Viscoplastic Modeling of a Novel Lightweight Biopolymer Drilling Fluid for Underbalanced Drilling

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. 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 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 D- glucosyl 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: April 15, 2011 Revised: February 9, 2012 Accepted: February 10, 2012 Published: February 11, 2012 2012 American Chemical Society 4056

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 Ashrafizadeh 20 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 =τ 0 +η () γ (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 (τ 0 ) 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 τ 0. 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 (2) 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 (τ 0 ) 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 studies 22,25,26 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 =τ 0 + k( γ) n (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 studies 26 28 have also successfully applied this model to the evaluation of drilling fluids, especially fluids with high concentrations of bentonite suspension. The model of Casson is given by eq 4. τ 0.5 = koc + k C() γ 0.5 (4) 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 non- Newtonian 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. 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( γ 0 +γ) n (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. τ n = ( γ 0 ) 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 k OM that was interpreted as a function of the shape and interaction of the particles and k M 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 4057

Table 1. Measured Average Shear Stresses (τ (Pa) ± sd a ) of Lightweight Biopolymer Drilling Fluid As a Function of Shear Rate at Various Clay Concentrations shear rate, γ (s 1 ) 0 2.5 5 7.5 10 2.639 1.46 ± 0.04 3.14 ± 0.05 15.21 ± 0.06 26.65 ± 0.08 37.63 ± 0.05 5.279 1.76 ± 0.01 3.95 ± 0.02 17.12 ± 0.08 27.19 ± 0.07 40.93 ± 0.01 26.4 2.99 ± 0.12 5.14 ± 0.04 20.42 ± 0.11 31.44 ± 0.07 46.54 ± 0.11 52.71 3.84 ± 0.02 7.14 ± 0.01 22.49 ± 0.04 35.64 ± 0.12 53.63 ± 0.09 79.28 5.07 ± 0.01 8.46 ± 0.01 24.88 ± 0.01 37.18 ± 0.04 59.44 ± 0.10 88.17 5.57 ± 0.03 9.18 ± 0.04 25.26 ± 0.01 39.79 ± 0.09 60.28 ± 0.03 158.3 9.99 ± 0.03 12.64 ± 0.02 29.71 ± 0.07 45.47 ± 0.03 70.73 ± 0.04 176 11.12 ± 009 13.67 ± 0.13 31.16 ± 0.01 48.09 ± 0.11 72.09 ± 0.02 