BAKER HUGHES INCORPORATED AND
`BAKER HUGHES OILFIELD
`OPERATIONS, INC.
`Exhibit 1022
`
`Page 1 of 11
`
`

`
` Society of Petroleum Engineers
`
`SPE 29553
`
`Current Use of Limited-Entry Hydraulic Fracturing
`in the Code|llNiobrara Formations—DJ Basin
`
`M.J. Eberhard*, D.E. Schlosser**
`
`*Halliburton Energy Services, **HS Resources
`
`SPE Members
`
`Copyright 1995. Society of Petroleum Engineers Inc.
`
`This paper was prepared for presentation at the 1995 SPE Rocky Mountain Meeting, Denver, March 20-22.
`
`This paper was selected for presentation by an SPE Program Committee following review of intonnation contained in an abstract submitted
`by the author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject
`to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its
`officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petro-
`Ieum Engineers. Permission to copy is restricted to an abstract of not more than 300 words.
`Illustrations may not be copied. The abstract
`should contain conspicuous acknowledgment of where and by whom the paper is presented. Write Publications Manager, SPE, PO. Box
`833836, Richardson, TX 75083~3836, U.S.A. Telex, 730989 SPEDAL.
`
`Abstract
`
`In the last several years, limited-entry perforating has
`been used for hydraulically fracturing the Codell and
`Niobrara formations in the Denver-Julesburg (DJ)
`Basin. Limited—entry perforating reduces stimulation
`costs with no apparent effect on production.
`
`Several papers have presented guidelines for designing
`a limited-entry treatment. A primary concern for
`treating multiple intervals is to ensure that both zones
`receive the necessary treatment. Currently, some
`operators simply ratio the number of perforations in
`each interval to the volume of treatment required for
`each interval. To ensure that both zones are being
`treated, a minimum pressure drop of 700 to 1,000 psi is
`usually used for limited-entry design. Changes in the
`perforation discharge coefficient and diameter during
`the treatment, combined with changes in the net treat-
`ing pressure, affect the perforation pressure drop
`calculation. To determine the actual pressure drop
`across the perforations, designers use a real—time
`spreadsheet calculation.
`
`will be presented, as well as the effect of proppant
`concentration and velocity through the perforation. The
`current spreadsheet calculation used on location to
`calculate the pressure drop across the perforations is
`also discussed.
`
`Introduction
`
`The Niobrara and Codell formations are the two
`
`primary production intervals for most of the wells being
`completed in the DJ Basin. The Niobrara is a rnicritic
`limestone‘ consisting of three benches. At a depth of
`approximately 6,800 ft, the overall interval is generally
`between 150 and 250 ft thick. The Ft. Hays formation,
`the lower member of the Niobrara group, separates the
`Niobrara and Codell. There is a transition at the top of
`the Codell from a carbonate to a calcareous sandstone
`
`to a fine-grained sandstone with a high clay content.’
`At a depth of approximately 7,000 ft, the Codell is
`typically 8 to 14 ft thick. Both the Codell and Niobrara
`are overpressured gas reservoirs with a low permeabil-
`ity ranging from 0.01 to 0.1 md.
`
`This paper reviews limited-entry treatments pumped in
`34 wells that verify spreadsheet calculations. Changes
`in the perforation discharge coefficient and diameter
`
`In the past, the Codell and Niobrara intervals were
`fractured separately. The Codell was fractured first
`with treatments ranging from 150,000 to 350,000 lb of
`
`References at the end of the paper.
`
`Page 1 of 11
`Page 1 of 11
`
`
`107
`
`

`
`SPE 29553
`2
`Current Use of Limited-Entry Hydraulic Fracturing in the Codell/Niobrara Formations——DJ Basin
`
`sand.’ Next, all three benches of the Niobrara were
`
`fractured in a single treatment. As operators started
`moving into marginal acreage, the economics of
`fracture treatments had to be improved. In addition to
`optimizing fracture treatment sizes, other methods of
`reducing costs had to be found. One way of reducing
`cost while improving fracture treatments was to com-
`
`plete both intervals at once.
