Download - Acid Placement in Long Horizontal Wells
8/11/2019 Acid Placement in Long Horizontal Wells
http://slidepdf.com/reader/full/acid-placement-in-long-horizontal-wells 1/9
Copyright 2007, Society of Petroleum Engineers
This paper was prepared for presentation at the European Formation Damage Conferenceheld in Scheveningen, The Netherlands, 30 May–1 June 2007.
This paper was selected for presentation by an SPE Program Committee following review ofinformation contained in an abstract submitted by the author(s). Contents of the paper, aspresented, have not been reviewed by the Society of Petroleum Engineers and are subject tocorrection by the author(s). The material, as presented, does not necessarily reflect anyposition of the Society of Petroleum Engineers, its officers, or members. Papers presented atSPE meetings are subject to publication review by Editorial Committees of the Society ofPetroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paperfor commercial purposes without the written consent of the Society of Petroleum Engineers isprohibited. Permission to reproduce in print is restricted to an abstract of not more than300 words; illustrations may not be copied. The abstract must contain conspicuous
acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O.Box 833836, Richardson, Texas 75083-3836 U.S.A., fax 01-972-952-9435.
AbstractIn several places around the world, notably the North Sea andthe Middle East, carbonate reservoirs are being accessed with
very long horizontal wells (2000 to 20,000 feet of reservoir
section.) These wells are often acid stimulated to remove drill-ing fluid filter cakes and to overcome formation damage
effects, or to create acid fractures or deep matrix stimulation to
enhance productivity. Good acid coverage with a relatively
small acid volume is required to economically obtain the
desired broad reservoir access.We have developed a model to predict the placement of
injected acid in a long horizontal well, and to predict the
subsequent effect of the acid in creating wormholes,
overcoming damage effects, and stimulating productivity. Themodel tracks the interface between the acid and the
completion fluid in the wellbore, models transient flow in the
reservoir during acid injection, considers frictional effects in
the tubulars, and predicts the depth of penetration of acid as afunction of the acid volume and injection rate at all locations
along the completion.
We have used this model to simulate treatments that are
typical of those performed in the North Sea and in the MiddleEast. We present a hypothetical example of acid placement in
a long horizontal section and an example of using the model to
history match actual treatment data from a North Sea chalkwell.
IntroductionHorizontal wells are drilled to achieve improved reservoir
coverage, high production rates, and to overcome water
coning problems. Acid stimulation is a cost effective methodto enhance the productivity of horizontal wells in carbonate
reservoirs. Acid can be injected using many acid placement
methods including bullheading down the production tubing,injection from coiled tubing, injection with or following a
diverting material, injection into intervals isolated by packers,
and injection from acid jetting tools. Effective stimulation
requires that a sufficient acid volume be placed in all desiredzones. The model presented here is aimed at predicting the
acid distribution and subsequent stimulation for a variety of
placement methods used in long horizontal wells.Eckerfield et al.
1 concluded in their work that movement o
interfaces formed between acid and completion fluid is
significantly affected by uneven reservoir flow distribution
which ultimately leads to nonuniform volume of acid injected
into the formation. Wellbore hydraulics were found to havemuch less impact because of the small wellbore volume
relative to the volume of acid injected. Gdanski2 described
recent advances in carbonate stimulation stating that zonacoverage of long carbonate sections remains a challenge and
most of the acidizing treatments are designed on the basis of
of rules devised on the basis of past experience.
Davies and Jones3 presented an acid placement model for
horizontal wells. The model was for barefoot completions in
sandstone formations and the simulator used a pseudo-steady
state reservoir model. They concluded that variations in
reservoir properties along the treatment interval significantly
impacted the acid placement. The need to include wellbore phenomena was also emphasized in their work.
A new model is presented in this paper to study the aciddistribution and evolution of skin during acidizing treatmentsin horizontal wells in carbonate reservoirs. The acid placemen
model couples models of wellbore flow, including interface
tracking, a wormhole model to predict the effect of the acid
injection on local injectivity, a skin evolution model that
combines the stimulation effect of the acid with other skineffects, and a transient reservoir inflow model. The mode
predicts the bottomhole pressure response during an acid
treatment, the distribution of acid along the treated sectionand the resulting distribution of stimulation.
