williams & associates,inc
TRANSCRIPT
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WILLIAMS & ASSOCIATES,INC..
M(po4[48,(ViqlpRKaho 83872 (208) 8834)l53 (208) 875-0147*
liydrogeology A$rle&I'$ sources Waste Afanagement e Geological Engineering e Afine flydrologye
'85 MR 18 All:42
March 14, 1985 .
Contract NRC-02-83-033FIN #B-73G9-3Communication #50
ld/h-YfSMr. Fred Ross W.1 Rec *d File \ElPr9.ct /h
- dN__ Ds:Ec! neDivision of Waste Management- WMMail Stop 623-SS
g,[?/[)~~!;U. S. Nuclear Regulatory CommissionWashington, D. C. 20555 Distribu! ion: _ ~ _ ~ .
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Dear Fred: .het ur_n ti_ lid,'_faMS)' ___ __~___._.~~( -
. .__ _ cI have enclosed a copy of the chapter used as a reference in thePalo Duro comment we discussed this date. The particular page ofinterest is 90.
Sincerely,
Gerry inter
8504000600 850314PDR WPWtES EECWILAB-7389 ppg1
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Advances in Well Test Analysis;
Robert C. Eariougher, Jr.
SeniorResearch Engineer.
Marathon Oil Co.
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\ Second Printing
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Henry L Doherty Memorial Fund of AIME
Society of Petroleum Engineers of Alk'E
New York 1977 Dallas
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Chapter 8
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Drillstem Testing
8.1 Introduction'
A drillstem rest (DST) is normally run in a zone of annulus, allows formation fluid to flow into the drilipipe,
undetermined potential in a well being drilled, although and continuously records the pressure during the test. Most
DST's are sometimes run in known productive zones in DST's include a shon productiort period (the initial flow
development wells. A DST provides'a temporary comple- period), a shon shut-in period (the initial buildup), a longer
tion of the test interval; the drillstring serves as the flow- flow period (the second flow period), and a longer shut-in
string. A good DST yields a sample of the type of reservoir period (the final buildup).8 8 Fig. 8.1 is a schematic DST
fluid present, an indication of flow rates, a measurement of pressure chart for a two-cycle test (note that pressure in-
static and flowing bottom-hole pressure, and a shon-term creases downward in most DST charts shown in this chap-
pressure transient test. The DST helps determine the possi- ter). He first cycle in Fig. 8.1 includes the initial flow and
bility of commercial production by virtue of the types of buildup periods, while the second cycle includes the second
fluids recovered and the flow rates observed. Analysis of the flow and final buildup periods. Early drillstem testing tech-
DST transient pressure data can provide an estimate of niques used only one cycle with a longer flow duration. Fig.
formation propenics and wellbore damage. Rose data may 8.2 shows tests with more than two cycles are possible.' 8
be used to estimate the well's flow potential with a regular (Note that pressure increases upward in that figure.)
completion that uses stimulation techniques to remove dam-age and increase effective wellbore size. a
To run a drillstem test, a special DST tool is attached to gthe drillstring and lowered to the zone to be tested." The gtool isolates the formation from the mud column in the g
i
\ %BASE UNC
AT THEsunFActyePiro Pirj
%P T 4 oe si es iia ise a4e
F ri #rr$ 8 TIME, t, MIN1 i
0- S 52
' pra E.E*A eli
U m & r*
SectMO||ArneA al PIRSV t>oh
CrCLE| CrCLE
TIM E' ---*- w .*,
,
Fig. 8.1 Schematic of a DST chart:(|} going into hole;(2) initial f i -
! flow period;(3) initial shut in period;(4)11nal Gow period;(5) final -
shut-in period; and (6) coming out of hole. p,.., = initial hydro- 3, ,, ,, , , ,
static mud pressure; p,n = initial Dowing pressure in first flow [ ta ts to to toperiod; p,, = final flowing pressure in first flow period; p,,, = Q TIME, t MINinitial shut in pressure; P.n = initial flowing pressure in secondflow period:pg, = final flowing pressure in second now period:p3, Fig. 8.2 Example of a three cycle drillstem test. Afler McAlister.
= final shut-in pressure; andp,s , = final hydrostatic mud pressure. Nutter, and I.cbourg.8
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W<,
DRILLSTEM TESTING 91
Dis chapter discusses the DST testing technique and relatively large-diameter packer,
presents methods for analyzing pressure data from both the he hydrospring tester valve is a hydraulic time-delayflow and shut in ponions of a DST. A series of example master valve that opens slowly and closes quickly. When the
DST pressure chans illustrates various DST operational packer is set, weight is applied to cock the hydrospring and
conditions and test malfunctions. A shon section on the activate the hydraulic time delay. A few minutes later, the
wireline formation tester is also included. hydraulic time delay closes the bypass ports and then opensthe hydmspring tester valve to stan the DST. During the
8.2 Drillstem Testing Tools and Technique test, the CIP valve is closed and opened to cause the shut-in
Most drillstem testing tools include two or more clock- and flow periods (Figs. 8.4b and 8.4c). The hydrospringdriven Bourdon-tube recording pressure gauges, one or two tester valve closes immediately when the weight of the pipe
packers, and a set of flow valves. De tool is attached to the is picked up. Then the bypass ports open. With both thedrillstem and is lowered to the test interval where the packer hydrospring tester and CIP valves closed, a fluid sample isis set, then the valves in the tool are opened and closed by isolated between those valves when the tool is removed from
manipulation of the drilipipe. He DST is run while the flow the hole (Fig. 8.4f).
valves are being manipulated. De optional handling sub and choke assembly aids inFig. 8.3 shows typical drillstem testing tools used by the making up the tool and also provides a receptacle for a
Hillibunon Co. for the three basic types of tests: the single- down-hole choke, if such a device is desired. He DST tool
packer test, the straddle-packer test, and the hook-wall contains two Bourdon-tube pressure recording elements.
packer test. Fig. 8.4 shows the operating states of a Hallibur- The upper element, in the flowstring, senses the pressure as
ton DST tool during a test. Johnston Schlumberger, Lynes, fluid flows into the drillstring during the test. He lowerInc., Arrow Testers, and others also offer DST service and pressure recorder, near the bottom of the tool (Figs. 8.3a
tools. through 8.3d), is " blanked off" from the flow portion of theAs shown in Fig. 8.3, the upper section of the DST tool is system. It records the annulus nressure below the packer
the same for all three test types. The uppermost part of the rather than the pressure of the fluid inside the drillstem. In a
tool is an impact-reversing sub that allows produced fluids to good test, the pressures from the two recorders will differbe reverse-circulated out of the drillpipe (Fig. 8.4e). The only by the hydrostatic head between them. in poor tests, itclosed-in pressure (CIP) valve is the main flow-control is often possible to detennine the kind of malfunction byvtive in the DST tool string. In conjunction with the hydro- comparing the two pressure charts.spring tester valve, it allows the two flow periods, the two Many DST tools include hydraulicjars and safetyjoints toclosed-in periods, and reverse circulation. aid in removing a stuck tool. If the tool cannot be u istuck by
As shown in Fig. 8.4a the CIP valve is cpen and the jarring, the drillstring may be backed off at a safety joint,hydrospring tester valve is closed as the DST tool is run into allowing recovery of the pipe and a portion of the tool.
the hole. The bypass ports are open while the tool is being Single-packer tests use either a nonrotating, expandingrun into and out of the hole to allow fluid to flow through the packer with a tail pipe extending to the bottom of the hole or
tool to help minimize pressure surges caused by running the a hook-wall packer. Both assemblies include a perforated
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pl CPEN 0LE STRADDLE PACKER TEST
e. TOOLS USED 08 ALL TmEt TYPE TESTS =
F 2 8.3 T) pical DST tooh used for three types of tests. Upper assembly (lefi)is similar on all three test types. Afier Edwards and Shryock."Courtesy Petroleum Engineer.
.
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ADVANCES IN WELL TEST ANALYSISt 92l
l anchor pipe and a blanked-off pressure recorder. During the closed and the hydrospring tester valve is closed, trapping a'
test, fluid flows from the formation through the perforated fluid sample under pressure. Then the bypass ports are
anchor pipe and into the drillstring. A temperature recorder opened, and pressure is equalized across the packer (Fig.
may or may not be included in the tool string. 8.4d). he packer is unseated, the reverse circulating valve
De straddle-packer test uses two packers, a perforated is opened, and mud is pumped down the annulus to displace
anchor pipe, and a blanked-off pressure recorder between the produced fluids up the drillstring for measurement at the
the packers. An equalizing tube connects the annulus above surface (Fig. 8.4e). As the pipe and tool are removed from
the top packer to the hole below the bottom packer. The the hole (Fig. 8.4f), the mud in the drillstring is allowed to
equalizing tube aids in bypassing wellbore fluid around the bleed into the annulus through the open reverse-circulating,
'
packers while running in and out of the hole and balances the valve.
load created on the drillstring by the annulus hydrostatic Hole condition may dictate the total time that the tool can;
pressure during the test. A third pressure recorder may be remain in the hole, since a primary consideration is complete
included below the bottom packer to indicate whether that removal of the tools at the end of the test. Rus, conditions
packer remains scaled throughout the test. existing in the well may dictate relatively short testing times.