`
`Limited-Entry Technique
`
`Limited-entry perforating is one method for completing
`multiple intervals with a single treatment. During a
`limited-entry treatment, operators maintain a pressure
`drop across the perforations (PM) greater than the
`stress differential between the intervals. A pressure
`drop across the perforations is created by forcing the
`treating fluid through a limited number of perforations
`of a known diameter. The size and number of perfora-
`tions placed opposite each interval are determined
`based on the percentage of the total treatment planned
`for each interval, and the total number of perforations
`required to produce the necessary pressure drop.‘
`
`During a limited-entry fracture treatment, PM should
`be monitored to ensure that all perforations are open
`and that the necessary pressure drop is maintained.
`With the advent of more advanced on-site computer
`systems, improved fluid friction correlations,“ and
`better quality control programs, predictions of PM are
`becoming more accurate.
`
`Calculations
`
`and fracture friction will be set to zero. As a result, PM
`will be the sole component of Pm in Eq. 1.
`
`During a fracturing treatment, the wellhead treating
`pressure (WHTP), pump rate, and proppant concentra-
`tions are constantly changing. Computer-based data
`acquisition systems (DAS) are used to record these
`three variables. Additional programs are then used to
`calculate hydrostatic pressure (Pm) and tubular friction
`pressure (PW).
`
`During a typical fracture treatment, the pump rate is
`stopped after the first half of the pad fluid is pumped to
`determine the instantaneous shut-in pre sure (ISIP).
`When the rate is zero, PM and PM are also zero, and
`the BHTP can be expressed as shown below:
`
`BHTP = Islfi + Phyd ................................ .. (2)
`
`where
`
`ISIPS = surface instantaneous shut-in pressure
`
`When pumping is resumed, this BHTP value can be
`used in Eq. 1 to estimate PM. However, for most cases,
`BHTP either increases or decreases during the treat-
`ment, depending on the fracture geometry.” The effect
`this change in BHTP has on the calculation of PM can
`be significant and should be considered whenever
`possible during PM calculations.
`
`PM can also be calculated from the following equation:
`
`137,, = 0.2369p
`
`2
`
`P
`
`d _i
`
`.................... (3)
`
`The standard equation for calculating the bottomhole
`treating pressure during a fracturing treatment is shown
`1_-I.__...
`DCIUWZ
`
`where
`
`BHTP = WHTP + 1;”,
`
`— P,,,-C,
`
`- Pf,“ ........ .. (1)
`
`Fracture-entry pressure (Pm) has several components,
`including perforation friction, near-wellbore tortuosity,
`and fracture friction. When the rate per perforation is
`low (< 0.2 bbl/min/pen’), PM is generally considered to
`be zero. In limited-entry jobs, however, this assumption
`is not the case, and determining the true bottomhole
`treating pressure (BHTP) becomes more difficult.
`Although near-wellbore tortuosity can be significant,
`for the purposes of this paper, near-wellbore tortuosity
`
`p = density of fluid (lb/gal)
`
`Q = total pump rate (bbl/min)
`
`N = number of perforations
`
`When abrasive fluids, such as those containing S"“u’.i
`are pumped, the diameter of the perforation (DP) and
`the coefficient of discharge(Cd) will change with
`respect to PPM and sand concentration during the
`treatment. Several attempts have been made to quantify
`changes in DP and Cd. Crump and Conway” demon-
`
`108
`
`Page 2 of 11
`Page 2 of 11
`
`

`
`SPE 29553
`
`M.J. Eberhard, D.E. Schlosser
`
`typical net pressure increase in the Niobrara is between
`0 to 200 psi, while typical increases in the Codell are
`400 to 600 psi. As a result, the BHTP is essentially the
`same for both intervals at the end of the treatments. The
`
`6-to-12 ratio of perforations is based on these BHTP
`conditions. Final results from multiple tracers run in
`early treatments indicate that all intervals were taking
`fluid throughout the entire treatment. Fig. 1 (Page 4)
`shows the results of one of the tracer surveys. Produc-
`tion results from limited-entry treatments are compa-
`rable to wells treated individually, further validating
`that the proper proportion of the treatment is being
`placed in each interval.