Model description
In a typical matrix acidizing process, the acid is being injectedinto the wellbore through production tubing, coiled tubing, ordrill pipe. The acid emanating from the tubing (whichever
type), or from ports in the tubing, displaces the residen
wellbore fluid, creating one or two interfaces between these
fluids. The acid behind the front flows into the formation andcreates wormholes in the reservoir rock, increasing the
injectivity of the contacted portions of the formation. The
effect of the acid on the formation injectivity at any location
along the well is accounted for with a local skin factor that ischanging in response to the acid injected at that point. Loca
injectivity is simultaneously affected by the transient nature o
the process – injection of any fluid will cause a pressure build
SPE 107780
An Acid-Placement Model for Long Horizontal Wells in Carbonate ReservoirsVarun Mishra, SPE, D. Zhu, SPE, and A.D. Hill, SPE, Texas A&M U., and K. Furui, SPE, ConocoPhillips
8/11/2019 Acid Placement in Long Horizontal Wells
http://slidepdf.com/reader/full/acid-placement-in-long-horizontal-wells 2/9
SPE 107780 2
_______________________________________________________________________________________________________________________________________
up in a porous medium. The transient pressure build up due to
injection and the acid stimulation that is increasing injectivity
are competing effects that must both be considered to properly predict acid placement.
This acidizing model for a long horizontal well integratesseveral sub models which are coupled. These include a
wellbore model which handles the pressue drop and material
balance in the wellbore; an interface tracking model to predict
the movement of interfaces between different fluids in thewellbore; a transient reservoir flow model; a skin factor modelaccounting for partial penetration and well completion effects;
and, an acid stimulation model that predicts wormhole growth
and the effects these have on local injectivity. Each model is
discussed in this paper separately.
Wellbore flow modelThis model incorporates the wellbore material balance andwellbore pressure drop.
Fig. 1 Schematic of a wellbore during an acidizing process
Figure 1 shows a part of the wellbore during an acid injection
process. For flow of an incompressible fluid in a horizontal
wellbore, we have
5
2)],([2),(
d
t xq f
x
t x p w f w ρ
−=∂
∂ (1)
),(),(
t xq x
t xq R
w −=∂
∂ (2)
Equation 1 describes the frictional pressure drop in thewellbore. The material balance, Eq. 2 shows that the change in
the wellbore flow rate is equal to the flow rate into the
formation at that point in the well.
Model for tracking fluid interfacesA model to track the interfaces created between various
injected fluids was presented by Eckerfield et al.1
Our acid placement model uses a discretized solution approach which is
integrated with the reservoir flow, wormhole, and skin models.
Figure 2 depicts a part of the wellbore where the interface
created between injected acid and wellbore fluid is traveling to
the right. The velocity of an interface located at xint is simply,
int
int
x x
w
A
q
dt
dx
== (3)
In jected acid
X in t |t=t X int | t=t+ t
Aq w
t
Fig. 2 Interface movement inside the wellbore
We solve this equation by discretizing the wellbore into smal
segments and assuming constant qw over each segment.
Reservoir flow modelDuring the acidizing process, the wellbore rate and the
reservoir inflow at any location are changing with time so
transient effects are occurring in the reservoir. A transien
inflow equation with variable injection rate is4
nn
j D
n
n
j
j
R
n
w sqt t pq p
i pkl
D D+⎥⎦
⎤⎢⎣⎡ −∑ ∆=−−
−=)()(2
11µ π (4)
where
1−−=∆ j
R
j
R
j
Rqqq (5)
)80907.0(ln2
1+≈ D D t p (6)
2
610395.4
wt
Dr c
kt t
φµ
−×= (7)
After dividing through by l, the length of a reservoir segment
and rearranging, qR n, the transient injection rate per unit length
of wellbore at time tn can be written as
Jxnw R Jx
n R b p paq −−−= )( (8)
where
])([
1091816.4
1
6
nn Dn D D
Jx st t p
k a
+−
×=
−
−
µ (9)
])([
)()(
1
111
11
nn Dn D D
n Dn D Dn
R
n
j j Dn D D
j R
Jx st t p
t t pqt t pq
b+−
−−⎥⎦
⎤⎢⎣
⎡−∆
=−
−−−
= −∑
(10)The constant in Eq. 9 is for oilfield units of bpm/ft for
injection rate, md for permeability, and cp for viscosity.
Wormhole modelWe have implemented two empirical models of the
wormholing process that occurs in carbonate acidizing. Thefirst of these is the volumetric model5, 6, which is based on the
assumption that a constant fraction of the rock volume is
dissolved in the region penetrated by wormholes. For radial
flow, the volumetric model is
8/11/2019 Acid Placement in Long Horizontal Wells
http://slidepdf.com/reader/full/acid-placement-in-long-horizontal-wells 3/9
SPE 107780 3 _________________________________________________________________________________________________________________________
bt wwh
hPV
V r r
πφ += 2
(11)
The key parameter in this model is PV bt, the number of porevolumes of acid needed to propagate a wormhole through a
core sample. The PV bt can vary from as low as one, or even
slightly lower, when acid is injected at near the optimal rate in
limestone, to as high as 50 when the wormholing process isnot efficient. We also note that the wormholing model
presented by Gdanski2, 7, 8, which is presented by Glasbergen
et al.8 as
h
V r wh
φ 25.035.27= (12)
for units of cm for r wh and m3/m for V/h, can be approximated
as a special case of the volumetric model with PV bt set to 1.1.
