WO2024248897A1

WO2024248897A1 - Evaluating wellbores for use as carbon capture underground storage wells

Info

Publication number: WO2024248897A1
Application number: PCT/US2024/011032
Authority: WO
Inventors: Siva Rama Krishna JANDHYALA; Walmy Cuello JIMENEZ
Original assignee: Halliburton Energy Services Inc
Current assignee: Halliburton Energy Services Inc
Priority date: 2023-05-30
Filing date: 2024-01-10
Publication date: 2024-12-05
Anticipated expiration: 2025-11-30
Also published as: US20240401431A1; AU2024279615A1

Abstract

A variety of methods and systems are disclosed, including, in one example, a method including: providing a composition for a cement disposed in a wellbore; selecting injection conditions for an invasive fluid for an injection or storage operation; predicting a depth of penetration of the invasive fluid into the cement with a depth of penetration model based at least in part on the injection conditions and the composition for the cement; predicting a material property of the cement with a cement property model based at least in part on the predicted depth of penetration; performing an integrity analysis based at least in part on the predicted material property; and performing the injection or storage operation in the wellbore based at least in part on the integrity analysis.

Description

EVALUATING WELLBORES FOR USE AS CARBON CAPTURE UNDERGROUND STORAGE WELLS

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 wellbore 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 or a resin-based system 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 or resin system may set in the annular space, thereby forming an annular sheath of hardened, substantially impermeable cement or resin (z.e., a cement sheath or annular sealant) 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] In wellbores where carbon dioxide (CO2) is present, such as in carbon capture underground storage (CCUS) wells, or in wellbores where other corrosive fluids are present, there may be additional considerations for the long-term integrity of the cement sheath. For instance, a cement sheath which is exposed to CO2 may begin to uptake the CO2 into the matrix of the cement which may cause chemical and physical changes within the cement. Cement exposed to CO2 behaves like a composite material with spatially varying mechanical properties such as Young’s modulus (YM), Poisson’s ratio (PR), and unconfined compressive strength (UCS). The carbonated portion of the cement may have different mechanical properties than the uncarbonated portion which may compromise the capability of the cement to sustain zonal isolation in the wellbore. As a carbonation front permeates the cement over time, the ability of the cement sheath to sustain zonal isolation may be reduced.

[0003] Over the life of an oil well, production of reservoir fluids depletes the reservoir leaving behind volume which may be used to store carbon dioxide. One challenge in evaluating an existing well’s viability as use as an underground storage well is that it is difficult to predict properties of the cement sheath once carbon dioxide is introduced into the reservoir. In particular, the stress-train response of the near wellbore region is a determining factor whether the wellbore can be utilized for carbon dioxide storage. The extent of carbonation may depend upon the conditions the carbon dioxide is introduced at and the duration of exposure. Other factors which may affect the physical properties of the cement after carbon dioxide exposure may include composition of the cement, historical well loads, previous carbon loads, new carbon loads, carbon to cement exposure conditions. Furthermore, the operational conditions which the CO2 is introduced into the wellbore such as temperature, pressure, and state of the CO2 such as gaseous CO2, liquid CO2, or CO2 dissolved in water (carbonic), each can affect the extent of carbonation. For a given wellbore, there may be operational conditions which would accelerate carbonation of the cement sheath which may cause premature failure of the cement sheath.

[0004] While there exist numerical simulators for modeling lifetimes of wells, the time- evolved mechanical properties of carbonated cement, including injection conditions, add additional degrees of freedom which may not be adequately captured by current numerical simulators.

BRIEF DESCRIPTION OF THE DRAWINGS

[0005] These drawings illustrate certain aspects of some of the examples of the present disclosure and should not be used to limit or define the method.

[0006] FIG. l is a workflow which illustrates a process for evaluating a wellbore.

[0007] FIGS. 2A and 2B are parity plots comparing predicted and measured depths of penetration of an invasive fluid in a chemically modified cement.

[0008] FIGS. 3A and 3B are parity plots comparing predicted and measured material properties of a chemically modified cement.

[0009] FIGS. 4 A and 4B show a schematic of a mesh model of a chemically modified cement sheath of a wellbore.

[0010] FIG. 5 is a plot of predicted shear stress experienced by chemically modified and chemically unmodified regions of a chemically modified cement.

[0011] FIG. 6 is a cross sectional view of a chemically modified cement plug sample.

[0012] FIG. 7 illustrates an injection operation in a wellbore.

[0013] FIG. 8 illustrates a system including a logging tool.

DETAILED DESCRIPTION

[0014] The present disclosure may generally relate to methods for evaluating an existing wellbore for use as an underground storage well. More particularly, examples of the present disclosure may be directed to methods and systems for predicting failure properties of a cement sheath upon carbonation, and further predicting risk of failure based on a stress state of the cement sheath compared to its predicted failure properties.

[0015] As used herein, “chemically modified cement” refers to a cement which has been exposed to a chemically reactive species for a sufficient duration of time to allow for substantial migration of the chemically reactive species into an inner-spatial region of the cement. Chemically reactive species may include, without limitation, carbon dioxide, carbonic acid, hydrogen sulfide, ammonia, hydrogen, and any combination thereof.

[0016] As used herein, “cement” may comprise one or more cementitious materials and/or resin, as well as non-cementitious materials and/or additives. Cementitious materials may include, without limitation, Portland cements, hydraulic cements, fly ash, pearlite, geopolymer, non- hydraulic cements, calcium-lime compositions, blast furnace slag, natural glass, shale, metakaolin, silica fume, pozzolans, kiln dusts, clays, slag cements, zeolite, pumice, lime, silica, calcium hydroxide, and any combinations thereof.

[0017] As used herein, a “resin” refers to any of a number of physically similar polymerized synthetics or chemically modified natural resins including thermoplastic materials and thermosetting materials. Resin may include, without limitation, epoxy-based resins, cyclic olefins, novolak resins, poly epoxide resins, phenol-aldehyde resins, urea-aldehyde resins, urethane resins, phenolic resins, furan resins, furan and furfuryl alcohol resins, phenolic/latex resins, phenol formaldehyde resins, bisphenol A diglycidyl ether resins, butoxymethyl butyl glycidyl ether resins, bisphenol A-epichlorohydrin resins, bisphenol F resins, diglycidyl ether bisphenol F resin, cyclohexane dimethanol diglycidyl ether, glycidyl ether resins, polyester resins and hybrids and copolymers thereof, polyurethane resins and hybrids and copolymers thereof, acrylate resins, and any combinations thereof.

[0018] As mentioned previously, one challenge in assessing long term mechanical properties of a cement and/or resin sheath is that conventional models are not well suited for determining the time-dependent mechanical properties of chemically modified cement. Advantages of the methods and systems presently disclosed include an improved ability to accurately predict these time-dependent properties of chemically modified cement. Particularly, the methods, systems, workflows, and models disclosed herein may be well suited for making these predictions.

[0019] Other advantages of the present disclosure may include an improved ability to accurately assess the viability of an existing wellbore for fluid injection (e.g., CO2), an improved ability to accurately account for a long-term effect of individual chemical species on spatially varying mechanical properties of a diverse range of cement formulations, an improved ability to accurately model the stress-strain response of a cement sheath to a fluid during and/or after injection of the fluid into a wellbore, an improved ability to optimize an injection rate, and/or operating condition of an injection fluid during an injection operation, taking into account wellbore conditions such as temperature and pressure. Another advantage includes an improved ability to accurately predict whether or not an injection operation will be fatally defective to an underground storage well, or otherwise result in failure of a cement sheath or barrier, and an improved ability to assess the risk of unmitigated seepage of a stored fluid out from a well.

