Model prediction of the impact of zinc oxide nanoparticles on the fluid loss of water-based drilling mud

The use of nanoparticles in the formulation of drilling mud has gained unparalleled research effort. Despite the advancement of nanotechnology, key challenges still remain which relates to attaining predictable properties for nano-drilling muds. In this work, Zinc Oxide (ZnO) nanoparticles were synthesized and applied to a water-based drillingmud. The characterization of the ZnO nanoparticles was done using Energy Dispersive X-Ray (EDX) Spectroscopy, Scanning Electron Microscopy (SEM), and X-Ray Diffraction (XRD). A basic fundamental approach was applied in deriving a novel model, which predicts the impact of the nanoparticles on the fluid loss of drilling mud during the filtration process. This was done taking into account the kinetics of mud cake formation and colloidal behavior of the nanoparticles. The new fluid loss model gave a better description of the fluid loss behavior of the nano-drilling mud when compared with the American Petroleum Institute (API) model using statistical measures. Subjects: Materials Science; Nanoscience & Nanotechnology; Chemical Engineering


PUBLIC INTEREST STATEMENT
Oil and gas exploration and development is gradually shifting from onshore to deep offshore, which are under extreme environmental conditions. Drilling operations represents a critical part of oil and gas development, hence the need to improve the rheological properties of the major ingredient of drilling operation, which is the drilling mud. Nanotechnology has provided the needed platform in improving drilling mud performance in deep offshore conditions. In this research work done, zinc oxide nanoparticles were synthesized and used as additives in drilling mud and its fluid loss studied. The fluid loss behaviour was studied using conventional oil and gas models and this was compared with a new model. The model was able to go a step further and predict fluid loss based on the nanoparticle properties.
Yue, Cai, Liu, & Wu, 2015). This is significantly due to the reduction in the cost involved and the chemical content of the drilling mud. Furthermore, properties such as fluid loss and rheology control, wellbore strengthening, wellbore and shale stabilization, magnetic properties, cuttings suspension, and thermal properties are improved (Abdo & Danish-Haneef, 2012;Afolabi, 2017;. With this, using nanoparticles as an additive can also improve the properties of drilling muds in meeting the challenges of tough downhole conditions. Despite the advancement of nanotechnology, a key challenge involves attaining predictable properties for the modified drilling mud (Gerogiorgis, Reilly, Vryzas, & Kelessidis, 2017;. Past research efforts have been channeled toward examining the use and impact of different types of nanoparticles such as iron oxide nanoparticles, aluminum oxide nanoparticles, silicon oxide nanoparticles, polymeric-coated nanoparticles, and titanium nitride nanoparticles in the preparation of drilling muds (Ismail, Aftab, Ibupoto, & Zolkifile, 2016;ShamsiJazeyi, Miller, Wong, Tour, & Verduzco, 2014;. The properties of the modified mud were investigated at different downhole conditions obtainable during drilling operations with improved results Yang et al., 2015). The known properties of drilling muds, which can be altered with the use of nanoparticles, are wellbore and shale stabilization, rheology and fluid loss control, wellbore strengthening, cuttings suspension, thermal properties of the drilling muds, and magnetic properties (Hoelscher et al., 2012;. The known predictive tools for describing drilling mud behavior allow for a generalized computation of drilling performance (Gerogiorgis et al., 2017;Reilly, Vryzas, Kelessidis, & Gerogiorgis, 2016). For example, the known rheological models used in the characterization of bentonite-based muds allow for a parameterized computation of fluid rheology . The work of Reilly et al. (2016) and Gerogiorgis et al. (2017) laid a good foundation for rheological models for nano-drilling fluids. Furthermore, extending the work to cover other aspects of drilling mud performance such as fluid loss behavior is required. There is currently no known model which incorporates the impact of nanoparticles on the fluid loss behavior of drilling muds. This would require modifying the existing API model (Vipulanandan, Raheem, Basirat, & Mohammed, 2014). The development of models for describing the fluid loss behavior of nanoparticle-enhanced drilling fluids is critical toward successful modeling, design, and cost-effective drilling operations . This work looked at the impact of zinc oxide nanoparticles on the fluid loss of water-based drilling mud. Also, a new fluid loss model which incorporates the contribution of the nanoparticles to the fluid loss behavior was developed. The characterization of the ZnO nanoparticles was done using Energy Dispersive X-Ray (EDX) Spectroscopy, Scanning Electron Microscopy (SEM), and X-Ray Diffraction (XRD). A basic foundational approach was used in deriving a model, which describes the fluid loss obtained from zinc oxide nanoparticle-enhanced drilling mud. This was done taking into account the kinetics of mud cake formation which is similar to the structural kinetics of the bentonite suspension described by Toorman (1997) and colloidal behavior of the nanoparticles (Gerogiorgis et al., 2017;Reilly et al., 2016).

