Viscoplastic Modeling of a Novel Lightweight Biopolymer Drilling Fluid

Article pubs.acs.org/IECR

Viscoplastic Modeling of a Novel Lightweight Biopolymer Drilling Fluid for Underbalanced Drilling Munawar Khalil and Badrul Mohamed Jan* Department of Chemical Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia ABSTRACT: This paper presents a concise investigation of viscoplastic behavior of a novel lightweight biopolymer drilling fluid. Eight different rheological models namely the Bingham plastic model, Ostwald−De−Weale model, Herschel−Bulkley model, Casson model, Sisko model, Robertson−Stiff model, Heinz−Casson model, and Mizhari−Berk model were used to fit the experimental data. The effect of concentration of clay, glass bubbles, starch, and xanthan gum on the fluid rheological properties was investigated. Results show that the fitting process is able to successfully predict the rheological behavior of the fluid very well. The predicted values calculated from the best selected model are in a good agreement with the experimental data both in low and high (1500 s−1) rate of shear. The result also indicated that the presence of clay, glass bubbles, and xanthan gum have significantly changed the fluid behavior, while the presence of starch has not. Results also showed that all of the tested fluid seems to follow pseudoplastic behavior except for the following three tested fluids: one is fluid with the absence of clay, second and third is fluids with no glass bubble or xanthan gum, respectively. The first fluid tends to follows a Newtonian behavior, while the other two fluids tend to follow dilatants behavior.

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INTRODUCTION Underbalanced drilling (UBD) has been considered as one of the best methods to reduce formation damage during drilling. UBD is usually preferred due to its many advantages during drilling processes, such as higher rate of penetration (ROP), lower perforation damage due to drilling, longer bit life, a rapid indication of productive reservoir zone, and the potential for dynamic flow testing while drilling, etc.1 Another benefit of UBD is its ability to provide reliable implementation of horizontal drilling, in which formation damage has always been one of the major concerns due to longer fluid contact times and greater prevalence of open-hole completions.2,3 Nowadays, UBD is commonly achieved with the use of compressible fluids such as air or natural gas (such as nitrogen) as a drilling fluid, or by reducing the oxygen content in air, depending on the specific reservoir condition encountered.4,5 However, such treatments in which compressible or multiphase fluids are used in wellbores often make UBD challenging and difficult to be conducted. Often times this requires special additional instruments or equipment, and this posts additional works. These problems would be minimized with the use of glass bubbles as a density reducing agent in an incompressible lightweight drilling fluid.6 With fluid density as low as 6.5 to 6.8 lbm/gal., the novel incompressible lightweight drilling fluid would be able to provide underbalanced conditions during drilling without major problems in the field.7,8 Glass bubbles have been extensively used as filler in paints, glues, and other liquids. Recent study has also showed the successful application of bubbles in the formulation of a super-light-weight completion fluid (SLWCF) for underbalanced perforation.8,9 Specific drilling fluid properties are required to maximize well productivity. The use of UBD requires not only low-density fluids but also specific fluid properties. At the moment, virtually most of the drilling fluids used in offshore operations are either oil, crude, or synthetic oil.10 Unfortunately most of the © 2012 American Chemical Society

continuous phases of these fluids are toxic and considered unfriendly to the environment. Thus, to address these issues, a comprehensive study is proposed to formulate a novel and environmentally friendly lightweight water-based drilling fluid. The novelty of the proposed work lies in the attempt to engineer a fluid which is stable, low density, and environmentally friendly. In our previous studies,11,12 we have successfully formulated a water based lightweight drilling fluid with glass bubbles as the density reducing agent, and a natural biopolymer, that is, polysaccharide xanthan gum and starch as viscosity modifier. In the study, we have developed a novel lightweight water-based mud system using glass bubbles as a density reducing agent and two types of biopolymers, xanthan gum and starch, as additives. Secreted by Xanthamonas sp., xanthan gum is an exocellular biopolymer which has a main chain based on a linear backbone of 1,4-linked β-D-glucose residues, and a trisaccharide side chain attached to alternate Dglucosyl residues.13 Starch granules, on the other hand are composed of two types of α-glucan, namely, amylase and amylopectin, produced from green plants as an energy storage.14,15 These two biopolymers were used since they are not toxic to the environment and within the government regulation. They have also been widely used in drilling fluid and enhanced oil recovery (EOR).16,17 This study is a continuation work of our previous study, which presented a comprehensive investigation on the effect of concentration of clay, glass bubbles, and biopolymers on the rheological behavior of the fluid. In the upstream petroleum industry, information on rheological properties of drilling fluids is very important to Received: Revised: Accepted: Published: 4056

April 15, February February February

2011 9, 2012 10, 2012 11, 2012

dx.doi.org/10.1021/ie200811z | Ind. Eng. Chem. Res. 2012, 51, 4056−4068

Industrial & Engineering Chemistry Research

Article

ensure the success of drilling operation.18 Accurate knowledge on the fluid viscoplastic behavior as well as its prediction as a function of its surrounding such as formation transient temperature and pressure, the presence of brine and/or formation water, etc., are very crucial. Drilling fluid experts have comprehensively investigated and generated numerous models to describe the rheological behavior of the fluid during, before, and after drilling operations. Nasiri and Ashrafizadeh20 reported that most drilling fluids in the market are categorized as a non-Newtonian fluid and their rheological behavior could be described by several models.19,21 In the early time of the development of complex drilling fluids, the Bingham plastic model and Ostwald−De−Weale model (or commonly known as the Power Law model) were the most traditional models used to describe viscoplastic behavior of drilling fluid.20 The model of Bingham plastic can be expressed by eq 1. τ = τ0 + η∞(γ)

fluids with high concentrations of bentonite suspension. The model of Casson is given by eq 4. τ0.5 = k OC + k C(γ)0.5

Another complex model containing three parameters, namely the Sisko model has also been considered as one of the most popular models in estimating the rheological behavior of drilling fluids. This model was developed to accommodate the unique feature of the fluid with both Newtonian and nonNewtonian properties. Mathematically, this model combines both the Newtonian (linear relationship) and non-Newtonian (Power Law relationship) to better describe the fluid viscoplastic behavior.28 This model was previously used to estimate the flow properties of hydrocarbon-based lubricating greases.29 However, a recent study conducted by Khalil et al.21 has also shown that this model is able to satisfactorily model the rheological behavior of lightweight completion fluid containing glass bubbles as density reducing agent. The Sisko model is given by eq 5.

(1)

Khalil et al.22 reported that the Bingham plastic model was widely used to describe several types of fluids in the petroleum industry. This is due to its advantage in which its Bingham yield point (τ0) could easily be determined.21 However, recent studies indicated that this model frequently fails to represent the rheological behavior of very complex drilling fluids containing polymers, especially in low shear rates.22,23 This is because the Bingham plastic model is not adequate to describe fluids with complex rheological behavior. As a result it produces an unrealistic high value of τ0.18 Thus, to overcome this shortcoming, many fluid experts have attempted to fit experimental data to the Ostwald−De−Weale (power law) model. The model is given by eq 2. τ = k(γ)n

τ = a(γ) + b(γ)n

(5)

Furthermore, another improved model, the Robertson−Stiff model, was also proposed to estimate the rheological behavior of drilling fluid. In addition to the Casson model, the threeparameters of the Robertson−Stiff model has also been able to describe the flow behavior of drilling fluid with high amount of bentonite suspension satisfactorily well.18,27 This model is also suitable for other complex fluids in upstream oil and gas industry such as cement slurries.30 The Robertson−Stiff model is expressed by eq 6. τ = K(γ̇0 + γ)n

(2)

(6)

To have a better estimation of viscoplastic behavior of drilling fluid made of a complex polymer, another rheological model called the Heinz−Casson model was proposed. This model is a modification of the existing model of Casson. The model lacks application in the upstream oil and gas industry. This model has successfully been used in describing the flow behavior of some complex fluids such as petroleum jelly for cream formulation and concentrated xanthan gum solution.31,32 The Heinz−Casson model is given by eq 4.