This can be derived by equating the right hand sides of Eqs. 11
and 12 and neglecting the r w2 term in Eq. 11.
An improved empirical model of the wormholing process is
that presented by Buijse and Glasbergen9. In this model, thewormhole propagation rate varies with the acid flux in a
manner based on the commonly observed “optimal flux” behavior. The user of this model supplies the optimal acid flux
and the optimal PV bt based on laboratory tests. We have
implemented both the volumetric and the Buijse models ofwormhole propagation in our acid placement simulator. If the
PV bt input to the volumetric model is close to the value
determined by the Buijse model at the acid flux occurring in
the simulated acid treatment, the results from these two
models are similar.
Skin factor and well completion model
The changing injectivity during acid injection is accounted forwith a local skin factor, s(x), which includes the effects of thecompletion, possible formation damage, and the stimulation
effect of the acid. In addition, injectivity of individual zones
along a long horizontal well are affected by a partial penetration effect which can be treated as a skin effect. This
partial penetration effect is described separately in the next
section.
The effects of the completion, formation damage, and
stimulation are all coupled and depend on the completion type.For a cased, perforated completion, we used the perforation
skin factor model of Furui et al.10, 11 For this type of model, we
assume that wormholes propagating from the tips of
perforations can be considered as extensions of the effectivelengths of the perforations.
For an openhole or slotted/perforated liner completion, weassume radial flow of the acid through a possibly damaged
zone that extends to a radial distance, r d. For this case, if the
pressure drop in the region penetrated by wormholes is small,
the evolving skin factor is
For r wh<r d :
⎟⎟ ⎠
⎞⎜⎜⎝
⎛ −⎟⎟
⎠
⎞⎜⎜⎝
⎛ =
w
d
wh
d
d r
xr
xr
xr
xk
k x s
)(ln
)(
)(ln
)()( (13)
And for r wh>r d :
⎟⎟ ⎠
⎞⎜⎜⎝
⎛ −=
w
wh
r
xr x s
)(ln)( (14)
The radius of the region penetrated by wormholes, r wh, is
obtained from the wormhole model.
Partial penetration skin model Acid injection in long horizontal wells is often into relativelyshort, isolated sections of the well. Because the section treated
is connected to the entire reservoir, the injectivity is higher
than it would be if the reservoir ended at the end of the
completion interval. A partial penetration skin factor, which
will be negative, can be used to account for this effect. This partial penetration effect is important when injecting into
relatively small intervals of horizontal wells and is not widely
recognized, so a brief review is in order.
Fig. 3 A partially completed vertical well
The effect on productivity of completing a vertical well inonly a portion of the reservoir has been described numerous
times, beginning with Muskat12. For a well completed along a
thickness, hw, in a reservoir of thickness h (Fig. 3), and in the
absence of any other skin effects, the steady-state productivity
index is
⎟⎟ ⎠
⎞⎜⎜⎝
⎛ +
=
cw
e sr
r B
kh J
ln2.141 µ
(15)
where sc is the partial completion (also called partia
penetration) skin factor. When hw is less than h, sc is positive
accounting for the lessened productivity of the partially
completed well. Models to calculate sc have been presented in
many studies, including those of Cinco-Ley et al.13, Odeh14
and Papatzacos15. The productivity index could also be written
using the completed thickness in the inflow equation:
⎟⎟ ⎠
⎞⎜⎜⎝
⎛ +
='
ln2.141 cw
e
w
sr
r B
kh J
µ
(16)
h
Zw
hw
hw = CompletionthicknessZw = Elevation
r w
8/11/2019 Acid Placement in Long Horizontal Wells
http://slidepdf.com/reader/full/acid-placement-in-long-horizontal-wells 4/9
SPE 107780 4
_______________________________________________________________________________________________________________________________________
If hw is less than h, sc’ must necessarily be negative to give the
same productivity index as Eq. 15.
When hw is relatively small compared with h, these partialcompletion effects are large. For example, when hw/h is 0.25,
sc is 8.8 using the Papatzacos model when the completion iscentered in an isotropic reservoir. If ln(re/r w) is 8, a typical
value, the corresponding sc’ is -3.8. Thus, when calculating
productivity or injectivity based on the completion zone
thickness, the well appears to be stimulated because thereservoir is thicker than the completed interval.