Materials
Analytical grade zinc nitrate hexahydrate and sodium hydroxide were supplied by Equilab Solutions, Nigeria. The solutions prepared using these chemicals was done using deionized water. The bentonite clay was of drilling grade standard as indicated in the API specification 13-A for drilling fluid materials.

Synthesis of zinc oxide (Zno) nanoparticles
0.1M zinc nitrate solution was made by adding 15 g of zinc nitrate hexahydrate [Zn NO 3 ð Þ 2 :6H 2 O in 500 ml of distilled water and stirred using a Stuart® magnetic stirrer (Model Number: US152). A total of 1.0M sodium hydroxide [NaOH] solution was also prepared by adding 20 g of NaOH pellets in 500 ml of distilled water, and the solution was stirred continuously to ensure homogeneity. Dropwise amount of NaOH solution was added to the Zn NO 3 ð Þ 2 solution under continuous stirring for 12 h. The formed precipitate was separated from the solution using a centrifuge at 8,000 RPM for 15 min and settled pellets were collected. The pellets were dehydrated using an oven working at 80°C for 80 min. The dried pellets were homogenized by grinding with a pestle until a smooth fine white powder was obtained. The obtained powder was kept in bottles which are air-tight for additional analysis.

Characterization of zinc oxide (Zno) nanoparticles
Characterization of ZnO nanoparticles was done based on XRD analysis, and SEM/EDX analysis. The XRD analysis was done using a diffractometer (PAN Analytical X-Pert Pro) operated at 30 kV and 40 mA. The pattern obtained from the XRD analysis was logged by CuKα radiation around 1.54060 _ A. The Scherrer equation (Equation 1) was used in estimating the size of the ZnO nanoparticles: where β is the line broadening at half the maximum intensity (FWHM), K is a dimensionless shape factor, with a value close to unity, D is the nanoparticle size in nm, λ is the X-ray wavelength, and θ is the Bragg's angle of reflection. The size, elemental identification, and morphological characteristics of the ZnO nanoparticles was analyzed using the Phenom® ProX desktop Scanning Electron Microscope (SEM)/Energy Dispersive X-Ray (EDX) machine.

Formulation and composition of nano-drilling mud
Three samples (S 1 , S 2 , S 3 ) of nanofluids were prepared by adding 1.0, 1.5, and 2.0 wt.% of zinc oxide nanoparticles in 350 ± 5.0 mL of fresh water. The dispersed nanoparticles were stirred using a Hamilton beach mixer (Model HMD 300) at a speed of 11,000-RPM until zinc oxide nanofluids were obtained. These nanofluids act as the base fluids for the preparation of the drilling mud. 6.5 wt.% of bentonite clay was added to the prepared nanofluid. The suspensions containing the bentonite and nanoparticles were stirred for 5 min using the Hamilton Beach mixer. Lumps adhering to the wall of the cup were integrated to the mud and the stirring was repeated for another 15 min leading to a total stirring time of 20 min after which the nanoparticle-enhanced water-based drilling mud with 6.5 wt.% of bentonite clay was obtained.

Fluid loss experimentation
The OFITE Low-Pressure Low Temperature (LPLT) filter press was used to determine the fluid loss and mud cake-building properties of the prepared nanoparticle-enhanced drilling mud. The design of the OFITE filter press comprises of a cell body where samples of the prepared drilling mud are held, an inlet for pressure, a base cover for placing filter paper (for low pressure, 3½″ (9.0 cm)) and screen (60 Mesh), and drainage discharge tube for filtrate into a calibrated container. Two timers, one set for 7.5 ± 0.1 min and the second set for 30 ± 0.1 min, were both started and pressure on the cell adjusted at 100 ± 5 psi (690 ± 35 KPa). Both of these steps were concluded in less than 15 s. The pressure was supplied by compressed carbon dioxide, CO 2 . At 7.5 ± 0.l min on the first timer, the container was removed and any liquid adhering to the drain tube was discarded. The dried 10 cm 3 calibrated cylinder was placed beneath the drain tube and the filtrate collected till the completion of the second timer fixed at 30 min.

