spe-9883-pa

7
Prefracture Injection Surveys: A Necessity for Successful Fracture Treatments Thomas E. Bundy, SPE, Conoco Inc. Summary Successful fracture treatments over large intervals are often difficult to obtain. In the Laredo Lobo gas field in Webb and Zapata Counties, TX, successful fracture treatments over large intervals are critical for economic success of the field. Conoco Inc. uses a prefracture injec- tivity test along with temperature and gamma ray logs to ensure that the entire completed. interval will be treated during the fracture job. If the entire completed interval is not being treated, the logs act as a road map to determine where additional perforations are required. Introduction Postfracture evaluation logs run in the Laredo Lobo field show that often only a portion of the completed interval was treated. Successful fracture jobs are difficult because the wells are completed over intervals as large as 61 m (200 ft) that often contain several individual pay sands. A typical log section is shown in Fig. 1. Suc- cessful fracture treatments over large intervals are critical for the future of Laredo field, as wells completed over small, easy-to-stimulate intervals are often uneconomical. Many techniques have been used to treat these large intervals. In the early life of the field, staged treatments with ball sealers were used widely. Currently, the use of ball sealers has been abandoned because postfracture evaluation logs have proved them ineffective. Staged treatments with temporary sand, gel, or mechanical plugs, although effective, are often impractical because of high pressures and small shale intervals that separate the pay sands. The most effective treatments involve the limited-entry technique to divert the fracture fluid across the entire interval. However, the success of the limited- entry treatments has been hampered by poor perforating efficiencies and low fracture rates. 0149·2136/82/0005·9883$00.25 Copyright 1982 Society of Petroleum Engineers of AIME MAY 1982 The low fracture rates in the Laredo field, which are caused by tubing and pressure restrictions, require that a minimum perforation pressure drop be used in the limited-entry fracture design. To distribute the fracture fluid accurately across the completed interval with a minimum perforation pressure drop, the fracture gra- dients of the individual zones in the completed interval must be known. In the Laredo field, the fracture gra- dients of the individual zones cannot be determined until the well is fractured. If the fracture gradients of the in- dividual zones are assumed incorrectly, the fracture job will not treat the entire completed interval. This paper proposes that a prefracture injectivity test be run to check assumptions made in the design of a limited-entry fracture treatment. Temperature and gam- ma ray logs run in conjunction with the test are used to determine whether the entire completed interval is being treated and to find any mechanical problems with the well before an expensive fracture job is pumped. Theory Most fracture jobs designed to treat large intervals fail because the fracture fluid is not distributed properly over the entire completed interval. When a particular zone in the completed interval does not receive enough fluid, it screens out early in the fracture job because the necessary fracture width is not created. The limited-entry technique has been the most effec- tive means to distribute the fracture fluid across the com- pleted interval. In limited-entry treatments, a minimum pressure drop of 2100 kPa (300 psi) is maintained across the perforations to force fluid into all the perforations. 1 Many limited-entry treatments fail because the fracture design includes the assumption that a single fracture will be created across the entire completed interval. In prac- tice, several independent fractures will be created across the completed interval when sufficient barriers separate the individual pay zones. When several independent 995

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Page 1: SPE-9883-PA

Prefracture Injection Surveys: A Necessity for Successful Fracture Treatments Thomas E. Bundy, SPE, Conoco Inc.

Summary Successful fracture treatments over large intervals are often difficult to obtain. In the Laredo Lobo gas field in Webb and Zapata Counties, TX, successful fracture treatments over large intervals are critical for economic success of the field. Conoco Inc. uses a prefracture injec­tivity test along with temperature and gamma ray logs to ensure that the entire completed. interval will be treated during the fracture job. If the entire completed interval is not being treated, the logs act as a road map to determine where additional perforations are required.

Introduction Postfracture evaluation logs run in the Laredo Lobo field show that often only a portion of the completed interval was treated. Successful fracture jobs are difficult because the wells are completed over intervals as large as 61 m (200 ft) that often contain several individual pay sands. A typical log section is shown in Fig. 1. Suc­cessful fracture treatments over large intervals are critical for the future of Laredo field, as wells completed over small, easy-to-stimulate intervals are often uneconomical.

Many techniques have been used to treat these large intervals. In the early life of the field, staged treatments with ball sealers were used widely. Currently, the use of ball sealers has been abandoned because postfracture evaluation logs have proved them ineffective. Staged treatments with temporary sand, gel, or mechanical plugs, although effective, are often impractical because of high pressures and small shale intervals that separate the pay sands. The most effective treatments involve the limited-entry technique to divert the fracture fluid across the entire interval. However, the success of the limited­entry treatments has been hampered by poor perforating efficiencies and low fracture rates.

