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SPE 27424 Simple Method Predicts Downhole Shaped-Charge Performance R.E. Ott, SPE, Mobil E&P US Inc.; W. T. Bell, Consultant; J.W. Harrigan Jr., SPE, Schlumberger Wireline and Testing; and T. G. Golian, Shaped Charge Specialist Inc. Copyright 1994, Society of Petroleum Engineers Original SPE manuscript received for review July 9, 1993. Revised manuscript received April 12, 1994, and accepted for publication April 25, 1994. Reprinted herein, the paper was originally published in SPE Production & Facilities (August 1994), 171-178. The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain the conspicuous acknowledgement of where and by whom the paper is presented. Write Publications manager, SPE, P.O. Box 833836, Richardson, TX 75083-3836 U.S. A. Telex, 730989 SPEDAL.

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Summary

A simple method is proposed for predicting downhole shaped-charge gun performance based on the use of API RP-43, Edition 5, Sec. 1 data. API Sec. 1 has been the preferred method for assessing perforation gun system performance because of the simplicity of the test and its use of standard field guns fired at maximum shot densities and positioned as they would be in an actual well. The validity of the proposed method is demonstrated, allaying past concerns regarding the translation of data from Sec. 1 nonrock, nonstressed concrete targets to downhole conditions. The new method is based on an observed linear relationship between Edition 5, Sec. 1 and Sec. 2 penetration information. The applicability of the well-known Thompson relationship between formation compressive strength and perforator penetration to Edition 5, Sec. 2 and therefore to Sec. 1 data is shown. Incorporating necessary corrections for casing entrance hole size, downhole effective formation stress, and casing configurations different from those in the API test completes the translation of surface data to downhole conditions.

Introduction Well performance is significantly affected by the extent of perforated hole penetration into the formation and the hole size in the casing, together with other fixed geometric parameters, such as shot density and gun

phasing.1 Values of perforation penetration and hole size commonly available to the completion designer are provided by API RP-43, Edition 52 published data. These data are derived from tests at the surface and provide only limited simulation of subsurface conditions regarding formation physical properties and stress. Surface data can significantly vary from that to be expected downhole and must be converted to in-situ values before proceeding with well flow performance calculations.3 This conversion of RP 43, Edition 5 surface test performance to downhole involves consideration of the specific downhole formation physical properties, formation in-situ stress, casing properties, and the specific gun-to-casing configuration.

This paper reviews the factors affecting downhole penetration and casing entrance hole size for perforating guns, discusses API data as a basis for predicting downhole performance, reviews API test results and results of tests performed specifically for this paper, and proposes a procedure for translating surface API data to downhole conditions.

Factors Affecting Downhole Performance of Perforating Guns

Gun-to-Casing Clearance. Clearance, the distance between the gun OD and the casing ID along the axis of the shaped-charge jet, can have a significant effect on total penetration, L, and casing entrance hole size, deh.4 As Fig. 1 shows, the estimated downhole L/deh of a commercial 3⅜-in. gun perforating 7-in. casing varies from 14.45 in./0.35 in. to 7.65 in./0.21 in. when operated in the common eccentric running position (Fig. 1a). Values are constant when clearance is controlled (Figs. 1b and 1c), typical methods for positioning guns. The importance of the gun-to-casing arrangement is evident; it is the estimated downhole L/deh used in mathematical models to calculate will flow.1,5

Formation Strength. Compressive strength of the formation being penetrated influences perforation

2 R.E. OTT, W. T. BELL, J.W. HARRIGAN Jr. AND T.G. GOLIAN

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penetration depth. Thompson6 disclosed a semi-log relationship between formation wet compressive strength and total penetration depth (casing thickness + cement thickness + formation penetration) for API Edition 4 Section 2 type targets. Penetration performance in unstressed sandstones and limestones of different compressive strengths is available in the literature.6,7

The high-strength end of Thompson’s relationship (beyond 14,000 psi) was modified by data from Weeks’ 8 formula, resulting in the composite representation in Fig. 2. As Fig. 2 indicates, a perforating gun that provides a penetration of 11.8 in. in rock with a wet compressive strength of 7,000 psi (Point A) will penetrate less than 7 in. in a 14,000 psi formation (Point B). On the other hand, it would penetrate 15 in. in a 3,000 psi material (Point C).

Use of mean wet uniaxial compressive strength, S, values is suggested in applying the above relationship.9 S is defined as the average of compressive strength values taken perpendicular and parallel to the bedding plane of saturated rock. It is related to the commonly used dry compressive strength measured perpendicular to bedding plane, Sd, as follows10:

S=0.73Sd. ……………...………………………….(1)

When the value of S is unavailable, it may be approximated using formation porosity by means of Fig. 3, which is derived from the results of tests in several sandstones and limestones.3,6,9,11 These tests were performed in cores taken from surface outcrops, and results might be somewhat different in downhole formations. Data are limited below about 15% porosity for sandstones. Additional work should be done to improve the definition of the porosity/compressive strength relationship over a broader range of porosity and over a larger number of formation rocks. Nevertheless, in the range of 18% to 23% porosity, substantial and consistent data are available, providing a good curve fit.

Formation Effective Stress. Formation effective stress is the overburden stress, po, minus the reservoir or pore pressure, pp

3,12:

σ=po-pp, ……………………………...……………(2)

where all factors are measured in psi.

