METHOD FOR DESIGNING SPACER TRAINS FOR REVERSE CIRCULATION CEMENTING

Description

BACKGROUND

During wellbore operations, interface dynamics between two fluids may be primarily influenced by density differences between them. When heavier fluids are disposed below lighter fluids in a fluid column such as in a ‘bottom-heavy’ configuration, the density differences may reduce fluid channeling. However, when the heavier fluids are disposed above lighter fluids such as in a ‘top heavy’ configuration, the density differences may cause the fluid channeling.

The top-heavy configuration may occur during reverse cementing operations where a cement slurry may be pumped directly from the surface into an annular space rather than being pumped down the casing string, such as in conventional/forward cementing operations. For example, an inadequate cement flow rate during the reverse cementing may cause heavy fluids to be positioned above lighter fluids, resulting in intermixing and maldistribution of the fluids such as the fluid channeling, resulting in inadequate cement coverage across the wellbore. While increasing the thickness (rheology) of pumped fluids can reduce channeling, there are limits to fluid thickness before the fluids become difficult to mix and pump effectively.

BRIEF DESCRIPTION OF THE DRAWINGS

These drawings illustrate certain aspects of some of the embodiments of the present method and should not be used to limit or define the method.

FIGS. 1A-1B illustrate fluid interfaces in a downhole environment, in accordance with examples of the present disclosure.

FIGS. 2A-2C illustrate fluid interfaces in a downhole environment, in accordance with examples of the present disclosure.

FIG. 3 illustrates fluid interfaces in a downhole environment in a developed annulus, in accordance with examples of the present disclosure.

FIG. 4 illustrates a fluid interface between two fluids during displacement of a fluid, in accordance with examples of the present disclosure.

FIG. 5 is a block flow diagram illustrating a method for designing a fluid train comprising a plurality of spacer fluids, in accordance with examples of the present disclosure.

FIG. 6 illustrates a system for the preparation of a spacer fluid train and subsequent delivery of the spacer fluid train to an application site, in accordance with examples of the present disclosure.

FIG. 7 illustrates a system for reverse circulation of the fluids designed based on displacement efficiency, in accordance with examples of the present disclosure.

DETAILED DESCRIPTION

Techniques of the present disclosure generally relate to designing a fluid train comprising a plurality of spacer fluids gradually with increasing densities and volumes to bridge the density difference between relatively less dense drilling fluid and relatively more dense cement in reverse cementing operations. The methods disclosed herein include determining the number of spacer fluid stages, the volume of each spacer stage, the rheological properties (thickness) of each spacer stage, and the rheological properties and volume of the final tail cement. The methods disclosed herein allow for increased displacement efficiency at the wellbore shoe as well as reducing the volume of cement required for displacement and achieving a desired height for the cement column within the casing.

FIG. 1A is a diagram illustrating fluid interfaces in a downhole environment in an illustrative reverse cementing operation utilizing a single spacer fluid. Typically, the cement is heavier (denser) than the spacer fluid and the drilling fluid leading to an unstable top-heavy configuration. In FIG. 1A at time t1, cement, spacer, and drilling fluid are disposed in the wellbore and the intermixing between the fluids is minimal. At time t2, the fluids are placed further into the wellbore and the cement has channeled through the spacer to the drilling fluid. At time t3 when the cement is fully placed in the wellbore, the cement and spacer are intermixed leaving the cement unevenly dispersed within the wellbore.

FIG. 1B is a diagram illustrating fluid interfaces in a downhole environment in an illustrative reverse cementing operation utilizing a spacer train which includes multiple spacers. At time t1, three spacers which incremental density and volume are introduced into the wellbore between the drilling fluid and cement such that the density gap between the drilling fluid and cement is bridged while maintaining a stable interface. At time t2 the, the fluids are placed further into the wellbore and the interfaces between the fluids remain stable. At time t3 when the cement is fully placed in the wellbore, the stable fluid interfaces have minimized intermixing of the fluids leading to even distribution of the cement in the wellbore.