0149·2136/82/0005·9883$00.25 Copyright 1982 Society of Petroleum Engineers of AIME

MAY 1982

The low fracture rates in the Laredo field, which are caused by tubing and pressure restrictions, require that a minimum perforation pressure drop be used in the limited-entry fracture design. To distribute the fracture fluid accurately across the completed interval with a minimum perforation pressure drop, the fracture gra­dients of the individual zones in the completed interval must be known. In the Laredo field, the fracture gra­dients of the individual zones cannot be determined until the well is fractured. If the fracture gradients of the in­dividual zones are assumed incorrectly, the fracture job will not treat the entire completed interval.

This paper proposes that a prefracture injectivity test be run to check assumptions made in the design of a limited-entry fracture treatment. Temperature and gam­ma ray logs run in conjunction with the test are used to determine whether the entire completed interval is being treated and to find any mechanical problems with the well before an expensive fracture job is pumped.

Theory Most fracture jobs designed to treat large intervals fail because the fracture fluid is not distributed properly over the entire completed interval. When a particular zone in the completed interval does not receive enough fluid, it screens out early in the fracture job because the necessary fracture width is not created.

The limited-entry technique has been the most effec­tive means to distribute the fracture fluid across the com­pleted interval. In limited-entry treatments, a minimum pressure drop of 2100 kPa (300 psi) is maintained across the perforations to force fluid into all the perforations. 1

Many limited-entry treatments fail because the fracture design includes the assumption that a single fracture will be created across the entire completed interval. In prac­tice, several independent fractures will be created across the completed interval when sufficient barriers separate the individual pay zones. When several independent

995

Page 2: SPE-9883-PA

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.-f-I ... , I ;

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I I t:o I , Fig. 1-Typical Laredo field completion interval, Well B-Webb

County, TX.

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,.,N %%

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Fig. 2-Pressure balance schematic.

fractures are created, each fracture must receive enough fluid to treat the individual zone effectively. If an in­dividual zone does not receive enough fluid, it will screen out early in the fracture job.

In the Laredo field, it is often hard to detennine when sufficient barriers exist between individual pay zones. To be safe, the fracture designs for the Laredo field must include the assumption that an individual fracture will be created in each pay zone .

The amount of fluid required for each zone is deter­mined by the zone height. For the typical fracture fluid and volumes used in Laredo field, 1.5 m (5 ft) of fracture height is created for each 0.16 m3/min (1.0 BPM) in­jected i(lto a zone and, for typical pad volumes, a minimum of 0.8 m 3 Imin (5 BPM) is required to create the necessary fracture width in an individual zone to avoid a screen-out. These parameters were detennined empirically by postfracture evaluation logs and vary from field to field.

The fluid distribution across the completed interval is detennined by the number of perforations in each zone. The amount of fluid injected into each zone is deter­mined by Eq. 1.

q=~ N 2

Cd4

£lpp, ........................ (1) p

where

q = injection rate, m 3 Imin (BPM), d = diameter of perforations, m (in.),

£lpp = pressure drop across the perforations, Pa (psi),

p = specific gravity of fluid, water = 1, N = number of open holes, and C = 0.0366 m4Pa/(m3/min)2 or

0.323 in2Ibm/(BPM) 2 .

Once the optimal pressure drop across the perforations is detennined, the required number of perforations for each zone can be calculated easily.

The optimal pressure drop across the perforations is the maximum pressure drop in the range of 2100 to 6900 kPa (300 to 1,000 psi) that can be maintained at the an­ticipated fracture rate and still allow enough perforations to fracture and produce the well without any problems. 3 Maximizing the pressure drop will help ensure that the fluid will be diverted into all the perforations. In the Laredo field, where surface pressures usually restrict the fracture rate to a maximum of 4 m 3 Imin (25 BPM), the pressure drop is limited to 2100 kPa (300 psi).

The pressure drop across the perforations is constant throughout the completed interval only when the fonna­tion treating pressure is constant across the interval. (The fonnation treating pressure is the fracture gradient times the depth.) In the Laredo field, fracture gradients vary from zone to zone across the completed interval. To compensate for different treating pressures in individual zones, the distribution and number of perforations must be adjusted accordingly. The number of required per­forations in a zone is detennined by Eq. 1 after the per­foration pressure drop is calculated by perfonning a

JOURNAL OF PETROLEUM TECHNOLOGY

Page 3: SPE-9883-PA

pressure balance for the fracture job. The pressure balance is shown schematically by Fig. 2 and mathematically by Eq. 2.