Stress reduces penetration (Fig. 4).3,13,14 Conceptually, increasing stress makes the formation appear stronger. When predicting downhole performance from API test results, the effect can result in either a reduction or a gain in estimated penetration. The magnitude and nature of the effect will depend on stress in the formation compared with the stress in the RP 43, Edition 5 tests. Specifics are developed later.

Hydrostatic Pressure. Although wellbore pressure tends to reduce penetration, the correlation for these hydrostatic

pressure effects is included in the formation effective stress correction described above.15

Casing Strength. Casing grade affects perforation entrance hole diameter, deh, to a significant degree but exerts only a negligible effect on penetration across the typical API Sec. 1 test range of single casing-wall thicknesses.16

In single-casing completions, deh varies with the midrange Brinell hardness, H, of the particular casing grade, according to the following expression17:

dehdownhole=dehSec. 1[3,186.6/(2,250+4.2Hdownhole]0.5, ..(3)

where dehSec. 1 is measured in the Grade L-80 casing specified in RP 43 Sec. 1, Edition 5. Fig. 5 provides a graphical representation of Eq. 3. As Fig. 5 indicates, deh in P-110 casing would decrease about 4.5% from the API Sec. 1 reference value, while deh in Grade J-55 pipe would increase about 3%. Table 1 provides the relationship between casing grade and physical properties.17 Casing-wall thickness typically manifests a negligible effect of deh.16 However, the exit hole in the casing will decrease a few percent in thicker casings.

Note that the literature sets forth three different relationships for estimated downhole deh size. The one indicated in Eq. 3 is most common; the second18 agrees within about 2%. The third16 shows an effect that is significantly greater than the others and is not supported by data developed on today’s charges.

In multicasing completions, deh in the inner concentric casing may be predicted from Eq. 3. Values of deh for the second and third strings must be determined from tests simulating downhole configurations because no simple, reliable predictive relationships exist.

Penetration will be reduced by the presence of additional strings. The reduction can be approximated by modifying the API Sec. 1 penetration, LAPI, to take into account the additional strings and cement, LAPI’. The remaining penetration value is then translated downhole, as discussed later. The most common approach for addressing multiple casings is Eq. 4. LAPI’ for a three-string configuration is:

LAPI’=LAPI-3.5(h1+h2)-htc, ……..…………………..(4)

where h1 and h2 are the first and second string wall thicknesses and htc is the total cement thickness between the first and third strings.

The approach involves the use of data generated in the Exxon Perforator Evaluation.19

Predicting Downhole Performance From API Data

RP 43 Edition 5 procedures were developed primarily to provide a basis for comparing performance levels of different commercial charges under controlled surface test

SIMPLE METHOD PREDICTS DOWNHOLE SHAPED-CHARGE GUN PERFORMANCE 3

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conditions. The foregoing factors that influence L and deh of the perforator downhole are only partially simulated, depending on the particular API test (e.g., Sec. 1, Sec. 2). Nevertheless, API tests are designed to measure performance under specific reference conditions, and the results of these tests can provide the basis for predicting downhole performance.

API Section 1 – Evaluation of Perforating Systems Under Surface Conditions: Concrete Targets. Shown schematically in Fig. 6, the Sec. 1 test simulates the important downhole gun-to-casing configuration depicted in Fig. 1, providing directly the desired reference L and deh. Specific formation strength and effective stress are not simulated. The test provides data from standard field guns fired at maximum shot densities through L-80 casing into controlled-strength concrete where no less than 8 to 12 charges are fired under ambient-temperature and atmospheric-pressure test conditions. The gun is positioned as it will be run in the well (eccentered, centralized, or positioned) to reflect clearance effects accurately (Fig. 1).

Compressive strength of the concrete target is specified to be 5,000 psi minimum based on dry test briquet measurements made at the time that the shooting test is performed. Compressive strengths have been seen to range as high as 9,000 psi, which can give rise to penetration differences with the same gun/charge as high as 28% or about 7% per 1,000-psi change in dry compressive strength.20

The actual internal dry compressive strength, Sdry, of the target is different from the briquet value, Sdb. A replot of data from the literature10 (Fig. 7) shows that internal strength is very close to:

Sdry=0.67Sdb. ………..……………………………..(5)

The information presented in Fig. 7 is somewhat limited, and additional work might be profitable directed toward better defining briquet vs. target internal compressive strengths for API Sec. 1 targets.

As will be seen later, the internal dry compressive stength is further corrected to provide an equivalent, or pseudo, mean wet compressive strength for use in predicting downhole L. In terms of deh, the API-specified L-80 casing provides a good basis for predicting hole size in other grades of pipe using Eq. 3.

In addition to providing the desired downhole configuration, this test provides the most complete and best measure of gun system performance of all the API tests. It satisfies the concern that individually fired charges may not always perform as they do within a gun system at high shot density. Statistics also are better because more data are provided at conditions of specific interest.

In some instances, API data will not be available for a particular casing size. For example, assume that data are available on a 3⅜-in. gun eccentered in 5½-in. casing but the downhole configuration involves 7-in. casing. In such a case, there are two approaches for predicting downhole L and deh performance. The preferred approach is to request that the service company perform a Sec. 1 test in the desired casing size. The second approach involves estimating Sec. 1 performance in the casing of interest. L values at the higher clearance can be estimated by assuming that the distance from the center of the gun to the end of the perforated hole is constant.21 The accuracy of this approximating diminishes at higher clearances (Fig. 1). Regarding deh, extrapolation of data to larger gun-to-casing clearances is open to significant inaccuracies, emphasizing the need for tests in the casing of interest.