[0020] FIG. l is a workflow 100 which illustrates a process to assess viability of an existing well for conversion to an injection well. As illustrated, workflow 100 may comprise a number of blocks, with blocks representing a performable operation and depending on one or more inputs and/or conditions. It is noted that while workflow 100 may be performed sequentially in the order shown, the order by which individual blocks of workflow 100 are performed may be adjusted, adapted, and/or rearranged to suit a particular application. For example, it is noted that while workflow 100 is illustrated as comprising a specific number of blocks, one or more blocks may be omitted and/or added to workflow 100 to ensure carrying out of an intended function of workflow 100.

[0021] Beginning in block 102, a composition of a cement is determined or provided. Depending on the particular circumstances associated with the forming of an existing well, a composition of a cement may or may not be known at the time that block 102 is performed. For example, it may be the case that an exact cement composition of a wellbore sheath is known due to its having been properly recorded and logged at the time the wellbore was drilled and the cement pumped. In other cases, the cement composition may be only partially known or unknown, such that only a single, a few, or none of the components making up a wellbore cement are known. In these cases, it may be desirable to determine the identity and/or concentrations of the cement components using, for example, laboratory techniques or other in-situ techniques.

[0022] In block 104, the state of a wellbore may be assessed. Metrics for assessing a state of a wellbore may include, without limitation, an amount of corrosion to a casing, cement sheath, or cement barrier, an extent of deterioration to a bond between a cement sheath and a casing, density or porosity of a cement, a cement quality of an annulus, one or more dimensionless or dimensional quantities associated therewith, such as one or more dimensional or dimensionless measurements or quantities derived from measurements by an acoustic logging tool, ultrasonic logging tool, electromagnetic logging tool, pipe inspection tool, or the like. These quantities may be obtained immediately prior or in the days, weeks, or months leading up to an injection operation, or may have been previously logged and recorded. A wellbore may be characterized as being generally continuous or uniform along the length of a wellbore or may be nonuniform and/or discontinuous. For example, it may be the case that certain regions of a wellbore or wellbore casing are assessed as satisfactory, but that another region is assessed as unsatisfactory. Example criteria for judging if a wellbore or wellbore casing is satisfactory for performing an operation may include, for example, sonic attenuation of a casing lower than a threshold value, transit time of an acoustic wave lower than a threshold value, Young’s Modulus lower than a threshold value, Poisson’ s Ratio lower than a threshold value, ultimate compressive strength lower than a threshold value, or the like. An acoustic wave attenuated by a corroded casing or bond may be a longitudinal wave (P-wave), shear wave (S-wave), flexural wave (F-wave), or a stoneley wave. Whether or not a wellbore meets a threshold requirement may influence a determination as to an injection operation. For example, an injection operation may or may not be performed if a wellbore meets or fails to meet a threshold requirement. In one or more examples, a profile along an entire length of a wellbore may be logged or measured or selected regions of interest. Regions of interest may include, without limitation, at a depth of intersection between subterranean rock layers, such as at an interface between a caprock and a sub-caprock region, or between two rock-types, at a region of changing porosity and/or permeability, regions of high porosity and/or permeability, cavernous regions, at regions of changing dip and/or inclination angle, fault regions, at regions of increased risk of seismic activity, or any region having subsurface geological import. In one or more examples, it may be advantageous to assess the state of the wellbore at a region of interest to ensure that the wellbore is suitable for an injection operation.

[0023] In block 106, a penetration depth of an invasive fluid into a cement sheath or barrier may be predicted and/or modeled. Invasive fluids may comprise any of the chemically reactive or non-reactive species previously mentioned and may be introduced into a wellbore during an injection operation. Penetration of an invasive fluid into a cement is dependent on both time and concentration of the invasive fluid, its chemical identity, as well as the temperature and pressure conditions of the wellbore and cement composition of a cement. In a wellbore, temperature and pressure may vary along the wellbore’s profile, thereby causing penetration rate of the invasive fluids into an inner spatial region of a cement to vary at different injection zones or depth regions of a wellbore. Depth of penetration of an invasive fluid into a cement over time may be modeled using a number of modeling techniques and may, in some examples, account for varying penetration rates of the invasive fluid at different depth regions or injection zones along a wellbore’s profile. One example of a depth of penetration model is provided below, having the form:

Latex)] * time^a& (eq. 1) where DOP is a depth of penetration, VFwater is a volume fraction of water, C2S and C3S are mass averaged amounts of dicalcium silicate and tricalcium silicate of a cement blend respectively, FQ is a foam quality, PSD is a particle size distribution factor, such as the ratio of a full width half max and mode of a particle size distribution, Latex is a mass percent of an active amount of fluid loss polymer in the cement blend, time is a time of exposure to an invasive fluid, and ao, ai, a2, as, a4, as, and ae are constants determinable by any regression technique, error minimization technique, least squares fitting, curve-fitting technique, numerical methods, or the like.

[0024] A more general form of a depth of penetration model for calculating depth of penetration of an invasive fluid is provided below:

DOP = (%, a, t) (eq. 2) where DOP is a depth of penetration as a function of at least x, a, and t, where x is a vector comprising one or more representative quantities (e.g., concentrations) of a cement component in a cement blend, a is a vector comprising one or more determinable constants, and t is a time of exposure to an invasive fluid.

[0025] Another form of an operation to be used in a depth of penetration model for calculating depth of penetration is provided below:

DOP = (%, a, t, p, T, P) (eq. 3) where DOP is a depth of penetration as a function of at least x, a, t, and p where x is a vector comprising one or more representative quantities (e.g., concentrations) of a cement component in a cement blend, a is a vector comprising one or more determinable constants, t is a time of exposure to an invasive fluid, p is a vector comprising one or more measured, dimensional, or dimensionless quantities corresponding to a measured or correlated property of one or more of the cement components (e.g., of the blend), T is a temperature, and P is a pressure. It is noted that in one or more examples, T and/or P may be a function of depth (d), and that any of the mathematical expressions herein disclosed may be modified such that DOP is also a function of depth.

[0026] Another form of a depth of penetration model to be used in accordance with this disclosure is provided below:

where DOP is a depth of penetration, VFwater is a volume fraction of water in an original cement slurry (e.g., at the time of pouring), C2S and C3S are mass averaged amounts of dicalcium silicate and tricalcium silicate of a cement blend respectively, FQ is a foam quality factor, PSD is a ratio of a full width half max and mode of a particle size distribution, Latex is a mass percent of an active amount of fluid loss polymer in the cement blend, time is a time of exposure of a cement to an invasive fluid, E is an activation energy of a reaction, T is temperature, P is pressure, and aO, al, a2, a3, a4, a5, a6, and a7 are determinable constants determinable by any regression technique, error minimization technique, least squares fitting, curve-fitting technique, numerical method, or the like.

