of concrete simulates the hydrocarbon-
`bearing rock (Figure 2). The perforator's jet must penetrate the wall of a steel carrier, a fluid layer,
`and a steel wellbore casing before entering the concrete. An effective jet is one that creates a
`smooth, well-rounded hole through the casing as well as a deep, uniform hole in the concrete.
`
`This paper reports the results of an effort to improve the penetration performance of a 2.11-inch
`diameter perforator with a steel body, loaded with 39 gm of HMX explosive. Figure 3 is a pair of
`conceptual diagrams of the baseline and the improved perforators. Features of the baseline and
`improved designs follow:
`
`*AUTODYN 2D is a trade mark of Century Dynamics Inc.
`†JEPETA is a trade mark of Shock Transients, Inc.
`
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`Liner Diameter
`Liner Shape
`Thickness Profile
`
`Baseline
`1.60 in (4.06 cm)
`Conical
`Linear (Tapered)
`
`Improved
`1.73 in (4.39 cm)
`Bell
`Variable (Arbitrary)
`
`Figure 1. Section of a jet gun prior to
`firing. After a well is drilled, a steel casing
`is lowered into place and cement is pumped
`into the annulus between the casing and the
`rock. The jet gun is then lowered to the
`appropriate depth and fired to connect the
`hydrocarbon-bearing rock to the wellbore.
`The jet gun has a steel wall (hollow carrier)
`with thin, scalloped areas through which
`the perforators fire. Perforators are
`sequentially initiated with a detonating cord.
`Thick steel charge cases minimize charge-
`to-charge interference. In the diagram
`above, the gun is vertical, and perforators
`are oriented along vertical planes separated
`by an angle of 60º. After firing the jet gun, the hydrocarbon-bearing rock has many channels or
`perforations through which gas and/or oil flows into the wellbore.
`
`Well Fluid
`
`Casing
`
`Cement
`
`Hydrocarbon-
`Bearing Rock
`
`Detonating Cord
`
`Perforator
`
`Hollow Steel
`Carrier
`
`Scallop
`
`305 cm [120 in]
`
`Casing
`
`152 cm
`[60 in]
`
`Cylindrical
`Steel Form
`
`Concrete
`
`Concrete
`
`Fluid
`
`Casing
`
`Diameter
`
`Jet Gun
`
`Penetration
`
`Figure 2. Perspective cutaway of the API RP 43, Section 1 target [API, 1991] and top view of the target
`showing the eccentric placement of the jet gun within the casing. For this work, the jet gun's outer
`diameter was 11.43 cm (4.50 inches) in diameter, and the casing's outer diameter was 17.78 cm (7.00
`inches).
`
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`Charge Case
`
`Explosive
`Liner
`
`Figure 3. Conceptual
`diagrams of perforators; the
`actual liner shapes are
`proprietary. The baseline
`perforator has a conical liner
`of linear thickness variation,
`and the improved perforator
`has a bell-shaped liner of a
`slightly larger diameter, with a
`variable thickness. The
`improved liner's surface area is
`greater than that of the baseline, and points along the improved liner travel further than points along
`the baseline liner. All of these factors contribute to an improved jet that is more energetic than the
`baseline, and one that creates a deeper and wider perforation in concrete.
`
`Baseline Perforator
`
`Improved Perforator
`
`TEST RESULTS
`
`The baseline and improved perforators were tested against the API target of Figure 2 and against the
`"quality control" (QC) target of Figure 4. Results were as follows:
`
`Entry Hole
`Diameter
`Total Target
`Penetration
`Diameter Hole at Bottom
`
`Target
`API
`QC
`API
`QC
`QC
`
`Baseline
`0.46 in (1.17 cm)
`0.54 in (1.37 cm)
`37.61 in (96 cm)
`41.24 in (105 cm)
`0.05 in (0.13 cm)
`
`Improved
`0.37 in (0.94 cm)
`0.35 in (0.89 cm)
`48.13 in (122 cm)
`49.43 in (126 cm)
`0.20 in (0.51 cm)
`
`Perforator
`
`QC Target
`
`ASTM C33-67 Concrete
`
`0.318 cm (0.125 in) A-36 Steel
`1.717 cm (0.680 in) Water
`
`0.953 cm (0.375 in) A-36 Steel
`
`Figure 4. Perforator and cross-section of quality-control (QC) target; the QC target simulates the API RP
`43 Section 1 target in preliminary testing. A single perforator is fired (vertically) through a target
`consisting of flat steel plates representing the gun wall and casing, enclosing water and backed up by
`stacked, four-inch diameter cylinders of cast concrete. The air gap between the perforator and the target
`was 1.575 cm (0.620 in) thick.