API Sec. 2 – Evaluation of Perforators Under Stress Conditions: Berea Target. Designed to measure L under simulated stress conditions, the Sec. 2 test uses a Berea sandstone target. Use of the stressed target was intended to provide penetration values representative of those expected downhole. An effective stress of 3,000 psi was selected as the best compromise between downhole simulation and cost of testing. Fig. 8 compares the Edition 5 stressed target configuration with the former Edition 4 unstressed system. A mild steel target face plate is used for both systems to simulate casing, and three shots are made, one at a time. All shots are made at 0.5-in. gun-casing clearance.

As indicated in Fig. 9, the 3,000 psi stress level accounts for most of the effect expected in a reservoir. Fig. 9 is a replot of Fig. 4 data normalized to the 3,000 psi stress level and fitted to a single curve. The validity of the information in Fig. 9 has been confirmed by recent test data. Caution should be exercised at stress levels much below 3,000 psi because the accuracy diminishes as a result of perforator and rock strength dependency.

Translating Sec. 2 performance to downhole conditions involves a number of considerations. The fixed 0.5-in. clearance requires adjustments to L as described in the previous section. Moreover, L values derived from the Sec. 2 test are subject to variations in Berea target properties. Berea porosity is controlled by API Edition 5 specifications to 19% to 21%, corresponding to an S range of 6,100 to 7,900 psi. That range can give rise to a P variation of 15% within the test specification.6,20 Thus, any use of data for comparing competitive charges directly or predicting downhole values must consider target strength variations.

Entrance hole in the mild steel face-plate used in Sec. 2 testing cannot be converted to downhole conditions; the Sec. 1 test must be used for hole size data.


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API Sec. 3 – Evaluation of Perforator Systems at Elevated Temperature Conditions. Although not directly applicable to the context of this paper, Sec. 3 provides the basis for establishing that the perforator system, including charges, will perform reliably at rated temperature, pressure, and exposure time. Gun performance, as measured under Sec. 3 simulated downhole conditions of temperature and pressure, should be within about 5% of performance at ambient temperature and atmospheric pressure. Generally, Sec. 3 test results at temperature have been observed to be better than those at ambient temperature by about 5% for published exposure times.

Sec. 3 data may not always be available. The test is optional under API Edition 5 procedures; i.e., the test is not required, nor do the data have to be filed with the API.2

API Sec. 4 – Evaluation of Perforation Flow Performance Under Simulated Downhole Conditions. Test configuration is similar to Sec. 2 (Fig. 8b). The test is designed to provide a measure of perforation flow performance in either quarry rock or an actual will core. A set of standard conditions for testing in Berea is also provided. Shots are made under site-specific simulated conditions of overburden load and pore pressure. Tests involve individual shots at a single clearance, as in Sec. 2, but the Sec. 4 test clearance can be adjusted at the discretion of the service company or operator.

When field cores are used, the test provides a direct measurement of L under site-specific downhole conditions subject to adjustments in L to accommodate gun-to-casing clearance. If Berea is used, L must be adjusted for rock compressive strength and clearance. In either case, the deh data are unreliable, as in the Sec. 2 test. Sec. 1 deh performance must be used for predicting downhole values.

The Sec. 4 test includes provisions for measuring flow performance of the perforation. Flow test results can be used to determine the perforator damaged-zone permeability reduction factor,2 a useful parameter in well flow analysis.

Sec. 4 is also an optional test. Data are typically not available on a gun of interest or in a specific formation at unique downhole conditions. Edition 5 does not require the test to be performed, not do the data have to be filed with the API.2

A New Method for Predicting Downhole Performance

Sec. 1 has long been the preferred method for assessing perforating gun system performance. Reasons for this popularity include the simplicity of the test and the use of standard field guns fired at maximum shot densities and positioned as they would be in the well. Moreover, Sec. 1

has always been relied on for casing hole size data. However, questions have persisted regarding target properties and stress effects. A particular concern was that charges of different sizes and types might perform differently in the nonrock, nonstressed, lower-strength concrete target.

Consequently, the industry has continued to rely on Sec. 2 for penetration values because real rock (Berea) is used, and the test has always been conducted under some degree of downhole simulation – first pressure and temperature, and now the effect stress elements of Edition 5. However, data recently developed by the RP 43 committee and the authors indicate that average Sec. 1 data can be used in lieu of Sec. 2 data for penetration performance with essentially the same level of confidence. As a result, a simplier method for predicting downhole performance is proposed.

A review of published API data suggests a linear relationship between Sec. 1 and 2 performance (Fig. 10). Although there is dispersion in the data, a ratio of 0.69 fits the data reasonably well, and the ratio is considered valid in view of the large number of data points, which tend to minimize the effects of variations in target physical characteristics. Moreover, the ratio has been verified with recent Edition 5 data together with the supplementary test data presented in Table 2 and Fig. 11. The raw data in Table 2 and Fig. 11, uncorrected for differences in target physical properties, confirmed essentially the same linear relationship with a ratio of 0.70. It is suggested that the relative accuracy and reproducibility of Sec. 1 and 2 tests are, for all practical purposes, identical. Consequently, results from either test are applicable for converting API data to downhole conditions.

A somewhat surprising observation is presented in Fig. 12. Significant differences are not observed between results of tests in the unstressed Sec. 2, Edition 4 target and the stressed Sec. 2, Edition 5 configuration. The information in Fig. 12 suggests the penetration differences expected to result from the use of Edition 5 with its different target geometry factors compared with Edition 4,3.13,22 as well as the applied stress, are not materializing. It appears that the target configuration for the Edition 4, Sec. 2 test effectively simulates the effects of the 3,000-psi applied stress of Edition 5. The steel container and cement used for the Edition 4 target (Fig. 8a) apparently reduces penetration in a manner similar to an applied stress of 3,000-psi.