=t::.Pp +BHTP2 -PH +t::.Pf 2 2 2

=t::.Pp +BHTP3 -PH +t::.Pf' ............. (2) 3 3 3

where

P s = surface treating pressure, t::.Pp = perforation pressure drop, PH = hydrostatic pressure, t::.Pj = pipe friction pressure loss, and

BHTP = bottomhole treating pressure.

As shown in Eq. 2, the perforation pressure drop across an individual zone will decrease when the BHTP in­creases. With a lower pressure drop, the number of per­forations must be increased to maintain the required frac­ture rate.

The calculated number of perforations must be in­creased to compensate for efficiency of the perforating gun. Perforating efficiency is the number of perforations that will take fluid divided by the number of perforations that actually were shot. The number of perforations that will take fluid is determined from information obtained during the fracture job by Eqs. 3 and 4.

t::.pp=Ps-ISIP-t::.pj ....................... (3)

and

........................... (4)

where ISIP=instantaneous shut-in tubing pressure, Pa (psi).

Most Laredo field operators perforate the wells under­balanced with through-tubing guns. Hydraulic calcula­tions have shown that a 4.2-cm (1'X6-in.) hollow carrier gun has an average efficieHcy of 35 %. The efficiency for individual wells has ranged from a low of 10% to a high of 95%.

A limited-entry fracture job should be successful if the perforations are distributed properly across the complete interval and if the height of the completed interval is sized properly according to the anticipated fracture rate. However, many properly designed fracture jobs fail because of unknown perforating efficiencies and unknown fracture gradients in the individual zones. The success of a limited-entry fracture job depends on a known number of perforations taking fluid. The fracture gradients of the individual zones must be known when a minimum perforation pressure drop must be used to distribute a limited fracture rate across the completed in­terval. In the Laredo field, a minimum perforation pressure drop must be used because the fracture rate is limited by tubing and pressure restrictions. The actual distribution of the fracture fluid cannot be determined until an injection test or fracture job is performed.

MAY 1982

Successful limited-entry treatments can be obtained, despite poor perforating efficiencies and unknown frac­ture gradients, through use of temperature and gamma ray logs run in conjunction with a prefracture injectivity test. The injectivity test is pumped at the anticipated fracture rate and is tagged with a radioactive tracer. The temperature log is used to determine the amount of fluid entering each zone and the gamma ray log is used to determine the fracture height(s). If a zone is not receiv­ing fluid, additional perforations can be added as re­quired. Additionally, any mechanical problems with the well, such as channeling or casing splits, will be found during the test. With a prefracture injectivity test, the in­itial assumptions are checked and corrected before an ex­pensive fracture job is pumped.

Test Design In the Laredo field, the prefracture injectivity test is run as part of a prefracture ball out. The pre fracture ballout is recommended to ensure that all perforations are broken down and will take fluid. In Laredo, we used 2 % KCl water an\f 4.5 kg/3.8 m3 (10 lbmll,OOO gal) gel (friction reducer), a surfactant, and clay stabilizers for the fluid in the injectivity test. A typical test procedure is as follows.

1. Load hole with fluid. 2. Run a 5-minute injection test at the anticipated

fracture rate. Shut-down, record the ISIP, and calculate number of open holes.

3. Re-establish injection, drop ball sealers, and displace balls to perforations.

4. Shut down and surge balls off perforations. 5. Run a 5-minute injection test, tag the last 8 m 3 (50

bbl) with 20 mCi (740 x 106 Bq) of liquid 131 iodine tracer.

6. Overdisplace the tracer by at least 4.8 m3 (30 bbl) with clean fluid.

7. Run a temperature/gamma ray log across the com­pleted interval immediately following the injection test. If possible, log 91 m (300 ft) above and below the perforations.

