Contents lists available atScienceDirect
Journal of Petroleum Science and Engineering
journal homepage:www.elsevier.com/locate/petrolEvaluation of mechanical properties of cement slurries containing SBR latex
subjected to high temperatures
Ramón Victor Alves Ramalho
a,∗, Salete Martins Alves
b, Julio Cezar de Oliveira Freitas
a,
Bruno Leonardo de Sena Costa
a, Ulisses Targino Bezerra
caLaboratório de Cimentos, Federal University of Rio Grande do Norte, Natal, Rio Grande do Norte, 59072-970, Brazil bEscola de Ciências e Tecnologia, Federal University of Rio Grande do Norte, Natal, Rio Grande do Norte, 59072-970, Brazil cFederal Institute of Education, Science and Technology of Paraíba, João Pessoa, 58015-430, Brazil
A R T I C L E I N F O Keywords: Portland cement SBR latex Compressive strength Elastic deformation Design of experiments A B S T R A C T
The oil and gas industry uses different techniques to increase the productivity index of a reservoir, and steam injection is one of the most widely used in the world. In this technique, heated water vapor at high temperatures (between 300 and 400 °C) is injected under pressure into the reservoir, increasing the pressure in situ and re-ducing the oil viscosity present in the rock. Notwithstanding this, another physical consequence is the expansion and contraction of the casing column, an effect that can affect the cement sheath and lead to failure. In this context, SBR latex is used to improve theflexibility of the cement matrix by reducing the amount of fatigue failure, besides what, the mechanical behavior should be carefully adjusted to the well conditions. Therefore, this work aims to study the mechanical behavior of cement slurry systems additivated with SBR latex and applied to oil wells cementing that are subject to steam injection. Through a central composite factorial design, the authors studied the compressive strength behavior by varying the slurry density from 1.75 g/cm³ (14.6 ppg) to 1.89 g/cm³ (15.8 ppg), curing time between 4 days and 28 days and concentration of SBR latex between 0 L/m³ and 534.722 L/m³ (0 gal/ft³ and 4 gal/ft³). The results showed that increasing the SBR latex concentration, within the given ranges, decreased the compressive strength of the specimens. Through the study it was possible verified the potential of statistical tool in the aid of determination of the best systems.
1. Introduction
Reservoirs containing heavy and extra-heavy oil usually require complex extraction processes. The operation of these reservoirs create, with recurrence, new production technologies that are economically favorable to assist the oil production. Because of its high viscosity and difficult to flow, companies use a heat source to stimulate its produc-tion.
The most common methods used are in situ combustion, downhole heaters,fluid injection and the steam injection (cyclical or continuous), since they promote a great heat exchange. The cyclic steam injection reduces the oil viscosity, generating cleaning effects that aid the re-servoir natural energy to produce the oil. This process is characterized by three periods: (i) injection and well shut in period, (ii) soaking period (time necessary to dissipate the heat in the reservoir) and (iii) production period (opening), until the cycle is repeated. The execution of all these phases can vary in order to optimize production. These
processes can raise the well temperature above 300 °C, generating ex-tensive damages to well cementing (Alikhlalov and Dindoruk, 2011). At these temperatures, the cement sheath can be heavily damaged by a strength retrogression phenomenon (Costa et al., 2017). In addition to the high temperatures already mentioned, cement slurries are also ex-posed to high pressures, reaching up to 200 MPa (30,000 psi) de-pending on the height and density of the material column above and processes that the well is subjected to (Salehi et al., 2017).
The strength retrogression occurs when the cement sheath is ex-posed to high temperatures, generally above 110 °C. At these tem-peratures, there is a conversion of calcium silicate hydrate (C-S-H) into calcium-rich phases and, consequently, the reduction in compressive strength and increase of permeability (Swayze, 1954; Taylor, 1997). The strength retrogression can also cause other problems as chemical attacks, durability issues, sustained casing pressure, shrinkage and leakage affecting the wellbore life span and zonal isolation (Saleh et al., 2019). In addition, the C-S-H phase usually converted into other phases,
https://doi.org/10.1016/j.petrol.2019.03.076
Received 2 August 2018; Received in revised form 28 March 2019; Accepted 28 March 2019
∗Corresponding author.