264 14.81 ± 0.02 17.44 ± 0.03 38.47 ± 0.01 54.93 ± 0.12 76.95 ± 0.11 a Abbreviation: sd, standard deviation. particle in the system. The Mizhari Berk model is given by eq 8. τ 0.5 = k OM + k M () γ n M 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 (τ 0 ) 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. METHODOLOGY Materials. Two types of biopolymers were used in this study, soluble starch (C 6 H 10 0 5 ) n (MW: 162 g/mol as monomer) and xanthan gum (C 35 H 49 O 29 ) n (MW: 933 g/mol as monomer). To reduce the density of the mixture, 3 M (8) Scotchlite hollow-glass spheres (rating: 4000 psi) were added in the formulation. A bactericide known as paraformaldehyde OH(CH 2 O) n H (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 4058

Table 2. Rheological Models of Lightweight Biopolymer Drilling Fluid and the Calculated Model s Parameters and Statistical Parameters as a Function of Clay Concentration rheological model 0 2.5 5 7.5 10 Bingham-plastic τ 0 = 1.3280 τ 0 = 3.8460 τ 0 = 17.230 τ 0 = 28.300 x 0 = 42.920 η = 0.0524 η = 0.0541 η = 0.0816 η = 0.1075 η =0.1568 R 2 = 0.9938 R 2 = 0.9891 R 2 = 0.9767 R 2 = 0.9764 R 2 = 0.9285 SSE = 1.0680 SSE = 2.0140 SSE = 9.9420 SSE = 17.460 SSE =118.30 RMSE = 0.3906 RMSE = 0.5364 RMSE = 1.1920 RMSE = 1.5790 RMSE = 4.1110 Ostwald De Weale k = 0.1781 k = 1.1100 k = 10.680 k = 19.150 k = 28.540 n = 0.7924 n = 0.0485 n = 0.2087 n = 0.1732 n = 0.1751 R 2 = 0.9781 R 2 = 0.9973 R 2 = 0.9086 R 2 = 0.9058 R 2 = 0.9557 SSE = 3.7820 SSE = 6.0420 SSE = 38.980 SSE = 69.730 SSE = 73.270 RMSE = 0.7350 RMSE = 0.9290 RMSE = 2.3600 RMSE = 3.1500 RMSE = 3.2350 Herschel Bulkley τ 0 = 1.3560 τ 0 = 2.9480 τ 0 = 15.440 τ 0 = 25.400 τ 0 =33.010 η = 0.0498 η = 0.1820 η = 0.3681 η = 0.6175 η = 2.9980 n = 1.0090 n = 0.7857 n = 0.7347 n = 0.6932 n = 0.4932 R 2 = 0.9938 R 2 = 0.9987 R 2 = 0.9896 R 2 = 0.9968 R 2 = 0.9953 SSE = 1.0660 SSE = 0.2442 SSE = 4.4130 SSE = 2.3630 SSE = 7.7220 RMSE = 0.4214 RMSE = 0.2017 RMSE =0.8576 RMSE = 0.6276 RMSE =1.1340 Casson k OC = 0.6205 k OC = 1.4820 k OC = 3.6940 k OC = 4.8290 k OC = 5.9400 k C = 0.1988 k C = 0.1653 k C = 0.1471 k C = 0.1561 k C =0.1888 R 2 = 0.9880 R 2 = 0.9977 R 2 = 0.9876 R 2 = 0.9943 R 2 =0.9910 SSE = 2.0700 SSE = 0.4324 SSE = 5.2870 SSE = 4.2400 SSE =14.850 RMSE = 0.5438 RMSE = 0.2485 RMSE = 0.8691 RMSE = 0.7783 RMSE = 1.4560 Sisko a = 0.0532 a = 0.0436 a = 0.1839 a = 0.0804 a = 0.0797 b = 1.4770 b = 2.6880 b = 1.2e 4 b = 24.610 b = 33.450 n = 0.0451 