When designing the test, make sure a liquid tracer is chosen and that the tracer is overdisplaced by at least 4.8 m3 (30 bbl) with clean fluid. Overdisplacement of the tracer is required to remove all radioactive residue from the wellbore. The gamma ray logging tool still can pick up the tracer when it is overdisplaced because the tracer leaks off into the formation. The use of a radioactively tagged sand is not recommended because when it is over­displaced over 36 cm (14 in.) into the fracture that is created it cannot be picked up by the gamma ray tool. Failure to overdisplace either tracer will leave radioac­tive residue in the wellbore and ruin the log. The saturated gamma ray log shown in Fig. 3 is an example of failing to overdisplace the tracer. The gamma ray log shown in Fig. 4 clearly shows the fracture height because the tracer was overdisplaced correctly with 4.8 m3 (30bbl).

No special equipment is required for the pre fracture in­jection test. The radioactive tracer may be added to the slick water at the blender tub or through a chemical in­jection pump at the blender discharge. If ball sealers are used during the injection test, they should be heavier than the fluid being pumped. The remaining required equipment is standard fracture pumping equipment.

997

Page 4: SPE-9883-PA

OEPTH FT.

8~00

PRE-FRAC INJECTED TEST TEMP - GR LOGS SURVEY

(Logs Were Run Immediately After The Test)

.. 00

8700

8800

8900

9000

TEMPERATURE LOG

GR INCREASING

9100 +-__ .-__ -.-__ + ________ -1.. _______ -'----'_-'-

190 210 230 2~0

TEMP F·

Fig. 3-Prefracture injection test temperature/gamma ray survey, Well A-Webb County, TX.

We have incorporated the injectivity test into the prepad stage of the actual fracture job when time per­mits. This can be done when there is enough time to run the injectivity test and fracture the well the same day. The purpose of the logs is to ensure that the entire inter­val is taking fluid. If the entire interval is not taking fluid, additional perforations can be added and the well still can be fractured the same day.

Note that there has been no apparent damage to the well after an injectivity test is performed, despite the fact that the Lobo sands have up to 40% clays. In fact, the well's production often increases after an injection test because the perforations are opened up.

DEPTH

Analysis The analysis of the injection test is based primarily on the temperature log. The temperature log operates on the premise that geothermal gradient will shift at a particular point in relationship to the amount of fluid that passes that point. This relationship, which was proved mathematically by Tixier and Witterholt,2 is shown by an actual test in Fig. 3. The gradient shift of 18°C (33 OF) at Point 1 on the temperature log represents the total injection rate or 3.2 m3/min (20 BPM). The gra­dient shift of lO.5°C (l9°F) at Point 2 implies that 19/33 of the total injection rate or 1. 8 m 3 (11.5 BPM) passed

.300 PRE- FRAC INJECTION TEST TEMP - GR SURVEY

(Log. Were Run Immediately After The Test)

.400

.~oo

8600

.'00

.800+---.---r---,-~~-----~------~--~-

100 110 190 210 230

Fig. 4-Prefracture injection test temperature/gamma ray survey, Well B-Webb County, TX.

998 JOURNAL OF PETROLEUM TECHNOLOGY

Page 5: SPE-9883-PA

.. 0 a::

~

~ U .. C

0

0 >-

0 ~

10 4-----------~------------------~ f20 BPW)

.8

6 (II 5 8PM)

4 (72 BPIII)

o .1 7 • 8 (D.T:IZOF) (D.T:lt"F)

't. of Totol Groditnl Shift

1.0 (6T: 33°F)

Fig. 5-Flow rate/temperature shift relationship, Well A-Webb County, TX.

this point. The total amount of fluid injected into the top set of perforations is the difference between the flow rate at Point 1 and Point 2 or 1.4 m3/min (8.5 BPM). In a similar manner it can be determined that the middle set of perforations received 0.7 m3/min (4.3 BPM) and the lower set of perforations took 1.2 m 3 Imin (7.2 BPM). The flow rate/temperature shift relationship is shown in Fig. 5.

The points where the gradient shifts are taken must have similar mineralogy to ensure that the gradient shifts are not caused by different thermal conductivities of the rock. If the completed interval contains different minerals with different heat transfer properties, the flowrate/temperature shift relationship will not be a straight line. The gradient shifts shown in Fig. 3 are shown on the gamma ray log in Fig. 6. Fig. 6 shows that all the gradient shifts were taken in relatively clean shales.

The gradient shift is seen easily in Fig. 3 at Point 1. At Points 2 and 3, the gradient shift must be found by draw­ing an asymptotic line parallel to the geothermal gradient at the maximum temperature reading between the per­forated intervals. To simplify evaluation of the temperature log, it is recommended that the log be plot­ted on a reduced scale.