E-mail addresses:ramonramalho31@outlook.com(R.V.A. Ramalho),salete.martins@gmail.com(S.M. Alves),juliofreitasj@hotmail.com(J.C.d.O. Freitas), bruno_engmat@yahoo.com.br(B.L.d.S. Costa),dartarios@yahoo.com.br(U.T. Bezerra).
Available online 03 April 2019
0920-4105/ © 2019 Elsevier B.V. All rights reserved.
such as α-C2SH that is highly crystalline and denser than the C-S-H
phase, resulting in severe increase permeability. The addition of silica flour (SF) in proportions of 35%–40% by weight of cement (BWOC) reduces the CaO/SiO2ratio, generating more stable products at
tem-peratures above 110 °C (Iverson, 2010;Luke, 2004;Nelson and Guillot, 2006; Pernites and Santra, 2016; Swayze, 1954). In addition to the retrogression phenomenon, the processes of expansion and contraction caused for cyclic steam injection, promoted by temperature variations, cause serious damage to the cement matrix due to its low tensile strength.
To try to avoid the damaging effects of the temperature and pressure cycles, over the years latex has been used in oil wells cementing in order to add someflexibility to the system. The use of flexible cement in wells subjected to steam injection is required due to matrix expansion caused during the steam injection, and after temperature stabilization, it tends to return to its previous dimensions. The contraction and ex-pansion deformations can create cracks, ruptures and, consequently, loss of hydraulic isolation in the well, reducing the well operating life (Alikhlalov and Dindoruk, 2011).
The oil well cementing industry commonly use polymer based ad-ditives for various purposes. Latex has been used in oil well cementing operations because of itsflexible features; also it was used as fluid loss control additive and to inhibit the gas migration by blocking the cement matrix. This polymeric material is a milky suspension of tiny particles (200 nm–500 nm diameter). The commercial latices are prepared from a variety of monomers, such as: vinyl acetate, vinyl chloride, acrylics, acrylonitrile, styrene, butadiene and ethylene. Currently, the most usual utilized latex types in cement slurries are styrene-butidiene rubber (SBR) latex, stlatex, styrene-acrylate (SA) latex and ethylene-vinyl acetate (EVA) copolymer etc. SBR latex is widely used as poly-meric additive in cement slurries because of its elasticity and its ex-cellent properties, such as waterproofing and hardness (Fan et al., 2018; Jafariesfad et al., 2017;Nelson and Guillot, 2006).
The latex used was copolymers of styrene-butadiene rubber manu-factured by emulsion polymerization, where water is used as a solvent and thefinal product is commercialized as aqueous dispersion. Latex molecular formula results in a specific behavior for cement matrix, once that monomers of styrene are rigid and monomers of butadiene are flexible (Benali and Ghomari, 2017).Nelson and Guillot (2006)stated that when the latex is added as part of the liquid phase of a Portland cement system, the results are slurries contain 20%–35% less water due solids content of the latex.
When there are areas with presence of gas in subsurface, one of the routes of migration of this gas is through spaces in the well cement sheath. This process can occur with the cement fresh or after cured. To promote this action against gas migration, the additive is composed by an aqueous dispersion of solid polymer particles and surfactants and protective colloids that act to stabilize the dispersion. SBR latex (styrene butadiene latex) particles tend to coalesce upon contact with gas, that is, they form an impermeable polymer barrier, controlling fluid loss.
The SBR latex is also well known as an agent that improves shear-bond strength, acts on the rheological parameters of the slurry and increases the elastic deformation capacity by resisting shrinkage-com-pensating and bonding actions. In addition it is recognized as an agent that provides better shear-bond strength and greater elastic deforma-tion due to shrinkage compensadeforma-tion and bonding acdeforma-tions (Diab et al., 2013,2014;Nelson and Guillot, 2006).
