Note : Les descriptions sont présentées dans la langue officielle dans laquelle elles ont été soumises.
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BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention pertains to the matrix rate treatment of wells and
more in particular to the sequential treatment of formation strata by the
temporary closing of perforations in the well casing during the treatment.
2. Description of the Prior Art
It is common Practice in completing oil and gas wells to set a
string of pipe, known as casing, in the well and use cement around the outside
of the casing to isolate the various formations penetrated by the well. To
; 10 establish fluid communication between the hydrocarbon bearing formations and
the interior of the casing, the casing and cement sheath are perforated.
; At various times during the life of the well, it may be desirable
to increase the production rate of hydrocarbons through a matrix treatment
stimulation. Matrix treatments are stimulation treatments which are injected
at pressures below the fracture pressure of the formation. In other words,
the fluid is being forced into the formation at a rate such that the pores of
the formation accept the flow without fracturing the formation. A common
example of a matrix rate treatment is matrix acidization whereby an acid-
bearing fluid is injected into the formation so that the acid can permeate
into the near wellbore area of the formation and increase permeability.
~ Generally, acidization is limited to within a few feet of the wellbore. The
`~ purpose of a matrix acidization treatment is to dissolve near wellbore damage
such as clays and formation fines which clog or constrict the formations'
fissures and channels. Other types of well treatment fluids such as solvent
surfactants can also be applied in matrix rate treatments.
It is the objective in a matrix treatment stimulation to inject the
treating fluid into the zones of the formation where treatment is required.
But as the length of the perforated pay zone or the number of perforated pay
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zones increases, the placement of the fluid treatment in the regions of the
pay zones where it is required becomes more difficult due to differences in
formation characteristics. For instance, the strata having the highest
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permeability will most li~ely consume the major portion of a given stimulation
2 treatment leaving the least permeable strata virtually untreated. Therefore,
techniques have been developed to divert the treating fluid from its path of
4 least resistance so that the low permeability zones are also treated.
One technique for achieving diversion involves the use of partic-
6 ulatcs such as roc~ salt and benzoic acid flakes. Typically particulates aresolids having limited solubility in the treating fluid but are soluble in the
8 produced fluids. The particulates are added to the treating fluid during the
treatment and plug the formation as they are carried by the fluid through the
perforations and into the formation pores. As certain sections of the forma-
tion get plugged, the treating fluid is diverted and forced to flow into the
12 unplugged sections of the formation. The formation is unplugged after the
treatment by dissolving the particulates as the well is either flushed or
14 produced. Dissolving the particulates can at times be a difficult task. The
major drawback of particulates is that if the proper fluid which will dissolve
16 the particulates cannot be brought into contact with the particulates, the
particulates will remain solid particles blocking the flowpaths for the
18 produced fluids into the well, thereby permanently damaging the production
capability of the well and defeating the purpose of the treatment.
Ball sealers provide a diverting technique which avoids this problem.
Ball sealers are small rubber coated balls which are sized to seal off the
22 perforations inside the casing. When ball sealers are used, they are pumped
- into the wellbore along with the treating fluid. The balls are carried down
24 the wellbore and onto the perforations by the directional flow of the fluidthrough the perforations into the formation. The balls seat upon the perfora-
26 tions and are held there by the pressure differential across the perforations.The major advantages of utilizing ball sealers as a diverting agent are their28 ease of use, positive shut-off, independence of formation conditions, and
- inertness. The ball sealers are simply injected at the surface and transported
by the treating fluid to the perforations to be plugged. Other than a ball
injector, no special or additional treating equipment is required. The ball
32 sealers are designed to have an outer covering sufficiently compliant to seal
a jet or bullet formed perforation and to have a solid, rigid core which
34 resists extrusion into or through the perforation. Therefore, the ball
sealers will not penetrate the formation and permanently damage the flow
36 characteristics of the well.
Although ball sealers have been frequently and successfully used as
38 diverting agents in fracturing operations, they have rarely been used as
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diverting agents in matrix rate treatments because in matrix treatments they
2 generally have been ineffective. Their ineffectiveness is due to the relative-
ly low flow rate of the treating fluid through the perforations during a
4 matrix treatment. The seating efficiency of most commercially available ball
sealers used according to present-day practices is a function of the flow
6 rate through the perforations. It has been generally accepted in the art
that the greater the flow rate of the treating fluid through the perforations,
8 the greater the seating efficiency of the ball sealers will be. When the
flow rate through the perforations is very low, the seating efficiency of
- 10 ball sealers, as presently used, is extremely low because the low flow rate
will not effectively carry the ball sealers to the perforations before they
12 sink past the perforations. Since ball sealers have been so ineffective indiverting matrix rate treatments, they have rarely been used in such treatments.
14 SUMMARY OF THE INVENTION
The method of the present invention overcomes the limitations of
16 the current ball sealer diversion methods when the treating fluid is pumped; at matrix rates. The present invention utilizes buoyant ball sealers having-
18 a density less than the treating fluid. Use of the buoyant ball sealers
surprisingly produces 100% seating efficiency, i.e., each injected ball
sealer will seat on and seal an unsealed perforation.