The injection test in Fig. 3 indicates that three separate fractures were being created, because there are three distinct gradient shifts. This test found a potential prob­lem with the fluid distribution. The tOf and bottom set of perforations received 1.4 and 1.2 m Imin (8.5 and 7.2 BPM), respectively, which is well above the 0.8 m3/min- (5-BPM)-per-zone minimum. However, .the middle zone, which received only 0.7 m3/min (4.3 BPM), could screen out at some point during the job.

MAY 1982

1

I

r:# ~l

1 "

t:? GRADIENT ~ =-<

SHIrT PF~N~T..e.S+-+-H-+-+-++-I

of'-~

~

r> ~

11..- '1E I ~ ~ ,-

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8800

Per"

J' ,. I

8900

I'

9000 i

4

GR - INDUCTION LOG (WELL Al

I ,

Fig. 6-GR-induction log Well A-Webb County, TX.

The perforation distribution originally was designed to divide the 3.2-m3/min (20-BPM) rate evenly among the three zones. To ensure that the middle zone was treated effectively, the overall injection rate was increased to 4.0 m3 Imin (25 BPM) from 3.2 m3 Imin (20 BPM). The increased rate was possible in this well because it was shallower than most Laredo field wells.

The injection test shown in Fig. 4 indicates that a single fracture was created across the top three sets of perforations, because there was a single gradient shift. The test also indicated that no fluid was injected into the lower set of perforations. The gamma ray log supported this analysis. The lower zone was reperforated before the fracture job. The fracture design must include the assumption that two independeI1t fractures will be created. The gamma ray induction log for this well is shown in Fig. 1.

The injection test cannot determine whether the lower zone is not taking fluid because of poor perforations or because the zone had a higher fracture gradient than the rest of the completed interval. In either case, additional perforations are required to obtain the correct fluid distribution.

It is interesting to note that the tests shown in Figs. 3 and 4 were run in wells located on the same lease and completed in the same zone. In one well, three fractures were created, and, in the second well, only two fractures were created (assuming the lower zone will take fluid once it is reperforated). This is important because the more independent fractures created across the completed interval the more accurate the fluid distribution must be to avoid a screenout. The maximum size of the com­pleted interval often is determined by the number of in­dependent fractures that will be created as opposed to

999

Page 6: SPE-9883-PA

DEPTH FT

.600

'100

'800

.900

'_0

(0)00

1~200 +---r-----.----r---,..---.---,-----,----r--..,...--230 240 260 210

TEMP F-

2.0 290 300 310 320

Fig. 7-Pre- /post fracture log comparison, Well C-Zapata County, TX.

total height of the individual pay zones. The gamma ray logs are used to support the

temperature log analysis, to determine the fracture height(s), and to detect any mechanical problems with the well. The fracture height is difficult to determine from the temperature log because it must be run im­mediately after the injection test so that the gradient shift can be picked up. If the temperature log is not run im­mediately after the injection test, the temperature gra­dients between the zones deteriorate and it is difficult to determine the amount of fluid entering each zone. The postinjection test temperature loss shown in Fig. 7 was run 16 hours after the injection test. The temperature gra­dients have deteriorated to the point where it is impossi­ble to determine the amount of fluid that entered each

OEPTH FT

8~00

8600

8100

8800

•• 00

9000

INJECTION SURVEY-

PRODUCTION .PROFILE COMPARISON

zone. It was assumed that the two zones in Fig. 7 took equal amounts of fluid because each zone was cooled equally.

The gamma ray log also is used to detect any mechanical problems with the well, such as channeling or casing splits. If the tracer material is found in the wrong place, a mechanical problem is found and the ap­propriate remedial procedure can be taken.

Results To date, Conoco has run 10 pre fracture injectivity tests in the Laredo field. Five of these tests detected problems with the fluid distribution, which had to be corrected with additional perforations. One test found the fracture fluid being injected through a split in the casing 1200 m

SPINNER SURVEY

"00 +----r----r---+----r----t-..,...-r-----~'--......L...-~

190 210 230 50 100

-I_ Of GAS FLaw

Fig. 8-lnjection survey/production profile comparison, Well A-Webb County, TX.

1000 JOURNAL OF PETROLEUM TECHNOLOGY

Page 7: SPE-9883-PA

(4,000 ft) above the perforated interval. Only four tests indicated that the actual and the design fluid distributions were the same.

Postfracture evaluation logs have proved that the prefracture test will predict the fluid distribution ac­curately during the fracture job. The temperature logs shown in Fig. 7 show the agreement between the injec­tion test and the fracture job. The log run during the in­jection test indicated that both zones would be fractured, and the postfracture log proved that they were.

