FIELD OF INVENTION
This invention relates to methods and systems for
determining acidizing fluid injection rates and more specifically, to methods
and systems for determining acidizing fluid injection rates for stimulation of
5 a subterranean formation.
BACKGROUND TECHNICAL INFORMATION
Hydrocarbons, such as oil and gas, are commonly obtained from
subterranean formations that may-be located onshore or offshore.-- The
development of subterranean operations and the processes involved in
10 removing hydrocarbons from a subterranean formation typically involve a
number of different steps such as, for example, drilling a wellbore at a
desired well site, treating the wellbore to optimize production of
hydrocarbons, and performing the necessary steps to produce and process
the hydrocarbons from the subterranean formation.
15 Acid treatments are used to stimulate and increase the
production of hydrocarbons in a subterranean formation comprising acidsoluble
components, such as those present in. carbonate and sandstone
formations. This is commonly referred to as acidizing. One such aqueous
acid treatment, referred to as "matrix acidizing," involves the introduction of
20 an acid into a subterranean formation under pressure so that the acid flows
through the pore spaces of the formation. The acid of the aqueous acid
treatment reacts with acid soluble materials contained in the formation to
increase the size of the pore spaces and increase the permeability of the
formation.
25 In carbonate formations, matrix acidizing creates conductive
flow channels known as wormholes that bypass the damage in the
formation. The wormholes are formed when the matrix of the porous and
permeable rock is dissolved by reactive fluids. The fluid injection rate is an
especially important consideration in developing deep penetrating
30 wormholes. When the injection rate is too low, the acidizing fluid may only
dissolve the rock in the vicinity of the wellbore and wormholes may not
form. When the injection rate is too high, the treatment may form thick and
shallow wormholes that do not penetrate deep enough into the formation.
Traditionally, treatment fluids associated with acid
treatments such as matrix-acidizing are injected at the maximum pressure
5 differential and injection rate ("MAPDIR"). While this injection rate is
simple, it uses large volumes of acid, is limited by pump and tubing
capacity, and may not achieve optimal stimulation of the subterranean
formation.
10 BRIEF DESCRIPTION OF THE DRAWINGS
These drawings illustrate certain aspects of some of the
embodiments of the present disclosure and should not be used to limit or
define the claims.
Figure 1 is a process flow diagram illustrating a method for
15 determining an injection rate for an acidizing treatment fluid according to
certain embodiments of the present disclosure.
Figure 2 is a diagram illustrating an example of a
subterranean formation in which an acidizing treatment may be performed
in accordance with certain embodiments of the present disclosure.
20 Figure 3A and 3B are graphs illustrating breakthrough curves
for acidizing fluids in a core flood experiment, in accordance with certain
embodiments of the present disclosure.
Figure 4 is a diagram of an example information handling
system, according to certain embodiments of the present disclosure.
25 Figure 5 is a graph illustrating data relating to total skin over
time for a chelating agent injected at the maximum pressure differential and
injection rate and according to an injection rate profile determined according
to certain embodiments of the present disclosure.
Figure 6 is a graph illustrating data relating to total skin over
30 time for hydrochloric acid injected at the maximum pressure differential and
injection rate and according to an injection rate profile determined according
to certain embodiments of the present disclosure.
" O- D E L irt 1 B 9 ~ B 4 - 2 & 1 S I B "••_ jB
Figure 7 is a graph illustrating data relating to wormhole
penetration for hydrochloric acid injected at the maximum pressure
differential and injection rate and according to an injection rate profile
determined according to certain embodiments of the present disclosure.
5 Figure 8 is a graph illustrating data relating to total skin over
time for a chelating agent injected at the maximum pressure differential and
injection rate and according to an injection rate profile determined according
to certain embodiments of the present disclosure.
Figure 9 is a graph illustrating data relating to wormhole
10 penetration for a chelating agent injected at the maximum pressure
differential and injection rate, at 2 barrels per minute, at 8 barrels per
minute, and according to an injection rate profile determined according to
certain embodiments of the present disclosure.
Figure 10 is a graph illustrating data relating to total skin
15 over time for a chelating agent injected at maximum pressure differential
and injection rate according to certain embodiments of the present
disclosure.
Figure 11 is a graph illustrating data relating to total skin
over time for a chelating agent injected according to an injection rate profile
20 determined according to certain embodiments of the present disclosure.
Figure 12 is a graph illustrating data relating to wormhole
penetration for a chelating agent injected at the maximum pressure
differential and injection rate, at 2 barrels per minute, and according to an
injection rate profile determined according to certain embodiments of the
25 present disclosure.
While embodiments of this disclosure have been depicted,
such embodiments do not imply a limitation on the disclosure, and no such
limitation should be inferred. The subject matter disclosed is capable of
considerable modification, alteration, and equivalents in form and function,
30 as will occur to those skilled in the pertinent art and having the benefit of
this disclosure. The depicted and described embodiments of this disclosure
are examples only, and not exhaustive of the scope of the disclosure.
DESCRIPTION OF INVENTION W.R.T. DRAWINGS
E L K I 8 - 9 - 0 4 - 2 Q - I 5 1 5 - #5
Illustrative embodiments of the present disclosure are
described in detail herein. In the interest of clarity, not all features of an
actual implementation may be described in this specification. It will of
course be appreciated that in the development of any such actual
5 embodiment, numerous implementation-specific decisions may be made to
achieve the specific implementation goals, which may vary from one
implementation to another. Moreover, it will be appreciated that such a
development effort might be complex and time-consuming, but would
nevertheless be a routine undertaking for those of ordinary skill in the art
10 having the benefit of the present disclosure.
As used herein, "volume fraction" refers to a fraction of the
total volume of a fluid used in a subterranean formation operation. Use of
this term does not imply any particular number of volume fractions. For
example, in certain embodiments, there could be one volume fraction, ten
15 volume fractions, one hundred volume fractions, or any other suitable
number of fractions. Volume fractions may make up equal portions of the
volume or nonequal portions of the volume. Use of this term is directed to
theoretical fractions of the fluid volume, and does not necessarily imply any
physical division.
20 The present disclosure relates to methods for use in
subterranean formations, and more particularly, methods for determining
acidizing fluid injection rates for stimulation of subterranean formations.
More specifically, the present disclosure provides methods
comprising: selecting a first injection rate for injecting an acidizing fluid
25 into a subterranean formation; calculating a first objective flinction based on
the first injection rate; selecting a second injection rate for injecting the
acidizing fluid into the subterranean formation; calculating a second
objective function based on the second injection rate; comparing the second
objective function with the first objective function to determine whether the
30 second objective function is indicative of more effective stimulation, less
effective stimulation or the same stimulation as the first objective function;
if the second objective function is indicative of more effective stimulation
than the first objective function, then comparing the second objective
function to a third objective function calculated based on a third injection
rate; and if the second objective function is indicative of the same
stimulation or less effective stimulation than the first objective function,
then selecting a design rate for injecting the acidizing fluid into the
5 subterranean formation based on the first injection rate. In certain
embodiments, calculating objective functions comprises determining a
wellbore pressure and a fluid distribution. In certain embodiments, the
present disclosure also provides methods for stimulating a subterranean
formation that comprise injecting an acidizing fluid into the subterranean
10 formation at an injection rate calculated based on the methods described
herein.
