Environmentally Friendly Additives for Aqueous Drilling Fluid Systems: Optimum Flow Characteristics and Models

. Recently, renewable additives are incorporated to design novel drilling fluid formulations with properties meeting the needs of downhole atmospheres and environmental regulations. The work deals with the investigation, optimization, and modeling of the rheological properties of new aqueous drilling fluid systems incorporated with green sliver nanoparticles and mastic gum and the estimation and optimization of the flow mathematical models. The average range of the experimental values for apparent viscosity, plastic viscosity, yield point, and low-shear-rate yield point for the prepared drilling fluids are 22-38 cP, 8-24 cP, 26-32 lb/100ft 2 , 18-35 lb/100ft 2 respectively, while the optimum values estimated by ANOVA are 38.79 cP, 25.12 cP, 33.47 lb/100ft2, and 42.16 lb/100ft2 respectively. The optimum rheological properties are achieved by incorporating 17.07 ml of mastic gum and 1.6 ml of silver NPs colloids. The outcomes showed that the green additives looked talented to be applied for governing drilling fluid characteristics within the oil industry-recommended standards. The results of modeling the flow of the optimized drilling fluid indicated that it is Pseudo plastic fluid that exhibited non-Newtonian behavior and shear thinning. The Bingham-plastic flow model was explored to be the topmost model that can describe the flow behavior of the optimized drilling fluid system.


Introduction
The selection and maintenance of suitable drilling fluid and the testing and control of its properties is an essential issue because of its relation to most drilling operational problems and its considerable effect on the total well drilling cost [1].The additives that are used to preserve the fluid properties are mostly expensive.In addition, the circulation loss problems including the rate of the rotary bit and operational delays, and caught drill pipe are all profoundly affected by the drilling fluid properties.
Drilling fluids should meet some basic requirements and have the following functions: Hole cleaning, preventing formation fluids flow to the well bore, maintaining wellbore stability, cooling and lubricating the bit, transmission of hydraulic horsepower, and minimizing formation damage [2].The quality and source of the water used in formulation the fluid, the characteristics features of the formation to be drilled, and the ecological and environmental considerations are the main issues overriding the selection of type of drilling fluids to be used on a specific well.
Water-based fluid, oil-based and synthetic-based drilling fluids are the foremost types of drilling fluids [3].However, environmentally friendly drilling fluids that contain the least possible content of pollutants are required.Therefore, careful selection and formulation of raw materials is very important.Biopolymers and Nanoparticles (NPs) are two different materials used for this purpose, they also have some desirable function that led to minimize drilling problem and better drilling operation.Different types of natural polymers including carboxymethyl cellulose, guar gum and potato starch [4], Katira gum [5], modified starches [6] cassava starch, breadfruit starch bush mango seed and corn fiber [7], and wood fiber [8] have been tested and used in drilling fluids to provide rheology and filtration loss control [9].Synthetic polymers were also used for the same purposes [10][11][12][13][14][15].
In other words, nanotechnology is a subject undergoing intense attention, and vast capital was used to invest in research and development to apply the technology in different industries including the oil and gas industry [16][17][18][19].Nanomaterials are engineered materials with at least one dimension in the range of 1-100 nm.The nature of nanomaterial is the fineness and very high specific surface area with huge area interactions resulting in requiring a very low concentration of nanomaterial to offer great improvement in fluid properties.Different types of nanomaterials are produced with many outstanding properties which found significant roles in drilling fluids, enhanced oil recovery, cementing, and well stimulation.They are added to drilling fluids in low volumetric fractions to rising mud cake quality, minimize friction, reduce pipe sticking problems, preserve borehole stability, shield reservoir, and improve the recovery of oil and gas [20][21][22][23][24][25].However, the gap between field-scale implementation and laboratory tests regarding using nano-additives to enhance drilling fluids properties should be filled with the purpose of meeting the modern drilling process requirement [26].
The objectives of this investigation are the preparation of a new aqueous drilling fluid system and studying the effect of the incorporation of green metallic nanoparticles (Ag NPs) and locally available natural polymer (mastic gum) on rheological properties based on an espoused design of experiments, in addition to optimization and modeling of the rheological and flow characteristics.

Preparation of the green additives
The first green additive mastic gum was purchased from local market.The grains were grinded and converted to powder then 10 gram of mastic powder were mixed with 100 ml (25% methanol) and heated at 55 o C using a magnetic stirrer hot plate till getting homogeneous solution (colloid).The second green additive; the green Ag NPs have been prepared by biosynthesis route based on mixing cactus plant extract with an aqueous solution of silver nitrate and then irradiation the mixture directly using a microwave technique [27].A stock solution of the NPs (concentration = 25 ppm) was diluted with 10 ml distilled water to obtain a solution of concentration equal to 16.67 ppm.