Kinetics of mud cake formation
A non-dimensional parameter similar to what was used by Toorman (1997) is used in describing the changes in the concentration of clay particles in a bentonite suspension. The value of the non-dimensional parameter is between 0 (low concentration of bentonite suspension) and 1 (high concentration of bentonite suspension). The concentration of clay particles, C, is used as a measure of the number of clay particles in the bentonite suspension at any given time. The non-dimensional parameter, ζ, is related to the concentration of clay particles at any given time and initial concentration of clay particles, C o : In the absence of shear such as under static filtration where pressure forces are dominant, the rate of diffusion of clay particles to the surface of a mud cake depends on the difference between the maximum concentration of clay particles before the start of filtration, ζ 0 (value of 1) and the concentration of clay particles at any given point in time during the filtration process, ζ. Hence, the rate of diffusion of clay particles is expressed as: The rate of clay particle build-up on the mud cake is dependent on the time of consolidation of particles on the mud cake, t and concentration of clay particles in the bentonite suspension at any point in time, ζ. The rate of build-up is expressed as: The net rate expression is the difference between the rate of diffusion of clay particles to the mud cake surface and that of build-up: Assuming a first-order rate kinetics for the diffusion and build-up expressions, m ¼ n b ¼ 1: At equilibrium, the rate of diffusion equals the rate of build-up. Therefore, dζ dt ¼ 0. Simplifying: The equilibrium parameter in Equation (8) describes the structural state of the formed mud cake. In other words, it helps describe the state of consolidation of clay particles on the drilling mud cake and steady growth with time.

Colloidal behaviour of nanoparticles
The theory of colloidal particle behavior in bentonite suspension follows the description of (Gerogiorgis et al., 2017). The equation derived by the authors for the maximum inter-particle distance between nanoparticles, h np , is given in Equation (9): where r np is the radius of nanoparticles, and ; is the volume fraction of nanoparticles. The dimensionless ratio of nanoparticle size to inter-particle distance, α, of the nanoparticles in a bentonite suspension is expressed in Equation (10): Equation (10) represents the dimensionless ratio of nanoparticle size to inter-particle distance.

Fluid loss model for nano-drilling mud
The API fluid loss model describing the static filtration process as described by (Darley & Gray, 1988) is given below: where P is the pressure differential, k is the permeability of mud cake, μ is the viscosity of the filtrate, V f is the volume of filtrate, A is the area of mud cake, V f Vc is the ratio of the volume of filtrate to a volume of mud cake, and t is the time. For a given suspension, V f Vc and k in Equation (11) is constant with respect to time. According to Vipulanandan et al. (2014), both the permeability of a mud cake,k; and the ratio V f Vc are functions of time. In order to account for the time variation of V f Vc , Equation (12) is proposed as a product of ζ e and α: The volume of mud, V m , is the sum of the volume of filtrate, V f and the volume of mud cake, V c : The ratio of fraction of solids in the mud cake, f c to fraction of solids in the mud, f m is given by Equation (17): The time variation in the permeability of the formed mud cake is proposed as a product of the initial permeability of the cake and the non-dimensional structural parameter in Equation (8): k o is the initial permeability of the formed mud cake. Equations (13) and (19) express the time dependence of V f Vc and k as described by (Vipulanandan et al., 2014). Substituting Equations (13) and (19) into Equation (11) yields: Substituting for α in Equation (20) and simplifying: The fluid loss model incorporating the contribution of nanoparticles becomes: The maximum fluid loss becomes:

Results and discussion
4.1. Characterization of zinc oxide (ZnO) nanoparticles

SEM/EDX analysis of ZnO nanoparticles
The surface characteristics of the synthesized ZnO nanoparticles was investigated using SEM analysis. SEM images in Figure 1 were obtained at a magnification of 2,000x (30 μm) and clearly shows the spherical nature of the nanoparticles. It also depicts that the ZnO nanoparticles appear as aggregates. The aggregation of the ZnO nanoparticles is due to the high surface area-to-volume ratio of the nanoparticles. Elemental identification analysis using EDX study also established the existence of Zinc Oxide in the synthesized nanoparticles. The elemental composition of the synthesized was Zinc (72.6%) and Oxygen (27.4%). The EDX spectrum of the synthesized nanoparticles is shown in Table 1 and Figure 2.

XRD analysis of ZnO nanoparticles
The crystallinity of the synthesized ZnO nanoparticles was investigated using XRD. The XRD spectra of the synthesized ZnO nanoparticles ae represented in Figure 3.  Table 2 shows the calculated values for the ZnO nanoparticle sizes, which correspond to the various peaks, identified in the XRD spectrum. The average size of the produced ZnO nanoparticles was 14.96 nm.