In certain embodiments, if the third objective function is
indicative of more effective stimulation than the second objective function,
the methods of the present disclosure further comprise: repeating the steps
15 of selecting an injection rate, calculating an objective function, and
comparing the objective functions for additional injection rates.
In some embodiments, the selecting, calculating, and
comparing steps are performed for each of a plurality of volume fractions to
determine a design rate profile. In some embodiments, the method further
20 comprises injecting the acidizing fluid into the subterranean formation
according to the design rate profile.
In certain embodiments, the present disclosure provides
methods comprising: selecting one or more preliminary indicators;
determining one or more numeric values for the preliminary indicator for an
25 acidizing fluid and a subterranean formation; comparing the one or more
numeric values for the preliminary indicators to one or more preliminary
indicator thresholds; determining based on the comparison of the numeric
values for the preliminary indicators and the preliminary indicator
thresholds whether to inject the acidizing fluid according to a maximum
30 pressure differential and injection rate or according to one of a design rate or
a design rate profile; and injecting the acidizing fluid according to the
design rate, design rate profile, or the maximum pressure differential and
injection rate.
I P O DELH-I• 0 9 - Q 4 - 2 8 1 S 1 5 : . J5
Among the many potential advantages to the methods and
compositions of the present disclosure, only some of which are alluded to
herein, the methods of the present disclosure may provide improved
methods for determining injection rates or rate profiles for acidizing
5 treatments. For example, in certain embodiments, the calculated injection
rates or injection rate profiles of the present disclosure may significantly
increase stimulation as compared to traditionally-determined injection rates.
In some embodiments, the present disclosure may provide methods for
determining injection rates faster and more efficiently then existing
10 methods, saving time and computational power. In some embodiments, the
methods of the present disclosure may be used during injection to provide
updated real-time adjustments to an injection rate or rate profile.
Figure 1 depicts a process flow 100 for determining an
injection rate or rate profile for an acidizing treatment. The use of arrows in
15 Figure 1 is not meant to require any particular order in which the methods of
the present disclosure must be performed, and any order of performing these
steps is contemplated by the present disclosure and claims. In certain
embodiments, the method comprises selecting a first injection rate 101,
calculating a first objective function based on the first injection rate 103,
20 selecting a second injection rate 106, calculating a second objective function
based on the second injection rate 108, and comparing the second objective
function to the first objective function calculated based on the first injection
rate 109. In some embodiments, the process flow 100 may comprise
calculating wellbore pressure and fluid distribution for a first injection rate
25 102 and/or calculating wellbore pressure and fluid distribution for the
second injection rate 107. Generally, any of the steps of process flow 100
may be implemented by a processor of an information handling system
executing software in the form of computer readable instructions stored in a
memory device coupled to the processor.
30 In some embodiments, the process flow 100 may comprise
calculating a higher objective function based on a higher injection rate and
selecting a second injection rate 106 based on the higher objective function.
In certain embodiments, the process flow 100 may comprise calculating a
!PO D E L H I 0 9 - & 4 : - 2 . i i 5 1 5 : ^ 5
lower objective function based on a lower injection rate 104, and selecting a
second injection rate 106 based on the lower objective function. In some
embodiments, calculating the higher and/or lower objective functions 104
may comprise calculating wellbore pressure and fluid distribution in a
5 manner similar to steps 102 and 107. In certain embodiments, the lower
objective function and/or the higher objective function may be compared to
the first objective function 105 in order to select the second injection rate
106.
In some embodiments, the acidizing treatment fluid may be
10 injected at the injection rate determined by the process flow 100. In certain
embodiments, it may be necessary to repeat steps 106-110 to determine the
injection rate. In certain embodiments, the total volume of the acidizing
fluid may be divided into finite volume fractions. In some embodiments,
the total volume is divided into equal volume fractions. In certain
15 embodiments, this process 100 can be performed for each volume fraction to
determine a design rate profile, which is simply a combination or series of
rates at which the fluid is injected at step 111. In certain embodiments, the
acidizing treatment fluid may be injected into a wellbore or subterranean
formation according to the design rate profile.
20 Any injection rate may be selected as the first injection rate
101. For example, in certain embodiments, the highest allowable injection
rate can be used as the first injection rate. In some embodiments, the lowest
allowable rate may be used as the first injection rate. In certain
embodiments, the first injection rate may be between the highest allowable
25 injection rate and the lowest allowable injection rate. In certain
embodiments, the highest or lowest allowable rate may depend on the
constraints of the system, fluids, and/or equipment. If step 101 is carried
out for a subsequent volume fraction, the previous volume fraction injection
rate may be selected 101 as the first injection rate. The highest allowable
30 injection rate may be decreased 106 to determine the second injection rate.
In some embodiments, the injection rate may be increased and decreased to
determine the second injection rate 106 within the constraints of the system.
IP O • DE-L-H' X Q-9-- O^4- 2 0-1 S 1 S '•_ 3 S
In certain embodiments, the wellbore pressure and fluid
distribution in the reservoir may be calculated 102. In certain embodiments,
a numerical model may be used to calculate fluid distribution and wellbore
pressure. For example, in certain embodiments, a pseudo-steady-state
5 model may be used to calculate the wellbore pressure and fluid distribution
in the reservoir. For such a model, at each injection rate, the pressure and
the flow rates both along the wellbore and into the formation are calculated
at discrete points along the wellbore, subject to specified pressure and flow
boundary conditions. Wellbore pressure depends on the flow rate along the
10 wellbore, the hydrostatic head of the acidizing fluid, the wellbore
configuration and completion details, and the leakoff rate into the formation.
In some embodiments, the pressure drop along the wellbore at a point z due
to a flow rate along the wellbore q is given by Equation (1):
(1) d-^=F(q)+ pgcosO
15 where pw is wellbore pressure, F is the sum of the frictional and inertial
pressure drops, and pgcosd is hydrostatic head of a fluid of density p.
Frictional pressure drop depends on wellbore geometry, fluid rheology, and
the flow regime, and can be written in terms of experimentally or
theoretically derived expressions.
20 Calculating flow distribution requires calculating the
pressure drop in the formation between the reservoir and the wellbore. The
pressure gradient in the formation depends on the flow rate into the
formation, the formation properties, the fluid properties, and the radial
position from the wellbore. In certain embodiments, to calculate the
25 pressure drop between the reservoir and the wellbore, the formation is
divided radially into different regions, each having constant formation and
fluid properties. In certain embodiments, the formation has regions of
varying permeability. In some embodiments, such regions can be
determined from the calculated position of the fluid fronts and the initial
30 permeability profile.