The present invention!s method for diverting treating fluid during
- 22 a matrix treatment involves flowing the treating fluid downward within the
casing and through the perforations into the formation surrounding the perfo-
24 rated parts of the casing. At the appropriate time during the treatment,
ball sealers are introduced into the treating fluid and pumped down the
26 casing to the casing perforations. Ball sealers are selected which have a
density less than the density of the treating fluid within the casing but
28 which are capable of being downwardly transported to the perforations by the
downward flow of the fluid within the casing. Therefore, the injection of
the treating fluid into the casing must be established at a rate such that
the downward velocity of the fluid in the casing above the perforations is
32 sufficient to impart a downward drag force on the ball sealers greater in
-~ magnitude than the upward buoyancy force acting on the ball sealers thereby
34 transporting the ball sealers to the perforations. However, the velocity of
the treating fluid must be sufficiently low to provide a matrix rate treatment
36 which does not fracture the fonmation. Once the ball sealers have reached
the perforations, they will all seat on and plug those perforations taking
38 fluid. The treating fluid will then be diverted to the remaining open perfora
tions.
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After the treatment of the hytrocarbon-bearing strata is com-
2 pleted, the pressure on the fluit in the casing is relieved causing the
ball sealers to be released from those perforations on which they were
4 seated. The ball sealers, being lighter than the treatiDg fluid, will
buoyantly rise within the casing. A ball catcher may be provided to trap
6 all of the ball sealers upstream of any equipment which they might clog or
damage.
8The method of the present invention provides certainty in di-
version heretofore unknown in matrix rate well treatment operations.
10BRIEF DESCRIPTION OF THE DRAWINGS
FIGURE 1 is an elevation view in section of a well illustrating
12 the practice of the present invention.
FIGURE 2 is an elevation view partially in section of a typical ;
- 14 arrangement of wellhead equipment placed on a production well to control
the flow of hydrocarbons from the well including a ball catcher adapted to
16 trap the ball sealers upstream of any equipment which they might clog or
damage.
18FIGURE 3 is a graph of the seating efficiency versus the flow
-` rate of the fluid per perforation based on experiments.
~ 20FIGURE 4 is a graph of the fluid velocity within the casing
`; versus the normalized density contrast between a ball sealer and a treating
22 fluid based on experiments.
FIGURE 5 is a graph of the seating efficiency versus the normalized
24 density contrast between a ball sealer and a treating fluid based on
experiments.
26 DESCRIPTION OF THE PREFERRED EMBODIMENTS
Utilization of the present invention according to the preferred
28 embodiment is depicted in FIGURE 1. The well 1 of FIGURE 1 has a casing 2
run to the bottom of the wellbore and cemented around the outside to hold
the casing in place and isolate the penetrated formations or intervals.
The cement sheath 3 extends upward from the bottom of the wellbore at least
32 to a point above the producing strata 5. For the hydrocarbons in the
producing strata 5 to be produced, it is necessary to establish fluid
34 communication between the producing strata 5 and the interior of the casing2. This is accomplished by perforations 4 made through the casing 2 and
36 the cement sheath 3 by a jet or bullet perforation gun as is well known in
the art.
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The hydrocarbons flowing out of the producing strata 5 through the
2 perforations 4 and into the interior of the casing 2 are transported to the
surface through a production tubing 6. A production packer 7 is installed
4 near the lo~er eDd of the production tubing 6 and above the highest perfora-tion to achieve a pressure seal between the production tubing 6 and the
6 casing 2. Production tubings are not always used and, in those cases, the
entire interior volume of the casing is used to conduct the hydrocarbons to
8 the surface of the earth.
In the past, when it was desired to use ball sealer diversion
during a fracture treatment, the prior art taught that the preferred density
of the ball sealers be greater than the density of the treating fluid. It is
12 worth examining the prior art ball sealer seating mechanism to be able to
contrast it to the present invention which allows the use of ball sealers for
14 diversion at matrix rates. The velocity of ball sealers more dense than the
fluid in the wellbore is comprised of two components. Each ball sealer has a
16 "settling" velocity which is due to the difference in the densities between- the ball sealer and the fluid and is always a vertically downward velocity.
,~, 18 The second component of the ball sealer's velocity is attributable to the
drag forees imposed upon the ball sealer by the moving fluid shearing around
the ball sealer. This velocity compoGent will be in the direction of the
fluid flow. Within the production tubing and within the casing above the
22 perforations, the velocity component due to the 1uid flow will be generally
downward.
24 Just above the perforated part of the casing the fluid takes on ahorizontal velocity component directed radially outward toward and through
26 the perforations 4. Thé flow through any perforation must be sufficient todraw the ball sealer 10 to the perforation before the ball sealer sinks past
28 that perforation. If the flow of the treating fluid through the various
perforations does not draw the ball sealer to a perforation by the time the
ball sealer sinks past the lowest perforation, the ball sealer will simply
sink into the rathole zegion 8 where it will remain.