In wellbore construction, displacement and removal of drilling fluid from casing and formation surfaces is necessary to ensure a strong bond between the casing and formation to cement. A spacer fluid is utilized to displace drilling fluid, clean surfaces, and separate the cement and drilling fluid during placement of the cement in the wellbore. The design of the spacer fluid train affects the displacement efficiency and final cement distribution in the wellbore. Some factors which affect cement placement near the tail end of cement include wellbore geometry and standoff, stability of interfaces between different fluids which may be a function of density difference and rheology across an interface, volume of fluids, and distance traveled by the interface. In general, increasing spacer volumes increases displacement efficiency of the tail cement and increasing tail cement volume increases displacement efficiency at the casing shoe and increases the cement column in the casing. Furthermore, fluids with sharp interfaces reduce cement remaining in the casing during reverse cementing and increases tail cement displacement at the casing shoe.

The displacement efficiency (DE) of a fluid train is a function of f (B, M, SO) given by equation 1, equation 2, and equation 3.

B = difference ⁢ in ⁢ density ⁢ 
 or ⁢ hydrostatic ⁢ gradient ⁢ of ⁢ fluids friction ⁢ gradient ⁢ of ⁢ the ⁢ second ⁢ fluid = Δ ⁢ ρ ( ∇ P ) displacing ⁢ fluid Equation ⁢ 1 M = friction ⁢ gradient ⁢ of ⁢ second ⁢ fluid friction ⁢ gradient ⁢ of ⁢ first ⁢ fluid Equation ⁢ 2 S ⁢ O = Stand - off Equation ⁢ 3

It should be noted that Equation 1 is an example and that other variations of Equation 1 may be used. For example, a friction gradient may be calculated via correlations. Also, (average μ) U/k, from, can be used instead of the friction gradient to calculate B and M.

One method to increase the displacement efficiency is to reduce the hydrostatic gradient between fluids (Δρ) by increasing the number of individual spacers in the spacer train where each spacer has an incremental increase in density. The methods disclosed herein allow for calculation of the number of spacer fluids and associated density of each spacer fluid to achieve a desired design objective for a reverse cementing operation. In a top-heavy configuration, for a given density difference, optimal fluid placement may be achieved when the second fluid (e.g., top fluid) is designed such that the friction pressure gradient is close to or more than that of the density gradient difference while maintaining rheological hierarchy.

Table 1 indicates conditions of viscosity and density that result in stable and unstable fluid conditions for reverse circulation. The “thinner fluid” may be a drilling fluid and the “thicker fluid” may be a spacer fluid or cement. It should be noted that Table 1 does not account for eccentricity in the annulus. These rules are applicable for a unidimensional geometry such as, for example, a concentric interface, inside of a pipe.

Fluid displacement efficiency (“DE”) may be described in mathematical terms:

dP dx = - μ ⁢ U k + ρ ⁢ g Equation ⁢ 2

• • where P=fluid pressure;
  • U=velocity of flow;
  • μ=viscosity of fluid;
  • k=geometry factor; and
  • g=gravitational constant.
    Integrating Equation 2 over an interface expands the equation to:

P 2 - P 1 = [ ( μ 1 - μ 2 ) ⁢ U k + ( ρ 2 - ρ 1 ) ⁢ g ] ⁢ δ ⁢ x , Equation ⁢ 3

where δx is the distance between point 1 for P₁ and point 2 for P₂, and Equation 3 may represent stable conditions. Conversely, when P₂<P₁ the system may be unstable and viscous fingering may occur.

The displacement efficiency may be defined to quantify the displacing fluid and/or the displaced fluid. In some non-limiting examples, the displacement efficiency may be defined as Volumetric Displacement Efficiency (η_v), which is the measure of the extent to which the displaced fluid is replaced by the displacing fluid. It is defined by Equation 5.

η v = Volume ⁢ of ⁢ displacing ⁢ fluid ⁢ in ⁢ annulus volume ⁢ of ⁢ annulus = ∑ ( c · v i ) V annulus , Equation ⁢ 5

where c is the concentration of the displacing fluid in the computational cells; v_i is the volume of the corresponding cell, which is summed up over all the cells in the domain.

In other non-limiting examples, the displacement efficiency may be defined as Cross-sectional Displacement Efficiency (η_cs), which quantifies the amount of displacing fluid (fluid B) at a given depth in the annulus. It is defined by Equation 6.

