BACKGROUND
[0001] In well cementing, such as well construction and remedial cementing, cement
compositions are commonly utilized. Cement slurries may be used in a variety of subterranean
applications. For example, in subterranean well construction, a pipe string (e.g., casing, liners,
expandable tubulars, etc.) may be run into a well bore and cemented in place. The process of
cementing the pipe string in place is commonly referred to as "primary cementing." In a typical
primary cementing method, a cement slurry may be pumped into an annulus between the walls of
the well bore and the exterior surface of the pipe string disposed therein. The cement slurry may
set in the annular space, thereby forming an annular sheath ofhardened, substantially impermeable
cement (i.e., a cement sheath) that may support and position the pipe string in the well bore and
may bond the exterior surface of the pipe string to the subterranean formation. Among other
things, the cement sheath surrounding the pipe string functions to prevent the migration of fluids
in the annulus, as well as protecting the pipe string from corrosion. Cement slurries also may be
used in remedial cementing methods, for example, to seal cracks or holes in pipe strings or cement
sheaths, to seal highly permeable formation zones or fractures, to place a cement plug, and the
like.
[0002] A particular challenge in well cementing is the development of satisfactory
thickening time in a cement slurry within a reasonable time period after placement in the
subterranean formation. Oftentimes several cement slurries with varying additives are tested to
see if they meet the material engineering requirements for a particular well. The process of
selecting the components of the cement slurry are usually done by a best guess approach by
utilizing previous slurries and modifying them until a satisfactory solution is reached. The process
may be time consuming and the resulting slurry may be complex. Furthermore, the cement
components available in any one particular region may vary in slurry from those of another region
thereby further complicating the process of selecting a correct slurry.
BRIEF DESCRIPTION OF THE DRAWINGS
[0003] These drawings illustrate certain aspects of some of the embodiments of the present
disclosure and should not be used to limit or define the disclosure.
[0004] FIG. 1 illustrates a method to design for thickening time.
[0005] FIG. 2 illustrates introduction of a cement slurry into a well bore.
[0006] FIG. 3 is a parity plot for a cement thickening time test.
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DETAILED DESCRIPTION
[0007] The present disclosure may generally relate to cementing methods and systems.
More particularly, embodiments may be directed to designing cement slurries based at least
partially on thickening time model.
[0008] Cement slurries may contain cement, supplementary cementitious additives, inert
materials, and chemical additives. A cement slurry for use in cementing wellbores is typically
mixed at a well bore pad site using cement mixing equipment and pumped into the well bore using
cement pumps. After the cement slurry is mixed, there is a time lag between when the cement is
in a liquid state and when the cement begins to set. As the cement slurry begins to set, the slurry
gradually becomes more viscous until fully set. There may be an upper limit of viscosity beyond
which the cement slurry becomes too viscous to pump. In general, the upper limit of viscosity is
typically defined to be when the fluid has a consistency of greater than 70 Bearden units of
consistency ("Be"). However, there may be other considerations where the cement slurry would
be considered unpumpable and thus a Be value of 30, 50, 70, 100, or any other value may be
selected as being "unpumpable." To determine the consistency or Be value of a cement slurry, an
atmospheric or a pressurized consistometer may be used in accordance with the procedure for
determining cement thickening times set forth in API RP Practice 1 OB-2, Recommended Practice
for Testing Well Cements, First Edition, July 2005. The time to reach the selected Bearden units
of consistency is reported as thickening time. It is often a design criteria for a cement slurry to
have a long enough thickening time such that there is enough time to pump the required volume
of cement into the wellbore while also not having too long of a thickening time where there is
excessive downtime from waiting on the cement to set. The thickening time for a cement slurry
may be a function of pressure, temperature, density of the cement slurry, and composition of the
cement slurry.
[0009] A thickening time model may account for pressure, temperature, density, and
chemical composition of a cement slurry. The thickening time model may include two main
components, the first being effects of water on thickening time and the second being effects of
composition on thickening time. The first component is generally a function of the density of the
cement slurry which may be controlled by varying the amount the amount of water that is added
to a dry cement blend to produce the cement slurry. The second component is generally a function
of the chemical identity of the components that make up the cement slurry and their corresponding
mass fractions in the cement slurry.
[0010] At a given temperature, a thickening time model may include two mam
components, a component that models thickening time of the blend of cementitious components
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along with inerts, and a component that models thickening time of cement additives. Equation 1
is a general model equation for thickening time where TT is the thickening time which is a function
of TTb which is a component that models thickening time of the blend of cementitious
components, and of ITa which is a component that models thickening time of cement additives.
Equation 1
TT = f(TTw TTb)
[0011] A thickening time model of the blend of cementitious components may account for
pressure, temperature, ramp rate, density, and chemical composition of a cement slurry. The
models thickening time of the blend of cementitious components may include two main
components, the first being effects of water on thickening time and the second being effects of
composition on thickening time. The first component is generally a function of the density of the
cement slurry which may be controlled by varying the amount the amount of water that is added
to a dry cement blend to produce the cement slurry. Further the type or source of water may affect
the thickening time as dissolved ions in the water may interact with the cement components and
additives. For example, a cement composition prepared with sea water may be expected to have a
different thickening time than a cement composition prepared with fresh water. The second
component is generally a function of the chemical identity of the components that make up the
cement slurry and their corresponding mass or volume fractions in the cement slurry.
[0012] A relationship between water and thickening time may be expressed as a power
law function as in equations 2 and 3. Equation 2 shows that the thickening time is proportional to
the amount of water used in the preparing of the cement slurrv. In equation 2, water is a mass or
" blend
volume ratio of water to the other components in the cement slurry such as Portland cement,
supplementary cementitious materials and inert materials, and n is a measurement of sensitivity
to change in water of the blend where n may be a constant or a function of the blend materials. In
some instances, n may also be a function of the type of water. To determine n, two cement slurries
at different densities may be mixed and the thickening time may be analyzed using laboratory
methods. Thereafter, equation 2 or 3 may be used to calculate the value of n for the water. Equation
3 shows an alternate form of the relationship between water and thickening time as a function f
comprising a polynomial. Other forms of function f may be log, exponential, power law,
trigonometric, integral, differential, or combinations thereof
(
water)n
TT a blend
3
Equation 2
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Equation 3
(
water (water)
2
)
TT a f blend+ blend + ...
[0013] A relationship between the effects of water on thickening time may be an
exponential relationship as shown in equation 4. While only two forms for the effect of water on
thickening time are described below, the effect of water on thickening time may be expressed in
any suitable manner such as a logarithmic model, integral model, derivative model, or any other
suitable model.