32 The present invention contemplates the use of ball sealers 10
having a density less than the density of the treating fluid. With-n the
34 wellbore, each ball sealer has a velocity comprised of two components. Thefirst velocity component is directed vertically upward, a "rising" velocity,
36 and is caused by the buoyancy of the ball sealer in the fluid. The second
velocity component is attributable to the drag forces imposed upon the ball
38 sealer by the motion of the fluid shearing past the ball sealer. Above theperforations, this second velocity component will be directed generally
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downward. It is essential that the downward fluid velocity in the productio~
2 tubing 6 and inside the casing 2 above the perforations 4 be sufficient to
impart a downward drag force on the ball sealers which is greater in magnitude
4 than the upward force of buoyancy scting on the ball sealers. This results
in the ball sealers being carried downward to the section of the casing which
6 has been perforated. However, the fluid velocity must be at a matrix rate
which is less than t~at which would cause the formation to fracture.
8 When ball sealers are utilized in accordance with the method of the
present invention, they will never remain in the rathole region 8; that is,
below the lowest perforation through which the treating fluid is flowing, due
to the buoyancy of the ball sealers. Below the lowest perforation accepting
12 the treating fluid, the fluid in the wellbore remains stagnant. Hence, there
~ are no downwardly directed drag forces acting on the ball sealers to keep
.~ 14 them below the lowest perforation taking the treating fluid and the upwardly
` buoyant forces acting on the ball sealers will therefore dominate in this
16 interval. Consequently, the practice of the present invention results in the
` vertical velocity of each ball sealer being a function of its vertical position
18 within tbe casing. Below the lowest perforation, and possibly higher if
little fluid is flowing down to and through the lower perforations, the net
~ 20 vertical velocity of each ball sealer will be upward due to the do3inance of
-~ the buoyancy force over any downward fluid drag force. Above the highest
22 perforation, and possibly lower if little fluid is flowing through the higher
perforations, the net vertical velocity of each ball sealer will be downward
24 due to the dominance of the downward fluid drag force over the buoyancy
force.
26 The ball sealers having a density less than the density of the
~- treating fluid will remain within, or move toward, the perforated interval of
28 the casing through which fluid is flowing until the ball sealers seat upon a
perforation. While within that interval of the casing, the motion of the
fluid toward and through the perforations will exert drag forces on the ball
sealers to move them toward the perforations where they will seat and be held
32 there by the pressure differential. When the ball sealers reach the perforated
interval, the drag forces caused by fluid flowing through the perforations
34 will cause some of the ball sealers to seat on some of the perforations, us-
ually the perforations receiving disproportionately high volumes of fluid.
36 Individual perforations will be sealed until a portion of the perforated
interval becomes sufficiently sealed to reduce the flow rate through the
38 interval. Reduction of the flow rate reduces the downward drag forces imparted
on the suspended ball sealers to a level less than the upward buoyancy forces.
When this level is reached, any suspended ball sealers within the partially
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sealed portion will rise until the drag force of fluid flowing into the
2 perforations cause the ball sealers to be carried onto such perforations.
If, during the treatment a lower perforation is opened as a result of the
4 treatDent, the downward flow and resulting drag forces will cause the ball
sealers to be carried to the lower perforations. In this manner, a suspended
6 buoyant ball sealer may actually move down, up, and back down the perforated interval until an open perforation receiving fluid is found.
8 The net result of the use of the present invention is that the ball
sealers injected into the well and transported to the perforated zone of the
~ 10 casing will always seat upon and plug the perforations through which fluid is
`~ flowing with an invariable 100% efficiency. That is, each and every ball
12 sealer will seat and plug a perforation as long as there is a perforation
through which fluid is flowing such that the fluid flow down the casing above
-~ 14 the uppermost perforation is sufficient to impart a downward drag force on
each ball sealer greater in magnitude than the buoyancy force acting on that
16 ball sealer.
.~; Upon completion of a treatment using ball sealers having a density
` 18 less than the treating fluid, as taught by the present invention, all ball
~`- sealers will unseat from the perforations and naturally migrate upward.
Therefore, some means should be provided to catch the ball sealers before
. they pass into production equipment which they might clog or damage. A ball
` 22 catcher 30 which will accomplish this is depicted in FIGURE 2.
~IGURE 2 shows a typical arrangement of wellhead equipment for a
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24 producing well. The well casing 2 extends slightly above the ground level
and supports the wellhead or "christmas tree" 20. The production tubing 6 is
26 contained within the casing 2 and connects with the lower end of the mastervalve 21. The master valve 21 controls the flow of oil and gas from the
28 well. Above the master valve 21 is a tee 25 which provides communication
with the well either through the crown valve 22 or the wing valve 23.
Various workover equipment can be attached to the upper end of the crown
valve 22 and communication between that equipment and the well is accom-
32 plished by opening the crown valve 22 and the master valve 21. Ordinarilythe crown valve 22 is maintained in a closed position. Production from the
34 well flows through the tee 25 laterally through the wing valve 23. The wing
valve 23 directs the flow of fluids from the wellhead to the gathering
36 flowline 26.