[0027] Additional or alternative model parameters to be used in a depth of penetration model operation may include, without limitation, permeability and/or porosity of a cement, mass averaged CaO and SiO2 content, particle size distribution (e.g., D30, D50, D70, or D90), concentration of light weight and/or heavy weight additives (e.g., beads), iron oxide content, concentration of inert materials, concentration of mechanical property modifiers, concentration of loss circulation materials (LCMs), and any combinations thereof. LCMs may include, for example, elastomer-based solids, coarse materials, angular materials, fibers, flakes, granular materials, bentonite, crystalline polymers, and the like. A D50 particle size distribution, referenced in an example above, indicates 50% of particles of a sample being above the D50 value, with the remaining 50% below the D50 value. In addition, a depth of penetration model may account for formation-specific properties, such as an estimated concentration of an invasive fluid in regions contacting the wellbore cement, permeability and/or porosity of a formation or region of a formation surrounding the wellbore, geologic composition of a formation or region of a formation, a pre-existing amount of an invasive fluid already present in a formation or region of a formation at a given time. Other parameters might include an initial depth of penetration, an injection condition, a geometric parameter of a cement sheath, and any combinations thereof.

[0028] As illustrated in workflow 100, an input to block 106 may comprise one or more injection conditions. Injection conditions may include, without limitation, volumetric flow rate of an injection fluid, composition of an injection fluid, concentration of one or more reactive and/or unreactive species in an injection fluid, temperature of an injection fluid, temperature of a wellbore, temperature of a formation, pressure of an injection fluid, pressure of a wellbore, pressure of a formation, pH of an injection fluid, and any combinations thereof. A volumetric flow rate may be, for example, from about 0.02 cubic meters per day to about 2500 cubic meters per day, or any ranges therebetween. Pressure may be, for example, from about 650 kilopascals to about 210 megapascals, or any ranges therebetween. In one or more examples, a specific injection condition may be used to select an appropriate depth of penetration model or may be integrated as a model parameter or set of model parameters in a given depth of penetration model. For example, a depth of penetration model may be designed for a particular application based on prespecified factors. Prespecified factors may include, for example, one or more geologic conditions of a formation. In cases where a depth of penetration model is selected based on a prespecified condition, selection may occur automatically or manually. For example, a particular depth of penetration model may be selected from a plurality of distinct depth of penetration models, with the selection being performed directly by an operator or programmatically, such as with a software or computer-implemented algorithm. In some examples, selection of a particular depth of penetration model may be alternatively or additionally based on a result of a wellbore state assessment as performed in block 104 and/or a known, estimated, or otherwise provided composition of a cement as determined in block 102.

[0029] It should be understood that the depth of penetration models herein described are exemplary. In one or more examples, a depth of penetration model may comprise a linear, multilinear, parabolic, exponential, derivative, integral, hyperbolic, trigonometric, Gaussian process regression, spline regression, or multi-variate adaptive regression spline model, or any combination thereof. Alternatively, a depth of penetration model may comprise or be substituted with a black box model, such as a machine learning model or other artificially intelligent algorithm without departing from the spirit and scope of the disclosure. Where used, a single machine learning model (e.g., end-to-end or for a single block in workflow 100), or a plurality of machine learning models (e.g., in series) may be trained using a single, or a plurality of training datasets. For example, a cement property dataset derived from a plurality of set cement samples may be used to generate a training dataset or may be otherwise used in a training dataset to train a machine learning model. Machine learning and/or artificially intelligent algorithms to be used in in a black box model may include, without limitation, a supervised, semi-supervised, unsupervised, and/or reinforced model, a binary classification model, a multiclass classification model, a regression models, decision trees, a random forest classifier, logistic regression, support vector machine algorithms (SVM), a Naive Bayes classifier, k-nearest neighbors (K-NN) algorithms, clustering, k-means clustering, a dimensionality reduction algorithm, a gradient boosting algorithm, a probabilistic classifier, the like, and any combination thereof. A variety of techniques may be used to fit a model to data to produce a depth of penetration model or otherwise carry out the intended function of a depth of penetration model.

[0030] In block 108, depth of penetration determined by a depth of penetration model in block 106 may be used to predict one or more properties of a chemically modified cement. Prediction of one or more properties may be performed using a cement property model. As with block 106, alternative techniques, models, and/or algorithms may be used in addition to or in substitution for a cement property model as would be readily apparent to one skilled in the art, including any of the techniques herein described.

[0031] Factors used in a cement property model when predicting properties of a chemically modified cement in block 106 may include, without limitation, volume fractions of chemically modified and chemically unmodified portions of a cement in a wellbore or region of a wellbore respectively, wellbore geometry, mechanical properties of a chemically unmodified cement, mechanical properties of a chemically modified cement, wellbore design factors, duration of exposure, environmental factors, wellbore conditions such as temperature and pressure, depth of a particular region, any interaction terms, statistical parameters, geometric parameters, error correction factors, and any combinations thereof. Geometric parameters may include, without limitation, volume, thickness, average radius, length, surface area, arc length, outer diameter, inner diameter, depth, or any other dimensional parameter associated with characterizing the shape of a wellbore or wellbore region. Other factors may include, without limitation, penetration depth determined in block 106, logging data, one or more results from a previous measurement, tabulated data corresponding to certain cement compositions, cement forming conditions recorded at the original time of cementing (e.g., thickening time, temperature, pressure, bottomhole conditions, any additives of supplementary materials used in a cement blend or slurry, etc.), specific surface area, water requirement, oxide content, silica content, lime content, calcium content, reactivity, and any combinations thereof. For example, these factors may be included in a cement property model as one or more model parameters of the cement property model, or a cement property model may be selected based on these factors. In the case where a cement property model is selected based on one or more of these factors, selection may be manual or automatic as with a depth of penetration model in block 106.

[0032] Material properties predicted in block 108 may include, without limitation, ultimate compressive strength (UCS), Young’s Modulus of elasticity (YM), tensile strength (TS), Poisson’s Ratio (PR), flexural strength, bulk modulus, shear modulus, and shear strength, as well as any other measured, dimensional, or dimensionless parameter associated with or correlated to a material, spatially varying, mechanical, or other property of a cement. The American Petroleum Institute (API) publishes API RP 10B-2 (Recommended Practice for Testing Well Cements), which outlines the standard methods testing of cement slurries and set cements to determine various cement physical properties. Material properties predicted in block 108 may include any of these cement physical properties. In addition, material properties may include static and/or dynamic properties. For the purposes of this disclosure, static properties refer to physical properties which are measured or determined by destructive testing. Examples of destructive testing may include crushing tests (in accordance with ASTM D7012-10) in the presence or absence of confined pressure, pull out tests (in accordance with ASTM C900-19), hardness tests (in accordance with ASTM D785 and/or ASTEM E10), and scratch resistance tests in accordance with (ISO 4586). Dynamic properties may refer to physical properties which are measured or determined by nondestructive testing. Examples of nondestructive testing may include testing methods using sonic or ultrasonic waves in compression and/or shear mode, ultrasonic pulse velocity methods, acoustic methods, and flat-jack methods.

[0033] One example of a cement property model has the form:

where CPmodified is an overall cement property of a chemically modified cement, VFmodified is a volume fraction of a chemically modified portion in a chemically modified cement, CPcontroi is a measured or estimated cement property of a chemically unmodified cement, and CPmodified-portion is a cement property of the modified portion of a chemically modified cement.

[0034] Another example of a cement property model has the form:

Interaction (eq. 7) where MP is an overall material property of a chemically modified cement, VFmodified is a volume fraction of a chemically modified portion in a chemically modified cement, MPcontroi is a measured material property of a chemically unmodified cement, MPmodified is a material property of the modified portion of a chemically modified cement, and where Interaction is an interaction term. The interaction term may account for imbalances attributed to nonlinear relationships between modified or unmodified portions of a chemically modified cement on an overall material property.