The formulation of the drilling fluid samples
The aqueous fluid samples were formulated based on the API standard specifications by mixing the pre-determined amounts of the materials in a mixer.First NaOH was mixed with water, then bentonite was added slowly, barite was added then gradually, finally gum solution and the Nano-martial solution were added respectively.The time of mixing was set to be ten minutes to get better mixing for the whole fluid mixtures.The main constituents of the drilling fluids (with constant quantities) of all the experiments are 350 ml tap water, 25g Bentonite, 10g Barite and 0.25 g NaOH.

Experimental DesignThe time
Ten experiments were designed using statistical software based on Response Surface Methodology.RSM is an operative statistical means used to investigate the interaction between several descriptive variables and one or more response variables.The RSM process involves designing sets of experiments to measure adequate and consistent response and develop the best fittings mathematical models.Stat graphics software SIGMA PLUS Neuilly sur Seine, version 5.1, France for experimental design and treating responses was used for data analysis.The polynomial model is represented in Equation 1: Where: Y: is the response or dependent variable;  1 and  2 are the independent variables; and, β 0 ,  1 . 2 . 11 . 22 . 12 are the regression coefficients.
The substantial differences between the effects of independent variables (p<0.05) are determined by analyses of variance (ANOVA).Pareto chart is used to recognize the effect level of the independent parameters on each considered response, the perpendicular line (significant front) displays the effects that are statistically significant at 95% confidence level.Dependent parameter (responses) is optimized by the use of major trends as well as the empirical regression sample [28,29].
The mud samples were formulated based on an espoused experimental design.The operating variables are the mastic gum and nanoparticles content.The continuous phase for mixing the fluids is the tap water.Table 1 shows the experimental design used for the experiments used for the formulation of the drilling fluids samples.

The Flow of Drilling Fluids
The mathematical description of the flow of drilling fluids relies on the concepts of shear stress and shear rate and their measurement.To determine the shear rate of a drilling mud the amount of force applied to it is considered.In oil field terms, this could be determined by the flow rate of the fluid through a specific geometric configuration. 3 Results and Discussion

Experimental results
Based on the adopted experimental design, the average values of the rheological properties of the drilling fluids are determined.The average values are listed in Table (2).

Response Surface analysis results
The rheological parameters were optimized and modeled using statistical software.The RSA results are illustrated in Figures (1)(2)(3)(4).The apparent viscosity presents the resistance of fluid flow produced by friction between solids, liquids, and solids and the shearing layers.ANOVA results for apparent viscosity are shown in Figure 1.As can be seen by Pareto chart (Figure 1A), the apparent viscosity is influenced by the content of the two additives, however the content of the mastic gum seemed more significant, and this is reflected by the extent of the slope (the higher intensity of the effect of the gum content).The positive sign of the slope of the gum content of the effect reveals that apparent viscosity increases when the content of the gum increases.The effect of the nanoparticles content has contrary effect.Further justification of the results is clarified by the main effects plot (Figure 1B)   Table 3 (equation 9) shows the estimated second-order equation using the experimental data.
The plastic viscosity was estimated with an R 2 value of 95.62 % which indicated the good fitting of the model.An optimum value for plastic viscosity = 25.12 cP matching to 17.07 ml gum and 1.6 ml Nanoparticles was estimated.
The yield point (YP) is a mesure of initial flow resistance of fluid, it is the least shearing stress required to yield slip-wise fluid movement.The yield point is affected by the surface characteristics and volume concentration of the fluid solids, and the type and concentration of the ions within the fluid phases.YP is used to estimate the mud's capability to kick cuttings out of the annulus.Drilling fluid with a higher YP reflects that it has the capability to transport cuttings better than a fluid of comparable density but with a lesser YP. Figure (3) shows the RSA results of the YP of the samples of drilling fluids.Table 3 (equation 10) shows the second-order equation estimated from analysis the experimental data.The yield point was predicted with an R 2 value of 81.43 % which indicated an acceptable model fitting.An optimum value for YP = 33.47(lb/100ft 2 ) matching to 9.6 ml gum and 4.4 ml Nanoparticles was estimated.
The Pareto chart and main effects plot for the low-shear-rate yield point (LSRYP) are depicted in Figure 4.It can be noted from Pareto chart (Figure 4A) that both the operating variables are significant; however, the effect of the gum content is more significant.The positive slope of the effect of the content of the gum confirmed that low-shear-rate yield point increases with increasing the gum content, while the negative effect of the nanoparticles indicated an inverse effect.Extra justification is observed obviously by the main effects plot (Figure 4B).
Table 3 (equation 11) shows the estimated model using the experimental data.The low-shearrate yield point was predicted with an R 2 value of 95.62 % which indicated an excellent model fitting.An optimum value for LSRYP = 42.16(lb/100ft 2 ) matched to 17.07 ml gum and 1.6 ml Nanoparticles was estimated.
It is worth noting that the RSA results predicted that the optimum rheological properties of the new drilling fluid formulated with mastic gum and the green metallic nanoparticles could be achieved using 17.07 ml gum and 1.6 ml green silver nanoparticles.The very small particle size of the nanoparticles which exhibit immense specific surface area with massive interactions is behind the need for a very slight concentration of NPs to contribute to the improvement of fluid characteristics.
On the other hand, the interaction of the nanoparticles with the bentonite structure plays a vital role [30].The Bentonite basic layer structure is made up of two sheets of silica upper a sheet of Aluminum.Thin aqueous films of organic materials and positively charged ions isolate the silica sheets.In the presence of NPs, the drilling fluid properties change owing to traveling the NPs toward the surface of the clay wall because of Vander Walls and Coulombic forces leading to the formation of a new surface.It was reported that in the absence of nanoparticles, the net attractive forces between the microscale bentonite particles lead to the aggregation of the bentonite particles.NPs increase electrostatic double-layer repulsive forces and make net forces between microscale bentonite particles change to unattractive ICSTCE 2023 https://doi.org/10.1051/e3sconf/202340502022 E3S Web of Conferences 405, 02022 (2023) [31].The phenomenon is called NPs "halo" effect.This effect may be behind the low values of the rheological properties of the new fluid that contain a low concentration of NPs.Nevertheless, an opposite approach was suggested when using high concentrations of nanoparticles such as MgO NPs [32].