n = 0.1471 n = 11.45 n = 0.0581 n = 0.1029 R 2 = 0.9939 R 2 = 0.9981 R 2 = 1.769 R 2 = 0.9962 R 2 = 0.9908 SSE = 1.0480 SSE = 0.3480 SSE = 1180 SSE = 2.7890 SSE = 15.220 RMSE = 0.4180 RMSE = 0.2408 RMSE = 14.030 RMSE = 0.6818 RMSE = 1.5920 Robertson Stiff K = 0.0514 K = 0.3483 K = 1.9360 K = 5.1160 K = 16.320 γ 0 = 25.680 γ 0 = 24.350 γ 0 = 62.610 γ 0 = 53.830 γ 0 = 18.320 n = 1.0030 n = 0.6910 n = 0.5122 n = 0.4111 n = 0.2808 R 2 = 0.9938 R 2 = 0.9987 R 2 = 0.9860 R 2 = 0.9959 R 2 = 0.9969 SSE = 1.0680 SSE = 0.2457 SSE =5.9670 SSE = 3.0050 SSE =5.1820 RMSE = 0.4219 RMSE = 0.2024 RMSE = 0.9972 RMSE = 0.7078 RMSE = 0.9294 Heinz Casson γ 0 = 1.3640 γ 0 = 2.9130 γ 0 = 27.280 γ 0 = 62.670 γ 0 = 286.20 k = 0.0503 k = 0.1430 k = 0.2705 k = 0.4281 k = 1.4790 n = 1.0090 n = 0.7857 n = 0.7346 n = 0.6932 n = 0.4932 R 2 = 0.9938 R 2 = 0.9987 R 2 = 0.9896 R 2 = 0.9968 R 2 = 0.9953 SSE = 1.0680 SSE = 0.2442 SSE = 4.4130 SSE = 2.3630 SSE = 7.7220 RMSE = 0.4214 RMSE = 0.2017 RMSE = 0.8576 RMSE = 0.6276 RMSE = 1.1340 Mizhari Berk k OM = 1.0260 k OM = 1.6050 k OM = 3.8870 k OM = 4.9930 k OM = 5.6080 k M = 0.0777 k M = 0.1181 k M = 0.0713 k M = 0.0891 k M = 0.3641 n M = 0.6476 n M = 0.5533 n M = 0.6193 n M = 0.5924 n M = 0.3972 R 2 = 0.9925 R 2 = 0.9984 R 2 = 0.9914 R 2 = 0.9969 R 2 = 0.9948 SSE = 1.2870 SSE = 0.2894 SSE = 3.6810 SSE = 2.3020 SSE = 8.5940 RMSE = 0.4631 RMSE = 0.2196 RMSE = 0.7832 RMSE = 0.6194 RMSE = 1.1970 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 R- square, 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

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. 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. 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 (R 2 ) 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 Table 3. Measured Average Shear Stresses (τ (Pa) ± sd a ) of Lightweight Biopolymer Drilling Fluid as a Function of Shear Rate at Various Concentrations of Glass Bubbles shear rate, γ (s 1 ) 0 12.5 18.75 21.25 25 2.639 0.38 ± 0.01 2.37 ± 0.05 4.17 ± 0.01 5.49 ± 0.04 13.70 ± 0.11 5.279 0.46 ± 0.03 2.99 ± 0.11 4.95 ± 0.04 6.07 ± 0.01 15.15 ± 0.02 26.4 0.69 ± 0.12 4.17 ± 0.12 6.47 ± 0.07 8.83 ± 0.06 18.34 ± 0.01 52.71 1.08 ± 0.08 6.40 ± 0.08 8.15 ± 0.11 10.59 ± 0.12 20.44 ± 0.09 79.28 1.35 ± 0.06 7.45 ± 0.09 9.85 ± 0.12 12.13 ± 0.11 22.67 ± 0.04 88.17 1.51 ± 0.11 8.17 ± 0.04 10.79 ± 0.14 13.13 ± 0.10 23.46 ± 0.14 158.3 2.54 ± 0.17 11.24 ± 0.01 13.44 ± 0.04 16.95 ± 0.03 28.33 ± 0.09 176 2.97 ± 0.03 11.97 ± 0.01 14.97 ± 0.02 17.81 ± 0.04 29.76 ± 0.07 264 5.15 ± 0.04 14.67 ± 0.07 18.63 ± 0.06 21.50 ± 0.09 36.36 ± 0.06 a Abbreviation: sd, standard deviation. 4060