The significance of the observation is that Thompson’s data (Fig. 2), which was generated using a target configuration identical to Sec. 2, Edition 4, essentially manifests an effective stress level of 3,000 psi. It follows that Sec. 2, Edition 5 data can be applied directly to the Thompson data in Fig. 2 to predict downhole L at different levels of mean wet compressive strength.


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Moreover, because Sec. 1, Edition 5 has been shown to have a specific linear relationship to Sec. 2 (Fig. 11), the Sec. 1 data may be applied directly to the Thompson curves (Fig. 2) in place of the Sec. 2 information by simply observing an appropriate target compressive strength correction.

Fig. 13 shows an example of these relationships. Points A and B represent Edition 5, Sec. 2 and 1 data, respectively, from Table 2. For Point B (Sec. 1) to maintain the Thompson relationship with Point A (Sec. 2), it will have to be projected horizontally to the left until it intersects the appropriate Thompson curve. The projection results in Point C, which provides the equivalent, or pseudo, mean wet compressive strength for Sec. 1.

Applying the foregoing procedure to the information in Table 2, the average correction factor for determining equivalent Sec. 1 mean wet compressive strength was found to be 0.41. Thus,

Sw=0.41Sdb, ………………..………………………(6)

where Sw is the equivalent mean wet compressive strength and Sdb is the compressive strength of the dry briquet. The correction factor was applied to the dry-briquet compressive strengths in Table 2 to determine the calculated strengths. These data were used to predict Sec. 2 performance using the Thompson relationship. As indicated in Table 2, agreement between the measured Sec. 2 penetration and the penetration predicted by Sec. 2 from the corrected Sec. 1 data was generally quite good. Further support for the validity of using the foregoing procedure in predicting downhole penetration performance, notwithstanding the small target configuration of Fig. 8a, is evidenced by the equivalent results obtained in the large tests described in the literature.22

As indicated in Table 2, several perforators varied from the average. While the information in Table 2 is published API data, the manufacturers of the three perforators (B, D, and O) expressed concern over the recorded target strengths. Nevertheless, removing the three perforators from the calculations does not change the overall average significantly and does not in any way invalidate the procedure. The variations support the earlier suggestion that additional work should be directed toward better defining briquet vs. internal target strength.

The logic underlying the procedure for predicting downhole penetration performance from API Edition 5 data may be summarized as follows: Observation of a linear relationship between Sec. 1 and 2 API data for both Editions 4 and 5 (Figs. 10 and 11); essentially identical results from Sec. 2 tests for both Editions 4 and 5 (Fig. 12); validity of applying Section 2 data to Thompson’s curve because Thompson’s target configuration was identical to Sec. 2, Edition 4 target; and validity of

applying Sec. 1, Edition 5 data directly to Thompson’s curve, observing an appropriate compressive strength correction (Fig. 13) that is confirmed by publishing Edition 5, Sec. 1 and 2 data.

Once the Sec. 1, Edition 5 penetration is corrected for strength, influence of stress levels higher or lower than the reference 3,000-psi effective stress can be corrected by means of Fig. 9, which provides good accuracy under most downhole stress conditions, particularly at stress levels of 3,000-psi or higher. As suggested by Fig. 4 and the literature,3,13 the accuracy will be reduced at stress levels below 3,000 psi.

The actual formation penetration required for prediction of well flow performance can be determined by subtracting the thickness of the cement sheath and casing from the total penetration (corrected for API target strength, downhole formation strength, and effective stress) as follows for single casing strings:

Lp=Ls-0.5(dw-di), ………………………………….(7)

where Lp=downhole perforation length (in the formation), Ls=penetration LAPI corrected for formation strength and effective stress, dw=wellbore diameter, and di=casing ID.

For multiple casing strings, the first and second casing strings and the cement between the first and third strings must be subtracted from the API test penetration (use LAPI’ from Eq. 4) before applying corrections for downhole conditions. Therefore, only the third casing string, di3, and the thickness of the cement sheath remain to be subtracted from the total penetration, LS’:

Lp=LS-0.5(dw-di3). …………………………………(8)

Although the multiple string method (using Eqs. 4 and 8) provides a reasonable estimate for downhole Lp, accurate test data should be obtained from the service company on the multistring configuration of interest.

Finally, for deep penetrating perforators used in natural completions, average casing entrance hole diameter, deh, is determined by applying the correction factor from Fig. 5 to the Sec. 1, Edition 5 average deh data. If the downhole casing ID is not more than about 1 in. larger than that used in the API test (e.g., API casing was about 4½ in. in diameter, downhole is 5½ in.), the API average deh may be used for downhole deh determinations. However, if the casing ID is more than 1 in. larger (e.g., API shot in 4½-in. pipe, downhole is 7 in.), a special test must be performed to ensure reasonably accurate downhole deh predictions.

If the completion of interest involves a big-hole perforator and a gravel pack or completion where gas flow is anticipated, deh information must be determined in Sec. 1 tests in the specific casing of interest. Further, the predicted downhole deh data must be determined using the


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average of the squares of the diameters of the individual entrance holes.

A Specific Example of the Procedure

A nomograph (Fig. 14) derived from the foregoing relationships facilitates correcting Sec. 1, Edition 5 test data to approximate downhole performance. Table 3 gives a hypothetical example.