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`Perforations created by the baseline design tapered to a small diameter. Those created by the
`improved design were deeper and did not taper to a small diameter. The latter are more effective in
`bringing hydrocarbons (gas or oil) to the wellbore. The improved design has been named the Owen-
`STI NTX SDP™*. The "STI" in the name recognizes the contribution of Shock Transients, Inc., to the
`design; "NTX" stands for "New Technology, X Series;" and "SDP" stands for "super-deep penetrator."
`
`THEORY
`
`The improved perforator was designed to maximize its efficiency: the liner absorbed a greater
`amount of the explosive's energy than did the liner for the conventional, baseline perforator. Figure 5
`is a plot of velocities as functions of time for several points along a liner. The plot illustrates the
`difference between the velocity histories for baseline and the improved perforators. Further details of
`the design process can be found in [Davison and Arvidsson, 1985] and [Davison and Nordell, 1992].
`
`Velocity (cm/µs)
`t = t for Efficient Shaped Charge
`c
`
`Extrapolated
`Velocities
`
`0.35
`0.30
`0.25
`0.20
`0.15
`0.10
`0.05
`0.00
`0
`
`1
`
`2
`
`3
`
`t = t for Inefficient Shaped Charge
`c
`4
`5
`6
`7
`8
`9
`Time (µs)
`Figure 5. Velocity as a function of time for several points along a shaped charge liner. tc, the collapse
`time, is the time at which the liner reaches the axis of symmetry, giving up its kinetic energy to the jet and
`slug. The kinetic energy of a jet element is proportional to that of the associated liner element at the
`moment of collapse, and the kinetic energy of a liner element is proportional to the square of its velocity.
`For an inefficient shaped charge the liner reaches the axis of symmetry while the velocity curve is steep.
`For an efficient shaped charge the liner reaches the axis of symmetry when the velocity curve has begun
`to level off. Shaped charges with bell-shaped liners are more efficient than those with conical or trumpet-
`shaped liners. The liner surface area is greater, and points along the liner are further from the axis of
`symmetry, allowing more time for the explosive to act on it.
`
`The following is a summary of the shaped charge design approach: (1) Compute the perforator
`jetting with the definitive AUTODYN 2D program; (2) Compute the hole shape using the analytical
`penetration theory; (3) Derive liners that give jets of maximum energy and holes of maximum size; (4)
`Test the most promising designs; and (5) Iterate to converge on the "best" design(s).
`
`Usage of AUTODYN 2D in shaped charge calculations is described in [Birnbaum and Cowler,
`1989]. The liner is characterized as a jetting thin shell coupled to a fully two-dimensional
`representation of the explosive. The jet is modeled in accordance to the theory described in [Pugh et
`al., 1952].
`
`*Owen-STI NTX SDP is a trade mark of Owen Oil Tools, Inc.
`
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`The JEPETA program takes the jet produced by the jetting thin shell model in AUTODYN 2D and
`computes its effect on a target. JEPETA includes the influence of target strength and jet breakup. It
`starts with the equations of [Eichelberger, 1956] and [Birkhoff et al., 1948] and continues with those of
`[Allen, 1977].
`
`L j
`p
`For JEPETA, the incremental penetration  p is 
`, where  Lj is the length of the jet
`/
`
`increment including air spaces,  is the ratio of  Lj to the length of the solid particles in the jet
`increment, and 
`j. The incremental hole
`j for respective target and jet densities t and
`t
`volume V is proportional to the incremental jet kinetic energy; the ratio of energy to volume, ES, is
`the target's specific energy. The jet's incremental kinetic energy depends on its incremental length,
`diameter, and velocity. The hole radius is r
`V
`p
`/
`.