It is widely observed in the literature that the compressive strength of the cement matrix with the SBR latex additive is less than without the additive, however, the polymer may increase theflexural strength of the cement matrix, contributing to greater durability and ability to withstand physical changes (Barluenga and Hernández-Olivares, 2004; Qu and Zhao, 2017;Sun et al., 2006;Wang et al., 2006,2016).
The latex SBR structure is composed byflexible chains of butadiene with ramifications of rigid styrene chains. These long molecular
intertwine chairs make the composite structure more amorphous and less fragile. The cement slurry additived with this polymer has im-provements in mechanical properties, plastic characteristics, resistance to abrasion and impermeability (Barluenga and Hernández-Olivares, 2004;Wang et al., 2006).
The mechanical properties is defined as the reaction of the cement material to the applied loads and deformations. They can be subdivided into elastic and strength properties. The Young's modulus, an example of elastic property, has consistent relevance in studies of cementitious materials for oil well cementing (Lavrov and Torsæter, 2016).
Thus, this study aims to investigate the performance of SBR latex on cement slurries applied into wells subjected to steam injection using statistical tools to analyze the mechanical properties. In short, the ce-ment samples were cured at 52 °C (simulating the bottom hole static temperature - BHST) and then subjected to 300 °C (simulating a steam injection cycle); after this cycle the samples were mechanically tested and their results were treated statistically.
2. Methodology
The present study analyzed the mechanical properties of cement slurries varying the SBR latex additive concentrations between 0 gal/ft³ and 4 gal/ft³, curing times (4 and 28 days) and slurry density (14.6 ppg and 15.8 ppg).
During the curing time, the specimens were exposed to conditions that simulate wells that have steam injection, reaching temperatures close to 300 °C. Therefore, the specimens were placed during three days in a HPHT curing chamber at 300 °C (572 °F) and a pressure of 2,000 psi, simulating the temperature of steam injection.
Then, compressive tests were carried out to determine the values of compressive strength and Young's modulus of the specimens. At the end, the results were analyzed statistically.
2.1. Materials
The slurries were formulated using class G Portland cement (PC) and following the specifications of API RP10B-2 (API, 2013).
Silicaflour (SF) with 40% BWOC was used as anti-retrogression agent in all slurries. It is a material formed by 99% of silicium oxide (SiO2) and it is the most used material as anti-retrogression agent in oil
and gas industry (Bezerra et al., 2011;Tabatabaee Moradi et al., 2015). An anti-foaming silicone based agent was also used to reduce the tendency to form foam due to the presence of latex in the slurries, being all slurries additived with 0.03 gal/ft ³.
The class G Portland cement used in this work had a specific gravity (SG) of 3.14 g/cm³, the silicaflour SG was 2.65 g/cm³, the fresh water SG was 1.00 g/cm³, the anti-foaming SG was 0.98 g/cm³, and the SBR latex had a SG of 1.03 g/cm³.
The Table 1 describes the components concentration for the 17 experiments.
2.2. Samples preparation
The slurries were formulated to obtain a total volume of 600 ml. The calculations were performed according to the API RP10B-2 (API, 2013). After the formulation, each slurry was placed into three cylindrical metallic moulds, 50 mm in diameter (D) and 100 mm high (L). The sample size was non-API to allow the installation of an extensometer, a mechanism necessary to capture Young's modulus.
The curing times used throughout the essays varied from 4 days to 28 days. However, because the slurries were tested in conditions similar to a well subjected to steam injection, a thermal cycle has been applied. The last three days of the curing time of all slurries occurred in a high pressure and high temperature chamber (HPHT), model Chandler 1910, at 300 °C and pressure of 2,000 psi (Table 2).
an oil well, where occurs the cement curing. Thus, the cement slurry curing process occurs in approximate field conditions. The second temperature value, 300 °C, represents the temperature reached during the steam injection process. Therefore, along with the increase of pressure, the cement slurries are exposed to the approximate conditions of the real thermal cycle.