Qualifications/Limitations While the proposed method is approximate, the accuracy of a downhole penetration prediction is entirely acceptable in terms of well flow calculation differences (e.g., in sensitivity analysis), assuming, of course, that API test data are representative of production charges and that the data are generated in accordance with API test specifications. Such assumptions are entirely reasonable in view of recent field audits23 that have checked production-line quality control data against field charges and API published data.

The data presented in this paper show that most charges follow the general relationships quite well when using raw information directly from the API data sheets or from the different companies/manufacturers conducting the tests. Only occasionally will a specific charge vary from the general relationships to any significant degree.

Normalization of data (correction for different target properties permitted within the API specification) is not required when the proposed method is used to predict downhole penetration. Actual target values are used directly, with correction being made automatically by the nomograph (using Thompson’s relationship). However, normalization would be required when API data are used directly to compare relative performance of commercial charges.

Conclusions

1. API Sec. 1, Edition 5 test data are applicable to, and recommended for, prediction downhole values of shaped-charge gun penetration and entrance hole size in casing.

2. A simple method for predicting the downhole penetration and entrance hole size in casing is proposed that is based solely on use of Sec. 1 data.

3. Use of Sec. 4 is recommended to verify penetration predictions and to provide important flow performance parameters.

4. Additional work should be performed to improve the definition of the relationship of porosity and compressive strength over a broader range of porosity and over a larger number of formation types.

5. Additional testing should be done to define more clearly briquet vs. target internal compressive strength for API Sec. 1 targets.

Nomenclature

deh = entrance hole diameter, L, in. di = casing ID, L, in. di3 = ID of third casing string, L, in. dw = wellbore diameter, L, in. htc = total cement thickness between first and third

strings, L, in. h1,h2 = first and second string casing thicknesses, L, in. H = Brinell hardness, dimensionless L = penetration, L, in. LAPI = RP 43, Sec. 1 penetration, L, in. L’API = LAPI adjusted for multiple casings Lp = downhole perforation length, in. Ls = penetration LAPI corrected for formation strength

and effective stress, in. po = overburden stress, m/Lt2, psi pr = pore pressure, m/Lt2, psi S = average compressive strength, m/Lt2, psi Sd = dry compressive strength measured

perpendicular to bedding plane, m/Lt2, psi Sdb = compressive strength of dry briquet, m/Lt2, psi Sdry = internal dry compressive strength, m/Lt2, psi Sw = equivalent mean wet compressive strength,

m/Lt2, psi σ = formation effective stress, m/Lt2, psi

Acknowledgements

We express our thanks to our respective companies for supporting this work. Appreciation is extended to L.A. Behrmann of Schlumberger for his insightful comments regarding target and rock strength characteristics. Others participating significantly include personnel from Western Atlas, Goex, Jet Research Center, Owen Oil Tools, and P.E. Moseley & Assocs., as well as various members of the API RP 43 committee.

References

1. Karakas, M. and Tariq, S.M.: “Semianalytical Productivity Models for Perforated Completions,” SPEPE (Feb. 1991) 73; Trans., AIME, 291.

2. RP 43, Recommended Practices for Evaluation of Well Perforators, fifth edition, API, Washington, DC (Jan. 1991).

3. Halleck, P.M.: “The Effects of Stress and Pore Pressure on Penetration of Jet Perforators in Berea Sandstone,” final report, API Project 86-36, API, Dallas.

4. Bell, W.T.: “Perforating Techniques for Maximizing Well Productivity,” paper SPE 10033, presented at the 1982 API Intl. Petroleum Exhibition and Technical Symposium, Beijing, march 16-25.


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5. Locke, S.: “An Advanced Method for Predicting the Productivity Ratio of a Perforated Well,” JPT (Dec. 1981) 2481.

6. Thompson, G.D.: “Effects of Formation Compressive Strength on Perforator Performance,” Perforating, Reprint Series, SPE, Richardson, TX (1991) 31, 69-75.

7. Hallack, P.M., and Behrmann, L.A.: “Penetration of Shaped Charges in Stressed Rocks,” Proc., Rock Mechanics Contributions and Challenges, Colorado School of Mines, Golden (1990).

8. Weeks, S.G.: “Formation Damage or Limited Perforating Penetration? Test Well Shooting May Give a Clue,” JPT (Sept. 1974) 979.

9. Behrmann, L.A., Pucknell, J.K., and Bishop, S.R.: “Effects of Underbalance and Effective Stress on Perforation Damage in Weak Sandstone: Initial Results,” paper SPE 24770 presented at the 1992 SPE Annual Technical Conference and Exhibition, Washington, DC, Oct. 1992.

10. Behrmann, L.A. and Halleck, P.M.: “Effect of Concrete and Berea Strengths on Perforator Performance and Resulting Impact on the New API RP-43,” paper SPE 18242 presented at the 1988 SPE Annual Technical Conference and Exhibition, Houston, Oct. 2-5; Perforating, Reprint Series, SPE, Richardson, TX (1991) 83.

11. SPAN-PC Version 2A User Guide. C200358, Schlumberger Perforating and Testing Center, Rosharon, Texas (1993).

12. Saucier, R.J. and Lands, J.F.: “A Laboratory Study of Perforations in Stressed Formation Rocks,” JPT (Sept. 1978) 1347; Trans., AIME, 265.

13. Halleck, P.M.: “Further Effects of Stress on Penetration and Flow Performance of Jet Perforators,” final report, API Project 87-36, API, Dallas.