`
`Table 1: Typical Code|IINiobrara Treatment
`Schedule
`
`
`
`Concentration%
`
`
`
`
`
`
`Volume Descrition
`
`PE
`
`m
`EH
`
`
`
`I-IT
`Iflji
`
`
`
`P *
`
`Per 1,000 gal
`
`Data Acquisition
`
`All treatments were recorded on the same data acquisi-
`tion system. In addition to recording the standard
`pressure, rate, and density variables, this system also
`records all real-time calculated values. All the treat-
`
`ments used for this paper were recalculated using the
`same program.
`
`The software program calculates BHTP at time t
`(BH'I'Pcm) based on the following equation:
`
`frict
`BHTPMC = WHTP + PM — P
`
`............... .. (4)
`
`To calculate PM and PM, the program breaks the
`wellbore into 15 segments and then tracks each seg-
`ment as it moves down the wellbore. The software also
`
`has several options available for calculating pipe
`friction.
`
`strated that Cd can increase by 15%. Willingham, et al.,
`showed that the values for Cd can range from 0.62 to
`0.95," depending on whether abrasive fluid has been
`pumped through the perforations. Cramer” presented
`a hydraulic perforation erosion constant of
`0.00418 in./1,000 lb of 20/40 mesh sand pumped. This
`constant is used to calculate the diameter increase of a
`
`0.375-in. perforation, based on proppant volume
`pumped through a perforation. Changes in DP and Cd
`will also be evaluated in this paper.
`
`Well Information
`
`In 1994, over 300 limited-entry treatments were
`pumped within the Wattenberg field. For this paper,
`limited-entry treatments in 34 wells were evaluated. All
`treatments are in the Codell/Niobrara intervals.
`
`Of the 34 wells evaluated, 27 were completed with
`4 1/2-in., 11.6-lb/ft, I-70 casing cemented in a 7 7/8-in.
`hole. Each well was perforated with six shots in the
`Niobrara and 12 shots in the Codell.
`
`The remaining seven wells were completed with
`2 7/8-in., 6.40-lb/ft, N—80 casing cemented in a 7 7/8-in.
`hole. Each of these wells was perforated with four shots
`in the Niobrara and seven shots in the Codell.
`
`Both well types were perforated with jets. In the 27
`wells having 4 1/2-in. casing, 3 1/8-in. OD carrier guns
`with 10-g charges were used. For the seven wells
`having 2 7/8-in. casing, 2 1/16-in. OD carrier guns with
`8-g charges were used. Both gun types had a 0.31-in.
`perforation diameter.”
`
`During a standard treatment, 412,000 lb of sand and
`104,000 gal of fluid were placed into both intervals.
`The perforation placement was designed to place one-
`third of the treatment into the Niobrara and the remain-
`
`ing two-thirds of the treatment into the Codell. Table 1
`
`shows the various stages of a typical Codell/Niobrara
`treatment.
`
`When treated individually, the initial BHTP in the
`Niobrara is typically 450 to 700 psi higher than in the
`Codell. (To help break down the Niobrara perforations,
`HCl is pumped ahead of the treatment.) Based on this
`stress differential, the proper ratio of perforations is 7
`in the Niobrara and 11 in the Codell. However, a
`
`109
`
`Page 3 of 11
`Page 3 of 11
`
`

`
`SPE 29553
`Current Use of Limited—Entry Hydraulic Fracturing in the Codell/Niobrara Formations—DJ Basin
`;__:
`
`LI
`computer systems. Calc"lating pipe friction and
`a
`changes in the BHTP are not
`s accurate, however.
`
`When Eq. 1 is used to calculate PM, the value for
`BHTP is generally calculated from Eq. 2, and an ISIP is
`taken during pad. This BHTP vflue is then used for the
`remainder of the treatment. In Codell/Niobrara treat-
`ments, the net pressure can increase from 50 to 500 psi
`during pumping. If the increase in net pressure is
`ignored, PPM will be overcalculated by the net pressure
`value, as the following equation shows.
`
`............
`
`(5)
`
`Fig. 2 shows the effect that the change in net pressure
`has in calculation PM for one well. In this paper, ANet
`is the difference between the ISIP taken during the pad
`and the final ISIP at the end of the treatment. For the
`final ISIP, the DAS-calculated value for BHTP was
`used, which is a more accurate calculation of the final
`PM The ANet was then divided by the number of data
`points and applied linearly throughout the treatment.
`
`For real-time calculation of PM, an accurate prediction
`of the ANet is required. Net pressure can be determined
`based on other treatment results on wells in the area, or
`3-D models can be used to predict ANet throughout the
`treatment.
