Methods to assess risk of gas breakout in a well and gas breakout risk assessment systems

Abstract

A computer-implemented method to assess risk of gas breakout in a well includes determining a rate of migration of a gas injected into a well containing a section of cement. The method also includes predicting, based on the rate of migration, an amount of time for a breakout to occur, wherein the breakout occurs when the gas penetrates the section of the cement to a location of interest. The method further includes determining an effective diffusivity of the gas when the gas achieves breakout. The method further includes assessing a risk of a gas breakout based on the rate of migration and the effective diffusivity of the gas.

Description

METHODS TO ASSESS RISK OF GAS BREAKOUT IN A WELL AND GAS BREAKOUT RISK ASSESSMENT SYSTEMSBackground

[0001] The present disclosure relates generally to methods to assess risk of gas breakout in a well and gas breakout risk assessment systems.

[0002] The oil and gas industry has seen a growing interest in using wells for the purpose of gas storage. For example, some wells are earmarked for carbon dioxide (CO2) injection. Gas is sometimes injected through perforations into a depleted reservoir. One risk introduced by this process is the possibility of gas breakout. Breakout is the unwanted event of gas from injection zone migrating through set cement and reaching a prescribed location above the injection zone. In some cases, migrated gas reacts with set cement affecting subsequent migration process. For example, injected CO2 may react with set cement causing permeability changes, thus affecting subsequent migration of CO2. Further, changes in temperature and pressure along the cemented annulus may affect the rate of migration. All these factors (i.e. reaction, temperature, pressure, and cement composition) determine the risk of gas breakout at the surface.Brief Description of the Drawings

[0003] Illustrative embodiments of the present disclosure are described in detail below with reference to the attached drawing figures, which are incorporated by reference herein, and wherein:

[0004] FIG. 1 is a schematic, side view of a well environment where a gas breakout risk assessment system is deployed;

[0005] FIG. 2A is an exemplary plot of a pressure profile of the gas as the gas traverses through the formation of FIG 1 ;

[0006] FIG. 2B is an exemplary plot of two temperature profiles of the gas as the gas traverses through the formation of FIG. 1;

[0007] FIG. 3 is a block diagram of the gas breakout risk assessment system of FIG. 1; and

[0008] FIG. 4 is a flow chart of a process to assess risk of gas breakout in a well.

[0009] The illustrated figures are only exemplary and are not intended to assert or imply any limitation with regard to the environment, architecture, design, or process in which different embodiments may be implemented.Detailed Description

[0010] In the following detailed description of the illustrative embodiments, reference is made to the accompanying drawings that form a part hereof. These embodiments are described in sufficient detail to enable those skilled in the art to practice the invention, and it is understood that other embodiments may be utilized and that logical structural, mechanical, and chemical changes may be made without departing from the spirit or scope of the invention. To avoid details not necessary to enable those skilled in the art to practice the embodiments described herein, the description may omit certain information known to those skilled in the art. Therefore, the following detailed description is not to be taken in a limiting sense, and the scope of the illustrative embodiments is defined only by the appended claims.

[0011] The present disclosure relates to methods to assess risk of gas breakout in a well and gas breakout risk assessment systems. More particularly, the gas breakout risk assessment system described herein is configured to perform operations determined herein to assess risk of gas breakout based on the amount of time taken for gas to breakout (i.e., time for gas to travel to a prescribed location above the injection zone), and the flux of the outflowing gas can be predicted once a breakout occurs by accounting for any temperature and pressure changes along the flow path affecting the migration rate and the reactions affecting the set cement diffusivity. For example, an increase in pressure increases the viscosity and density of the gas thereby making the gas more difficult to migrate. Similarly, an increase in temperature increases the reaction rate and / or migration rate due to higher kinetic energy.

