viscoplastic modeling of a novel lightweight biopolymer drilling fluid for underbalanced drilling

Viscoplastic Modeling of a Novel Lightweight Biopolymer DrillingFluid for Underbalanced DrillingMunawar 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 theexperimental data. The effect of concentration of clay, glass bubbles, starch, and xanthan gum on the fluid rheological propertieswas 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 andhigh (1500 s−1) rate of shear. The result also indicated that the presence of clay, glass bubbles, and xanthan gum havesignificantly changed the fluid behavior, while the presence of starch has not. Results also showed that all of the tested fluid seemsto follow pseudoplastic behavior except for the following three tested fluids: one is fluid with the absence of clay, second andthird is fluids with no glass bubble or xanthan gum, respectively. The first fluid tends to follows a Newtonian behavior, while theother two fluids tend to follow dilatants behavior.

■ INTRODUCTIONUnderbalanced drilling (UBD) has been considered as one ofthe best methods to reduce formation damage during drilling.UBD is usually preferred due to its many advantages duringdrilling processes, such as higher rate of penetration (ROP),lower perforation damage due to drilling, longer bit life, a rapidindication of productive reservoir zone, and the potential fordynamic flow testing while drilling, etc.1 Another benefit ofUBD is its ability to provide reliable implementation ofhorizontal drilling, in which formation damage has always beenone of the major concerns due to longer fluid contact times andgreater prevalence of open-hole completions.2,3

Nowadays, UBD is commonly achieved with the use ofcompressible 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 multiphasefluids are used in wellbores often make UBD challenging anddifficult to be conducted. Often times this requires specialadditional instruments or equipment, and this posts additionalworks. These problems would be minimized with the use ofglass bubbles as a density reducing agent in an incompressiblelightweight drilling fluid.6 With fluid density as low as 6.5 to 6.8lbm/gal., the novel incompressible lightweight drilling fluidwould be able to provide underbalanced conditions duringdrilling without major problems in the field.7,8 Glass bubbleshave been extensively used as filler in paints, glues, and otherliquids. Recent study has also showed the successful applicationof bubbles in the formulation of a super-light-weightcompletion fluid (SLWCF) for underbalanced perforation.8,9

Specific drilling fluid properties are required to maximize wellproductivity. The use of UBD requires not only low-densityfluids but also specific fluid properties. At the moment, virtuallymost of the drilling fluids used in offshore operations are eitheroil, crude, or synthetic oil.10 Unfortunately most of the

continuous phases of these fluids are toxic and consideredunfriendly to the environment. Thus, to address these issues, acomprehensive study is proposed to formulate a novel andenvironmentally friendly lightweight water-based drilling fluid.The novelty of the proposed work lies in the attempt toengineer a fluid which is stable, low density, and environ-mentally friendly. In our previous studies,11,12 we havesuccessfully formulated a water based lightweight drilling fluidwith glass bubbles as the density reducing agent, and a naturalbiopolymer, that is, polysaccharide xanthan gum and starch asviscosity modifier. In the study, we have developed a novellightweight water-based mud system using glass bubbles as adensity reducing agent and two types of biopolymers, xanthangum and starch, as additives. Secreted by Xanthamonas sp.,xanthan gum is an exocellular biopolymer which has a mainchain based on a linear backbone of 1,4-linked β-D-glucoseresidues, and a trisaccharide side chain attached to alternate D-glucosyl residues.13 Starch granules, on the other hand arecomposed of two types of α-glucan, namely, amylase andamylopectin, produced from green plants as an energystorage.14,15 These two biopolymers were used since they arenot toxic to the environment and within the governmentregulation. They have also been widely used in drilling fluid andenhanced oil recovery (EOR).16,17 This study is a continuationwork of our previous study, which presented a comprehensiveinvestigation on the effect of concentration of clay, glassbubbles, and biopolymers on the rheological behavior of thefluid.In the upstream petroleum industry, information on

rheological properties of drilling fluids is very important to

Received: April 15, 2011Revised: February 9, 2012Accepted: February 10, 2012Published: February 11, 2012

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

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ensure the success of drilling operation.18 Accurate knowledgeon the fluid viscoplastic behavior as well as its prediction as afunction of its surrounding such as formation transienttemperature and pressure, the presence of brine and/orformation water, etc., are very crucial. Drilling fluid expertshave comprehensively investigated and generated numerousmodels 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 categorizedas a non-Newtonian fluid and their rheological behavior couldbe described by several models.19,21 In the early time of thedevelopment of complex drilling fluids, the Bingham plasticmodel and Ostwald−De−Weale model (or commonly knownas the Power Law model) were the most traditional modelsused to describe viscoplastic behavior of drilling fluid.20 Themodel of Bingham plastic can be expressed by eq 1.

τ = τ + η γ∞( )0 (1)

Khalil et al.22 reported that the Bingham plastic model waswidely used to describe several types of fluids in the petroleumindustry. This is due to its advantage in which its Bingham yieldpoint (τ0) could easily be determined.21 However, recentstudies indicated that this model frequently fails to representthe rheological behavior of very complex drilling fluidscontaining polymers, especially in low shear rates.22,23 This isbecause the Bingham plastic model is not adequate to describefluids with complex rheological behavior. As a result it producesan unrealistic high value of τ0.

18 Thus, to overcome thisshortcoming, many fluid experts have attempted to fitexperimental data to the Ostwald−De−Weale (power law)model. The model is given by eq 2.

τ = γk( )n(2)

Compared to the previous model, the Ostwald−De−Wealemodel is preferred to describe drilling fluid with complexrheological behavior, especially at low shear rates, due to itspower law relationship.19 However, at extremely low shear rate,the absence of the Bingham yield point (τ0) often times makesthis model fail to provide a good result in describing fluidviscoplastic properties. Hence, to overcome this issue, anotherrheological model namely the Herschel−Bulkley (yield powerlaw) model is developed. The model considers threeparameters to accommodate the shortcoming of the Binghamplastic model to describe fluid properties with apower equationand the poor result from the Oswald−De−Weale at anextremely low shear rate.24 Most of the studies22,25,26 haveindicated that the model could be considered as one of themost common models to describe the rheological behavior ofdrilling/completion fluids and/or cement slurries. TheHerschel−Bulkley model is given by eq 3.

τ = τ + γk( )n0 (3)

Recent advances in drilling technology and harsh drillingenvironments require an accurate rheological model. Anothermodel that is commonly used to express the viscoplasticproperties of fluids is the Casson model. This model wasinitially used to describe the rheological properties of inks andpaints. However, recent studies26−28 have also successfullyapplied this model to the evaluation of drilling fluids, especially

fluids with high concentrations of bentonite suspension. Themodel of Casson is given by eq 4.

