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Predictive analytics for the Vipulanandan rheological model and its correlative effect for nanoparticle modification of drilling mud.

Afolabi, Richard O.; Yusuf, Esther O.; Okonji, Chude V.; Nwobodo, Shalom C.


Richard O. Afolabi

Esther O. Yusuf

Chude V. Okonji

Shalom C. Nwobodo


Modelling the flow of nanoparticle modified drilling mud (or nano-drilling muds) requires the use of existing generic time-independent models with the addition of nanoparticle terms having a number of parameters incorporated. These parameters quantify the uncertainties surrounding nanoparticle contributions to drilling mud rheology. However, when the parameters in the overall model become too large, the tuning of each parameter for proper flow description can be challenging and time-consuming. In addition, the predictive capability of known models for the different regimes associated with the flow of nano-drilling muds is limited in scope and application. For example, computational analysis involving nano-drilling muds have been described using Herschel-Buckley, Power-Law, Bingham Plastic, Robertson-Stiff, Casson, Sisko, and Prandtl-Eyring. However, these models have been shown over time to have limited predictive capability in accurately describing the flow behavior over the full spectrum of shear rates. Recently, a new rheological model, the Vipulanandan model, has gained attraction due to its extensive predictive capability compared to known generic time-independent models. In this work, a rheological and computational analysis of the Vipulanandan model was carried out with specific emphasis on its modification to account for the effects of nanoparticles on drilling muds. The outcome of this novel approach is that the Vipulanandan model can be modified to account for the effect of interaction between nanoparticles and clay particles. The modified Vipulanandan show better prediction for a 6.3 wt% mud with R2 of 0.999 compared to 0.962 for Power law and 0.991 for Bingham. However, the R2 value was the same with Herschel Buckley model but the RMSE value show better prediction for the Vipulanandan model with a value of 0.377 Pa compared to the 0.433 Pa for Herschel Buckley model.


AFOLABI, R.O., YUSUF, E.O., OKONJI, C.V. and NWOBODO, S.C. 2019. Predictive analytics for the Vipulanandan rheological model and its correlative effect for nanoparticle modification of drilling mud. Journal of petroleum science and engineering [online], 183, article ID 106377. Available from:

Journal Article Type Article
Acceptance Date Aug 12, 2019
Online Publication Date Aug 15, 2019
Publication Date Dec 31, 2019
Deposit Date Aug 22, 2019
Publicly Available Date Aug 16, 2020
Journal Journal of Petroleum Science and Engineering
Print ISSN 0920-4105
Electronic ISSN 1873-4715
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 183
Article Number 106377
Keywords Drilling mud; Bentonite mud; Vipulanandan; Nanoparticles; Rheology; Modelling
Public URL


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