14. Halleck, P.M. et al.: “Reduction of Jet Perforator Penetration in Rock Under Stress,” paper SPE 18245 presented at the 1988 SPE Annual Technical Conference and Exhibition, Houston, Oct. 2-5; Perforating, Reprint Series, SPE, Richardson, TX (1991) 31, 105.

15. Behrmann, L.A. and Halleck, P.M.: “Effects of Wellbore Pressure on Perforator Penetration Depth,” paper SPE 18243 presented at the 1988 SPE Annual Technical Conference and Exhibition, Houston, Oct. 2-5; Perforating, Reprint Series, SPE, Richardson, TX (1991) 31, 98.

16. Robinson, R.L., Herrmann, V.O., and DeFrank, P.: “How Well Conditions Influence Perforations,” Proc., 12th Annual Technical Meeting, CIM Petroleum and Natural Gas Div., Edmonton, Alta., Canada (May 1961).

17. Schlumberger Tubing-Conveyed Perforating, Schlumberger, Houston (1988).

18. Regalbutto, J.A., Leidel, D.J., and Sumner, C.R.: “Perforator Performance in High Strength Casing and Multiple Strings of Casing,” paper presented at the API Pacific Coast Joint Meeting, Bakersfield, Nov. 1983.

19. “The Evaluation of the Potential Degradation of Perforation Charges as a Result of Exposure to Elevated Temperature,” Exxon Perforator Performance Evaluation, Phase II report, Exxon, Houston (Oct. 1985).

20. Sukup, R.A. et al.: “Simple Method Tracks Charge Performance,” paper SPE 17172 presented at the 1988 SPE Formation Damage Symposium, Bakersfied, Feb. 8-9, Perforating, Reprint Series, SPE, Richardson, TX (1991) 31, 197.

21. Klotz, J.A., Krueger, R.F., and Pye, D.S.: “Maximum Productivity in Damaged Formations Requires Deep, Clean Perforations,” paper SPE 4792 presented at the 1974 SPE Formation Damage Control Symposium, New Orleans, Feb. 7-8.

22. Halleck, P.M.: “Minimum Size and Stress Requirements for a Possible API Standard Test Target for Performance Evaluation of Shaped Charge Oil Well Perforators in Stressed Rocks,” final report, API Project 88-36, API, Dallas.

23. Jimenez, M. Jr. et al.: “Tests Reveal Perforating Charge Performance,” Oil & Gas J. (Jan. 6, 1992).

SI Metric Conversion Factors

in. x 2.54* E+00=cm

psi x 6.894 757 E+00=kPa

* Conversion factor is exact. SPEPF

8 R.E. OTT, W.T. BELL, J.W. HARRIGAN Jr. AND T.G. GOLIAN

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TABLE 1 – RELATIONSHIP BETWEEN CASING GRADES AND PHYSICAL PROPERTIES

Casing Rockwell “B”

Rockwell “C” Brinell

Minimum Yield (kpsi)

Tensile Strength

(kpsi) H-40 J-55 K-55 C-75 L-80 N-80 C-95 S-95 P-105 P-110 Y-150

68 to 87 81 to 95 93 to 102 93 to 103 93 to 100 95 to 102 96 to 102

14 to 25 14 to 26 14 to 23 16 to 25 18 to 25 22 to 31 25 to 32 27 to 35 36 to 43

114 to 171 152 to 209 203 to 256 203 to 162 203 to 243 209 to 254 219 to 254 238 to 294 254 to 303 265 to 327 327 to 400

40 55 55 75 80 80 95 95

105 110 150

60 to 84 75 to 98 95 to 117 95 to 121 95 to 112 98 to 117

103 to 117 109 to 139 117 to 143 124 to 154 159 to 202

TABLE 2 – DATA FROM API RP 43 SUBCOMMITTEE TASK GROUP

Fifth Edition

Sec. 1 Sec. 2 Fourth Edition Sec. 2 Thompson Curve

Liner Type

Explo- sive

Weight

Gun/ Charge

Gun/ Charge

Size (in.)

On File With API?

All Tests Same

D.S.C.?

Total PEN (in.)

BriquetCompr.

Str. (kpsi)

CalculatedStrength

(kpsi)

Total PEN (in.)

Porosity(%)

CalculatedStrength

(kpsi)

Ratio Sec. 2/ Sec. 1

Total PEN (in.)

Ratio 5th/4th Sec. 2

PredictedSec. 2 From Sec. 1

Ratio Predicted/Test Data

Cu/Pb

6.5 6.5 20 21 32 13 15

19.5 32

A B C D E F G H I

2 2 5

3-3/8 4

3-1/8 2-1/8

4 4

Yes

Yes

Yes ?

Yes Yes Yes

? ? ?

No

10.20 12.80

22.80

13.13 14.80 16.63 24.78

7.20

8.64

8.04 8.49

6.75

2.95

3.54

3.30 3.48

2.77

7.40 8.40 12.21 14.70 17.30 10.00 10.97 11.73 16.68

20.90

21.00

19.75

19.40

6.19

6.11

7.21

7.53

0.73 0.66

0.64

0.76 0.74 0.71 0.67

7.50

10.90

15.40

13.47 17.18

0.99

1.12

1.12

0.87 0.97

9.68

18.28

10.74

16.45

1.15

1.24

0.96

0.99 Average for Cu/Pb-type charges. 0.70 1.01

Tung.