For a given injection rate (flow rate), pressure drop may be
determined for each region using the region's characteristic permeability
together with Darcy's law for a Newtonian fluid, a modified form of Darcy's
law for power-law fluids, or a line-source pressure distribution for the
compressible reservoir fluids.
The difference between the wellbore pressure and the
5 average reservoir pressure is given by the sum of all the individual pressure
drops for these regions, which for a flow rate q along the wellbore is given
by Equation (2):
(2) pw(z) - PcoOO = -a{z) di + P(y.) ( g ) " +
10 where (-dq/dz) is the corresponding flow rate into the formation at the point
z, the terms a{z) and /?(z) are due to the instantaneous resistance to flow of
the displaced fluid and the injected fluid, respectively, and the term x(z)
includes all terms due to the compression history of the displaced fluid.
Flow distribution is determined at each injection rate by solving Equations
15 (1) and (2) for pw(z) and q(z) subject to pressure and flow-rate boundary
conditions.
Referring back to Figure 1, in some embodiments, an
objective function 103 is calculated based on the first injection rate. In
certain embodiments, an objective function may be any mathematical
20 function indicative of an objective of the treatment. Examples of objective
functions that may be suitable for some embodiments of the present
disclosure include, but are not limited to a total interval skin function, a total
wellbore skin function, a individual layer skin function, a wormhole
penetration function, a cumulative wormhole penetration function, a
25 function for fluid placement in a layer, and any combination thereof. For
example, in some embodiments, the objective may be minimum total
interval skin, minimum total wellbore skin, minimum individual layer skin,
maximum wormhole penetration, cumulative wormhole penetration,
maximum fluid placement in a layer, reaching a particular value of total
30 interval skin individual layer skin, any other suitable objective, or any
combination thereof. In certain embodiments, the objective function may
depend on wellbore pressure, fluid distribution, and the injection rate.
As used herein, "skin" is a dimensionless factor calculated to
determine the production efficiency of a well by comparing actual
conditions with theoretical or ideal conditions. A positive skin value
indicates some damage or influences that are impairing well productivity. A
5 negative skin value indicates enhanced productivity, typically resulting from
stimulation. As used herein, the term "layer" does not imply or require a
region of any particular shape, length, thickness, and/or continuity.
Consistent with the present disclosure, a layer may comprise a single
contiguous region or shape.
10 In certain embodiments, a second injection rate is selected
106. The second injection rate may be any injection rate other than the first
injection rate. In some embodiments, the second injection rate may be
selected by increasing or decreasing the first injection rate. For example, in
some embodiments, the first injection rate is the maximum allowable
15 injection rate and the second injection rate is less than the maximum
allowable injection rate. In some embodiments, the first injection rate may
be the lowest allowable injection rate and the second injection rate is greater
than the lowest allowable injection rate.
In certain embodiments, steps 104 and 105 are performed to
20 determine whether to increase or decrease the first injection rate to select a
second injection rate 106. In certain embodiments, a higher objective
function is calculated based on an injection rate higher than the first
injection rate 104. In certain embodiments, a lower objective function is
calculated based on an injection rate lower than the first injection rate 104.
25 In certain embodiments, the higher and/or lower objective functions are
calculated 104 in a similar manner as the first objective function 103. In
some embodiments, calculating the objective functions 104 may comprise
calculating wellbore pressure and fluid distribution in the reservoir (not
shown) in a manner similar to step 102. In some embodiments, the higher
30 and/or lower objective functions are compared to the first objective function
105. In certain embodiments, the higher and/or lower objective functions
may be compared to each other (not shown). In certain embodiments the
second injection rate is selected 106 based on the comparison of the
I P O • D E L H I 8: 9 - B 4— 2 6 1 5 1 5 : , ^ 5
objective functions. For example, if the lower objective function is
indicative of more effective stimulation than the first objective function,
then the second injection rate may be selected by decreasing the first
injection rate or if the higher objective function is indicative of more
5 effective stimulation than the first objective function, then second injection
rate may be selected by increasing the first injection rate.
In some embodiments, the wellbore pressure and fluid
distribution in the reservoir is calculated for the second injection rate 107 in
the same manner as it was calculated for the first injection rate in step 102.
10 In certain embodiments, the second objective function is
calculated based on the second injection rate 108. In certain embodiments,
the second objective function is compared to the first objective function
109. In certain embodiments, the objective functions are compared 109 to
determine whether the second objective function is indicative of more
15 effective stimulation of the treatment interval. In certain embodiments,
more effective stimulation of the treatment interval may be indicated by
lower total interval skin, lower individual layer skin, greater wormhole
penetration, improved fluid distribution, any other metric that indicates
more effective stimulation, or any other suitable metric.
20 In certain embodiments, if the second objective function is
indicative of more effective stimulation than the first objective function,
steps 106-109 may be repeated for a third injection rate. The third injection
rate may be selected in the same manner as step 106, and a third objective
function may be calculated (similar to step 108) and compared to the second
25 objective function (similar to 109). In certain embodiments, steps 106-109
may be repeated for additional injection rates until an objective function is
indicative of the same stimulation or less effective stimulation 111.
For example, the objective function may be minimum total
skin for the treatment interval. In that example, if the total skin of the
30 treatment interval for the second injection rate is lower than the total skin
for the first injection rate, then the total skin of the treatment interval for the
second injection rate may be indicative of more effective stimulation of the
treatment interval. In certain embodiments, a third injection rate would be
: PO D E L H I B - 9 - - Q 4 - 2 Q - 1 5 1 5 ^ 35
selected, the total skin of the treatment interval for the third injection rate
would be calculated, and the total skin of the treatment interval for the
second injection rate and third injection rate would be compared. In some
embodiments, additional injection rates may be selected and their
5 corresponding total skin values may be compared until the total skin of
treatment interval for an injection rate is indicative of the same stimulation
or less effective stimulation than the total skin of the treatment interval for
the prior injection rate.
In certain embodiments, if the total skin of the treatment
10 interval for the second injection rate is higher than the total skin of the first
injection rate, then the total skin of the treatment interval for the second
injection rate may be indicative of the same stimulation or less effective
stimulation than the total skin of the treatment interval for the first injection
rate. In certain embodiments, a design rate would then be selected for
15 injecting an acidizing fluid into the subterranean formation based on the first
injection rate. In certain embodiments, the design rate would then be used
to inject the treatment fluid into the wellbore.
In certain embodiments, if the second objective function is
indicative of the same stimulation or less effective stimulation than the first
20 objective function, then the first injection rate may be used as the design rate
for the first volume fraction. In some embodiments, a single injection rate
or design rate may be used for the entire fluid volume. In certain
embodiments, the process 100 may be performed for the other volume
fractions to determine an design rate profile. In certain embodiments, steps
25 104-105 may also be repeated for other volume fractions. In some
embodiments, the first injection rate for a subsequent volume fraction may
be the design rate of the previous volume fraction. In certain embodiments,
an acidizing fluid may be injected into a subterranean formation according
to the design or design rate profile determined by the process 100.