`h  
`Some focusing (diameter reduction) of a powdered metal jet occurs when it passes through concrete and
`rocks such as sandstone and limestone [Aseltine, 1985]. In addition to focusing, rocks (and, to a lesser
`degree, concrete) also disturb jets, because of asymmetries and constrictions, reducing their effectiveness.
`When rocks contain hydrocarbons in their pores, the disturbance decreases, suggesting that crushing of
`the rock is a factor in the disturbance. Finally, jets are disrupted by reflections of shocks off target
`boundaries such as those of the QC configuration shown in Figure 4.
`
`Of the four effects (focusing, disturbance, crushing, and disruption) observed and described by Aseltine,
`the first, focusing, causes the jet to be more effective than otherwise by concentrating the particles on the
`axis of symmetry. It remains dense and continuous, and it can be modeled as such in JEPETA.
`
`The other three effects result from asymmetries or non-uniformities and are not modeled by the JEPETA
`computer program, which considers targets to be uniform and infinite in diameter. Consequently, JEPETA
`over-predicts penetration when these effects occur.
`
`AUTODYN 2D ANALYSIS
`
`The liners for the baseline and improved perforators were pressed from powdered metal, primarily
`tungsten and copper. The average density for the baseline liner was determined from the weight in air
`and in water to be 11.04 gm/cm³. Liners were sectioned axially into thirds, and densities for each
`third were measured. As indicated in Figure 6, a curve was fit through the data. The curve was used
`for making adjustments to thicknesses in the AUTODYN 2D analysis of the baseline so that the liner
`mass distribution would be correct. The adjustment was made in reverse to obtain the correct
`thicknesses for fabrication of the improved design.
`
`Figure 7 is a set of velocity curves for the baseline and a set for the improved design. The following
`table lists features of the two jets:
`
`Jet Feature
`Tip/Tail Velocity (cm/ s)
`Mass (gm)
`Kinetic Energy (kJ)
`
`Baseline
`0.703/0.101
`10.8
`62.4
`
`Improved
`0.695/0.118
`11.9
`68.8
`
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`Both the mass and the kinetic energy of the jet from the improved design were 10% greater than that
`of the baseline. The increase was greatest at the aft end of the jet, which had the greatest effect deep
`within the target.
`
`Figure 6. Liner density as a function of radius.
`Measured densities are marked with "pluses" on the
`figure above. The line is an exponential fit through
`the measurements. At each point, the thickness in
`the AUTODYN 2D calculation was adjusted by the
`ratio of the actual density to that assumed in the
`analysis to obtain the thickness for liner fabrication.
`This process assured that the masses in the
`AUTODYN 2D calculation were properly
`distributed along the liner.
`
`Density (gm/cm³)
`
` Exponential Fit to Data
`
`Average Density
`11.04 gm/cm³
`
`15
`
`14
`
`13
`
`12
`
`11
`
`10
`0.0
`
`Figure 8 is a pair of plots showing the theoretical
`hole shapes and energy depositions for the baseline
`and improved designs. For the JEPETA analysis, a jet density of 14.0 gm/cm³ and a breakup time of 140 
`s were assumed. The breakup time value is large for a shaped charge of this size, but it is appropriate for a
`focused jet of powdered metal penetrating concrete, as discussed above. The constriction in the hole
`created by the baseline design appears to have disturbed the jet, making it less effective.