(
water)
TT a e nblena
Equation 4
[0014] A relationship describing effects of composition on thickening time may be a linear
combination of individual contributions from each cement component as shown in equation 5. In
equation 5, xi and x1 are the mass fraction of component i andj, respectively, in the cement blend
and f31b {31i1, f32b etc are model parameters which characterize reactivity of component i and j, or
interaction between component i and j. Components may be any cement components such as
cementitious materials as well as inert materials which do not contribute to cement reactions. For
some components, f3 may be constant, whereas for other components f3 may be depended upon
temperature and pressure, for example. f3 for any component may be experimentally determined.
Equation 5
TT a L/if31i + LiLJ xixJf31iJ + L/i2f32i ...
[0015] An alternate form of a relationship describing effects of composition on thickening
time may be an exponential relationship as shown in equation 6.
Equation 6
[0016] Another form of a relationship describing the effects of composition on thickening
time may be integrated with the effects of water as shown in equation 7.
Equation 7
(
water )n
TT a T£ixif31i + LiLJxixJf31ij + LiXi2/32i ...
[0017] A relationship describing effect of inert materials on thickening time may be a
linear combination of volume fractions of different orders, as described in Equation 8.
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Equation 8
TT oc [vo (Vinerts) + V1 (Vinerts)
2
+ ... ·l
Vsolids Vsolids
In equation 8, Vinens is the volume of inert materials the blend, Vsolids is the volume of all the
particulate materials including cementitious materials, supplementary cementitious materials,
additives, and inert materials. Vo and V1 are model parameters which are dependent upon the
physical and or chemical identity of the inert material. Inert materials may be any materials which
do not participate in cementitious reactions such as, without limitation, weighting materials and
loss circulation materials, for example. Another relationship of inert materials on thickening time
may be linear combination of mass fractions of different orders as shown in equation 9.
Equation 9
TT OC [Mo (Minerts) + Ml (Minerts)
2
+ ... ·l
Msolids Msolids
In equation 9, Minerts is the mass of inert materials the blend, Msolids is the mass of all the particulate
materials including cementitious materials, supplementary cementitious materials, additives, and
inert materials. Mo and M1 are model parameters which are dependent upon the physical and
chemical identity of the inert material. Using equations 2-9 a number of models of thickening time
ofthe blend (TTb) may be derived. A generalized thickening time model of the blend is illustrated
in equation 10. In equation 10, TTo is a thickening time of a Portland cement at a reference
temperature, pressure, and mass fraction of water in the cement slurry. In general, the mass
fraction of water to cement for TT o is taken to be 1: 1. The correction factor in equation 10 is a
function of effects of water on thickening time and the effects of composition on thickening time
and the effects of inert materials. In the simplest case where a cement slurry is prepared using only
Portland cement and water, equation 11 may be used to model the thickening time. In equation
11, n is a measurement of sensitivity to change in water of the Portland cement where n may be a
constant or a function of the mass ratio Portland cement in the cement slurry. The constant n may
be determined by mixing slurries at different water to Portland ratios and measuring the change
in thickening time using a consistometer.
Equation 10
TTb = TT0 X Correctrion Factor
Equation 11
(
water )n
TTb = TTo port l an d
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[0018] In a more typical case where a cement slurry is prepared with Portland cement,
supplementary cementitious materials, and inert materials, equation 12 may be used to model the
thickening time.
Equation 12
rrb = TTo (:z:~~f x (IixJ1i)
[0019] If there are interactions between the components of the cement slurry, equation 13
may be used to model the thickening time.
Equation 13
[0020] In the thickening time models above f3i and f3iJ are model parameters which
characterize reactivity of component i and j, or interaction between component i and j. For some
components, f3 may be constant, whereas for other components f3 may be depended upon
temperature and pressure, for example. f3 for any component may be experimentally determined.
One method of obtaining f3i for a cement component may be to select a Portland cement with a
known or measured TTo where TTo is measured at a reference temperature, pressure, and density.
Thereafter a volume of the cement component whose f3i is unknown may be mixed with the
selected Portland cement and water to the reference density. A thickening time test may be
performed at the reference temperature and pressure and any of equations 9-11 may be used to
determine the f3i value for the cement component.
[0021] There may be other methods to determine f3i including measuring physicochemical
properties of the materials and correlating the physico-chemical properties to f3i· For
example, measuring physico-chemical properties of a cement component may include many
analytical techniques and procedures including, but not limited to, microscopy, spectroscopy, xray
diffraction, x-ray fluorescence, particle size analysis, water requirement analysis, scanning
electron microscopy, energy-dispersive X-ray spectroscopy, surface area, specific gravity
analysis, thermogravimetric analysis, morphology analysis, infrared spectroscopy, ultravioletvisible
spectroscopy, mass spectroscopy, secondary ion mass spectrometry, electron energy mass
spectrometry, dispersive x-ray spectroscopy, auger electron spectroscopy, inductively coupled
plasma analysis, thermal ionization mass spectroscopy, glow discharge mass spectroscopy x-ray
photoelectron spectroscopy, mechanical property testing, Young's Modulus testing, rheological
properties, Poisson's Ratio. One or more of the proceeding tests may be consider API tests, as set
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forth in API RP Practice 1 OB-2, Recommended Practice for Testing Well Cements, First Edition,
July 2005.
[0022] Once the analytical techniques have been performed on the cement components,
the data may be categorized and correlated. Some categories may include, but are not limited to,
specific surface area, morphology, specific gravity, water requirement, etc. In some examples, the
components may be categorized by relative amounts, including amount of at least one following:
silica, alumina, iron, calcium, sodium, potassium, magnesium, sulfur, oxides thereof, and
combinations thereof For example, the components may be categorized based on an oxide
analysis that includes without limitation, silica content, calcium oxide content, and alumina
content among other oxides that may be present in the cement component. In addition, correlations
between the cement components may be generated based on the data or categorization of the data.
Additionally, correlations may be defined or generated between properties of the cement
components based on the data. For example, the various categories of properties may be plotted
against one another. In some examples, water requirement versus specific surface area may be
plotted. Accordingly, the water requirement of the cement component may be correlated to the
specific surface area so that the specific surface area is a function of water requirement. Specific
surface area may be used to predict reactivity of a cement component (or components). However,
specific surface area may not always be available for each material as specific surface area analysis
typically requires a specialized instrument. Accordingly, if the water requirement may be obtained
for the cement component, the correlation between water requirement and specific surface area
may be used to obtain an estimate for specific surface area, which may then be used to predict
reactivity. In addition to correlations between specific surface area and reactivity, correlations
may also be made between specific surface area and other mechanical properties such as tensile
strength and Young's modulus. Other correlations include oxide content to reactivity such that for
a given oxide analysis, a reactivity /3i may be calculated.