η cs @ depth ⁢ of ⁢ interest = Area ⁢ occupied ⁢ by ⁢ displacing ⁢ fluid Total ⁢ area ⁢ of ⁢ annular ⁢ cross ⁢ section = 
 ∑ ( c · a i ) Area c ⁢ ross ⁢ section Equation ⁢ 6

FIGS. 2A-2C illustrate fluid interfaces in a downhole environment, in accordance with examples of the present disclosure. FIG. 2A illustrates a fluid interface 100 in a concentric annulus 102 with a downhole tubular 103, such as casing for example. Fluid B may be disposed/pumped in annulus 102 to displace fluid A, as indicated by the directional arrows 106. The fluid interface 100 is an ideal flat interface without fluid channeling. The fluid interface 100 in the concentric annulus 102 may be flat or substantially flat because the mean-velocity of the total fluid is the same throughout the annulus 102. Total fluid level within the tubular 103 is indicated at times t₁, t₂, and t₃. R_i is the inner radii of the annulus 102 and R_o is the outer radii of the annulus 102. Stand-off (SO) may be a distance between an external surface of a tubular such as, for example, casing, and the borehole wall.

FIG. 2B illustrates the fluid interface 100 in an eccentric annulus 108 with the downhole tubular 103. Due to the eccentric annulus 108, fluid channeling at interface 100 occurs as Fluid B travels further on the wider side 110 of the annulus 108 compared to the narrower side 112. As shown, stretching (e.g., channeling) of the fluid interface 100 occurs in the eccentric annulus 108, as the total fluid on the narrower side 112 of the annulus 108 moves very slowly compared to the total fluid on the wider side 110. Total fluid level within the tubular 103 is indicated at times t₁, t₂, and t₃.

FIG. 2C illustrates the eccentric annulus 108, with reduced fluid channeling at the interface 100, compared to FIG. 2B, achieved via the design of the properties of fluid B, using techniques as described herein. As shown, displacement efficiency of the fluid A using the designed fluid B is increased/optimized. Total fluid level within the tubular 103 is indicated at times t₁, t₂, and t₃.

FIG. 3 illustrates a developed annulus after introducing a spacer fluid train comprising “n” number of spacer fluids which bridge the density gap between 16 ppg (pounds per gallon) cement and 9 ppg drilling fluid. In embodiments, the number of spacer fluids in the spacer fluid train are selected such that the interfaces between the fluids introduced into the wellbore remain stable during placement of the fluids in the wellbore.

FIG. 4 illustrates a fluid interface between two fluids during displacement of a fluid, in accordance with examples of the present disclosure. A fluid interface 200 may be disposed between a first fluid A and a second fluid B. Each fluid having a different viscosity (μ₁, μ₂) and density (ρ₁, ρ₂). At least fluid B may be pumped into a wellbore 202 indicated by directional arrows 204. In some examples, the fluids may include drilling fluid, cement, spacer fluids, and/or water. Fluid B may displace fluid A.

FIG. 5 is a block flow diagram illustrating method 300 for designing a fluid train comprising two or more spacer fluids. Method 300 begins with step 302 where data regarding the cement job is gathered. Some exemplary data includes wellbore geometry, properties of drilling fluid including density and rheology, and properties of cement including density and rheology, allowable spacer density range (minimum, maximum values), and possible volume increments, for example. Further data which may be defined include design objective functions such as maximum tail cement displacement efficiency, minimum height of cement column, and maximum first occurrence time of cement at casing shoe.

From step 302, method 300 proceeds to step 304 where a plurality of spacer fluid train designs are generated. Each spacer fluid train design includes two or more spacer fluid designs where each spacer fluid has a specified density, yield point, plastic viscosity, and volume. In embodiments, a design of experiment approach is utilized to generate the plurality of spacer fluid train designs. In embodiments, generating the plurality of spacer fluid train designs includes utilizing a user input of spacer density increments, spacer volume increments, and/or target displacement efficiency at the casing shoe as shown in Table 2.

An example design of experiment for designing a spacer fluid train comprising two spacer fluids is shown in Table 3. In Table 2, Δρ_1,2 is the density difference between the cement and first spacer fluid, rheo 2 is the rheology of the first spacer fluid, v2 is volume of the first spacer fluid, Δρ_2,3 is the density difference between the first spacer fluid and the second spacer fluid, rheo 3 is the rheology of the second spacer fluid, v3 is volume of the second spacer fluid, and v4 is the volume of the cement. Although only two spacer fluids are shown in Table 3 the spacer fluid train design can include any number of spacer fluids such as 2 spacer fluids, 5 spacer fluids, 10 spacer fluids, 20 spacer fluids, or any number therebetween or greater.