As indicated in Fig. 8.4a, the CIP valve is open and the Experience in the area is the best way to determine total
hydmspring tester valve is closed while the tool is run into allowable testing time. When allowed testing time is short,
the hole. He bypass ports are open, so mud may flow both the division of the test between the various test periods is
around the outside of the tool and through the packer while important. Pages 22 through 24 of Ref. 5 provide guidelines
the tool is :a motion. Both pressure recorders are in com- for choosing the length of the flow and shut-in periods in a
munication with the mud column and should record hydro- DST - whether total test time is limited or not. Table 8.1
static pressure as they are lowered into the hole (Fig 8.1). summarizes that material.
When the packer is set, the bypass ports close and the in a standard DST, the initial flow period is usually short,
hydrospring tester valve opens, resulting in the configura- 5 to 10 minutes; the idea is simply to release the high
tion shown in Fig. 8.4b. Both pressure recorders should hydrostatic mud pressure. The initial shut-in period should
show the same pressure response. To shut in the tool for a be sufficiently long to allow the measured pressure to ap-
buildup, the CIP valve is closed (Fig. 8.4c). He CIP valve proach stabilizedformarion pressure. Experience indicates
is opened for the second flow and closed for the second that I hour is usually required for the initial shut-in period.sa
buildup. After the final buildup, the CIP valve remains De second flow period should be long enough to allow flow
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-m-RUNNING FLOWING FORMATION EQUALIZlNG REVERSE PULLING
IN FORMATION CLOSED IN PRESSURE CtRCULATING OUT
o b c d e f
Fig. 8.4 DST-tool operating states for an open-hole forrnation test. Fluid nmement is shown by arrows. After Edwards and ShryocL'Counesy Petroleum Engineer.
--- - _
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93CQlLLSTEM TESTING
. stabilization; Table 8.1 provides guidelines. The length of ble for a rnoderate bottom-hole pressure increase compared
the final shut in period depends on test behavior during the with total pressure drawdown, but it can lead to significant
final flow period. Recommendations are given in Table 8. l . ermrs in the buildup analysis for high. productivity wellsDe multiflow evaluator, a tool that allows unlimited unless the well flows at the surface for a substantial portion
sequences of pmduction and shut-in, has been available for of the flow period.'drillstem testing since 1%5.8 The tool includes a fluid If the pressure in the flowstring recorderincreases linearly
chamber to recover an uncontaminated formation. fluid with time, liquid flow rate into the drillstring is constant (for )sample under pressure at the end of the flow period. a constant-inver-diameter drillstring) until liquid reaches the |
'
surface. Such a constant flow rate implies that flow rate is
independent of drawdown, since bottom-hole flowing pres-8.3 Analyzing Drillstem-Test Pressure Data sure is increasing. Eq. 2.2 indicates that flow rate from a '
Normal Drillstem-Test Pressure Buildup Analysis porous medium to a wellbore must decrease with decreasing
Drillstem-test pressure buildup data are analyzed much drawdown (increasing flowing bottom-hole pressure), so ,
like any other pressure buildup data; the techniques of Sec- something other than the formation must be controlling the',
tion 5.2 apply. In a DST. the flow period is about the same flow rate under such circumstances. He controlling factor is
duration as the shut-in period, so pressure buildup data must critical flow" (flow rate independent of pressure drop, see
be analyzed with the Horner plot.p,, vs log [(t, + At)/At). Section 13.6) through the perforations in the anchor pipe. In
The value used for t, is usually the length of the preceding such an instance, the flowing pressure data from the flow-
flow period. However,if the initial flow period is very long, string recorder are useless although shut-in data are analyz-
it is more accurate to use the sum of the flow-period lengths able. Fortunately, all data from the blanked-off recorder can8
for i, for the final buildup. be analyzed in the normal fashion.
In liquid-producing wells, the flow rate during a drillstem Wellbore storage is not often significant in the builduptest decreases with time since the backpressure exerted on portion of a DST since the well is closed in near the forma-the formation face increases as the produced fluid moves up tion face. However,if analysis results appear suspicious, the
the drillstring. Flow rate may stabill:e ifformation f7uids log-log data plot (Section 5.2) should be made to determine
flow to the surface. The increasing flowing pressure is what part of the data should be analyzed. lf thick sections are
evident in Figs. 8.1 and 8.2. Normally, the decreasing flow being tested in low-permeability or gas reservoirs, wellborerate over the flow period is neglected in analyzing DST storage can be significant in a DST. Although productionpressure buildup data and the average flow rate over the flow during the DST flow period appears to be wellbore-storage
period is used. Neglecting the flow-rate decrease is reasona- dominated until flow starts at the surface, the flow rate maybe estimated, so normal analysis methods should apply if the
varying rate is considered or if the rate variation is less than 5TABLE 8.1-RECOMMENDED FLOW AND SHUT-IN TIMES FORDRILLSTEM TESTING WHEN EXPERIENCE IN THE AREA IS NOT
to 10 percr.nt.
AVAILABLE. If the shut-in period is long enough, and if wellboreUnf nnation from Pages 22 24 of Ref. 5.) storage is not dominant, a Homer plot of the buildup data
Mgm should have a straight line section with slope -m, as indi-Test Situation During
Penc1 Test Recommended Time (minutes) cated in Section 5.2. The value of m may be used to estimate
In tial All Short-release 3 to 5 Permeability from Eq. 5.6:flow hydrostatic mud
k162.6 qB . ..(8.1)Mpressure . ....... . ...
*Initial All 60 minutes unless 30
isfe'o','M5 If g and h are not known, kh/p may be estimated by re-Sh # " "'
45 minutes then arranging Eq. 8.1. The flow rate normally used is the aver-
Final Strong, continuing 60 minutes 60 age over1,. The skin factor is estimated from Eq. 5.8:
flow blow
, ygg [\ t,t, + 1 jBlow dies Shut in when blow s = 1.1513 Fine-Per(At = 0)/dies m
,
Reservoir fluid 60 minutes - 60produced at longer to gauge ksurface flow rates if -log + 3.2275 .... ........(8.2).
time is available #Ca ,sr
The term log [(r, + 1)/t,) is included since it may bei '[ow dNn"g
't tl nnut-in
flow period important in drillstem testing. The term is normally ne-Blow dies during Minimum shut-in Two times glected when t, >> 1 or when the skin factor is high.
n w time00* P'"od yo*,*,$*, ice DST analyses com:nonly report damage ratio:
Reservoir fluid Shut in time equal 30 Jm. p p,f
P - Per - A , , . . . . . . . . . . . . . . . (8.3),
produced at to one-half ._
Psurface during flow time lactual
9a the case i euqup. so no buildup anasyne Fioepenoa esta may b..n.w.o oca.,yrer .wnoo cnn.e e no ne t=mpi.s.i. Eq. 2.9:
h_
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N*
ADVANCES IN WELL TEST ANALYSIS'
94
pfw; and the final hydrostatic mud pressure,p3,,,. He flow141.2 qBg , *(g,4) and shut-in period durations are usually also reponed. Such, *
khlimited data may be used to estimate reservoir propenies.
initial, or average, reservoir pressure is estimated by he .mtial resemir pressure is taken asextrapolating the Homer straight line to infinite shut-in time,
. . .(8.8)(t, + at)/at = 1. Since a DST is a shon-duration test, there p, = p = p,w . .
is generally no need to correct the extrapolated pressure for ne value of m for the semilog straight line is approximated,
drainage shape as done in Chapter 6. The extrapolated p, byshould be about the same for both the initial and final shut-in Ptn PAv ,(g,9)periods, if it is significantly different, a very small reservoir m= ,
or a bad test is indicated. He definition of a significnt log [(t, + at)/at]difference depends on the reliability of the data and the where at is the total final shut-in time (time when pf,, was
buildup extrapolation, but a typical value might be 5 per- read). Permeability may be estimated from Eq. 8.1. (If thecent. When such a difference occurs, the test should be initial and final shut-in pressures are the same, m estimated
repeated with a longer final flow period, if possible. from Eq. 8.9 will be zero and the approximate method will4
if rate varies significantly during the flow period, then the not be usable.) ne damage ratio is estimated frommultiple-rate analysis techniques in Chapter 4 should be #M 0.183 (p,w -pn) .(8.10)used. Odeh and Selig$' propose a simplilled analysis tech- , .