The corresponding situation for acid injection into a short
interval of a horizontal well is shown in Fig. 4. Because we
are assuming radial flow from the completed interval in our
reservoir flow model, there will be a large partial penetrationeffect which we can account for with a negative skin factor.
Fig. 4 Horizontal well partially open to the reservoir
Fig. 5 Ellipsoidal flow geometry
We have developed a simple model to calculate this type of
skin factor as follows. Consider a horizontal well partially
open to the reservoir as in Fig. 4. Ellipsoidal flow exists due tothe partial opening of the wellbore in the reservoir as in Fig. 5.
The ellipsoidal inflow equation is
⎟⎟
⎠
⎞⎜⎜
⎝
⎛
−
+=∆
1
1ln
)2(
2.141ξ
ξ µ
e
e
ak
q p (17)
where
)(sinh1
Dr −=ξ (18)
ar r D /= (19)
The radial flow equation based on a completed interval of
length 2a is
⎥⎥⎦
⎤
⎢⎢⎣
⎡+⎟⎟
⎠
⎞⎜⎜⎝
⎛ =∆ c
w
sr
r
ak
q p 'ln
)2(
2.141 µ (20)
Equating the pressure drops given by Eqs. 17 and 20 givesthe horizontal well partial penetration skin factor as
⎥⎥⎦
⎤
⎢⎢⎣
⎡
++−+++=
⎥⎥⎦
⎤
⎢⎢⎣
⎡
−+=
)11(
)11(2ln)1()1(2ln'
2
2
D D
D Dwwc
r r h
r r r eher sξ
ξ
(21)
Solution approachThe models for wellbore flow, partial penetration and
completion skin factor, front tracking, reservoir inflow
wormhole growth, and skin evolution were incorporated into anumerical simulator. The solution method for these coupled
models is described in the Appendix.
ResultsWe illustrate the predictions of the horizontal well acid
placement model presented here with two contrastingexamples. In the first example, acid is injected at a relatively
low rate into a long section of a horizontal well. This is the
situation where wellbore flow conditions are most likely to be
significant. The second example, the simulation of an actual
North Sea acid treatment, is a case of high rate injection into avery short interval.
Example 1 – Small volume injection into a long interval. Inthis case, we investigate the effects of acid volume and acid
injection rate on the placement of injected acid and the
resulting distribution of acid along the well. The conditions for
this case are presented in Table 1. The volumetric model ofwormhole growth was used in this example.
Table 1 Data for Case 1
Well length 1000 ft
Number of grid blocks 50
Grid block length 20 ft
Completion Open hole
Damage radius 0.5 ft
Permeability 2 md
Index of anisotropy 1
Permeability impairment
ratio
0.5
Reservoir rock Limestone
Acid 15 % Hcl
Reservoir pressure 3200 Psi
Wormhole model Volumetric
Pore volume for
breakthrough (PV bt)
2
Injection rate 2 bpm
Duration of pumping 100 Min
Assuming that the acid is being injected from a tubing tai
located at one end of the completed interval, the progressionof acid placement with time is shown in Fig. 6. By the end of
200 barrels of acid injection at 100 minutes of pumping time
acid has not yet reached the far end of the completed interval
8/11/2019 Acid Placement in Long Horizontal Wells
http://slidepdf.com/reader/full/acid-placement-in-long-horizontal-wells 5/9
SPE 107780 5 _________________________________________________________________________________________________________________________
For better acid coverage with this small volume treatment (thetotal volume pumped in 100 minutes is only 8.4 gal/ft), some
method of diversion is required.
0.00
0.05
0.10
0.15
0.20
0.25
0 200 400 600 800 1000
Position along well (ft)
A c i d v o l u m e ( b b l
/ f t )
10 min
40 min
80 min
100 min
Fig. 6 Acid coverage over the entire length of wellbore
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
0 200 400 600 800 1000Position along well (ft)
W o r m h o l e l e n g t h ( i n )
10 min
40 min
80 min
100 min
Fig. 7 Wormhole length distributions at different times
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0 200 400 600 800 1000
Position along well (ft)
A c i d v o l u m e ( b b l / f t )
500 bbls acid (21 gal/ft)
200 bbls acid (8.4 gal/ft)
Fig. 8 Acid placement profiles for 200 and 500 bbls of acid
The distribution of wormhole lengths along the wellbore
created by this acid injection is shown in Fig. 7. By 100
minutes of acid injection, wormholes had extended 6 inches
into the formation at the heel of the completed intervalInjection of larger volumes of acid improves the coverage of
acid in this long interval. With 500 bbl of acid injected, the far
end of the completed interval has received a significan
amount of acid injection, with good acid coverage along mostof the interval (Fig. 8). For a well with only minor damage, as
was assumed for this case, although the acid is increasing the
local injectivity, and thus retarding the progress of the acid
down the wellbore, the injectivity is changing slowly, and thusdoes not have a strong effect on the acid placement. Another
illustration of this is obtained by changing the efficiency of the
acid treatment by changing the PV bt parameter used in thevolumetric model. Figure 9 compares the acid placement for
cases ranging from PVbt of 0.5 (very rapidly propagating
wormholes) to inert fluid (no wormholes, hence no change in
injectivity during injection). The acid coverage changes a little
depending on how efficiently the acid is increasing injectivity but it is not a large effect.