[0012] After gas such as CO2 is injected into a well or through the cement around a well, a gas breakout risk assessment system described herein determines a rate of migration of the gas. In some embodiments, the gas breakout risk assessment system determines a length of a breakout section through which the gas migrates (e.g., the length of the cement through which the gas migrates, or the length of another downhole path through which the gas migrates), and determines the rate of migration based on the length of the breakout section. In some embodiments, the gas breakout risk assessment system determines a depth of penetration of the gas, where the depth of penetration of the gas is an extent to which the gas has migrated through the section of cement. In one or more of such embodiments, the gas breakout risk assessment system determines the rate of migration based on the depth of penetration of the gas. In one or more of such embodiments, thegas breakout risk assessment system determines the rate of migration based on the depth of penetration of the gas as a function of time. In one or more of such embodiments, determining the depth of penetration of gas comprises determining the depth of penetration of gas as a function of time. In some embodiments, the gas breakout risk assessment system determines a composition of the cement, and determines the rate of migration based on the composition of the cement. In one or more of such embodiments, the gas breakout risk assessment system assesses / obtains variables associated with the composition of cement, and determines the rate of migration based on the variables associated with the composition. Examples of the variables include, but are not limited to, a volume fraction of water to cement slurry volume, effective quantity of reactive silicates present in the composition of cement, foam quality of foam cement present in the composition of cement, particle size distribution factor of the composition of cement, and an amount of permeability modifier of an additive present in the composition of cement.

[0013] The gas breakout risk assessment system predicts, based on the rate of migration, an amount of time for a breakout to occur, where the breakout occurs when the gas penetrates the section of the cement to a location of interest, such as the surface, the top surface of the cap rock, or another location of interest. The gas breakout risk assessment system determines an effective diffusivity of the gas when the gas achieves breakout.

[0014] The gas breakout risk assessment system assesses a risk of a gas breakout based on the rate of migration and the effective diffusivity of the gas. In some embodiments, the gas breakout risk assessment system determines an effective permeability of the gas when the gas achieves breakout based on the effective diffusivity, and assesses the risk of the gas breakout based on the effective permeability. In one or more of such embodiments, the gas breakout risk assessment system determines, a flux of the gas when breakout occurs based on the effective permeability, and assesses the risk of the gas breakout based on the flux of the gas. In one or more of such embodiments, the gas breakout risk assessment system determines that breakout has not occurred in response to a determination that the flux of the gas is 0.

[0015] As described herein, in some embodiments, gas injected into the well migrates at different rates due to different downhole conditions along different paths the gas travels along. In that regard, the breakout risk assessment system performs operations described herein to determine a second rate of migration of the gas injected into a well containing a second section of cement, andpredict, based on the second rate of migration, a second amount of time for a second breakout to occur, where the second breakout occurs when the gas reaches a second location of interest. The breakout risk assessment system then determines a second effective diffusivity of the gas when the gas achieves breakout, and assesses a second risk of a second gas breakout based on the second rate of migration and the second effective diffusivity of the gas. In one or more of such embodiments, the breakout risk assessment system determines a second composition of the second cement, and determines the second effective diffusivity of the gas based on the second composition of the second cement. In one or more of such embodiments, the breakout risk assessment system compares different risks of the gas to determine which cement composition provides the lowest risk. In some embodiments, the breakout risk assessment system performs operations described herein to sequentially or simultaneously determine additional rates of gas migration, predict gas breakouts based on the different rates of gas migration, determine corresponding effective diffusivity of the gas, and assess the different risks of gas breakout. In one or more of such embodiments, the breakout risk assessment system compares the different risks to determine which cement composition provides the lowest risk of gas breakout. Additional descriptions of the foregoing methods to assess risk of gas breakout in a well and gas breakout risk assessment systems are described in the paragraphs below and are illustrated in FIGS. 1-4.

[0016] Turning now to the figures, FIG. 1 is a schematic, side view of a well environment 100 where a gas breakout risk assessment system 184 is deployed. In the embodiment of FIG. 1, a wellbore 106 of a well 102 extends from a wellhead 136 at surface through a section 112 containing cap rocks, and another section 110 of reservoir rock formation. Wellbore 106 is encased by a cement 111 that is at least partially wrapped around wellbore 106. Gas is pumped through wellbore 106 downhole, and through one or more perforations (not shown) in directions illustrated by arrows 114 and 116 through wellbore 106 and into cement 111, where the gas travels along different directions indicated by arrows 122, 124, and 126, respectively.

[0017] Gas breakout risk assessment system 184 is configured to model the migration of gas along different paths as a function of one or more of time, temperature, pressure, and cement composition changes while accounting for effects of potential reactions and variations in temperature (T) and pressure (P) along the wellbore depth. In that regard, equation 1 is an example model form for depth of migration of the gas.

[0018] where / [Composition] governs how the cement sheath composition affects migration rate.

