1. Introduction

2. Modification of rheological properties

The rheology of drilling fluids should exhibit shear thinning characteristics to have less resistance at high shear rates. At low shear rates, (for instance when mud circulation is being stopped) the viscosity should be high enough to prevent transported cuttings from falling back downhole in the wellbore based on Stokes' Law. Apparent viscosity (AV); which is defined as the ratio of stress to rate of strain of liquid, plastic viscosity (PV); the resistance to flow of fluid, yield point (YP); the minimum shear stress required in order to move the fluid, and gel strength at 10 s and 10 min to measure the fluid capability to act like a gel and suspend cuttings and weighting materials when circulation is ceased, are the rheological properties investigated in this study. One of the common models for the rheology of drilling fluid is the Herschel-Buckley model (Eq (1)),(1)${}_{\mathrm{}}{}^{}$where τ is the shear stress (lb/100 ft2), τ0 is the yield point (lb/100 ft2), K is the consistency index, γ is the shear rate (s−1), and n is the flow behaviour index(dimensionless) that needs to be less than 1 for shear thinning fluids.

Nanoparticles can enhance the rheological properties of drilling fluids using various mechanisms which mostly depend on continuous phase of drilling fluids and nanoparticle characteristics. Silica nanoparticles can typically enhance the apparent viscosity of water as the continuous phase of drilling fluids (Mao et al., 2015a, Mao et al., 2015b, Sharma et al., 2012, Taraghikhah et al., 2015) or displacing fluids in enhanced oil recovery processes (Chegenizadeh et al., 2016, Rafati et al., 2016). It has been well established that the viscosity of nanofluids is much higher than the viscosity of conventional dispersions at the same volume concentration of dispersed particles. As viscosity is defined as internal friction between two layers of a fluid under shear stress, once nanoparticles are dispersed in the fluid there is a possibility of increasing friction between layers of the fluid, which results in an increase in viscosity of nanofluid (Sundar et al., 2013, Sharma et al., 2016). This enhancement in viscosity of nanofluids can be estimated through homogeneous solid–fluid interaction models. The available theoretical formulas for the estimation of viscosity of nanofluids have been developed initially from the Einstein model (Einstein, 1906), which is based on the assumption that the fluid contains suspensions of spherical shapes. However, his model was developed based on the simple assumptions and only worked at low concentrations of small nanoparticles. Later, modified models by other investigators have been introduced (Batchelor, 1977, Brinkman, 1952, Godson et al., 2010, Nguyen et al., 2007, Rea et al., 2009) that could be used for larger nanoparticles at higher concentrations, pressure and temperature. In addition, it has been found that the effective viscosity of nanofluids depends not only on the concentration of nanoparticles, but also on their sizes. This results have been confirmed through both molecular dynamics simulations of hard-sphere potential (Rudyak et al., 2008, Rudyak et al., 2009) and experimental studies (Rudyak, 2013, Timofeeva et al., 2010). It should be noted that in designing drilling fluids, different additives can be used to increase the rheological properties into an acceptable and desirable range required for hole cleaning, lubricating and cooling downhole equipment among others. However, these properties may not exceed beyond specific levels, inappropriate increase of properties may have negative effects during fluid circulation in the wellbore such as excessive frictions and weight that impose higher capacity pumps, and sand/cutting removal issues. Therefore, the aim of using nanoparticles is to attain desirable properties with lower cost and improved efficiencies.

Silica nanoparticles can also improve the rheological stability of emulsion based and invert emulsion based drilling fluids as they have a large free energy of adsorption and can attach to the oil-water interface depending on their degree of hydrophobicity (Agarwal et al., 2011, Ghosn et al., 2017). Metal NPs can also improve the rheological stability of drilling fluids due to their high thermal conductivities that can dissipate heat efficiently because of Brownian motion (Einstein, 1956). Therefore, fluid is less affected by the temperature increase and keeps its liquid form, rather than degrading into a solid form. Results from several studies demonstrated that nanofluids have higher thermal conductivities compared to base fluids (Liu et al., 2005, Ding et al., 2006, Aybar et al., 2015). Different investigations on thermal conductivity of nanofluids showed enhancements from 12.4% to 80% can be obtained with carbon nanotubes dispersions in different fluids (Smith et al., 2017). Table 1 lists most of the recent studies on modification of rheological properties of drilling fluids by addition of nanoparticles.

Amanullah et al. (2011) investigated the effect of nanomaterials on several WBFs. They used a number of commercial nanomaterials to overcome challenges associated with conventional drilling fluids. Fluids were prepared with concentration of 0.14 wt% NPs and compared with a base sample. Their results showed no significant changes to the viscosity profile, however superior gelling properties were observed.

