Precise Method to Estimate the Herschel-Bulkley Parameters from Pipe Rheometer Measurements
Accurate characterization of the rheological behavior of non-Newtonian fluids is critical in a wide range of industries as it governs process efficiency, safety, and end-product quality. When the rheological behavior of fluid may vary substantially over a relatively short period of time, it is desir...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-04-01
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| Series: | Fluids |
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| Online Access: | https://www.mdpi.com/2311-5521/6/4/157 |
| _version_ | 1797537694422663168 |
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| author | Elie Magnon Eric Cayeux |
| author_facet | Elie Magnon Eric Cayeux |
| author_sort | Elie Magnon |
| collection | DOAJ |
| description | Accurate characterization of the rheological behavior of non-Newtonian fluids is critical in a wide range of industries as it governs process efficiency, safety, and end-product quality. When the rheological behavior of fluid may vary substantially over a relatively short period of time, it is desirable to measure its viscous properties on a more continuous basis than relying on spot measurements made with a viscometer on a few samples. An attractive solution for inline rheological measurements is to measure pressure gradients while circulating fluid at different bulk velocities in a circular pipe. Yet, extracting the rheological model parameters may be challenging as measurement uncertainty may influence the precision of the model fitting. In this paper, we present a method to calibrate the Herschel-Bulkley rheological model to a series of differential pressure measurements made at variable bulk velocities using a combination of physics-based equations and nonlinear optimization. Experimental validation of the method is conducted on non-Newtonian shear-thinning fluid based on aqueous solutions of polymers and the results are compared to those obtained with a scientific rheometer. It is found that using a physics-based method to estimate the parameters contributes to reducing prediction errors, especially at low flow rates. With the tested polymeric fluid, the proportion difference between the estimated Herschel-Bulkley parameters and those obtained using the scientific rheometer are −24% for the yield stress, 0.26% for the consistency index, and 0.30% for the flow behavior index. Finally, the computation requires limited resources, and the algorithm can be implemented on low-power devices such as an embedded single-board computer or a mobile device. |
| first_indexed | 2024-03-10T12:19:51Z |
| format | Article |
| id | doaj.art-fe6a74a5c451404f8ea3b899d7bdcd2e |
| institution | Directory Open Access Journal |
| issn | 2311-5521 |
| language | English |
| last_indexed | 2024-03-10T12:19:51Z |
| publishDate | 2021-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fluids |
| spelling | doaj.art-fe6a74a5c451404f8ea3b899d7bdcd2e2023-11-21T15:35:45ZengMDPI AGFluids2311-55212021-04-016415710.3390/fluids6040157Precise Method to Estimate the Herschel-Bulkley Parameters from Pipe Rheometer MeasurementsElie Magnon0Eric Cayeux1Total, R&D, 4029 Stavanger, NorwayEnergy Department, Norwegian Research Centre, 4021 Stavanger, NorwayAccurate characterization of the rheological behavior of non-Newtonian fluids is critical in a wide range of industries as it governs process efficiency, safety, and end-product quality. When the rheological behavior of fluid may vary substantially over a relatively short period of time, it is desirable to measure its viscous properties on a more continuous basis than relying on spot measurements made with a viscometer on a few samples. An attractive solution for inline rheological measurements is to measure pressure gradients while circulating fluid at different bulk velocities in a circular pipe. Yet, extracting the rheological model parameters may be challenging as measurement uncertainty may influence the precision of the model fitting. In this paper, we present a method to calibrate the Herschel-Bulkley rheological model to a series of differential pressure measurements made at variable bulk velocities using a combination of physics-based equations and nonlinear optimization. Experimental validation of the method is conducted on non-Newtonian shear-thinning fluid based on aqueous solutions of polymers and the results are compared to those obtained with a scientific rheometer. It is found that using a physics-based method to estimate the parameters contributes to reducing prediction errors, especially at low flow rates. With the tested polymeric fluid, the proportion difference between the estimated Herschel-Bulkley parameters and those obtained using the scientific rheometer are −24% for the yield stress, 0.26% for the consistency index, and 0.30% for the flow behavior index. Finally, the computation requires limited resources, and the algorithm can be implemented on low-power devices such as an embedded single-board computer or a mobile device.https://www.mdpi.com/2311-5521/6/4/157non-Newtoniannon-thixotropicHerschel-Bulkleypipe rheometer |
| spellingShingle | Elie Magnon Eric Cayeux Precise Method to Estimate the Herschel-Bulkley Parameters from Pipe Rheometer Measurements Fluids non-Newtonian non-thixotropic Herschel-Bulkley pipe rheometer |
| title | Precise Method to Estimate the Herschel-Bulkley Parameters from Pipe Rheometer Measurements |
| title_full | Precise Method to Estimate the Herschel-Bulkley Parameters from Pipe Rheometer Measurements |
| title_fullStr | Precise Method to Estimate the Herschel-Bulkley Parameters from Pipe Rheometer Measurements |
| title_full_unstemmed | Precise Method to Estimate the Herschel-Bulkley Parameters from Pipe Rheometer Measurements |
| title_short | Precise Method to Estimate the Herschel-Bulkley Parameters from Pipe Rheometer Measurements |
| title_sort | precise method to estimate the herschel bulkley parameters from pipe rheometer measurements |
| topic | non-Newtonian non-thixotropic Herschel-Bulkley pipe rheometer |
| url | https://www.mdpi.com/2311-5521/6/4/157 |
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