[0035] Another example of a cement property model has the form:

where CP is an overall cement property of a chemically modified cement, VFmodified is a volume fraction of a chemically modified portion in a chemically modified cement, CPcontroi is a measured cement property of a chemically unmodified cement, and CPmodified is a cement property of the modified portion of a chemically modified cement.

[0036] Another example of a cement property model has the form:

where CP is an overall material property of a chemically modified cement, VFmodified is a volume fraction of a chemically modified portion in a chemically modified cement, CPcontroi is a measured or estimated material property of a chemically unmodified cement, and CPmodified is a material property of the modified portion of a chemically modified cement, and where Interaction is an interaction term.

[0037] Additional model parameters which may be included in or integrated into one or more operations used in a cement property model include, without limitation, shape, or geometry of a cement. For example, equation (10) shows how an assumption of a cylindrical geometry of a cement sheath would be integrated into a cement property model operation. It should be understood that alternative geometries, including simple (e.g., annular) as well as more complex or nonconventional geometries may be used in accordance with one or more aspects of the present disclosure, including with a cement property model. Particularly, a VFmodified model parameter in a cement property model may have the form:

where VFmodified is a volume fraction of a chemically modified portion of a chemically modified cement, DOP is a depth of penetration, R is a radius of a cylinder, r is a radius of a cylinder without an outer penetrated portion, and L is a length of the cylinder. Alternatively, VFmodified may be adjusted and/or adapted to other geometries to suit a particular wellbore geometry. It is noted that DOP may be determinable by a depth of penetration model or as described in this disclosure’s discussion of block 106.

[0038] Non-limiting examples of various geometries which may be used when determining one or more model parameters (e.g., VFmodified) of a cement property model, or used when selecting a cement property model may include any of a cylindrical geometry, an oblong cylinder geometry, a telescoping cylinder geometry, an oblique cylinder geometry, a hollow cylinder geometry, an annular geometry, a nested cylinder geometry, an n^th-order prism geometry, the like, or any combinations thereof. In one or more examples, a more sophisticated wellbore-specific geometry may be used in a cement property model. For example, a three-dimensional image of one or more regions of a wellbore, up to and including large stretches or an entire length of the wellbore, may be generated and used in a cement property model and used to precisely calculate one or more interspatial properties of one or more regions of a cement sheath or barrier. A large stretch may be greater than about 20 meters, greater than about 50 meters, or greater than about 100 meters. Three-dimensional imaging of a wellbore, casing, cement sheath, cement barrier, and/or surrounding formation may be performed using imaging technique including, without limitation, measurements by an ultrasonic imaging tool, sonic imaging tool, EM imaging tool, optical imaging tool, or any alternative imaging tool as would be readily apparent to one skilled in the art. In one or more examples, three-dimensional imaging of a wellbore allows for accurate determination of VFmodified, thereby affording a high degree of accuracy to an output of a cement property model. [0039] Other model parameters which may be included with, integrated into, or used to select a cement property model may include, without limitation, design factors, duration of exposure, and environmental factors. Design factors may comprise one or more original design features of a wellbore, such as an original permeability of a cement, an original amount (e.g., concentration) of one or more cement components present in a cement, an original chemical resistance to invasion by an invasive chemical species or invasive fluid (e.g., carbonation resistance), an original material property. In addition, original design factors may comprise any of the model parameters previously mentioned with respect to the depth of penetration model. Duration of exposure may comprise an amount of time elapse during which a cement is exposed to an invasive fluid. For example, a duration of exposure may be at least 1 day, at least 50 days, at least 100 days, at least 1,000 days, or any ranges therebetween. Environmental factors may comprise, to use non-limiting examples, a wellbore condition, such as temperature or pressure during a time of exposure, a type of chemical species present in an environment, solubility/dissolution of a chemical species, an amount of moisture in the formation and/or in an injection fluid, and any combinations thereof.

[0040] A cement property model in accordance with the present disclosure may alternatively, or additionally, include or be derived from a model having the form:

where CPmodified is a material property of a chemically modified portion of a chemically modified cement, CPcontroi is a measured or estimated material property of a chemically unmodified cement, Design is a variable or vector representing one or more cement composition factors, Duration is a time of exposure to an invasive fluid, and Environment is a variable or vector representing one or more environmental factors. For example, Environment may comprise indicators corresponding to an amount of a particular phase of a fluid present in the formation and/or an injection fluid. For example, Environment may comprise an indicator which represents if a fluid is in a dry state, a moisture saturated state, or a water dissolved state. A cement property model operation as shown above may be used to model a ratio of a material property of a chemically modified portion to a control (e.g., chemically unmodified portion). This quantity may be used to relate a cement property to a design factor, duration of exposure, and/or environment factor.

[0041] In one or more examples, a cement property dataset may be used in determining a material property of a cement. A cement property dataset may comprise one or more measurements by a laboratory technique. In some examples, a plurality of cement slurries may be prepared, with cement slurries comprising cement and a volume fraction of water. Such slurries may comprise any suitable composition, including any of the cementitious components, resins, and/or non- cementitious components previously described. Once prepared, such cement slurries may be allowed to cure, and form set cement samples. In some examples, cured set cement samples may be exposed to one or more invasive species. Material properties of set cement samples may be obtained, for example, according to any of the destructive and/or nondestructive techniques herein described. Alternatively, by any of the techniques described by U.S. Patent Application No. 18/116,224, the entirety of which is incorporated herein by reference. A cement property dataset may be generated from these obtained material properties and used to predict cement properties of a cement, such as in block 108 of workflow 100 using a numerical simulator.

[0042] In block 110, integrity analysis of a wellbore may be performed. An “integrity analysis” herein refers to an analysis of the response of near wellbore materials (rock, cement sheath, and casing, for example) to the pressure, temperature, and/or lithostatic loads exerted on them before, during, and/or after injection of an injection fluid. An integrity analysis may be performed using one or more of the predicted material properties modeled in block 108. In one or more examples, an integrity analysis of a wellbore may account for shear stresses applied at one or more regions or depths of a wellbore, cement sheath, cement barrier, bonding, casing, or regions near a wellbore. For a chemically modified cement, there may exist a stress gradient at an interface between a chemically modified and chemically unmodified portion. For example, stiffness of a chemically modified portion may be increased with respect to a chemically unmodified portion, thereby resulting in a greater sheer stress at the interface and/or throughout the chemically modified portion. This elevated shear stress state can result in an increased risk of failure if a shear strength of the chemically modified portion is insufficient. For example, if chemical modification to a portion of a cement causes the portion to lose tensile strength, become brittle, or otherwise results in a reduced ability to withstand a shear force applied thereto, the chemically modified portion may fracture when exposed to shear stresses exerted thereon by a formation, thereby weakening a cement sheath or barrier, and compromising its ability to seal out an injected fluid. This weakening and/or fracturing of a cement sheath or barrier may allow, over time, additional penetration of an invasive fluid into previously unmodified regions of a cement.

