Analysis of Tool Joint Effects for Accurate Friction Pressure Loss Calculations
Authors: Jeong Yeon-Tae , Shah Subhash N. 
Published: December 2007

Abstract
The prediction of friction pressure losses is very important in many oil-field operations, including drilling, completion, fracturing, acidizing, workover and production. Many theoretical and experimental studies have dealt with the flow of fluids through pipes and annuli for friction pressure loss calculations. Most of these studies have concentrated upon the fluids rheological models, pipe roughness, and geometrical parameters. However, the important effect of tool-joint in conjunction with the drillpipe in estimating the friction pressure loss in annulus has yet not been investigated. The tool joint is a necessary part to extend the drillpipe. The space between the tool joint and casing is narrower than the space between drillpipe and casing because of the larger diameter of the tool joint than the drillpipe. Therefore, there will be an additional pressure loss due to effect on the fluid flowing in the annulus expansion and contraction.
This paper presents the experimental data of the tests performed with three different fluids and discusses the results in light of the effect of tool joints on the annular friction pressure loss. It is found that the effect of the presence of tool joints on the annular friction pressure is significant and an accurate prediction method for annular pressure loss is proposed.

Introduction
The prediction of accurate frictional pressure loss in annulus is important in the present well construction technology. The frictional pressure loss of fluids in circular pipe is strongly influenced by the rheological properties of fluids1–3, pipe roughness4,5, and the geometry of conduit6–10. The rheological behavior of simple fluids can be described by Newton's law of viscosity while for non-Newtonian fluids several constitutive equations or models are available. The most simple and widely used model is the Ostwald de-Waele or power law model. The rheological behavior of fluids used in this study can be characterized by this model.
The pipe roughness can be neglected under laminar flow condition but is significant in turbulent flow. Friction losses are higher in rough pipes for both Newtonian and non-Newtonian fluids. The correction to account for pipe roughness is incorporated in the calculation of friction factor4,5.
For concentric annular flow, the geometry of conduit can be expressed by the equivalent diameter. Several equivalent diameter definitions are proposed6–10. However, for simplicity and convenience, the following two equations are widely used. First equation is based upon the definition of the hydraulic radius, rH, which is the ratio of the cross sectional area to the wetted perimeter of the flow channel. The equivalent diameter, de1, is equal to four times the hydraulic radius and for concentric annulus it is the difference between the internal diameter of the outer conduit, and the outside diameter of the inner conduit, i.e. de1=(d2-d1). The second most popular equivalent diameter equation used is based upon Lamb's work11 and the slot flow approximation for annulus2. Lamb developed the relationship between pressure gradient and total flow rate in laminar flow regime in annulus. As the outer diameter of pipe approaches to zero, Lamb's equation reduces to the pipe flow equation. This equation is compared with the annular flow equation that is approximated as a rectangular slot. Therefore, the second equivalent diameter equation available is, de2=0.816(d2-d1).
The design engineer simply extends the pipe flow equations to annular geometry. The same equations, which are used for pipe flow, are used to calculate the Fanning friction factor, f, and generalized Reynolds number, Nreg, for annular flow by simply replacing the pipe diameter with an equivalent diameter. Obviously, the annular friction factors calculated with de1 are higher than those calculated with de2. To be on the conservative side, the values of friction factor calculated in this study are based upon de1.
The conventional drillpipe is still widely used in many oil field applications in spite the increased use of coiled tubing in some applications. The tool joints are essential parts with drillpipe. The gap between the tool joint and casing is narrower than the gap between the drillpipe and casing because of the larger diameter of tool joint compared to the drillpipe. Therefore, for the fluid flow in the annulus, there will be an additional pressure loss due to the expansion and contraction effects.