τ = + γk k ( )0.5OC C

0.5(4)

Another complex model containing three parameters, namelythe Sisko model has also been considered as one of the mostpopular models in estimating the rheological behavior ofdrilling fluids. This model was developed to accommodate theunique feature of the fluid with both Newtonian and non-Newtonian properties. Mathematically, this model combinesboth the Newtonian (linear relationship) and non-Newtonian(Power Law relationship) to better describe the fluidviscoplastic behavior.28 This model was previously used toestimate the flow properties of hydrocarbon-based lubricatinggreases.29 However, a recent study conducted by Khalil et al.21

has also shown that this model is able to satisfactorily modelthe rheological behavior of lightweight completion fluidcontaining glass bubbles as density reducing agent. The Siskomodel is given by eq 5.

τ = γ + γa b( ) ( )n(5)

Furthermore, another improved model, the Robertson−Stiffmodel, was also proposed to estimate the rheological behaviorof drilling fluid. In addition to the Casson model, the three-parameters of the Robertson−Stiff model has also been able todescribe the flow behavior of drilling fluid with high amount ofbentonite suspension satisfactorily well.18,27 This model is alsosuitable for other complex fluids in upstream oil and gasindustry such as cement slurries.30 The Robertson−Stiff modelis expressed by eq 6.

τ = γ + γK( )n0 (6)

To have a better estimation of viscoplastic behavior ofdrilling fluid made of a complex polymer, another rheologicalmodel called the Heinz−Casson model was proposed. Thismodel is a modification of the existing model of Casson. Themodel lacks application in the upstream oil and gas industry.This model has successfully been used in describing the flowbehavior of some complex fluids such as petroleum jelly forcream formulation and concentrated xanthan gum solution.31,32

The Heinz−Casson model is given by eq 4.

τ = γ + γk( ) ( )n n n0 (7)

Another complex model, the Mizhari−Berk model which hasthree parameters has also been proposed to model the flowbehavior of the formulated lightweight biopolymer drilling fluid.In its early development, this model was previously used todescribe the rheological properties of fluid with a dispersingparticle in its system, such as concentrated orange juice or fluidsused in food engineering.33 In addition, the Mizhari−Berkmodel has also been found to have very promising potentialapplication in the upstream oil and gas industry. The model hassuccessfully been used to model the flow behavior of super-light-weight completion fluid (SLWCF).21 This is because thepurposed parameters in this model, the constant of kOM thatwas interpreted as a function of the shape and interaction of theparticles and kM which is a function of the dispersing medium,provides a better solution in determining the flow behavior ofglass bubbles along with other material that act as dispersing

Industrial & Engineering Chemistry Research Article

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particle in the system. The Mizhari−Berk model is given by eq8.

τ = + γk k ( )n0.5OM M

M(8)

As mentioned earlier, the main objective of this study is toprovide a comprehensive investigation on the effect of fluidcomponents concentrations, such as clay, glass bubbles and thetwo biopolymers, namely starch and xanthan gum, on the flowbehavior of the fluid. To assess this effect, a statistical-basedmodel fitting analysis was carried out on all of the eight modelspreviously mentioned. This is to find the best model to predictthe rheological behavior of the formulated drilling fluid.Experimental data, such as shear rate and shear stress ofdifferent fluids at various concentration of clay, glass bubblesand biopolymers were fitted to each model. Using nonlinearregression analysis and adopting the Levenberg−Marquardttechnique, the calculated model parameters and severalstatistical 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’smain component, glass bubbles, xanthan gum, starch, and clay,on the viscoplastic behavior of the fluid. This is conducted byfitting the experimental data of fluid shear stress as a function ofthe applied shear rate to the eight well-established rheologicalmodels frequently used in describing the viscoplatic behavior offluid in the oil and gas industry. This information is essential inselecting the appropriate procedure in handling fluid in thefield, selecting the appropriate pump to be used to pump thefluid downhole and up to the surface, etc. In addition, someinformation on the model’s parameters that are used todescribe 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 forcerequired to initiate fluid flow. Meanwhile, the knowledge on theother two fluid parameters, the fluid consistency (k) and indexflow (n), give field engineers information on the type of fluid,Newtonian, non-Newtonian with shear thinning (pseudo-plastic) behavior, or non-Newtonian fluid with shear thickening(dilatant) behavior.

■ METHODOLOGY

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

Scotchlite hollow-glass spheres (rating: 4000 psi) were added inthe formulation. A bactericide known as paraformaldehydeOH(CH2O)nH (MW: 30.03 g/mol as monomer) was used toprotect the biopolymers against parasites. To improve the fluidrheological properties, clay (samples were taken fromWyoming, USA) was used. Sodium chloride was used as anadditive to improve fluid properties.

Formulation of Lightweight Biopolymer DrillingFluid. To formulate water based lightweight biopolymerdrilling fluid, all of the raw materials, distillated water, glassbubbles, starch, xanthan gum, clay, paraformaldehyde, andsodium chloride, were mixed using a digital mixer (IKA RW20) at 500 rpm. In the first test, the clay concentration wasvaried at four different values, 2.5%, 5%, 7.5%, and 10% w/v,while the amount of other components were fixed (xanthangum, 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). Tounderstand the effect of clay concentration on the rheologicalproperties of the fluid, a controlled test was conducted byformulating a fluid with 0% w/v of clay concentration. In thesecond step, the concentration of glass bubbles was varied atfour 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 controlledtest was also conducted at 0% w/v of glass bubblesconcentration. In the next step, tests were conducted byformulating a fluid with various amounts of biopolymer, that is,starch and xanthan gum. The concentration of starch was variedat 1%, 1.5%, 1.75%, and 2% w/v, while other component werefixed (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/vof starch concentration. Finally, tests were performed byvarying 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 wereconducted at ambient pressure and temperature.

Viscoplastic Measurements. In this study, viscoplasticparameters such as shear rate and shear stress of the lightweightbiopolymer drilling fluid were determined using a rotationalviscometer equipped with MV2P spindle (Haake Viscotestermodel VT 550, with repeatability and accuracy of ±1%,comparability of ±2%). The study of fluid rheological behaviorwas conducted by measuring the shear stress at various appliedshear rates ranging from 2.639 to 264 s−1. To ensurerepeatability and accuracy of the measurement, readings were

Table 1. Measured Average Shear Stresses (τ (Pa) ± sda) of Lightweight Biopolymer Drilling Fluid As a Function of Shear Rateat Various Clay Concentrations (% w/v)

shear rate, γ (s−1) 0 (% w/v) 2.5 (% w/v) 5 (% w/v) 7.5 (% w/v) 10 (% w/v)

2.639 1.46 ± 0.04 3.14 ± 0.05 15.21 ± 0.06 26.65 ± 0.08 37.63 ± 0.055.279 1.76 ± 0.01 3.95 ± 0.02 17.12 ± 0.08 27.19 ± 0.07 40.93 ± 0.0126.4 2.99 ± 0.12 5.14 ± 0.04 20.42 ± 0.11 31.44 ± 0.07 46.54 ± 0.1152.71 3.84 ± 0.02 7.14 ± 0.01 22.49 ± 0.04 35.64 ± 0.12 53.63 ± 0.0979.28 5.07 ± 0.01 8.46 ± 0.01 24.88 ± 0.01 37.18 ± 0.04 59.44 ± 0.1088.17 5.57 ± 0.03 9.18 ± 0.04 25.26 ± 0.01 39.79 ± 0.09 60.28 ± 0.03158.3 9.99 ± 0.03 12.64 ± 0.02 29.71 ± 0.07 45.47 ± 0.03 70.73 ± 0.04176 11.12 ± 009 13.67 ± 0.13 31.16 ± 0.01 48.09 ± 0.11 72.09 ± 0.02264 14.81 ± 0.02 17.44 ± 0.03 38.47 ± 0.01 54.93 ± 0.12 76.95 ± 0.11

aAbbreviation: sd, standard deviation.