[0023] FIG. 1 illustrates a method 100 of using the models of thickening time discussed
above. Method 100 may begin at step 102 where bulk material availability such as cement,
supplementary cementitious materials, and cement additives available may be defined. Bulk
material availability is typically location dependent whereby some geographic locations may have
access to bulk materials that other geographic locations do not. Further, bulk materials such as
mined materials and cements may vary across geographic locations due to differences in raw
materials for manufacturing and manufacturing methods, as well as natural variations among
deposits of mineable minerals across geographic locations. After defining materials available,
method 100 may proceed to steps 104 and 106. In step 104, a proposed cement composition may
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be selected which may include cement components and mass fractions thereof. The cement
components may include any one of a cement, a supplementary cementitious additive, an inert
material, and/or a chemical additive defined in step 102. In step 106, engineering parameters of
the cement may be selected which may include temperature, density, and required thickening time.
From step 106, method 100 may proceed to step 110. In step 110 the thickening time of the
proposed cement composition may be calculated using any of the above thickening time models.
For example, equation 7 may be used with a selected effect of water on thickening time from
equations 1-2 and the effect of composition on thickening time from equations 3-6. In examples
where a cement component is selected in step 104 for which af3i value is not known, the unknown
Pi value may be calculated in step 112 using any of the above mentioned methods. From step 110,
method 100 may proceed to step 116 where the calculated thickening time from step 110 may be
compared to the required thickening time defined in step 106. If the calculated thickening time is
not within tolerance of the required thickening time, method 100 may proceed back to step 104
where a second proposed cement composition may be selected which may include disparate
cement components and/or disparate mass fractions thereof If the calculated thickening time is
within tolerance of the required thickening time, method 100 may proceed to step 120. In step
120, the proposed cement composition may be prepared, and the thickening time measured to
verify that the cement composition has the required thickening time.
[0024] Cement compositions described herein may generally include a hydraulic cement
and water. A variety of hydraulic cements may be utilized in accordance with the present
disclosure, including, but not limited to, those comprising calcium, aluminum, silicon, oxygen,
iron, and/or sulfur, which set and harden by reaction with water. Suitable hydraulic cements may
include, but are not limited to, Portland cements, pozzolana cements, gypsum cements, high
alumina content cements, silica cements, and any combination thereof. In certain examples, the
hydraulic cement may include a Portland cement. In some examples, the Portland cements may
include Portland cements that are classified as Classes A, C, H, and G cements according to
American Petroleum Institute, API Specification for Materials and Testing for Well Cements, API
Specification 10, Fifth Ed., July 1, 1990. In addition, hydraulic cements may include cements
classified by American Society for Testing and Materials (ASTM) in C150 (Standard
Specification for Portland Cement), C595 (Standard Specification for Blended Hydraulic Cement)
or C1157 (Performance Specification for Hydraulic Cements) such as those cements classified as
ASTM Type I, II, or III. The hydraulic cement may be included in the cement composition in any
amount suitable for a particular composition. Without limitation, the hydraulic cement may be
included in the cement compositions in an amount in the range of from about 10% to about 80%
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by weight of dry blend in the cement composition. For example, the hydraulic cement may be
present in an amount ranging between any of and/or including any of about 10%, about 15%,
about 20%, about 25%, about 30%, about 35%, about 40%, about 45%, about 50%, about 55%,
about 60%, about 65%, about 70%, about 75%, or about 80% by weight of the cement
compositions.
[0025] The water may be from any source provided that it does not contain an excess of
compounds that may undesirably affect other components in the cement compositions. For
example, a cement composition may include fresh water or saltwater. Saltwater generally may
include one or more dissolved salts therein and may be saturated or unsaturated as desired for a
particular application. Seawater or brines may be suitable for use in some examples. Further, the
water may be present in an amount sufficient to form a pumpable slurry. In certain examples, the
water may be present in the cement composition in an amount in the range of from about 33% to
about 200% by weight of the cementitious materials. For example, the water cement may be
present in an amount ranging between any of and/or including any of about 33%, about 50%,
about 7 5%, about 100%, about 125%, about 150%, about 175%, or about 200% by weight of the
cementitious materials. The cementitious materials referenced may include all components which
contribute to the compressive strength of the cement composition such as the hydraulic cement
and supplementary cementitious materials, for example.
[0026] As mentioned above, the cement composition may include supplementary
cementitious materials. The supplementary cementitious material may be any material that
contributes to the compressive strength of the cement composition. Some supplementary
cementitious materials may include, without limitation, fly ash, blast furnace slag, silica fume,
pozzolans, kiln dust, and clays, for example.
[0027] The cement composition may include kiln dust as a supplementary cementitious
material. "Kiln dust," as that term is used herein, refers to a solid material generated as a byproduct
of the heating of certain materials in kilns. The term "kiln dust" as used herein is intended
to include kiln dust made as described herein and equivalent forms of kiln dust. Depending on its
source, kiln dust may exhibit cementitious properties in that it can set and harden in the presence
of water. Examples of suitable kiln dusts include cement kiln dust, lime kiln dust, and
combinations thereof Cement kiln dust may be generated as a by-product of cement production
that is removed from the gas stream and collected, for example, in a dust collector. Usually, large
quantities of cement kiln dust are collected in the production of cement that are commonly
disposed of as waste. The chemical analysis of the cement kiln dust from various cement
manufactures varies depending on a number of factors, including the particular kiln feed, the
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efficiencies of the cement production operation, and the associated dust collection systems.
Cement kiln dust generally may include a variety of oxides, such as Si02, Alz03, Fe203, CaO,
MgO, S03, Na20, and K20. The chemical analysis of lime kiln dust from various lime
manufacturers varies depending on several factors, including the particular limestone or dolomitic
limestone feed, the type of kiln, the mode of operation of the kiln, the efficiencies of the lime
production operation, and the associated dust collection systems. Lime kiln dust generally may
include varying amounts of free lime and free magnesium, lime stone, and/or dolomitic limestone
and a variety of oxides, such as Si02, Ab03, Fe203, CaO, MgO, S03, Na20, and K20, and other
components, such as chlorides. A cement kiln dust may be added to the cement composition prior
to, concurrently with, or after activation. Cement kiln dust may include a partially calcined kiln
feed which is removed from the gas stream and collected in a dust collector during the manufacture
of cement. The chemical analysis of CKD from various cement manufactures varies depending
on a number of factors, including the particular kiln feed, the efficiencies of the cement production
operation, and the associated dust collection systems. CKD generally may comprise a variety of
oxides, such as Si02, Ah03, Fe203, CaO, MgO, S03, Na20, and K20. The CKD and/or lime kiln
dust may be included in examples of the cement composition in an amount suitable for a particular
application.