`
`0.6
`0.4
`0.2
`Relative Radius, R/Ro
`
`0.8
`
`1.0
`
`The API RP 43 test configuration of Figure 2 was assumed for the analysis. The following values
`were used:
`
`ES
`Strength
`Density
`(J/cm³)
`(kbar)
`(kpsi)
`(gm/cm³)
`Material
`Layer
`–
`–
`–
`0.0013
`Air
`Gap
`4000
`10.3
`150
`7.86
`4140 Steel
`Scallop
`20
`–
`–
`1.00
`Water
`Fluid
`3100
`6.2
`90
`7.86
`L80 Steel
`Casing
`800
`0.37*
`5.4*
`2.20
`Concrete ASTM C33-67
`*Compressive
`**Actual thickness of the API annulus is 55 inches
`
`Thickness
`(cm)
`(in)
`1.575
`0.620
`0.318
`0.125
`1.727
`0.680
`1.151
`0.453
`200
`79**
`
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`Velocity (cm/µs)
`
`Improved
`
`0.695 cm/µs
`Vj
`
`VC
`
`vV
`
`0
`
`0
`
`2
`
`8
`6
`4
`Cumulative Mass (gm)
`
`10
`
`12
`
`1.0
`0.8
`0.6
`0.4
`0.2
`0.0
`
`Velocity (cm/µs)
`
`Baseline
`
`0.703 cm/µs
`
`Vj
`
`VC
`
`vV
`
`0
`
`0
`
`2
`
`8
`6
`4
`Cumulative Mass (gm)
`
`10
`
`12
`
`1.0
`0.8
`0.6
`0.4
`0.2
`0.0
`
`Figure 7. Velocities as functions of mass for the baseline and improved perforators. Plotted are the liner
`collapse velocity V0, the relative velocity v, the stagnation point (collapse point) velocity VC, and the jet
`velocity Vj. Note that Vj = VC + v. The heavy line is the mass- or momentum-averaged jet velocity profile
`that results when fast particles at the back of the jet interact with slower ones in front; the resulting jet tip
`velocity is indicated.
`
`Calc. Exp.
`
`Radius (cm)
`
`Baseline
`Improved
`(Constriction)
`
`2.0
`
`1.5
`
`1.0
`
`0.5
`
`0.0
`
`0
`
`20 40 60 80 100 120 140 160
`Total Target Penetration (cm)
`
`0.8
`
`0.6
`
`0.4
`
`0.2
`
`0.0
`
`Energy Deposition (gm·cm/µs)
`Improved
`
`Baseline
`
`0
`
`20 40 60 80 100 120 140 160
`Total Target Penetration (cm)
`
`Figure 8. Theoretical hole profiles and energy depositions from JEPETA analysis and measurements on
`the holes in the experiments. Total target penetration starts at the face of the well casing (it includes the
`casing thickness). The energy deposition is the amount of jet kinetic energy required to reach a given
`penetration into the target. The radius of the hole tended to be greater for the improved design, and more
`energy was deposited deep in the target. The hole for the baseline design had a constriction at a penetration
`of approximately 70 cm that was eliminated by the improved design. Although the total target penetration
`computed by JEPETA for the baseline design (146 cm) was greater than the penetration computed for the
`improved design (135 cm), the experiments gave an opposite trend (96 cm for the baseline and 122 cm for
`the improved design).
`
`The specific energy values for the metals in the table above are estimates based on published data for
`copper jets penetrating steel targets [DiPersio and Simon, 1968], adjusted by the inverse square
`root of the jet density, as suggested by hypervelocity impact data, for example [Maiden et al., 1960].
`The 800 J/cm³ specific energy value for the concrete was estimated from the data reported here for
`the improved design. The 20 J/cm³ specific energy value for the water is hypothetical.
`
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`DISCUSSION
`
`Using the hydrocode AUTODYN 2D, an improved design was derived that showed promise
`because it had a greater jet kinetic energy than the baseline and would use the additional energy deep
`within the target. The JEPETA calculations indicated that the improved design would widen the hole
`in cement, the nominal rock-simulating target medium, and would consequently decrease the
`disturbance to the jet as it created the perforation.
`
`The experiments confirmed a wider hole and less disturbance, as evidenced by a 28% increase in the
`penetration. The productivity of an oil or gas well is proportional to the flow, which is primarily
`proportional to the depth of a perforation [Halleck and Dogulu, 1997]. Hence the 28% increase in
`penetration depth equates to a 28% increase in productivity.