4*d "nique that is useful for large rate variations when t, is lessthan shut-in time. They suggest modifying t, as given by or from5
Eq. 5.29: j, p, _ p'' '' '
'_
u 4., m(4.43 + log t,)_
j , ''I'E ~ ''l ) where t, is in hours. Eqs. 8.9 through 8.1I should be used
t,* = 2 t, - .(8.5) only when more complete data are not available since they,
can be significantly in error.2 1 gj(tj - tj )Type-curve matching may be used to analyze pressure1-i
buildup data from drillstem tests. When wellbore storage is""
Similarly, q is modified as indicated by Eq. 5.30: significant, the type curves in Appendix C. Figs. C.8 (Ref.12) or C.9 (Ref.13), may be useful. Type curve methods
y
... . (8.6) are more useful for analyzing flow-period data, as discussedq* = 'I . I gj(tj - tj y) .- .. .
* i- i following Example 8.1.n
He modificd values, t,* and q', are used in the Horner plot Example 8.1 Drillstem Test Analysis by theand normal analysis given by Eqs. 8. I through 8.4.
. HomerMethodFor all practical purposes, the radius of investigation
Figs. 8.5 and 8.6 show DST data given by Ammann? forduring a DST is equivalent to the radius of drainage given in
an open-hole test in the Arbuckle formation.Eq. 2.41: We first check the recorded hydrostatic mud pressure
A' ..(8.7) against the value calculated from gauge depth and mudr, = 0.029 . ..... .
M8 density. From Fig. 8.6, the depth to the gauge is 4,174 ft andmud density is 10.1 lb./ gal. Herefore, the hydrostatic mud
If a barrier to flow exists within the .adius of investigation pressure is)
it might affect the semilog plot. In that case, the distance to lb./cu ftthe barrier may be estimated from material in Chapter 10 or p . = (4,174 ft) 10.1 7.4805
1
Ref.11. Generally, DST's are much.too shon to see theinfluence of a boundary. If changes in the slope of the [ 0.43310 psi /ft }
\ 62.3664 lb./cu ft / |
semilog plot of DST data are interpreted as reservoir discon.tinuities, the results should be viewed with a great deal of = (4,174 ft)(0.5247 psig/ft)
skepticism. W90 psip
Drillstem Test Buildup Analysis With Limited DataFrom Fig. 8.6,
ne analys.is procedure expla.med previously cannot beused if the pressure data available are incomplete. Dat is pm,,, = 2,314 psig, so the deviation is 5.66 percent, and
usually the case immediately after the DST is completed, p3,,, = 2,290 psig, so the deviation is 4.57 percent.
since thefull pressure record is read in the service companyoffices, not at the wellsite. However, a few key data points Rese deviations are primarily a result of errors and varia-
are read at the wellsite and given to the engineerjust after the tion in the mud density. The difference of 1.04 percent
test. Rese include the initial hydrostatic mud pressure, between pm., and p3,,, may be a result cf mud loss. Such
pa ,; the initial shut-in pressure, p,w; the pressure at the end differences in the range of 0.5 to i percent are indicative of
and m; the final shut-in pressure, the accuracy ofp, estimated from a DST.of each flow period,pm P
__ ..
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Y.--
95DRILLSTEM TESTING
| Depth 4174 Clock No 1547 12 hou, T 166710*
,r~-- No 241
i ,,- - 1i ~r_ ,_Fi P.ned oimod sa P.usue m Pen.d O.e.s la r _-- : - Fio. P ed f Osand ta P,ee v.,
M, 9'j5Q l Two 0 8L Q T 0 8LTase 0.fL T e 0.dk M 9d5 T e 0.fL 9Q T 0 8L. 4mr 9. mr e c mr c. - e c I me c mr c.
ci
0 .000 57 .000 35 .000 12 .000 1&5
I .008 35 .042 1664 .108 37 .0825 1669
2 .016 32 .084 1701 .216 50 .165 16993 .024 32 .126 1708 .324 65 .2475 1706
8 .032 32 .168 1711 .432 80 .110 1711
S .040 ss .210 1713 .540 97 .4125 1711
e .252 1716 .6&R 112 .&95 1711
7 .294 1716 .756 110 .5775 1711
P .336 1716 .R64 1&5 .nna 1716
9 .378 1716 .7&25 1716
to .420 171R .R25 171R
tt
12
13
14
15
a.co.e t ._ 1 n a || 3e 17 unau ,ss
utMAars:
' " - ' - ' " * * ' -SPECIAL PRESSURE DATA----"
Fig. 8J Pressure vs time measurements for a DST from the Arbuckle formation: Example 8.1. After Ammann.'
Following an initial flow period of 5 minutes, the shut-in both shut-in periods. Each shut-in has a straight line that
period is 60 minutes (Fig. 8.5). Rus, we make a Horner plot extrapolates to p, = 1.722 psig. Although not shown, the
of the final flow-peri < d data with r, = 2 hours, the length of log log data plot indicates no significant wellbore storage
the second flow period. Times in minutes are obtained by effects during the buildup periods.
using the time. recording interval shewn below each set of To analyze the pressure buildup data we must first esti-
readings in Fig. 8.5. Fig. 8.7 is the Homer plot for data from mate the average flow rate during each flow period. Hedrilipipe was initially empty for this test, so the pressureexisting before opening the tool for the first flow was atmo-r
. . . . . ...... ....
Q [,, [ '""* [ | spheric. At the end of the first flow period, the pressure was.m . ~=, ,
~. t:=--
,! 35 psi (Fig. 8.5). Assuming that all fluid flowing during that'0, . . . . ~ . - g
g.t time was drilling mud, we may estimate the height of the
O. "
]* .'. = /," ".~4'J.* " " ' " " .| { mud column. From the calculation of hydrostatic mud pres-sure, the mud exerts a pressure of 0.5247 psi /ft of column- a-'O ..:- , "2"i ,. _. , .
height, so 35 psiis equivalent to 35/0.5247 = 67 ft of mud.;__-- ::"O g * !3"bh Fig. 8.6 reports that 75 ft of oil- and gas-cut mud were
-
:" = ~ --:8 --0 0,:|y|::' O ~-- . . -,,, ,,
recovered. nis agrees well enough with the estimated 67-ft- i.. m.: - . . . - , - - -
- ~ _ t. value to use that value for production during the first flow |#2 # "" D ''" l~~ ~"~
'~~ '" ~' *" H 9 period. Fig. 8.6 reports that 240 ft of 2.5-in.-ID drill collar;,,,,_, , , , , , , , , , , ,
j [ were used in the tool string. De capacity of the drill collar is,_ , , , , , ' O.00607 bbl /ft, so 67 ft is equivalent to (67)(0.00607) =is g
_
,,
0.407 bbl. Assuming that 0.407 bbi of fluid was producedI e. jIp......,-%..-
_t.,u ,1_u a i. ..ese . v i -= . u . <.. --
Im , , , , , , ,i,,,. . .. n .. i.. .. n .
-- gi e imn*L op i m.
I keTao- oiu ons* "'
. ."| :,~'a "^ p- ;'''L""M''''{N'T E | |,.,
*
- If' J J_
J._. !g g ,- m. -- . -- .
" , _ " . . 'C' '.: 4 , iroo - a -. !- ' "-
l' ,~ w stoet -m -or Pst/crct.t-~~ ' -~
W] e,_.R ",: . . g1 : i, , e
; , , , . ,.
i , ' ^ ' i" ~ ~
SLOnt==m =131 Pst/CrCt.t~
1) **h.'-D | .a~'- -
!''''1 ' '' E'
I
NI 2205 22 I - - 1990
30 g
,FORh4ATION TEST DATA-- -a--**
itp+At)/AtI Filt. 8.6 Drillstem-test data sheet for a DST from the Arbuckle! formation; Example 8.I. After An.mann.' Fig. 8.7 Homer plot for data of Example 8.l. After Ammann.7l
|
lI__
. _ _ -
_ -
96 ADVANCES IN WELL TEST ANALYSIS+
from the formation in the first 5-minute flow period, we associated buildup are more reliable. In any case, the mate-- estimate an initial rate of rial above illustrates the approach. Ammann' gives a more
q = (0. ;07 bbl /5 min)(1,440 min /D) = 117 STB /D. c mplete analysis.'
To estimate skin factor we assume 4 = 0.15 and c, = 25Eq. 8.1 now can be used to estimate kh/p. Assuming B = x 10-8, and use Eq. 8.2 for the second flow period:1.0 RB/ STB and using m = 131 psi / cycle from Fig. 8.7,
= (162.6 17XI) = 145 md ft/cp. s = 1.1513 1,713 - 145 + jog 2+1
If we take h = 16 ft, the tested interval, , .
k -log + 3.22751I78
- = 145/16 = 9.1 md/cp. _(0.15)(25 x 10-*X8.75/24)8 . )M
= 81.5.De pressure increases from 35 psi (at the end of the first
flow period) to 145 psi at the end of the second ficw period. He well is severely damaged. We estimate pressure drop
Measured oil gravity was 44 ' API' so oil specific gravity is across the skin fmm Eq. 8.4:
0.806, corresponding to a gradient of about 0.349 psi /ft. A ,= (141.2X36.8)(1) *
Assuming that all the fluid produced was oil, the pressure P 285increase of 145 - 35 = 110 psi corresponds to 315 ft of oil.