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 0 12.5 18.75 21.25 25 Bingham-plastic τ 0 = 0.1634 τ 0 = 3.2250 τ 0 = 5.0180 τ 0 = 6.7520 τ 0 = 15.350 η = 0.0172 η = 0.0474 η = 0.0542 η = 0.0607 η = 0.0822 R 2 = 0.9734 R 2 = 0.9716 R 2 = 0.9832 R 2 = 0.9698 R 2 = 0.9837 SSE = 0.5039 SSE = 4.1060 SSE = 3.1390 SSE = 7.1540 SSE = 7.0030 RMSE = 0.2683 RMSE = 0.7659 RMSE = 0.6697 RMSE = 1.0110 RMSE = 1.0000 Ostwald De Weale k = 0.0125 k = 0.9391 k = 1.8080 k = 2.8080 k = 8.9650 n = 1.0710 n = 0.4895 n = 0.4061 n = 0.3555 n = 0.2317 R 2 = 0.9696 R 2 = 0.9846 R 2 = 0.9575 R 2 = 0.9695 R 2 =0.9147 SSE = 0.5758 SSE = 2.2280 SSE = 7.9470 SSE = 7.2400 SSE = 36.590 RMSE = 0.2868 RMSE = 0.5642 RMSE = 1.0650 RMSE = 1.0170 RMSE = 2.2860 Herschel Bulkley τ 0 = 0.4888 τ 0 = 1.7940 τ 0 = 3.8920 τ 0 = 4.6870 τ 0 = 13.650 η = 0.0015 η = 0.3139 η = 0.2298 η = 0.4722 η = 0.3464 n = 1.4430 n = 0.6689 n = 0.7456 n = 0.6414 n = 0.7465 R 2 = 0.9961 R 2 = 0.9971 R 2 = 0.9968 R 2 = 0.9989 R 2 = 0.9962 SSE = 0.0741 SSE = 0.4242 SSE = 0.5956 SSE = 0.2655 SSE = 1.6160 RMSE = 0.1111 RMSE = 0.2659 RMSE = 0.3151 RMSE = 0.2103 RMSE = 0.5190 Casson k OC = 0.0187 k OC = 1.3520 k OC = 1.7800 k OC = 2.1280 k OC = 3.4420 k C = 0.1333 k C = 0.1559 k C = 0.1550 k C = 0.1562 k C = 0.1540 R 2 = 0.9679 R 2 = 0.9951 R 2 = 0.9963 R 2 = 0.9985 R 2 = 0.9934 SSE = 0.6077 SSE = 0.7015 SSE = 0.6995 SSE = 0.3551 SSE = 2.8220 RMSE = 0.2946 RMSE = 0.3166 RMSE = 0.3161 RMSE = 0.2252 RMSE = 0.6349 Sisko a = 0.0177 a = 0.0289 a = 0.0417 a = 0.0389 a = 0.1735 b = 0.7686 b = 1.6280 b = 3.5494 b = 4.4690 b = 1.3e 4 n = 0.6631 n = 0.2641 n = 0.1372 n = 0.1692 n = 14.58 R 2 = 0.9805 R 2 = 0.9951 R 2 = 0.9966 R 2 = 0.9984 R 2 = 1.171 SSE = 0.3702 SSE = 0.7099 SSE = 0.6422 SSE = 0.3812 SSE = 931.7 RMSE = 0.2484 RMSE = 0.3440 RMSE = 0.3272 RMSE = 0.2521 RMSE = 12.460 Robertson Stiff K = 3.1e 5 K = 0.5336 K = 0.5453 K = 1.2310 K = 1.6290 γ 0 = 114 γ 0 = 10.570 γ 0 = 26.560 γ 0 = 17.740 γ 0 = 57.260 n = 2.0250 n = 0.5921 n = 0.6216 n = 0.5069 n = 0.5355 R 2 = 0.9981 R 2 = 0.9976 R 2 = 0.9965 R 2 = 0.9984 R 2 = 0.9941 SSE = 0.0353 SSE = 0.3513 SSE = 0.6500 SSE = 0.3798 SSE = 2.5450 RMSE = 0.0767 RMSE = 0.2420 RMSE = 0.3291 RMSE = 0.2516 RMSE = 0.6513 Heinz Casson γ 0 = 0.7850 γ 0 = 1.3130 γ 0 = 4.1750 γ 0 = 5.5630 γ 0 = 22.430 k = 0.0021 k = 0.2099 k = 0.1714 k = 0.3029 k = 0.2586 n = 1.4430 n = 0.6689 n = 0.7456 n = 0.6414 n = 0.7465 R 2 = 0.9961 R 2 = 0.9971 R 2 = 0.9968 R 2 = 0.9989 R 2 = 0.9962 SSE =0.0741 SSE = 0.4242 SSE = 0.5956 SSE = 0.2655 SSE = 1.6160 RMSE = 0.1111 RMSE = 0.2659 RMSE = 0.3151 RMSE = 0.2103 RMSE = 0.5190 Mizhari Berk k OM = 0.6617 k OM = 1.1590 k OM = 3.1870 k OM = 524.80 k OM = 3.6440 k M = 0.0065 k M = 0.2428 k M = 1256 k M = 522.4 k M = 0.0753 n M = 0.9867 n M = 0.4320 n M = 116.2 n M = 0.0006 n M = 0.6176 R 2 = 0.9982 R 2 = 0.9965 R 2 =0 R 2 = 0.7803 R 2 = 0.9973 SSE = 0.0350 SSE = 0.5080 SSE = 186.90 SSE = 52.1 SSE = 1.1710 RMSE = 0.0763 RMSE = 0.2910 RMSE = 5.5820 RMSE = 2.9470 RMSE = 0.4417 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 (calculated SSE and RMSE values) and the closest R 2 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 R 2 = 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. 4061

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/cm 3 ). 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 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 (R 2 ) 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 R 2 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 R 2 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 R 2 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 developed 33 to describe the rheological behavior of fluid with a dispersing particle within the system. The model constant k OM was related to the shape and interaction of particles. It gives rise to the yield stress, and k M is a function of the dispersing medium. Thus, in this study, the interpretation of this model matches the physical Table 5. The Measured Average Shear Stresses (τ (Pa) ± sd a ) of Lightweight Biopolymer Drilling Fluid as a Function of Shear Rate at Various Starch Concentration shear rate, γ (s 1 ) 0 1 1.5 1.75 2 2.639 0.72 ± 0.02 1.34 ± 0.03 4.49 ± 0.11 8.14 ± 0.04 12.50 ± 0.02 5.279 0.82 ± 0.12 1.42 ± 0.01 6.07 ± 0.01 9.14 ± 0.04 14.32 ± 0.04 26.4 2.15 ± 0.04 3.46 ± 0.08 8.83 ± 0.06 13.05 ± 0.08 17.84 ± 0.01 52.71 3.82 ± 0.05 5.01 ± 0.07 10.59 ± 0.07 15.90 ± 0.11 20.28 ± 0.11 79.28 5.28 ± 0.11 6.19 ± 0.11 12.13 ± 0.03 16.97 ± 0.16 22.62 ± 0.10 88.17 5.59 ± 0.07 6.45 ± 0.16 13.13 ± 0.12 18.05 ± 0.13 23.46 ± 0.08 158.3 8.24 ± 0.03 9.15 ± 0.17 16.95 ± 0.10 22.19 ± 0.10 28.01 ± 0.09 176 8.96 ± 0.12 10.12 ± 0.05 17.81 ± 0.06 23.04 ± 0.01 29.34 ± 0.02 264 12.42 ± 0.10 13.65 ± 0.07 21.50 ± 0.04 28.18 ± 0.01 35.11 ± 0.03 a Abbreviation: sd, standard deviation. 4062

