A Generalised and Consistent Pressure Drop and Flow Regime Transition Model for Drilling Hydraulics Suitable for Slimhole, Underbalanced and Horizontal Wells
Authors: Bailey W.J. , Peden J.M. 
Published: December 2007

Abstract
Generalised 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, makes no assumptions about conduit geometry, can include the presence of a laminar plug flow region, accommodate drillpipe rotation effects and account for the effects of annular eccentricity. Simple, explicit and general formulations for approximating pressure losses over Measurement While Drilling tools (MWD's) and Positive Displacement Motors (PDM's) 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 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 real drilling fluids flowing in both circular and annular conduits.

Introduction
The efficiency and effectiveness of drilling slimhole, horizontal and underbalanced wells is markedly improved when reasonable certainty can be ascribed to all parts of the circulating system. Accurate quantification of system losses enhances the validity of calculated equivalent circulating density - ECD, and other drilling parameters and indicators. Advantages of more precise ECD estimates include: proper maintenance of the integrity of underbalanced conditions; prevents lost circulation; indicates the likelihood of a potential kick and improves overall drilling efficiency through improved hole cleaning. Unfortunately, the typically high annular pressure drops associated with slimhole (high aspect ratio, Di/Do) drilling operations cannot be accurately predicted through conventional laminar and turbulent flow functions (with such losses b ing as much as 80% of total system parasitic loss). This is due to the use of the slot-flow assumption used to allow formulation of tractable annular flow functions. Errors attributable solely to this approximation increase significantly as the aspect ratio increases.
Certain non-Newtonian turbulent flow friction factor correlations are also unsuited for specific applications due to the particular fluid types, and conduit geometry, upon which they were constructed. Consequently, confidence based on quantities calculated using conventional pressure loss functions may be low, with potentially detrimental implications for primary and incidental calculated quantities.
This paper attempts to resolve some of these issues by presenting a number of new formulations suitable for application to hydraulic calculations for slimhole, underbalanced and horizontal wells. The role of the reological model is discussed first to establish their proper application within the context of the proposed model. In the section headed 'New Rheological Parameter' the in situ (or 'generalised') flow behaviour index is introduced with appropriate solution procedures. This is followed by a definition of a GRN under the section 'Generalised Reynolds Number.