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466287 First-Principles Rheological Modelling of Smart Drilling Nanofluids

The development of first-principles models for the rheology of nanofluids is essential because it can effectively guide their tailored preparation: characterising the nanofluid behaviour as a function of shear rate, nanoparticle volume fraction and temperature is critical toward modelling, design and planning of cost-effective drilling campaigns. Upon successful validation, these models have general applicability to all function forms of nanoparticle-enhanced drilling fluids, eliminating the need for limited-value approximations and ad hoc parameterisations of fluid rheology.

First-principle rheological models describing the shear stress and viscosity of novel nanoparticle-based fluids have been derived on the basis of an isoelectric point assumption (Reilly et al., 2016). Model development relies on establishing a force balance between the Stokes drag force exerted upon the (idealised nanoparticle) sphere and the van der Waals interparticle attraction force described by the Hamaker equation. The interparticle distance variation is accounted for by means of an equation which relies on an equilibrium assumption between thickening and thinning rates (Pouyafar & Sadough, 2013). Nanoparticle interactions have been modelled employing an exclusive consideration of particle pairs, with a centre-to-centre separation distance of four radii at zero shear rate. Nevertheless, nanoparticles have been considered adequately dispersed at high shear rates, as a result of the attenuation of local energy gradients because of the interaction of vortices generated by particle rotation. The maximum separation distance can be computed on the basis of a homogeneous particle distribution assumption (Masoumi et al., 2009). The variation of interparticle distances between a minimum and a maximum estimated value has been approximated using a shear-dependant probability distribution, assuming that all particle pairs exist at one of these two states. These dispersion effects have been quantified as additional contributions to base fluid properties.

A univariate equation with a single fitting parameter characterised experimental data from two sources (Barry et al., 2015; Gerogiorgis et al., 2015) with a high coefficient of determination (0.999 in both cases). Coefficients of determination were more rigorously assessed using a logarithmic transformation (0.994 and 0.993, respectively), correcting for a highly asymmetric dataset (a skewness of 2.6 and 2.2 has been computed, respectively). A more elaborate trivariate equation characterised viscosity for variations in shear rate, concentration of nanoparticles, and temperature with high predictive potential (0.986). The coefficient of determination has been rigorously assessed using a logarithmic transformation (calculated to be 0.983). Temperature effects have been explicitly accounted for with an Arrhenius relationship: the activation energy of 11.24 kJ/mol computed is in accordance with values measured in traditional fluids (Khalil et al., 2011). Significant error attenuation improvements in viscosity estimation have been observed when comparing the novel correlation with the standard Herschel-Bulkley model, for a range of shear rates (5 s^{-1} to 1020 s^{-1}); in contrast to the Herschel-Bulkley model which failed to yield a coefficient of determination higher than 0.90, the first-principles model has achieved coefficients over 0.98, for both datasets and univariate as well as trivariate model instances (Reilly et al., 2016).

**LITERATURE REFERENCES**

1. Barry, M.M. et al., 2015. Fluid filtration and rheological properties of nanoparticle additive and intercalated clay hybrid bentonite drilling fluids. *J. Pet. Sci. Eng.*, **127**: 338–346.

2. Gerogiorgis, D.I., Clark, C., Vryzas, Z., Kelessidis, V.C., 2015. Development and parameter estimation for an enhanced multivariate Herschel-Bulkley rheological model of a nanoparticle-based smart drilling fluid. *Comput.-Aided Chem. Eng.* **37**: 2405-2410.

3. Khalil, M., Jan, B.M. & Raman, A.A.A., 2011. Rheological and statistical evaluation of nontraditional lightweight completion fluid and its dependence on temperature. *J. Pet. Sci. Eng.* **77**(1): 27–33.

4. Mahmoud, O. et al., 2016. Nanoparticle-based drilling fluids for minimizing formation damage in HP/HT applications, SPE Paper 178949, in: *SPE International Conference and Exhibition on Formation Damage Control*.

5. Masoumi, N., Sohrabi, N., Behzadmehr, A., 2009. A new model for calculating the effective viscosity of nanofluids. *Journal of Physics D: Applied Physics*, **42**(5): 055501 (6).

6. Pouyafar, V. & Sadough, S.A., 2013. An enhanced Herschel–Bulkley model for thixotropic flow behavior of semisolid steel alloys. *Metallurgical and Materials Transactions B*, **44**(5): 1304–1310.

7. Reilly, S.I., Vryzas, Z., Kelessidis, V.C., Gerogiorgis, D.I., 2016. First-principles rheological modelling and parameter estimation for nanoparticle-based smart drilling fluids, *Comput.-Aided Chem. Eng.* (in press).

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