Using mastic gum as an alternative to xanthan gum
For comparison purposes and to identify the effect of using mastic gum in drilling fluids as alternative to the commercial xanthan gum that is used widely, drilling fluid samples without Ag NPs formulated with 17.07 ml (1.7g) of mastic gum solution (based on the optimized RSA results) and a reference drilling fluid formulated with (1.7g) Xanthan gum were prepared and tested for rheological properties.Figure 5 illustrates the results.The results revealed that the new fluid prepared with mastic gum has lower rheological values and a competitive filtration value (filter cake thickness and filter loss volume) compared to the reference fluid as shown in (Figure 5).The results of rheological seemed logic as the crude mastic gum resin is of lower viscosity [33].compared to the commercial well-purified xanthan gum.A similar trend was observed using Katira gum [5].In other words, the drilling fluid with mastic gum could have higher rheological characteristics when formulated using a higher content of mastic gum.
Therefore, a set of fluid samples containing double the amount of mastic gum (34.17 ml) was prepared and tested; the average results are shown in Figure 5 (the green color columns).Although, the new additive with the optimized content values based on RSM estimations (17.07 ml) seemed capable to be used for governing drilling fluid properties recommended by the applied industrial standards.The fluid with double content of mastic gum seemed very competitive in rheological and filtration characteristics to the fluid with the commercial xanthan gum.

Modeling the flow behavior of the optimized drilling fluid
On the other hand, to achieve precise results for pressure drops and hydraulic calculations, it is absolutely necessary to recognize the best rheological flow model that accurately represents the shear stress-shear rate analysis [34].Bingham-plastic, Casson, and Power Law models are employed for identifying the flow characteristics of the RSM-optimized drilling fluid.The Bingham model is expressed as: where, τ = shear stress, γ = shear rate, YP = yield point, PV = plastic viscosity.
The Power Law model is expressed as: The logarithmic function of Equation ( 13) is as follows: log=log+ Where n is dimensionless, it denotes the fluid flow behavior index which specifies the ability of a fluid to shear thin, and k is the viscosity index (lb/100ft 2 ), which denotes the consistency coefficient.When n < 1, the fluid is shear thinning and when n > 1, the fluid is shear thickening.The fluid is classified as Pseudo plastic when the flow behavior index is between zero and 1 [14].Pseudo-plastic flow reflected that the fluid displayed shear-thinning; (i.e., the apparent viscosity declines as the shear rate rises).For drilling fluids, this is a recommended characteristic and most drilling fluids are pseudo-plastics.
Mathematically, the Casson model is expressed as: Where koc is Casson yield stress (Pa.s), kc is Casson plastic viscosity in mPa.s.
The three flow models are plotted as shear stress versus shear rate calculated from viscometer dial readings (equations 6 and 7) respectively.The model's relationships are illustrated graphically in Figures 6A, 6B, and 6C respectively.4 shows the parameters and model equations estimated from the plots of the three models.The results of modeling the flow of the optimized drilling fluid indicated that the optimized fluid system exhibited non-Newtonian behavior.In addition to that, Bingham and Casson flow models showed good relationships with the experimental values as behold from the regression coefficient values (Table 4).However, it is obvious to note that the Binghamplastic model gave a better estimate than the other two models (R 2 = 93.14).Based on the optimum flow model, Bingham plastic fluid needs a high-stress level to flow like viscous fluids [35].For fast drilling, PV should be as low as possible and this could be achieved by minimizing colloidal solids.To carry cuttings out of the hole, YP must be high sufficiently, but not so large as to produce extreme pump pressure when initiating fluid flow.