[0019] In some embodiments, the foregoing functional form also incorporates the effect of any reactions. In some embodiments, the exact form is deduced using first principles modeling. In some embodiments, gas breakout risk assessment system 184 is configured to model the migration of gas along different paths as a function of one or more of time, temperature, pressure, and cement composition changes while accounting for effects of potential reactions and variations in temperature (T) and pressure (P) along the wellbore depth. In that regard, equation 1 is an example model form for depth of migration of the gas. In some embodiments, gas breakout risk assessment system 184 models the foregoing process using measured gas migration depths on set cement cores of different compositions subjected to different temperature and pressure conditions during exposure. For the case of CO2 migrating through and reacting with set cement, Equation 2 represents an example model form.

[0021] Equation 2 indicates that the volume fraction of water in the cement slurry (VFwater), effective quantity of reactive silicates (C2S + C3), foam quality in case of foamed cement (FQ), particle size distribution PSD Factor) and the amount of permeability modifier like Latex (Latex) can affect the depth of migration. In some embodiments, the composition factors beyond the ones shown in Equation 2 affects the migration rate.

[0022] In some embodiments, gas breakout risk assessment system 184 assesses a first step of risk by predicting rate of migration through the annular geometry using equations similar to 1 and 2. In one or more of such embodiments, the predictions are specific to the composition used in the job, the type of gas migrating and the temperature and pressure conditions in the well of interest. In some embodiments, gas breakout risk assessment system 184 utilizes the rate of migration topredict time to breakout, i.e., time taken for gas to travel from injection location to the prescribed location above it.

[0023] In the second step, gas breakout risk assessment system 184 utilizes Darcy Law to predict the flux of gas.where Permeability is an effective permeability of the annulus at the time of breakout, and is calculated as follows:

[0026] In equation 4, diffusivity of gas at the time of breakout is calculated using quantities in equation 1 as follows:where the integrals in Equation 5 are the average values from bottom (injection location) to the top (prescribed location) of the annulus.

[0028] Although FIG. 1 illustrates gas breakout risk assessment system 184 as a surface-based system, in some embodiments, some components of gas breakout risk assessment system 184 are located downhole, remotely, and / or in the cloud. Additional descriptions of gas breakout risk assessment system 184 and operations performed by the processors of gas breakout risk assessment system 184 are described in the paragraphs below.

[0029] FIG. 2A is an exemplary plot 200 of a pressure profile of the gas as the gas traverses through the formation of FIG 1. In the embodiment of FIG. 2A, axis 202 represents pressure and axis 204 represents time. Further, dash line 212 represents the pressure at breakout (e.g., surface 108), and line 214 represents the pressure at the injection site of the gas when the gas enters the cement such as cement 111 of FIG. 1.

[0030] FIG. 2B is an exemplary plot of two temperature profiles of the gas as the gas traverses through the formation of FIG. 1. In the embodiment of FIG. 2B, axis 252 represents depth and axis 254 represents temperature. Further, line 262 represents a first temperature profile and line 264 represents a second temperature profile, where the first temperature profile indicates cooling of annulus around the injection location, potentially due to injection of cold fluid, whereas the secondtemperature profile indicates gradual increase in annulus temperature with depth. The gas breakout risk assessment system is configured to perform the operations and equations described herein to model the depth of migration as a function of time, temperature, pressure, and cement composition changes while accounting for effects of potential reactions and variations in pressure and temperature along the wellbore depth, assess the risks of the gas along different flow paths, compare the different risks, and determine which cement composition provides the lowest risk.

[0031] FIG. 3 is a block diagram 300 of the gas breakout risk assessment system 184 of FIG. 1, and that is configured to perform the operations illustrated in process 300 of FIG. 4. Gas breakout risk assessment system 184 includes a storage medium 306 and a processor 310. The storage medium 306 may be formed from data storage components such as, but not limited to, read-only memory (ROM), random access memory (RAM), flash memory, magnetic hard drives, solid state hard drives, CD-ROM drives, DVD drives, floppy disk drives, as well as other types of data storage components and devices. In some embodiments, the storage medium 306 includes multiple data storage devices. In further embodiments, the multiple data storage devices may be physically stored at different locations. In one of such embodiments, the data storage devices are components of a server station, such as a cloud server. Formation data, gas data, and cement data are stored at a first location 320 of storage medium 306. Further, instructions to determine a rate of migration of a gas injected into a well containing a section of cement are stored at a second location 322 of storage medium 306. Further, instructions to predict, based on the rate of migration, an amount of time for a breakout to occur, wherein the breakout occurs when the gas penetrates the section of the cement to a location of interest are stored at a third location 324 of storage medium 306. Further, instructions to determine an effective diffusivity of the gas when the gas achieves breakout are stored at a fourth location 326 of storage medium 306. Further, instructions to assess a risk of a gas breakout based on the rate of migration and the effective diffusivity of the gas are stored at a fifth location 328 of storage medium 306. Additional instructions to perform operations described herein are also stored at various locations of storage medium 306.