2.3. Uniaxial compressive test
Compressive strength tests were performed at room temperature, using a Shimadzu autograph model AG-I test machine charging speed of 0.3 MPa/s with accuracy of ± 0.3% of showed force, loading limit of 100 kN and controlled by the TRAPEZIUM program 2. The samples were 03 cylindrical specimens for each composition with 50 mm in diameter and 100 mm high. The sample size was non-API to allow the installation of an extensometer.Fig. 1shows a sample positioned and with extensometer coupled to apply the load in the compressive strength test.
After being demolded, the specimens were wiped and measured with a caliper to determine its retraction. Then, the compressive strength tests were carried out. For each formulation 03 samples were used and the mechanical properties were determined through the average between them.
In addition, the elastic properties of Young's modulus were obtained through a stress-strain curves recorded in the single-axial compressive test. In this test, a cylindrical specimen is loaded with a compressive load at its top and bottom faces. In a one-axial test, Young's modulus is the slope of the axial stress versus axial strain curve (Lavrov and Torsæter, 2016). This is possible because when a specimen is com-pressed in one direction, it does not shorten only along the loading direction, but there is also expansion in the side directions.
The authors used a extensometer Epsilon Tecnology Corp models 3975-0008-ST and 3542RA1-080M-250M-ST to obtain the transverse and longitudinal deformations, parameters necessary to calculate the
Young's modulus of the specimens.
2.4. Design of experiments
After analyzing carefully which variables could potentially affect the mechanical characteristics studied, a Central Composite Rotatable Design (CCRD) 2³ was defined, including three repetitions at the central point.
Three variables were selected to be studied. In this way, it is pos-sible to determine the influence of each variable to the result of the experiments. Slurry density is an important variable in the use of ce-ment slurries, since different scenarios require different densities. The curing time is a variable that is minimal controlled by the operator, each well has different periods to slurry hardening. Finally, the latex SBR, the main additive used in this study, its concentration as a selected variable generates conclusions about its efficiency and applicability. Variables levels for the experimental design are present inTable 3.
The used values were obtained from the definition of the maximum amplitude values studied for each factor equalized to the wider values of the codes. Then, an interpolation was performed to obtain the other values.
The axial points, 1.68 and its corresponding negative value,−1.68, were defined by the (Eq.(1)) and n is the number of selected variables.
=
α 2n4 (1)
The Central Composite Rotatable Design (CCRD) proposes a sim-plification in the experimental work, reducing the number of experi-ments and making it possible to explore the entire experimental space. Table 1
Compositions of the slurries.
Sample Density in ppg [g/ cm³] Components concentration Ratio of water/ cement (%) Oil well cement (%) Silica source (% BWOC) Anti-foaming (gps) Latex (gps) 1 14.8 66.22 46.77 40 of SF 0.03 0.8 2 14.8 66.22 46.77 40 of SF 0.03 0.8 3 14.8 45.74 46.45 40 of SF 0.03 3.2 4 14.8 45.74 46.45 40 of SF 0.03 3.2 5 15.6 52.92 49.87 40 of SF 0.03 0.8 6 15.6 52.92 49.87 40 of SF 0.03 0.8 7 15.6 32.36 49.53 40 of SF 0.03 3.2 8 15.6 32.36 49.53 40 of SF 0.03 3.2 9 14.6 59.85 45.79 40 of SF 0.03 2 10 15.8 39.75 50.43 40 of SF 0.03 2 11 15.2 66.02 48.48 40 of SF 0.03 0 12 15.2 31.82 47.92 40 of SF 0.03 4 13 15.2 48.92 48.20 40 of SF 0.03 2 14 15.2 48.92 48.20 40 of SF 0.03 2 15 15.2 48.92 48.20 40 of SF 0.03 2 16 15.2 48.92 48.20 40 of SF 0.03 2 17 15.2 48.92 48.20 40 of SF 0.03 2 Table 2
Curing time conditions.