Compared to the previous model, the Ostwald−De−Weale model is preferred to describe drilling fluid with complex rheological behavior, especially at low shear rates, due to its power law relationship.19 However, at extremely low shear rate, the absence of the Bingham yield point (τ0) often times makes this model fail to provide a good result in describing fluid viscoplastic properties. Hence, to overcome this issue, another rheological model namely the Herschel−Bulkley (yield power law) model is developed. The model considers three parameters to accommodate the shortcoming of the Bingham plastic model to describe fluid properties with apower equation and the poor result from the Oswald−De−Weale at an extremely low shear rate.24 Most of the studies22,25,26 have indicated that the model could be considered as one of the most common models to describe the rheological behavior of drilling/completion fluids and/or cement slurries. The Herschel−Bulkley model is given by eq 3. τ = τ0 + k(γ)n

(4)

τn = (γ̇0)n + k(γ)n

(7)

Another complex model, the Mizhari−Berk model which has three parameters has also been proposed to model the flow behavior of the formulated lightweight biopolymer drilling fluid. In its early development, this model was previously used to describe the rheological properties of fluid with a dispersing particle in its system, such as concentrated orange juice or fluids used in food engineering.33 In addition, the Mizhari−Berk model has also been found to have very promising potential application in the upstream oil and gas industry. The model has successfully been used to model the flow behavior of superlight-weight completion fluid (SLWCF).21 This is because the purposed parameters in this model, the constant of kOM that was interpreted as a function of the shape and interaction of the particles and kM which is a function of the dispersing medium, provides a better solution in determining the flow behavior of glass bubbles along with other material that act as dispersing

(3)

Recent advances in drilling technology and harsh drilling environments require an accurate rheological model. Another model that is commonly used to express the viscoplastic properties of fluids is the Casson model. This model was initially used to describe the rheological properties of inks and paints. However, recent studies26−28 have also successfully applied this model to the evaluation of drilling fluids, especially 4057



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Table 1. Measured Average Shear Stresses (τ (Pa) ± sda) of Lightweight Biopolymer Drilling Fluid As a Function of Shear Rate at Various Clay Concentrations (% w/v) shear rate, γ (s−1) 2.639 5.279 26.4 52.71 79.28 88.17 158.3 176 264 a

0 (% w/v) 1.46 1.76 2.99 3.84 5.07 5.57 9.99 11.12 14.81

± ± ± ± ± ± ± ± ±

0.04 0.01 0.12 0.02 0.01 0.03 0.03 009 0.02

2.5 (% w/v) 3.14 3.95 5.14 7.14 8.46 9.18 12.64 13.67 17.44

± ± ± ± ± ± ± ± ±

5 (% w/v)

0.05 0.02 0.04 0.01 0.01 0.04 0.02 0.13 0.03

15.21 17.12 20.42 22.49 24.88 25.26 29.71 31.16 38.47

± ± ± ± ± ± ± ± ±

0.06 0.08 0.11 0.04 0.01 0.01 0.07 0.01 0.01

7.5 (% w/v) 26.65 27.19 31.44 35.64 37.18 39.79 45.47 48.09 54.93

± ± ± ± ± ± ± ± ±

0.08 0.07 0.07 0.12 0.04 0.09 0.03 0.11 0.12

10 (% w/v) 37.63 40.93 46.54 53.63 59.44 60.28 70.73 72.09 76.95

± ± ± ± ± ± ± ± ±

0.05 0.01 0.11 0.09 0.10 0.03 0.04 0.02 0.11

Abbreviation: sd, standard deviation.

Scotchlite hollow-glass spheres (rating: 4000 psi) were added in the formulation. A bactericide known as paraformaldehyde OH(CH2O)nH (MW: 30.03 g/mol as monomer) was used to protect the biopolymers against parasites. To improve the fluid rheological properties, clay (samples were taken from Wyoming, USA) was used. Sodium chloride was used as an additive to improve fluid properties. Formulation of Lightweight Biopolymer Drilling Fluid. To formulate water based lightweight biopolymer drilling fluid, all of the raw materials, distillated water, glass bubbles, starch, xanthan gum, clay, paraformaldehyde, and sodium chloride, were mixed using a digital mixer (IKA RW 20) at 500 rpm. In the first test, the clay concentration was varied at four different values, 2.5%, 5%, 7.5%, and 10% w/v, while the amount of other components were fixed (xanthan gum, 0.5% w/v; starch, 1.5% w/v; glass bubbles, 21.25% w/v; NaCl, 0.75% w/v; paraformaldehyde, 0.125% w/v). To understand the effect of clay concentration on the rheological properties of the fluid, a controlled test was conducted by formulating a fluid with 0% w/v of clay concentration. In the second step, the concentration of glass bubbles was varied at four different concentrations, 12.5%, 18.75%, 21.25%, and 25% w/v, while the amount of other components were fixed (clay, 2.5% w/v; xanthan gum, 0.5% w/v; starch, 1.5% w/v; NaCl, 0.75% w/v; paraformaldehyde, 0.125% w/v). Here, a controlled test was also conducted at 0% w/v of glass bubbles concentration. In the next step, tests were conducted by formulating a fluid with various amounts of biopolymer, that is, starch and xanthan gum. The concentration of starch was varied at 1%, 1.5%, 1.75%, and 2% w/v, while other component were fixed (clay, 2.5% w/v; xanthan gum, 0.5% w/v; glass bubbles, 21.25% w/v; NaCl, 0.75% w/v; paraformaldehyde, 0.125% w/ v). In addition a controlled test was also carried out at 0% w/v of starch concentration. Finally, tests were performed by varying xanthan gum concentrations at 0%, 0.25%, 0.5%, 0.75%, and 1%. Other components were fixed (clay, 2.5% w/v; starch, 1.5% w/v; glass bubbles, 21.25% w/v; NaCl, 0.75% w/v; paraformaldehyde, 0.125% w/v). All of the experiments were conducted at ambient pressure and temperature. Viscoplastic Measurements. In this study, viscoplastic parameters such as shear rate and shear stress of the lightweight biopolymer drilling fluid were determined using a rotational viscometer equipped with MV2P spindle (Haake Viscotester model VT 550, with repeatability and accuracy of ±1%, comparability of ±2%). The study of fluid rheological behavior was conducted by measuring the shear stress at various applied shear rates ranging from 2.639 to 264 s−1. To ensure repeatability and accuracy of the measurement, readings were

particle in the system. The Mizhari−Berk model is given by eq 8. τ0.5 = k OM + kM(γ)n M

(8)