= 1,486 psig.Note there are only 240 ft of drill collar (Fig. 8.6); above thatthere is drilipipe with a capacity of 0.01422 bbl /ft.' Assum- From Eq. 8.3, the damage ratio is
ing that the oil flows through the dense mud, we can estimate 1,722 - 145 ,g7'3'the volume ofoilin the pipe: 1,722 - 145 - 1,486
V. = (240 ft drill collar - 67 ft mud)(0.00607 bbl /ft) Ris indicates the well is producing at only about 6 percent
+ [315 ft oil - (240 - 67) ft oil in drill collar] of its ideal capacity. Stimulation would be required for asuccessful completion.
x (0.01422 bbl /ft) Although we have sufficient data for a Horner-type= 1.05 + 2.02 analysis, we may apply Eqs. 8.10 and 8.11 to compare= 3.07 bbi oil recovered. methods for estimating the damage ratio. From Eq. 8.10, the
damage ratio ish us,
0.183(1,718 - 145) = 13.7,3.07 bbt x 1,440 min /D 21
9 = 36.8 STB /D.1 0 min
and from Eq. 8.11,it isUsing Eq. 8.1 and m = 21 psi / cycle from Fig. 8.7, and I 718 - 145
assumingB = 1.0 RB/ STB, "
21(4.43 + log 2)
5 = (162.6X36.8X1) = 285 md ft/cp. Dese values agree reasonably well with the result estimated" from the skin factor.
or
b = 17.8 md/cp.M
Example 8.1 illustrates some of the problems that canhis is almost twice the value estimated from the first shut-in occur in DST pressure analysis. The problem of estimatingperiod - not unusual in drillstem-test analysis. Part of the flow rate is a real one, and must be dealt with by using
|discrepancy may be a result of an error in measurement of a pressures, densities, volumes of the various fluids pro-
: flow-period length or in reported pipe sizes. In working this duced, and pipe capacities -if flow does not occur at thel example, Ammann' states that there was no drill collar surface. Inconsistent or inaccurate fluid-volume and pipe-
while his data indicate that there was. Most likely, this is size data, as occur in Example 8.1, make analysis difficultwhere most of the discrepancy arises. Errors are also un- and should be avoided if possible. Normally, one does no,doubtedly introduced by the assumption of the type of fluid analyze pressure data from the first flow and shut-in periods.entering the drillstring (all mud in the first flow period, all Results fron, analyzing those data tend to be less accurateoil in the second flow period). Another possible source of than results from analyzing the second flow and shut-insome of the discrepancy may be that part of the production periods because of longer flow duration and likely absenceduring the first flow period is a result of decompression of of mud production during the second flow period.the wellbore fluid from hydrostatic mud pressure, about
Analyzing Flow-Pen. d Datao| 2,300 psig, to the formation pressure of about 1,700 psig.
ne over-pressure in and near the wellbore can affect both if rate variation can be estimated during the flow period, it
the flow rate and the pressure during the first flow period. is possible to analyze pressure data from the flow periodGenerally, the results from the second flow period and with methods given in Section 4.2. Such multiple-rate
__
i .W -'
97*DRILLSTEM TESTING
analyses can be particularly useful for wells with substantial they are not recommended. Ramey, Agarwal, and Martin'.
flowing bottom-hole pressure increase that either do not provide type curves that include skin effect that may be used
flow to the surface or have insufficient surface flow time at a to analyze DST flow-period data as long asflow does not
stable rate to provide reliable analysis results from the shut- reach the surface and there is no significant change in the*
in pressure data.. wellbore storage coefficient (pipe inner diamater). Figs.
Occasionally, the pressure exerted by the produced fluid 8.8A through 8.8C* are the Ramey-Agarwal. Martin type
column can reach the reservoir pressure, causing production curves. In those figures, the dimensionless pressure ratio is
to stop during the flow period - the well kills itself. In such defined as
cases, data from the shut-in period cannot be s.nalyzed.However, flow. period data can be analyzed by multiple-rate Poa " g " p, _ p g g)
pg_
, , . . . . .(8.12)
techniques (Section 4.2) or by type-curve matching tech- where p, is the pressure existing in the drillstring im-.
niques presented in Refs. 9 and 14 through 17. The typecurves in Refs.14 through 16 do not consider ikin factor, so 'See footnote on Page 24.
' . .c- . . ~S . :: n -- _~~ ~--="-===. .=v==.==.=..:. == :=. ===.|=..=. ===. " ==.=..:=.n : ==. . :.1;; . . . -m - . .. ... w =. - . .E=="'m.J==*i
-
~2:'d ;:|'-c ' c ti;::2:h. A - A20""=====: ".".!::===4 =:m=::==r.
i: 'tt.ii.;.;:'"t;r. .;r. =5:'ta;:b, ,Nw : .e v. =. . =. . .=.=. , ".E ="E=.=:. . ==R ::.: . =..=...,
1
| -s,, . ..% =as ;:"'EEE:'t 3 ~G='ItsN"*'" ?t ' *:'? E@N',k;'''2'.k '388 ; E EEUU 8 L >!:EEE C ' EU"'
.. . .. <,
I I
:r '":E_=::|"="~=" ::,2 C t h;* .Jt:2. :.'ti;'t.';'=.- - 3: =
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.
- -."..." .=..M...=.L.. --- . . =.n..M.|;;"". . -
_ ... ... . ... m..
., :====2nv: Mt=;'act:inti,'n ='th,.1. %..C. .,".*.:::=. =.=.*.1'||=L.,=g=gg=| ||:=.r . j :3.1 i:
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== . = n.. =. .e!in..n.w=.=:.. :;t,,4.,m.1:.'ss.tr..n_m":..i. *-- ==n*::::=== A=u i':::
>
. . - wa 1
,u. .= =a,=. .c.w arrm._EE -- '"'-=== :. == ===o=.. .r=:. . - < -=== = . = n = e.g .,..
=.'u:M".".". .=.,gt :.*qu ".E"ik%1|* * ';ikin.it tNg=|:==0 |||| 0 '.=m3|:t == ~ - i:|*
E====:2. . - =_.t" =1.J. h.11%.'I..'h.t,.=...t, ,.ih1.,5 =.. S ==:" .==113. ==..*": .: .|:.'
o,., 6- I..m... i .. =_. ... . . ..m
h.=- 4.=23. :h.nu.x.r. ;g .&m [email protected] . =. .=.==. " :===gg=..a., r...: a< .= u. :.u... ;Et.i ,M =.. .=._=_==.=.. n EE" .'=e t.:'
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eus.a' .=m malGEi :.e' a : := == .m" --- --- -
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.
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r..=u pA6M.i'il i=e:vasanr gyw..==g==!g:=== Mad -MuE.i ,, iiE=Ei =!!!!! !'i - .- "a r.. a.,nt. . 2Dh ==t =.==. . = :..: . .
=== === =...:= iE5L e... @*v, e. .. .. .v1 === -= ns = e. . m J:,s.u. ='i:. J D t n==:r==1a.
. . . .
o. m_=..n.== i=:EE_ggg ... ..aE== == :=.:.=----- air a n.m.h=.c: .u. m. . g n = g =. = _ u. = , a....
--~ =.s-,
. .._ . . w me '
cc::=tj ucr:,r - 315E=c..e an n=r- = . . = =-
. .:==g===m.====..::.=ili!====.;.=..=.liiLa. x..c, .u.nb.. . n. y p:, . c . =. r. . _=.==.E !.r == =:
=-===: . .-. :. .:=. = =. s.. ..cua - =. .
> ===:e = : === t =: = :,=,r r a,s .v. '-...._ . . < . . _
==== ; =>
::A:: A; == ". |||||||: C |.
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. U : " i . '113 |||:g=1- === : - - - '
1 =1%".*n .1 1 E'i1'ir''l|||:-- - :>'a-= = = = * - - - ' - ~ ~ * = = = = = = = ' - - = = - -
as =P=||=||=n=sC ==g=. ;=*.=ggn !|LUir
|"
|
= *sw========:"":"=....=..=.. . .l11.Lr. . i..W W_ *1,%.=.:. : M. . . ' . j : _i: .- .....=: . g
= ::|.>
,a .E". ||||=m=.=.:.:=..U.""g"E"E""n.=.="u g'",'=,.|i.r, . P. i . . -LW..M..W. . 3 a : n. ==E E"30".. X"
E_ -=.=_: == .:n.g ====c u ._ r= .e. : .v. . mann ::. . === n ==m'---. =-. . . .. .