Temperature Curing time in each place Entire time 52 °C 1–25 days in thermostatic bath 4–28 days 300 °C 3 days in curing chamber (terrmal cycle)
Fig. 1. Sample before the compressive strength test.
Table 3
Variables selected for the experimental design.
Real Variables Code −1.68 −1.00 0.00 1.00 1.68 Slurry density (ppg) x1 14.60 14.80 15.20 15.60 15.80
SBR Latex concentration (gal/ ft3)
x2 0.00 0.80 2.00 3.20 4.00
In order to carry out experimental design, the variables were com-bined in all possible ways using factorials points (+1 and - 1), tota-lyzing eight essays and six more tests using an axial point (+1.68 or −1.68) at a time in each variable combined with the center point va-lues (0) in the other variables. Finally, three essays were done analyzing the central point values in the three variables. These repetitions at the central points analyze the stability of the system results by estimating the experimental error, and it is indispensable to assess the process's reproducibility (Obeng et al., 2005).
The error term used for all statistical treatment was the pure error. It is possible to use the residual SS error term, but it is best suited for fractional design and to Placket and Burman planning. Therefore, be-cause a Central Composite Rotatable Design (CCRD) was used, the pure error was selected, considering a confidence interval of 95%. 2.4.1. Identification of the statistical model
Through analysis of variance, ANOVA, it is possible to determine a statistically reliable regression model that is capable to determine predictive response values through a statistical model (Bispo et al., 2017). Thus, it was possible to determine quadratic equations with slurry density, SBR latex concentration and curing time for the model. The data found experimentally were adjusted to a second-order model, Eq.(2):
∑
∑ ∑
∑
= + + + + = < = Y β β x β x x β x ε j k j j i j k ij i j j k jj j 0 1 1 2 (2) Where Y represents the value of the mechanical property studied andβ0represents the average dataset. The quadratic and interactionparameters are represented byβj, βjj and βij, respectively. Parameters xiand xjrepresent the values of independent variables and ε is the
standard random error normal distribution. The results were obtained and processed using a statistical software capable to generates response surface plots based on the equation of the model, the second-order model equation. The precision quality of this equation was expressed by the coefficient of determination R2and the statistical significance was
determined by the F test (analysis of variance).
3. Results and discussion
The results obtained in the experimental phase are presented in this section. Results were analyzed according to their respective compres-sive strength. An experimental design was used to organize the test methodology and to refine the discussion of the results.
3.1. Experimental results
Table 4shows the organization of experiments defined by the CCRD and the responses are compressive strength and Young's modulus.
3.2. Compressive strength analysis
To use a cement slurry in the primary cementing of oil wells, it must have minimum mechanical requirements, regardless the conditions which it will be subjected. The situation caused by forces acting on subsurface of rock formations promotes an extremely hostile scenario for Portland cement arrays. These matrixes suffers mechanical efforts and the influence of other variables, such as temperature.
Table 4presents the values of compressive strength in MPa for the 17 formulations provided by experimental design. These tests were performed independently, however, using the same materials and methods. From these results it is possible to develop a model capable of indicating a compressive strength response to any factor variation.
3.2.1. Second-order model equation
The second-order model equation estimates the surface of responses
through a model that returns compressive strength values from the input of variable values. This equation is determined by taking into consideration the coefficients of the estimated effects for each element (Burkert et al., 2006).
Table 5shows the effect of the variables and interaction effect of the variables in relation to the response. It can be observed that the linear variables have a strong influence on the response of compressive strength, while the quadratic interaction has a small influence, i.e. there is small influence of one variable over another or over itself when in excess.
Compressive strength = 20.43 + 2.06 (Den) + 0.30(Den)2 - 2.78 (Lat) + 1.41(Lat)2 + 2.39 (Cur) - 0.53(Cur)2+ 0.06(Den x Lat)
-0.03(Den x Cur) - 0.76(Lat x Cur) (3)
From the second-order model equation, it is possible to determine the predicted values, response surfaces and estimate the behaviors.