`
`Pipe friction is dependent on the tubular configuration,
`fluid rheology, sand concentration, and treatment rate.
`Because of varying sand concentrations and fluid
`
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`
`Fig. ]—Multiple tracer log of a limited-entry treatment.
`
`Evaluation of PM
`
`To evaluate PM and its associated variables Cd and Dp,
`the program compares the PM calculated from Eq. 1 to
`the PM calculated from Eq. 3. Independent variables are
`used by each equation to calculate PM. This method
`was also used in early versions of the real-time perfora-
`tion friction spreadsheet to verify the number of open
`perforations as well as Pm.
`
`WHTP is a direct measurement; with the accuracy of
`today’s transducers, WHTP will be very consistent.
`Calculating the hydrostatic pressure of the wellbore
`fluid is also fairly straightforward with current on-site
`
`E .
`
`. '85
`
`
`
`
`
`E
`
`Without change In BHTP
`
`
`
` With change in an-m> PressureDropAcrossthePerforetlons(psl) §§§é‘§§
`
`0
`
`350.000
`250.000 M01300
`100,000
`150,000
`50.0% 100,000
`Cumulative Send Volume Pumped (lb)
`
`400.000
`
`4so,ooo
`
`Fig. 2—P’mf calculated with and without the change in
`BHTP.
`
`110
`
`Page 4 of 11
`Page 4 of 11
`
`

`
`M.J. Eberhard, D.E. Schlosser 5
`SPE 29553
`
`
`
`Adiustsd Friction
`
`\ D
`
`A$CI|cu|I‘bd Frlctlon
`
`0
`
`so,ooo1oo.ooo15o,oooaoo,ooo2so.oooaoo.ooo:so.oooaoo,ooo45o,ono
`cumulative sand Volume Pumped (lb)
`
`E 3
`
`PressureDropacrossthePerloratlons(psl) §
`
`
`
`
`
`Fig. 3—PWf based on DAS-calculatedfriction vs.
`adjusted friction (4 I/2-in. casing)
`
`rheology in the wellbore, the friction pressure calcu-
`lated by the DAS for determining PPM must be used. A
`fracturing fluid system of CMHPG polymer crosslinked
`with zirconium was
`sed in all 34 wells described in
`
`this paper. To help ensure accurate PM values, each
`treatment was reviewed to verify that the wellbore
`configuration and fluid properties for each stage were
`correct.
`
`For the fracturing fluid system used in these wells, DAS
`
`has three different friction calculation options:
`
`0 Option 1 calculates friction based on an integration
`of the base fluid and crosslinked fluid properties
`depending on wellbore temperature.
`
`- Option 2 uses the A, e, and s method developed by
`Melton and Malone" to calculate friction based on
`fl-In I-noon an] 11' our] V‘
`lllb UGDD SK/I. ll QIILI I.\ .
`
`- Option 3 uses a modification of the equation
`
`developed by Lord and McGowen.5
`
`After results from all three calculations were compared,
`Option 3 seemed to best represent the observed friction
`in 4 1/2-in. casing.
`
`Option 3 was used to recalculate all 27 of the treatments
`down 4 1/2-in. casing, and Eq. 5 was used to calculate
`PM. The values calculated for PM in the later stages of
`the treatment were surprisingly low when ANet was
`included.
`
`Next, all seven treatments down 2 7/8-in. casing were
`recalculated based on Option 3, and negative PMS were
`calculated. Since a negative PM is not possible, the
`calculation of PM was incorrect. When the results from
`Option 3 were compared to values calculated for P
`based on Eq. 3, it was detemiined the Pm value gePrir¢=:r-
`ated from the DAS needed to be reduced by 21%.
`correction was made to all 2 7/8-in. treatments, result-
`
`ing in realistic calculations of PM. The same correction
`was made to the friction numbers calculated for
`
`4 1/2-in. casing, also resulting in more realistic calcula-
`tions of PPM. Fig. 3 compares PM based on both DAS-
`calculated friction and adjusted friction for a 4 1/2-in.
`well. Fig. 4 shows the same comparison for a 2 7/8-in.
`well.