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0 200 400 600 800 1000
Position along well (ft)
A c i d v o l u m e ( b b l / f t )
PVbt=0.5
PVbt=2
PVbt=10
Inert fluid
Fig. 9 Acid placement profiles for different values of PV bt
One of the interesting predictions of this model is the
downhole pressure response during acid injection. Bottomhole
pressure measurements are becoming more and more commonduring acid injection and can provide very useful diagnostic
information about the treatment. The predicted pressure
responses for a wide range of PV bt are shown in Fig. 10. When
an inert fluid is injected, the pressure builds up because of thetransient nature of the reservoir flow. With acid injection, the
simultaneous stimulation is tending to decrease the injection
pressure. Thus, depending on how efficiently the acid is
increasing the near-well permeability, the injection pressure
may rise or fall, as shown in Fig. 10. Comparison of actuatreatment response with predictions like these provide a means
of diagnosing the effectiveness of acid stimulation, and if donein real time can be used to optimize a treatment on the fly.
The final aspect of this hypothetical case that we studied
was the effect of the wormhole model on the predicted acid
placement. Figure 11 shows the wormhole length distributionfrom the volumetric model with PV bt set to 2.5 compared with
the predicted placement using the Buijse model with the PV bt
opt equal to 1.5. With the Buijse model, the wormhole
propagation is varying with acid flux, with the maximum
wormhole propagation being at the optimal injectioncondition. In this particular case, the acid fluxes are near the
8/11/2019 Acid Placement in Long Horizontal Wells
http://slidepdf.com/reader/full/acid-placement-in-long-horizontal-wells 6/9
SPE 107780 6
_______________________________________________________________________________________________________________________________________
optimum, but somewhat higher. For the range of acid fluxes
occurring in this treatment, the PV bt from the Buijse model
varies from about 2 to about 2.5. The volumetric model, whichassumes a constant PV bt independent of acid flux, gives a
similar prediction of acid placement, and hence, wormholedistribution, when a value of 2.5 was used for PV bt.
3100
3200
3300
3400
3500
3600
3700
3800
0 20 40 60 80 100 120Time (min)
P r e s s u r e ( p s i )
PVbt=0.5
PVbt=2
PVbt=10
Inert fluid
Fig. 10 Pressure response during acid injection
0.00
1.00
2.00
3.00
4.00
5.00
6.00
0 200 400 600 800 1000Position along well (ft)
W o r m h o l e l e n g t h ( i n )
Buijse's Model for PVbt-opt = 1.5
Volumetric model for PVbt = 2.5
Fig. 11 Comparison of wormhole distributions from the
volumetric and Buijse’s models
Example 2 – North Sea short interval, high volume acid
treatment. In this case, we present predictions for an actual North Sea horizontal well completed in a chalk formation. The
6000 ft-long horizontal well was completed with sixteen
individual 10 foot-long perforated intervals spaced along thewell. Each interval is perforated with one shot per foot with
the perforations oriented downward. In this stimulation
treatment, each zone was isolated with packers and
individually treated with 15% HCl. The treating string was
equipped with pressure gauges between the packers and oneither side of the packers enabling the operator to monitor the
downhole treating pressure and to determine if the packers
were set and not leaking. We used our acid placement model
to history match the treating pressure response for one of thezones treated.
The pressure records from the three downhole gauges are
shown in Fig. 12. There is a clear indication of the packers
being set. The pressure gauge on the heel side of the firs
packer shows no pressure response to injection, indicating tha
it is set. Then at about 22 minutes, the second packer is set, asindicated by the rapid pressure falloff recorded by the gauge
beyond the second packer. We began simulation of thetreatment at the 22 minute time, when both packers were se
and acid injection into the isolated interval began.