`
`In gas wells the velocity down a perforation and into the wellbore can be large in some cases, in
`particular, cases in which the wells have a large pressure drop between the rock and the wellbore
`and have holes through the casing that are reasonably large (that do not choke the flow). For these
`cases, the flow can be retarded by friction caused by roughness of the walls of the perforation. The
`retardation is reduced by increasing the diameter of the perforation. It follows that the improved
`perforator will be especially effective for gas wells of this type.
`
`CONCLUSIONS
`
`Calculations with AUTODYN 2D yielded an improved perforator design characterized by a
`potential to deposit a greater amount of energy deep within hydrocarbon-bearing rocks and their
`simulants (for example, concrete). Experiments comparing a baseline design to an improved design
`with 10% more jet kinetic energy confirmed that the depth and diameter of the perforation could be
`increased by this design strategy. The depth of the perforation increased by 28% and the diameter at
`hole bottom, by 300%.
`
`REFERENCES
`
`[Allen, 1977] F.J. Allen, Discussion and Extension of Methods of Calculating Shaped Charge Jet
`Penetration, BRL Memo Report 2773, July 1977. ADB020661.
`
`[API, 1991] Evaluation of Well Perforators, Recommended Practice RP 43, American Petroleum
`Institute (API), January 1991.
`
`[Aseltine, 1985] Aseltine, C.L., "Flash X-Ray Analysis of the Interaction of Perforators with Different
`Target Materials," Proceedings of the 60th Annual Technical Conference and Exhibition, SPE, September
`1985. SPE Paper Number 14322.
`
`[Birkhoff et al., 1948] G. Birkhoff, D.P. MacDougal, E.M. Pugh, and G. Taylor, "Explosives with Lined
`Cavities," J. Appl. Phys., 19, p. 563, June 1948.
`
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`[Birnbaum and Cowler, 1989] N. Birnbaum and M. Cowler, "A Combined Numerical/Analytical
`Approach for Shaped Charge Design," Proceedings of the Eleventh International Symposium on
`Ballistics, ADPA, Paper WM-20, v. 2, p. 179, May 1989.
`
`[Davison and Arvidsson, 1985] D. Davison and B. Arvidsson, "Optimization of a 90 mm Shaped Charge
`Warhead" (with B.K. Arvidsson), Second Symposium on the Interaction of Non-Nuclear Munitions with
`Structures, USAF, p. 186, April 1985.
`
`[Davison and Nordell, 1992] D. Davison and A. Nordell, "Optimization Process Giving an Exceptional
`Boost in Shaped Charge Jet Energy with No Weight Penalty," Proceedings of the 13th International Sym-
`posium on Ballistics, ADPA, Paper WM-27, v. 2, p. 521, June 1992.
`
`[DiPersio and Simon, 1968] R. DiPersio and J. Simon, The Effect of Target Hardness on the
`Penetration Capability of Shaped-Charge Jets, BRL Report 1408, July 1968. AD 838991.
`
`[Eichelberger, 1956] R.J. Eichelberger, "Experimental Test of the Theory of Penetration by Metallic Jets,"
`J. Appl. Phys., 27, 1, p. 63, January 1956.
`
`[Halleck and Dogulu, 1997] P.M. Halleck and Y.S. Dogulu, "The Basis and the Use of the API
`RP43 Flow Test for Shaped-Charge Oil Well Perforators," Journal of Canadian Petroleum
`Technology, 36, 5, p. 53, May 1997.
`
`[Maiden et al., 1960] C.J. Maiden, J. Charest, and H.P. Tardif, "An Investigation of Spalling and
`Crater Formation by Hypervelocity Projectiles," Proceedings of the Fourth Symposium on
`Hypervelocity Impact, v. 3, paper no. 38, April 1960.
`
`[Pugh et al., 1952] E.M. Pugh, R.J. Eichelberger, and N. Rostoker, "Theory of Jet Formation by
`Charges with Lined Conical Cavities," J. Appl. Phys., v. 23, no. 5, p. 532, May 1952.
`
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