From step 304, method 300 proceeds to step 306 where the plurality of spacer fluid train designs generated in step 304 as well as the data regarding the cement job from step 302 are input into a displacement simulator. The displacement simulator simulates the annular displacement of the fluids introduced into the wellbore in reverse cementing including the final placement and position of cement spacer fluid train and drilling fluid as well as time-variant position of the fluids. The calculated displacement can include solutions to objective functions such as tail cement displacement efficiency, height of cement column, first occurrence time of cement at casing shoe.

From step 306, method 300 proceeds to step 308 where the calculated solutions to objective functions from step 306 are compared to the design objective functions defined in step 302 to determine if one or more of the spacer fluid train designs generated in step 304 meet the design objective functions. Additionally in embodiments, in step 308 response surface methodology is utilized to analyze the results of the displacement simulation to determine the significant factors affecting the objective functions. In embodiments, where the one or more spacer fluid train designs generated in step 304 meet the design objective functions, method 300 may proceed to step 314 by arrow 312. Alternatively, if the spacer fluid train designs generated in step 304 do not meet the design objective functions method 300 may proceed to step 304 by arrow 310 where the design of experiment is altered to generate a new plurality of spacer fluid train designs. In embodiments, the design of experiment is altered by adding or reducing the number of spacer fluid train designs, adding or reducing the number of spacer fluids in spacer fluid train designs, altering the number of factors utilized to calculate the design objectives according to the significance of each factor. In some embodiments, factors may include fluid properties such as density, plastic viscosity, and volume of the spacer fluid which are adjusted utilizing a mathematical optimization technique, such as gradient descent to generate a gradient descent response, random selection of new factors, and/or linearized version of the constraints and/or the displacement efficiency equation. In some examples, input parameters such as wellbore geometry, standoff, a first fluid density (ρ₁), rheology, and/or fluid flow rate may be set (constrained) in step 302 such that properties (e.g. density and/or rheology) of at least one spacer fluid in the spacer fluid train is known before-hand and cannot be altered. Thus, if a density is constrained, then a known target density of a subsequently introduced spacer fluid may be used to estimate fluid density of the subsequently introduced spacer fluid to achieve a required displacement efficiency. If density is not constrained, then a known target rheology of a subsequently introduced spacer fluid may be used to estimate fluid rheology of the subsequently introduced spacer fluid to achieve a required displacement efficiency.

Once a spacer fluid train design which is acceptable and the constraints are satisfied (e.g., thresholds are met for the design), method 300 proceeds to step 314 via arrow 312. In step 314 the spacer fluids described by the fluid train from step 310 is prepared, e.g. by combining spacer fluid components such as water and additives. From step 314, method 300 proceeds to step 316 where the spacer fluid train is introduced into a wellbore with reverse circulation.

In embodiments, the spacer fluids of the present disclosure include water and optionally an additive. The spacer fluids are prepared to have the properties, including density and rheology, of the spacer fluid train as determined in the method disclosed herein. In embodiments, the spacer fluid further includes a suspension agent. Examples of suitable suspending aids may include viscosifiers include swellable clays such as bentonite or biopolymers such as cellulose derivatives (e.g., hydroxyethyl cellulose, carboxymethyl cellulose, carboxymethyl hydroxyethyl cellulose). The spacer fluids have a density in line with the designed density from the spacer fluid train. In some embodiments, the spacer fluids may have a density in the range of from about 4 pounds per gallon (“ppg”) to about 24 ppg. In other embodiments, the spacer fluids may have a density in the range of about 4 ppg to about 17 ppg. In yet other embodiments, the spacer fluids may have a density in the range of about 8 ppg to about 13 ppg. Embodiments of the spacer fluids may be foamed or unfoamed or comprise other means to reduce their densities such as lightweight additives. The water may be from any source provided that it does not contain an excess of compounds that may undesirably affect other components in the fluid train. For example, a spacer fluid may include fresh water or saltwater. Saltwater generally may include one or more dissolved salts therein and may be saturated or unsaturated as desired for a particular application. Seawater or brines may be suitable for use in some examples. Further, the water may be present in an amount sufficient to form a pumpable slurry.

FIG. 6 illustrates a system 400 for the preparation of a designed fluid(s) and subsequent delivery of the designed fluid to an application site, in accordance with examples of the present disclosure. As shown, the designed fluid(s) may be mixed and/or stored in a vessel 402. Vessel 402 may be any such vessel suitable for containing and/or mixing the designed fluids, including, but not limited to drums, barrels, tubs, bins, jet mixers, re-circulating mixers, and/or batch mixers. The designed fluids may then be pumped via pumping equipment 404.