[0028] In some examples, the cement composition may further include one or more of
slag, natural glass, shale, amorphous silica, or metakaolin as a supplementary cementitious
material. Slag is generally a granulated, blast furnace by-product from the production of cast iron
including the oxidized impurities found in iron ore. The cement may further include shale. A
variety of shales may be suitable, including those including silicon, aluminum, calcium, and/or
magnesium. Examples of suitable shales include vitrified shale and/or calcined shale. In some
examples, the cement composition may further include amorphous silica as a supplementary
cementitious material. Amorphous silica is a powder that may be included in embodiments to
increase cement compressive strength. Amorphous silica is generally a byproduct of a ferrosilicon
production process, wherein the amorphous silica may be formed by oxidation and condensation
of gaseous silicon suboxide, SiO, which is formed as an intermediate during the process
[0029] In some examples, the cement composition may further include a variety of fly
ashes as a supplementary cementitious material which may include fly ash classified as Class C,
Class F, or Class N fly ash according to American Petroleum Institute, API Specification for
Materials and Testing for Well Cements, API Specification 10, Fifth Ed., July 1, 1990. In some
examples, the cement composition may further include zeolites as supplementary cementitious
materials. Zeolites are generally porous alumino-silicate minerals that may be either natural or
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synthetic. Synthetic zeolites are based on the same type of structural cell as natural zeolites and
may comprise aluminosilicate hydrates. As used herein, the term "zeolite" refers to all natural and
synthetic forms of zeolite.
[0030] Where used, one or more of the aforementioned supplementary cementitious
materials may be present in the cement composition. For example, without limitation, one or more
supplementary cementitious materials may be present in an amount of about 0.1% to about 80%
by weight of the cement composition. For example, the supplementary cementitious materials may
be present in an amount ranging between any of and/ or including any of about 0.1 %, about 1 0%,
about 20%, about 30%, about 40%, about 50%, about 60%, about 70%, or about 80% by weight
of the cement.
[0031] In some examples, the cement composition may further include hydrated lime. As
used herein, the term "hydrated lime" will be understood to mean calcium hydroxide. In some
embodiments, the hydrated lime may be provided as quicklime (calcium oxide) which hydrates
when mixed with water to form the hydrated lime. The hydrated lime may be included in examples
of the cement composition, for example, to form a hydraulic composition with the supplementary
cementitious components. For example, the hydrated lime may be included in a supplementary
cementitious material-to-hydrated-lime weight ratio of about 10: 1 to about 1: 1 or 3: 1 to about 5: 1.
Where present, the hydrated lime may be included in the set cement composition in an amount in
the range of from about 10% to about 100% by weight of the cement composition, for example.
In some examples, the hydrated lime may be present in an amount ranging between any of and/or
including any of about 10%, about 20%, about 40%, about 60%, about 80%, or about 100% by
weight of the cement composition. In some examples, the cementitious components present in the
cement composition may consist essentially of one or more supplementary cementitious materials
and the hydrated lime. For example, the cementitious components may primarily comprise the
supplementary cementitious materials and the hydrated lime without any additional components
(e.g., Portland cement, fly ash, slag cement) that hydraulically set in the presence of water.
[0032] Lime may be present in the cement composition in several forms, including as
calcium oxide and or calcium hydroxide or as a reaction product such as when Portland cement
reacts with water. Alternatively, lime may be included in the cement composition by amount of
silica in the cement composition. A cement composition may be designed to have a target lime to
silica weight ratio. The target lime to silica ratio may be a molar ratio, molal ratio, or any other
equivalent way of expressing a relative amount of silica to lime. Any suitable target time to silica
weight ratio may be selected including from about 10/90 lime to silica by weight to about 40/60
lime to silica by weight. Alternatively, About 10/90 lime to silica by weight to about 20/80 lime
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to silica by weight, about 20/80 lime to silica by weight to about 30/70 lime to silica by weight,
or about 30/70 lime to silica by weight to about 40/63 lime to silica by weight.
[0033] Other additives suitable for use in subterranean cementing operations also may be
included in embodiments of the cement composition. Examples of such additives include, but are
not limited to: weighting agents, lightweight additives, gas-generating additives, mechanicalproperty-
enhancing additives, lost-circulation materials, filtration-control additives, fluid-losscontrol
additives, defoaming agents, foaming agents, thixotropic additives, and combinations
thereof In embodiments, one or more of these additives may be added to the cement composition
after storing but prior to the placement of a cement composition into a subterranean formation. In
some examples, the cement composition may further include a dispersant. Examples of suitable
dispersants include, without limitation, sulfonated-formaldehyde-based dispersants (e.g.,
sulfonated acetone formaldehyde condensate) or polycarboxylated ether dispersants. In some
examples, the dispersant may be included in the cement composition in an amount in the range of
from about 0. 01% to about 5% by weight of the cementitious materials. In specific examples, the
dispersant may be present in an amount ranging between any of and/or including any of about
0.01 %, about 0.1 %, about 0.5%, about 1%, about 2%, about 3%, about 4%, or about 5% by weight
of the cementitious materials.
[0034] In some examples, the cement composition may further include a set retarder. A
broad variety of set retarders may be suitable for use in the cement compositions. For example,
the set retarder may comprise phosphonic acids, such as ethylenediamine tetra(methylene
phosphonic acid), diethylenetriamine penta(methylene phosphonic acid), etc.; lignosulfonates,
such as sodium lignosulfonate, calcium lignosulfonate, etc.; salts such as stannous sulfate, lead
acetate, monobasic calcium phosphate, organic acids, such as citric acid, tartaric acid, etc.;
cellulose derivatives such as hydroxyl ethyl cellulose (HEC) and carboxymethyl hydroxyethyl
cellulose (CMHEC); synthetic co- or ter-polymers comprising sulfonate and carboxylic acid
groups such as sulfonate-functionalized acrylamide-acrylic acid co-polymers; borate compounds
such as alkali borates, sodium metaborate, sodium tetraborate, potassium pentaborate; derivatives
thereof, or mixtures thereof Examples of suitable set retarders include, among others, phosphonic
acid derivatives. Generally, the set retarder may be present in the cement composition in an
amount sufficient to delay the setting for a desired time. In some examples, the set retarder may
be present in the cement composition in an amount in the range of from about 0. 01% to about 10%
by weight of the cementitious materials. In specific examples, the set retarder may be present in
an amount ranging between any of and/or including any of about 0.01 %, about 0.1 %, about 1%,
about 2%, about 4%, about 6%, about 8%, or about 10% by weight of the cementitious materials.
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[0035] In some examples, the cement composition may further include an accelerator. A
broad variety of accelerators may be suitable for use in the cement compositions. For example,
the accelerator may include, but are not limited to, aluminum sulfate, alums, calcium chloride,
calcium nitrate, calcium nitrite, calcium formate, calcium sulphoaluminate, calcium sulfate,
gypsum-hemihydrate, sodium aluminate, sodium carbonate, sodium chloride, sodium silicate,
sodium sulfate, ferric chloride, or a combination thereof In some examples, the accelerators may
be present in the cement composition in an amount in the range of from about 0. 01% to about 10%
by weight of the cementitious materials. In specific examples, the accelerators may be present in
an amount ranging between any of and/or including any of about 0.01 %, about 0.1 %, about 1%,
about 2%, about 4%, about 6%, about 8%, or about 10% by weight of the cementitious materials.