[0032] FIG. 4 is a flow chart of process 400 to assess risk of gas breakout in a well. Although the operations in process 400 are shown in a particular sequence, certain operations may be performed in different sequences or at the same time where feasible.

[0033] At block 402, the gas breakout risk assessment system determines rate of migration of a gas injected into a well containing a section of cement. In some embodiments, the breakout risk assessment system determines a depth of penetration of the gas, an determines the rate of migration comprises determining the rate of migration based on the depth of penetration of the gas. In some embodiments, the gas break risk assessment system determines a length of a breakout section through which the gas migrates, and determines the rate of migration comprises determining the rate of migration based on the length of the breakout section. In some embodiments, the gas breakout risk assessment system determines a composition of the cement, and determines the rate of migration based on the composition of the cement.

[0034] At block 404, the gas breakout risk assessment system predicts, based on the rate of migration, an amount of time for a breakout to occur. At block 406, the gas breakout risk assessment system determines an effective diffusivity of the gas when the gas achieves breakout. At block 408, the gas breakout risk assessment system assesses a risk of a gas breakout based on the rate of migration and the effective diffusivity of the gas. In some embodiments, the gas breakout risk assessment system determines an effective permeability of the gas when the gas achieves breakout based on the effective diffusivity, and assesses the risk of the gas breakout based on the effective permeability. In one or more of such embodiments, the gas breakout risk assessment system determines, based on the effective permeability, a flux of the gas when breakout occurs, and assesses the risk of the gas breakout based on the flux of the gas. In some embodiments, the breakout risk assessment system performs operations described herein to sequentially or simultaneously determine additional rates of gas migration, predict gas breakouts based on the different rates of gas migration, determine corresponding effective diffusivity of the gas, and assess the different risks of the gas breakout. In one or more of such embodiments, the breakout risk assessment system compares the different risks to determine which cement composition provides the lowest risk of gas breakout.

[0035] The above-disclosed embodiments have been presented for purposes of illustration and to enable one of ordinary skill in the art to practice the disclosure, but the disclosure is not intended to be exhaustive or limited to the forms disclosed. Many insubstantial modifications and variations will be apparent to those of ordinary skill in the ail without departing from the scope and spirit of the disclosure. For instance, although the flowcharts depict a serial process, some of the steps / processes may be performed in parallel or out of sequence, or combined into a singlestep / process. The scope of the claims is intended to broadly cover the disclosed embodiments and any such modification. Further, the following clauses represent additional embodiments of the disclosure and should be considered within the scope of the disclosure.

[0036] Clause 1, a computer- implemented method to assess risk of gas breakout in a well, comprising: determining a rate of migration of a gas injected into a well containing a section of cement; predicting, based on the rate of migration, an amount of time for a breakout to occur, wherein the breakout occurs when the gas penetrates the section of the cement to a location of interest; determining an effective diffusivity of the gas when the gas achieves breakout; and assessing a risk of a gas breakout based on the rate of migration and the effective diffusivity of the gas.

[0037] Clause 2, the computer-implemented method of clause 1, further comprising: determining a depth of penetration of the gas, wherein the depth of penetration of the gas is an extent to which the gas has migrated through the section of cement, wherein determining the rate of migration comprises determining the rate of migration based on the depth of penetration of the gas.

[0038] Clause 3, the computer-implemented method of clause 2, wherein determining the depth of penetration of gas comprises determining the depth of penetration of gas as a function of time.

[0039] Clause 4, the computer-implemented method of clause 1, further comprising: determining a composition of the cement, wherein determining the rate of migration comprises determining the rate of migration based on the composition of the cement.

[0040] Clause 5, the computer-implemented method of clause 4, further comprising assessing one or more variables associated with the composition of cement, the one or more variables comprising one or more of a volume fraction of water to cement slurry, effective quantity of reactive silicates present in the composition of cement, foam quality of foam cement present in the composition of cement, particle size distribution factor of the composition of cement, and an amount of permeability modifier of an additive present in the composition of cement.