.-"""" = : * || =,1
===| nn== :==E.. hli"==i" i..=..=...'::.::.:i:=.| : '..:= ' %.d1 Ci,t',||.V ',,k,c. 9 c's&11!,u.,.,t ",T, t, ;'n .'
== = n= .. . . ,. .. --
iu, t.g. ::. :z. ,-.--
| gming :- =ge,=====.: rmac =|t e.:. .u sI
"" "" :; =.. 8 =|;;'*.' WNJ: %.%.V. '|n.- E E = =.. . g=.=. :n;-
gi g =ad.||=...:"li N"", in .Ig .! : .-- <g ...EE=g.= A'O I"/ - I t ~- P'E EEE:: - Ei?
,
E=" -=EMM : REMEER'!!!Mi'|'
A' " ' " 'M - ?ai :::::=1. ==.==..=.::= ===.an..: 23.::::Elg==.=.=.i2 ;'.'== = n===== =.== .= ====.= . +.eu .Y.y i.t" r. "." M.==
a.=. ===. .. .. . .- .. - .m a, === =: . :..
g:M"=====:M=| :n*==n'"" |||"uf r= r'ik.. ' *, ;r '. ,a .Wt==0 ' == U'
o ======== g ==.= E.E..: 38mm..a.:.*E18EE' _I'.:.
_ . _ . . @. _M w 8 :'. .i._ . . = = . .... .._.. . . . . . . . . . . . .a > . . . . ...
so-. so-a e so . som som
to/CoFig. 8.8A Semilog type curve for DST flow period data. Best form for early- and late.tiine data. Does not apply to tests that flow at the f
surface. After Ramey. Agarwal. and Martin." Counesy CIM. j
|<
- -- - - - -
- _
i
C . * * * * = * *
l 98 ADVANCES IN WELL TEST ANALYSIS
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f Fig. 8.SC Log-log type curve for DST flow-period data. Best form for early-time data. Does not apply so tests that flow at the surface.| After Ramey, Agarwal and Martin.* Courtesy CIM.
8
_ _ _ _ __ _ - _ _ _ _ _ _ _ _ ___
*,
,A.
ezm- - ,
summmmmmmmmmmmmmmuum _.._ ...-
ADVANCES IN WELL TEST ANALYSIS100
matches. Eqs. 8.16 and 8.17 apply to all three curvemediately before the flow period begins. For the initial flow
matches. The semilog type curve, Fig. 8.8 A, usually shouldperiod,p, would be atmospheric pressure or the pressure be best when both early and relatively late-time data areexerted by any fluid cushion in the drillstring; for the finalflow period,p, would be the pressure at the end of the first
available. Fig. 8.8B provides poor resolution of early-time
flow period. In Fig. 8.8, the dimensionless time is defineddata, while Fig. 8.8C is useful for early-time data.
Type curves in Figs. 8.8A through 8.8C can be used toby Eq. 2.3a:
e nven ently estimate permeability and skin factor from#
0.0002637kt '(8*13) DST flow-period data. However, they are not applicable i
# ' * * *'
4 c,r, when fluid influx to the drillstem is at essentially constantrate; that is, when flow occurs at the surface. Rey are also
and the dimensionless wellbore-storage coefficient is de. not applicable when the wellbore storage coefficientfined by Eq. 2.18: changes (because of pipe size or compressibility changes). |
Co = .(8.14) Such changes are illustrated by Figs. 8.20 and 8.21.56146 C.. . .
For a DST flow period, the wellbore storage coefficient Example 8.2 Analysis 0f Drillstem-Test flow Data by
usually results from a rising liquid level in the drilipipe. Type-Curve Matching
Thus, Eq. 2.16 applies: Ramey, Agarwal, and Martin' give the pressure data inTable 8.2 for the second flow period of a DST. Other data
I" .(8.15)C= . . .. . . ...
p 8\, are
( 144 &J p, = 3,475 psig (initial 4 = 0.16
where V, is the volume per unit length of the drillpipe in shut in pressure) c, = 8.0 x 10-8 psi-'
barrels per foot. Note that this monograph uses different p. = 643 psig p = 1.0 cp
units for C than do Ramey, Agarwal, and Martin.' r, = 3.94 in, h = 17 ft
he type-curve matching technique is similar to the V. = 0.0197 bbl /ft p = 52.78 lb./cu ft.
method described in Section 3.3, with one important sim-
plification: the pressure ratio in Fig. 8.8 always goes from,
TABLE 8.2-DSTDATA FOR FLOW-PERIOD ANALYSISzero to one and is independent of flow rate and formation OF EXAMPLE 8.2.properties. Rus, when plotting data on the tracing paper (From Ramey, Agarwal, and Miller.')
.
laid over the grid of Fig. 8.8A,8.8B, or 8.8C, the pressure p, - p.,,(t)
ha)scale is fixed. When the tracing. paper data plot is siid t M 9. - 9.match one of the type curves, only horizontal motion is ' 643 1.0000used. Dat simplifies the matching technique. Once the 3 665 0.9922
experimental data have been matched to one of the type g2 gjg86
curves, data from both the overlay and the underlying type 12 737 0.9668
curve are read at a convenient match point. Three data items @ $ @j$3are required: the parameter on the curve matched, (Coe8)n; 21 974 0.91842
the time-scale match point, tu, from the data plot; and the 2j Q gjggcorresponding point from the type curve,(to/Co)n. Perme- 30 1.005 0.8722
ability may be estimated from the time. scale match point by y {;8$ @jy39 1,128 0.8287using
170 0.81391,208421, 0.800545
k = 3,389 p C ......(8.16) 48 1,248 0 7864- . ..... ...h 'w w 51 1,289 0.7719
54 1,318 0.7617It is not necessary to know the flow rate to estimate permea- 57 1,361 0.7465
bility by this method. It is necessary to estimate the wellbore y {j$ @jystorage coefficient from Eq. 8.15, so the fluid density must 66 1,467 0.7090
be known Skin factor is estimated from the parameter on the y };$ @j$curve matched: 75 1,570 0.6727
s=I In 4#'E#es (c,e ),.78 1,602 0.6614
ss 81 1.628 0.6522g g7 84 1,655 0.6427- - -
2 0 89359 C . 87 1,683 0.6328-
90 1,713 0.6222As usual, it .is necessary to have values for porosity, total 93 1,737 0.6137
system compressibility, formation thickness, and wellbore $6 ggg7 gj9 4
|radius to estimate the skin factor. Damage ratio then may be 102 1,819 0.5847
105 1,845 0.5756( estimated from Eq. 8.3.
| Ramey, Agarval, and Martin'suggest that all three type kN k',N$ 0$$curves be used to analyze DST flow-period data. hat re- [jj |y @jgquires plotting the data three times and making three curve 120 1,%9 - 0.5318
--- - - - - - - _ _ _ _ _ _ _ _ _ _ _ _ _
Y. .. . . - - . . . - - |
i-l
DRILLSTEM TESTlWG 101 |
Fig. 8.9 shows the data of Table 8.2 matched to Fig. rate conditions, so the early data should not be considered in-
8.8A. The matchpoint data are the curve match. Clearly, they do not match the entire Co * 1e
E' * * ' ' * " " '#' ' I"
(Co * )" = 10''' do not completely match other curves in Fig. 8.8A. Unfor-e
(to/Co), = 0.65, tunately, several curves can be matched with the late-time ;'
data. The match shown in Fig. 8.9 is the lowest value ofand
Co * for which the most points matched the curve. Atlowerer = 10 minutes = 0.1667 hour.u Coe ' values fewer points match; at higher values no more2
points match.We estimate permeability from Eq. 8.16, but to do this the Ramey, Agarwal, and Martin' report that (1) core |
wellbore storage coefficient must first be estimated from analysis showed an average permeability of 35.4 md for theEq. 8.15: zone tested; and (2) a Horner-type analysis of the second ]
0.0197 shut-in period (with average flow rate) indicated k = 22.2C= = 0.0537 bbl / psi. md, and a damage ratio of 1.16.52.78 32.17
144 32.17
Then, using Eq. 8.16,
g , (3,389)(l.0)(0.0537)(0.65)Example 8.2 illustrates the mechanics of using Figs. 8.8A
(17)(0.1667) through 8.8C for analysis of DST flow-period data. It alsoillustrates that the technique should be used with caution.
= 41.7 md. Periods of constant rate flow during a DST (manifested by aUsing the parameter on the matched curve and Eq. 8.17, linearp vs t trace on the DST chart) are not unusual. When
.(0.16)(8.0 x 10-')(17)(3.94/12)2(10'').they occur, they can rule out analysis by curve matchingwith Figs. 8.8A through 8.8C-or at best make the resultss=I In
2 . (0.89359)(0.0537) - have doubtful validity.