A ball catcher 30, shown in section, is located downstream of the
38 wing valve and upstream of the flow controlling choke 24. The produced fluid
will pass through the ball catcher 30 but the ball sealers will be trapped
therein. After the produced fluid passes through the choke 24 it moves into
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a gathering flowline 26 which will transport the fluid to a separation facility
2 and then either to holding tanks or to a pipeline.
The ball catcher 30 is basically a tee having a deflector insert 34
4 containing a deflector grid 35 inserted into the downstream end of the tee.
The deflec~or grid 35 allows fluid to pass through it but it will not allow -;
6 objects the size of the ball sealers to proceed further downstream. Preferably
the deflector grid 35 is angled within the ball catcher 30 so that when the
8 ball sealers strike the deflector grid 35, they will be deflected into the
tee's deadleg 32. A deadleg cap 33 is attached to the lower end of the
deadleg 32 and can be easily removed, when the wing valve is closed and the
: pressure bled down, to allow the removal of the trapped ball sealers.
12 EXPERIMæNTS
Experiments were conducted to test the seating efficiencies of ball
14 sealers when the ball sealers have a density greater than the treating fluid
-~ and when the ball sealers have a density less than the density of the treating
16 fluid. The laboratory experiments were designed to simulate ball sealers
~` seating on perforations in a casing. The experimental equipment included an
18 8-foot long piece of 3-inch ~ cite tubing to represent a section of casing.The lucite tubing was mounted vertically in the laboratory and its lower fnd
~- 20 sealed closed. Between 3 and 4 feet from the bottom of the tubing, five
~ vertically aligned holes were drilled through the wall of the tubing to
- ~22 represent perforations. The holes were 3~8-inch in diameter and spaced 2
inches apart on center. L~cit~
24 A 90 elbow was placed on the upper end of the ~ e tubing and
was connected by a flowline to a pump. The pump drew fluid from a reservoir
26 tank and pumped it at various controlled rates through the flowline and into
the upper end of the tubing. The fluid flowed down the ~ucite tubi~g,
28 through the perforations and returned by a flowline to the reservoir tank.
To inject the ball sealers, a suitable hole was made in the elbow
and a l-inch diameter piece of tubing welded in the hole. The end of the 1-
inch tubing was centered to be coaxial with the lucite tubing at the upper
32 end of the lucite tubing. The ball sealers were introduced into the lucite tubing through the l-inch tubing.
34 The flow of fluid into the upper end of .he ~ucite tubing was
measured. It was assumed that the flow through each perforation was the same
36 and therefore the flow through each perforation was taken to be 1/5 of the
measured flow into the upper end of the lucite tubing.
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During the first phase of experiments, water, having a density of
2 1.0 grams per cubic centimeter (g/cc), was used as the fluid. Rigid ball
` sealers were made from four different materials having different densities.
4 The balls were all 3/4" in diameter and were made respectively from polypro-
i pylene (0.84-0.86 g/cc density), nylon (~.ll glcc density), acetal (1.39 g/cc
6 density) and teflon (2.17 gtcc density). Although these ball sealers did not
have an elastomeric cover, in actual practice, ball sealers are usually
8 covered with an elastomer so that they effect a better seal. However, for r
the purpose of these experiments which was to observe seating characteristics
10 and not sealing characteristics, the elastomeric covering was not essential.
The experiment generally involved establishing a specific flow rate
12 of the fluid through the perforations, injecting the ball sealers through thel-inch tubing into the upper end of the 8-foot lucite tubing and observing
~14 whether or not the ball sealers seated on the perforations. The experimental`;~program was conducted with ball sealers made of all four materials being
16 injected into the tubing with the water flowing through the tubing at various flow rates.
-18 A single set of tests involved injecting ten balls of the same
material, one at a time, into the top of the 8-foot lucite tubing. An
20 observation was made whether or not the ball sealer seated on one of the
perforations. If a ball seated on a perforation, that ball was released from
22 the perforation prior to dropping the next ball, so that there were always
five open perforations for each ball to seat upon. During a single set of
24 tests the fluid and its flow rate remained unchanged. After all ten balls
had been dropped, the number that seated upon perforations was defined as
26 the seating efficiency under those conditions and expressed as a percentage.
Tests were conducted to define a regression curve plotting seating
28 efficiency against flow rate for each of the ball sealers tested. The data
from those regression curves was then used to make the graph of FIGURE 3.
30 The graph of FIGURE 3 plots seating efficiency for the ball sealers tested
versus flow rate. Since there were five perforations in the lucite tubing,
32 the flow rate through each casing is readily obtainable by dividing the totalflow rate by five. FIGURE 3 shows that the seating efficiency of ball sealers
34 having a density greater than that of the treating fluid significantly decreases
~ith decreasing flow rate. By comparison, the seating efficiency of the
36 buoyant ball sealer (.84 g/cc) remains at 100% down to a flow rate of about
lS gallons per minute. Below this flow rate seating efficiency drops to zero
38 percent. As will be illustrated and discussed later, adjustments would be
necessary in the density contrast to obtain 100% seating efficiency at flow
40 rates below lS gpm for this particular situation.
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As discussed previously, the reason why ball sealers have tra-
2 ditionally not been used for matrix rate treatments is that their seating
efficiency is very poor at matrix flow rates. PIGURE 3 verifies this pre-
4 sumption for ball sealers having a density 8reater than the treating fluid.