[0043] Integrity analysis in block 110 may be performed by creating a model of a wellbore, cement sheath, casing, and/or regions surrounding a wellbore and/or by performing calculations at a plurality of depths and/or azimuths of the wellbore. For example, a model used in block 110 may have been created and/or modified in blocks 106 and/or block 108 or may be generated and/or created in block 110. A model used in block 110 may be a 3D model, such as a mesh model, for example. As previously discussed, modeling of a wellbore, wellbore casing, cement sheath, cement barrier, and/or regions surrounding a wellbore may be preceded by any of the imaging or sensing techniques herein described. Preexisting logs may also be used to generate and/or incorporated into a model. Alternatively, or additionally, integrity analysis in block 110 may be performed using a numerical simulator. In one or more examples, a numerical simulator may be a computer-implemented algorithm for performing numerical operations at a plurality of locations (e.g., depths, azimuths, custom regions) of a wellbore. For example, a numerical simulator used in an integrity analysis in block 110 may model one or more material properties of a cement disposed in a wellbore exposed to an invasive fluid and experiencing a load exerted thereon by a surrounding formation. In one or more examples, a numerical simulator may perform operations wherein a comparison between modeled properties and failure properties are made, to be discussed later in detail. For example, a numerical simulator may repeat calculations at one or more depths, azimuths, and/or regions at regular time intervals over the course of, for example, a prespecified amount of time. These calculations may compare, for example, a maximum shear stress, maximum shear strength, maximum tensile strength, maximum interface stress, and/or maximum interface strength to one or more failure properties. A maximum value may be a maximum specified threshold which a material would ideally be prevented from exceeding. A prespecified amount of time may be from about 1 day to about 100 years. Alternatively, from about 1 day to about 25 years, about 25 years to about 50 years, about 50 years to about 100 years, and any ranges therebetween.

[0044] Following an injection operation, concentration of an injection fluid immediately surrounding an injection zone would diminish overtime as the fluid diffuses throughout permeable regions of the formation. Time-dependent concentration of an invasive fluid in a formation may also be accounted for by a numerical simulator in block 110. Length of time intervals within a specified timespan may vary, depending on the desired resolution of an output of a numerical simulator. For example, a numerical simulator may produce an output at individual time intervals within a prespecified amount of time. In one or more examples, a numerical simulator may perform a calculation for one or more depths, azimuths, and/or regions at regular or irregular time intervals until a numerical simulator produces an output corresponding to mechanical failure of one or more regions of a wellbore. Mechanical failure may be an isolated failure of a single region, or a generalized failure across an entire length or significant stretch of a wellbore.

[0045] Integrity analysis performed in block 110 may comprise or be derived from a prediction of a stress-strain response. Predicting of stress-strain response may be performed at a single or a plurality of depths along the length of a wellbore. Outputs of an integrity analysis may comprise material stresses, material temperatures, and/or material deformations. For example, a material stress may be a shear stress applied at an interface between chemically modified and chemically unmodified portions of a composite cement in a cement sheath, or a shear stress applied to an outer surface of a cement sheath by a formation, or a shear stress applied to a bond between a cement sheath and casing. Likewise, material deformation may comprise elastic and/or inelastic deformation of a portion of a cement sheath, a bond between cement sheath and casing, a bond between a cement sheath and a formation, and the like. Likewise, a material temperature may be the temperature of a portion of a cement sheath or cement barrier, a temperature of the formation at a given depth, a temperature of a casing, and the like.

[0046] As mentioned, in block 110, modeling of an injection well may be performed by inputting in-situ loads and material properties into a model. These in-situ loads may be known beforehand or may be determined by a variety of suitable techniques including, without limitation, sonic imaging, borehole breakout analysis, earthquake focal mechanisms, in-situ stress measurements, anisotropy analysis, acoustic emissions monitoring, rock mechanics testing, geophysical surveying, seismic profiling, electrical resistivity imaging, magnetic resonance imaging, acoustic logging, and the like. In one or more examples, a load input into a model or numerical simulator in block 110 may comprise a pressure load, a temperature load, gravity load, an in-situ rock stress, overburden, lithostatic load or pressure, differential lithostatic pressure (e.g., due to variations in thickness or density of overlying rock layers or uneven distribution of pressure in a formation), induced stresses or residual stresses (e.g., as a result of drilling the wellbore), tectonic stress, geothermal stress, thermal expansion, or the like. In one or more examples, contiguous materials may have differing coefficients of thermal expansion, thereby resulting in material stress at the interface between contiguous materials when temperature fluctuates. An “applied shear stress” may be such an in-situ load, be it known beforehand, measured, or determined inferentially, and which may be input into a numerical simulator. In some examples, operations performed by a numerical simulator may be performed by electronic hardware shown and described in FIG. 8.

[0047] In block 112, an evaluation of the risk of failure may be performed. An output from an integrity analysis in block 110 may be used to evaluate the risk of failure. Risk evaluation in block 112 may include evaluating the stresses calculated in block 110 with respect to one or more failure properties.

[0048] As previously mentioned, near wellbore materials may respond to pressure, temperature, and/or lithostatic loads. Stresses resulting from these loads may be evaluated with respect to (e.g., compared to) one or more failure properties to assess the risk of failure of the cement sheath. A failure property is a mechanical property of a cement wherein the cement may be susceptible to undue deformation compromising its ability to act as a barrier between fluids stored behind the barrier. These failure properties of a particular cement composition may be experimentally determined or estimated. Estimation of a particular failure property may, in some examples, be based on experimental data derived from similar cement compositions. A “similar cement composition” herein refers to a cement composition having an identical or nearly identical composition. A failure property may comprise or be derived from, without limitation, tensile strength, ultimate compressive strength, elastic modulus, yield strength, ductility, toughness, or the like.

[0049] A failure property may also be known beforehand or calculated based on cement composition. In one or more examples, an integrity requirement may be specified or predetermined such that an injection operation in block 116 is performed if the integrity requirement is met. For example, an integrity requirement may comprise an engineering parameter, such as a value corresponding to a maximum allowable amount of deformation or strain of a material or bond between materials. In other examples, such an engineering parameter may not be a preset or predetermined value, but may be determined based on measured, calculated, and/or known material properties of the materials, such as a material property determined in block 108. In one or more examples, an output of an evaluation performed in block 112 may comprise a probability, such as a probability of failure of a cement. If risk of failure of a cement falls within an acceptable range, workflow 100 may indicate that it is safe to perform an injection operation in the wellbore. As with operations performed in block 110, operations performed in block 112 may be performed by electronic hardware shown and described in FIG. 8.

[0050] If it is determined while evaluating in block 112 that a wellbore can tolerate an injection operation having one or more injection conditions as specified in block 106, workflow 100 may proceed to block 116. In some examples, workflow 100 may proceed to block 118 if it is determined that a wellbore cannot tolerate an injection operation. In block 118, one or more injection conditions may be modified. Modification of an injection condition may be performed automatically or manually and may be based on an integrity analysis performed in block 112 or on any of the inputs and/or outputs of any models or operations used in any of the previous blocks in workflow 100. Upon modifying one or more injection conditions, workflow 100 may return back to block 106. Workflow 100 may alternatively return back to any of blocks 108, 110, and/or 112 after block 118. In one or more examples, workflow 100 may result in a determination that no storage operation is recommendable, and workflow 100 may terminate. Returning to a previous block after block 118 may allow workflow 100 to generate new data corresponding to modified injection conditions. New data may comprise an updated depth of penetration, updated material properties, an updated numerical or three-dimensional model, as well as an updated integrity analysis. Repeating any of blocks 106, 108, 110, and/or 112 may occur as many times as needed until an integrity requirement is obtained, or an output of an integrity analysis optimized. In one or more examples, modifying a wellbore condition in block 114 and repeating blocks 106, 108, 110, and/or 112 may be performed until a minimum or maximum value is reached. A minimum or maximum value may correspond to an engineering parameter representing, for example, a sum total deformation or strain of materials evaluated during modeling of an injection well in block 110, or a deformation or strain of materials evaluated at one or more specific regions (e.g., region of interest). An engineering parameter may comprise or be based on one or more statistical parameters (e.g., mean, median, mode, standard deviation, etc.) representing one or more material attributes of the wellbore, cement sheath, cement barrier, materials surrounding the wellbore, and/or one or more selected regions thereof. Material attributes may comprise or be associated with (e.g., via correlations) to any of the previously mentioned measured, static, dynamic, predicted, or other dimensional or dimensionless variables herein described, such as a material property.

