Functional and practical analytical pressure surges model through herschel bulkley fluids

Substantially large pressure surges are generated while drilling a well due to tripping operations in which a central drillstring is being moved up or down through non-Newtonian fluid. The presence of these subsurface surge pressures must be considered and determined in almost every well drilled. Wells exhibiting high geothermal temperature gradient further complicate the determination of wellbore pressures since the classical viscometer does not characterize the non-Newtonian nature of fluids accurately at elevated temperatures. More importantly, rheological model selection also plays a key role for effectively proposing safe tripping speeds without violating the mud window constraints. Herschel-Bulkley rheological model has gained more reputation among others due to better predictions of wellbore hydraulic pressures as suggested by the American Petroleum Institute. A new practical and dimensional analytical model was developed for Herschel Bulkley (HB) fluid to calculate pressure surges caused by drillstring movement for non-Newtonian fluids under the fully developed flow (steady state) conditions in the laminar flow range in a slot geometry. The proposed analytical method was applied on unweighted fresh water sepiolite mud as a non-Newtonian fluid since the sepiolite muds are among the few water based muds performing adequately at extreme temperatures as the synthetic and oil base muds. Already measured rheological constants of selected fluid system using both HTHP dynamic rheometer and classical viscometer were considered to obtain surge pressures at ambient to extreme temperature ranges. The results are compared with already developed Burkhardt method for Bingham Plastic fluid and Schuh method for Power Law fluid and other proposed numerical and analytical solutions. Substantial differences on the pressure surges between the conventional viscometer and the HTHP rheometer measurements were also presented. The precision of the developed model is shown to be acceptable for most practical applications. Being operationally easy and applicable with a convenient solution code make the proposed model straightforward to be used as a part of drilling software.