[0036] Cement compositions generally should have a density suitable for a particular
application. By way of example, the cement composition may have a density in the range of from
about 8 pounds per gallon ("ppg") (959 kg/m3) to about 20 ppg (2397 kg/m3), or about 8 ppg to
about 12 ppg (1437. kg/m3), or about 12 ppg to about 16 ppg (1917.22 kg/m3), or about 16 ppg to
about 20 ppg, or any ranges therebetween. Examples of the cement compositions may be foamed
or unfoamed or may comprise other means to reduce their densities, such as hollow microspheres,
low-density elastic beads, or other density-reducing additives known in the art.
[0037] The cement slurries disclosed herein may be used in a variety of subterranean
applications, including primary and remedial cementing. The cement slurries may be introduced
into a subterranean formation and allowed to set. In primary cementing applications, for example,
the cement slurries may be introduced into the annular space between a conduit located in a
wellbore and the walls of the wellbore (and/or a larger conduit in the wellbore), wherein the
wellbore penetrates the subterranean formation. The cement slurry may be allowed to set in the
annular space to form an annular sheath of hardened cement. The cement slurry may form a barrier
that prevents the migration of fluids in the wellbore. The cement composition may also, for
example, support the conduit in the wellbore. In remedial cementing applications, the cement
compositions may be used, for example, in squeeze cementing operations or in the placement of
cement plugs. By way of example, the cement compositions may be placed in a well bore to plug
an opening (e.g., a void or crack) in the formation, in a gravel pack, in the conduit, in the cement
sheath, and /or between the cement sheath and the conduit (e.g., a micro annulus).
[0038] Reference is now made to FIG. 2, illustrating use of a cement slurry 200. Cement
slurry 200 may comprise any of the components described herein. Cement slurry 200 may be
designed, for example, using the thickening time models describe herein. Cement slurry 200 may
be placed into a subterranean formation 205 in accordance with example systems, methods and
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cement slurries. As illustrated, a well bore 210 may be drilled into the subterranean formation 205.
While wellbore 210 is shown extending generally vertically into the subterranean formation 205,
the principles described herein are also applicable to well bores that extend at an angle through the
subterranean formation 205, such as horizontal and slanted well bores. As illustrated, the well bore
210 comprises walls 215. In the illustration, casing 230 may be cemented to the walls 215 of the
wellbore 210 by cement sheath 220. In the illustration, one or more additional conduits (e.g.,
intermediate casing, production casing, liners, etc.), shown here as casing 230 may also be
disposed in the wellbore 210. As illustrated, there is a wellbore annulus 235 formed between the
casing 230 and the walls 215 of the wellbore 210. One or more centralizers 240 may be attached
to the casing 230, for example, to centralize the casing 230 in the well bore 210 prior to and during
the cementing operation. The cement slurry 200 may be pumped down the interior of the casing
230. The cement slurry 200 may be allowed to flow down the interior of the casing 230 through
the casing shoe 245 at the bottom of the casing 230 and up around the casing 230 into the well bore
annulus 235. The cement slurry 200 may be allowed to set in the wellbore annulus 235, for
example, to form a cement sheath that supports and positions the casing 230 in the wellbore 210.
While not illustrated, other techniques may also be utilized for introduction of the cement slurry
200. By way of example, reverse circulation techniques may be used that include introducing the
cement slurry 200 into the subterranean formation 205 by way of the well bore annulus 235 instead
of through the casing 230. As it is introduced, the cement slurry 200 may displace other fluids
250, such as drilling fluids and/or spacer fluids that may be present in the interior of the casing
230 and/or the well bore annulus 235. While not illustrated, at least a portion of the displaced fluids
250 may exit the wellbore annulus 235 via a flow line and be deposited, for example, in one or
more retention pits. A bottom plug 255 may be introduced into the wellbore 210 ahead of the
cement slurry 200, for example, to separate the cement slurry 200 from the fluids 250 that may be
inside the casing 230 prior to cementing. After the bottom plug 255 reaches the landing collar 280,
a diaphragm or other suitable device should rupture to allow the cement slurry 200 through the
bottom plug 255. The bottom plug 255 is shown on the landing collar 280. In the illustration, a
top plug 285 may be introduced into the wellbore 210 behind the cement slurry 200. The top plug
260 may separate the cement slurry 200 from a displacement fluid 265 and also push the cement
slurry 200 through the bottom plug 255.
[0039] The following statements may describe certain embodiments of the disclosure but
should be read to be limiting to any particular embodiment.
[0040] Statement 1. A method of designing a cement slurry comprising: (a) selecting at
least a cement and concentration thereof, water and concentration thereof, and, optionally, at least
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one supplementary cementitious material and a concentration thereof, such that a cement slurry
comprising the cement, the water, and, if present, the at least one supplementary cementitious
material, meet a density requirement; (b) calculating a thickening time of the cement slurry using
a thickening time model; (c) comparing the thickening time of the cement slurry to a thickening
time requirement, wherein steps (a)-( c) are repeated if the thickening time of the cement slurry
does not meet or exceed the thickening time requirement, wherein each repeated step of selecting
comprises selecting different concentrations and/or different chemical identities for the cement
and/or the supplementary cementitious material than previously selected, or step (d) is performed
if the thickening time of the cement slurry meets or exceeds the thickening time requirement; and
(d) preparing the cement slurry.
[0041] Statement 2. The method of claim 1 wherein the cement is selected from the group
consisting of Portland cements, pozzolana cements, gypsum cements, high alumina content
cements, silica cements, and combinations thereof.
[0042] Statement 3. The method of any of statements 1-2 wherein the at least one
supplementary cementitious material is selected from the group consisting of fly ash, blast furnace
slag, silica fume, pozzolans, kiln dust, clays, and combinations thereof, and optionally, wherein
the cement slurry further comprises at least one inert material.
[0043] Statement 4. The method of any of statements 1-3 wherein the thickening time
model comprises the following equation: TT = TT0 (water)n L xJ3i where TT is the thickening
blend
time, ITo is characteristic thickening time at a reference temperature, water and blend are the mass
fraction of the water and blend in the cement slurry, where blend is the cement and the at least one
supplementary cementitious material, if present, xi is a mass fraction of component i in the blend,
Pi is a reactivity of component i, and n is a measurement of sensitivity to change in water.