3.2.2. Analysis of variance: ANOVA
To a model be defined as highly significant, it should be tested through some factors. Some of these tests can be done through analysis of variance (ANOVA), such as the sequential F-test, and the results are presented inTable 6.
Therefore, it is necessary to obtain a F test value (6.11) greater than the F table (4.88) to ensure the viability of the model equation. This requirement was achieved, since the F test value was 1.73 times greater than the F result from the table. The F table was determined through the F distribution table for confidence interval of 95%.
The coefficient of determination (R2) provides a measure regarding
the variation proportion using the regression equation in relation to the response variation. In general, the R2is expressed in decimal terms, meaning how the model equationfits the observed responses. The R2
value is determined by the coefficient between the regression sum of square and the total sum of square (Iemma, 2014). The perfect model adjustment occurs when R2is equal to 1 and it is just going to happen if
the residue does not exist and every average variation happens due to the regression, which is improbable. In this study the R2was 0.887.
Even for an appropriate model, it is also necessary to obtain a F test (6.11) of regression greater than the F test of the lack offit (4.88). This comparison legitimate the viability of the model.
3.2.3. Observed and predicted values
The comparation of the observed and predicted responses allows the authors to analyze the quality of the model proposed previously. For a good model, these values must be close and the deviations between them should be distributed normally (non-biased behavior).
Fig. 2compares the predicted values by the model and observed values using a two-dimensional approximation. It is possible to observe the proximity of the 17 experiments performed (Table 4) in relation to second-order model equation.
The relative spacing above or below the line are relatively propor-tional, with no biased behavior. On average, there was a variation of 8.73% when comparing each real value with the value predicted by the model. Therefore, the empirical model was validated because, despite the dispersal, the behavior was considered normal and consistent.
3.2.4. Response surfaces
Based on previous results, the model was used to generate the re-sponse surfaces between two variables.
The response surface (Fig. 3) showed a concentration of optimized values, i.e. greater compressive strength at its extreme positions. The graph shows a directly proportional influence of slurry density and an inversely proportional influence of the SBR latex.
The hot-coloured bands are concentrated for almost the whole ex-tent of the specific mass variation, indicating that when comparing these two factors, the concentration of the polymeric additive has a
superior influence in the results than the influence of the specific mass variation, since it has reached high values of compressive strength in several densities.
This surface showed that the quadratic factors are not significant, when compared with the linear factors. The variable “latex con-centration” had the most important impact, so the “slurry density” had a more linear behavior than the“SBR latex concentration”.
The curing time and the slurry density (Fig. 4) act similarly and proportionate to the increase of the compressive strength of the cement slurry.
The curing time behaved practically proportional to the compres-sive strength, that is, the higher the curing time the greater the cement compressive strength. This behavior is justified because, in general, the cement matrix reaches a stabilization in the hydration process after approximately 28 days of curing, where approximately 70% of the anhydrous compounds had already reacted (Nelson and Guillot, 2006). Throughout this process, the cement resistance keeps increasing
until stabilization. Since the greatest experimental time was 28 days, the highest compressive strength obtained was also associated to this age.
The relation between the curing time and the SBR latex con-centration (Fig. 5) shows that the curing time has a proportional trend and that the SBR latex concentration has a inverse proportional ten-dency for compressive strength responses. The low hot-coloured bands indicate the dependence of specific values of the factors in order to Table 4
Experimental results according to CCRD.