[0051] If it is determined in workflow 100 that a wellbore may tolerate an injection operation according to one or more injection conditions, workflow 100 may proceed to block 116. Block 116 may comprise an injection operation. An injection operation performed in block 116 is described in more detail in later discussion of FIG. 7 and may generally involve: an injection fluid; a depleted wellbore, porous formation, or salt cavern; a wellhead; and surface equipment. Injection fluid may comprise any of the invasive fluids previously described, as well as supplementary injection materials such as carrier fluids and/or additives. For example, carrier fluids and/or additives may be included in an injection fluid to stabilize a phase or condition of an invasive fluid forming a part of an injection fluid. Injection of an injection fluid in block 116 may be performed at any of the injection conditions specified in another block in workflow 100.

[0052] FIG. 2A shows a parity plot comparing predicted and measured depths of penetration of invasive fluids. The predicted values were calculated using equation 1, shown in the foregoing. The invasive fluids used were carbonic CO2 (carbonic acid), dry CO2, and wet CO2. The data shown in FIG. 2A represent six different cement formulations, tested at the same temperature and pressure.

[0053] FIG. 2B shows a parity plot comparing predicted and measured depths of penetration of invasive fluids. The predicted values were calculated using equation 4, shown in the foregoing. The data shown in FIG. 2B represent a single cement formula, tested at two temperature/pressure conditions. As shown in both FIG. 2A and 2B, the parity plots show a relatively good fit between the measured (experimental) and predicted values.

[0054] FIG. 3 A shows a parity plot comparing predicted and measured material properties for different types of cement compositions exposed under varying environments and for different durations (e.g., exposure time). The material property in FIG. 3A is an ultimate compressive strength. An R2 value was determined to be 0.92, with a p-value of less than 0.0001.

[0055] FIG. 3B shows a parity plot comparing predicted and measured material properties for different types of cement compositions exposed under varying environments and different durations. The material property in FIG. 3B is Young’s Modulus of Elasticity. An R2 value was determined to be 0.96, with a p-value of less than 0.0001.

[0056] FIG. 4A shows a mesh model of a wellbore 400 in accordance with certain examples of the present disclosure. As illustrated, wellbore 400 is disposed in a subterranean formation 402 and comprises a casing 404 and a cement sheath 406 bonded to the casing. As illustrated, cement sheath 406 may be disposed between casing 404 and rock. Upon performing an injection operation, an invasive fluid may permeate through rock and eventually into an outer portion of cement sheath 406 to form a chemically modified portion 408, thereby altering one or more material properties thereof. Chemically unmodified portion 410 may be disposed between chemically modified portion and casing. Chemically unmodified portion 410 and/or interface 412 between chemically modified portion 408 and chemically unmodified portion 410 may have a reduced tolerance to shear stress applied to cement sheath 406 by rock disposed in subterranean formation 402. This may compromise the ability of wellbore 400 to seal off injected fluids from migrating back to a terrestrial surface after an injection operation. As illustrated, a mesh model may be used in block 110 to model wellbore 400 for performing an integrity analysis. A mesh model may include one or more grid lines 414, with grid line 414 representing a contour, an azimuth, axis, or plane of a particular region. Grid lines 414 may provide a basis for calculating shear-strain response and/or for performing one or more operations carried out in block 112.

[0057] FIG. 4B is a close-up view of a mesh model of a particular region of a wellbore 400. As illustrated, injection fluid 416 may be disposed within casing 404 during an injection operation, from which an invasive fluid may be introduced into a subterranean formation comprising rock. Depending on injection conditions, the identity of a cement making up cement sheath 406, and/or one or more other factors such as pressure or temperature of a wellbore depth/region, the extent that an injection fluid 416 may penetrate a cement sheath 406 or barrier to form chemically modified portion 408 may vary. As illustrated in both FIGS. 4A and 4B, the geometry of a wellbore 400 may be cylindrical or approximately cylindrical. As previously discussed, geometry of wellbore 400 in a mesh model may be more precisely tuned to fit the actual dimensions of wellbore 400 using one or more three-dimensional imaging techniques with an imaging tool, logging data, or the like, or may alternatively comprise any suitable geometry for approximating the wellbore. This may allow for more accurate predictions of material properties of cement sheath 406.

[0058] FIG. 5 is a plot illustrating shear stress as a function of radial location in cement sheath 406 (e.g., referring to FIGS. 4 A and 4B). As illustrated, depending on depth of penetration, a shear stress experienced by a chemically modified portion 408 and chemically unmodified portion 410 may vary. Spike 506 is observed at interface 412. This increased shear stress experienced by chemically modified portion 408 and induced by an invasive fluid may compromise the ability of wellbore 400 to seal off injected fluids from migrating back to a terrestrial surface after an injection operation, especially if interface 412 creeps too close to casing 404. Interface 412 may be disposed at an approximate radial location of between about 0 inches to about 48 inches. Alternatively, from about 0 inches to about 5 inches, about 5 inches to about 10 inches about 10 inches to about 12 inches, about 12 inches to about 18 inches, about 18 inches to about 24 inches, about 24 inches to about 32 inches, about 32 inches to about 48 inches, or any ranges therebetween.

[0059] FIG. 6 is a cross sectional view of a chemically modified cement plug sample 600. In FIG. 6, the darker inner core 602 is chemically unmodified (e.g., uncarbonated) and the outer lighter shell 604 is chemically modified (e.g., carbonated). As illustrated, a depth of penetration 610 is observed at the outer lighter shell 604, having an invasion distance, or depth of penetration 610 into the cement plug sample 600. Darker inner core 602 may comprise chemically unmodified portion 410 (e.g., referring to FIGS 4A and 4B) and is undisturbed by an injection fluid 416. As illustrated and discussed in previous figures, chemical modification to a portion of a cement may result in reduced ability to counteract shear forces applied to a cement sheath, thereby limiting the wellbore’s ability to effectively seal out an injected fluid from a wellbore.