[0044] Statement 5. The method of any of statements 1-3 wherein the thickening time
model comprises the following equation: TT = TT0 (::~;f C'LixJ3i) + (LiLJXixJPiJ) +
···where TT is the thickening time, ITo is characteristic thickening time at a reference
temperature, water is the mass of the water, blend is the mass of the cement and the at least one
supplementary cementitious material, if present, in the cement slurry, n is a measurement of
sensitivity to change in water, xi is mass fraction of component i, x1 is mass fraction of component
j, Pi is a model parameter which characterizes reactivity of component i, and piJ is a model
parameter which characterizes interaction between component i and j.
[0045] Statement 6. The method of any of statements 1-3 wherein the thickening time
model comprises the following equation: TT = TT0 (water)n e'Lixdli where TT is the thickening
blend
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time, ITo is characteristic thickening time at a reference temperature, water is the mass fraction
of the water, blend is the mass fraction of the cement and the at least one supplementary
cementitious material, if present, in the cement slurry, xi is a mass fraction of component i in the
cement slurry, Pi is a model parameter which characterizes reactivity of component i, and n is a
measurement of sensitivity to change in water.
[0046] Statement 7. A method comprising: preparing a slurry comprising a cement, water,
and a supplementary cementitious material; measuring a thickening time of the slurry; and
calculating a reactivity (/Ji) for the supplementary cementitious material using a thickening time
model.
[0047] Statement 8. The method of statement 7 wherein the cement is selected from the
group consisting of Portland cements, pozzolana cements, gypsum cements, high alumina content
cements, silica cements, and combinations thereof
[0048] Statement 9. The method of any of statements 7-8 wherein the supplementary
cementitious material is selected from the group consisting of fly ash, blast furnace slag, silica
fume, pozzolans, kiln dust, clays, and combinations thereof and optionally, wherein the cement
slurry further comprises at least one inert material.
[0049] Statement 10. The method of any of statements 7-8 wherein the thickening time
model comprises the following equation: TT = TT0 (water)n :L xipi where TT is the thickening
blend
time, ITo is characteristic thickening time at a reference temperature, water and blend are the mass
fraction of the water and blend in the cement slurry, where blend is the cement and the at least one
supplementary cementitious material xi is a mass fraction of component i in the blend, Pi is a
reactivity of component i, and n is a measurement of sensitivity to change in water.
[0050] Statement 11. The method of any of statements 7-8 wherein the thickening time
model comprises the following equation: TT = TT0 (::~;f CL xipi) + (Li l, J xixJ PiJ) +
···where TT is the thickening time, ITo is characteristic thickening time at a reference
temperature, water is the mass of the water, blend is the mass of the cement and the at least one
supplementary cementitious material in the cement slurry, n is a measurement of sensitivity to
change in water, xi is mass fraction of component i, x1 is mass fraction of component j, Pi is a
model parameter which characterizes reactivity of component i, and PiJ is a model parameter
which characterizes interaction between component i and j.
[0051] Statement 12. The method of any of statements 7-8 wherein the thickening time
model comprises the following equation: TT = TT0 (water)n e'iixdJi where TT is the thickening
blend
time, ITo is characteristic thickening time at a reference temperature, water is the mass fraction
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of the water, blend is the mass fraction of the cement and the at least one supplementary
cementitious material in the cement slurry, xi is a mass fraction of component i in the cement
slurry, f3i is a model parameter which characterizes reactivity of component i, and n is a
measurement of sensitivity to change in water.
[0052] Statement 13. The method of claim 7 further comprising: (a) selecting at least a
cement and concentration thereof, water and concentration thereof, and, at least one
supplementary cementitious material and a concentration thereof, such that a second cement slurry
comprising the cement, the water, and, the at least one supplementary cementitious material, meet
a density requirement; (b) calculating a thickening time of the second cement slurry using a
thickening time model; (c) comparing the thickening time of the second cement slurry to a
thickening time requirement, wherein steps (a)-( c) are repeated if the thickening time of the second
cement slurry does not meet or exceed the thickening time requirement, wherein each repeated
step of selecting comprises selecting different concentrations and/or different chemical identities
for the cement and/or the supplementary cementitious material than previously selected, or step
(d) is performed if the thickening time of the cement slurry meets or exceeds the thickening time
requirement; and (d) preparing the second cement slurry.
[0053] Statement 14. The method of statement 13 wherein the thickening time model
comprises the following equation: TT = TT0 (water)n 'L xif3i where TT is the thickening time,
b1end
ITo is characteristic thickening time at a reference temperature, water and blend are the mass
fraction of the water and blend in the second cement slurry, where blend is the cement and the at
least one supplementary cementitious material xi is a mass fraction of component i in the blend,
f3i is a reactivity of component i, and n is a measurement of sensitivity to change in water.
[0054] Statement 15. The method of statement 13 wherein the thickening time model
comprisesthefollowingequation: TT = TT0 (::~;f (l,ixif3i) + (LiLJxixJf3i1) + ··· whereTT
is the thickening time, ITo is characteristic thickening time at a reference temperature, water is
the mass of the water, blend is the mass of the cement and the at least one supplementary
cementitious material in the second cement slurry, n is a measurement of sensitivity to change in
water, xi is mass fraction of component i, x1 is mass fraction of component j, f3i is a model
parameter which characterizes reactivity of component i, and f3iJ is a model parameter which
characterizes interaction between component i and j.
[0055] Statement 16. The method of statement 13 wherein the thickening time model
comprises the following equation: TT = TT0 (water)n e'Lrxrf3r where IT is the thickening time,
b1end
ITo is characteristic thickening time at a reference temperature, water is the mass fraction of the
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water, blend is the mass fraction of the cement and the at least one supplementary cementitious
material in the second cement slurry, xi is a mass fraction of component i in the second cement
slurry, f3i is a model parameter which characterizes reactivity of component i, and n is a
measurement of sensitivity to change in water.
[0056] Statement 17. A method comprising: selecting, based at least in part on a
thickening time model, a thickening time requirement and a density requirement, at least a cement
and concentration thereof, a water and concentration thereof, and optionally, at least one
supplementary cementitious material and concentration thereof, such that a slurry comprising the
cement and concentration thereof, the water and concentration thereof, and, if present, the at least
one supplementary cementitious material and concentration thereof, meets or exceeds the
thickening time requirement; and preparing the cement slurry.
[0057] Statement 18. The method of statement 17 wherein the thickening time model
comprises the following equation: TT = TT0 (water)n Li xif3i where TT is the thickening time,
blend
ITo is characteristic thickening time at a reference temperature, water and blend are the mass
fraction of the water and blend in the cement slurry, where blend is the cement and the at least one
supplementary cementitious material xi is a mass fraction of component i in the blend, /3i is a
reactivity of component i, and n is a measurement of sensitivity to change in water.