As mentioned earlier, the main objective of this study is to provide a comprehensive investigation on the effect of fluid components concentrations, such as clay, glass bubbles and the two biopolymers, namely starch and xanthan gum, on the flow behavior of the fluid. To assess this effect, a statistical-based model fitting analysis was carried out on all of the eight models previously mentioned. This is to find the best model to predict the rheological behavior of the formulated drilling fluid. Experimental data, such as shear rate and shear stress of different fluids at various concentration of clay, glass bubbles and biopolymers were fitted to each model. Using nonlinear regression analysis and adopting the Levenberg−Marquardt technique, the calculated model parameters and several statistical parameters, namely, R-square, sum of square error (SSE), and root-mean-square error (RMSE), were determined. As discussed earlier, the main objective of this study is to present a concise investigation on the effect of the four fluid’s main component, glass bubbles, xanthan gum, starch, and clay, on the viscoplastic behavior of the fluid. This is conducted by fitting the experimental data of fluid shear stress as a function of the applied shear rate to the eight well-established rheological models frequently used in describing the viscoplatic behavior of fluid in the oil and gas industry. This information is essential in selecting the appropriate procedure in handling fluid in the field, selecting the appropriate pump to be used to pump the fluid downhole and up to the surface, etc. In addition, some information on the model’s parameters that are used to describe the rhelogical behavior of the fluid is also important. Such parameters include the three parameters of the Herschel− Bulkley model. In this model, Herschel−Bulkley yield stress (τ0) data allow drilling engineers to predict the minimum force required to initiate fluid flow. Meanwhile, the knowledge on the other two fluid parameters, the fluid consistency (k) and index flow (n), give field engineers information on the type of fluid, Newtonian, non-Newtonian with shear thinning (pseudoplastic) behavior, or non-Newtonian fluid with shear thickening (dilatant) behavior.

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METHODOLOGY

Materials. Two types of biopolymers were used in this study, soluble starch (C6H1005)n (MW: 162 g/mol as monomer) and xanthan gum (C35H49O29)n (MW: 933 g/mol as monomer). To reduce the density of the mixture, 3 M 4058



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Table 2. Rheological Models of Lightweight Biopolymer Drilling Fluid and the Calculated Model’s Parameters and Statistical Parameters as a Function of Clay Concentration (% w/v) 0 (% w/v)

2.5 (% w/v)

5 (% w/v)

7.5 (% w/v)

10 (% w/v)

Bingham-plastic

rheological model

τ0 = 1.3280 η∞ = 0.0524 R2 = 0.9938 SSE = 1.0680 RMSE = 0.3906

τ0 = 3.8460 η∞ = 0.0541 R2 = 0.9891 SSE = 2.0140 RMSE = 0.5364

τ0 = 17.230 η∞ = 0.0816 R2 = 0.9767 SSE = 9.9420 RMSE = 1.1920

τ0 = 28.300 η∞ = 0.1075 R2 = 0.9764 SSE = 17.460 RMSE = 1.5790

x0 = 42.920 η∞ =0.1568 R2 = 0.9285 SSE =118.30 RMSE = 4.1110

Ostwald−De−Weale

k = 0.1781 n = 0.7924 R2 = 0.9781 SSE = 3.7820 RMSE = 0.7350

k = 1.1100 n = 0.0485 R2 = 0.9973 SSE = 6.0420 RMSE = 0.9290

k = 10.680 n = 0.2087 R2 = 0.9086 SSE = 38.980 RMSE = 2.3600

k = 19.150 n = 0.1732 R2 = 0.9058 SSE = 69.730 RMSE = 3.1500

k = 28.540 n = 0.1751 R2 = 0.9557 SSE = 73.270 RMSE = 3.2350

Herschel−Bulkley

τ0 = 1.3560 η∞ = 0.0498 n = 1.0090 R2 = 0.9938 SSE = 1.0660 RMSE = 0.4214

τ0 = 2.9480 η∞ = 0.1820 n = 0.7857 R2 = 0.9987 SSE = 0.2442 RMSE = 0.2017

τ0 = 15.440 η∞ = 0.3681 n = 0.7347 R2 = 0.9896 SSE = 4.4130 RMSE =0.8576

τ0 = 25.400 η∞ = 0.6175 n = 0.6932 R2 = 0.9968 SSE = 2.3630 RMSE = 0.6276

τ0 =33.010 η∞ = 2.9980 n = 0.4932 R2 = 0.9953 SSE = 7.7220 RMSE =1.1340

Casson

kOC = 0.6205 kC = 0.1988 R2 = 0.9880 SSE = 2.0700 RMSE = 0.5438

kOC = 1.4820 kC = 0.1653 R2 = 0.9977 SSE = 0.4324 RMSE = 0.2485

kOC = 3.6940 kC = 0.1471 R2 = 0.9876 SSE = 5.2870 RMSE = 0.8691

kOC = 4.8290 kC = 0.1561 R2 = 0.9943 SSE = 4.2400 RMSE = 0.7783

kOC = 5.9400 kC =0.1888 R2 =0.9910 SSE =14.850 RMSE = 1.4560

Sisko

a = 0.0532 b = 1.4770 n = −0.0451 R2 = 0.9939 SSE = 1.0480 RMSE = 0.4180

a = 0.0436 b = 2.6880 n = 0.1471 R2 = 0.9981 SSE = 0.3480 RMSE = 0.2408

a = 0.1839 b = −1.2e4 n = −11.45 R2 = −1.769 SSE = 1180 RMSE = 14.030

a = 0.0804 b = 24.610 n = 0.0581 R2 = 0.9962 SSE = 2.7890 RMSE = 0.6818

a = 0.0797 b = 33.450 n = 0.1029 R2 = 0.9908 SSE = 15.220 RMSE = 1.5920

Robertson−Stiff

K = 0.0514 γ̇0 = 25.680 n = 1.0030 R2 = 0.9938 SSE = 1.0680 RMSE = 0.4219

K = 0.3483 γ̇0 = 24.350 n = 0.6910 R2 = 0.9987 SSE = 0.2457 RMSE = 0.2024

K = 1.9360 γ̇0 = 62.610 n = 0.5122 R2 = 0.9860 SSE =5.9670 RMSE = 0.9972

K = 5.1160 γ̇0 = 53.830 n = 0.4111 R2 = 0.9959 SSE = 3.0050 RMSE = 0.7078

K = 16.320 γ̇0 = 18.320 n = 0.2808 R2 = 0.9969 SSE =5.1820 RMSE = 0.9294

Heinz−Casson

γ̇0 = 1.3640 k = 0.0503 n = 1.0090 R2 = 0.9938 SSE = 1.0680 RMSE = 0.4214

γ̇0 = 2.9130 k = 0.1430 n = 0.7857 R2 = 0.9987 SSE = 0.2442 RMSE = 0.2017

γ̇0 = 27.280 k = 0.2705 n = 0.7346 R2 = 0.9896 SSE = 4.4130 RMSE = 0.8576

γ̇0 = 62.670 k = 0.4281 n = 0.6932 R2 = 0.9968 SSE = 2.3630 RMSE = 0.6276

γ̇0 = 286.20 k = 1.4790 n = 0.4932 R2 = 0.9953 SSE = 7.7220 RMSE = 1.1340

Mizhari−Berk

kOM = 1.0260 kM = 0.0777 nM = 0.6476 R2 = 0.9925 SSE = 1.2870 RMSE = 0.4631





taken three times, and the average of the three readings was used. To ensure consistency and repeatability, a newly freshmade sample was used in all of the tests. Rheological and Statistical Evaluations. To evaluate the rheological behavior of the lightweight biopolymer drilling fluid, measurements were fitted to the proposed eight rheological

models. The fitting was conducted using commercial statistical software, Matlab version 7.9. Statistical parameters including Rsquare, sum of square error (SSE), and root-mean-square error (RMSE), were also calculated using Matlab. High Shear Rate Validation. To investigate the ability of the developed models to predict the rheological properties of 4059



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the fluid at high rate of shear (1500 s−1), a validation study was conducted to compare the predicted stress from the model with the real experimental data. In this study, high pressure high temperature NI rheometer model 5600 (Nordman Instrument, Inc. Houston, Texas) was used to measure the shear stress at high shear rate (1500 s−1). The shear stress at high shear rate (1500 s−1) from the experimental data was compared to the predicted values from model and its accuracy is calculated.