A total flow rate of under 25 gallons per minute, corresponding to a per
6 perforation flow rate of about 5 gpm, simulates a relatively high flow rateat which a matrix treatment could be conducted without fracturing the forma-
8 tion. At this rate, ball sealer efficiencies for the denser than fluid ballsis at or near zero percent. When the density of the ball sealers is greater
than the density of the fluid, the seating efficiency of the ball sealers is
primarily a function of the flow rate through the perforation. The greater
12 the flow rate through the perforation the greater will be the seating effi-ciency. However, the seating efficiency of ball sealers having a density
14 greater than the density of the fluid is strictly a statistical phenomenon.A variation in the number, spacing and orientation of the perforations is
16 highly likely to affect the precise seating efficiency which can be expected
in a given situation. Therefore, since the seating of ball sealers having a
18 density greater than the density of the fluid is a statistical phenomenon,
there is always the possibility that too few or too many of the ball sealers
will seat to get the desired diversion. Nevertheless, at matrix rates the
seating efficiency of heavier than fluid ball sealers will invariably be very
22 poor.
In contrast to the performance of the ball sealers having a density
24 greater than the density of the fluid is the performance of the buoyant ball
sealer. As noted above, the .84 g/cc ball sealer has a seating efficiency of
26 lOO~ at flow rates above lS gpm. The seating efficiency of a ball having adensity less than the fluid density will always be 100% provided the downward
28 flow of fluid in the casing above the perforstions is sufficient to impart a
downward drag force on the ball sealers which is greater in magnitude than
the upward buoyancy force acting on the ball sealers. In other words, if the
downward flow of fluid within the casing is sufficient to transport the ball
32 sealers downward to the perforations, they will always seat. The quantum
jump in the seating efficiency of the buoyant ball from 0% to 100% at about
34 15 gpm represents the lowest flow rate at which the buoyant ball can be
transported down the well. In this particular example, below a flow rate of
36 about 15.3 gpm, the upward buoyancy of the ball overcomes the downward flowof the treating fluid thus preventing downward transport of the ball sealers
38 to the perforations. On the other hand, when the downward flow within the
casing transports the ball sealers to the level of the perforations, the ball
sealers seat. A predictable, non-statistical diversion process is thereby
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attained since the number of perforations plugged by the ball sealers will be
2 equal to the lesser of the number of ball sealers injected into the casing or
the number of perforations accepting fluid.
4 The relationship between density contrast and the fluid velocity
needed to transport the ball sealers down the casiDg was investigated.
6 FIGURE 4 is a graph of the normalized density contrast between the ball
sealers and the fluid plotted against the velocity of the fluid downward
8 within the casing. The normalized density contrast is the difference in
density between the ball sealer and the fluid divided by the density of the
;~ 10 fluid. A positive normalized density contrast means the density of the ball
sealer is greater than the density of the fluid and a negative normalized
12 density contrast means the density of the ball sealer is less than the
density of the fluid. It follows that a normalized density contrast of zero
14 means that the ball sealer and the fluid have the same density. The graph of
:~ FIGURE 4 is based upon several tests which involved placing a ball sealer
16 within a vertical piece of lucite tubing and flowing fluid downward throughthe tubing. The velocity of the fluid was adjusted until the ball sealer was
18 maintained in a fixed position at the midpoint of the tubing. In that equilib-
rium positio~ the drag forces of the fluid shearing past the ball sealer were
equal in magnitude to the buoyancy forces acting on the ball sealer. Ball
sealers of several densities were used in conjunction with two fluids, water
22 and 1.3 g/cc calcium chloride brine, to yield the plot of FIGURE 4.
- The solid line defines the equilibrium condition wherein the ball
24 sealer will remain stationary within the casing, moving neither upward nor
downward. Below the line in FIGURE 4 the velocity of the fluid in the
26 casing would be insufficient to overcome the force of buoyancy and the ballsealers will rise in the casing. Above the line in FIGURE 4 the velocity of
28 the fluid in the casing exerts a drag force on the ball sealers greater in
magnitude than the force of buoyancy acting on the ball sealers. Therefore,
the ball sealers will be transported down the casing.
All points on the line and below it correspond to a certain nor-
32 malized density contrast and a certain casing velocity which will result ina seating efficiency of zero percent because the ball sealers are not trans-
34 ported down to the perforations. However, if the normalized density contrastand casing velocity define a point which is above the line plotted in FIGURE 4,
36 the seating efficiency will be 100% because ball sealers are transported tothe perforations on which they will seat. Their buoyancy will maintain them
38 at a position at or above the lowermost perforation and the downward fluid
velocity in the casing above the uppermost perforation will maintain the ball
sealers at or below the level of the uppermost perforation.