Economics The $30,000 average cost of the injectivity test is paid for easily by eliminating the need for refracturing and by recovering the maximum amount of reserves from a completed interval. Each of the five wells that were reperforated had at least a 3 .I-m (10-ft) interval that was not being fractured adequately. If a zone is not fractured adequately, much of its reserves will be left in the ground. With a 3.I-m (IO-ft) zone containing a minimum of 1.4 x 10 7 m 3 (500 MMcf) of gas reserves, worth $1.5 million at current gas prices, the economics are obvious. The elimination ofrefractures is also impor­tant because the average Laredo fracture job costs $150,000, and the refractures have a limited chance of success.

Other Logs Many operators have tried to use spinner surveys or noise logs before the fracture job to determine which per­forations are open; the idea is that if a zone will produce, it also will take fracture fluid. Fig. 8 shows a comparison between postinjectivity test log and a spinner survey measuring the well's production after the injection test. The temperature log shows clearly that all the zones took fluid. However, the spinner survey indicates that 85 % of the production is coming from the top set of perforations and that very little production is coming from the lower set. Spinner surveys or noise logs cannot be used to determine the injection profile because they reflect the productivity of the individual zones in the completed in­terval, not how much fracture fluid they will take during the fracture job.

Conclusions Pre fracture injection surveys are required to check the assumptions made during the fracture design that control the fluid distribution across the completed interval dur­ing the fracture job. The major assumptions are: (1) the number of independent fractures that will be created across the completed interval, (2) the fracture gradients of the individual zones in the completed interval, and (3) the perforating efficiency of the perforating gun used. Failing to account for these assumptions accurately could result in an early screenout in a portion of the com­pleted interval.

These factors are particularly important in deep wells where the fracture rate is limited by high pressures, and

MAY 1982

where through-tubing perforating guns are used widely. With a limited fracture rate, the number of independent fractures must be known so that the size of the completed interval can be chosen. In the Laredo field, each in­dependent fracture requires a minimum injection rate of 0.8 m3 (5 BPM). The fracture gradients of the individual zones must be known to distribute the limited fracture rate accurately. In deep wells, a small difference in the fracture gradients of the individual zones in the com­pleted interval will result in large differences in the in­dividual treating pressures. The different treating pressures of the individual zones can have a substantial effect on the fluid distribution across the completed in­terval. The importance of the individual fracture gra­dients cannot be reduced by increasing the perforation pressure drop because the limited fracture rates require that the perforation pressure drop be kept to a minimum. The use of through-tubing guns results in a poor and in­consistent perforating efficiency. In practice, these fac­tors cannot be determined until the well is fractured.

The need for a pre fracture injection survey is shown by six of the 10 Conoco tests in the Laredo field requiring remedial action before the well could be fracture-treated successfully. In five tests, the remedial action consisted only of addjng additional perforations. If the tests had not been run, a major portion of recoverable reserves contained in the zones not being treated would have been lost. In a sixth well, a $150,000 fracture job would have been wasted because of a casing split above the com­pleted interval.

Nomenclature d = diameter of perforations, m (in.)

P s = wellhead treating pressure, Pa (psi) !:!'Pf = tubing friction pressure loss, Pa (psi)

!:!.P H = hydrostatic pressure, Pa (psi) !:!.Pp = perforation pressure drop, Pa (psi)

q = injection rate, m 3 fmin (BPM) p = specific gravity of fluid, water= 1

References I. Wahl, H.A.: Conoco Frac Design Manual, Conoco Inc., Ponca

City, OK (1976). 2. Witterholt, E.J. and Tixier, M.P.: "Temperature Logging in In­

jection Wells," paper SPE 4022 presented at the SPE 47th Annual Meeting, San Antonio, TX, Oct. 8-11, 1972.

3. Howard, a.c. and Fast, C.F.: Hydraulic Fracturing, Monograph Series, SPE, Dallas (1970) 2, 100.

SI Metric Conversion Factors bbl x 1.589 873 E-OI OF CF-32)f1.8 ft x 3.048* E-Ol

*Conversion factor is exact. JPT

Original manuscript received in Society of Petroleum Engineers office April 6, 1981. Paper accepted for publication Sept. 16, 1981. Revised manuscript received March 5, 1981. Paper (SPE 9883) first presented at the 1981 SPE/DOE Low Permeability Sym· posium held in Denver, May 27-29.

1001