Rafał Wiśniowski, Krzysztof Skrzypaszek and Tomasz Małachowski from the Faculty of Drilling, Oil and Gas at AGH University of Krakow published a paper in the journal Energies (volume 13, issue 12, article 3192) titled "Selection of a Suitable Rheological Model for Drilling Fluid Using Applied Numerical Methods". Its DOI is 10.3390/en13123192 and it was published in 2020. The paper deals with the fluid used when drilling oil wells.

Why the fit matters

The starting point for the authors is that the better a rheological model matches the properties of a real fluid, the smaller the error in the technological parameters calculated for drilling. Reining in that error is a condition for planning those parameters properly.

Which models, and how to fit them

The paper names the classic models: Newtonian, Bingham plastic, Casson, Ostwald-de Waele and Herschel-Bulkley. Beside them, the authors suggest looking at the Vom Berg and Hahn-Eyring models, which had not previously been used to describe drilling fluids. Parameters for the Bingham plastic, Casson, Ostwald-de Waele and Newtonian models are, in their proposal, found by linear regression; for Herschel-Bulkley, Vom Berg and Hahn-Eyring the suggested route is non-linear regression.

The Rheosolution program

The theoretical reasoning and the mathematical relations worked out at the Department of Drilling and Geoengineering, within AGH's Faculty of Drilling, Oil and Gas, led the authors to build their own program, Rheosolution. Its job is to automate the search for the optimum rheological model of a drilling fluid. The abstract gives examples of how the model selection method is applied in practice.

Tests on real measurement data gave different answers depending on the fluid. For a plain cement slurry the best-fitting model was Ostwald-de Waele; once the PSP 042 superplasticizer was added, the Vom Berg model came out on top. A plain bentonite mud was described best by the Casson model, and a polymer-inhibited mud by the Hahn-Eyring model. In the authors' view the multi-parameter models, Vom Berg and Hahn-Eyring, perform well for fluids with polymer or superplasticizer additives.

All the data come from the paper's abstract (OpenAlex), the DOI metadata and the full open-access text.