[0058] Statement 19. The method of statement 17 wherein the thickening time model
comprisesthefollowingequation: TT = TT0 (::~;f (Lixif3J + (LiLJxixJf3iJ + ··· whereTT
is the thickening time, ITo is characteristic thickening time at a reference temperature, water is
the mass of the water, blend is the mass of the cement and the at least one supplementary
cementitious material in the cement slurry, n is a measurement of sensitivity to change in water,
xi is mass fraction of component i, x1 is mass fraction of component j, f3i is a model parameter
which characterizes reactivity of component i, and J3iJ is a model parameter which characterizes
interaction between component i and j.
[0059] Statement 20. The method of statement 17 wherein the thickening time model
comprises the following equation: TT = TT0 (water)n e"Lrxrf3r where IT is the thickening time,
blend
ITo is characteristic thickening time at a reference temperature, water is the mass fraction of the
water, blend is the mass fraction of the cement and the at least one supplementary cementitious
material in the cement slurry, xi is a mass fraction of component i in the cement slurry, J3i is a
model parameter which characterizes reactivity of component i, and n is a measurement of
sensitivity to change in water.
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EXAMPLE
[0060] Cement slurries were prepared according to Table 1. The values in Table 1 are the
mass fractions of each cement component in the slurry. Table 2 lists the Pi values for the
supplementary cementitious materials as determined by the methods outlined above and using
equation 9. Five slurries were prepared to 14lb/gal (1,678 kg/m3
) and tested for thickening time
at a temperature of 200 °F (93.3 °C) in a pressurized consistometer in accordance with the
procedure for determining cement thickening times set forth in API RP Practice lOB-2,
Recommended Practice for Testing Well Cements, First Edition, July 2005. The predicted
thickening time was calculated using equation 12.
Table 1
Cement
Fly Natural Kiln Crystalline Measured Predicted
Slurry Class G Class H Ash Glass Slag Dust Silica TT (mins) TT (mins)
1
2
3
4
5
0 0.6 0 0.4 0 0 0 89 113
0.85 0 0 0 0 0 0.15 121 110
0 0.25 0.35 0.4 0 0 0 131 153
0 0.5 0.5 0 0 0 0 368 373
0.25 0 0 0 0.25 0.5 0 34 30
Table 2
Material /3;
Fly Ash 4.96
Cement Kiln
Dust 1.69
Crystalline
Silica 1.24
Hematite 2.24
[0061] The results of the thickening time test are shown in the parity plot in FIG. 3. The
parity plot shows a good fit for the measured thickening time to the predicted thickening time.
[0062] The disclosed cement compositions and associated methods may directly or
indirectly affect any pumping systems, which representatively includes any conduits, pipelines,
trucks, tubulars, and/or pipes which may be coupled to the pump and/or any pumping systems and
may be used to fluidically convey the cement compositions downhole, any pumps, compressors,
or motors (e.g., topside or downhole) used to drive the cement compositions into motion, any
valves or related joints used to regulate the pressure or flow rate of the cement compositions, and
any sensors (i.e., pressure, temperature, flow rate, etc.), gauges, and/or combinations thereof, and
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the like. The cement compositions may also directly or indirectly affect any mixing hoppers and
retention pits and their assorted variations.
[0063] It should be understood that the compositions and methods are described in terms
of"comprising," "containing," or "including" various components or steps, the compositions and
methods can also "consist essentially of' or "consist of' the various components and steps.
Moreover, the indefinite articles "a" or "an," as used in the claims, are defined herein to mean one
or more than one of the elements that it introduces.
[0064] For the sake of brevity, only certain ranges are explicitly disclosed herein.
However, ranges from any lower limit may be combined with any upper limit to recite a range not
explicitly recited, as well as, ranges from any lower limit may be combined with any other lower
limit to recite a range not explicitly recited, in the same way, ranges from any upper limit may be
combined with any other upper limit to recite a range not explicitly recited. Additionally,
whenever a numerical range with a lower limit and an upper limit is disclosed, any number and
any included range falling within the range are specifically disclosed. In particular, every range
of values (of the form, "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 to set forth every
number and range encompassed within the broader range of values even if not explicitly recited.
Thus, every point or individual value may serve as its own lower or upper limit combined with
any other point or individual value or any other lower or upper limit, to recite a range not explicitly
recited.
[0065] Therefore, the present disclosure is well adapted to attain the ends and advantages
mentioned as well as those that are inherent therein. The particular examples 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.
Although individual examples are discussed, the disclosure covers all combinations of all those
examples. Furthermore, no limitations are intended to the details of construction or design herein
shown, other than as described in the claims below. Also, the terms in the claims have their plain,
ordinary meaning unless otherwise explicitly and clearly defined by the patentee. It is therefore
evident that the particular illustrative examples disclosed above may be altered or modified and
all such variations are considered within the scope and spirit of the present disclosure. Ifthere is
any conflict in the usages of a word or term in this specification and one or more patent(s) or other
documents that may be incorporated herein by reference, the definitions that are consistent with
this specification should be adopted.
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CLAIMS
What is claimed is:
1. A method of designing a cement slurry comprising:
(a) selecting at least a cement and concentration thereof, water and concentration thereof,
and, optionally, at least one supplementary cementitious material and a concentration thereof, such
that a cement slurry comprising the cement, the water, and, if present, the at least one
supplementary cementitious material, meet a density requirement;
(b) calculating a thickening time of the cement slurry using a thickening time model;
(c) comparing the thickening time of the cement slurry to a thickening time requirement,
wherein steps (a)-(c) are repeated if the thickening time of the cement slurry does not meet or
exceed the thickening time requirement, wherein each repeated step of selecting comprises
selecting different concentrations and/or different chemical identities for the cement and/or the
supplementary cementitious material than previously selected, or step (d) is performed if the
thickening time of the cement slurry meets or exceeds the thickening time requirement; and
(d) preparing the cement slurry.
2. The method of claim 1 wherein the cement is selected from the group consisting of Portland
cements, pozzolana cements, gypsum cements, high alumina content cements, silica cements, and
combinations thereof
3. The method of claim 1 wherein the at least one supplementary cementitious material is selected
from the group consisting of fly ash, blast furnace slag, silica fume, pozzolans, kiln dust, clays,
and combinations thereof, and optionally, wherein the cement slurry further comprises at least one
inert material.
4. The method of claim 1 wherein the thickening time model comprises the following equation:
TT = TT0 (:z:~~) n Lixtfli
where TT is the thickening time, TTo is characteristic thickening time at a reference temperature,
water and blend are the mass fraction of the water and blend in the cement slurry, where blend is
the cement and the at least one supplementary cementitious material, if present, xi is a mass
fraction of component i in the blend, f3i is a reactivity of component i, and n is a measurement of
sensitivity to change in water.