Exp. No Coded Variables Variables Responses
x1 x2 x3 Slurry density (ppg) SBR latex concentration (gal/ft³) Curing time (days) Compressive strength (MPa) Young's modulus (MPa)
1 −1 −1 −1 14.8 0.8 9 17.40 2920.63 2 −1 −1 1 14.8 0.8 23 26.62 4942.67 3 −1 1 −1 14.8 3.2 9 16.19 3138.16 4 −1 1 1 14.8 3.2 23 19.26 2988.89 5 1 −1 −1 15.6 0.8 9 23.67 5057.14 6 1 −1 1 15.6 0.8 23 29.72 6751.76 7 1 1 −1 15.6 3.2 9 19.62 4542.28 8 1 1 1 15.6 3.2 23 25.64 4668.08 9 −1.68 0 0 14.6 2 16 17.69 3654.15 10 1.68 0 0 15.8 2 16 23.08 6021.73 11 0 −1.68 0 15.2 0 16 29.81 6594.07 12 0 1.68 0 15.2 4 16 17.18 3172.56 13 0 0 −1.68 15.2 2 4 15.57 3141.03 14 0 0 1.68 15.2 2 28 20.44 4343.99 15 0 0 0 15.2 2 16 19.45 4405.41 16 0 0 0 15.2 2 16 20.39 3987.10 17 0 0 0 15.2 2 16 21.76 4155.04 Table 5
Table of regression coefficients for the compressive strength analysis.
Factor Effect Std. Error t(2) p −95% +95%
Mean 20.4268 0.6690 30.5330 0.0011 17.5483 23.3053 Slurry density (L) 2.0676 0.3142 6.5812 0.0223 0.7159 3.4194 Slurry density (Q) 0.3091 0.3458 0.8938 0.4658 −1.1788 1.7969 SBR Latex concentration (L) −2.7783 0.3142 −8.8434 0.0125 −4.1301 −1.4266 SBR Latex concentration (Q) 1.4105 0.3458 4.0789 0.0552 −0.0774 2.8983 Curing time (L) 2.3839 0.3142 7.5880 0.0169 1.0322 3.7357 Curing time (Q) −0.5312 0.3458 −1.5362 0.2643 −2.0190 0.9566 1 x 2 0.0560 0.4105 0.1365 0.9039 −1.7101 1.8222 1 x 3 −0.0282 0.4105 −0.0688 0.9514 −1.7944 1.7379 2 x 3 −0.7693 0.4105 −1.8742 0.2018 −2.5355 0.9969
The second-order model equation, Eq.(3), was obtained for compressive strength as a function of the variables slurry density (Den), SBR latex concentration (Lat) and curing time (Cur).
Table 6
ANOVA for the quadratic model.
Source of variation Sum of square Degrees of freedom Mean square F test Regression 279.86 9 31.10 6.11 Residual 35.61 7 5.09 Lack offit 32.92 5 6.58 4.88 Pure error 2.70 2 1.35 Total 315.47 16 aF 0.05; 9; 7(Ftable) = 4.88.
Fig. 3. Response surface plots for the compressive strength as function of the SBR latex concentration and the slurry density.
Fig. 4. Response surface plots for the compressive strength as function of the curing time and the slurry density.
Fig. 5. Response surface plots for the compressive strength as a function of the curing time and the SBR latex concentration.
Table 7
Table of regression coefficients or effects estimates for the Young's modulus analyses.
Factor Effect Std. Error t(2) p −95% +95%
Mean 4190.91 121.2988 34.5503 0.000837 3669.005 4712.819 Slurry density (L) 806.24 56.9630 14.1537 0.004955 561.146 1051.330 Slurry density (Q) 202.81 62.6960 3.2349 0.083735 −66.947 472.572 SBR Latex concentration (L) −738.76 56.9630 −12.9690 0.005893 −983.846 −493.663 SBR Latex concentration (Q) 218.85 62.6960 3.4907 0.073174 −50.905 488.614 Curing time (L) 418.57 56.9630 7.3481 0.018021 173.476 663.659 Curing time (Q) −184.48 62.6960 −2.9425 0.098695 −454.241 85.277 1 x 2 −107.79 74.4257 −1.4482 0.284539 −428.014 212.442 1 x 3 −6.55 74.4257 −0.0879 0.937940 −326.773 313.683 2 x 3 −467.52 74.4257 −6.2817 0.024418 −787.745 −147.289
achieve better results, thus, the expanded green bands highlight unu-sual areas.