The system 400 may also include a computer 406 for calculating the required displacement efficiency as well as utilize the fluid design model to prepare the designed fluids. The computer 406 may include any instrumentality or aggregate of instrumentalities operable to compute, estimate, classify, process, transmit, receive, retrieve, originate, switch, store, display, manifest, detect, record, reproduce, handle, or utilize any form of information, intelligence, or data for business, scientific, control, or other purposes. The computer 406 may be any processor-driven device, such as, but not limited to, a personal computer, laptop computer, smartphone, tablet, handheld computer, dedicated processing device, and/or an array of computing devices. In addition to having a processor, the computer 406 may include a server, a memory, input/output (“I/O”) interface(s), and a network interface. The memory may be any computer-readable medium, coupled to the processor, such as RAM, ROM, and/or a removable storage device for storing data and a database management system (“DBMS”) to facilitate management of data stored in memory and/or stored in separate databases. The computer 406 may also include display devices such as a monitor featuring an operating system, media browser, and the ability to run one or more software applications. Additionally, the computer 406 may include non-transitory computer-readable media. Non-transitory computer-readable media may include any instrumentality or aggregation of instrumentalities that may retain data and/or instructions for a period of time. Computer 406 includes software which implements a method for designing a fluid train comprising two or more spacer fluids such as the method disclosed herein and in FIG. 5.

FIG. 7 illustrates a system 500 for reverse circulation of the designed fluid train, in accordance with examples of the present disclosure. Although a land-based operation is illustrated, examples of the present disclosure are also applicable to offshore operations. It should be noted that the techniques as described herein are applicable to forward cementing operations and reverse cementing operations.

Casing 501 may be installed in a wellbore 502 in a subterranean formation 503. A wellhead 504 may be attached to the top of the casing 501. An annulus 506 is defined between the wellbore 502 and the casing 501. A conduit 508 (e.g., feed line) may be connected to the casing 501 to fluidly communicate with the annulus 506. The conduit 508 may be in fluid communication with a pump 510. The conduit 508 may be connected to a source 512 (e.g., a container) to provide the designed fluid(s).

A return line 514 may be connected to the wellhead 504 to fluidly communicate with the casing 501. The designed fluids A and/or B (e.g. spacer fluids in a fluid train) may enter the annulus 506 directly from the conduit 508 to reverse circulate the designed fluid A and/or the designed fluid B. Fluid B may displace fluid A to the surface 515 via the return line 514 indicated by directional arrows 516.

Accordingly, the present disclosure may relate to techniques for designing optimized fluids for downhole fluid displacement applications such as during cementing, for example. The systems and methods may include any of the various features disclosed herein, including one or more of the following statements.

Statement 1. A method comprising: receiving wellbore data comprising (i) wellbore geometry, density and rheology of a drilling fluid, and (ii) density and rheology of a cement slurry, and receiving a design objective function; generating a plurality of spacer fluid train designs where each of the plurality of spacer fluid train designs comprise two or more spacer fluids where each spacer fluid has a specified density, yield point, plastic viscosity, and volume; calculating a solution to an objective function and annular displacement for each of the plurality of spacer fluid train designs in a reverse cementing operation using a displacement simulator having inputs comprising the wellbore data and the plurality of spacer fluid train designs; comparing each solution to the objective function to the design objective function; selecting a spacer fluid train design from the plurality of spacer fluid train designs which meets the design objective function; and preparing a spacer fluid train based on the selected spacer fluid train design.

Statement 2. The method of statement 1 wherein the design objective function comprises at least one objective selected from the group consisting of maximum tail cement displacement efficiency, minimum height of cement column in casing, maximum first occurrence time of cement at casing shoe, and combinations thereof.

Statement 3. The method of any of statements 1-2 further comprising receiving user input data comprising at least one of spacer density increment, spacer volume increment, or target displacement efficiency at a casing shoe.

Statement 4. The method of any of statements 1-3 wherein generating the plurality of spacer fluid train designs comprises generating spacer fluid designs using the user input data.

Statement 5. The method of any of statements 1-4 wherein the solution to the objective function comprises at least one objective selected from the group consisting of maximum tail cement displacement efficiency, minimum height of cement column, maximum first occurrence time of cement at casing shoe, and combinations thereof.

Statement 6. The method of any of statements 1-5 further comprising generating at least one additional plurality of spacer fluid train designs in response to the solution to the objective function and/or annular displacement for each of the plurality of spacer fluid train designs.