30 In certain embodiments, fluids may be injected according to
a combination of the design rate, design rate profile, and/or the MAPDIR
during an acidizing treatment. In some embodiments, an acidizing fluid
may be injected according to the MAPDIR for some volume steps and
IPO DEL,H-X O9- - ©4-- 2 B-I 5 I 5- J,jf 5
according to an injection rate determined according to process 100 for other
volume steps. In certain embodiments, a diverting fluid may be injected
according to the MAPDIR and an acidizing fluid may be injected according
to a design rate or a design rate profile.
5 Certain embodiments of the methods and compositions
disclosed herein may directly or indirectly affect one or more components or
pieces of equipment associated with the preparation, delivery, recapture,
recycling, reuse, and/or disposal of the disclosed compositions. For
example, with reference to Figure 2, the disclosed methods and
10 compositions may directly or indirectly affect one or more components or
pieces of equipment associated with an example of a well and treatment
system, according to one or more embodiments. Referring now to Figure 2,
a well 260 is shown during an operation according to certain embodiments
of the present disclosure in a portion of a subterranean formation of interest
15 210 surrounding a wellbore 220. The subterranean formation of interest 210
may comprise acid-soluble components. The subterranean formation may
be a carbonate formation, sandstone formation, mixed carbonate-sandstone
formation, or any other subterranean formation suitable for an acidizing
treatment. The wellbore 220 extends from the surface 230 and through a
20 portion of the subterranean formation 210 surrounding the horizontal
portion of the wellbore. Although shown as vertical deviating to horizontal,
the wellbore 220 may include horizontal, vertical, slant, curved, and other
types of wellbore geometries and orientations, and the treatment may be
applied to a subterranean zone surrounding any portion of the wellbore. The
25 wellbore 220 can include a casing 240 that is cemented or otherwise secured
to the wellbore wall. The wellbore 220 can be uncased or include uncased
sections. Perforations can be formed in the casing 240 to allow fluids
and/or other materials to flow into the subterranean formation 210. In cased
wells, perforations can be formed using shape charges, a perforating gun,
30 hydro-jetting and/or other tools.
The well is shown with a work string 270 depending from the
surface 230 into the wellbore 220. A pump and blender system 250 is
coupled to the work string 270 to pump the acidizing fluid 200 into the
wellbore 220. The working string 270 may include coiled tubing, jointed
pipe, and/or other structures that allow fluid to flow into the wellbore 220.
The working string 270 can include flow control devices, bypass valves,
ports, and or other tools or well devices that control a flow of'fluid from the
5 interior of the working string 270 into the subterranean zone 210. For
example, the working string 270 may include ports adjacent the wellbore
wall to communicate the acidizing fluid 200 directly into the subterranean
formation 210, and/or the working string 270 may include ports that are
spaced apart from the wellbore wall to communicate the acidizing fluid 200
10 into an annulus in the wellbore 220 between the working string 270 and the
wellbore wall.
The working string 270 and/or the wellbore 220 may include
one or more sets of packers 280 that seal the annulus between the working
string 270 and wellbore 220 and/or a downhole portion of the wellbore 220
15 to define an interval of the wellbore 220 into which particulate materials
and/or treatment fluids will be pumped.
As shown, the wellbore 220 penetrates a portion 210 of the
subterranean formation, which may include a hydrocarbon-bearing
reservoir. In some cases, an acidizing fluid 200 may be pumped through the
20 working string 270 and into the portion 210 of the formation. In some
embodiments, the acidizing fluid 200 may create wormholes 295 in the
portion 210 of the subterranean formation.
In some embodiments, the injection of the acidizing fluid 200
may be monitored at the well site. In some embodiments, wellbore
25 conditions may be monitored during injection. In certain embodiments,
monitored wellbore conditions may be used to determine updated injection
rates with process 100 shown in Figure 1. Examples of wellbore conditions
that may be suitable for use in the methods of the present disclosure include,
but are not limited to temperature, pressure, skin, fluid distribution, flow
30 rate, pH, any physical or chemical property of the formation or formation
fluids, and any combination thereof. For example, in certain embodiments,
the injection rate could be updated with the methods of the present
disclosure during injection using conditions such as fluid distribution and
wellbore pressure.
In some embodiments, wellbore conditions of the present
disclosure could be measured by sensors. In certain embodiments, sensors
5 could be located in the wellbore. For purposes of this disclosure, the term
"sensors" is understood to comprise sources (to emit and/or transmit energy
and/or signals), receivers (to receive and/or detect energy and/or signals),
and transducers (to operate as a source and/or receiver). In certain
embodiments, information from the sensors may be fed into a system or tool
10 that can determine an injection rate or rate profile according to the methods
of the present disclosure.
In certain embodiments, acidizing fluids for use with the
methods of the present disclosure may be selected based on the type of
subterranean formation, desired stimulation, wellbore conditions, and other
15 factors. In certain embodiments, acidizing fluids may comprise acids,
chelating agents, additives, and the like, and any combination thereof.
Examples of acids that may be suitable for use in the methods of the present
disclosure include, but are not limited to hydrochloric acid ("HO"),
hydrofluoric acid, acetic acid, formic acid, sulfamic acid, chloracetic acid,
20 carboxylic acids, organic acids, any other acid capable of dissolving the
subterranean formation, and any combination thereof. Examples of
chelating agents that may be suitable for use in the methods of the present
disclosure include, but are not limited to ethylenediaminetetraacetic acid
("EDTA"), glutamic acid N,N-diacetic acid ("GLDA"), and the like, and
25 any combination thereof.
The acidizing fluids of the methods of the present disclosure
may comprise aqueous fluids, non-aqueous fluids, emulsified fluids, and
any combinations thereof. Any pairs or combinations of substantially
immiscible base fluids may be used in the methods and systems described
30 herein, including, but not limited to "water-based" fluids and "oil-based
fluids."
Aqueous or water-based fluids that may be suitable for use in
the methods and systems of the present disclosure may comprise water from
any source. Such aqueous fluids may comprise fresh water, salt water (e.g.,
water containing one or more salts dissolved therein), brine (e.g., saturated
salt water), seawater, or any combination thereof. In most embodiments of
the present disclosure, the aqueous fluids comprise one or more ionic
5 species, such as those formed by salts dissolved in water. For example,
seawater and/or produced water may comprise a variety of divalent cationic
species dissolved therein. In certain embodiments, the density of the
aqueous fluid can be adjusted, among other purposes, to provide additional
particulate transport and suspension in the compositions of the present
10 disclosure. In certain embodiments, the pH of the aqueous fluid may be
adjusted (e.g., by a buffer or other pH adjusting agent) to a specific level,
which may depend on, among other factors, the types of viscosifying agents',
acids, and other additives included in the fluid. One of ordinary skill in the
art, with the benefit of this disclosure, will recognize when such density
15 and/or pH adjustments are appropriate.