The result tabulated in Table 1 shows that both the increment of shear rate and the concentration of clay yield a higher amount of stress for the fluid. The faster the fluid is sheared, the greater the stress. In addition the stress seems to increase dramatically as the concentration of clay is increased. This is especially true at higher clay concentration (greater than 5% w/v). The increment of stress in this case is very unique. Some of the data seem to follow a linear relationship and others seem to follow a power relationship. Thus, to accommodate this unique pattern, the experimental data in Table 1 was fitted to the eight proposed rheological models discussed previously. This step will determine the model best to describe the fluid rheological behavior. Table 2 shows the result of the fitting process of the experimental data to the eight proposed rheological models along with their corresponding calculated parameters. Several statistical parameters namely R-square, sum of square error (SSE), and root-mean-square error (RMSE) are also presented in Table 2. On the basis of the fitting process, it was observed that as clay concentration is increased, more complex fluid rheological models are needed to describe the fluid viscoplastic behavior. It is apparent that the two most traditional models, the Binghamplastic and the Ostwald−De−Weale model, may not be sufficient to describe the fluid behavior at higher clay concentration. The reduction in the value of coefficient of determination (R2) as well as the increment of its errors (SSE and RMSE) for the two models as the concentration of clay is increased indicates the model is not able to estimate the fluid behavior at high clay concentration. Statistically, in the absence of clay, the tested fluid could be modeled by almost all of the proposed models. Moreover, the result also shows that the fluid tends to behaves more like a Newtonian fluid as the calculated values of the index flow (n) for several models such as the Herschel−Bulkley model, the Robertson−Stiff model, and the Heinz-Casson model are very close to 1. However, at high clay concentration, the fluid behavior seems to be altered and transformed to follow a pseudopastic behavior. This is shown from the calculated value of index flow (n) which is less than 1. Increment of yield point of the fluid is observed as clay concentration is increased. The increase is more profound at higher clay concentration. It infers that the addition of clay would increase the minimum energy required to initiate fluid flow. The presence of water and high clay concentration may also lead to a gelling phenomenon resulting in very thick mud slurries due to swelling.35 Higher clay concentration causes the final fluid to be thicker and more viscous. Thus, to minimize this problem, salt (in this case sodium chloride) was added to

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RESULTS AND DISCUSSION Effect of Clay. It has been widely reported that the presence of clay, especially at high concentration, in drilling fluid has a

Figure 1. Plot of shear rate vs shear stress for lightweight biopolymer drilling fluid at various clay concentrations: ●, 0% w/v (: the Sisko model); ▼, 2.5% w/v (: the Herschel−Bulkley model); ★, 5% w/v (: the Mizhari−Berk model); ▲, 7.5% w/v (: the Mizhari−Berk model); ■, 10% w/v (: the Robertson−Stiff model).

significant effect on the fluid flowing properties. In oil-well drilling, besides its function as viscosifier to aid the transport of drill cuttings from the bottom of the well to the surface, it also acts as a filtration control agent to minimize fluid invasion into the pores of productive formations.22 It is believed that its swelling properties make clay exhibit an excellent carrying capacity and act to suspend cuttings during drilling proccesses.34 In the first test of this study, we determined the effect of clay concentration on the rheological behavior of the fluid. Table 1 summarized the measured shear stresses of the fluid as a function of shear rate at various clay concentrations.

Table 3. Measured Average Shear Stresses (τ (Pa) ± sda) of Lightweight Biopolymer Drilling Fluid as a Function of Shear Rate at Various Concentrations of Glass Bubbles (% w/v) shear rate, γ (s−1) 2.639 5.279 26.4 52.71 79.28 88.17 158.3 176 264 a

0 (% w/v) 0.38 0.46 0.69 1.08 1.35 1.51 2.54 2.97 5.15

± ± ± ± ± ± ± ± ±

0.01 0.03 0.12 0.08 0.06 0.11 0.17 0.03 0.04

12.5 (% w/v) 2.37 2.99 4.17 6.40 7.45 8.17 11.24 11.97 14.67

± ± ± ± ± ± ± ± ±

18.75 (% w/v)

0.05 0.11 0.12 0.08 0.09 0.04 0.01 0.01 0.07

4.17 4.95 6.47 8.15 9.85 10.79 13.44 14.97 18.63

± ± ± ± ± ± ± ± ±

0.01 0.04 0.07 0.11 0.12 0.14 0.04 0.02 0.06

21.25 (% w/v) 5.49 6.07 8.83 10.59 12.13 13.13 16.95 17.81 21.50

± ± ± ± ± ± ± ± ±

0.04 0.01 0.06 0.12 0.11 0.10 0.03 0.04 0.09

25 (% w/v) 13.70 15.15 18.34 20.44 22.67 23.46 28.33 29.76 36.36

± ± ± ± ± ± ± ± ±

0.11 0.02 0.01 0.09 0.04 0.14 0.09 0.07 0.06

Abbreviation: sd, standard deviation. 4060



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Table 4. Rheological Models of Lightweight Biopolymer Drilling Fluid and Its Corresponding Model and Statistical Parameters at Various Concentrations of Glass Bubbles (%w/v) rheological model Bingham-plastic


Herschel−Bulkley

Casson

Sisko

Robertson−Stiff

Heinz−Casson

Mizhari−Berk

0 (% w/v)

12.5 (% w/v)

18.75 (% w/v)

21.25 (% w/v)

25 (% w/v)

τ0 = 0.1634 η∞ = 0.0172 R2 = 0.9734 SSE = 0.5039 RMSE = 0.2683 k = 0.0125 n = 1.0710 R2 = 0.9696 SSE = 0.5758 RMSE = 0.2868 τ0 = 0.4888 η∞ = 0.0015 n = 1.4430 R2 = 0.9961 SSE = 0.0741 RMSE = 0.1111 kOC = 0.0187 kC = 0.1333 R2 = 0.9679 SSE = 0.6077 RMSE = 0.2946 a = 0.0177 b = 0.7686 n = −0.6631 R2 = 0.9805 SSE = 0.3702 RMSE = 0.2484 K = 3.1e−5 γ̇0 = 114 n = 2.0250 R2 = 0.9981 SSE = 0.0353 RMSE = 0.0767 γ̇0 = 0.7850 k = 0.0021 n = 1.4430 R2 = 0.9961 SSE =0.0741 RMSE = 0.1111 kOM = 0.6617 kM = 0.0065 nM = 0.9867 R2 = 0.9982 SSE = 0.0350 RMSE = 0.0763