Table 6. Rheological Models of Lightweight Biopolymer Drilling Fluid and Its Corresponding Model and Statistical Parameters at Various Starch Concentrations (%w/v) rheological model 0 (%w/v) 1 (%w/v) 1.5 (%w/v) 1.75 (%w/v) 2 (%w/v) Bingham-plastic τ 0 = 1.1210 τ 0 = 1.9450 τ 0 = 6.5010 τ 0 = 10.300 τ 0 = 14.880 η = 0.0445 η = 0.0460 η = 0.0621 η = 0.0727 η = 0.0816 R 2 = 0.9877 R 2 = 0.9823 R 2 = 0.9574 R 2 = 0.9532 R 2 = 0.9654 SSE = 1.5490 SSE = 2.3880 SSE = 10.750 SSE =16.190 SSE = 14.890 RMSE = 0.4704 RMSE = 0.5840 RMSE = 1.2390 RMSE = 1.5210 RMSE = 1.4580 Ostwald De Weale k = 0.2159 k = 0.4322 k = 2.6040 k = 5.0210 k = 8.4340 n = 0.7240 n = 0.6126 n = 0.3706 n = 0.2968 n = 0.2407 R 2 = 0.9978 R 2 = 0.9926 R 2 = 0.9804 R 2 =0.9716 R 2 = 0.9489 SSE = 0.2816 SSE = 0.9951 SSE = 4.9490 SSE = 9.8290 SSE = 21.990 RMSE = 0.2006 RMSE = 0.3770 RMSE = 0.8408 RMSE = 1.1850 RMSE = 1.7730 Herschel Bulkley τ 0 = 0.3173 τ 0 = 0.9012 τ 0 = 3.8000 τ 0 =6.8370 τ 0 =11.820 η = 0.1629 η = 0.2160 η = 0.6832 η =0.9169 η = 0.7279 n = 0.7711 n = 0.7280 n = 0.5833 n = 0.5603 n = 0.6181 R 2 = 0.9986 R 2 = 0.9973 R 2 = 0.9966 R 2 = 0.9959 R 2 = 0.9968 SSE = 0.1777 SSE = 0.3633 SSE = 0.8563 SSE = 1.4200 SSE = 1.3850 RMSE = 0.1721 RMSE = 0.2461 RMSE = 0.3778 RMSE = 0.4865 RMSE = 0.4805 Casson k OC = 0.6348 k OC = 0.9480 k OC = 2.0680 k OC =2.7170 k OC = 3.3720 k C = 0.1786 k C = 0.1687 k C = 0.1609 k C =0.1597 k C =0.1556 R 2 = 0.9973 R 2 = 0.9971 R 2 = 0.9942 R 2 = 0.9944 R 2 = 0.9975 SSE = 0.3385 SSE = 0.3852 SSE = 1.4680 SSE = 1.9370 SSE = 1.0710 RMSE = 0.2199 RMSE = 0.2346 RMSE = 0.4580 RMSE = 0.5260 RMSE = 0.3911 Sisko a = 0.0249 a = 0.0301 a = 0.0338 a = 0.0403 a = 0.1701 b = 0.3190 b = 0.8544 b = 3.8480 b = 6.8790 b = 1.3e 4 n = 0.5192 n = 0.3361 n = 0.2145 n = 0.1657 n = 13.99 R 2 = 0.9985 R 2 = 0.9983 R 2 = 0.9977 R 2 = 0.9983 R 2 = 1.054 SSE = 0.1934 SSE = 0.2257 SSE = 0.5873 SSE = 0.6028 SSE = 884.50 RMSE = 0.1795 RMSE = 0.1940 RMSE = 0.3129 RMSE = 0.3170 RMSE = 12.140 Robertson Stiff K = 0.1817 K = 0.2937 K = 1.4830 K = 2.7100 K = 3.2720 γ 0 = 3.0760 γ 0 = 6.7540 γ 0 = 10.830 γ 0 = 13.520 γ 0 = 26.900 n = 0.7545 n = 0.6818 n = 0.4751 n = 0.4121 n = 0.4153 R 2 = 0.9986 R 2 = 0.9969 R 2 = 0.9953 R 2 = 0.9937 R 2 = 0.9943 SSE = 0.1733 SSE = 0.4232 SSE = 1.1800 SSE = 2.1740 SSE = 2.4580 RMSE = 0.1699 RMSE = 0.2656 RMSE = 0.4434 RMSE = 0.6020 RMSE = 0.6400 Heinz Casson γ 0 = 0.1611 γ 0 = 