= 6.5.Computer Matching Drillatem-Test Da ta
Ramey, Agarwal, and Martin * indicate that the flow rateit does appear feasible to use all the data obtamed during a
. .
was constant owing to critical flow at early flow time. This DST for test analysis.'' Such analysis requires a numericalcurve. matching technique does not apply under constant- reservoir simulator and uses i history-matchmg approach to
,
vary formation properties until the DST pressure and ratebehavior are matched by the simulator. Since the technique
t n/co uses all the data, it should be particularly useful whenT, ! 'f conventional interpretation techniques cannot be applied
; g' ' ' ' 'I with confidence.' *' 6 ol1 o
o
as -o - 8.4 Trouble Shootmg Drillstm-Test Pressure Charts,
Because of the complexity of the DST tool operation, ;*,
there are many opportunities for test failure. Therefore, it is )c e''eto'* o} o ,important to carefully examine the DST charts and decide ifoi
J "*~ ~
the test was mechanically and operationally successful. That
.! g should be done at the wellsite so that the option of rerunning |the test may be exercised if necessary. '
| ;
i o.7 - x - To recognize a poor DST, one must be familiar with DSTchart characteristics. Murphy'' and Timmerman and vanct
hPoollen ' provide such information. A good DST chart has8
,
the following characteristics.| | 6- a
I o.s - x e marcn po/NT ,,. g g gg'" ''0 "'* * # 2. Recorded initial and final hydrostatic mud pressures(t,/c,/,eass are the same and are consistent with depth and mud weight.
3. Flow and buildup pressures are recorded as smooth,i,; , , ,g , , ,
a . e e e a ee a curves.-
8 'O 'O' Frequently,' bad hole conditions, tool malfunctions, andFLOW TIME, t, MINUTES other difficulties can be identified from the DST charts.
l Fig. 8.9 T) pe. curve match for DST flow data of Example 8.2; type Figs. 8.10 through 8.23 illustrate many situations. Thecurve of Fig. 8.8A. After Ramey. Agarwal and Martin.' captions explain the characteristic indicated by each figure.
-
'* * -- ws. .
w
ADVANCES IN WELL TEST ANALYSIS102
w m w$m
hW ~N , _ _ _ _ _ _ _ . _ - _ _ . - - _
' \/ \ / - - i
| | f \ #
%_--_-----_-J\ ,v
TI M E __*I*E Fig. 8.15 Clock ran away.
Fig. 8.10 Tight hole condition. This may cause pressure surging ortool sticking.
f-mw s, \-3 / w <s esa e / \
\,l 3 1 t ;*
f \ / $ \ / \ /s
3gs .-
1TIME W
Fig. 8.ll leaking drilipipe iw mud ioss to some formation. or both. TI M E --*
are indicated by the hydrostatic mud-pressure decrease shown Fig. 8.16 The S shape of the latter part of the flow curve and thehere. A leaking drillpipe may be confirmed if an abnormally large early part of the bui;4ap curve indicates fluid communicationamount of mud is recovered with the produced fluids, in this case around the packer. This may be caused by a fracture or a poorly
test data must be disregarded. wated packer.
w ' '* %
$ \ '
n r/ \\ l"
E \ w '
{~N'
,
w % / \ /\TIME ~ E '(| Fig. 8.12 Delay while going into the hole without mud low.o
|TI ME -_->
|Fig. 8.17 An S shape occurring only in the buildup portion of IheI *
~ 'g curve indicates gas is going into solution in the wellbore, Thisf s f
} l mechanism is characterized by a sharp transition between the flow
(-- |j
( fi
and buildup curves.ji
t s_
Tl ME --*
Fig. 8.13 The stair-s tepping pattern in the buildup curves indicatesa malfunctioning pressure gauge or recorder. Such test data cannot
be analyzed. w ^ss/ \g
0 ( '
t'
y ,
8 u
k [ '\ TIME :|
I\ Fig. 8.18 An S-shaped curve occurs only in the first flow periodj\s when the volume below the chwed-in pressure valve is large
compared w:th the volume of the fluid flowed during the flow##E ~
period. A wellbore storage effect caused by the relatively largeFig. 8.14 Clock stopped. volume between the hydrospring tester and CIP valves.
__)_._ _ . _ _ . _ _ _ _ _ _ _ ____ . _ _ _ __ - - - _ ___
. . . - - -
103DRf LLSTEM VESVING
8.5 Wireline Formation TestsA quick and inexpensive alternative to a drillstem test.
g may be a test run with a wireline formation tester.88 8i That
' O lf I tool, run on a wireline from a logging truck, includes a pad' a
E on an expanding mechanisnr that presses against the forma-
htion face, a means for establishing fluid communicationbetween the formation and the tool, a sampie chamber, and a
pressure transducer with surface recorder.The tester is lowered into the well on a logging cabicy,u g _,,
Fig. 8.19 This behavior indicates a plugged bottom-hole choke or while the mechanism is collapsed. The tool is located oppo-perforated anchor. The up-and-down nature of the pressure curve is site the formation to be tested, the mechanism is expanded,caused by momentary breakthrough and release of the pressure,
and fluid communication is established. Formation fluidflows into the chamber and the pressure response 's re-i
corded. A new version of the tool may be set and used at,%g several locations during a single run."
-
b) Interpretation of wireline-formation-tester pressure datag
{ is semiqualitative, so the information obtained is inferior to
fthat of a normal DST. More recent tools with larger fluidchambers (~12 gal vs 2.75 to 5 gal) tend to give rea-sonable fluid-recovery and p, results. Although permea-
Tsuc--.bility may be estimated from the wireline formation tester, ,
Fig. 8.20 The flat ponion in the second flow period indicates thethe degree of uncertainty is high. The skin factor cannot bewell is flowing at the surface.estimated. A general rule forinterpretation based on experi-ence in Canada and in the Rocky Mountain region is pre-
w /N sented in Refs. 22 and 23./ \$ '9 i 1y \w'
E s_s'v
ReferencesTiuc -- I
1. Manhews. C. S. and Russell. D. G.: Pressure Buildup andFig. 8.21 A decrease in slope in either flow period indicates fillup Flow Tests in Wells. Monograph Series. Society of Petroleumof the drill collar and transition to a drilipipe of a larger internal Engineers of AIME. Dallas (l%7)l, Chap. 9.
diameter.2. van Poollen. H. K.:" Status of Drill.StemTesting Techniques
and Analysis." J. Pet. Tech. (April 1%1) 333-339. AlsoReprint Series. No. 9 - Pressure Analysis Methods. Society
w #~s
[ of Petroleum Engineers of AIME Dallas (1%7) 104-110.
k,\f 93. McAlister J. A., Nutter. B. P., and Lebourg M.: "A NewfO System of Tools for Better Control and Interpretation off. *, Drill-StemTests."J.Per. Tech.(Feb.1%5)207 214;Trans..s
, AIME,234.o
4. Edwards. A. G. and Winn, R. H.: "A Summary of ModemTools and Techniques Used in Drill Stem Testing." Publica-TJ ME ---+tion T 4069. Halliburton Co. Duncan. Okla. (Sept.1973).
Fig. 8.22 This behasior typically occurs in Fas reservoirs uhen. flow occurs at the surface. The pressure decrease at Point G is 5. " Review of Basic Formation Evaluation." Form J.328.
caused by the water cushion flowing at the surface. w hich Johnston Schlumberger. Houston (1974).:
decreases average density of the flowing column. 6. Edwards. A. G. and Shryock S. H.: "New Generation DrillO
Stem Testing Tools / Technology." Per. Eng. (July 1974)46.St.56.58.61,
/~s
g 7. Ammann, Charles B.:" Case Historiesof Analyses of Charac-w$ | teristics of Reservoir Rock From Drill-Stem Tests."1. Per.
/$ g Tech. (May 1960) 27 36.W gN'-''
,-8. Kazemi. Hoswin: " Damage Ratio From Drill. Stem Tests
| With Variable Back Pressure." paper SPE 1458 presented at( the SPE.AIME California Regional Meeting. Santa Barbara.
Nov. 17. I 8.1966.TIME ---en
Fig. 8.23 The rippled appearance in the flow curse indicates that9. Ramey Henry J.. Jr., Agarsal. Ram G.. and Martin. lan:
gas has broken through the liquid in the drillstring and the well is" Analysis of' Slug Test' or DST Flow Period Data." J. Cdn.
flowing by heads. Per. Tech. (July. Sept. 1975) 37 42.
h-
_-
104 ADVANCES IN WELL TEST ANALYSIS |*
10. Odeh. A. S. and Selig. F.: " Pressure Build-Up Analysis. 17. Ramey. Henry J.. Jr., and Agarwal Ram G.: " AnnulusVariable-Rate Case." 1. Pet. Tech. (July I%3) 790-794; Unloading Rates as influenced by Wellbore Storage and SkinTrans.. AIME. 228. Also Reprint Series. No. 9 - Pressure Effect." Sm . Pet. Eng. J. (Oct. 1972) 453-462: Trans..Analysis Methmis. Society of Petroleum Engineers of AIME. AIME. 253.Dallas (1967) 131 135. 18. Brill. J. P.. Bourgoyne. A. T.. and Dixon. T. N.: " Numerical
11. Gibson. J. A. and Campbell. A. T.. Jr.: " Calculating the Simulation of Drillstem Tests as an Interpretation Tech.Distence to a Discontinuity From D.S.T. Data." paper SPE nique." J. Pet. Tc4 h. (Nov.1969) 1413-1420.3016 presented at the SPE AIME 45th Annual Fall Meeting.