`
`E
` ..'..8
`
`
`
`PressureDropacrossthePerforatlions(psl) §§
`
`AdlusudFrlellon
`
`I
`
`DAS-CIICIJIICOC Friction
`
`T
`
` 0
`
`50;“)
`
`100,000
`
`150,M0
`
`E0,N0
`
`250.U0
`
`3101310
`
`350,000
`
`400,000
`
`
`
`3W
`1W
`
`‘1N)
`III“
`w-.
`(500)
`
`Cumulative Sana‘ Volume Fumpod (iii)
`
`Fig. 4-—PWf based on DAS-calculatedfriction vs.
`adjusted friction (2 7/8-in. casing)
`
`Calculation of Cd and DP
`
`To calculate Cd and DP, designers set up a table for each
`well. This table includes the following information:
`
`-
`
`0
`
`-
`
`PW, calculated from Eq. 5
`
`pump rate, and sand concentration calculated from
`the DAS
`
`cumulative clean fluid or sand volumes (optional)
`
`111
`
`Page 5 of 11
`Page 5 of 11
`
`

`
`6
`
`Current Use of Limited-Entry Hydraulic Fracturing in the Codell/Niobrara Formations—DJ Basin
`
`SPE 29553
`
`Table 2 is an example of a Cd/DP data table. Based
`on this data, the initial values of the perforations,
`and the information developed by the earlier refer-
`enced authors,““‘ designers can estimate Cd and DP
`by using Eq. 3. This analysis procedure is also used
`on location for real-time calculations of PM.
`
`Table 2: Calculation of Cd and DP Based on
`Eq. 5 and Eq. 3 Results
`
`between all wells. Table 3 summarizes treatment
`results from the 27 4 1/2-in. wells treated. As shown in
`
`Table 4, results from the seven 2 7/8-in. wells were
`similar.
`
`As soon as sand enters the perforations, Cd changes
`immediately. Within the first 5,000 lb of sand per
`perforation, Cd has increased to 0.95. Final perforation
`diameters ranged from 0.36 to 0.49 in. The average
`final DP was 0.41 in. for an increase of 27.2%. This
`increase is twice as high as what was observed by
`CrI_1m_p and Conway.” Perforation diameter vs. the
`volume of sand pumped was plotted for all wells. These
`charts did not reveal a linear increase in DD with the
`volume of sand pumped throughout the treatment, but
`rather two separate erosion rates. Perforation erosion
`was fastest during the 3.5- to 5-lb/gal sand stages, with
`erosion rates ranging from 0.00376 to 0.0089 in./
`1,000 lb of sand. For the 5.5- to 8—1b/gal sand stages,
`perforation erosion slowed to rates ranging from 0.0019
`to 0.0043 in./1,000 lb of sand. Fig. 5 shows no clear
`correlation between these two variables.
`
`To evaluate the effect that rate has on perforation
`erosion, treatments were pumped at three different
`rates:
`
`-
`
`-
`-
`
`constant low rates (z3l bbl/min)
`
`constant high rates (=40 bbl/min)
`various increasing rates (=30 to 50 bbl/min)
`
`Treatments at a constant low pump rate had less
`perforation erosion but similar final Ppms as treatments
`at constant high pump rates. Realistic values for PM
`later in the treatment are 450 to 600 psi—not 700 to
`1,000 psi.
`
` 0
`
`20,000
`15,000
`10,000
`5_ooo
`Cumulative Sandmurnber Perforation: (lb)
`
`25,000
`
`Fig. 5——Change in D’, vs. volume of sand pumped.
`
`112
`
`Page 6 of 11
`Page 6 of 11
`
`—l(DUIMmA-h('.O IE
`
`III
`
`% E
`
`!
`
`ODCOCD(06000‘go);_|.4.5....
`
`(0J5H (D\l!
`
`E I
`
`E
`
`For the initial calculation, Cd = 0.72, DP = 0.31 in., and
`N = 18 are used for a pad fluid. If these values calculate
`Ll
`a PM higher than Eq. 5, the perforation diameter and C
`are increased until a reasonable match exists. Several
`
`data points are taken during the pad, and the same Cd
`and DP are used for all data points. Once sand is
`pumped, DP is held constant and Cd is increased until
`Cd = 0.95. From this point forward, Cd is held constant,
`and the perforation diameter is increased.