[0060] FIG. 7 illustrates injection of injection fluid 416 into an injection zone 704 during an injection operation in accordance with certain examples. Injection fluid 416 may comprise any of the invasive fluids herein described. As illustrated, injection zone 704 may be disposed in a lower region of wellbore 400, for example, below a caprock 708 or deep below a surface 712. Deep below surface 712 may be, for example, at a depth below 800 meters, below 1,000 meters, below 2,000 meters, or any ranges therebetween, below a terrestrial surface. Surface equipment 702 may be disposed on a surface 712 and may include one or more trucks, pumps, compressors, and/or tanks. Surface 712 may comprise a terrestrial surface, such as a land surface or a subsea terrestrial surface disposed below a body of water. Surface equipment 702 may be configured to deliver an injection fluid 416 to wellbore 400 via wellhead 724 fluidically coupled to wellbore 400 during an injection operation. Injection fluid 416 may be in a solid, gas, liquid, or vapor phase, or a supercritical state, or any combination thereof. The pressure may be sufficient to cause an injection fluid 416 to invade an injection zone 704 and permeate a permeable zone 714 of a subterranean formation 700. Caprock 708 may comprise an impermeable rock overlaid above permeable zone 714. Injection zone 704 may be permeable and/or porous. Permeable zone 714 and/or injection zone 704 may form a part of a depleted oil reservoir characterized by high porosity, low pore pressure gradient, high permeability, or as having undergone a reduction in pore pressure. Alternatively, permeable zone 714 and/or injection zone 704 may form a part of a salt cavern, or any formation suitable for an injection operation. A well barrier 710 may overlap with a caprock 708 and/or with the injection zone 704. Alternatively, well barrier 710 may overlap with injection zone 704 and a shoe of a previous casing or with a liner hanger assembly disposed at any depth within wellbore 400. More generally, well barrier 710 may simple be disposed in a subterranean formation 700. As illustrated, well barrier 710 may comprise casing 404 bonded to a cement sheath 406 (e.g., referring to FIGS. 4 A and 4B), the cement sheath 406 comprising a wellbore cement which, over time, may come to comprise both chemically modified portion 408 and chemically unmodified portion 410 as injection fluid 416 travels from injection zone 704 through permeable zone 714 and eventually migrates into a cement matrix of well barrier 710. After a volume of injection fluid 416 is allowed to invade permeable zone 714, injection zone 704 may be sealed off from surface 712 to prevent injection fluid 416 from escaping out of wellbore 400.

[0061] FIG. 8 illustrates a system 800 including a logging tool 812. As previously mentioned, assessment of a wellbore state may be performed in block 104 with logging tool 812. Logging tool 812 may be an acoustic logging tool, an ultrasonic logging tool, a pipe inspection tool, an MRI logging tool, an EM logging tool, an optical measurement tool, or the like. Logging tool 812 may comprise one or more downhole transmitters 822 and downhole receivers 824. Downhole receivers 824 may comprise a sensor. In operation, logging with logging tool 812 may be performed by lowering logging tool 812 into wellbore 400 on a conveyance 830. Measurements may be taken by logging tool 812 to survey one or more (e.g., one, two, three, or four) layers of casing 404, well barrier 710, a bond between well barrier 710, one or more regions of subterranean formation 700, and/or one or more regions at or near wellbore 400. Measurement may be conveyed via telemetry to surface equipment 702 (e.g., referring to FIG. 7), or stored for future reference in an internal memory disposed in logging tool 812. Surface equipment 702 may comprise a display and storage unit 814 comprising a processing device 802 such as, for example, computer 810, monitor 804, keyboard 806, and internal memory 808. Processing device 802 may be configured to perform numeric simulation with a numerical simulator as previously described, or otherwise used to predict depth of penetration, one or more material properties, or the like. Telemetry may comprise an electromagnetic signal, an optical signal (e.g., via a fiber optic cable), a compression wave (e.g., pulse telemetry) through a fluid medium, a radio signal, or the like. Measurements may inform an operator or computer algorithm regarding one or more parameters associated with a wellbore state, which may be used in workflow 100 (e.g., referring to FIG. 1) to, for example, establish a condition of a casing. These one or more parameters may comprise an extent of corrosion to a casing, sonic attenuation, one or more raw sensor measurements, cement bond, and/or cement, depletion state of a reservoir, permeability and/or porosity of a region in subterranean formation 700.

[0062] Accordingly, the present disclosure may provide methods and systems for evaluating a wellbore which may include any of the various features disclosed herein, including one or more of the following statements.

[0063] Statement 1 : A method comprising: providing a composition for a cement disposed in a wellbore; selecting injection conditions for an invasive fluid for an injection or storage operation; predicting a depth of penetration of the invasive fluid into the cement with a depth of penetration model based at least in part on the injection conditions and the composition for the cement; predicting a material property of the cement with a cement property model based at least in part on the predicted depth of penetration; performing an integrity analysis based at least in part on the predicted material property; performing the injection or storage operation in the wellbore based at least in part on the integrity analysis.

[0064] Statement 2: The method of statement 1, wherein the injection conditions comprise at least one condition selected from the group consisting of a volumetric flow rate, temperature, pressure, volume, phase, concentration, and any combinations thereof.

[0065] Statement 3: The method of any of the preceding statements, further comprising modifying at least one of the injection conditions based at least in part on the integrity analysis.

[0066] Statement 4: The method of any of the preceding statements, further comprising repeating the steps of predicting a depth of penetration, predicting a material property, and performing an integrity analysis until an output of the integrity analysis satisfies a predetermined criteria.

[0067] Statement 5: The method of any of the preceding statements, further comprising disposing a logging tool in the wellbore and performing a wellbore casing assessment prior to the injection or storage operation, wherein the injection or storage operation is performed if a sonic attenuation of the wellbore casing is below a threshold value.

[0068] Statement 6: The method of any of the preceding statements, further comprising specifying a timespan, wherein the predicted depth of penetration is determined based at least in part on an exposure of the cement to the invasive fluid during the specified timespan.

[0069] Statement 7: The method of any of the preceding statements, wherein predicting the material property of the cement is repeated using the cement property model for a plurality of time intervals within the specified timespan.

[0070] Statement 8: The method of any of the preceding statements, wherein the injection or storage operation comprises injecting an injection fluid comprising the invasive fluid into a permeable zone of a subterranean formation, the injecting conforming to the selected injection conditions.

[0071] Statement 9: The method of any of the preceding statements, wherein the integrity analysis is performed with a numerical simulator, wherein the injection or storage operation is performed if an output of the numerical simulator meets a predetermined criteria.

[0072] Statement 10: The method of any of the preceding statements, wherein an output of the numerical simulator comprises strain at each of a plurality of depths and azimuths at or near the wellbore.

[0073] Statement 11 : The method of any of the preceding statements, wherein the integrity analysis comprises providing a maximum material property of the cement and comparing the maximum material property to the predicted material property.

[0074] Statement 12: The method of any of the preceding statements, wherein the integrity analysis comprises comparing a load and a failure property of the cement.

[0075] Statement 13: The method of any of the preceding statements, wherein the integrity analysis comprises comparing, for a plurality of regions at or near the wellbore, a maximum shear stress and an applied shear stress.

[0076] Statement 14: The method of any of the preceding statements, wherein the depth of penetration model, the cement property model, or both are associated with at least one technique selected from the group consisting of a supervised machine learning algorithm, a semi-supervised machine learning algorithm, an unsupervised machine learning algorithm, a reinforced machine learning model, a binary classification model, a multiclass classification model, a regression models, decision trees, a random forest classifier, logistic regression, support vector machine algorithms (SVM), a Naive Bayes classifier, a k-nearest neighbors (K-NN) algorithm, clustering, k-means clustering, a dimensionality reduction algorithm, a gradient boosting algorithm, a probabilistic classifier, and any combinations thereof.

[0077] Statement 15: The method of any of the preceding statements, wherein the depth of penetration model has the form: DOP = f(x, a, t) where DOP is the depth of penetration as a function of at least x, a, and t, where x is a variable or a vector comprising one or more concentrations or amounts of a cement component in the cement, a is a variable or a vector comprising one or more determinable constants, and t is an exposure time.