The curvature of the response surface occurs because, although the regression shows that the model has aflat tendency, the variable latex concentration has a high quadratic value, showing a minimum interval on the response surface for this parameter.
There is a normal increase of the compressive strength values when the cement hydration reaction evolution is analyzed through time. However, after analyzed the latex influence, a decrease is noticed, since as the concentration of the polymer increases, a greater amount of amorphous structure is present in the cement slurry (Çolak, 2005).
Latex concentration is the only factor that is inversely proportional to compressive strength. At the end of its trend line, there is a stabili-zation behavior, indicating a decrease of it influence. The SBR latex becomes less effective at large concentrations. It is assumed that the lowest efficacy occurs due to the addition of SBR latex, providing an increase of pores and amorphous structure that reduces the compressive strength.
3.3. Young's modulus analysis
In addition to compressive strength, the elastic properties Young's modulus was also subjected to the same statistical analysis. These properties have great importance in oil well cementing operations.
When adding the SBR latex in the cement slurry, an improvement on its elastic properties is expected, since this is a characteristic of some polymeric additives used in oil wells (Bensted, 1996).
Table 7show the regression coefficients or effects estimates for the Young's modulus analyze. The effects column can be used to define the second-order model equations.
3.3.1. Second-order model equation
The second-order model equation Eq. (4) was obtained for the Young's modulus as a function of Slurry density (Den), SBR Latex (Lat) concentration and curing time (Cur). The effects of each variable were used in the equation.
Young's modulus = 4190.91 + 806.24 (Den) + 202.81(Den)2- 738.76 (Lat) + 218.85(Lat)2+ 418.57 (Cur)– 184.48(Cur)2-107.79(Den x
Lat)−6.55(Den x Cur) −467.52(Lat x Cur) (4)
According study toLavrov and Torsæter (2016)the static Young's modulus is typically on the order of 1 GPA to 10 GPA for oil well ce-ments. Considering the data presented inTable 4, the Young's modulus values varied from 3 GPA to 6 GPA, this behavior indicates that the addition of SBR latex reduced the Young's modulus values.
The risk of rupture is directly linked to the tensile strength. This risk is reduced when the ratio of tensile strength to Young's modulus is in-creased. Therefore, in order to increase the tensile strength and hinder the risk of rupture, the cement sheath must have a low Young's modulus (Thiercelin et al., 1997).
4. Conclusions
From the information analyzed through the use of statistical tools it was possible to verify that the latex showed a strong influence on the values of compressive strength. This behavior occurs because this ma-terial is capable to reduce the interaction between the hydration pro-ducts present in the matrix. It was also observed that the curing time also presented strong influence, once that the hydration products are determinant for the material tenacity, and that a significant influence of specific mass in relation to the quantity of latex. It was possible to consider from the study that.
From the quadratic models equations, obtain a calculation tool capable to estimate the parameters: compressive strength and Young's modulus. The results showed that the cement slurries additivated with
SBR latex had a significant gain in elastic behavior for applications in high temperature.
In addition to analyze and quantify the performance of latex ad-ditive to improve the requiredflexibility properties of a cement slurry used in oil wells subjected to steam injection, this study also shows the feasibility of using statistical analysis to understand the behavior of variables in a given scenario.
Through the statistical analysis presented in this work, it was pos-sible to predict compressive strength and Young's modulus of cement slurries at different densities, SBR latex concentrations and curing times. Therefore, this analysis presents a guidance with potential use-fulness for the adequacy of cement slurries for specific operations and elaboration of new studies.
Acknowledgements
The authors are grateful to ANP (Agência Nacional do Petróleo, Gás Natural e Biocombustíveis) for thefinancial support and for master's scholarship awarded to thefirst author.
Appendix A. Supplementary data
Supplementary data to this article can be found online athttps:// doi.org/10.1016/j.petrol.2019.03.076.
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