Examples of non-aqueous fluids (e.g., oil-based fluids) that
may be suitable for use in the methods of the present disclosure include, but
are not limited to oils, hydrocarbons, organic liquids, and the like. In certain
embodiments, such fluids may comprise mineral oil based fluids or mineral
20 oil/paraffin based fluids. In certain embodiments, the acidizing fluid may
comprise an invert emulsion fluid, which comprises an oil or oleaginous
fluid as the external or continuous phase and an aqueous or hydrophilic fluid
as the internal phase. In certain embodiments, an oil-based invert emulsionbased
treatment fluid may commonly comprise between about 50:50 to
25 about 95:5 by volume oil phase to water phase. In certain embodiments, the
invert emulsion fluid employs a natural oil (e.g., diesel oil or mineral oil) or
a synthetic base as the oil or oleaginous phase, and an acid or chelating
agent (with or without additives such as gelling agents, crosslinkers,
corrosion inhibitors, etc.) as the non-oleaginous phase.
30 Examples of additives that may be suitable for use in the
methods of the present disclosure include, but are not limited to surfactants,
additional acids, fluid loss control additives, gas, nitrogen, carbon dioxide,
foamers, corrosion inhibitors, corrosion inhibitor intensifies, scale
.; p O D E L H-I 8 B - B 4 - 2 0- I S 1 5 ^3 5
inhibitors, scale removing agents, catalysts, clay control agents, biocides,
friction reducers, antifoam agents, bridging agents, fiocculants, H2S
scavengers, CO2 scavengers, oxygen scavengers, lubricants, viscosifiers,
gelling agents, breakers, weighting agents, relative permeability modifiers,
5 wetting agents, coating enhancement agents, filter cake removal agents,
antifreeze agents (e.g., ethylene glycol), diverting agents, particulates, and
the like.
In certain embodiments, diverters may be used, among other
reasons, to divert or distribute the acidizing fluids of the present disclosure.
10 Diverters may be mechanical devices or chemical diverting agents and may
used to ensure uniform injection over the area to be treated. In some
embodiments, diverting agents known as chemical diverters function by
creating a temporary blocking effect that is safely cleaned up following the
treatment, enabling enhanced productivity throughout the treated interval.
15 In certain embodiments, experimentation may provide an
indication of whether an injection rate or rate profile determined by the
methods according to certain embodiments of the present disclosure would
significantly affect stimulation for given conditions. In some embodiments,
preliminary indicators may be indicative of whether an injection rate or rate
20 profile determined by methods according to certain embodiments of the
present disclosure would provide more effective stimulation than MAPDIR.
In certain embodiments, preliminary indicators may be variables or
functions. In certain embodiments, preliminary indicators are indicative of
more effective stimulation if the preliminary indicators for given conditions
25 exceed a preliminary indicator thresholds. Examples of preliminary
indicators that may be suitable for some embodiments of the present
disclosure include, but are not limited to a slope of a breakthrough curve, a
minimum pore volume to breakthrough, a power of interstitial velocity in an
equation for pore volume to breakthrough as a function of interstitial
30 velocity, or any combination thereof.
In certain embodiments, numeric values for the preliminary
indicators may be determined based on core flood experiments. For
example, in certain embodiments, core flood experiments may be performed
D E L H I e @ - B 4 - - 2 e i 5 I. 5 ;j g3 5
with an acidizing fluid and a core sample. Core flood experiments may
comprise injecting the acidizing fluid into a sample of rock. The sample of
rock may be a cylindrical rock core. In some embodiments, such
experiments allow measurement of pressure drop, permeability, relative
5 permeability, saturation change, formation damage caused by the fluid
injection, time required to form wormholes of a particular length, pore
volume to breakthrough, or interactions between the fluid and the rock. In
certain embodiments, the core material may come from an oil reservoir or
outcrop rock. The fluid in place at the start of the test is typically either a
10 simulated formation brine, oil (either crude oil or refined oil), or a
combination of brine and oil. Conditions of the core flood experiment may
be ambient temperature, low confining pressure, or high temperature and
pressure of a subject reservoir. Pressures and flow rates at both ends of the
core are measured, and the core can also be investigated using other
15 measurements such as nuclear magnetic resonance during the test. A core
flood experiment helps evaluate the effect of injecting fluids specially
designed to improve or enhance oil recovery.
As used herein, "pore volume" is the volume of fluid that
fills the portion of the subterranean formation to be treated or the volume of
20 fluid that can be contained in the core sample used in the core flood
experiment. Pore volumes to breakthrough ("PVBT") is a dimensionless
value that represents the amount of acid needed to propagate the wormholes
from the inlet of the core sample to the outlet. PVBT can be calculated by
dividing the volume of acid needed to propagate the wormholes from the
25 inlet to the outlet by the original pore volume of the core. For given
conditions (e.g., temperature, flow rate, acidizing fluid, formation type), a
lower PVBT indicates more efficient stimulation. By running core flood
experiments at different flow rates, measuring the breakthrough volume, and
calculating PVBT, an empirically-based breakthrough curve of PVBT
30 versus flow rate or interstitial velocity can be determined. Figures 3A and
3B are graphs of core flood data and breakthrough curves of PVBT versus
flow rate 3A and PVBT versus interstitial velocity 3B for EDTA at 71.6 °F,
EDTA at 176 °F, GLDA at 180 °F, and 7% HC1 at 158 °F.
I P O DELHI B:9 - 8 is porosity. {PVBT)minmum can be determined
from the minimum of the breakthrough curve, or by calculating it from
(Vi)minimum ra^using Equations (5)and (6) below. With reference to Figures
3A and 3B, the (PVBT)mMmum is the value of the fitted EDTA, GLDA, and
25 HC1 breakthrough curves at their minimums 301A and 301B. {Vi)minimum
ra,emay also be calculated by Equation (5):
\P) • K^1)minimum rate ~ ~^jj; l-,n/ '
where MF is the morphology factor and WB is the wormhole beta factor. Wg
and MF can be taken from literature or determined empirically with a linear
30 core flow test. MF depends on changes in rock structure through
permeability and porosity.
In some embodiments, the magnitude of the {PVBT)minimum
may be a preliminary indicator. In certain embodiments, for example, a
preliminary indicator threshold for (PVBT)minimum may be 0.75. In some
embodiments, if {PVBT)minimum is greater than 0.75, a calculated injection
5 rate or rate profile may provide more effective stimulation than MAPDIR.