16 3.2 7

11.5 15 19

22.7 22 25 26

J K L M N O P Q R S

2-1/8 1-9/16

2 1-11/16 2-1/8

4 4-1/2 3-3/8 4-5/8 3-3/8

Yes Yes Yes Yes Yes Yes

Yes

Yes Yes Yes Yes Yes Yes Yes

? No ?

18.30 6.67 11.46 12.14 15.05 21.18 18.17 20.30 13.43 17.75

6.26 6.26 5.45 5.4

8.89 6.22 6.32 7.58 9.52

2.57 2.57 2.23 2.23 3.64 2.55 2.59 3.11 3.90

9.40 4.17 7.21 9.17 10.55 13.67 13.04 14.36 11.66 13.05

20.00 20.00 20.00 20.00 20.00 20.00

20.40

6.98 6.98 6.98 6.98 6.98 6.98

6.63

0.51 0.63 0.63 0.76 0.70 0.65 0.72 0.71 0.87 0.74

8.08

13.50

1.13

0.97

4.56 7.85 8.07 10.00 15.89 12.41

9.92

1.09 1.09 0.88 0.95 1.16 0.95

0.85

Average for tungsten-type charges. 0.69 1.05

Unk.

22.7 22.7 12.5 22.7 32 32

T U V W X Y

3-3/8 5

2-3/4 3-3/8 4-5/8 3-3/8

Yes Yes Yes Yes Yes Yes

? ? ? ? ? ?

21.21 21.10 14.32 17.49 23.62 22.32

6.79 7.14 7.13 7.38 8.22 6.75

2.78 2.93 2.92 3.03 3.37 2.77

14.37 13.98 10.18 13.40 17.06 15.29

19.27 19.20 19.66 20.00 20.60 19.30

7.65 7.72 7.29 6.98 6.45 7.62

0.68 0.66 0.71 0.77 0.72 0.69

13.96 13.98 9.83 12.44 18.12 14.70

0.97 1.00 0.97 0.93 1.06 0.96

Average for unknown type charges. 0.70 Overall Averages: 0.697 1.024 1.01


SPE 27424

TABLE 3 – USE OF NOMOGRAPH Sec. 1 data (from API sheet) Briquet compressive strength, psi 7,560 Average total target penetration (LAPI), in. 15.6 Average casing entrance hole diam.,in. 0.28

Downhole conditions Mean wet uniaxial compressive strength (from field cores), psi 7,200 Downhole effective stress (Eq. 2), psi 6,000 Combined casing/cement thickness – 0.5 (wellbore dia.-casing ID), in. 1.5 Casing grade P-110

Point A Point B Point C Point D Point E Point F

Using the nomograph to determine penetration

Enter the nomograph with Section 1 briquet strength (7560 psi) and progress horizontally to right. Intersect line compensating for internal target strength (Eq. 6). Project vertically downward. Enter Section 1 average total target penetration (LAPI). For multiple casing strings, use modified Section penetrations (LAPI’) per Eq. 4. Intersection of horizontal and vertical projections represents Section 1 penetration at Section 1 equivalent target mean wet compressive strength (3100 psi from Eq. 6). Enter mean wet compressive strength of formation (7200 psi). If formation strength is not available, it can be estimated from formation porosity by entering nomograph at point G (porosity of 19.7% determined from formation logs or sidewall cores, etc.) and proceeding to formation type (sandstone) at point H and projecting vertically upward. Progressing from point D parallel to the family of curves and intersecting the vertical line from point E or point H provides downhole penetration adjusted for mean wet compressive strength.

Point I Point J Point K Point L Point M Point N Point O

Project horizontally from point F and intersect appropriate formation effective stress line (6,000 psi). Project vertically downward to determine total downhole penetration (10.1 in.). Continue vertical line to intersect combined casing and cement thickness (1.5 in.). Project horizontally to read downhole formation penetration (8.6 in.), which is used in well flow calculations.

Using the nomograph to determine casing hole size

Enter nomograph with midrange Brinell hardness of casing (P-110, 296 H from Table 1). Proceed vertically downward. Intersect multiplier line and reflect horizontally to left. Read multiplier (0.96), which is applied to average entrance diameter for a single casing string. Thus, API entrance hole of 0.28 is corrected to 0.27 in. downhole.

Fig. 1 – Example effect of gun-to-casing clearance.

Perforation

Gun Clearance Borehole9-5/8-in.

Casing, 7-in.

Cement

Formation

7.63 in./0.21 in.

12.38 in./0.28 in.

14.43 in./0.35 in.

12.38 in./0.28 in.

Avg. Pen. 11.71 in.E.H. 0.28 in.

A) Eccentered gun(Variable clearance,90° phasing)

E.H. 0.35 in.Avg. Pen. 14.43 in.

14.43 in./0.35 in.

B) Positioned gun

0° phasing)(0-in. clearance,

11.03 in./0.26 in.E.H. 0.26 in.Avg. Pen. 11.03 in.

90° phasing)(1.56-in. clearance,

C) Centralized gun

3-3/8 in.Gun


SPE 27424

Fig. 2 – Relationship of formation mean wet compressive strength to total shaped-charge penetration (casing thickness + cement thickness + formation penetration).6

Fig. 3 – Mean wet compressive strength as a function of formation porosity.3,6,9,11

B

A

C

0

5

10

15

20

25

30

35

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Mean wet compressive strength (kpsi)

Tota

l pen

etra

tion

(in.)