taken three times, and the average of the three readings wasused. To ensure consistency and repeatability, a newly fresh-made 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 statisticalsoftware, 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 ofthe developed models to predict the rheological properties of

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

rheological model 0 (% w/v) 2.5 (% w/v) 5 (% w/v) 7.5 (% w/v) 10 (% w/v)

Bingham-plastic τ0 = 1.3280 τ0 = 3.8460 τ0 = 17.230 τ0 = 28.300 x0 = 42.920η∞ = 0.0524 η∞ = 0.0541 η∞ = 0.0816 η∞ = 0.1075 η∞ =0.1568R2 = 0.9938 R2 = 0.9891 R2 = 0.9767 R2 = 0.9764 R2 = 0.9285SSE = 1.0680 SSE = 2.0140 SSE = 9.9420 SSE = 17.460 SSE =118.30RMSE = 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 = 28.540n = 0.7924 n = 0.0485 n = 0.2087 n = 0.1732 n = 0.1751R2 = 0.9781 R2 = 0.9973 R2 = 0.9086 R2 = 0.9058 R2 = 0.9557SSE = 3.7820 SSE = 6.0420 SSE = 38.980 SSE = 69.730 SSE = 73.270RMSE = 0.7350 RMSE = 0.9290 RMSE = 2.3600 RMSE = 3.1500 RMSE = 3.2350

Herschel−Bulkley τ0 = 1.3560 τ0 = 2.9480 τ0 = 15.440 τ0 = 25.400 τ0 =33.010η∞ = 0.0498 η∞ = 0.1820 η∞ = 0.3681 η∞ = 0.6175 η∞ = 2.9980n = 1.0090 n = 0.7857 n = 0.7347 n = 0.6932 n = 0.4932R2 = 0.9938 R2 = 0.9987 R2 = 0.9896 R2 = 0.9968 R2 = 0.9953SSE = 1.0660 SSE = 0.2442 SSE = 4.4130 SSE = 2.3630 SSE = 7.7220RMSE = 0.4214 RMSE = 0.2017 RMSE =0.8576 RMSE = 0.6276 RMSE =1.1340

Casson kOC = 0.6205 kOC = 1.4820 kOC = 3.6940 kOC = 4.8290 kOC = 5.9400kC = 0.1988 kC = 0.1653 kC = 0.1471 kC = 0.1561 kC =0.1888R2 = 0.9880 R2 = 0.9977 R2 = 0.9876 R2 = 0.9943 R2 =0.9910SSE = 2.0700 SSE = 0.4324 SSE = 5.2870 SSE = 4.2400 SSE =14.850RMSE = 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 = 0.0797b = 1.4770 b = 2.6880 b = −1.2e4 b = 24.610 b = 33.450n = −0.0451 n = 0.1471 n = −11.45 n = 0.0581 n = 0.1029R2 = 0.9939 R2 = 0.9981 R2 = −1.769 R2 = 0.9962 R2 = 0.9908SSE = 1.0480 SSE = 0.3480 SSE = 1180 SSE = 2.7890 SSE = 15.220RMSE = 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 = 16.320γ0 = 25.680 γ0 = 24.350 γ0 = 62.610 γ0 = 53.830 γ0 = 18.320n = 1.0030 n = 0.6910 n = 0.5122 n = 0.4111 n = 0.2808R2 = 0.9938 R2 = 0.9987 R2 = 0.9860 R2 = 0.9959 R2 = 0.9969SSE = 1.0680 SSE = 0.2457 SSE =5.9670 SSE = 3.0050 SSE =5.1820RMSE = 0.4219 RMSE = 0.2024 RMSE = 0.9972 RMSE = 0.7078 RMSE = 0.9294

Heinz−Casson γ0 = 1.3640 γ0 = 2.9130 γ0 = 27.280 γ0 = 62.670 γ0 = 286.20k = 0.0503 k = 0.1430 k = 0.2705 k = 0.4281 k = 1.4790n = 1.0090 n = 0.7857 n = 0.7346 n = 0.6932 n = 0.4932R2 = 0.9938 R2 = 0.9987 R2 = 0.9896 R2 = 0.9968 R2 = 0.9953SSE = 1.0680 SSE = 0.2442 SSE = 4.4130 SSE = 2.3630 SSE = 7.7220RMSE = 0.4214 RMSE = 0.2017 RMSE = 0.8576 RMSE = 0.6276 RMSE = 1.1340

Mizhari−Berk kOM = 1.0260 kOM = 1.6050 kOM = 3.8870 kOM = 4.9930 kOM = 5.6080kM = 0.0777 kM = 0.1181 kM = 0.0713 kM = 0.0891 kM = 0.3641nM = 0.6476 nM = 0.5533 nM = 0.6193 nM = 0.5924 nM = 0.3972R2 = 0.9925 R2 = 0.9984 R2 = 0.9914 R2 = 0.9969 R2 = 0.9948SSE = 1.2870 SSE = 0.2894 SSE = 3.6810 SSE = 2.3020 SSE = 8.5940RMSE = 0.4631 RMSE = 0.2196 RMSE = 0.7832 RMSE = 0.6194 RMSE = 1.1970



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

■ RESULTS AND DISCUSSIONEffect of Clay. It has been widely reported that the presence

of clay, especially at high concentration, in drilling fluid has a

significant effect on the fluid flowing properties. In oil-welldrilling, besides its function as viscosifier to aid the transport ofdrill cuttings from the bottom of the well to the surface, it alsoacts as a filtration control agent to minimize fluid invasion intothe pores of productive formations.22 It is believed that itsswelling properties make clay exhibit an excellent carryingcapacity and act to suspend cuttings during drillingproccesses.34 In the first test of this study, we determined theeffect of clay concentration on the rheological behavior of thefluid. Table 1 summarized the measured shear stresses of thefluid as a function of shear rate at various clay concentrations.