`
`Resufls
`
`In the 4 1/2-in. wells, treatment rates during pad ranged
`from 29.5 to 42 bbl/min with an average of 32.6 bbl/min.
`Initial values for Cd ranged from 0.72 to 0.90 with an
`average of 0.78; values for DP ranged from 0.31 to 0.36
`in. with an average of 0.32 in. Overall, there was very
`good agreement in the initial values for Cd and DP
`
`

`
`
`
`SEE 29553 M.J. Eberhard, D.E. Schlosser
`
`
`
`
`
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`0.30
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`0.41
`572
`243
`24
`433
`0.7
`32.3
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`IIEIMIEE
`
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`
`4; Initial and Fina! Results far 2 ‘.718-in. Wells
`
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`1.238 EKEIE3
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` 4 20.4 0.78 0.31 1,210 429 25.3 0.9 0.37
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`fijfl
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`17.2
`0.72
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`273
`30.2
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`
`EEHEIEEE
`
`113
`
`Page 7 of 11
`Page7of11
`
`

`
`8
`
`Current Use of Limited-Entry Hydraulic Fracturing in the Codell/Niobrara Formations—DJ Basin
`
`SPE 29553
`
`The plots shown in Figs. 6 through 8 show typical
`perforation erosion for the three treatments described
`above. Fig. 6 shows that for a constant-rate treatment,
`the change in Cd is gradual, and DP does not start to
`increase until 4.5 lb/gal slurry is going through the
`perforations. Fig. 7 shows a constant high-rate treat-
`ment. Note that the change in Cd is much more immedi-
`ate, and DP starts to increase when 3-lb/gal slurry enters
`the perforations. Fig. 8 shows an increasing rate
`treatment.
`
`0.5
`
`0.45
`
`(IbIga|I10),C,
`SandConcentration
`
`
`0
`
`20,000
`15,000
`10,000
`5,000
`Cumulative Sandmumber Perforation: (lb)
`
`25,000
`
`through the perforations was investigated. The equation
`for the velocity (v) through a nozzle is shown below:
`
`v = 35.2
`
`P
`”‘”'
`P
`
`...................................... .. (6)
`
`Velocity was calculated for each data point for all the
`treatments. Initial values during the pad ranged from
`304 to 453 ft/sec with an average of 389 ft/sec. Final
`values for were between 171 and 260 ft/sec with an
`
`average of 234 ft/sec (Table 3). A steep decrease in v
`occurs when the sand first starts; this decrease contin-
`
`ues until the velocity reaches = 350 ft/sec; below 350
`ftlsec, the rate of decrease becomes slower. Fig. 8
`shows that an increased pump rate does little to in-
`crease the velocity through the perforations.
`
`Real-Time Spreadsheet Calculation
`
`For the real-time calculation of PM, Eq. 5 is used.
`Table 5 shows the spreadsheet currently being used. A
`total net pressure increase value is entered along with
`total fluid. These values are used to calculate the ANet
`
`throughout the treatment. Next, the volume pumped
`when the ISIP is taken is entered into the spreadsheet.
`The net pressure increase used is based on the fluid
`pumped from the ISIP. The DAS value calculated for
`pipe friction, based on Option 3, is reduced by 21%.
`When PM is calculated, the friction correction value is
`added in. Perforation friction and the velocity through
`the perforations are also calculated based on Eqs. 2 and
`6. As described earlier, Cd and DP are adjusted to match
`both Ppms.
`
`(ltIsecI1,000)
`D,(In.),Volocllty
`
`
`
`
`
`
`
`33SandConcentration(lblgalll0),C.
`
`0
`
`20,000
`15.000
`10.000
`5,000
`Cumulative Snndlflurnber Porloratlons (lb)
`
`35.000
`
`Fig. 8—~Increasing rate treatment.
`
`114
`
`Page 8 of 11
`Page 8 of 11
`
`
`
`D,(in.),Velocity(ftIsecJ1.000)
`
`
`
`
`
`Fig. 6—Constant low-rate treatment.
`
`A
`3 045
`O.
`‘
`"'
`B
`"
`0.4
`u
`g
`3.