[0041] Clause 6, the computer-implemented method of clause 5, further comprising: determining an effective permeability of the gas when the gas achieves breakout based on the effective diffusivity; and assessing the risk of the gas breakout based on the effective permeability.

[0042] Clause 7, the computer-implemented method of clause 6, further comprising: determining, based on the effective permeability, a flux of the gas when breakout occurs; and assessing the risk of the gas breakout based on the flux of the gas.

[0043] Clause 8, the computer-implemented method of clause 7, further comprising determining that breakout has not occurred in response to a determination that the flux of the gas is 0.

[0044] Clause 9, the computer-implemented method of clause 1, further comprising: determining a second rate of migration of the gas injected into a well containing a second section of cement; predicting, based on the second rate of migration, a second amount of time for a second breakout to occur, wherein the second breakout occurs when the gas reaches a second location of interest; determining a second effective diffusivity of the gas when the gas achieves breakout; and assessing a second risk of a second gas breakout based on the second rate of migration and the second effective diffusivity of the gas.

[0045] Clause 10, the computer-implemented method of clause 9, further comprising: determining a second composition of the second cement, wherein determining the second effective diffusivity of the gas comprises determining the second effective diffusivity of the gas based on the second composition of the second cement.

[0046] Clause 11, the computer- implemented method of clause 9, further comprising comparing the first risk with the second risk to determine which cement composition provides the lowest risk.

[0047] Clause 12, the computer-implemented method of clause 9, further comprising: determining a third rate of migration of the gas injected into a well containing a third section of cement; predicting, based on the third rate of migration, a third amount of time for a third breakout to occur, wherein the third breakout occurs when the gas reaches a third location of interest; determining a third effective diffusivity of the gas when the gas achieves breakout; and assessing a third risk of a third gas breakout based on the third rate of migration and the third effective diffusivity of the gas; and comparing the first risk, the second risk, and the third risk to determine which cement composition provides the lowest risk.

[0048] Clause 13, the computer-implemented method of clause 1, further comprising: determining a length of a breakout section through which the gas migrates, wherein determining the rate of migration comprises determining the rate of migration based on the length of the breakout section.

[0049] Clause 14, a gas breakout risk assessment system, comprising: a storage medium; and one or more processors configured to: determine a depth of penetration of a gas injected into a well containing a section of cement, wherein the depth of penetration of the gas is an extent to which the gas has migrated through the section of cement; determine a composition of the cement; determine a rate of migration of the based on the depth of penetration and the composition of the cement; predict, based on the rate of migration, an amount of time for a breakout to occur, wherein the breakout occurs when the gas penetrates the section of the cement to a location of interest; determine an effective diffusivity of the gas when the gas achieves breakout; and assess a risk of a gas breakout based on the rate of migration and the effective diffusivity of the gas.

[0050] Clause 15, the gas breakout risk assessment system of clause 14, wherein the one or more processors are further configured to assess one or more variables associated with the composition of cement to determine the composition of the cement, wherein the one or more variables comprise one or more of a volume fraction of water to cement slurry, effective quantity of reactive silicates present in the composition of cement, foam quality of foam cement present in the composition of cement, particle size distribution factor of the composition of cement, and an amount of permeability modifier of an additive present in the composition of cement.

[0051] Clause 16, the gas breakout risk assessment system of clause 15, wherein the one or more processors are further configured to: determine an effective permeability of the gas when the gas achieves breakout based on the effective diffusivity; and assess the risk of the gas breakout based on the effective permeability.

[0052] Clause 17, the gas breakout risk assessment system of clause 15, wherein the one or more processors are further configured to: determine, based on the effective permeability, a flux of the gas when breakout occurs; and assess the risk of the gas breakout based on the flux of the gas.

[0053] Clause 18, the gas breakout risk assessment system of clause 15, wherein the one or more processors are further configured to: determine a second rate of migration of the gas injected into a well containing a second section of cement; predict, based on the second rate of migration, a second amount of time for a second breakout to occur, wherein the second breakout occurs when the gas reaches a second location of interest; determine a second effective diffusivity of the gas when the gas achieves breakout; and assess a second risk of a second gas breakout based on the second rate of migration and the second effective diffusivity of the gas.