The result tabulated in Table 1 shows that both theincrement of shear rate and the concentration of clay yield ahigher amount of stress for the fluid. The faster the fluid issheared, the greater the stress. In addition the stress seems toincrease dramatically as the concentration of clay is increased.This is especially true at higher clay concentration (greater than5% w/v). The increment of stress in this case is very unique.Some of the data seem to follow a linear relationship and othersseem to follow a power relationship. Thus, to accommodatethis unique pattern, the experimental data in Table 1 was fittedto the eight proposed rheological models discussed previously.This step will determine the model best to describe the fluidrheological behavior. Table 2 shows the result of the fittingprocess of the experimental data to the eight proposedrheological models along with their corresponding calculatedparameters. Several statistical parameters namely R-square, sumof square error (SSE), and root-mean-square error (RMSE) arealso presented in Table 2.On the basis of the fitting process, it was observed that as

clay concentration is increased, more complex fluid rheologicalmodels are needed to describe the fluid viscoplastic behavior. Itis apparent that the two most traditional models, the Bingham-plastic and the Ostwald−De−Weale model, may not besufficient to describe the fluid behavior at higher clayconcentration. The reduction in the value of coefficient ofdetermination (R2) as well as the increment of its errors (SSEand RMSE) for the two models as the concentration of clay isincreased indicates the model is not able to estimate the fluidbehavior at high clay concentration. Statistically, in the absenceof clay, the tested fluid could be modeled by almost all of theproposed models. Moreover, the result also shows that the fluidtends to behaves more like a Newtonian fluid as the calculatedvalues of the index flow (n) for several models such as theHerschel−Bulkley model, the Robertson−Stiff model, and theHeinz-Casson model are very close to 1. However, at high clayconcentration, the fluid behavior seems to be altered andtransformed to follow a pseudopastic behavior. This is shownfrom 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 athigher clay concentration. It infers that the addition of claywould increase the minimum energy required to initiate fluidflow. The presence of water and high clay concentration mayalso lead to a gelling phenomenon resulting in very thick mudslurries due to swelling.35 Higher clay concentration causes thefinal fluid to be thicker and more viscous. Thus, to minimizethis problem, salt (in this case sodium chloride) was added to

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

Table 3. Measured Average Shear Stresses (τ (Pa) ± sda) of Lightweight Biopolymer Drilling Fluid as a Function of Shear Rateat Various Concentrations of Glass Bubbles (% w/v)

shear rate, γ (s−1) 0 (% w/v) 12.5 (% w/v) 18.75 (% w/v) 21.25 (% w/v) 25 (% w/v)

2.639 0.38 ± 0.01 2.37 ± 0.05 4.17 ± 0.01 5.49 ± 0.04 13.70 ± 0.115.279 0.46 ± 0.03 2.99 ± 0.11 4.95 ± 0.04 6.07 ± 0.01 15.15 ± 0.0226.4 0.69 ± 0.12 4.17 ± 0.12 6.47 ± 0.07 8.83 ± 0.06 18.34 ± 0.0152.71 1.08 ± 0.08 6.40 ± 0.08 8.15 ± 0.11 10.59 ± 0.12 20.44 ± 0.0979.28 1.35 ± 0.06 7.45 ± 0.09 9.85 ± 0.12 12.13 ± 0.11 22.67 ± 0.0488.17 1.51 ± 0.11 8.17 ± 0.04 10.79 ± 0.14 13.13 ± 0.10 23.46 ± 0.14158.3 2.54 ± 0.17 11.24 ± 0.01 13.44 ± 0.04 16.95 ± 0.03 28.33 ± 0.09176 2.97 ± 0.03 11.97 ± 0.01 14.97 ± 0.02 17.81 ± 0.04 29.76 ± 0.07264 5.15 ± 0.04 14.67 ± 0.07 18.63 ± 0.06 21.50 ± 0.09 36.36 ± 0.06




http://pubs.acs.org/action/showImage?doi=10.1021/ie200811z&iName=master.img-000.png&w=239&h=174

aid the stabilization of shales and control swelling of the clays.The chloride ion (Cl−) from sodium chloride prevents waterfrom entering the clay matrix.35 In addition, salt is also neededto stabilize the biopolymers structure. Without salt, manypolysaccharides will be denatured. This is due to the reductionof contour length of the biopolymers where the macro-molecules tend to adopt more coiled conformation.35

On the basis of the result calculated from the modelparameters from each model and its statistical parameters, it isdetermined that at each tested clay concentration, the fluidrheological behavior could be described by several models.However, to determine the best model to predict fluidrheological properties, the model with the lowest error

(calculated SSE and RMSE values) and the closest R2 valueto 1 was selected. On the basis of the result summarized inTable 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 tobe suitable both for 5% and 7.5% w/w of clay. On the otherhand, fluid with 10% w/w of clay seems to be best describedusing the Robertson−Stiff model. Figure 1 shows the plot ofthe experimental data of shear rate vs shear stress and itspredicted values using the best selected models for the fluid atvarious clay concentrations.

Table 4. Rheological Models of Lightweight Biopolymer Drilling Fluid and Its Corresponding Model and Statistical Parametersat Various Concentrations of Glass Bubbles (%w/v)

rheological model 0 (% w/v) 12.5 (% w/v) 18.75 (% w/v) 21.25 (% w/v) 25 (% w/v)

Bingham-plastic τ0 = 0.1634 τ0 = 3.2250 τ0 = 5.0180 τ0 = 6.7520 τ0 = 15.350η∞ = 0.0172 η∞ = 0.0474 η∞ = 0.0542 η∞ = 0.0607 η∞ = 0.0822R2 = 0.9734 R2 = 0.9716 R2 = 0.9832 R2 = 0.9698 R2 = 0.9837SSE = 0.5039 SSE = 4.1060 SSE = 3.1390 SSE = 7.1540 SSE = 7.0030RMSE = 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 = 8.9650n = 1.0710 n = 0.4895 n = 0.4061 n = 0.3555 n = 0.2317R2 = 0.9696 R2 = 0.9846 R2 = 0.9575 R2 = 0.9695 R2 =0.9147SSE = 0.5758 SSE = 2.2280 SSE = 7.9470 SSE = 7.2400 SSE = 36.590RMSE = 0.2868 RMSE = 0.5642 RMSE = 1.0650 RMSE = 1.0170 RMSE = 2.2860

Herschel−Bulkley τ0 = 0.4888 τ0 = 1.7940 τ0 = 3.8920 τ0 = 4.6870 τ0 = 13.650η∞ = 0.0015 η∞ = 0.3139 η∞ = 0.2298 η∞ = 0.4722 η∞ = 0.3464n = 1.4430 n = 0.6689 n = 0.7456 n = 0.6414 n = 0.7465R2 = 0.9961 R2 = 0.9971 R2 = 0.9968 R2 = 0.9989 R2 = 0.9962SSE = 0.0741 SSE = 0.4242 SSE = 0.5956 SSE = 0.2655 SSE = 1.6160RMSE = 0.1111 RMSE = 0.2659 RMSE = 0.3151 RMSE = 0.2103 RMSE = 0.5190