Statement 7. The method of any of statements 1-6 wherein the additional pluralities of spacer fluid drain designs includes changes in at least one of number of spacer fluids in the spacer fluid train design and/or changes in a density, plastic viscosity, or volume of at least one spacer fluid in the spacer fluid train.

Statement 8. The method of any of statements 1-7 wherein the spacer fluid train designs comprise between 2 and 20 spacer fluids.

Statement 9. The method of any of statements 1-8 further comprising analyzing the annular displacement for each of the plurality of spacer fluid train designs using gradient descent to generate a gradient descent response, wherein generating additional pluralities of spacer fluid train designs comprises selecting at least one of spacer fluid has a specified density, plastic viscosity, or volume in response to the gradient descent response.

Statement 10. The method of any of statements 1-9 further comprising receiving user input data comprising at least one of a spacer fluid volume, a spacer fluid density, or a spacer fluid rheology and wherein generating additional pluralities of spacer fluid train designs comprises selecting at least one of spacer fluid based on the user input data.

Statement 11. The method of any of statements 1-10 further comprising calculating a solution to an objective function and annular displacement for each of the additional plurality of spacer fluid train designs in a reverse cementing operation using a displacement simulator having inputs comprising the wellbore data and the additional plurality of spacer fluid train designs; comparing each solution to the objective function to the design objective function; and selecting a spacer fluid train design from the additional plurality of spacer fluid train designs which meets the design objective function.

Statement 12. The method of any of statements 1-11 further analyzing the annular displacement using response surface modeling and determining significant factors, wherein generating additional pluralities of spacer fluid train designs comprises selecting at least one of spacer fluid has a specified density, plastic viscosity, or volume in response to the significant factors.

Statement 13. The method of any of statements 1-12 further comprising introducing the spacer fluid train into a wellbore in a reverse cementing operation.

Statement 14. The method of any of statements 1-13 further comprising displacing a drilling fluid in the wellbore using the spacer fluid train.

Statement 15. The method of any of statements 1-14 further comprising displacing the spacer fluid train with a cement slurry.

Statement 16. The method of any of statements 1-15 wherein the spacer fluid train comprises two or more spacer fluids, where each spacer has a different density between a density of the drilling fluid and the cement slurry.

Statement 17. A method comprising: a. receiving wellbore data comprising (i) wellbore geometry, (ii) density and rheology of a drilling fluid, and (iii) density and rheology of a cement slurry, and receiving a design objective function; b. generating a plurality of spacer fluid train designs where each of the plurality of spacer fluid train designs comprise two or more spacer fluids where each spacer fluid has a specified density, yield point, plastic viscosity, and volume; c. calculating a solution to an objective function and annular displacement for each of the plurality of spacer fluid train designs in a reverse cementing operation using a displacement simulator having inputs comprising the wellbore data and the plurality of spacer fluid train designs; d. comparing each solution to the objective function to the design objective function and selecting a spacer fluid train design from the plurality of spacer fluid train designs if the solution to the objective function meets the design objective function or repeating b-d if the solution to the objective function does not meet the design objective function; and e. preparing a spacer fluid train based on the selected spacer fluid train design.

Statement 18. The method of statement 17 wherein the design objective function comprises at least one objective selected from the group consisting of maximum tail cement displacement efficiency, minimum height of cement column, maximum first occurrence time of cement at casing shoe, and combinations thereof.

Statement 19. The method of any of statements 17-18 further comprising analyzing the annular displacement for each of the plurality of spacer fluid train designs using gradient descent to generate a gradient descent response, wherein generating additional pluralities of spacer fluid train designs comprises selecting at least one of spacer fluid has a specified density, plastic viscosity, or volume in response to the gradient descent response.

Statement 20. The method of any of statements 17-19 further analyzing the annular displacement using response surface modeling and determining significant factors, wherein generating additional pluralities of spacer fluid train designs comprises selecting at least one of spacer fluid has a specified density, plastic viscosity, or volume in response to the significant factors.

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.

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.

Therefore, the present embodiments are well adapted to attain the ends and advantages mentioned as well as those that are inherent therein. The particular embodiments disclosed above are illustrative only, as the present embodiments may be modified and practiced in different but equivalent manners. Although individual embodiments are discussed, all combinations of each embodiment are contemplated and covered by the disclosure. 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 embodiments 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.