Impact of ZnO nanoparticles on fluid loss of drilling mud
The effect of zinc oxide nanoparticles on the mud cake can be established to reduce the permeability of the drilling mud cake, thereby reducing the fluid loss volume. The high surface area and small size of nanoparticles enable them to form fine dispersions and tight packing structures, thereby effectively filling "fluid flow" gaps that exist between micron-size particles. This phenomenon also applies to the mud cake, which is formed during the static filtration process involving nano-modified drilling fluids. This reduces the mud cake permeability and subsequently fluid loss. The reduction in mud cake permeability by the zinc oxide nanoparticles is due to the plugging capability of the nanoparticles on the mud cake, thereby producing a low permeability medium. The works of Ghanbari, Kazemzadeh, Soleymani, & Naderifar (2016); Ragab & Noah (2014); Yang et al. (2015) have confirmed the plugging capabilities of nanoparticles in rock formations. This reduction in fluid loss can also be due to the   alignment of the clay particles in a face-to-face (FF) configuration, which reduced the surface area available for fluid penetration. The presence of the zinc oxide nanoparticles can be explained to cause a disruption in the interaction forces between the clay particles necessitating the rearrangement from face-to-edge (FE) to FF arrangement (Jung et al., 2011). The significance of mud cake permeability reduction is critical toward successful drilling operations. This helps to reduce the incidence of pipe sticking during drilling operations. Thus, the use of zinc oxide nanoparticles in a drilling mud leading to a low fluid loss and low permeability cake is desirable. The area of contact between a drill pipe and the filter cake is a function of the depth of burial of the pipe in the cake and, consequently, is a function of the cake thickness. For this reason, the mud cake has to be as thin as possible.

Cumulative fluid loss prediction
The cumulative fluid loss prediction was done using the new fluid loss model in Equation (23

Validating the maximum fluid loss prediction
In order to validate the maximum cumulative fluid loss prediction of Equation (23), a longterm filtration test was carried out using the procedure of Vipulanandan et al. (2014). Filtration time for the long-term test was 500 min. The short-term tests (30 min) have shown that Equation (22)   effect on fluid loss reduction. Figure  data. Also, both plots tend to converge to a maximum value as depicted by the formation of a plateau. The close convergence could be explained in two ways. First, the model developed in Equation (22) can predict both short-term filtration tests and long-term filtration tests. Secondly, the experimental cumulative fluid loss and the model prediction tend to reach a plateau or maximum value. This indicates that a maximum fluid loss has been attained. The convergence of the predicted values for the cumulative fluid loss with that of the experimental data also indicates that the effects of fluid loss reduction in the long run was mainly due to nanoparticles. This goes to confirm that the new fluid loss model tends to account for the contributory effect of the nanoparticles on the fluid loss reduction in terms of quantity (;) and size (r np ). Values of cumulative fluid loss beyond this maximum would remain constant at the same value. This is because there is no more fluid lost as indicated by the flat line obtained for fluid lost in Figure 7. After 500 min, the experimental cumulative fluid loss obtained was 59 cm 3 , while the model prediction was 60.58 cm 3 . The model prediction for the maximum fluid loss was at 61.86 cm 3 . The coefficient of determination, R 2 , for the model fitting for the long-term filtration test was estimated at 94.89%. The bulk of this can be attributed to the short-term filtration test, i.e. below filtration time of 100 min. Figure 8 shows the model prediction for the permeability of the mud cake for sample S 2 using Equation (19). The permeability model, just like the fluid loss model derived, can describe the permeability variation of the mud cake both in the short-and long-term filtration process. Long-term fluid loss test indicates that after filtration time of 100 min, the permeability values obtained through model prediction are decrease gradually. The low permeability values during long-term tests depends on the size of the nanoparticles and the amount of nanoparticles. Initial permeability reduction during mud cake build-up is due to the deposition of the micro-size particles present in the bentonite clay. This is often characterized by a rapid reduction in permeability of the mud cake during the filtration process (see Figure 8, between 0 and 100 min). Further reduction in the permeability of the mud cake would be due to the presence of nanoparticles. Such reduction in permeability is often a slow process due to the small size of the nanoparticles (see Figure 8, between 100 and 500 min).

Conclusion
ZnO nanoparticles were synthesized and characterized using XRD, EDX, and SEM. A basic foundational approach was applied in deriving a novel model, which describes the impact of the nanoparticles on the fluid loss of drilling mud during the filtration process. This was done taking into account the kinetics of mud cake formation and colloidal behavior of the nanoparticles. The new model gave a better description of the fluid loss behavior of the nano-drilling mud when compared with the API model using statistical measures.  Figure 8. The plot of the model prediction for the permeability of the mud cake for sample S 2 containing 1.5 wt.% of zinc oxide nanoparticles in 6.5 wt.% bentonite suspension at 25°C and 100 psi.