Agarwal et al. (2011) used clay and silica nanoparticles to stabilise invert emulsion drilling fluids at HTHP conditions. They found that nanoclay and nanosilica can individually or as a mixture stabilise the invert emulsion drilling fluids. They also indicated that the rheological properties of invert emulsion drilling fluids are functions of nanoparticle's wettability (hydrophobicity). Their results showed addition of barite reduces yield stress but it can be regained by increasing the concentration of silica nanoparticles. They also found that stable invert emulsion drilling fluids can be obtained using organically modified nanoclay and hydrophobic nanosilica. Their analysis of gel strength showed that relatively hydrophilic/hydrophobic nanosilica particles that are dispersed in water, and nanoclay particles that are dispersed in oil phase have significant effect on gel strength capacity.

Sharma et al. (2012) was the first to test a silica based NPs with an average particles diameter of 20 nm as an additive to drilling fluids. They analysed the effects of silica on rheological properties, and found that gel strength and YP were significantly decreased at concentration of 1 wt%, while there was a slight decrease at concentration of 3 wt%. Srivatsa and Ziaja (2012) also showed that the addition of silica increased the drilling fluid viscosity, with one sample achieving 30% increase in viscosity compared to the base drilling fluid. This is consistent with the recent work of Mao et al. (2015b) who also concluded that addition of NPs into drilling fluids cause an increase in viscosity. Taraghikhah et al. (2015) demonstrated similar results for the use of silica with concentrations up to 1 wt%, and Hassani et al. (2016) tested silica NPs, and a hybrid NPs consisting of carbon nanotubes and silica. Hassani and his co-workers showed that both types of NPs can increase the effective viscosity of the drilling fluids significantly, with silica NPs showed a superior behaviour compared to the hybrid NPs. Salih et al. (2016) found that the properties of WBFs containing nanosilica are comparable to the higher performance and stability associated with OBFs. Needaa et al. (2016) tested sepiolite NPs, which contains silica, and showed that there was an increase in PV and YP when compared to a base drilling fluid sample. It can therefore be concluded that enhanced drilling fluid rheologies are common trends amongst WBFs with the addition of silica NPs.

Abdo and Haneef (2013), tested a WBF with a low concentration of Palygorskite(Pal) with particle size between 10 and 20 nm. The samples with low concentrations of Pal displayed significant improvement in rheological properties including a 200% increase in gelling characteristics. And it was noted that all the fluids displayed shear thinning properties.

Abdo and Haneef (2013) tested bentonite with particle size between 4 and 9 nm, as an additive to WBFs and compared the results with API bentonite properties and a sample with local bentonite not at nanosize. The overall rheological properties such as AV, PV and YP decreased due to the addition of bentonite with nanosize diameter, as the solid content of the fluid was decreased.

Kosynkin et al. (2011) were the first who tested carbon-based NPs (graphene oxide) as a filtration additive in water-based drilling fluids at concentrations as low as 0.2 wt% with xanthan gum. Their experimental results showed that a combination of large-flake and powdered graphene oxide in a ratio of 3:1 can provide the best filtration results, having an average fluid loss of 6.1 mL over 30 min and leaving a filter cake of about 20 μm thick. This was promising compared to a standard suspension of clays and polymers that are used in the oil industry which showed an average fluid loss of 7.2 mL and a filter cake of 280 μm thick.

Later in 2013, Nasser et al. also tested the rheological properties of carbon-based NPs (graphite) in WBFs. They showed for NPs with the size of 40 nm, the drilling fluid viscosity was increased, and as temperature and shear rate increase, the viscosity decreases. In 2014, Ismail et al. examined the use of multi-walled carbon nanotubes (MWCNT) in drilling fluids. They found that adding low concentrations of MWCNT with the size of 30 nm, at normal temperature made no significant difference in the rheological properties compared to the base sample. However, in ester-based drilling fluids, gel strength and emulsion stability slightly were increased with addition of MWCNT. Later, Taha and Lee (2015) examined the use of carbon-based NPs graphene in WBFs, and similarly their observations showed improved rheological properties of drilling fluids.

Madkour et al. (2016) tested the use of MWCNT based biodegradable composites in oil based drilling fluids, and showed a significant increase (in some cases up to double) in AV, PV and YP as well as gel strengths over the commercial viscosifier that is used as a comparison, and found that the fluid followed the Herschel-Buckley model. Overall, carbon based NPs have been demonstrated to be effective rheological modifiers at HPHT (High Pressure, High Temperature) conditions, and provide stable drilling fluids (Liu et al., 2005, Ding et al., 2006, Farbod et al., 2015). Mahto and Jain (2013) is, so far, the only study have tested the rheological properties of WBFs with the addition of fly ash NPs. Fly ash is small dark flecks and is composed of silica, alumina, magnetite and other components, and is produced from the burning of powdered coal. Fly ash is currently the world's fifth largest raw material resource, with India producing up to 130 Mt of fly ash per year. Fly ash NPs with the size between 1 and 100 nm, were added in concentrations of 1, 2 and 3 wt% and resulted in a stable rheology without any major changes in AV, PV, YP or gel strengths.