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
0 10 20 30 40 50
Time (min)
P r e s s u r e ( p s i )
BHP-Zone
BHP-Below
BHP-Above
Isolation of bottom
zone achieved
Isolation of top zone
achieved
Start of acid injection in
the formation
Fig. 12 Pressure response of downhole gauges in Case 2
To history match the pressure response during this
treatment, we input the actual injection rate schedule recorded
to our model – Fig. 13 shows how we approximated the
changing rate schedule as a series of discrete rate changesAdditional data used in the model is given in Table 2.
Table 2 Input data for Case 2
Casing ID 6.625 inches
Coiled tubing OD 2.55 inches
Pipe roughness 0.0001
Zone length 10 ft
Reservoir pressure in zone 5350 psi
Reservoir compressibility 5E-06 psi-1
Permeability 5 md
Porosity 0.38
Initial formation damage none
Perforation length 7 inches
Perforation diameter 0.264 inches
Perforation spacing 1 spf
Perforation phasing 0 degree
Perforation orientation 90 degreeAcid type HCl
Acid density 69.91 lbm/ft3
Acid viscosity 1 cp
Acid concentration 15%
Wormhole model Volumetric
Number of grid blocks 10
Reservoir thickness 200 ft
8/11/2019 Acid Placement in Long Horizontal Wells
http://slidepdf.com/reader/full/acid-placement-in-long-horizontal-wells 7/9
SPE 107780 7 _________________________________________________________________________________________________________________________
0
2
4
6
8
10
12
14
16
0 10 20 30 40 50
Time (min)
I n j e c t i o
n r a t e ( b p m )
Treatment rate
Simulated rate
zonal isolation achieved
at 6 bpm
Pzone=9050 Psi
Acid Injection
Started
at 5 bpm
Response of
the whole well
(packers are
not set)
Acid injection
stopped
Fig. 13 Rate schedule for Case 2
From the data given about the well, we calculated the initial
skin factor as follows. For the given perforating conditions, we
obtained a perforation skin factor of 4.6 using the Furui etal.10,11 model. For this very short interval in a large reservoir,
we calculated a partial penetration skin factor with Eq. 21 of -
5.5. Combining these, and assuming no formation damage was
present initially, we use an initial total skin factor of -.9. Wethen adjusted the reservoir permeability and the PV bt in the
volumetric model to obtain a match of the actual treating
pressure (Fig. 14). This match ws obtained by setting the PV bt
to 4.5, which means the acid is propagating wormholesrelatively slowly into the matrix and that a large volume of
rock is being dissolved in the treated region. With PV bt of 4.5,the wormhole front is moving 4.5 times slower than the
injected fluid (spent acid) front.
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
0 20 40 60 80
Time (min)
P r e s s u r e ( p s i )
Treatment pressure
Simulated pressure
Fig. 14 History match of treatment pressure
For the high rate injection into such a short interval, acid
placement is not an issue, as shown in Fig. 15. More
importantly for this type treatment is what the model can tell
us about the effects of this large volume acid treatment from
the predicted depth of acid penetration into the formation. Notice that this interval has received 120 barrels of acid, about
500 gal/ft.
0
2
4
6
8
10
12
0 2 4 6 8 10
Position along well (ft)
A c i d v o l u m e ( b b l / f t )
120 bbls acid injected (504 gal/ft)
Fig. 15 Acid placement for Case 2
From the history-matched pressure response using a PV bt o
4.5, we predict that a radial region of wormholes has
propagated about 40 inches into the formation. The volumetricmodel presumes that the acid is dissolving a fixed fraction of
rock, given by6
bt Ac PV N =η (22)
Where the Acid Capacity No., NAc, is
( ) rock
HCl Ac N
ρ φ
ρ φβ
−=
1
15 (23)
For this high porosity chalk formation, η is 0.22, meaningthat in the regions where wormholes have formed, 22% of the
rock has been removed. With the initial porosity in this chalkformation being 38%, after this amount of dissolution, the
porosity would be 0.52. It is likely that this amount odissolution would result in the collapse of some of the
remaining rock in this region, leaving a large cavern.
Based on the dissolving power of 15 % HCl reacting withcalcite, 12 bbl of acid injection into a single perforation wil
dissolve 5.5 ft3 of solid. Assuming that the dissolution region
extends 40 inches from the wellbore, as predicted by the
volumetric model with PV bt = 4.5 as used in this history
match, the acid has likely dissolved a sufficient amount ofrock out to at least this distance to make the remaining rock
unstable.