`.5 0.35
`2
`o
`>"
`-
`5'
`
`0-3
`
`02
`
`9
`
`D
`'
`
`Pump Rule
`
`Sand Concentration
`
`V9'°¢“V
`
`20.W0
`15,WD
`1D,W0
`SMW
`Cumulative Sandlhlumher Perforation: (lb)
`
`, 0'
`A‘
`(1.9 3
`3
`0.1 u
`3
`0.6 v
`5
`0.5
`‘._=___
`5
`N c
`0.3 §
`o2
`8
`
`~
`-
`
`'
`
`0.1 8
`0
`15,W0
`
`Fig. 7—Constant high-rate treatment.
`
`Velocity through a Perforation
`
`Based on the observed relationship between pump rate
`and perforation erosion, the effects of the velocity
`
`

`
`SPE 29553
`
`M.J. Eberhard, D.E. Schlosser
`
`Table 5: Current Spreadsheet Calculation of Pm, Cd, D9, and v
`
`BHISIP
`Total Net
`Total Fluid
`
`6,385 psi
`295 psi
`104,000 gal
`
`Well Name
`
`1,531
`
`Cale.
`
`- si
`
`
`
`
`
`7,438
`5,767
`EIKEZIIEE
` I
`
`EEZE—E
`
`
`
` E32]
`
`EJ
`
`Conclusions
`
`Nomenclature
`
`Tracer surveys and production results indicate the
`perforation scheme being used is placing the
`necessary treatment in each interval.
`.
`.
`.
`.
`.
`0 An accurate value for pipe friction is essential for
`.
`the calculation of P f.
`P"
`- ANet should be included in the calculation of P .
`I
`.
`Perf
`If ANet is not included, final PM values are
`undercalculated by 50 to 500 psi for these treat-
`merits.
`
`-
`
`.
`
`Perforations will erode to a steady-state PM. The
`final value for PM is dependent on the velocity
`through the perforations. Increasing the pump rate
`during sand stages only has short-term effects on
`PM“ For thesc wens, a constant PM of 1,000 psi is
`not realistic.
`
`In all cases, all of the perforations were taking
`fluid. “Balling off” the perforations to ensure that
`all were open was not required. There. is no evi-
`dence that any perforations were lost in any of
`these treatments.
`
`II
`II
`JJ
`II,
`II\rl\dCl0lll6 I-II\/ PIJIIIY ICAIIJJ IO ll\Il
`In the DJ basin innrnacinn H-in nnrnn raft: Kc rlnf
`
`necessary to maintain limited entry. Therefore,
`horsepower requirements can be reduced.
`
`W:Q - bottomhole treating pressure (psi)
`BHTPCBIC
`= bottomhole treating pressure
`at time t (psi)
`= bottomhole ISIP durin
`g P
`.
`.
`= coefficient of discharge
`.
`.
`.
`= diameter of perforation (1n.)
`= H-eronmm-n c eh--rain nrnecm-A Inch
`IIIOI-Cllll-lLIl\t\l D Olll-II: Ill tllllool-Q19
`= surface instantaneous shut-1n
`pressure (psi)
`= number of perforations
`
`BHISIP
`P8“
`
`C
`*1
`DP
`mm
`LL’lL
`ISIPS
`
`ad
`
`si
`(P )
`
`N
`
`ghyd
`PW
`me
`Pperf
`PM‘
`
`Q
`v
`WHTP
`ANet
`P
`
`.
`i hygirlostitic Pressure (psi)
`: $1 u at "won pressure (RS1)
`' racturetentry pressure (PS1)
`_
`_
`= perforation Pressure drop (PS1)
`= pressure drop across the perforations
`at "me t (PS1)
`= total pump rate (bbl/min)
`= velocity through a nozzle (ft/sec)
`= wellhead treating pressure (psi)
`= change in net pressure at time t (psi)
`= density of fluid (lb/gal)
`
`115
`
`Page 9 of 11
`Page 9 of 11
`
`Rate
`bbllmin
`
`
`
`

`
`10
`
`Current Use of Limited-Entry Hydraulic Fracturing in the Codell/Niobrara Formations—DJ Basin
`
`SPE 29553
`
`10. Crump, J .B. and Conway, M.W.: “ Effects of
`Perforation-Entry Friction on the bottomhole
`Treating Analysis,” JPT (Aug. 1988), 1041.