In certain embodiments, the power of interstitial velocity in
an equation for PVBT as a function of interstitial velocity may be a
preliminary indicator. In certain embodiments, the preliminary indicator
threshold may be 0.1 or 1/3. In certain embodiments, if the power of
10 interstitial velocity in an equation for PVBT as a function of interstitial
velocity is greater than 0.1, then a calculated injection rale or rate profile
may provide more effective stimulation than MAPDIR.
In certain embodiments, a breakthrough curve may be fitted
to PVBT versus flow rate data from core flood experiments. In certain
15 embodiments, for example, Equation (6) may be fitted to the data:
(6) PVBT = 2^2 v-
Weff*MF*{l-e-wBiVi*MF) /2)2
where Vi is the interstitial velocity of the fluid in a core sample used in liner
core flood test or interstitial velocity in radial flow, WQ is the wormhole beta
factor, Wejfls the wormhole efficiency factor, and x is a fitting variable. We/f
20 WB,and MF can be determined empirically from a core flood experiment. In
certain embodiments, the other exponents of Equation (6) (x, 3/2, and 2)
may also be changed to fit the breakthrough curve to experimental data. In
certain embodiments, Equation (6) may be used to generate breakthroughs
curve like those in Figures 3A and 3B.
25 In certain embodiments, x is a preliminary indicator, and a
preliminary indicator threshold may be 0.1 or 1/3. In certain embodiments,
for example, if the fitting variable x is greater than 0.1, the injection rate or
rate profile determined by the methods of the present disclosure would
provide more effective stimulation than MAPDIR.
30 In certain embodiments, determining whether an injection
rate or rate profile determined by the methods of the present disclosure
would significantly affect stimulation may comprise identifying
; p O D E L HI • O 9 ~ 0 : 4 - 2 0 1 5 1 5 ^ 3 5
{PVBT)mMmum, (PVBT)higher rate, (Vi)minimum rale, and (Vi)higher raie- In some
embodiments, identifying (PVBT)minimum, (PVBT)higher rme, (Vi)mininmm rale, and
(Vi)higherratemay comprise estimating (Vi)mi„imum rale from Equation (5) or any
other method and estimating {PVBT)mi„imum, (PVBT)highermle, and (Vi)h
igher rate
5 from Equation (6) or any other function used to relate PVBT and Vi directly
or indirectly. In certain embodiments, determining whether an injection rate
or rate profile determined by the methods of the present disclosure would
significantly affect stimulation may comprise calculating a preliminary
indicator value based on these variables and comparing the preliminary
10 indicator value to the preliminary indicator threshold.
In certain embodiments, wormhole penetration depth may be
determined based on wormhole velocity, Vwh. In some embodiments, Vwh
may be related to PVBT and Vi by Equation (7):
(7) PVBT = — .
v ' Vwh.
15 Figure 4 is a block diagram showing an example information
handling system 400, according to aspects of the present disclosure.
Information handling system 400 may be used, for example, to carry out one
or more steps of the process flow of Figure 1, calculate or lit Equations (1)-
(7), and/or monitor and analyze core flood experiments. The information
20 handling system 400 may comprise a processor or CPU 401 that is
communicatively coupled to a memory controller hub or north bridge 402.
Memory controller hub 402 may include a memory controller for directing
information to or from various system memory components within the
information handling system, such as RAM 403, storage element 406, and
25 hard drive 407. The memory controller hub 402 may be coupled to RAM
403 and a graphics processing unit 404. Memory controller hub 402 may
also be coupled to an I/O controller hub or south bridge 405. I/O hub 405 is
coupled to storage elements of the computer system, including a storage
element 406, which may comprise a flash ROM that includes a basic
30 input/output system (BIOS) of the computer system. I/O hub 405 is also
coupled to the hard drive 407 of the computer system. I/O hub 405 may
also be coupled to a Super I/O chip 408, which is itself coupled to several of
I P O - D E L H I 8 i - i 4 - 2 8 1 5 1 5 ' : 3-5
the I/O ports of the computer system, including keyboard 409 and mouse
710. The information handling system 400 further may be communicably
coupled to one or more elements of a drilling system though the chip 408.
For purposes of this disclosure, an information handling
5 system may include any instrumentality or aggregate of instrumentalities
operable to compute, classify, process, transmit, receive, retrieve, originate,
switch, store, display, manifest, detect, record, reproduce, handle, or utilize
any form of information, intelligence, or data for business, scientific,
control, or other purposes. For example, an information handling system
10 may be a personal computer, a network storage device, or any other suitable
device and may vary in size, shape, performance, functionality, and price.
The information handling system may include random access
memory (RAM), one or more processing resources such as a central
processing unit (CPU) or hardware or software control logic, ROM, and/or
15 other types of nonvolatile memory. Additional components of the
information handling system may include one or more disk drives, one or
more network ports for communication with external devices as well as
various input and output (I/O) devices, such as a keyboard, a mouse, and a
video display. The information handling system may also include one or
20 more buses operable to transmit communications between the various
hardware components. It may also include one or more interface units
capable of transmitting one or more signals to a controller, actuator, or like
device.
For the purposes of this disclosure, computer-readable media
25 may include any instrumentality or aggregation of instrumentalities that may
retain data and/or instructions for a period of time. Computer-readable
media may include, for example, without limitation, storage media such as a
direct access storage device (e.g., a hard disk drive or floppy disk drive), a
sequential access storage device (e.g., a tape disk drive), compact disk, CD-
30 ROM, DVD, RAM, ROM, electrically erasable programmable read-only
memory (EEPROM), and/or flash memory; as well as communications
media such wires, optical fibers, microwaves, radio waves, and other
XF O D-E L HI 8: 9 - 8 4 - 2 & 1 5 1 5 ^ 3 S
electromagnetic and/or optical carriers; and/or any combination of the
foregoing.
To facilitate a better understanding of the present disclosure,
the following examples of certain aspects of preferred embodiments are
5 given. The following examples are not the only examples that could be
given according to the present disclosure and are not intended to limit the
scope of the disclosure or claims.
EXAMPLES
The acidizing treatment simulations of Examples 1 and 2
10 were performed for hydrochloric acid and a chelating agent according to the
pumping schedule in Table 1.
EXAMPLE 1
15 In this example, a simulation was performed for a chelating
agent injected into a sample of a subterranean formation spanning three
reservoir layers of different permeability according to the MAPDIR and
according to an injection rate profile determined by methods according to
certain embodiments of the present disclosure. Figure 5 shows the total skin
20 profile for each injection rate. Table 2 below lists the final total skin for
each injection rate. As shown in Figure 5 and Table 2, the final total skin
for the calculated rate profile was lower than the final total skin for the
MAPDIR.
EXAMPLE 2
25 In this example, a simulation was performed for hydrochloric
acid injected into a sample of a subterranean formation spanning three
reservoir layers of different permeability according to the MAPDIR and
according to an injection rate profile determined by methods according to
certain embodiments of the present disclosure. Figure 6 shows that the total
skin profile for each injection rate. As shown in Figure 6 and Table 2, the
final total skin for the calculated rate profile was lower than the final total
skin for the MAPDIR.