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It will take a very small fluid flow through a perforation to draw
2 a ball sealer to the perforation and seat it thereon when the amount of timethe fluid flow through the perforation has to act upon the ball sealer is
4 limited only by the length of the injection time. This, however, is a very
important limitation in that the ball sealer cannot take an infinite or a
6 very long time to reach the perforations. Although the treating fluid may
have a sufficient casing velocity to transport the buoyant ball sealers down
8 the well, it may take an inordinate amount of time to do so. Therefore, a
constraining factor is the amount of treating fluid which is transporting the
ball sealers down to the perforations. For the invention to be operable the
balls must seat before the entire amount of treating fluid is injected through
12 the perforations. Preferably, the ball sealers should be seated at an early
or intermediate stage of the injection process. Thus the ball sealers'
14 buoyancy cannot transport them upwardly at a rate which will make them traverse
more than the length of the entire interval of treating fluid injected into
16 the well. This concept and the limitations it imposes will be further discussed
in the Design Example.
18 As a final test of the seating efficiency of ball sealers having
varying density, a series of experiments were conducted which compared seating
efficiencies for various normalized density contrasts at a constant flow
rate. In this test, a 3-inch diameter section of lucite tubing containing
22 ten vertically aligned 3/8-inch perforations was used as the simulated casing.
The flow rate of the carrier fluid was maintained at a constant 15 gpm or
24 1.5 gpm per perforation. This flow rate was selected as being typical of amatrix rate treatment. During`the tests, treating fluid densities were
26 varied and ball sealers of varying density were selected so that a relatively
wide range of normalized density contrasts of between -0.27 and ~0.08 were
28 obtained.
The results of this test are shown in FIGURE 5 which is a plot of
seating efficiency versus normalized density contrast for a constant flow
rate of 15 gpm. As mi8ht be expected from the experiments previously discussed,32 the seating efficiencies of ball sealers having a positive density contrastwere less than lO0 percent. Furthermore, such ball sealers exhibit a steeply
34 decreasing seating efficiency as density contrast increases. These resultsare consistent with those shown in FIGURE 3 wherein the 2.17 g/cc ball sealer
36 had a substantially lower seating efficiency than the l.ll g/cc or 1.39 g/cc
ball sealers at comparable flow rates.
38 Of greater importance are the test results shown in FIGURE 5 for
the ball sealers having negative density contrasts. For normalized density
contrasts less than 0.00 but greater than about -0.15, the ball sealers
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achieved a seating efficiency of 100 percent. FIGURE 5 establishes that a
2 range of ball sealer densities will achieve 100 percent seating efficiency.
That range, however, is finite and will not encompass all buoyant ball
4 sealers. Beyond a density contrast of about -0.15, the ball sealers were sobuoyant that they could not be transported downwardly to the perforations by
6 the treating at the given flow rate of 15 gpm, hence the zero percent seating
efficiency.
.
8 The experimental results thoroughly support the results shown in
FIGURE 3 for the buoyant ball sealer having a density of 0.84. That ball
sealer which had a normalized density contrast of -0.16 attained a 100 per-
cent-seating efficiency beyond flow rates of about 15.3 gpm. Below that flow
12 rate, seating efficiency was zero. This result is consistent with ~IGURE Swhich shows seating efficiency at zero percent for a density contrast of -
14 0.16 at the given flow rate of lS gpm.
It is a rather unique situation when the normalized density contrast
16 equals zero. As noted previously, the normalized density contrast is zerowhen the density of the ball sealer is the same as the density of the fluid.
18 There were no tests conducted wherein the ball sealers had the exact same
density as the fluid, but the trend of the data indicates that the seating
efficiency for a normalized density contrast of zero is somewhat less than
100~. As shown in FIGURE 5, the seating efficiency at a normalized density
22 contrast approaching 0.00 g/cc from the positive direction is about 90~. As
density enters the negative region, seating efficiency im~ediately reaches
24 100%. Thus the data clearly suggests that only a negatively buoyant, and not
a neutrally buoyant, ball sealer can attain 100% seating efficiency. At
26 neutral buoyancy it is possible that the ball sealer is carried downward bythe fluid to the level of the lowermost perforation without seating and then
~8 further carried below the level of the lowermost perforation due to its
inertia. Ball sealers having zero density contrast can, if they overshoot
the lowermost perforation due to inertia, remain sus~ended in the rathole
without seating if the flow of fluid down the casing and through the perfora-
32 tions does not cause enough turbulence below the lowermost perforation tosomehow move ball sealers upward. This situation, as clearly illustrated by
34 FI&URE 5, is not possible if the ball sealers are even just slightly less
dense than the fluid since the buoyancy of the ball sealers will cause them
36 to rise at least to the level of the lowermost open perforation taking fluid
and seat on that perforation.
