Field Rheological Parameters Improve Stand Pipe Pressure Prediction While Drilling
Authors: Maglione Roberto , Robotti Giovanni 
Published: December 2007

Abstract
The equation of the rheological model of Herschel & Bulkley and the relevant expressions of pressure drops, valid both for circular and annular sections, are applied to determine the three characteristic parameters of a drilling fluid, having yield pseudoplastic behaviour, and flowing in the drilling hydraulic circuit, starting from circulation tests. A typical standard drilling hydraulic circuit consists of the surface circuit (stand pipe, rotary hose, swivel and kelly), the circular section (inside the drill string with variable diameters), the bit and the annular section (the gap between the wall borehole or casing and the drill string). In this circuit the drilling mud enters the drill pipe, comes out from the bit, flows up to the annulus up to the surface, where it after a short time for cleaning is put back in the circuit.
The parameters to be solved are the yield point, the consistency index k and the flow behaviour index n.
By means at least three flow tests at a certain drilling depth, with the bit off bottom, the pump rates and the relative stand pipe pressures are recorded.
The obtained N couple of values of stand pipe pressure and pump rate, the geometry of the hydraulic circuit and the fluid density are the input data for a numerical procedure to determine the three parameters of the considered drilling fluid.
In this way, using this numerical process, a non linear system of N equations (with N 3) with three unknowns (the three parameters of the fluid: n, k and) is solved determining the Herschel & Bulkley rheological parameters.
This procedure takes into account the more probable solution for each tentative value of the flow behaviour index np, considering the infinite couples of and k satisfying the input value of stand pipe pressure, and the mean square deviation is calculated for each tentative value of, np: the minimum value of the MSD gives the solution tern of the non linear system of N equations.
In this paper a brief description of the mathematical model and the numerical process used will he reported and a calculation using field data from circulation test carried out in a surface section of an ultradeep well located in the Po valley, will be done.
The results will be compared with the obtained results using the readings on the same drilling mud performed on Fann VG 35 viscometer and it can be seen that not always the rheological tern determined from the viscometer data coincides with the equivalent rheological tern found considering the drilling well as viscometer.
Besides the stand pipe pressure relative to an 17 1/2" run (from 2900 m to 3060 m) will be monitored using this procedure: calculated SPP data using the equivalent rheological tern and the rheological parameters from viscometer readings, using different rheological models such as Bingham, Ostwald & de Waele and Herschel & Bulkley, will be compared to field stand pipe pressure data. It can be seen that the overall average error between measured and calculated SPP (using the Herschel & Bulkley equivalent tern) has been drastically reduced to very low error while the calculated SPP using viscometer readings with the most rheological models today used in practice could lead to large errors misleading an accurate evaluation of the SPP on the rig floor.
This method could be useful not only to calculate and predict exactly the SPP, but also to evaluate with accuracy the annular pressure drop and the corresponding ECD in order to have the maximum allowable pump rates without fracturing the crossed formation, besides could be used to monitor the SPP behaviour for potential occurring problem in the hydraulic circuit such as wash out, plugged nozzles and in the case of gas kicks in the well.
Also this method, if applied to different drilling depths, could give information on the influence of pressure and temperature, existing in the well, on the rheology of the drilling mud.

Introduction
During drilling operations it is very important to know exactly the pressure drop along the hydraulic circuit for many reasons. The most important are the following:
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