Casson kOC = 0.0187 kOC = 1.3520 kOC = 1.7800 kOC = 2.1280 kOC = 3.4420kC = 0.1333 kC = 0.1559 kC = 0.1550 kC = 0.1562 kC = 0.1540R2 = 0.9679 R2 = 0.9951 R2 = 0.9963 R2 = 0.9985 R2 = 0.9934SSE = 0.6077 SSE = 0.7015 SSE = 0.6995 SSE = 0.3551 SSE = 2.8220RMSE = 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 = 0.1735b = 0.7686 b = 1.6280 b = 3.5494 b = 4.4690 b = −1.3e4

n = −0.6631 n = 0.2641 n = 0.1372 n = 0.1692 n = −14.58R2 = 0.9805 R2 = 0.9951 R2 = 0.9966 R2 = 0.9984 R2 = −1.171SSE = 0.3702 SSE = 0.7099 SSE = 0.6422 SSE = 0.3812 SSE = 931.7RMSE = 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 = 1.6290γ0 = 114 γ0 = 10.570 γ0 = 26.560 γ0 = 17.740 γ0 = 57.260n = 2.0250 n = 0.5921 n = 0.6216 n = 0.5069 n = 0.5355R2 = 0.9981 R2 = 0.9976 R2 = 0.9965 R2 = 0.9984 R2 = 0.9941SSE = 0.0353 SSE = 0.3513 SSE = 0.6500 SSE = 0.3798 SSE = 2.5450RMSE = 0.0767 RMSE = 0.2420 RMSE = 0.3291 RMSE = 0.2516 RMSE = 0.6513

Heinz−Casson γ0 = 0.7850 γ0 = 1.3130 γ0 = 4.1750 γ0 = 5.5630 γ0 = 22.430k = 0.0021 k = 0.2099 k = 0.1714 k = 0.3029 k = 0.2586n = 1.4430 n = 0.6689 n = 0.7456 n = 0.6414 n = 0.7465R2 = 0.9961 R2 = 0.9971 R2 = 0.9968 R2 = 0.9989 R2 = 0.9962SSE =0.0741 SSE = 0.4242 SSE = 0.5956 SSE = 0.2655 SSE = 1.6160RMSE = 0.1111 RMSE = 0.2659 RMSE = 0.3151 RMSE = 0.2103 RMSE = 0.5190

Mizhari−Berk kOM = 0.6617 kOM = 1.1590 kOM = 3.1870 kOM = 524.80 kOM = 3.6440kM = 0.0065 kM = 0.2428 kM = 1256 kM = −522.4 kM = 0.0753nM = 0.9867 nM = 0.4320 nM = −116.2 nM = −0.0006 nM = 0.6176R2 = 0.9982 R2 = 0.9965 R2 = 0 R2 = 0.7803 R2 = 0.9973SSE = 0.0350 SSE = 0.5080 SSE = 186.90 SSE = 52.1 SSE = 1.1710RMSE = 0.0763 RMSE = 0.2910 RMSE = 5.5820 RMSE = 2.9470 RMSE = 0.4417



Effect of Glass Bubbles. A glass bubble has been widelyknown as an effective density reducing agent due to itsextremely low density value (0.32 g/cm3).21 The addition ofglass bubbles, which are a silicon-based material, to fluids suchas drilling/completion fluid or cement slurries, allows thereduction 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. Glassbubbles often times do not fully mix in the fluid system.Additives or emulsifiers are usually added to the fluid toproperly mix the glass bubbles. In a study conducted by Khalilet al.22 in the application of glass bubbles to formulate superlightweight completion fluid (SLWCF), the glass bubbles tendto separate from the fluid system and form two or three layersof heterogeneous fluid after the mixture was left for a couple ofmonth. Apparently, unlike clay or polymers, glass bubbles arenot soluble in the fluid system. The glass bubble agent isdispersed during the mixing. Thus, a more complex andcomprehensive model is apparently needed to better under-stand the behavior of glass bubbles in the fluid system asdispersion rather than as solute.This paper determines the rheological parameters of the

lightweight biopolymer drilling fluid that were used to selectthe best model for rheological behavior of the fluids as a

function of glass bubbles concentration. The experimental datawere then fitted to the eight proposed models discussed earlier.Table 3 presents the measured shear stresses of the fluid as afunction of shear rate at various glass bubble concentrationsand its corresponding error. Table 4 shows the fitting result ofthe experimental data to the eight proposed rheological models.Results show that most of the models are statisticallyappropriate and sufficient in describing the rheological behaviorof the fluid at various concentrations of glass bubbles. Almostall of the calculated coefficient values of determination (R2) aresatisfactory (greater than 0.98). This indicates that thepredicted value using the proposed models fits the experimentaldata very well. This finding is also supported from the low valueof calculated error (SSE and RMSE). The best model with thelowest SSE and RMSE values and R2 value closest to 1 wasselected since the objective of this study is to determine thebest 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 behaviorof the fluid. In contrast, as the glass bubbles concentration isincreased to 12.5% w/v, the rheological properties of the fluidwould be best represented by the Robertson−Stiff model.However, when the glass bubbles concentration was set at18.75% and 21.25% w/v, there are two different types of modelapplied, the Herschel−Bulkley model and the Heinz−Cassonmodel. At these glass bubbles concentration (18.75% and21.25% w/v), both models produced similar magnitude of thelowest 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 0.9989for 18.75% and 21.25% w/v, respectively). Herschel−Bulkley isusually preferred since it is a well established model in the areaof drilling engineering. Moreover, when the glass bubblesconcentration was increased to 25% w/v, the rheologicalbehavior of the fluid was best described by the Mizhari−Berkmodel. It gives an R2 value of 0.9973, SSE of 1.1710, and RMSEof 0.4417. Figure 2 presents the accuracy of predicted rheogramof the lightweight biopolymer drilling fluid as the concentrationof glass bubbles was varied from 0% to 25% w/v. The resultalso shows that Mizhari−Berk equation is the best model forfluid without glass bubble and fluid with glass bubbles higherthan 25% w/v. The Mizhari−Berk model was developed33 todescribe the rheological behavior of fluid with a dispersingparticle within the system. The model constant kOM was relatedto the shape and interaction of particles. It gives rise to the yieldstress, and kM is a function of the dispersing medium. Thus, inthis study, the interpretation of this model matches the physical

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

Table 5. The Measured Average Shear Stresses (τ (Pa) ± sda) of Lightweight Biopolymer Drilling Fluid as a Function of ShearRate at Various Starch Concentration (% w/v)

shear rate, γ (s−1) 0 (% w/v) 1 (% w/v) 1.5 (% w/v) 1.75 (% w/v) 2 (% w/v)

