A New and Practical Application of Annular Hydraulics
Authors: Taylor Ray , Smalling Dave 
Published: December 2007

This paper was prepared for the 48th Annual Fall Meeting of the Society of Petroleum Engineers of AIME, to be held in Las Vegas, Nev., Sept. 30-Oct. 3, 1973. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgement of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made.
Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers Office. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines.

Introduction
A new rheological model, the annular shear model, has been devised as a workable field model for annular hydraulic calculations. The model provides an accurate profile that closely approximates that of the actual fluid model, yet retains enough simplicity for field usage.
Deep drilling ventures strive to extend protective casing points to maximum depths. As protective casing points to maximum depths. As increased formation pressures necessitate higher density fluids, greater care should be taken to avoid losing circulation at the weakest points within the wellbore.
Loss of circulation is influenced not only by fluid density, but also by the pressure losses incurred in the annulus. These pressure losses may exceed 0.5 ppg. Thus, equivalent circulating densities (ECD) need to be calculated accurately to avoid loss of circulation by extending or initiating fractures through increased pressures imposed while circulating. Equivalent circulating densities should be maintained at minimum values, and accuracy of these values may appreciably decrease chemical treatment and, thus, mud costs.

SCOPE OF THE PROBLEM
The large degree of deviation in pressure-loss calculations is a result of pressure-loss calculations is a result of the model chose to describe the rheological behavior of the fluid. Fluids are broadly classified into one of two categories - Newtonian or non-Newtonian.
Newtonian fluids follow Newton's law of viscous resistance. For these fluids, shear stress is directly proportional to the shear rate at a constant temperature and pressure. Such fluids immediately initiate movement when a force in excess of zero is applied, and a plot on Cartesian coordinates of shear stress (y-axis) vs shear rate (x-axis) for a Newtonian fluid is a straight line passing through the origin (Fig. 1). The slope of the resulting straight line (shear stress/shear rate) is the Newtonian viscosity of the fluid.
Newtonian fluids may be exemplified by fluids such as water, diesel oil, glycerine and gases. The viscosity of Newtonian fluids is a constant quantity and is independent of shear rate at a fixed temperature and pressure. Thus the flow behavior of a Newtonian fluid may be expressed by the equation,
,.......................(1)
where theta = equivalent Farm dial reading mu = Newtonian viscosity, cpR = equivalent Farm rpmR = 1.409V = velocity, fpmDh-Dp = hydraulic diameter, in.