Transient effects in oilfield cementing flows: Qualitative behaviour

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dc.contributor.authorMoyers-Gonzalez, M.A.
dc.contributor.authorFrigaard, I.A.
dc.contributor.authorScherzer, O.
dc.contributor.authorTsai, T.P.
dc.date.accessioned2009-11-29T19:43:57Z
dc.date.available2009-11-29T19:43:57Z
dc.date.issued2007en
dc.description.abstractWe present an unsteady Hele-Shaw model of the fluid-fluid displacements that take place during primary cementing of an oil well, focusing on the case where one Herschel-Bulkley fluid displaces another along a long uniform section of the annulus. Such unsteady models consist of an advection equation for a fluid concentration field coupled to a third-order non-linear PDE (Partial differential equation) for the stream function, with a free boundary at the boundary of regions of stagnant fluid. These models, although complex, are necessary for the study of interfacial instability and the effects of flow pulsation, and remain considerably simpler and more efficient than computationally solving three-dimensional Navier-Stokes type models. Using methods from gradient flows, we demonstrate that our unsteady evolution equation for the stream function has a unique solution. The solution is continuous with respect to variations in the model physical data and will decay exponentially to a steady-state distribution if the data do not change with time. In the event that density differences between the fluids are small and that the fluids have a yield stress, then if the flow rate is decreased suddenly to zero, the stream function (hence velocity) decays to zero in a finite time. We verify these decay properties, using a numerical solution. We then use the numerical solution to study the effects of pulsating the flow rate on a typical displacement.en
dc.identifier.citationMoyers-Gonzalez, M.A., Frigaard, I.A., Scherzer, O., Tsai, T.P. (2007) Transient effects in oilfield cementing flows: Qualitative behaviour. European Journal of Applied Mathematics, 18, pp. 477-512.en
dc.identifier.doihttps://doi.org/10.1017/S0956792507007048
dc.identifier.issn0956-7925
dc.identifier.urihttp://hdl.handle.net/10092/3208
dc.language.isoen
dc.publisherUniversity of Canterbury. Mathematics and Statisticsen
dc.rights.urihttps://hdl.handle.net/10092/17651en
dc.subject.marsdenFields of Research::290000 Engineering and Technology::290500 Mechanical and Industrial Engineering::290501 Mechanical engineeringen
dc.subject.marsdenFields of Research::230000 Mathematical Sciences::230100 Mathematicsen
dc.titleTransient effects in oilfield cementing flows: Qualitative behaviouren
dc.typeJournal Article
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