ConclusionsWe have developed an acid placement model for horizonta
wells in carbonate reservoirs which combines a wellbore flowmodel, including interface tracking, a wormhole model to
predict the effect of the acid injection on local injectivity, a
skin evolution model that combines the stimulation effect of
the acid with other skin effects, and a transient reservoir
inflow model. With this model, we find that
• Small volume treatments in long horizontal intervals
result in non-uniform acid placement, but that the
placement improves with increasing acid volume;
8/11/2019 Acid Placement in Long Horizontal Wells
http://slidepdf.com/reader/full/acid-placement-in-long-horizontal-wells 8/9
SPE 107780 8
_______________________________________________________________________________________________________________________________________
• Partial penetration effects are important when injecting
into relatively short intervals of long horizontal wells;
• The parameters in a wormholing model can be adjusted to
history match (or predict) the pressure response of an acid
treatment in a horizontal well;
• History matching of an acid treatment in a North Sea well
completed in a chalk formation required a relatively high
value of the pore volumes to breakthrough parameter,
suggesting that the acid is propagating slowly into therock, creating a cavity around the wellbore.
AcknowledgementsThe authors thank the sponsors of the Middle East CarbonateStimulation joint industry project at Texas A&M University
for support of this work.
Nomenclaturea = half length of open interval, ft
a jx = parameter in inflow equation, bbl/min-psi
A = cross-sectional area of wellbore, ft2
Ai = coefficients in solution matrix
b jx = parameter in inflow equation, bbl/min B = formation volume factor, dimensionless
Bi = coefficients in solution matrix
ct = total compressibility, psi-1 C i = coefficients in solution matrix
d = internal diameter of wellbore, ft
f f = fanning friction factor, dimensionlessh = reservoir thickness, ft
hw = length of completed interval, ft
J = productivity index, bbl/day/psi
J s = specific productivity index at any point in wellbore,
bbl/day/psi/ftk = permeability of reservoir rock, md
k d = permeability of damaged region, mdl = length of reservoir segment, ft L = length of wellbore, ft
N Ac = acid capacity number, dimensionless
p D = dimensionless pressure
pi = initial reservoir pressure, psi
pw = pressure at any point in the wellbore, psi
PV bt = pore volume for break through, dimensionless
q R = reservoir inflow rate per unit length of wellbore,
bbl/min/ft
qw = wellbore flow rate at any point, bbl/minr d = radius of damaged zone, ft
r D = dimensionless radius
r e = reservoir drainage radius, ft
r w = wellbore radius, ftr wh = radius of wormhole region, inches
s = skin factor, dimensionless sc = partial completion skin factor, dimensionless
sc’ = partial completion skin factor using hw for thickness
t = time, minutes
t D = dimensionless time
V = volume, ft3
x = position of any point along the wellbore length, ft
xint = location of interface from the heel of the well, ft
Z w = elevation of completed interval, ft
β 15 = gravimetric dissolving power of 15% HCl
dimensionless
ζ = pressure drop function, psi/ft/bbl/minη = wormholing efficiency, dimensionless
µ = viscosity of fluid, cp
ξ = ellipsoidal coordinate dimension
ρ = density of fluid in wellbore, lbm/ft3
ρ HCl = density of HCl, lbm/ft3
ρrock = density of rock, lbm/ft3
φ = porosity of the reservoir rock, fraction
∆q R = change in rate, bbl/min
∆t = time step, minute
References1. Eckerfield, L. D., Zhu, D., Hill, A. D., Thomas, R. L.
Robert, J. A., and Bartko, K.: “Fluid Placement Model forHorizontal-Well Stimulation,” SPE Drilling &
Completions, Volume 15, Number 3, September 2000.
2. Gdanski, R.: “Recent Advances in Carbonate
Stimulation,” SPE paper 10693 presented at the 2005International Petroleum Technology Conference, 21-23
November, Doha, Qatar.3. Jones, A. T. and Davies, D. R.: “Quantifying Acid
Placement: The Key to Understanding Damage Removain Horizontal Wells,” SPE paper 31146 presented at the
1996 SPE Formation Damage Control Symposium, 14-15
February, Lafayette, Louisiana.4. Lee, J., Rollins, J.B., and Spivey, J.P.: Pressure Transien
Testing , SPE Textbook Series, Vol. 9, SPE, Richardson
Texas (2003).
5. Hill, A. D., Zhu, D., and Wang, Y.: “The Effect ofWormholing on the Fluid-Loss Coefficient in Acid
Fracturing,” SPE Production and Facilities, 10, No. 4, p
257-263, November 1995.
6. Economides, M. J., Hill, A. D., and Ehlig-Economides
C.: Petroleum Production Systems, Prentice HallEnglewood Cliffs, NY, 1994.