19. Murphy. W. C.: "The Interpretation and Calculation of For-Houston. Oct. 4-7. 1970. mation Characteristics From Formation Test Data." Pamphlet
12. Earlougher. Robert C..Jr., and Kersch Keith M.: " Analysis T.101. Halliburton Co.. Duncan. Okla. (1970s.of 5hort-Time Transient Test Data by Type-Curve Match-
20. Timmerman E. H. and van Poolien. H. K.: " Practical Use ofing , J. Pet.Terh.(July l974)793-800;Trans.. AIME.257.Drill-Stem Tests." 1. Cdn. Pet. Tec h. ( April-June 1972)
13. McKinley, R. M.: " Wellbore Transmissibility From 31-41.Afterflow Dominated Pressme Buildup Data."/. Pet. Tech. 21. Moran. J. H. and Finklea. E. E.: " Theoretical Analysis of(July 1971) 863 872; Trans.. AIME 251.
Pressure Phenomena Associated With the Wireline Formation14. Papadopulos. lstavros S. and Cooper. Hilton H., Jr.: " Draw- Testei."1. Pet. Tec h. ( Aug. 1962) 899-908; Trans.. AIME.
down in a Well of Large Diameter." Water Resources Res. 225.(1%7) 3. No. I, 241 244.
22. Burnett. O. W. and Mixa. E.: " Application of the Formation15. Cooper. Hilton H., Jr.. Bredehoeft. John D., and Interval Tester in the Rocky Mountain Area." Drill. and
Papadopukis. Istavros S.: " Response of a Finite-Diameter Prod. Prar. API (1964) 131 140.Well to an instantaneous Charge of Water." Water Resources
23. Banks. K. M.: "Recent Achievements With the FormationRes. (1967) 3. No. I. 263 269. Tester in Canada." 1. CJn. Pet. Tec h. (July-Sept. 1%3)
16. Kohlhaas. Charles A.: "A Method for Analyzing Pressures 84-94.Measured During Drillstem-Test Flow Periods."/. Per. Trrh. 24. Schultz A. L., Bell. W. T., aad Urbanosky. H. J.: " Ad-(Oct.1972) 12781282; Trans. AIME. 253.
vances in Uncased-Hole. Wireline Formation-Tester Tech-niques."1. Pet. Tec h. (Nov. 1975) 1331 1336.
l
-u
.
. - . .
.,
_
.
Nomenclature
a = distance to an image well, Appendix B, ft h, = dimensionless thickness for horizontal fracturecases Appendix C and Section 11.3
a, = dimensionless distance to an image well, Appen-/ = productivity index,(STB /D)/ psidix B l' = modified productivity index for a deliverability
A = area, sq fttestb = intercept on Canesian plot of transient-test pres-
/* = productivity index for a deliverability testsure data, psib' = intercept on semilog plot of transient test pressure A = permeability, md
k = fracture permeability, mddata normalized by rate, psi /(STB /D) f
B = formation volume factor, RB/ STB k = matrin permeability, md
B, = gas formation volume factor, RB/scfk, , = maximum directional permeability, md j
'
k,.i. = minimum directional permeability, mdB, = oil formation volume factor, RB/ STBB, = water formation volume factor, RB/ STB k. = permeability to oil. md
k, = permeability in the radial (horizontal) direction,c = compressibility, psi-8 mdcf = formation (rock, pore volume) compressibility, k,, = relative permeability to gas, fraction
psia k. = relative permeability to oil, tractionc, = gas compressibility, psi 4 kr, = relative permeability to water, fractionc, = oil compressibility, psi 4
k. = peineability in the skin zonec., = apparent oil-phase compressibility, including ef-k, = permeability in the venical direction, mdfects of dissolved gas, psi 8f = average permeability for anisotropic system, md
c, = system total compressibility, psi 4, Eq. 2.38 K = Secenov's coefficient. litre / gram equivalentc, = water compressibility, psi 4
c. = apparent water-phase compressibility, including tog = logarithm, base 10
effects of dissolved gas, psid in a logarithm, base e
C = wellbore storage constant (coefficent, factor) L = length ordistance, ftm = * slope oflinear portion of semilog plot of pres-
RB/ psi sure transient data, psi / cycleCa = shape constant or factor
m(p) = real gas " potential" or pseudo pressure. Eq. 2.32,C = dimensionless wellbore storage constant (coeffi-psi 8/cpcient, factor)
n = slope of a Hall plot, psi /(STB /D)mD = non-Darcy flow coefficient, D/Mcfu = slope of the straight line portion of a Muskat plotE, = error in permeability estimated by simplified m
two-rate test analysis, fraction of pressure buildup data, cycle /hout
E, = enor in skin factor estimated by simplified two- m, = slope of the I/q vs log t plot for a constant pressure
rate test analysis, dimensionless skin units test (D/ STB)/c cleJEi = exponential integral, Eq. 2.7 m,,f = slope ofp,, vs Vt plot for horizontal-fracture well
test data, psi /Vhourse = 2.7182. m f = slope of p,, vs NTplot for vertical-fracture well
.
erf = enor function rtest data, psi /Vhours
exp = cF,,, = correction factor when calculating permeability
m' = slope of the data plot for a multiple-ate test,psi /(cycle STB /D)for a vertically fractured well, Section I 1.3 m , = slope (based on q,) of the data plot for a two-rate*
F, = ratio of porosity-compressibility product of frac, test, psVcycleture to total porosity compressibility product of
m'a = slope (basedonq3)of the data plot for adrawdownreservoir rock after a shut-in period, psi / cycle
Fm. = Higgins Leighton shape factor m'= slope of simplified or special data plot for aF' = ratioof pulselengthtototalcyclelength,Eq.9.13multiple rate test, psi / cycle8g = acceleration of gravity, ft/sec
g, = units conversion factor,32.17 lb,,, ft/(lbesec)m* = slope of the straightline on alinear plot ofp vs t,8
G, = primal geometric fraction for vertical pulse testingpsi / hour
Ga = reciprocal geometric fraction for vertical pulse# = mobility ratioM = molecular weight, Ib,,,/ mole
testing a = concentration of dissolved solids, gram-| G * = geometric fraction for vertical interference testing
equivalents / litre, Appendix D|
h = formatioi thickness, ft4<
~ -. _ - .