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50 The method of claim 1 wherein the thickening time model comprises the following equation:
where TI is the thickening time, ITo is characteristic thickening time at a reference temperature,
water is the mass of the water, blend is the mass of the cement and the at least one supplementary
cementitious material, if present, in the cement slurry, n is a measurement of sensitivity to change
in water, xi is mass fraction of component i, x1 is mass fraction of component j, f3i is a model
parameter which characterizes reactivity of component i, and f3iJ is a model parameter which
characterizes interaction between component i and j 0
60 The method of claim 1 wherein the thickening time model comprises the following equation:
(
TT = TT water)n 0 -- e'Lrxrf3r
blend
where TI is the thickening time, ITo is characteristic thickening time at a reference temperature,
water is the mass fraction of the water, blend is the mass fraction of the cement and the at least
one supplementary cementitious material, if present, in the cement slurry, xi is a mass fraction of
component i in the cement slurry, f3i is a model parameter which characterizes reactivity of
component i, and n is a measurement of sensitivity to change in water.
7 0 A method comprising:
preparing a slurry comprising a cement, water, and a supplementary cementitious material;
measuring a thickening time of the slurry; and
calculating a reactivity (/3i) for the supplementary cementitious material using a thickening
time model.
80 The method of claim 7 wherein the cement is selected from the group consisting of Portland
cements, pozzolana cements, gypsum cements, high alumina content cements, silica cements, and
combinations thereof.
90 The method of claim 7 wherein the supplementary cementitious material is selected from the
group consisting of fly ash, blast furnace slag, silica fume, pozzolans, kiln dust, clays, and
combinations thereof and optionally, wherein the cement slurry further comprises at least one inert
material.
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10. The method of claim 7 wherein the thickening time model comprises the following equation:
(
water)n'
TT = TTo blend L/dJi
where TT is the thickening time, ITo is characteristic thickening time at a reference temperature,
water and blend are the mass fraction of the water and blend in the cement slurry, where blend is
the cement and the at least one supplementary cementitious material xi is a mass fraction of
component i in the blend, f3i is a reactivity of component i, and n is a measurement of sensitivity
to change in water.
11. The method of claim 7 wherein the thickening time model comprises the following equation:
TT = rro(:~:~~f (~ x,p,) + ( ~~ x,xA;) + ···
where TT is the thickening time, ITo is characteristic thickening time at a reference temperature,
water is the mass of the water, blend is the mass of the cement and the at least one supplementary
cementitious material in the cement slurry, n is a measurement of sensitivity to change in water,
xi is mass fraction of component i, x1 is mass fraction of component j, f3i is a model parameter
which characterizes reactivity of component i, and fJiJ is a model parameter which characterizes
interaction between component i and j.
12. The method of claim 7 wherein the thickening time model comprises the following equation:
(
TT = TT water)n 0 -- e'Lrxrf3r
blend
where TT is the thickening time, ITo is characteristic thickening time at a reference temperature,
water is the mass fraction of the water, blend is the mass fraction of the cement and the at least
one supplementary cementitious material in the cement slurry, xi is a mass fraction of component
i in the cement slurry, {Ji is a model parameter which characterizes reactivity of component i, and
n is a measurement of sensitivity to change in water.
13. The method of claim 7 further comprising:
(a) selecting at least a cement and concentration thereof, water and concentration thereof,
and, at least one supplementary cementitious material and a concentration thereof, such that a
second cement slurry comprising the cement, the water, and, the at least one supplementary
cementitious material, meet a density requirement;
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(b) calculating a thickening time of the second cement slurry using a thickening time
model;
(c) comparing the thickening time of the second cement slurry to a thickening time
requirement, wherein steps (a)-( c) are repeated if the thickening time of the second cement slurry
does not meet or exceed the thickening time requirement, wherein each repeated step of selecting
comprises selecting different concentrations and/or different chemical identities for the cement
and/or the supplementary cementitious material than previously selected, or step (d) is performed
if the thickening time of the cement slurry meets or exceeds the thickening time requirement; and
(d) preparing the second cement slurry.
14. The method of claim 13 wherein the thickening time model comprises the following equation:
(
water)n'
TT = TT0 blend L/d3i
where TT is the thickening time, ITo is characteristic thickening time at a reference temperature,
water and blend are the mass fraction of the water and blend in the second cement slurry, where
blend is the cement and the at least one supplementary cementitious material xi is a mass fraction
of component i in the blend, f3i is a reactivity of component i, and n is a measurement of sensitivity
to change in water.
15. The method of claim 13 wherein the thickening time model comprises the following equation:
where TT is the thickening time, ITo is characteristic thickening time at a reference temperature,
water is the mass of the water, blend is the mass of the cement and the at least one supplementary
cementitious material in the second cement slurry, n is a measurement of sensitivity to change in
water, xi is mass fraction of component i, x1 is mass fraction of component j, f3i is a model
parameter which characterizes reactivity of component i, and f3iJ is a model parameter which
characterizes interaction between component i and j.
16. The method of claim 13 wherein the thickening time model comprises the following equation:
(
water)n TT = TT0 -- e'Lrxrf3r
blend
where TT is the thickening time, ITo is characteristic thickening time at a reference temperature,
water is the mass fraction of the water, blend is the mass fraction of the cement and the at least
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one supplementary cementitious material in the second cement slurry, xi is a mass fraction of
component i in the second cement slurry, Pi is a model parameter which characterizes reactivity
of component i, and n is a measurement of sensitivity to change in water.
17. A method comprising:
selecting, based at least in part on a thickening time model, a thickening time requirement
and a density requirement, at least a cement and concentration thereof, a water and concentration
thereof, and optionally, at least one supplementary cementitious material and concentration
thereof, such that a slurry comprising the cement and concentration thereof, the water and
concentration thereof, and, if present, the at least one supplementary cementitious material and
concentration thereof, meets or exceeds the thickening time requirement; and
preparing the cement slurry.
18. The method of claim 17 wherein the thickening time model comprises the following equation:
TT = TTo (:z:~~) n Lixipi
where TT is the thickening time, ITo is characteristic thickening time at a reference temperature,
water and blend are the mass fraction of the water and blend in the cement slurry, where blend is
the cement and the at least one supplementary cementitious material xi is a mass fraction of
component i in the blend, Pi is a reactivity of component i, and n is a measurement of sensitivity
to change in water.
19. The method of claim 17 wherein the thickening time model comprises the following equation:
where TT is the thickening time, ITo is characteristic thickening time at a reference temperature,
water is the mass of the water, blend is the mass of the cement and the at least one supplementary
cementitious material in the cement slurry, n is a measurement of sensitivity to change in water,
xi is mass fraction of component i, x1 is mass fraction of component j, Pi is a model parameter
which characterizes reactivity of component i, and PiJ is a model parameter which characterizes
interaction between component i and j.