[0054] Clause 19, a non-transitory computer-readable medium comprising instructions, which when executed by a processor, cause the processor to perform operations comprising: determining a depth of penetration of a gas injected into a well containing a section of cement, wherein the depth of penetration of the gas is an extent to which the gas has migrated through the section of cement; determining a composition of the cement; determining a rate of migration of the based on the depth of penetration and the composition of the cement; predicting, based on the rate of migration, an amount of time for a breakout to occur, wherein the breakout occurs when the gas penetrates the section of the cement to a location of interest; and determining an effective diffusivity of the gas when the gas achieves breakout; and assessing a risk of a gas breakout based on the rate of migration and the effective diffusivity of the gas.

[0055] Clause 20, the non-transitory computer-readable medium of clause 19, further comprising instructions, which when executed by a processor, cause the processor to perform operations comprising: determining a second rate of migration of the gas injected into a well containing a second section of cement; predicting, based on the second rate of migration, a second amount of time for a second breakout to occur, wherein the second breakout occurs when the gas reaches a second location of interest; determining a second effective diffusivity of the gas when the gas achieves breakout; assess a second risk of a second gas breakout based on the second rate of migration and the second effective diffusivity of the gas; determining a third rate of migration of the gas injected into a well containing a third section of cement; predicting, based on the third rate of migration, a third amount of time for a third breakout to occur, wherein the third breakout occurs when the gas reaches a third location of interest; determining a third effective diffusivity of the gas when the gas achieves breakout; and assessing a third risk of a third gas breakout based on the third rate of migration and the third effective diffusivity of the gas; and comparing the first risk, the second risk, and the third risk to determine which cement composition provides the lowest risk.

[0056] As used herein, the singular forms “a,” “an,” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprise” and / or “comprising,” when used in this specification and / or in the claims, specify the presence of stated features, steps, operations, elements, and / or components, but do not preclude the presence or addition of one or more other features, steps, operations, elements, components, and / or groups thereof. In addition, the steps and components described in the aboveembodiments and figures are merely illustrative and do not imply that any particular step or component is a requirement of a claimed embodiment.

Claims

What is claimed is:

1. A computer-implemented method to assess risk of gas breakout in a well, comprising: determining a rate of migration of a gas injected into a well containing a section of cement; predicting, based on the rate of migration, an amount of time for a breakout to occur, wherein the breakout occurs when the gas penetrates the section of the cement to a location of interest; determining an effective diffusivity of the gas when the gas achieves breakout; and assessing a risk of a gas breakout based on the rate of migration and the effective diffusivity of the gas.

2. The computer-implemented method of claim 1, further comprising: determining a depth of penetration of the gas, wherein the depth of penetration of the gas is an extent to which the gas has migrated through the section of cement, wherein determining the rate of migration comprises determining the rate of migration based on the depth of penetration of the gas.

3. The computer-implemented method of claim 2, wherein determining the depth of penetration of gas comprises determining the depth of penetration of gas as a function of time.

4. The computer-implemented method of claim 1, further comprising: determining a rate of migration, wherein determining the rate of migration comprises determining the rate of migration based on the composition of the cement.

5. The computer-implemented method of claim 4, further comprising assessing one or more variables associated with the composition of cement, the one or more variables comprising one or more of a volume fraction of water to cement slurry, effective quantity of reactive silicates present in the composition of cement, foam quality of foam cement present in the composition of cement, particle size distribution factor of the composition of cement, and an amount of permeability modifier of an additive present in the composition of cement.

6. The computer- implemented method of claim 5, further comprising: determining an effective permeability of the gas when the gas achieves breakout based on the effective diffusivity; and assessing the risk of the gas breakout based on the effective permeability.

7. The computer-implemented method of claim 6, further comprising: determining, based on the effective permeability, a flux of the gas when breakout occurs; and assessing the risk of the gas breakout based on the flux of the gas.

8. The computer- implemented method of claim 7, further comprising determining that breakout has not occurred in response to a determination that the flux of the gas is 0.

9. The computer-implemented method of claim 1, further comprising; determining a second rate of migration of the gas injected into a well containing a second section of cement; predicting, based on the second rate of migration, a second amount of time for a second breakout to occur, wherein the second breakout occurs when the gas reaches a second location of interest; determining a second effective diffusivity of the gas when the gas achieves breakout; and assessing a second risk of a second gas breakout based on the second rate of migration and the second effective diffusivity of the gas.

10. The computer-implemented method of claim 9, further comprising: determining a second composition of the second cement, wherein determining the second effective diffusivity of the gas comprises determining the second effective diffusivity of the gas based on the second composition of the second cement.