`
`11. Willingham, J.D., Tan, H.C., and Norman, L.R.:
`“Perforation Friction Pressure of Fracturing Fluid
`Slurries,” paper SPE 25891 presented at the SPE
`1993 Rocky Mountain Regional Meeting and Low
`Permeability Reservoir Symposium, Denver, April
`12-14.
`
`12.
`
`Cramer, D.D.: “The Application of Limited-Entry
`Techniques in Massive Hydraulic Fracturing
`Treatments,” paper SPE 16189 presented at the
`SPE Production Operations Symposium, Oklahoma
`City, March 8-10, 1987.
`
`13. Hessler, R.: Phone conversation on Nov. 10, 1994,
`Bran-Dex Wireline Services, PO Box 1061, Ster-
`
`ling, CO., 80751.
`
`14.
`
`Melton, L.L. and Malone, W.T.: “Fluid Mechanics
`Research and Engineering Applications in Non-
`Newtonian Fluid Systems,” SPEJ (March 1964) 55.
`
`Appendix A
`
`As fluid flows through an orifice, the geometry of the
`edges will contract the cross section of the fluid as it is
`discharged. This effect is known as the vena contracta.
`Diagram 1 shows this effect. The equation for the
`
`coefficient of discharge is shown below:
`
`C, = D,»/Dv
`
`Average initial Cd values for the wells in this paper
`were 0.79. As sand enters the perforation at high
`velocities, the edges of the perforation begin to erode.
`This erosion continues until Cd reaches a value of 0.95
`as shown in Diagram 2.
`
`Acknowledgments
`
`The authors thank the management of HS Resources
`and Hallibuzton Energy Services for permission to
`
`prepare and present this paper.
`
`References
`
`1. Holleberg, J., Dahm, J ., and Bath, J .2 “Geology and
`Production Performance of the Niobrara Low-
`
`Permeability Reservoir in the Denver-Julesburg
`Basin,” paper SPE 13886 presented at the SPE
`1985 Low Permeability Reservoir Symposium,
`Denver, May 19-22.
`
`2.
`
`“An Integrated Core Study and Stimulation Design
`Basis for the Codell Formation,” Halliburton
`
`Internal Laboratory Report SFA-A001-94, Febru-
`
`ary, 1994.
`
`3. Parker, M., Jacobs, R., and Yeager, R.: “Treatment
`Design Changes Improve Production Results for
`the Codell Formation,” paper SPE 21819 presented
`at the SPE 1991 Rocky Mountain Regional Meet-
`ing and Low Permeability Reservoir Symposium,
`Denve_r, April 15-17.
`
`4. LaGrone, K. and Rasmussen, J .: “A New Develop-
`
`ment in Completion Methods - The Limited-entry
`Technique,” JPT (July 1963), 693.
`
`5. Lord, D. and McGowen, J.: “Real-Time Treating
`Pressure Analysis Aided by New Correlation,”
`paper SPE 15367 presented at the 61st Annual
`Technical Conference and Exhibition, SPE, New
`
`Orleans, Oct. 5-8, 1986.
`
`6. Shah, S. and Lee, Y.: “Friction Pressure of
`
`Proppant-Laden Hydraulic Fracturing Fluids,
`PE (Nov. 1986), 437.
`
`” ODD
`DYE
`
`7. Shah, S.: “Effects of Pipe Roughness on Friction
`Pressures of Fracturing Fluids,” SPE PE (May.
`1990) 151.
`
`8. Nolte, K.G. and Smith, M.B.: “Interpretation of
`Fracturing Pressures," J
`1 (Sept 1981), 1767.
`
`9. Conway, M.W. et. al.: “Prediction of Formation
`Response from Fracture Pressure Behavior,” paper
`SPE 14263 presented at the 60th Annual SPE
`Technical Conference and Exhibition, Las Vegas,
`Sept. 22-25, 1985.
`
`116
`
`Page 10 of 11
`Page 10 of 11
`
`

`
`SPE 29553
`
`M.J. Eberhard, D.E. Schlosser
`
`11
`
`
`
`Final
`
`Initial
`Perforation
`
`Perforation
`
`Diagram I—Perforati0n with a sharp edge.
`
`Diagram 2—Perf0ration with an eroded edge.
`
`117
`
`Page 11 of 11
`Page 11 of 11