7. Gdanski, R.: “A Fundamentally New Model of AcidWormholing in Carbonates,” SPE 54719 presented at the
European Formation Damage Control Conference, The
Hague, The Netherlands, May 31 – June 1, 1999.
8. Glasbergen, Gerald, van Batenburg, Diederik, van
Domelen, Mary, and Gdanski, Rick: “Field Validation ofAcidizing Wormhole Models,“ SPE 94695 presented at
the 6th European Formation Damage Conference
Scheveningen, The Netherlands, May 25-27, 2005.
9. Buijse, M. and Glasbergen, G.: “A Semiempirical Modelto Calculate Wormhole Growth,” SPE paper 96982
presented at 2005 SPE Annual Technology ConferenceOctober 9-12, Dallas, Texas.
10. Furui, K., Zhu, D., and Hill, A. D.: “A New Skin Factor
Model for Perforated Horizontal Wells,” SPE 77363
presented at the SPE Annual Technical Conference and
Exhibition, Sept. 30 – Oct. 2, 2002, San Antonio, Texas.
11. Furui, K., Zhu, D., and Hill, A.D.: “A ComprehensiveSkin-Factor Model of Horizontal-Well Completion
Performance,” SPE Production and Facilities, Volume
20, Number 3, August 2005.
8/11/2019 Acid Placement in Long Horizontal Wells
http://slidepdf.com/reader/full/acid-placement-in-long-horizontal-wells 9/9
SPE 107780 9 _________________________________________________________________________________________________________________________
12. Muskat, M.: Flow of Homogeneous Fluids Through Porous Media, McGraw Hill Book Co., New York, N. Y.,
1937.
13. Cinco-Ley, H., Ramey, H. J., Jr., and Miller, F. G.:
“Pseudoskin Factors for Partially-PenetratingDirectionally-Drilled Wells,” SPE 5589 presented at the
SPE-AIME Annual Conference, Sept. 28-Oct. 1, 1975,
Dallas, Texas.
14. Odeh, A. S.: “An Equation for Calculating Skin FactorSue to Restricted Entry,” JPT , June 1980, p. 964-965.
15. Papatzacos, P.: “Aproximate Partial-Penetration
Pseudoskin for Infinite-Conductivity Wells,” SPE Reservoir Engineering , May 1987, p. 227-234.
Fig. A-1 Schematic of a segmented wellbore
Appendix A: Solution approach
),(),(
t xq x
t xq R
w −=∂
∂ (A-1)
Jxnw R Jx
n R b p paq −−−= )( (A-2)
),()()],([2),(
5
2
t xqqd
t xq f
x
t x pww
w f w ζ ρ
−=−=∂
∂ (A-3)
Eq. A-1 is the wellbore material balance. Eq. A-2 is achievedfrom the reservoir flow model and Eq. A-3 represents the
pressure drop in the wellbore, where ζ i is a function of qw.
])([ ,,,2/1,2/1, i Jxiw Ri Jxiiwiw b p pa xqq +−∆=− −+ (A-4)
For i=1, 2, 3, 4, 5
2/1,
1
,1, 2
)(
+
+
+
∆+∆
−=− iwi
ii
iwiw q
x x
p p ζ (A-5)For i=1, 2, 3, 4
Fig. A-1 is a schematic of segmented wellbore. These
equations are to be discretized in this domain and will be
solved simultaneously. Eq. A-1 and Eq. A-2 are coupled and
can be written in discretized form as Eq. A-4. Eq. A-5 iswritten as discretized form of pressure drop equation, Eq. A-3
Initial and boundary conditions can be applied on this domain
When the injection rate is specified at the heel, 9 equationscan be written for 5 segments. This set of 9 equations reduces
to a tri-diagonal matrix system as in Eq. A-6, where
coefficients Ai , Bi , and C i are defined by Eqs. A-7, A-8 and A
9 respectively.
⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜
⎝
⎛
+
+
+
+
++
=
⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜
⎝
⎛
⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜
⎝
⎛
−
−
−
−
−
−
−
−
55
44
33
22
11
5,
2/9,
4,
2/7,
3,
2/5,
2,
2/3,
1,
5
4
4
3
3
2
2
1
1
0
0
0
0
10000000
1)(1000000
01100000
001)(10000
00011000
00001)(100
00000110
0000001)(1
00000001
B p A
B p A
B p A
B p A
Q B p A
p
q
p
q
p
q
p
q
p
A
qC
A
qC
A
qC
A
qC
A
i
i
i
i
wi
w
w
w
w
w
w
w
w
w
(A-6)
i Jxii a x A ,∆= (A-7)
i Jxii b x B ,∆= (A-8)
2/)( 1 iiii x xC ζ ∆+∆= + (A-9)