, _ __.. ._ -
o
247
n = power in productivity index formula A u = Pressure change from transient test data at the. Pp = pressure psi m;tch point for type-curse analysis. psi
p,. = cntical pressure, psia 30.,, pressure drop at a well owing to operation of otherpp = dimensionless pressure wells in the reservoir, psi
(p,,)u = dimensionless pressure at the match point for Ap. = pressure drop across skin. psitype-curve analysis Ap,, = pressure difference between wellhead and bottom
p,,unn = Matthews Brons-Hazebrock-type dimensionless hole. psipressure An , = pre sure difference on straight-line portion ofm
h,unn = Matthews-Brons Hazebroek dimensionless pres- semilogplot I hour after beginning a transientsure for a square, water-drive system based on test; used in any kind of Ap vs log at plot, psiaverage pressure Ap3, = difference between observed and extrapolated
p,,ynn,. = Matthews-Brons-Hazebroek dimensionless pres- pressure at time Ar, Eq. 5.22, psisure for a square, water-drise system based on y = Dow rate, > 0 for production,< 0 for injection,boundary pressure STB /D for liquid. Msef/D for gas
p,,unn = Miller-Dyes Hutchinson-type dimensionless q,, = dimensionless flow ratespressure (q,,)u = dimensionless flow rate at match point for type- |p,,um, = dimensionless pressure of extrapolated straight curve matching
line at intercept of a Muskat plot q. = gas flow rate, Mcf/Dp,,, = dimensionless pressure ratio used in type-curve q. = oil flow rate. STB /D
matching DST flow-period data eu = flow rate at match point for type-curve matching,E, = dimensionless average reservoir pressure for STB /D
water-drive reservoir qs = flow rate during Nth rate period in a variable-ratep, = external pressure, psi test, STB /D or Mcf/D
pn, = pressure correctly extrapolated from past be- q, = sand-face flow rate expressed at standard condi-havior, psi tions, STB /D
pn = final flowing pressure in a DST (subscript I or 2 q, = water flow rate, STB /Dindicates now period), psi q = average flow rate, STB /D
pfn,,, = final hydrostatic mud pressure in a DST, psi q' = modified flow rate for pressure buildup analysispm = final shut in pressure in a DST, psi with variable rate before shut in, STB /D
p, = initial pressure, psi (1/q)m, = ordinate value at I hour on straight line plot ofpg = initial flowing pressure in a DST (subscript I or 2 (1/q) vs log t, D/ STB
indicates flow period). psi r = radius, ftp,.,,, = initial hydrostatic mud pressure in a DST. psi r, = radius of drainage as defined in Section 2.12, ftpm, = pressure at intercept (abscissa value = 0) of var- r,, = dimensionless radial distance
ious kinds off(p,) vsf(t) plots, psi r, = external radius, ftp,. = initial shut in pressure in a DST, psi rf = horizontal fracture radius, ftp., = pressure in dnlistnngjust before a flow period of a rf, = radial distance to fluid front number I, ft
DST. psir , = influence radius for interference testing, ftm
p,, = pseudocritical pressure. psia r, = radius of skin zone, ftp,,, = pseudoreduced pressure r, = wellbore radius, ftp. = pressure at standard conditions, psi r,,, = apparent or effective wellbore radius (includesp,, = tubing or wellhead flowing pressure, psi effects of wellbore damage or improvement), ftp,, = tubinF or wellhead shut-in pressure, psi r,. = radius to a water bank. ftp, = bottom-hole pressure, psi R, = solution gas-oil ratio, scf/ STB
p.,(At = 0) = bottom-hole pressure just before starting a tran- R,, = solution gas-water rati), scf/ STBsient well test, psi s = van Everdingen-Hurst skin factor
p.,n, = bottom-hole pressure correctly extrapolated from s , = pseudo skin factor resulting from sand consolida-epast behasior, psi tion
p.,, = flowing bottorn-hole pressure, psi s, = pseudo skin factor resulting from partial comple-p,,, = shut-in bottom-hole pressure, psi tion or restricted flow entrypm, = pressure on straight line portion of semilog plot I s.,,, = pseudo skin factor resulting from slanted well
hour after beginning a transient test; usually a s"= additional skin factor resulting from anisotropicspecial kind of pm., psi effects
fi = aseraFe reservoir pressure, psi S. = gas saturation, fraction
p* = false pressure, pressure obtained when linear p]or-S. = oil saturation, fraction,
! tion of the plot of p,, vs log [(t,, + At)/At is S, = water saturation, fraction5
extrapolated to (t,, + At)/At = 1. psi s = time, hours'
8p = pressure offset between two semilog straight lines tw = time to beginning of the semilog straight line,in transient test data plot for a naturally frac- hourstured system, psi t , = dimensionless timei
Ap = pressure change (or pulse response amplitude in (t,,/r,,8), = dimensionless time parameter from type curve atpuhe testing), psi
the match point for type-curve analysisApu, = Ap at beFinning of semilog straight hne, psi t,,a = dimensionless time based on drainage areaAp,n = dimensionless response amplitude for vertical t = dimensionless time based on external radius, r,
pulse tesung (t,,4), = dimensionless time at the beginning of( Ap,n ), = dimensionless response amplitude for sertical pseudosteady-state flow
pulse testing in an infinite acting system to,f = dimensionless time based on horizontal fractureApa a Ap at end of Qnear flow period (half-slope log log radius
line or Vt straight line) for a sertical fracture, to,f = dimensionless time based on half-fracture lengthpsi of a venical fracture
- - - .
(.
r''
.
248
t,. = time at the end of the infinite-acting period, hours x, = x distance from a centered well to the edge of its
I,a = time to end of the semilog straight line, hours square drainage region (half length of the side
i = time lag used in pulse testing, hours of a square), ft
(t,.)o = dimensionless time lag used in pulse testing xi = x distance from a well in the center of a squaret
(f ). = time lag in vertical pulse testing for an infinite- drainage region to the end of a sertical fracturethat is parallel to the x axis (half. length of at
acting system, hours sertical fracture), fttw = time value from transient-test data at the match x' = transformed x coordinate for an anisotropic sys-
point for type-curve analysis, hours tem, ftt, = equivalent time well was on production or injec- it = x length of a grid in a resersoir simulator, fttion before shut in, hours
y = y coordinate, ftt,' = modified production time for pressure buildupyo = dimensionless y coordinate Fig. 2.15 and Ap-
analysis with variable rate before shut in, hourspendit B
t,o. = dimensionless production time based on drainage y, = mole fraction of Component i in the gas phasearea
t,. = time at the beginning of pseudoster4ty state flow, y' = transformed y coordinate in an anisotropic sys-tem, ft
hours Ay = y length of a grid in a reservoir simulator, itIn = readjustment time, hourst, = stabilization time, hours : = real gas desiation factor
t, = intersection time of two semilog straight line :, = real gas deviation factor at initial conditions
segments on transient-test data plot, hoursAZe = vertical distance from upper formation boundary
to center of upper perforations; for sertical w ellt, = any time in a transient test, hourst, = any time in a transient test, hours testing; Fig.10.25; ft
t' = time that transient test data start deviating from AZn = vertical (response) distance between upper andlower perforations; for vertical pulse test:ng;semilog straight line, hours
at = running testing time, hours Fig.10.25; ft
Air = total cycle length in pulse testing, hours AZ,r = vertical distance from lower formation boundary
(AtoAs = dimensionless time at end of Horner or Miller-to flow perforations; for senical well testing:Fig.10.25; ftDyes-Hutchinson straight line for pressure AZ,, = venical distance from lower formation boundarybuildup test analysisto observation (static) perforations; for s ertical
(Arm), = dimensionless time at beginning or end of Muskatstraight line for pressure buildup analysis well testing; Fig.10.25; ft
A = differenceAtor, = dimensionless intersection time of two semilogstraight lines for falloff test in a composite y = specific gravity; referenced to water for liquids, to air
for gasessystem
Afon* = dimensionless time for deviation of data from firste = interporosity flow parameter
semilog straight line for falloff test in a com- 9 = angle between positisex axis and direction of A,,,, inan anisotropic reservoir, degrees
posite systemAta,. = time for reading dynamic pressure (used in reser. A = mobility, md/ep
voir simulation) from straight line of a buildup A, = mobility of gas phase, md/cpA = mobility of oil phase, md/cp
plot, hoursAtr, = time of intersection of two semilog straight liner A, = total flowing mobility, md/cp
for falloff test in a composite system, hours A, = mobility of water phase, md/cp
Ar * = time of deviation of data from first semilog u = viscosity, cpn
straight line for falloff test in a composite sys- N = gas siscosity, cpA. = gas viscosity at atmospheric preware and reservoirtem, hours '
(At) = time at match point for type-curve ma ching, temperature, cpr
A, = gas viscosity at initial conditions, cphours
Arp = shut in time corresponding to Dietz's average A = oil viscosity, cp
reservoir pressure, hours g, = water viscosity, cp
At, = pulse length used in pulse testing, hours p = density, ib,,/cu ft
Arpor = dimensionless pulse length used in vertical pulse p, = water density, Ib,,/cu ft
testing 4 = porosity, fraction
Ar. = shut-in time before drawdown test, hoursT = temperature. *R Subscripts
T, = critical temperature. *RT,, = pseudocritical temperature. *R a = apparent
b = base7,, = pseudoreduced tempetatureT,, = temperature at standard conditions, *R b5t = beginning of semilog straight line
C = calcu'atedV = volume, bbidyn = dynamic pressure value for use in resersoirV, = pore voiume, bbi
simulationV,, = drainage pore volume of Welli, bbtD = dimensionlessV,, = total system pore volume, bble = externalV, = volume produced, bbl
V, = wellbore volume per unit length, bbl /ft eia = end of infinite-acting periodel = end of linear flow periodV, = wellbore volume, bbt
est = end of straight line portionAV = change in volume, bbiW, = cumulative water injection, bbl ext = on extrapolated pressure trend
E = estimatedx = x coordinate, ftn = dimenuonless x coordinate, Fig. 2.15 and Ap- f = Ilowing
xf = in fracturependis B
|!u
_ --
,
- _ . _ - - __ _ _ _ _ . - _ _ . - = - - - - - - - - - - - - - - - - - - - - . - --- -- --
I 249* F = future s or 4 = shut-in or static
x = ge s = skin zonei = iaitial, index, component number s/ = beginning or end of straight-line ponion
int = intercept value, value of ordinate at zero abscissa t = totalsalue ir = true
j = index w = m ater
ma = in formation matrix w = wellAf = match point in type-cune matching wb = wellboren = total in summation x = intersection point of two semilog straight-lineA = last rate intenal in a multiple-rate flow test segments on transient-test data plot IN = total in summation Ihr = data from straight line portion of semilog plot at !
N = number of components in a mixture I hour of test time, extrapolated if necessaryo = oil 1,2 = layer, zone numbers, or time numbers
jOB = obsened value x = infinite-actinF system
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