A Generalized and Consistent Pressure Drop and Flow Regime Transition Model for Drilling Hydraulics

Abstract

Generalized laminar and turbulent pressure loss formulations are presented that are suitable for both annular and circular conduits. In so doing, a new rheological parameter is introduced that provides a consistent link between turbulent and laminar flow calculations and flow regime transition criteria.The approach presented is independent of the form of the rheological model of choice, it makes no assumptions about conduit geometry, can include the presence of a laminar plug flow region, accommodates drillpipe rotation effects and accounts for the effects of annular eccentricity. Simple, explicit and general formulations for approximating pressure losses over measurement while drilling tools and positive displacement motors are also presented to augment the suite of expressions required for comprehensive hydraulic calculation over the circulating system. Furthermore, procedures for establishing realistic bounds of confidence for laminar pressure loss functions are presented, enabling computation of the degree of certainty attributable to such a calculation. This procedure for establishing confidence intervals is applicable to any function requiring fitted parameters, hence it has a broader application potential than just drilling hydraulics. The model demonstrates good agreement with measured data from studies involving drilling fluids flowing in both circular and annular conduits.*Now with Schlumberger.

Experimental study and predictions of pressure losses of fluids modeled as Herschel–Bulkley in concentric and eccentric annuli in laminar, transitional and turbulent flows

“…The non-linear three parameters model proposed by Herschel and Bulkley (1926) has become in recent years the model of choice to simulate the behavior of such fluids, replacing the well-known two-rheological parameter models of Bingham and power-law. The choice has been done not only by the oil-drilling industry (Bailey and Peden, 2000;Becker et al, 2003;Hemphil et al, 1993;Maglione and Ferrario, 1996;Maglione et al, 1999Maglione et al, , 2000Kelessidis et al, 2007;Zamora et al, 2005) but also by many other industries such as food, painting, concrete, waste and mineral processing (Bartosik, 2010;De Larrard et al, 1998;Fordham et al, 1991;Ferraris, 1999).…”

Laminar, transitional and turbulent flow of Herschel–Bulkley fluids in concentric annulus

“…Reasons for the non-frequent use were not only the complexity in derivation of the model's three parameters (Nguyen and Boger, 1987;Hemphil et al, 1993) but also the fact that analytical solutions for laminar or turbulent flow in annuli are not possible, requiring either graphical or trial-anderror solutions (Govier and Aziz, 1972;Hanks, 1979;Fordham et al, 1991). The on-line use, however, of personal computers enabled Maglione et al (1999Maglione et al ( , 2000, Bailey and Peden (2000) and Becker et al (2003) to utilize Herschel-Bulkley rheological model in fluid mechanics computations of drilling fluids.…”

“…Some confirmation of the Reed and Pilehvari model was also provided by Subramanian and Azar (2000) but there were cases for which predictions were at odds with the measurements. The approach of Reed and Pilehvari has been followed also by Merlo et al (1995), Maglione et al (2000) and Bailey and Peden (2000) to cover all flow regimes for flow of Herschel-Bulkley fluids and of generalized non-Newtonian fluids in concentric annuli.…”

A model for extended-reach limit analysis in offshore horizontal drilling based on formation fracture pressure

“…ε is the dimensionless eccentricity(Bailey and Peden 2000); for concentric annulus, ε = 0; whereas ε = 1 for completely eccentric annulus; in other cases, Eq. (16) can be used to illustrate it.…”