τ0 = 3.2250 η∞ = 0.0474 R2 = 0.9716 SSE = 4.1060 RMSE = 0.7659 k = 0.9391 n = 0.4895 R2 = 0.9846 SSE = 2.2280 RMSE = 0.5642 τ0 = 1.7940 η∞ = 0.3139 n = 0.6689 R2 = 0.9971 SSE = 0.4242 RMSE = 0.2659 kOC = 1.3520 kC = 0.1559 R2 = 0.9951 SSE = 0.7015 RMSE = 0.3166 a = 0.0289 b = 1.6280 n = 0.2641 R2 = 0.9951 SSE = 0.7099 RMSE = 0.3440 K = 0.5336 γ̇0 = 10.570 n = 0.5921 R2 = 0.9976 SSE = 0.3513 RMSE = 0.2420 γ̇0 = 1.3130 k = 0.2099 n = 0.6689 R2 = 0.9971 SSE = 0.4242 RMSE = 0.2659 kOM = 1.1590 kM = 0.2428 nM = 0.4320 R2 = 0.9965 SSE = 0.5080 RMSE = 0.2910

τ0 = 5.0180 η∞ = 0.0542 R2 = 0.9832 SSE = 3.1390 RMSE = 0.6697 k = 1.8080 n = 0.4061 R2 = 0.9575 SSE = 7.9470 RMSE = 1.0650 τ0 = 3.8920 η∞ = 0.2298 n = 0.7456 R2 = 0.9968 SSE = 0.5956 RMSE = 0.3151 kOC = 1.7800 kC = 0.1550 R2 = 0.9963 SSE = 0.6995 RMSE = 0.3161 a = 0.0417 b = 3.5494 n = 0.1372 R2 = 0.9966 SSE = 0.6422 RMSE = 0.3272 K = 0.5453 γ̇0 = 26.560 n = 0.6216 R2 = 0.9965 SSE = 0.6500 RMSE = 0.3291 γ̇0 = 4.1750 k = 0.1714 n = 0.7456 R2 = 0.9968 SSE = 0.5956 RMSE = 0.3151 kOM = 3.1870 kM = 1256 nM = −116.2 R2 = 0 SSE = 186.90 RMSE = 5.5820

τ0 = 6.7520 η∞ = 0.0607 R2 = 0.9698 SSE = 7.1540 RMSE = 1.0110 k = 2.8080 n = 0.3555 R2 = 0.9695 SSE = 7.2400 RMSE = 1.0170 τ0 = 4.6870 η∞ = 0.4722 n = 0.6414 R2 = 0.9989 SSE = 0.2655 RMSE = 0.2103 kOC = 2.1280 kC = 0.1562 R2 = 0.9985 SSE = 0.3551 RMSE = 0.2252 a = 0.0389 b = 4.4690 n = 0.1692 R2 = 0.9984 SSE = 0.3812 RMSE = 0.2521 K = 1.2310 γ̇0 = 17.740 n = 0.5069 R2 = 0.9984 SSE = 0.3798 RMSE = 0.2516 γ̇0 = 5.5630 k = 0.3029 n = 0.6414 R2 = 0.9989 SSE = 0.2655 RMSE = 0.2103 kOM = 524.80 kM = −522.4 nM = −0.0006 R2 = 0.7803 SSE = 52.1 RMSE = 2.9470

τ0 = 15.350 η∞ = 0.0822 R2 = 0.9837 SSE = 7.0030 RMSE = 1.0000 k = 8.9650 n = 0.2317 R2 =0.9147 SSE = 36.590 RMSE = 2.2860 τ0 = 13.650 η∞ = 0.3464 n = 0.7465 R2 = 0.9962 SSE = 1.6160 RMSE = 0.5190 kOC = 3.4420 kC = 0.1540 R2 = 0.9934 SSE = 2.8220 RMSE = 0.6349 a = 0.1735 b = −1.3e4 n = −14.58 R2 = −1.171 SSE = 931.7 RMSE = 12.460 K = 1.6290 γ̇0 = 57.260 n = 0.5355 R2 = 0.9941 SSE = 2.5450 RMSE = 0.6513 γ̇0 = 22.430 k = 0.2586 n = 0.7465 R2 = 0.9962 SSE = 1.6160 RMSE = 0.5190 kOM = 3.6440 kM = 0.0753 nM = 0.6176 R2 = 0.9973 SSE = 1.1710 RMSE = 0.4417

(calculated SSE and RMSE values) and the closest R2 value to 1 was selected. On the basis of the result summarized in Table 2, it is apparent that for the fluid with the absence of clay, the best model is the Sisko model with calculated R2 = 0.9939, SSE = 1.048, and RMSE = 0.418. Meanwhile, the Herschel− Bulkley model seems to be the best model for fluid with 2.5% w/w of clay. Furthermore, the Mizhari−Berk model is found to be suitable both for 5% and 7.5% w/w of clay. On the other hand, fluid with 10% w/w of clay seems to be best described using the Robertson−Stiff model. Figure 1 shows the plot of the experimental data of shear rate vs shear stress and its predicted values using the best selected models for the fluid at various clay concentrations.

aid the stabilization of shales and control swelling of the clays. The chloride ion (Cl−) from sodium chloride prevents water from entering the clay matrix.35 In addition, salt is also needed to stabilize the biopolymers structure. Without salt, many polysaccharides will be denatured. This is due to the reduction of contour length of the biopolymers where the macromolecules tend to adopt more coiled conformation.35 On the basis of the result calculated from the model parameters from each model and its statistical parameters, it is determined that at each tested clay concentration, the fluid rheological behavior could be described by several models. However, to determine the best model to predict fluid rheological properties, the model with the lowest error 4061



Article

function of glass bubbles concentration. The experimental data were then fitted to the eight proposed models discussed earlier. Table 3 presents the measured shear stresses of the fluid as a function of shear rate at various glass bubble concentrations and its corresponding error. Table 4 shows the fitting result of the experimental data to the eight proposed rheological models. Results show that most of the models are statistically appropriate and sufficient in describing the rheological behavior of the fluid at various concentrations of glass bubbles. Almost all of the calculated coefficient values of determination (R2) are satisfactory (greater than 0.98). This indicates that the predicted value using the proposed models fits the experimental data very well. This finding is also supported from the low value of calculated error (SSE and RMSE). The best model with the lowest SSE and RMSE values and R2 value closest to 1 was selected since the objective of this study is to determine the best model to represent the rheological properties of the fluid. In the absence of glass bubbles, the Mizhari−Berk model tends to be the best model to describe the rheological behavior of the fluid. In contrast, as the glass bubbles concentration is increased to 12.5% w/v, the rheological properties of the fluid would be best represented by the Robertson−Stiff model. However, when the glass bubbles concentration was set at 18.75% and 21.25% w/v, there are two different types of model applied, the Herschel−Bulkley model and the Heinz−Casson model. At these glass bubbles concentration (18.75% and 21.25% w/v), both models produced similar magnitude of the lowest error value (SSE = 0.5956, RMSE = 0.3151; and SSE = 0.2655, RMSE = 0.2103 for 18.75% and 21.25% w/v, respectively) and the highest R2 values (0.9968 and 0.9989 for 18.75% and 21.25% w/v, respectively). Herschel−Bulkley is usually preferred since it is a well established model in the area of drilling engineering. Moreover, when the glass bubbles concentration was increased to 25% w/v, the rheological behavior of the fluid was best described by the Mizhari−Berk model. It gives an R2 value of 0.9973, SSE of 1.1710, and RMSE of 0.4417. Figure 2 presents the accuracy of predicted rheogram of the lightweight biopolymer drilling fluid as the concentration of glass bubbles was varied from 0% to 25% w/v. The result also shows that Mizhari−Berk equation is the best model for fluid without glass bubble and fluid with glass bubbles higher than 25% w/v. The Mizhari−Berk model was developed33 to describe the rheological behavior of fluid with a dispersing particle within the system. The model constant kOM was related to the shape and interaction of particles. It gives rise to the yield stress, and kM is a function of the dispersing medium. Thus, in this study, the interpretation of this model matches the physical

Figure 2. Plot of shear rate vs shear stress of lightweight biopolymer drilling fluid at various glass bubbles concentration: ●, 0% w/v (: the Mizhari−Berk model); ★, 12.5% w/v (: the Robertson−Stiff model); ▲, 18.75% w/v (: the Herschel−Bulkley model); ■, 21.25% w/v (: the Herschel−Bulkley model); ▼, 25% w/v (: the Mizhari−Berk model).