0.5604 γ 0 = 3.9150 γ 0 = 10.990 γ 0 = 24.970 k = 0.1256 k = 0.1572 k = 0.3985 k = 0.5137 k = 0.4499 n = 0.7711 n = 0.7280 n = 0.5833 n = 0.5603 n = 0.6181 R 2 = 0.9986 R 2 = 0.9973 R 2 = 0.9966 R 2 = 0.9959 R 2 = 0.9968 SSE = 0.1777 SSE = 0.3633 SSE = 0.8563 SSE = 1.4200 SSE = 1.3850 RMSE = 0.1721 RMSE = 0.2461 RMSE = 0.3778 RMSE = 0.4865 RMSE = 0.4805 Mizhari Berk k OM = 0.3427 k OM = 0.7807 k OM = 1.7790 k OM = 2.4800 k OM = 3.3550 k M = 0.3011 k M = 0.2398 k M = 0.3032 k M = 0.2772 k M =0.1634 n M = 0.4221 n M = 0.4463 n M = 0.4025 n M =0.4141 n M = 0.4921 R 2 = 0.9985 R 2 = 0.9978 R 2 = 0.9970 R 2 = 0.9966 R 2 = 0.9975 SSE = 0.1841 SSE = 0.2940 SSE = 0.7488 SSE =1.1690 SSE = 1.0630 RMSE = 0.1752 RMSE = 0.2213 RMSE = 0.3533 RMSE = 0.4414 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

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, 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 R 2, 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 non- Newtonian. 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 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 shear rate, γ (s 1 ) 0 0.25 0.5 0.75 1 2.639 1.61 ± 0.11 2.13 ± 0.02 4.49 ± 0.11 8.19 ± 0.02 10.16 ± 0.11 5.279 1.67 ± 0.04 2.88 ± 0.12 6.07 ± 0.03 9.14 ± 0.02 11.32 ± 0.03 26.4 1.84 ± 0.01 4.17 ± 0.05 8.83 ± 0.01 12.11 ± 0.02 14.14 ± 0.02 52.71 2.15 ± 0.09 6.50 ± 0.04 10.59 ± 0.07 14.81 ± 0.04 16.64 ± 0.04 79.28 2.49 ± 0.07 7.98 ± 0.10 12.13 ± 0.03 16.84 ± 0.10 18.55 ± 0.01 88.17 2.57 ± 0.04 8.36 ± 0.05 13.13 ± 0.03 18.09 ± 0.09 19.64 ± 0.10 158.3 3.30 ± 0.11 11.81 ± 0.06 16.95 ± 0.11 22.68 ± 0.06 25.31 ± 0.05 176 3.53 ± 0.07 12.81 ± 0.03 17.81 ± 0.09 23.48 ± 0.03 26.84 ± 0.02 264 5.38 ± 0.03 16.48 ± 0.08 21.52 ± 0.05 28.87 ± 0.02 35.41 ± 0.11 a Abbreviation: sd, standard deviation. 4064

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 0 (%w/v) 0.25 (%w/v) 0.5 (%w/v) 0.75 (%w/v) 1 (%w/v) Bingham-plastic τ 0 = 1.4570 τ 0 = 2.9860 τ 0 = 6.5010 τ 0 = 9.8080 τ 0 = 11.060 η = 0.0134 η = 0.0542 η = 0.0621 η = 0.0773 η = 0.0920 R 2 = 0.9702 R 2 = 0.9825 R 2 = 0.9574 R 2 = 0.9724 R 2 = 0.9947 SSE = 0.3450 SSE = 3.2760 SSE = 10.750 SSE = 10.590 SSE = 2.8320 RMSE = 0.2220 RMSE = 0.6841 RMSE = 1.2390 RMSE = 1.2300 RMSE = 0.6361 Ostwald De Weale k = 0.6058 k = 0.7442 k = 2.6040 k = 4.4670 k = 4.9440 n = 0.3552 n = 0.5502 n = 0.3706 n = 0.3221 n = 0.3306 R 2 = 0.7842 R 2 = 0.9869 R 2 = 0.9804 R 2 = 0.9606 R 2 = 0.9043 SSE = 2.4980 SSE = 2.4550 SSE = 4.9490 SSE = 