[0078] Statement 16: The method of any of the preceding statements, wherein the depth of penetration model has the form: DOP = [a₀ + (a_x

where DOP is the depth of penetration, VFwater is a volume fraction of water, C2S and C3S are mass averaged amounts of dicalcium silicate and tricalcium silicate in the cement respectively, FQ is a foam quality factor, PSD is a particle size distribution factor, Latex is a mass percent of an active amount of fluid loss polymer in the cement, time is the exposure time, E is an activation energy, T is a temperature, P is a pressure, and aO, al, a2, a3, a4, a5, a6, and a7 are one or more determinable constants.

[0079] Statement 17: The method of any of the preceding statements, wherein the cement property model has the form: CP = f (V F_modified, C P_controi, C P_modified) where CP is a material property of a chemically modified cement, VFmodiiied is a volume fraction of a chemically modified portion in a chemically modified cement, CPcontroi is a material property of a chemically unmodified portion of a cement, and CPmodiiied is a material property of a modified portion of a chemically modified cement.

[0080] Statement 18: The method of any of the preceding statements, wherein the predicting of the material property involves use of a function having the form: ^CPmodlf^ied = P control f (Design, Duration, Environment) where Design is a variable or vector representing one or more wellbore design factors, Duration is an exposure time, and Environment is a variable or vector representing one or more environmental factors.

[0081] Statement 19: A method of evaluating a wellbore comprising: preparing a plurality of cement slurries, wherein the plurality of cement slurries each comprise a cement and volume fraction of water; curing the plurality of cement slurries to form a plurality of set cement samples; exposing the plurality of set cement samples to an invasive fluid; allowing the invasive fluid to at least partially modify the plurality of set cement samples to form a plurality of chemically modified cement samples; measuring a cement property of each of the plurality of chemically modified cement samples to generate a cement property dataset; predicting a cement property of a cement exposed for a period of time to an invasive fluid based at least in part on the cement property dataset; and inputting the predicted cement property and one or more loads into a numerical simulator for modeling regions at or near the wellbore; and performing an integrity analysis of the cement based at least in part on an output of the numerical simulator.

[0082] Statement 20: The method of any of the preceding statements, wherein an output of the numerical simulator comprises strain determined at an interface between a carbonated portion and an uncarbonated portion of the cement.

[0083] 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 injection fluids downhole, any pumps, compressors, or motors (e.g., topside or downhole) used to drive the injection fluids into motion, any valves or related joints used to regulate the pressure or flow rate of the injection fluids, and any sensors (i.e., pressure, temperature, flow rate, etc.), gauges, and/or combinations thereof, and the like. The injection fluids may also directly or indirectly affect any mixing hoppers and retention pits and their assorted variations.

[0084] 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.

[0085] 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. [0086] 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. If there 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.

Claims

CLAIMS What is claimed is:

1. A method comprising: providing a composition for a cement disposed in a wellbore; selecting injection conditions for an invasive fluid for an injection or storage operation; predicting a depth of penetration of the invasive fluid into the cement with a depth of penetration model based at least in part on the injection conditions and the composition for the cement; predicting a material property of the cement with a cement property model based at least in part on the predicted depth of penetration; performing an integrity analysis based at least in part on the predicted material property; and performing the injection or storage operation in the wellbore based at least in part on the integrity analysis.

2. The method of claim 1, wherein the injection conditions comprise at least one condition selected from the group consisting of a volumetric flow rate, temperature, pressure, volume, phase, concentration, and any combinations thereof.

3. The method of claim 2, further comprising modifying at least one of the injection conditions based at least in part on the integrity analysis.

4. The method of claim 2, further comprising repeating the steps of predicting a depth of penetration, predicting a material property, and performing an integrity analysis until an output of the integrity analysis satisfies a predetermined criteria.

5. The method of claim 2, further comprising disposing a logging tool in the wellbore and performing a wellbore casing assessment prior to the injection or storage operation, wherein the injection or storage operation is performed if a sonic attenuation of the wellbore casing is below a threshold value.

6. The method of claim 1, further comprising specifying a timespan, wherein the predicted depth of penetration is determined based at least in part on an exposure of the cement to the invasive fluid during the specified timespan.

7. The method of claim 6, wherein predicting the material property of the cement is repeated using the cement property model for a plurality of time intervals within the specified timespan.

8. The method of claim 1, wherein the injection or storage operation comprises injecting an injection fluid comprising the invasive fluid into a permeable zone of a subterranean formation, the injecting conforming to the selected injection conditions.

9. The method of claim 1, wherein the integrity analysis is performed with a numerical simulator, wherein the injection or storage operation is performed if an output of the numerical simulator meets a predetermined criteria.

10. The method of claim 9, wherein the output of the numerical simulator comprises strain at each of a plurality of depths and azimuths at or near the wellbore.

11. The method of claim 1, wherein the integrity analysis comprises providing a maximum material property of the cement and comparing the maximum material property to the predicted material property.

12. The method of claim 1, wherein the integrity analysis comprises comparing a load and a failure property of the cement.

13. The method of claim 1, wherein the integrity analysis comprises comparing, for a plurality of regions at or near the wellbore, a maximum shear stress and an applied shear stress.

14. The method of claim 1, wherein the depth of penetration model, the cement property model, or both comprise at least one algorithm selected from the group consisting of a supervised machine learning algorithm, a semi-supervised machine learning algorithm, an unsupervised machine learning algorithm, a reinforced machine learning model, a binary classification model, a multiclass classification model, a regression models, decision trees, a random forest classifier, logistic regression, support vector machine algorithms (SVM), a Naive Bayes classifier, a k- nearest neighbors (K-NN) algorithm, clustering, k-means clustering, a dimensionality reduction algorithm, a gradient boosting algorithm, a probabilistic classifier, and any combinations thereof.

15. The method of claim 1, wherein the depth of penetration model has the form:

DOP = (%, a, t) where DOP is the depth of penetration as a function of at least x, a, and t, where x is a variable or a vector comprising one or more concentrations or amounts of a cement component in the cement, a is a variable or a vector comprising one or more determinable constants, and t is an exposure time.

16. The method of claim 1, wherein the depth of penetration model has the form:

17. The method of claim 1, wherein the cement property model has the form:

where CP is a material property of a chemically modified cement, VFmodiiied is a volume fraction of a chemically modified portion in a chemically modified cement, CPcontroi is a material property of a chemically unmodified portion of a cement, and CPmodiiied is a material property of a modified portion of a chemically modified cement.

18. The method of claim 17, wherein the predicting of the material property involves use of a function having the form:

where Design is a variable or vector representing one or more wellbore design factors, Duration is an exposure time, and Environment is a variable or vector representing one or more environmental factors.

19. A method of evaluating a wellbore comprising: preparing a plurality of cement slurries, wherein the plurality of cement slurries each comprise a cement and volume fraction of water; curing the plurality of cement slurries to form a plurality of set cement samples; exposing the plurality of set cement samples to an invasive fluid; allowing the invasive fluid to at least partially modify the plurality of set cement samples to form a plurality of chemically modified cement samples; measuring a cement property of each of the plurality of chemically modified cement samples to generate a cement property dataset; predicting a cement property of a cement exposed for a period of time to an invasive fluid based at least in part on the cement property dataset; and inputting the predicted cement property and one or more loads into a numerical simulator for modeling regions at or near the wellbore; and performing an integrity analysis of the cement based at least in part on an output of the numerical simulator.

20. The method of claim 19, wherein the output of the numerical simulator comprises strain determined at an interface between a carbonated portion and an uncarbonated portion of the cement.