Effect of Glass Bubbles. A glass bubble has been widely known as an effective density reducing agent due to its extremely low density value (0.32 g/cm3).21 The addition of glass bubbles, which are a silicon-based material, to fluids such as drilling/completion fluid or cement slurries, allows the reduction of the density of the final fluid significantly. However, due to its super-low density value and its silicon-based material, it is difficult to have a final homogeneous mixture. Glass bubbles often times do not fully mix in the fluid system. Additives or emulsifiers are usually added to the fluid to properly mix the glass bubbles. In a study conducted by Khalil et al.22 in the application of glass bubbles to formulate super lightweight completion fluid (SLWCF), the glass bubbles tend to separate from the fluid system and form two or three layers of heterogeneous fluid after the mixture was left for a couple of month. Apparently, unlike clay or polymers, glass bubbles are not soluble in the fluid system. The glass bubble agent is dispersed during the mixing. Thus, a more complex and comprehensive model is apparently needed to better understand the behavior of glass bubbles in the fluid system as dispersion rather than as solute. This paper determines the rheological parameters of the lightweight biopolymer drilling fluid that were used to select the best model for rheological behavior of the fluids as a

Table 5. The Measured Average Shear Stresses (τ (Pa) ± sda) of Lightweight Biopolymer Drilling Fluid as a Function of Shear Rate at Various Starch Concentration (% w/v) shear rate, γ (s−1) 2.639 5.279 26.4 52.71 79.28 88.17 158.3 176 264 a

0 (% w/v) 0.72 0.82 2.15 3.82 5.28 5.59 8.24 8.96 12.42

± ± ± ± ± ± ± ± ±

0.02 0.12 0.04 0.05 0.11 0.07 0.03 0.12 0.10

1 (% w/v) 1.34 1.42 3.46 5.01 6.19 6.45 9.15 10.12 13.65

± ± ± ± ± ± ± ± ±

1.5 (% w/v)

0.03 0.01 0.08 0.07 0.11 0.16 0.17 0.05 0.07

4.49 6.07 8.83 10.59 12.13 13.13 16.95 17.81 21.50

± ± ± ± ± ± ± ± ±

0.11 0.01 0.06 0.07 0.03 0.12 0.10 0.06 0.04

1.75 (% w/v) 8.14 9.14 13.05 15.90 16.97 18.05 22.19 23.04 28.18

± ± ± ± ± ± ± ± ±

0.04 0.04 0.08 0.11 0.16 0.13 0.10 0.01 0.01

2 (% w/v) 12.50 14.32 17.84 20.28 22.62 23.46 28.01 29.34 35.11

± ± ± ± ± ± ± ± ±

0.02 0.04 0.01 0.11 0.10 0.08 0.09 0.02 0.03




Article

Table 6. Rheological Models of Lightweight Biopolymer Drilling Fluid and Its Corresponding Model and Statistical Parameters at Various Starch Concentrations (%w/v) rheological model Bingham-plastic


Herschel−Bulkley

Casson

Sisko

Robertson−Stiff

Heinz−Casson

Mizhari−Berk

0 (%w/v)

1 (%w/v)

1.5 (%w/v)

1.75 (%w/v)

2 (%w/v)




τ0 = 10.300 η∞ = 0.0727 R2 = 0.9532 SSE =16.190 RMSE = 1.5210 k = 5.0210 n = 0.2968 R2 =0.9716 SSE = 9.8290 RMSE = 1.1850 τ0 =6.8370 η∞ =0.9169 n = 0.5603 R2 = 0.9959 SSE = 1.4200 RMSE = 0.4865 kOC =2.7170 kC =0.1597 R2 = 0.9944 SSE = 1.9370 RMSE = 0.5260 a = 0.0403 b = 6.8790 n = 0.1657 R2 = 0.9983 SSE = 0.6028 RMSE = 0.3170 K = 2.7100 γ̇0 = 13.520 n = 0.4121 R2 = 0.9937 SSE = 2.1740 RMSE = 0.6020 γ̇0 = 10.990 k = 0.5137 n = 0.5603 R2 = 0.9959 SSE = 1.4200 RMSE = 0.4865 kOM = 2.4800 kM = 0.2772 nM =0.4141 R2 = 0.9966 SSE =1.1690 RMSE = 0.4414

τ0 = 14.880 η∞ = 0.0816 R2 = 0.9654 SSE = 14.890 RMSE = 1.4580 k = 8.4340 n = 0.2407 R2 = 0.9489 SSE = 21.990 RMSE = 1.7730 τ0 =11.820 η∞ = 0.7279 n = 0.6181 R2 = 0.9968 SSE = 1.3850 RMSE = 0.4805 kOC = 3.3720 kC =0.1556 R2 = 0.9975 SSE = 1.0710 RMSE = 0.3911 a = 0.1701 b = −1.3e4 n = −13.99 R2 = −1.054 SSE = 884.50 RMSE = 12.140 K = 3.2720 γ̇0 = 26.900 n = 0.4153 R2 = 0.9943 SSE = 2.4580 RMSE = 0.6400 γ̇0 = 24.970 k = 0.4499 n = 0.6181 R2 = 0.9968 SSE = 1.3850 RMSE = 0.4805 kOM = 3.3550 kM =0.1634 nM = 0.4921 R2 = 0.9975 SSE = 1.0630 RMSE = 0.4209

appearance of the fluid in the absence of a glass bubble and fluid with high concentration of glass bubbles. In the absence of glass bubbles, agglomeration of xanthan gum and clay are assumed to act as dispersing particles. With the addition of glass bubbles, agglomeration tends to diminish. Under this condition, the Mizhari−Berk model is no longer valid to assess the rheological properties of the fluid as the dispersed particles in the fluid system are neglected. However, at glass bubble concentrations of 25% w/v, the Mizhari−Berk model holds. This could be due to the excess of glass bubbles, which act as dispersed particles in the fluid system. Hence, the Mizhari− Berk model remained as the selected model.