In certain embodiments, the wormhole penetration may be
calculated from PVBT and Vi according to Equation 7. Figure 7 shows the
final wormhole penetration for the calculated injection rate profile was
deeper than final wormhole penetration for injection at MAPDIR at most of
the measured depths.
The acidizing treatment simulations of Examples 3 and 4 were
performed according to the pumping schedule in Table 3.
Table 3
EXAMPLE 3
In this example, a simulation was performed for hydrochloric acid
injected into a sample of a subterranean formation spanning one reservoir
layer according to the MAPDIR and an injection rate profile determined by
20 methods according to certain embodiments of the present disclosure. Figure
8 shows the total skin profile for each injection rate. Table 4 lists the final
total skin for each injection rate. As shown in Figure 8 and Table 4, the
final total skin for the calculated injection rate profile was lower than the
final total skin for MAPDIR.
5 Figure 9 shows the final wormhole penetration for the
calculated rate profile was deeper than final wormhole penetration for
MAPDIR and constant rates at all measured depths.
10 EXAMPLE 4
In this example, a simulation was performed for a chelating agent
injected into a sample of a subterranean formation spanning one reservoir
layer according to the MAPDIR and an injection rate profile determined by
methods according to certain embodiments of the present disclosure. Figure
15 10 shows the total skin profile for the MAPDIR. Figure 11 shows the total
skin profile for the calculated injection rate profile. Table 5 lists the final
total skin for each injection rate. As shown in Figure 10, 1 1 and Table 5,
the final total skin for the calculated injection rate profile was lower than the
final total skin for MAPDIR.
20 Figure 12 shows the final wormhole penetration for the
calculated rate profile was deeper than final wormhole penetration for
MAPDIR and a constant rate at all measured depths.
Table 5
An embodiment of the present disclosure is a method
comprising: selecting a first injection rate for injecting an acidizing fluid
into a subterranean formation; calculating a first objective function based on
5 the first injection rate; selecting a second injection rate for injecting the
acidizing fluid into the subterranean formation; calculating a second
objective function based on the second injection rate; comparing the second
objective function with the first objective function to determine whether the
second objective function is indicative of more effective stimulation, less
10 effective stimulation, or the same stimulation as the first objective function;
if the second objective function is indicative of more effective stimulation
than the first objective function, then comparing the second objective
function to a third objective function calculated based on a third injection
rate; and if the second objective function is indicative of the same
15 stimulation or less effective stimulation than the first objective function,
then selecting a design rate for injecting the acidizing fluid into the
subterranean formation based on the first injection rate.
An embodiment of the present disclosure is a method
comprising: selecting a first injection rate for injecting an acidizing fluid
20 into a subterranean formation for each of a plurality of volume fractions and
calculating a first objective function based on the first injection rate;
selecting a second injection rate for injecting the acidizing fluid into the
subterranean formation for each of the plurality of volume fractions and
calculating a second objective function based on the second injection rate;
25 comparing the second objective function with the first objective function for
each of the plurality of volume fractions to determine whether the second
objective function is indicative of more effective stimulation, less effective
stimulation, or the same stimulation as the first objective function; if the
second objective function is indicative of more effective stimulation than the
30 first objective function, then comparing the second objective function to a
third objective function calculated based on a third injection rate for each of
the plurality of volume fractions; and if the second objective function is
indicative of the same stimulation or less effective stimulation than the first
X F O D E- L H I 0 9 - © 4- - 2:0-1 5 I 5 ] 3 6
objective function, selecting a design rate for each of the plurality of volume
fractions for injecting the acidizing fluid into the subterranean formation
based on the first injection rate for each of the plurality of volume fractions;
determining a design rate profile based on the design rates selected for each
,5 of the plurality of volume fractions.
An embodiment of the present disclosure is a method
comprising: selecting one or more preliminary indicators; determining
one or more numeric values for the preliminary indicators for an acidizing
fluid and a subterranean formation; comparing the one or more numeric
10 values for the preliminary indicators to one or more preliminary indicator
thresholds; determining based on the comparison of the numeric values for
the preliminary indicators and the preliminary indicator thresholds whether
to inject the acidizing fluid according to a maximum pressure differential
and injection rate or according to one of a design rate or a design rate
15 profile; and injecting the acidizing fluid according to the design rate, design
rate profile, or the maximum pressure differential and injection rate.
An embodiment of the present disclosure is a non-transitory
computer readable medium containing a set of instructions that, when
executed by a processor of an information handling system, cause the
20 processor to select a first injection rate for injecting an acidizing fluid into a
subterranean formation; calculate a first objective function based on the first
injection rate; select a second injection rate for injecting the acidizing fluid
into the subterranean formation; calculate a second objective function based
on the second injection rate; compare the second objective function with the
25 first objective function to determine whether the second objective function
is indicative of more effective stimulation, less effective stimulation, or the
same stimulation as the first objective function; if the second objective
function is indicative of more effective stimulation than the first objective
function, then compare the second objective function to a third objective
30 function calculated based on a third injection rate; and if the second
objective function is indicative of the same stimulation or less effective
stimulation than the first objective function, then select a design rate for
I-P'G D E L H I G 5 - 9 4 - 2 - Q I 5 1 5 : 56
injecting the acidizing fluid into the subterranean formation based on the
first injection rate.
Therefore, the present disclosure is well adapted to attain the
ends and advantages mentioned as well as those that are inherent therein.
5 The particular embodiments disclosed above are illustrative only, as the
present disclosure may be modified and practiced in different but equivalent
manners apparent to those skilled in the art having the benefit of the
teachings herein. While numerous changes may be made by those skilled in
the ail, such changes are encompassed within the spirit of the subject matter
10 defined by the appended claims. Furthermore, no limitations are intended to
the details of construction or design herein shown, other than as described in
the claims below. It is therefore evident that the particular illustrative
embodiments disclosed above may be altered or modified and all such
variations are considered within the scope and spirit of the present
15 disclosure. In particular, every range of values (e.g., "from about a to about
b," or, equivalently, "from approximately a to b," or, equivalently, "from
approximately a-b") disclosed herein is to be understood as referring to the
power set (the set of all subsets) of the respective range of values. The
terms in the claims have their plain, ordinary meaning unless otherwise
20 explicitly and clearly defined by the patentee.

WE CLAIM:
1. A method comprising:
selecting a first injection rate for injecting an acidizing fluid into a
subterranean formation;
5 calculating a first objective function based on the first injection rate;
selecting a second injection rate for injecting the acidizing fluid into
the subterranean formation;
calculating a second objective function based on the second injection
rate;
10 comparing the second objective function with the first objective
function to determine whether the second objective function is indicative of
more effective stimulation, less effective stimulation, or the same
stimulation as the first objective function;
if the second objective function is indicative of more effective
15 stimulation than the first objective function, then comparing the second
objective function to a third objective function calculated based on a third
injection rate; and
if the second objective function is indicative of the same stimulation
or less effective stimulation than the first objective function, then selecting a
20 design rate for injecting the acidizing fluid into the subterranean formation
based on the first injection rate.