2.639 0.72 ± 0.02 1.34 ± 0.03 4.49 ± 0.11 8.14 ± 0.04 12.50 ± 0.025.279 0.82 ± 0.12 1.42 ± 0.01 6.07 ± 0.01 9.14 ± 0.04 14.32 ± 0.0426.4 2.15 ± 0.04 3.46 ± 0.08 8.83 ± 0.06 13.05 ± 0.08 17.84 ± 0.0152.71 3.82 ± 0.05 5.01 ± 0.07 10.59 ± 0.07 15.90 ± 0.11 20.28 ± 0.1179.28 5.28 ± 0.11 6.19 ± 0.11 12.13 ± 0.03 16.97 ± 0.16 22.62 ± 0.1088.17 5.59 ± 0.07 6.45 ± 0.16 13.13 ± 0.12 18.05 ± 0.13 23.46 ± 0.08158.3 8.24 ± 0.03 9.15 ± 0.17 16.95 ± 0.10 22.19 ± 0.10 28.01 ± 0.09176 8.96 ± 0.12 10.12 ± 0.05 17.81 ± 0.06 23.04 ± 0.01 29.34 ± 0.02264 12.42 ± 0.10 13.65 ± 0.07 21.50 ± 0.04 28.18 ± 0.01 35.11 ± 0.03





appearance of the fluid in the absence of a glass bubble andfluid with high concentration of glass bubbles. In the absence ofglass bubbles, agglomeration of xanthan gum and clay areassumed to act as dispersing particles. With the addition of glassbubbles, agglomeration tends to diminish. Under this condition,the Mizhari−Berk model is no longer valid to assess therheological properties of the fluid as the dispersed particles inthe fluid system are neglected. However, at glass bubbleconcentrations of 25% w/v, the Mizhari−Berk model holds.This could be due to the excess of glass bubbles, which act asdispersed 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 glassbubbles in the fluid system tends to change the fluid behaviorfrom dilatant to near pseudoplastic. It indicates that in theabsence of glass bubbles, the fluid tends to behaves more likedilatant 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 greaterthan 1. It has been established in literature that for a Newtonianfluid, n = 1; for pseudoplastic fluid, n < 1; and for dilatants, n >1.36 In contrast, addition of a high glass bubble concentrationcaused the fluid to follow a pseudoplastic behavior. Thecalculated values of index flow (n) are less than 1. This resultshows that clay and glass bubbles have a pivotal role in

Table 6. Rheological Models of Lightweight Biopolymer Drilling Fluid and Its Corresponding Model and Statistical Parametersat 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 τ0 = 1.1210 τ0 = 1.9450 τ0 = 6.5010 τ0 = 10.300 τ0 = 14.880η∞ = 0.0445 η∞ = 0.0460 η∞ = 0.0621 η∞ = 0.0727 η∞ = 0.0816R2 = 0.9877 R2 = 0.9823 R2 = 0.9574 R2 = 0.9532 R2 = 0.9654SSE = 1.5490 SSE = 2.3880 SSE = 10.750 SSE =16.190 SSE = 14.890RMSE = 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 = 8.4340n = 0.7240 n = 0.6126 n = 0.3706 n = 0.2968 n = 0.2407R2 = 0.9978 R2 = 0.9926 R2 = 0.9804 R2 =0.9716 R2 = 0.9489SSE = 0.2816 SSE = 0.9951 SSE = 4.9490 SSE = 9.8290 SSE = 21.990RMSE = 0.2006 RMSE = 0.3770 RMSE = 0.8408 RMSE = 1.1850 RMSE = 1.7730

Herschel−Bulkley τ0 = 0.3173 τ0 = 0.9012 τ0 = 3.8000 τ0 =6.8370 τ0 =11.820η∞ = 0.1629 η∞ = 0.2160 η∞ = 0.6832 η∞ =0.9169 η∞ = 0.7279n = 0.7711 n = 0.7280 n = 0.5833 n = 0.5603 n = 0.6181R2 = 0.9986 R2 = 0.9973 R2 = 0.9966 R2 = 0.9959 R2 = 0.9968SSE = 0.1777 SSE = 0.3633 SSE = 0.8563 SSE = 1.4200 SSE = 1.3850RMSE = 0.1721 RMSE = 0.2461 RMSE = 0.3778 RMSE = 0.4865 RMSE = 0.4805

Casson kOC = 0.6348 kOC = 0.9480 kOC = 2.0680 kOC =2.7170 kOC = 3.3720kC = 0.1786 kC = 0.1687 kC = 0.1609 kC =0.1597 kC =0.1556R2 = 0.9973 R2 = 0.9971 R2 = 0.9942 R2 = 0.9944 R2 = 0.9975SSE = 0.3385 SSE = 0.3852 SSE = 1.4680 SSE = 1.9370 SSE = 1.0710RMSE = 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 = 0.1701b = 0.3190 b = 0.8544 b = 3.8480 b = 6.8790 b = −1.3e4

n = 0.5192 n = 0.3361 n = 0.2145 n = 0.1657 n = −13.99R2 = 0.9985 R2 = 0.9983 R2 = 0.9977 R2 = 0.9983 R2 = −1.054SSE = 0.1934 SSE = 0.2257 SSE = 0.5873 SSE = 0.6028 SSE = 884.50RMSE = 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 = 3.2720γ0 = 3.0760 γ0 = 6.7540 γ0 = 10.830 γ0 = 13.520 γ0 = 26.900n = 0.7545 n = 0.6818 n = 0.4751 n = 0.4121 n = 0.4153R2 = 0.9986 R2 = 0.9969 R2 = 0.9953 R2 = 0.9937 R2 = 0.9943SSE = 0.1733 SSE = 0.4232 SSE = 1.1800 SSE = 2.1740 SSE = 2.4580RMSE = 0.1699 RMSE = 0.2656 RMSE = 0.4434 RMSE = 0.6020 RMSE = 0.6400


Mizhari−Berk kOM = 0.3427 kOM = 0.7807 kOM = 1.7790 kOM = 2.4800 kOM = 3.3550kM = 0.3011 kM = 0.2398 kM = 0.3032 kM = 0.2772 kM =0.1634nM = 0.4221 nM = 0.4463 nM = 0.4025 nM =0.4141 nM = 0.4921R2 = 0.9985 R2 = 0.9978 R2 = 0.9970 R2 = 0.9966 R2 = 0.9975SSE = 0.1841 SSE = 0.2940 SSE = 0.7488 SSE =1.1690 SSE = 1.0630RMSE = 0.1752 RMSE = 0.2213 RMSE = 0.3533 RMSE = 0.4414 RMSE = 0.4209



transforming the fluid behavior from Newtonian/dilatant tonon-Newtonian, and then to pseudoplastic.Effect of Starch. In this section, the effect of starch on the

rheological properties of lightweight biopolymer drilling fluidwas examined. In a drilling operation, a natural-basedbiopolymer, namely starch, is added as thickening and fluidloss control agent. It is known that the gelatinization propertyof starch is the one responsible for its ability to control fluidviscosity and fluid loss in oil and gas drilling operations.37