In addition, the result also showed that the presence of glass bubbles in the fluid system tends to change the fluid behavior from dilatant to near pseudoplastic. It indicates that in the absence of glass bubbles, the fluid tends to behaves more like dilatant fluid as the calculated values of the fluid index flow (n) for several models such as the Herschel−Bulkley model, Robertson−Stiff model, and Heinz-Casson model are greater than 1. It has been established in literature that for a Newtonian fluid, n = 1; for pseudoplastic fluid, n < 1; and for dilatants, n > 1.36 In contrast, addition of a high glass bubble concentration caused the fluid to follow a pseudoplastic behavior. The calculated values of index flow (n) are less than 1. This result shows that clay and glass bubbles have a pivotal role in 4063



Article

whenever starch is added to the base fluid, the Sisko model seems more appropriate to represent the fluid rheological properties. However, at high starch concentration (2% w/v), the Sisko model can no longer represent the fluid well and the Mizhari−Berk model was selected instead. The calculated values of R2, SSE, and RMSE are 0.9975, 1.0630, and 0.4209, respectively. Figure 3 shows the rheogram of the lightweight biopolymer drilling fluid as the concentration of starch is varied from 0% to 2% w/v. The accuracy the prediction is also shown. Furthermore, at high concentration of starch (2%), the result showed that the Mizhari−Berk model is statistically appropriate and sufficient to describe the fluid flow properties. However, the addition of starch tends to change the fluid behavior to some sort of a combination of Newtonian and non-Newtonian fluid. The fluid rheological property would be best described by the Sisko model. In Figure 3, it can be seen that at higher shear rate, the fluid seems to follow the Newtonian as the plot of shear rate against shear stress is linear. However, at low and extremely low shear rates, the fluid tends to behave like nonNewtonian. Apparently the relationship between shear rate and shear stress is no longer linear. This phenomenon holds until the starch concentration reaches 1.75% w/v. At higher starch concentration (2% w/v), excess starch acts as dispersed particles. This explains why the fluid behavior would be best described by the Mizhari−Berk model. On the basis of the results, it is also observed that unlike the previous two fluid components, clay and glass bubbles, the addition of starch does not seem to change the calculated values of the fluid behavior (n) index significantly. The calculated n values of the Herschel−Bulkley model for the fluid with and without the presence of starch is less than 1. This indicates that the fluid would follow the pseudoplastic behavior regardless of the amount of starch in the fluid. Effect of Xanthan Gum. In the last stage of this study, the effect of xanthan gum concentration on fluid rheological behavior was investigated. In drilling fluid, xanthan gum is preferred because it is biodegradable and it is also compatible with other filtration-reducing agents such as bentonite clay or carboxymethylcellulose (CMC).34 During the tests, the amount of xanthan gum added to the fluid system was varied in the range of 0% to 1% w/v. Rheology measurements were obtained for the fluid at various concentrations of xanthan gum (Table 7). The experimental measurements were then fitted to the eight proposed models as discussed earlier. Table 8 shows model parameters of the rheological models of the fluid at various concentration of xanthan gum. The results show variations in the model selection to describe fluid properties as

Figure 3. Plot of shear rate vs shear stress of the lightweight biopolymer drilling fluid at various starch concentrations: ●, 0% w/v (: the Hershel-Bulkley model); ★, 1% w/v (: the Sisko model); ▼, 1.5% w/v (: the Sisko model); ▲, 1.75% w/v (: the Sisko model); ■, 2% w/v (: the Mizhari−Berk model).

transforming the fluid behavior from Newtonian/dilatant to non-Newtonian, and then to pseudoplastic. Effect of Starch. In this section, the effect of starch on the rheological properties of lightweight biopolymer drilling fluid was examined. In a drilling operation, a natural-based biopolymer, namely starch, is added as thickening and fluid loss control agent. It is known that the gelatinization property of starch is the one responsible for its ability to control fluid viscosity and fluid loss in oil and gas drilling operations.37 According to Atweel et al.,39 gelatinization is a process of collapsing (disruption) molecular order within the starch granule, manifesting in irreversible changes in properties such as granular swelling, native crystallite melting, loss of birefringence, and starch solubilization.38 The concentration of starch was varied to determine its effect on the rheological behavior of the formulated fluid. The concentration of starch was varied from 1% to 2% w/v, while keeping other components constant. Moreover, tests were conducted by formulating a fluid with 0% w/v starch concentration. Table 5 presents the measured shear stress as a function of shear rate at various starch concentration. On the basis of the fitted result (Table 6), it was observed that in the absence of starch, the model of Herschel−Bulkley is the best model to represent the base fluid. In contrast,

Table 7. The measured Average Shear Stresses (τ (Pa) ± sd)a of Lightweight Biopolymer Drilling Fluid As a Function of Shear Rate at Various Concentration of Xanthan Gum (% w/v) shear rate, γ (s−1) 2.639 5.279 26.4 52.71 79.28 88.17 158.3 176 264 a

0 (% w/v) 1.61 1.67 1.84 2.15 2.49 2.57 3.30 3.53 5.38

± ± ± ± ± ± ± ± ±

0.11 0.04 0.01 0.09 0.07 0.04 0.11 0.07 0.03

0.25 (% w/v) 2.13 2.88 4.17 6.50 7.98 8.36 11.81 12.81 16.48

± ± ± ± ± ± ± ± ±

0.5 (% w/v)

0.02 0.12 0.05 0.04 0.10 0.05 0.06 0.03 0.08

4.49 6.07 8.83 10.59 12.13 13.13 16.95 17.81 21.52

± ± ± ± ± ± ± ± ±

0.11 0.03 0.01 0.07 0.03 0.03 0.11 0.09 0.05

0.75 (% w/v) 8.19 9.14 12.11 14.81 16.84 18.09 22.68 23.48 28.87

± ± ± ± ± ± ± ± ±

0.02 0.02 0.02 0.04 0.10 0.09 0.06 0.03 0.02

1 (% w/v) 10.16 11.32 14.14 16.64 18.55 19.64 25.31 26.84 35.41

± ± ± ± ± ± ± ± ±

0.11 0.03 0.02 0.04 0.01 0.10 0.05 0.02 0.11




Article

Table 8. Rheological Models of the Lightweight Biopolymer Drilling Fluid with Their Corresponding Model and Statistical Parameters at Various Concentrations of Xanthan Gum (%w/v) rheological model Bingham-plastic


Herschel−Bulkley

Casson

Sisko

Robertson−Stiff

Heinz−Casson

Mizhari−Berk

0 (%w/v)

0.25 (%w/v)

0.5 (%w/v)

0.75 (%w/v)

1 (%w/v)

τ0 = 1.4570 η∞ = 0.0134 R2 = 0.9702 SSE = 0.3450 RMSE = 0.2220 k = 0.6058 n = 0.3552 R2 = 0.7842 SSE = 2.4980 RMSE = 0.5974 τ0 = 1.7050 η∞ = 0.0013 n = 1.4280 R2 = 0.9904 SSE = 0.1114 RMSE = 0.1363 kOC = 0.9881 kC = 0.0731 R2 = 0.9138 SSE = 0.9974 RMSE = 0.3775 a = 0.0152 b = 1.7980 n = −0.0898 R2 = 0.9790 SSE = 0.2429 RMSE = 0.2012 K = 1.7e6 γ̇0 = 374.50 n = 2.3130 R2 = 0.9902 SSE = 0.1135 RMSE = 0.1375 γ̇0 = 1.8650 k = 0.0018 n = 1.4280 R2 = 0.9904 SSE = 0.1114 RMSE = 0.1363 kOM = 1.2950 kM = 0.0014 nM = 1.1860 R2 = 0.9934 SSE = 0.0767 RMSE = 0.1130