2. A method as claimed in claim 1, further comprising injecting the
acidizing fluid into the subterranean formation at the design rate.
3. A method as claimed in claim 2, further comprising monitoring the
25 subterranean formation during the injecting and adjusting the injecting
based on the monitoring.
4. A method as claimed in claim 1, wherein if the third objective
function is indicative of more effective stimulation than the second objective
function, the method further comprises: repeating the steps of selecting an
injection rate, calculating an objective function, and comparing the objective
functions for additional injection rates.
5. A method as claimed in claim 1, wherein calculating objective
5 functions further comprises determining a wellbore pressure and a fluid
distribution.
6. A method as. claimed in claim 1, wherein selecting a second
injection rate comprises:
calculating a higher objective function based on an injection rate
10 higher than the first injection rate; and
selecting a second injection rate based on the higher objective
function.
7. A method of claim 1, wherein selecting a second injection rate
comprises:
15 calculating a lower objective function based on an injection rate
lower than the first injection rate; and
selecting a second injection rate based on the lower objective
function.
8. A method as claimed in claim 1, wherein the objective functions are
20 selected from the group consisting of: a total interval skin function, a total
wellbore skin function, a individual layer skin function, a wormhole
penetration function, a cumulative wormhole penetration function, a
function for fluid placement in a layer, and any combination thereof.
9. A method as claimed in claim 1, wherein one or more of the steps of
25 selecting, calculating, and comparing are performed using an information
handling system.
10. A method comprising:
selecting a first injection rate for injecting an acidizing fluid into a
subterranean formation for each of a plurality of volume Ixactions and
calculating a first objective function based on the first injection rate;
selecting a second injection rate for injecting the acidizing fluid into
5 the subterranean formation for each of the pluralily of volume fractions and
calculating a second objective function based on the second injection rate;
comparing the second objective function with the first objective
function for each of the plurality of volume fractions to determine whether
the second objective function is indicative of more effective stimulation,
10 less effective stimulation, or the same stimulation as the first objective
function;
if the second objective function is indicative of more effective
stimulation than the first objective function, then comparing the second
objective function to a third objective function calculated based on a third
15 injection rate for each of the plurality of volume fractions:
if the second objective function is indicative of the same stimulation
or less effective stimulation than the first objective function, selecting a
design rate for each of the plurality of volume fractions for injecting the
acidizing fluid into the subterranean formation based on the first injection
20 rate for each of the plurality of volume fractions; and
determining a design rate profile based on the design rates selected
for each of the plurality of volume fractions.
11. A method as claimed in claim 10, wherein the method further
comprises: injecting the treatment fluid into the subterranean formation
25 according to the design rate profile.
12. A method as claimed in claim 11, further comprising monitoring the
subterranean formation during the injecting and adjusting the injecting
based on the monitoring.
13. A method as claimed in claim 10, wherein if the third objective
function is indicative of more effective stimulation than the second objective
function for one or more volume fractions, the method further comprises:
repeating the steps of selecting an injection rate, calculating an objective
5 function, and comparing the objective functions for additional injection
rates for each of the one or more volume fractions.
14. A method a3 claimed in claim 10, wherein selecting a second
injection rate comprises:
calculating a higher objective function based on an injection rate
10 higher than the first injection rate; and
selecting a second injection rate based on the higher objective
function.
15. A method as claimed in claim 10, wherein selecting a second
injection rate comprises:
15 calculating a lower objective function based on an injection rate
lower than the first injection rate; and
selecting a second injection rate based on the lower objective
function.
16. A method as claimed in claim 10, wherein calculating at least one of
20 the objective functions comprises determining a wellbore pressure and a
fluid distribution.
17. A method comprising:
selecting one or more preliminary indicators;
determining one or more numeric values for the preliminary
25 indicators for an acidizing fluid and a subterranean formation:
comparing the one or more numeric values for the preliminary
indicators to one or more preliminary indicator thresholds;
X F Q- D E L H I 8 9 - 8- 4 - 2 B1 5 1 5 ' 3- S
- 3 3 -
determining based on the comparison of the numeric values for the
preliminary indicators and the preliminary indicator thresholds whether to
inject the acidizing fluid according to a maximum pressure differential and
injection rate or according to one of a design rate or a design rate profile;
5 and
injecting the acidizing fluid according to the design rate, design rate
profile, or the maximum pressure differential and injection rate.
18. A method as claimed in claim 17, further comprising calculating the
design rate or design rate profile.
10 19. A method as claimed in claim 17, wherein the preliminary indicators
are indicative of whether the design rate or design rate profile would result
in more effective stimulation of the subterranean formation than the
maximum pressure differential and injection rate.
20. A method as claimed in claim 17, wherein the preliminary indicators
15 are selected from the group consisting of: a slope of a breakthrough curve, a
minimum pore volume to breakthrough, a power of interstitial velocity in an
equation for pore volume to breakthrough as a function of interstitial
velocity, or any combination thereof.
21. A method as claimed in claim 20, wherein the one or more
20 preliminary indicator values are selected from the group consisting of: 0.15
for the slope of the breakthrough curve, 0.75 for the minimum pore volume
to breakthrough, and 0.1 for the power of interstitial velocity in an equation
for pore volume to breakthrough as a function of interstitial velocity, or any
combination thereof.
25 22. A method as claimed in claim 17, wherein the step of determining
based on the comparison of the preliminary indicator values and the
preliminary indicator thresholds whether to inject the acidizing fluid
according to a maximum pressure differential and injection rate or according
to a design rate or a design rate profile further comprises calculating the
I P O D E L H I 6 S - S 4 - 2 Q 1 5 1 5 : 38
- 3 4 -
design rate profile if at least one preliminary indicator value exceeds the
corresponding preliminary indicator threshold.
23. A non-transitory computer readable medium containing a set of
instructions that, when executed by a processor of an information handling
5 system, cause the processor to
select a first injection rate for injecting an acidizing fluid into a
subterranean formation;
calculate a first objective function based on the first injection rate;
select a second injection rate for injecting the acidizing fluid into the
10 subterranean formation;
calculate a second objective function based on the second injection
rate;
compare the second objective function with the first objective
function to determine whether the second objective function is indicative of
15 more effective stimulation, less effective stimulation, or the same
stimulation as the first objective function;
if the second objective function is indicative of more effective
stimulation than the first objective function, then compare the second
objective function to a third objective function calculated based on a third
20 injection rate; and
if the second objective function is indicative of the same stimulation
or less effective stimulation than the first objective function, then select a
design rate for injecting the acidizing fluid into the subterranean formation
based on the first injection rate.