11. The computer-implemented method of claim 9, further comprising comparing the first risk with the second risk to determine which cement composition provides the lowest risk.

12. The computer-implemented method of claim 9, further comprising: determining a third rate of migration of the gas injected into a well containing a third section of cement; predicting, based on the third rate of migration, a third amount of time for a third breakout to occur, wherein the third breakout occurs when the gas reaches a third location of interest; determining a third effective diffusivity of the gas when the gas achieves breakout; and assessing a third risk of a third gas breakout based on the third rate of migration and the third effective diffusivity of the gas; and comparing the first risk, the second risk, and the third risk to determine which cement composition provides the lowest risk.

13. The computer- implemented method of claim 1, further comprising: determining a length of a breakout section through which the gas migrates, wherein determining the rate of migration comprises determining the rate of migration based on the length of the breakout section.

14. A gas breakout risk assessment system, comprising: a storage medium; and one or more processors configured to: determine a depth of penetration of a gas injected into a well containing a section of cement, wherein the depth of penetration of the gas is an extent to which the gas has migrated through the section of cement; determine a composition of the cement;determine a rate of migration of the based on the depth of penetration and the composition of the cement; predict, based on the rate of migration, an amount of time for a breakout to occur, wherein the breakout occurs when the gas penetrates the section of the cement to a location of interest; determine an effective diffusivity of the gas when the gas achieves breakout; and assess a risk of a gas breakout based on the rate of migration and the effective diffusivity of the gas.

15. The gas breakout risk assessment system of claim 14, wherein the one or more processors are further configured to assess one or more variables associated with the composition of cement to determine the composition of the cement, wherein the one or more variables comprise one or more of a volume fraction of water to cement slurry, effective quantity of reactive silicates present in the composition of cement, foam quality of foam cement present in the composition of cement, particle size distribution factor of the composition of cement, and an amount of permeability modifier of an additive present in the composition of cement.

16. The gas breakout risk assessment system of claim 14, wherein the one or more processors are further configured to: determine an effective permeability of the gas when the gas achieves breakout based on the effective diffusivity; and assess the risk of the gas breakout based on the effective permeability.

17. The gas breakout risk assessment system of claim 16, wherein the one or more processors are further configured to: determine, based on the effective permeability, a flux of the gas when breakout occurs; and assess the risk of the gas breakout based on the flux of the gas.

18. The gas breakout risk assessment system of claim 16, wherein the one or more processors are further configured to: determine a second rate of migration of the gas injected into a well containing a second section of cement; predict, based on the second rate of migration, a second amount of time for a second breakout to occur, wherein the second breakout occurs when the gas reaches a second location of interest; determine a second effective diffusivity of the gas when the gas achieves breakout; and assess a second risk of a second gas breakout based on the second rate of migration and the second effective diffusivity of the gas.

19. A non-transitory computer-readable medium comprising instructions, which when executed by a processor, cause the processor to perform operations comprising:determining a depth of penetration of a gas injected into a well containing a section of cement, wherein the depth of penetration of the gas is an extent to which the gas has migrated through the section of cement; determining a composition of the cement; determining a rate of migration of the based on the depth of penetration and the composition of the cement; predicting, based on the rate of migration, an amount of time for a breakout to occur, wherein the breakout occurs when the gas penetrates the section of the cement to a location of interest; and determining an effective diffusivity of the gas when the gas achieves breakout; and assessing a risk of a gas breakout based on the rate of migration and the effective diffusivity of the gas.

20. The non-transitory computer-readable medium of claim 19, further comprising instructions, which when executed by a processor, cause the processor to perform operations comprising: determining a second rate of migration of the gas injected into a well containing a second section of cement; predicting, based on the second rate of migration, a second amount of time for a second breakout to occur, wherein the second breakout occurs when the gas reaches a second location of interest; determining a second effective diffusivity of the gas when the gas achieves breakout; assess a second risk of a second gas breakout based on the second rate of migration and the second effective diffusivity of the gas; determining a third rate of migration of the gas injected into a well containing a third section of cement; predicting, based on the third rate of migration, a third amount of time for a third breakout to occur, wherein the third breakout occurs when the gas reaches a third location of interest; determining a third effective diffusivity of the gas when the gas achieves breakout; and assessing a third risk of a third gas breakout based on the third rate of migration and the third effective diffusivity of the gas; and comparing the first risk, the second risk, and the third risk to determine which cement composition provides the lowest risk.

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