According to Atweel et al.,39 gelatinization is a process ofcollapsing (disruption) molecular order within the starchgranule, manifesting in irreversible changes in properties suchas granular swelling, native crystallite melting, loss ofbirefringence, and starch solubilization.38 The concentrationof starch was varied to determine its effect on the rheologicalbehavior of the formulated fluid. The concentration of starchwas varied from 1% to 2% w/v, while keeping othercomponents constant. Moreover, tests were conducted byformulating a fluid with 0% w/v starch concentration. Table 5presents the measured shear stress as a function of shear rate atvarious 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 isthe best model to represent the base fluid. In contrast,

whenever starch is added to the base fluid, the Sisko modelseems more appropriate to represent the fluid rheologicalproperties. However, at high starch concentration (2% w/v),the Sisko model can no longer represent the fluid well and theMizhari−Berk model was selected instead. The calculatedvalues of R2, SSE, and RMSE are 0.9975, 1.0630, and 0.4209,respectively. Figure 3 shows the rheogram of the lightweightbiopolymer drilling fluid as the concentration of starch is variedfrom 0% to 2% w/v. The accuracy the prediction is also shown.Furthermore, at high concentration of starch (2%), the resultshowed that the Mizhari−Berk model is statistically appropriateand sufficient to describe the fluid flow properties. However,the addition of starch tends to change the fluid behavior tosome sort of a combination of Newtonian and non-Newtonianfluid. The fluid rheological property would be best described bythe Sisko model. In Figure 3, it can be seen that at higher shearrate, the fluid seems to follow the Newtonian as the plot ofshear rate against shear stress is linear. However, at low andextremely low shear rates, the fluid tends to behave like non-Newtonian. Apparently the relationship between shear rate andshear stress is no longer linear. This phenomenon holds untilthe starch concentration reaches 1.75% w/v. At higher starchconcentration (2% w/v), excess starch acts as dispersedparticles. This explains why the fluid behavior would be bestdescribed 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, theaddition of starch does not seem to change the calculatedvalues of the fluid behavior (n) index significantly. Thecalculated n values of the Herschel−Bulkley model for thefluid with and without the presence of starch is less than 1. Thisindicates that the fluid would follow the pseudoplastic behaviorregardless of the amount of starch in the fluid.

Effect of Xanthan Gum. In the last stage of this study, theeffect of xanthan gum concentration on fluid rheologicalbehavior was investigated. In drilling fluid, xanthan gum ispreferred because it is biodegradable and it is also compatiblewith other filtration-reducing agents such as bentonite clay orcarboxymethylcellulose (CMC).34 During the tests, the amountof xanthan gum added to the fluid system was varied in therange of 0% to 1% w/v. Rheology measurements were obtainedfor the fluid at various concentrations of xanthan gum (Table7). The experimental measurements were then fitted to theeight proposed models as discussed earlier. Table 8 showsmodel parameters of the rheological models of the fluid atvarious concentration of xanthan gum. The results showvariations in the model selection to describe fluid properties as

Figure 3. Plot of shear rate vs shear stress of the lightweightbiopolymer 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 Siskomodel); ■, 2% w/v (: the Mizhari−Berk model).

Table 7. The measured Average Shear Stresses (τ (Pa) ± sd)a of Lightweight Biopolymer Drilling Fluid As a Function of ShearRate at Various Concentration of Xanthan Gum (% w/v)

shear rate, γ (s−1) 0 (% w/v) 0.25 (% w/v) 0.5 (% w/v) 0.75 (% w/v) 1 (% w/v)

2.639 1.61 ± 0.11 2.13 ± 0.02 4.49 ± 0.11 8.19 ± 0.02 10.16 ± 0.115.279 1.67 ± 0.04 2.88 ± 0.12 6.07 ± 0.03 9.14 ± 0.02 11.32 ± 0.0326.4 1.84 ± 0.01 4.17 ± 0.05 8.83 ± 0.01 12.11 ± 0.02 14.14 ± 0.0252.71 2.15 ± 0.09 6.50 ± 0.04 10.59 ± 0.07 14.81 ± 0.04 16.64 ± 0.0479.28 2.49 ± 0.07 7.98 ± 0.10 12.13 ± 0.03 16.84 ± 0.10 18.55 ± 0.0188.17 2.57 ± 0.04 8.36 ± 0.05 13.13 ± 0.03 18.09 ± 0.09 19.64 ± 0.10158.3 3.30 ± 0.11 11.81 ± 0.06 16.95 ± 0.11 22.68 ± 0.06 25.31 ± 0.05176 3.53 ± 0.07 12.81 ± 0.03 17.81 ± 0.09 23.48 ± 0.03 26.84 ± 0.02264 5.38 ± 0.03 16.48 ± 0.08 21.52 ± 0.05 28.87 ± 0.02 35.41 ± 0.11





a function of xanthan gum concentration. In the absence ofxanthan gum, the fluid is best described by the Mizhari−Berkmodel. This result shows the presence of dispersed particles inthe fluid system. It is assumed that glass bubbles and clay play apivotal role in rheological property of the fluid. However, oncea small amount of xanthan gum (0.25% w/v) is added, the fluidbecomes highly viscous. The best selected rheological model ofthe fluid is the Robertson−Stiff model. The three-parametersRobertson−Stiff model has been successfully been used in themodeling of drilling fluid with high concentrations of bentonitesuspension. It is assumed that this phenomenon is alsoapplicable for the addition of xanthan gum in the mixture. Inthis case, the Robertson−Stiff model is made to accommodate

the fluid thickness due to the presence of xanthan gum asthickening agent, similar to a thick drilling fluid saturated withbentonite. Furthermore, as the amount of xanthan gum isincreased to 0.5% w/v, the fluid seems to behave as bothNewtonian and non-Newtonian fluid. The best model todescribe its rheological properties is the Sisko model. The fluidseems to follow the linear relationship (Newtonian) at highershear rate and Power Law relationship (non-Newtonian) atlower rate of shear. However, at higher concentration ofxanthan gum (0.75% w/v or higher), the dispersed particlesseem to show an opposite effect. It is found that the best modelto describe the fluid rheological behavior is the Mizhari−Berkmodel; at high concentrations of xanthan gum, the excess

Table 8. Rheological Models of the Lightweight Biopolymer Drilling Fluid with Their Corresponding Model and StatisticalParameters 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 τ0 = 1.4570 τ0 = 2.9860 τ0 = 6.5010 τ0 = 9.8080 τ0 = 11.060η∞ = 0.0134 η∞ = 0.0542 η∞ = 0.0621 η∞ = 0.0773 η∞ = 0.0920R2 = 0.9702 R2 = 0.9825 R2 = 0.9574 R2 = 0.9724 R2 = 0.9947SSE = 0.3450 SSE = 3.2760 SSE = 10.750 SSE = 10.590 SSE = 2.8320RMSE = 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 = 4.9440n = 0.3552 n = 0.5502 n = 0.3706 n = 0.3221 n = 0.3306R2 = 0.7842 R2 = 0.9869 R2 = 0.9804 R2 = 0.9606 R2 = 0.9043SSE = 2.4980 SSE = 2.4550 SSE = 4.9490 SSE = 15.150 SSE = 50.880RMSE = 0.5974 RMSE = 0.5922 RMSE = 0.8408 RMSE = 1.4710 RMSE = 2.6960

Herschel−Bulkley τ0 = 1.7050 τ0 = 1.7510 τ0 = 3.8000 τ0 = 7.3090 τ0 = 10.470η∞ = 0.0013 η∞ = 0.2548 η∞ = 0.6832 η∞ = 0.5619 η∞ = 0.1571n = 1.4280 n = 0.7278 n = 0.5833 n = 0.6530 n = 0.9048R2 = 0.9904 R2 = 0.9985 R2 = 0.9966 R2 = 0.9992 R2 = 0.9962SSE = 0.1114 SSE = 0.2738 SSE = 0.8563 SSE = 0.3079 SSE = 1.9970RMSE = 0.1363 RMSE = 0.2136 RMSE = 0.3778 RMSE = 0.2265 RMSE = 0.5769