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10760Z3
DESIGN EXAMPIE
2 For purposes of illustrating the operation of the present inven-
tion, a design of a matrix rate acidization treatment employing buoyant ball
4 sealers is discussed below. It is to be assumed that two wells, one equipped
with a 3 inch (ID) production casing and the other with 6 inch (ID) casing,
6 are to be ~atrix acidized. Each well has an extensive stratum or zone in the
producing interval, the perforations of which are to be selectively sealed
8 off using the ball sealer technique of the present invention to assure that
. ~ all perforations are acidized. The characteristics of each well are identical
and are as follows:
Formation - Sandstone
12 Treating Acid - 3000 gallons of an HCl-HF mud acid
Well depth (H) = 5000 feet
14 Formation permeability (k) = 50 millidarcies
Perforated interval length (h) = 50 feet
16 Fracture gradient (FG) = .6 psi/ft
Bottom hole pressure (Pb) = FG x H
18 = (.6 psi/ft) (5000 ft) = 3000 psi
Reservoir pressure (Pr) = 1000 psi
Acid density (pf) = 1.030 g/cc
Downhole acid viscosity (~) = 0.78 centipoise
22 Drainage radius of well (re) = 660 feet
Average wellbore radius (rw) = 0.1875 feet
24 For field application of a matrix rate acidization, a key limit-
ing factor is that the injection pressure and hence the injection rate must
26 be limited to avoid fracturing the formation. The maximum injection rate
that is possible without fracturing the formation is governed by Darcy's
2B radial flow equation, namely:
4.917 x 10-6 k h (Pb - P )
32 Qmax ~ ln (re/rW) r
34 where Qmax = maximum injection rate (bbl/min)
Substituting the known information given above into Darcy's equation, it
36 can be readily determined that ~ax equals 3.85 barrels per minute or
` 1076~23
0.36 ft3/sec. Based on this maximum injection rate, the ~aximum average
2 flow velocity (Vmax) through the casing can be calculated by dividing ~ax
by the cross sectional area of the casing. For the 3 inch casing Vmax
4 equals 7.3~1 ft/sec and for the 6 inch casing Vmax equals 1.837 ft/sec.
Therefore, the downward velocity of the treating fluid which is necessary
6 to transport the ball sealers to the perforations will be limited by the
maximum casing velocity that can be employed without formation fracture.
8 As noted previously, another essential factor in designing the
matrix treatment is that the treating fluid must be capable of transporting
the ball sealers down the well in a finite time. If the ball sealers move
down the production casing too slowly they may not seat on the perforations
12 during the time in which the treating fluid is being injected. It is,
therefore, inherent in practicing the invention that the relative dista~ce
14 in the treating fluid which the ball sealers buoyantly rise be no more thanthe total length of the treating fluid interval injected in the production
16 casing. The total length of the treating fluid interval is equal to the
total volume of the treating fluid divided by the cross sectional area of
18 the casing. For the 3000 gallons of treating acid called for in this
example (401 cubic feet), the length of the fluid interval is 8184 feet for
the 3 inch tubing and 3069 feet for the 6 inch casing. The time necessary
for all of the treating fluid to be injected into the formation is readily
22 calculated by dividing the sum of the fluid interval length and the depth
of the well by the velocity of the treating fluid through the casing:
24 t = ~ V H
26 where L = the length of the fluid interval
t = time for fluid injection
28 H = well depth (5000 ft~
V = average fluid velocity in casing
The minimum time, tmin, for fluid injection is, of course, the time re-
quired when the fluid is injected at its maximum velocity, Vmax. Carrying
32 out the necessary computations for the 3-inch casing, tmin equals 1793
seconds (about 30 minutes) and for the 6-inch casing, tmi~ equals 4392
34 seconds (about 73 minutes).
;
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7602~
Based on the calculated injection times given above, the maximum
2 upward velocity of the ball sealers is the time necessary for the ball
sealers to upwardly move the length of the treating fluid interval or
4 U5ax = t ~ where Umax = maximum ball sealer velocity
min
6 Calculating for Umax, Umax e~uals 4.564 feet per second for the 3-inch
casing and 0.690 feet per second for the 6 inch casing.
8 For all practical purposes, however, the actual upward velocity
of the ball sealers must be substantially less than Umax since one would
never design a system which would seat the ball sealers on the perforations
after almost all of the treating fluid was injected. Secondly, the treating
12 fluid would be injected at slightly less than V~ax to ensure an adequate
safety factor to prevent fracturing. Therefore, for practicing the present
14 invention it is preferable that actual upward velocity of the ball sealer
in the treating fluid be no greater than about one third of Umax.
16 By setting U = .25 Umax for purposes of illustration, the preferred
upward velocity of the ball sealers for the present example should be no
18 greater than 1.141 fps for the 3-inch casing and 0.175 fps for the 6-inch
casing. Upon selecting the size of the ball sealers to be used and knowing
the characteristics of the treating fluid (density, viscosity) and upward
velocity of the ball sealers (U), the Reynolds number for the ball sealers
22 can be calculated. The ~eynolds number can then be used to establish the
drag coefficient or friction factor for the spherical ball sealers, which
- 24 in this example is about 0.44 for both cases. (see, for example, Perry's
Chemical Engineers Handbook, Fifth Edition, p. 5-62.)
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1076~23
:Assuming Newtonian fluid behavior, the desired density of the ball sealers
~-2 can be calculated using the terminal velocity equation for a sphere.
iSolving that equation for density contrast, the equation becomes:
6 ~ _ 3U p
8 Pf PB 4g Db
where pf = treating fluid density = 1.07 g/cc
PB = ball sealer density in g/cc
12 DB = ball sealer diameter = 1 inch = .0833 feet
g = gravitational constant = 32.17 ft/sec
; 14 CD = drag coefficient for gall sealers = 0.44
Calculating for ~p using the given data in the example, op equals 0.171 g/cc
16 for the 3-inch casing case and 0.004 g/cc for the 6-inch casing case.