Conclusions
The oil and gas business are risky and face challenging requiring all operations and materials to be employed in safe and economical way.Thus, drilling fluid is required to be environmentally friendly and function adequately.The current study concluded that the use of low concentration of mastic gum up to 17.07 ml of (10g/100ml) mastic gum colloid, and 1.6 ml of (16.67 ppm) colloid of green Ag nanoparticles in the drilling fluid mix (about 400 ml) can adjust the characteristics of the fluid system.Both of the additives showed a significant effect.The fluid system optimized by RSM showed promising rheological and filtration properties.The optimized fluid system flow model seemed to be the best fit with the Bingham model.A fluid system based on mastic gum without Ag NPs compared to that based on commercial xanthan gum seemed to have lower rheological values and competitive filtration values.However, using a higher concentration of the low-viscosity mastic gum resulted in formulating a fluid system with higher rheological properties competitive to that incorporated with the commercial viscosity modifier (xanthan gum).The environmentally friendly drilling fluid system formulated and studied in the current work could be employed in drilling operations effectively and safely from performance and environmental considerations.
. The actual and equivalent hydrostatic pressure of the fluid is highly affected by the fluid viscosity as the fluid viscosity has a vital role in removing the cuttings and the pressure losses from the annular.Plastic viscosity (PV) is mud's viscosity when inferred to an infinite shear rate with the attention of the mathematics of the Bingham model.The plastic viscosity RSA results of the drilling mud samples are shown in Figure (2).

Fig. 2 .
Fig. 2. Pareto chart (A) and main effects plot (B) for Plastic viscosity.It can be noted from Pareto chart Figure (2A) that both the operating variables are significant; however, the effect of the gum content is more significant, and appeared to play a topmost role influencing plastic viscosity of the drilling fluid.The positive slope of the effect of the gum content naked that plastic viscosity increases with growing the gum content, while the negative effect of the nanoparticles indicated an inverse effect.The main effects plot Figure(2B) elucidates the situation.The biopolymer chains are extremely long when compared to bentonite particle dimensions.The polymer chains link with multitudes of the clay particles in the aqueous fluid system, the combined effect is responsible for the creation of high viscosity.

Fig. 3 .
Fig. 3. Pareto chart (A) and main effects plot (B) for Yield point.The effect of the content of the two additives on yield point is illustrated in Figure(3).From Pareto chart (Figure3A), it can be predicted that the quadratic content of the gum is the only significant variable influenced the yield point.The positive slope indicates that YP increases with increasing the gum content.However, there is a maximum gum content above it the yield point will decrease as shown in the main effects plot of Figure (3B).

Fig. 5 .
Fig. 5. Rheological and filtration characteristics of the fluid systems with mastic gum versus xanthan gum.

Fig. 6 .
Fig. 6.The optimized fluid flow models A: Bingham-plastic model, B: Casson model, C: Power Law model.The three models of flow differ most notably from a Newtonian fluid by the presence of a yield stress.Table4shows the parameters and model equations estimated from the plots of the three models.

Table 1 .
The experimental design of the operating variables.
The flow model's plots are plots of shear stress versus shear rate, or plots of flow pressure versus flow rate.Shear rate and shear stress are expressed as follow:

Table 2 .
The average values of rheological properties of the fluids

Table 3 (
equation 8)shows the estimated empirical regression model equation (second-order) using the experimental data.The apparent viscosity was estimated with a high R-value of 95.62 % which indicated the exact fitting of the model.An optimum value for Apparent viscosity = 38.79cP was estimated matching to 17.07 ml mastic gum and 1.6 ml silver nanoparticles

Table 3 .
Mathematical models and parameters of the rheological properties

Table 4 .
The parameters of the flow models of the optimized drilling fluid