τ0 = 11.060 η∞ = 0.0920 R2 = 0.9947 SSE = 2.8320 RMSE = 0.6361 k = 4.9440 n = 0.3306 R2 = 0.9043 SSE = 50.880 RMSE = 2.6960 τ0 = 10.470 η∞ = 0.1571 n = 0.9048 R2 = 0.9962 SSE = 1.9970 RMSE = 0.5769 kOC = 2.7620 kC = 0.1870 R2 = 0.9850 SSE = 7.9650 RMSE = 1.0670 a = 0.1578 b = −14.2 n = −31.54 R2 = 0.0918 SSE = 483 RMSE = 8.9720 K = 0.2565 γ̇0 = 85.550 n = 0.8391 R2 = 0.9955 SSE = 2.3740 RMSE = 0.6290 γ̇0 = 12.000 k = 0.1422 n = 0.9049 R2 = 0.9962 SSE = 1.9970 RMSE = 0.5769 kOM = 3.1800 kM = 0.0478 nM = 0.7257 R2 = 0.9977 SSE = 1.2440 RMSE = 0.4554

the fluid thickness due to the presence of xanthan gum as thickening agent, similar to a thick drilling fluid saturated with bentonite. Furthermore, as the amount of xanthan gum is increased to 0.5% w/v, the fluid seems to behave as both Newtonian and non-Newtonian fluid. The best model to describe its rheological properties is the Sisko model. The fluid seems to follow the linear relationship (Newtonian) at higher shear rate and Power Law relationship (non-Newtonian) at lower rate of shear. However, at higher concentration of xanthan gum (0.75% w/v or higher), the dispersed particles seem to show an opposite effect. It is found that the best model to describe the fluid rheological behavior is the Mizhari−Berk model; at high concentrations of xanthan gum, the excess

a function of xanthan gum concentration. In the absence of xanthan gum, the fluid is best described by the Mizhari−Berk model. This result shows the presence of dispersed particles in the fluid system. It is assumed that glass bubbles and clay play a pivotal role in rheological property of the fluid. However, once a small amount of xanthan gum (0.25% w/v) is added, the fluid becomes highly viscous. The best selected rheological model of the fluid is the Robertson−Stiff model. The three-parameters Robertson−Stiff model has been successfully been used in the modeling of drilling fluid with high concentrations of bentonite suspension. It is assumed that this phenomenon is also applicable for the addition of xanthan gum in the mixture. In this case, the Robertson−Stiff model is made to accommodate 4065



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unlike the precedence test for starch, the second type of biopolymer used in this study, xanthan gum, seems to have a great effect on the fluid rheological behavior similar to the case of clay and glass bubbles. The result on this test seems similar to the result on the effect of glass bubbles on fluid rheological properties. As observed previously, the presence of glass bubbles in the fluid system tend to change the fluid behavior from being dilatant to pseudoplastic. The result on the effect of xanthan gum seems similar. The result shows that in the absence of xanthan gum, the fluid behaves more like dilatant fluid as the calculated n values for several models, that is, the Herschel−Bulkley, Robertson−Stiff, and Heinz-Casson models, are greater than 1. However, as xanthan gum is added to the fluid system, the fluid behavior tend to behave more like a pseudoplastic as the calculated n values are less than 1. High Shear Rate Validation. In field application (for example pumping), it is no secret that drilling fluid will be subjected to a very high shear rate (>1000 s−1). The application of high shear rate often times mitigates the accuracy of such a model in predicting the flow behavior of drilling fluid. This may be due to the change of fluid behavior at high range of shear rate. Thus, to investigate the model accuracy in predicting the shear stress of the fluid at a high shear rate, a specific validation study was performed. Table 9 presents the result of the comparison of shear stress predicted using the model and the experimental data, as well as their accuracies. On the basis of the results in Table 9, it can be concluded that most of the models can be used to predict the value of stress at a high rate of shear. The calculated accuracy of the differences between the predicted value which is calculated based on the model and the experimental data is between 93% and 99%. It is apparent that some data show a relatively low accuracy value. This is most likely due to the difference of viscometers used in the analysis.

Figure 4. Plot of shear rate vs shear stress for lightweight biopolymer drilling fluid at various starch concentrations: ●, 0% w/v (: the Mizhari−Berk model); ▼, 0.25% w/v (: the Robertson−Stiff model); ■, 0.5% w/v (: the Sisko model); ★, 0.75% w/v (: the Mizhari−Berk model); ◆, 1% w/v (: the Mizhari−Berk model).

Table 9. Validation of shear stress (τ (Pa)) at high rate of shear (1500 s−1) at various concentrations of clay, glass bubbles, starch and xantan gum (% w/v) Clay

a

shear stress (τ)

0 (% w/v)

2.5 (% w/v)

predicteda experimental accuracy (%)

81.138 80.994 98.76

shear stress (τ)

0 (% w/v)


56.815 55.184 97.04

shear stress (τ)

0 (% w/v)


46.132 44.019 95.20

shear stress (τ)

0 (% w/v)

0.25 (% w/v)


44.459 46.182 96.27

53.962 54.654 98.73

5 (% w/v)

7.5 (% w/v)

10 (% w/v)

123.643 120.685 97.55

135.214 137.651 98.23

21.25 (% w/v)

25 (% w/v)

56.123 54.165 96.38

95.032 99.116 95.88

1.75 (% w/v)

2 (% w/v)

62.031 60.915 98.17

78.687 77.651 98.67

0.5 (% w/v)

0.75 (% w/v)

1 (% w/v)

52.459 55.943 93.77

73.935 73.561 99.49

128.019 125.166 97.72

59.902 94.770 62.741 91.451 95.47 96.37 Glass Bubble 12.5 (% w/v)

18.75 (% w/v)

43.604 57.526 44.161 59.166 98.74 97.23 Starch 1 (% w/v)

1.5 (% w/v)

45.226 52.459 47.616 55.165 94.98 95.09 Xanthan

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CONCLUSION

Eight different rheological models were used to represent the rheological behavior of a novel lightweight biopolymer drilling fluid. The effect of additives concentrations, sich as clay, glass bubbles, starch, and xanthan gum on the rheological properties of the fluid were studied. The results indicate that the fitting process has successfully determined the best selected model among the eight proposed models as the amount of clay, glass bubbles, starch, and xanthan gum are varied. The finding also shows that all of the predicted values are in a good agreement with experimental data, both in low and high rate of shear. Furthermore, the result also shows that the presence of clay, glass bubbles, and xanthan gum have a significant effect on the rheological properties of the fluid. On the basis of the result, in the absence of clay, the fluid behaves as a non-Newtonian fluid. However whenever clay is introduced into in the system, the fluid tends to be pseudoplastic. Moreover, the absence of glass bubbles and xanthan gum (independently) in the fluid tends to cause the fluid to be dilatant. However as the two fluid components are added, the fluid seems to change to pseudoplastic. The result shows that starch does not change the rheological behavior of the fluid significantly. The fluid tends to follow pseudoplastic behavior regardless of the amount of starch in the drilling fluid.

Calculated using the best method from previous data fitting.

xanthan gum tends to form agglomerations that act as dispersed particles in the fluid system. To assess the performances of the models, a comparison between the experimental and predicted rheograms of the tested fluids at various concentrations of xanthan gum was conducted. Figure 4 presents both of the experimental and predicted rheogram of the lightweight biopolymer drilling fluid as the concentration of xanthan gum is varied from 0% to 1% w/v. All of the predicted values seem to be in a good agreement with the experimental data. In addition, results also shows that 4066



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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: 603-7967 6869. Fax: 6037976 5319. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors would like to thank the following parties for their help and contributions in making this technical paper a reality: Ministry of Science Technology and Innovation Malaysia (MOSTI) under Project No: 13-02-03-3067, 3M Asia Pacific, Pte. Ltd., Scomi Oil and Gas (Malaysia) Sdn. Bhd.

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Viscoplastic Modeling of a Novel Lightweight Biopolymer Drilling Fluid

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