0

5

10

15

20

25

30

0 5 10 15 20 25 30 35

Porosity (%)

Mea

n w

et c

ompr

essi

ve s

tren

gth

(kps

i)

Sandstone

Limestone


SPE 27424

Fig. 4 – Stress-induced penetration reduction ratio (reference, 0-psi stress).3,13,14

Fig. 5 – Entrance hole size in single casing string vs. Brinell Hardness H (reference, L-80 casing as used in RP 43, Sec. 1, Edition 5).16

A (3.0 g)

B (22 g)

C (22 g)

D (3.2 g)

E (10 g)

Weights shown areexplosive load

0.5

0.6

0.7

0.8

0.9

1

0 2 4 6 8 10 12

Effective stress (kpsi)

Pene

trat

ion

mul

tiplie

r

J55

P110

0.86

0.88

0.90

0.92

0.94

0.96

0.98

1.00

1.02

1.04

1.06

1.08

1.10

100 150 200 250 300 350 400

Brinell hardness

Entr

ance

hol

e m

ultip

lier

L-80

Ref

. (22

3 H

)


SPE 27424

BRIQUETTEST

CASING

WATER

STEEL

28-DAY

SPECIMEN

CONRETE

FORM

Fig. 6 – Sec. 1 RP 43 test.

Ratio = 0.67

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 5 10 15 20 25 30 35 40 45

Cure time (days)

Rat

io "

in s

itu"

/ briq

uet c

ompr

essi

ve s

tren

gth

Fig. 7 – Actual (“in-situ”) dry compressive strength vs. briquet measurement: RP 43 Section 1 Target.10


SPE 27424

Fig. 9 – Effective-stress-induced penetration changes. Curve represents data from Fig. 4 normalized to 3,000 psi stress.3,13,14

Pressure vessel

Well Pressure1500 psi3000 psi

Core Pressure1000 psi

atmospheric

Berea3-9/16-in OD Core

4-in or 7-in OD Core

Steel Container

Rubber stress sleeve

Cement

Gun

Stressing fluid inlet Core vent

AEdition 4

0 applied effective stress

BEdition 5

3000 psi effective stress

0.8

0.9

1

1.1

1.2

1.3

1.4

0 1 2 3 4 5 6 7 8 9 10 11 12

Effective stress (kpsi)

Pene

trat

ion

mul

tiplie

r

Fig. 8 – Sec. 2 RP 43 Test: Edition 4 vs. Edition 5.

14 W. T. BELL, T.G. GOLIAN, R.C. ELLIS AND P.E. MOSELEY

SPE 60129

Line represents the average of the Sect 2 / Sect 1 ratios.

Average Ratio = 0.692

0

2

4

6

8

10

12

14

16

18

20

22

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30Section 1 concrete penetration (in.)

Sect

ion

2 B

erea

pen

etra

tion

(in.)

Fig. 10 – Comparative penetration data: Sec. 1 vs. Sec. 2, RP 43 Edition 4, plotted from published API data on file in 1990.

Cu/Pb

Tungsten

Unknown

Line represents the average of the Sect 2 / Sect 1 ratios.

Average Ratio = 0.697

0

2

4

6

8

10

12

14

16

18

20

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Section 1 Concrete penetration (in.)

Sect

ion

2 B

erea

pen

etra

tion

(in.)

Fig. 11 – Comparative penetration data, Sec. 1 vs. Sec. 2, RP 43 Edition 5, plotted from recent tests (Table 2) and from published API data on file in 1992.


SPE 27424

Cu/Pb

Tungsten

5th Edition / 4th EditionSection 2 penetrationOverall Ratio = 1.02

0

2

4

6

8

10

12

14

16

18

20

0 2 4 6 8 10 12 14 16 18 20

4th Edition Section 2 Berea penetration (in.)

5th

Editi

on B

erea

pen

etra

tion

(in.)

Fig. 12 – Comparative penetration data, Sec. 2, RP 43 Edition 4 vs. Sec. 2, Edition 5, plotted from recent tests (Table 2).

C B

A

0

5

10

15

20

25

30

35

0 5 10 15 20 25 30

Mean wet compressive strength (kpsi)

Tota

l pen

etra

tion

(in.)

Fig. 13 – Relationship of data generated in API study (Table 2) to total penetration vs. mean wet compressive strength curve.6,8

16 W. T. BELL, T.G. GOLIAN, R.C. ELLIS AND P.E. MOSELEY

SPE 60129

Conc

rete

AB

0

2

4

6

8

10

12

14

16

Sect

ion

1 B

riq. C

s (k

psi)

0 in.

1.0 in.

2.0 in.

3.0 in.

LK

0

5

10

15

20

25

30

Dow

nhol

e fo

rmat

ion

pene

trat

ion,

in.

Casing pluscement thickness

F

E

DC

0

5

10

15

20

25

30

35

0 2 4 6 8 10 12 14 16 18 20 22 24

Mean wet compressive strength, kpsi

Test

targ

et a

vera

ge p

enet

ratio

n, in

.

HG

0

5

10

15

20

25

30

Poro

sity

, %

Sandstone

Limestone

0

1

2310 616 & above

J

I

0 5 10 15 20 25 30 35

Downhole total target penetration, in.

Effective stresspenetration correction lines(Effective stress in psi/1000)

Common casing grades

Y150P110S95L80 N80J55H40

M

NO

0.9

0.92

0.94

0.96

0.98

1

1.02

1.04

1.06

1.08

1.1

100 150 200 250 300 350 400

Casing Brinell hardness

Entr

ance

hol

e m

ultip

lier

L-80

Ref

. (22

3 B

HN

)

Fig. 14 – Nomograph to predict downhole penetration and entrance hole size in casing.

Documents

spe27424