15.150 SSE = 50.880 RMSE = 0.5974 RMSE = 0.5922 RMSE = 0.8408 RMSE = 1.4710 RMSE = 2.6960 Herschel Bulkley τ 0 = 1.7050 τ 0 = 1.7510 τ 0 = 3.8000 τ 0 = 7.3090 τ 0 = 10.470 η = 0.0013 η = 0.2548 η = 0.6832 η = 0.5619 η = 0.1571 n = 1.4280 n = 0.7278 n = 0.5833 n = 0.6530 n = 0.9048 R 2 = 0.9904 R 2 = 0.9985 R 2 = 0.9966 R 2 = 0.9992 R 2 = 0.9962 SSE = 0.1114 SSE = 0.2738 SSE = 0.8563 SSE = 0.3079 SSE = 1.9970 RMSE = 0.1363 RMSE = 0.2136 RMSE = 0.3778 RMSE = 0.2265 RMSE = 0.5769 Casson k OC = 0.9881 k OC = 1.2430 k OC = 2.0680 k OC = 2.6150 k OC = 2.7620 k C = 0.0731 k C = 0.1746 k C = 0.1609 k C = 0.1698 k C = 0.1870 R 2 = 0.9138 R 2 = 0.9981 R 2 = 0.9942 R 2 = 0.9993 R 2 = 0.9850 SSE = 0.9974 SSE = 0.3555 SSE = 1.4680 SSE = 0.2741 SSE = 7.9650 RMSE = 0.3775 RMSE = 0.2253 RMSE = 0.4580 RMSE = 0.1979 RMSE = 1.0670 Sisko a = 0.0152 a = 0.0377 a = 0.0338 a = 0.0518 a = 0.1578 b = 1.7980 b = 1.5820 b = 3.8480 b = 6.9470 b = 14.2 n = 0.0898 n = 0.2580 n = 0.2145 n = 0.1418 n = 31.54 R 2 = 0.9790 R 2 = 0.9979 R 2 = 0.9977 R 2 = 0.9990 R 2 = 0.0918 SSE = 0.2429 SSE = 0.3978 SSE = 0.5873 SSE = 0.3988 SSE = 483 RMSE = 0.2012 RMSE = 0.2575 RMSE = 0.3129 RMSE = 0.2578 RMSE = 8.9720 Robertson Stiff K = 1.7e6 K = 0.4013 K = 1.4830 K = 1.7280 K = 0.2565 γ 0 = 374.50 γ 0 = 11.580 γ 0 = 10.830 γ 0 = 22.190 γ 0 = 85.550 n = 2.3130 n = 0.6609 n = 0.4751 n = 0.4962 n = 0.8391 R2 = 0.9902 R2 = 0.9986 R2 = 0.9953 R2 = 0.9986 R2 = 0.9955 SSE = 0.1135 SSE = 0.2690 SSE = 1.1800 SSE = 0.5510 SSE = 2.3740 RMSE = 0.1375 RMSE = 0.2117 RMSE = 0.4434 RMSE = 0.3031 RMSE = 0.6290 Heinz Casson γ 0 = 1.8650 γ 0 = 1.3960 γ 0 = 3.9150 γ 0 = 10.950 γ 0 = 12.000 k = 0.0018 k = 0.1854 k = 0.3985 k = 0.3669 k = 0.1422 n = 1.4280 n = 0.7278 n = 0.5833 n = 0.6530 n = 0.9049 R2 = 0.9904 R2 = 0.9985 R2 = 0.9966 R2 = 0.9992 R2 = 0.9962 SSE = 0.1114 SSE = 0.2738 SSE = 0.8563 SSE = 0.3079 SSE = 1.9970 RMSE = 0.1363 RMSE = 0.2136 RMSE = 0.3778 RMSE = 0.2265 RMSE = 0.5769 Mizhari Berk k OM = 1.2950 k OM = 1.1490 k OM = 1.7790 k OM = 2.5890 k OM = 3.1800 k M = 0.0014 k M = 0.2139 k M = 0.3032 k M = 0.1811 k M = 0.0478 n M = 1.1860 n M = 0.4686 n M = 0.4025 n M = 0.4897 n M = 0.7257 R2 = 0.9934 R2 = 0.9984 R2 = 0.9970 R2 = 0.9993 R2 = 0.9977 SSE = 0.0767 SSE = 0.3068 SSE = 0.7488 SSE = 0.2617 SSE = 1.2440 RMSE = 0.1130 RMSE = 0.2261 RMSE = 0.3533 RMSE = 0.2089 RMSE = 0.4554 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 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 4065