Based on the fluid density of 1.070 g/cc, the minimum ball densities are
18 calculated to be 0.898 and 1.066 g/cc for the 3 and 6-inch cases. Thus a
two-fold increase in tubing diamater of from 3 to 6 inches, as illustrated
in this example, necessitated more than a forty-fold reduction in calculated
density differential. One designing a ball sealer application employing
22 the present invention would, therefore, need to carefully compute the
desired ball sealer density based on the characteristics of the well and
24 the treating fluid. Small differences in ball sealer density could make a
major difference in performance. For example, in the case of the 6-inch
26 casing, the calculated lower density limit is 1.066 gJcc and the upper
limit is the density of the treating fluid, namely 1.070 g/cc. Thus,
28 selection of a suitable buoyant ball sealer for that situation would confine
one to the relatively narrow range of between 1.066 g/cc and 1.070 g/cc, or
a differential of only 0.004 g/cc.
.: .. .- . .-. .: .
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1076~023
FIELD EXAMPLES
2 1. A South Texas brine disposal well completed in three sandstone
intervals at about 3600 feet was treated using the method of this invention.
4 Pretreatment analysis consisted of an injectivity test which indicated that
the well was potentially damaged and a temperature survey which indicated
6 that essen~ially all of the fluid was e~tering the uppermost of the three
completed intervals.
8 Removal of the near-wellbore damage was achieved by a matrix acid
stimulation using hydrochloric acid tlSX HCl), and mud acid (12% HCl and
3X HF), and ball sealers for providing fluid diversion away from the upper
zone and into the lower two zones. Ball sealers were selected having
12 density in the range from 1.050-1.060 g/cm3). Ball sealers having the
above density were selected so that they would be readily transported to
14 the perforations by the treating fluids at the anticipated matrix injection rate of 2-3 BPM.
16 The treatment was designed to seal off 94 of the 112 perforationspresent in the three intervals. The treating rate averaged about 2-1/2 BPM
18 and the bottomhole treating pressure averaged about 2100 psi, a pressure
well beneath the fracturing pressure of this fonmation. Pressure increases
of up to 200 psi were observed as the ball sealers sealed off perforations
and diverted the acids into unacidized regions.
22 Upon completion of the acid stimulation, injectivity had increased to
4.5 BPM at 950 psi surface pressure in contrast to 1 BPM at 1000 psi ini-
24 tially. A temperature survey conducted following the treatment indicated
that all three zones were stimulated.
26 2. In a second test it was required that a matrix acid treatment
be conducted on two productive intervals in a carbonate formation located
28 at a depth of 15,700 feet. The two productive intervals were flanked above
and below by previously fractured intervals. Utilizing the methods of this
invention, buoyant ball sealers were used to successfully matrix acidizethe two interior intervals.
32 In this treatment ball sealers having a density range from 1.10
to 1.11 g/cm3 were utilized in conjunction with 28 percent HCl having a
34 density of 1.14 g/cm3, so that the ball sealers would be buoyant with
- respect to the stimulation fluid. Acid and ball sealers were staged so
36 that 330 ball sealers would be available in the first 110 bbls of 28 percent
HCl to preferentially close off the fractured zones. An additional 150 bbls
38 of 28 percent HCl was injected with ball sealers to treat the remaining 82
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1076~23
perforations in the two zones requiring the matrix acidization. The treat-
2 ment was carried out at a rate of 8-13 BPM with bottomhole pressure under
8000 psi, such conditions being suitable for matrix acidizing this deep
4 carbonate formation. During the treatment, the average bottomhole pressure
contiDually rose in response to ball sealers sealing off perforations and
6 diverting the hydrochloric acid into other unstimulated regions.
Following the treatment, a downhole flowmeter survey was conducted
8 to definitively ascertain whether all zones had been stimulated and were
currently producing. Results of that survey clearly indicated all intervals
were contributing to production, thereby establishing that the treatment had
been diverted away from the two fractured intervals leading to a successful
12 matrix stimulation of the remaining two intervals. Overall results included
a productivity increase from 2800 BOPD at 390 psi to 4600 BOPD at 1000 psi
14 flowing tubing pressure.
The principle of the invention and the best mode in which it is
16 contemplated to apply that principle have been described. Although the
present invention has been discussed primarily with regard to matrix rate
18 acid treatments, it should be emphasized that other types of well treatment operations conducted at matrix rates and applying the principles of the
present invention can be employed. For example, any other type of well
treatment wherein a carrying fluid is transporting ball sealers to casing
22 perforations can utilize the techniques of the present invention. Specificexamples would be solvent stimulation treatments, surfactant stimulation
24 treatments, inhibitor injection treatments, oil, water or emulsion injections,
and certain types of squeeze cementing operations. Therefore, it is to be
26 understood that the foregoing examples were illustrative only and that other
treatments, operations and techniques can be employed without departing from
28 the true scope of the invention defined in the claims:
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