Casson kOC = 0.9881 kOC = 1.2430 kOC = 2.0680 kOC = 2.6150 kOC = 2.7620kC = 0.0731 kC = 0.1746 kC = 0.1609 kC = 0.1698 kC = 0.1870R2 = 0.9138 R2 = 0.9981 R2 = 0.9942 R2 = 0.9993 R2 = 0.9850SSE = 0.9974 SSE = 0.3555 SSE = 1.4680 SSE = 0.2741 SSE = 7.9650RMSE = 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 = 0.1578b = 1.7980 b = 1.5820 b = 3.8480 b = 6.9470 b = −14.2n = −0.0898 n = 0.2580 n = 0.2145 n = 0.1418 n = −31.54R2 = 0.9790 R2 = 0.9979 R2 = 0.9977 R2 = 0.9990 R2 = 0.0918SSE = 0.2429 SSE = 0.3978 SSE = 0.5873 SSE = 0.3988 SSE = 483RMSE = 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 = 0.2565γ0 = 374.50 γ0 = 11.580 γ0 = 10.830 γ0 = 22.190 γ0 = 85.550n = 2.3130 n = 0.6609 n = 0.4751 n = 0.4962 n = 0.8391R2 = 0.9902 R2 = 0.9986 R2 = 0.9953 R2 = 0.9986 R2 = 0.9955SSE = 0.1135 SSE = 0.2690 SSE = 1.1800 SSE = 0.5510 SSE = 2.3740RMSE = 0.1375 RMSE = 0.2117 RMSE = 0.4434 RMSE = 0.3031 RMSE = 0.6290


Mizhari−Berk kOM = 1.2950 kOM = 1.1490 kOM = 1.7790 kOM = 2.5890 kOM = 3.1800kM = 0.0014 kM = 0.2139 kM = 0.3032 kM = 0.1811 kM = 0.0478nM = 1.1860 nM = 0.4686 nM = 0.4025 nM = 0.4897 nM = 0.7257R2 = 0.9934 R2 = 0.9984 R2 = 0.9970 R2 = 0.9993 R2 = 0.9977SSE = 0.0767 SSE = 0.3068 SSE = 0.7488 SSE = 0.2617 SSE = 1.2440RMSE = 0.1130 RMSE = 0.2261 RMSE = 0.3533 RMSE = 0.2089 RMSE = 0.4554



xanthan gum tends to form agglomerations that act as dispersedparticles in the fluid system.To assess the performances of the models, a comparison

between the experimental and predicted rheograms of thetested fluids at various concentrations of xanthan gum wasconducted. Figure 4 presents both of the experimental andpredicted rheogram of the lightweight biopolymer drilling fluidas the concentration of xanthan gum is varied from 0% to 1%w/v. All of the predicted values seem to be in a good agreementwith the experimental data. In addition, results also shows that

unlike the precedence test for starch, the second type ofbiopolymer used in this study, xanthan gum, seems to have agreat effect on the fluid rheological behavior similar to the caseof clay and glass bubbles. The result on this test seems similarto the result on the effect of glass bubbles on fluid rheologicalproperties. As observed previously, the presence of glassbubbles in the fluid system tend to change the fluid behaviorfrom being dilatant to pseudoplastic. The result on the effect ofxanthan gum seems similar. The result shows that in theabsence of xanthan gum, the fluid behaves more like dilatantfluid as the calculated n values for several models, that is, theHerschel−Bulkley, Robertson−Stiff, and Heinz-Casson models,are greater than 1. However, as xanthan gum is added to thefluid system, the fluid behavior tend to behave more like apseudoplastic as the calculated n values are less than 1.

High Shear Rate Validation. In field application (forexample pumping), it is no secret that drilling fluid will besubjected to a very high shear rate (>1000 s−1). The applicationof high shear rate often times mitigates the accuracy of such amodel in predicting the flow behavior of drilling fluid. This maybe due to the change of fluid behavior at high range of shearrate. Thus, to investigate the model accuracy in predicting theshear stress of the fluid at a high shear rate, a specific validationstudy was performed. Table 9 presents the result of thecomparison of shear stress predicted using the model and theexperimental 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 ofstress at a high rate of shear. The calculated accuracy of thedifferences between the predicted value which is calculatedbased on the model and the experimental data is between 93%and 99%. It is apparent that some data show a relatively lowaccuracy value. This is most likely due to the difference ofviscometers used in the analysis.

■ CONCLUSION

Eight different rheological models were used to represent therheological behavior of a novel lightweight biopolymer drillingfluid. The effect of additives concentrations, sich as clay, glassbubbles, starch, and xanthan gum on the rheological propertiesof the fluid were studied. The results indicate that the fittingprocess has successfully determined the best selected modelamong the eight proposed models as the amount of clay, glassbubbles, starch, and xanthan gum are varied. The finding alsoshows that all of the predicted values are in a good agreementwith 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 therheological properties of the fluid. On the basis of the result, inthe absence of clay, the fluid behaves as a non-Newtonian fluid.However whenever clay is introduced into in the system, thefluid tends to be pseudoplastic. Moreover, the absence of glassbubbles and xanthan gum (independently) in the fluid tends tocause the fluid to be dilatant. However as the two fluidcomponents are added, the fluid seems to change topseudoplastic. The result shows that starch does not changethe rheological behavior of the fluid significantly. The fluidtends to follow pseudoplastic behavior regardless of the amountof starch in the drilling fluid.

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

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

Clay

shear stress(τ)

0(% w/v)

2.5(% w/v)

5(% w/v)

7.5(% w/v)

10(% w/v)

predicteda 81.138 59.902 94.770 123.643 135.214experimental 80.994 62.741 91.451 120.685 137.651accuracy (%) 98.76 95.47 96.37 97.55 98.23

Glass Bubble

shear stress(τ)

0(% w/v)

12.5(% w/v)

18.75(% w/v)

21.25(% w/v)

25(% w/v)


Starch

shear stress(τ)

0(% w/v)

1(% w/v)

1.5(% w/v)

1.75(% w/v)

2(% w/v)


Xanthan

shear stress(τ)

0(% w/v)

0.25(% w/v)

0.5(% w/v)

0.75(% w/v)

1(% w/v)

predicteda 44.459 53.962 52.459 73.935 128.019experimental 46.182 54.654 55.943 73.561 125.166accuracy (%) 96.27 98.73 93.77 99.49 97.72aCalculated using the best method from previous data fitting.




■ AUTHOR INFORMATIONCorresponding Author*E-mail: [email protected]. Tel.: 603-7967 6869. Fax: 603-7976 5319.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThe authors would like to thank the following parties for theirhelp 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 for underbalanced drilling

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