Summary The rheological model of Herschel and Bulkley reported in 1926 can be applied to determine the characteristic parameters of a drilling fluid. In this paper, an in-situ characterization approach is proposed. During flow tests at fixed drilling depths inside the well the pump rates and the relative stand pipe pressures (SPP's) are recorded. This allows one to determine in-situ the Herschel and Bulkley rheological parameters and the behavior of the drilling mud circulating in the well. The results are compared to those obtained in the laboratory using a Fann VG 35 viscometer for the same drilling mud. It is found that the rheological triad from the viscometer data does not always coincide with the rheological triad from the in-situ drilling test. Thus, the calculated SPP using viscometer readings could lead to misleading errors for an actual process. This method could be useful not only to calculate and predict the SPP, but also to evaluate with accuracy the annular pressure drop in order to obtain the maximum allowable pump rates without fracturing the formations. We discuss the sensitivity of the results in relation to the equivalent viscosity of the drilling fluids considered to some of the main practical drilling parameters, such as the flow velocity and pressure spatial distribution along the wellbore profile and, with reference to the mud structure, sensitivity to pressure and temperature. Considering the drilling well essentially as a viscometer (WAV) enables one to investigate the performance of the drilling hydraulic circuit and also the effects of the true effective viscosity (here called equivalent viscosity) and of the rheological behavior of the muds in all types of wells, and overall in deep wells with great accuracy. Introduction During well drilling operations it is very important to know the exact pressure drop for many reasons:for optimizing the pressure drop at the drilling bit in order to get the maximum impact force on the formation and, as a consequence, to increase the rate of penetration;for optimizing the flow rate in the annular gap between the drill pipe and the borehole wall for better transport of the drilling cuttings to the surface and optimizing the hole cleaning efficiency;to avoid fracture of the formations crossed due to the underestimation of the annular pressure drop;to detect any unexpected changes of the stand pipe pressure, due to a change in the hydraulic drilling circuit (i.e., washout, plugged nozzles and fluid kick) and make opportune decisions to restore the original conditions;to better design the mud pumps available on the drilling rig. In addition, in drilling ultradeep wells, high temperatures and pressures can influence the rheological properties of the drilling fluids in several ways. Physically, decreases in temperature and increases in pressure both affect the mobility of the system and lead to an increase of apparent viscosities and viscoelastic relaxation times.1 The effect of pressure is expected to be greater with oil-based systems due to the oil phase compressibility.2 Electrochemically, an increase in temperature augments the ionic activity of electrolytes and the solubility of any partially soluble salt that may be present in the mud. This could alter the balance between the interparticle attractive and repulsive forces and in doing so the degree of dispersion and flocculation of the mud systems. Sometimes this can also deeply affect the emulsion stability of oil-based muds.3 All these phenomena have a profound impact on rheological properties, especially as far as viscoelasticity and thixotropy are concerned. Chemically, all hydroxides react with clay minerals at temperatures above 90°C. For many kinds of muds, this can result in a change of the structure and therefore also in a change of the mud rheological properties. Because of the large number of variables involved, the behavior of the drilling muds at high temperatures and pressures may be very complex to explain, so that it can be very difficult to set general guidelines for each group of muds (water-based muds, oil-based muds, etc.) or even for the same kind of mud (small differences in the composition can result in considerable differences in the rheological behavior). Several different types of rheometers can be used to investigate the mud rheology at high pressure and temperature (HPHT) conditions. The most remarkable studies over the years were conducted by Annis4 and by Hiller,5 who studied effects of high temperatures (up to 150°C) and high pressures (up to 500 bar) on the rheology of water-based muds, considering them to have plastic behavior. During the same period, Combs and Whitmire6 performed experiments at high temperatures and high pressures on all invert emulsion muds, and measured effective viscosity variations by a capillary viscometer. Sinha7 investigated water-based clay suspensions as well as oil-based muds using a falling bob consistometer, and concluded that the equivalent viscosity of water-based muds, compared to inverted emulsion muds and oil-based muds, is not affected to the same extent by the variations of temperature and pressure. He also concluded that the temperature is the dominant variable in the case of water-based muds. McMordie8 carried out experiments (with temperatures up to 180°C and pressures up to 965 bar) on colloidal suspensions of asphalt in oil-based muds. He proved9 that the viscosity of oil-based muds at constant temperature and pressure may be described well by modification of the power law expression. Later, Bailey et al.10 studied, using the Huxley and Bertram HPHT rheometer, the behavior of the viscosity of low toxicity inverted oil emulsions at high temperature (up to 200°C) and high pressure (up to 1,000 bar). They concluded that the Bingham model is not that accurate for predicting the rheological behavior of low toxicity oil muds at high temperatures. At the same time, other experiments on the same kind of muds were performed at high temperatures (from 32 to 150°C) and pressures (from 69 to 1,034 bar) in a coaxial cylinder viscometer by Politte.11 He found that oil-based muds behave as plastic fluids, and concluded that the plastic viscosity is strictly related to the viscosity of the oil at high temperatures and pressures, while the yield point is only weakly affected by pressure, and mostly depends on temperature in a very complex way.

For the purpose of the present paper the analytical formulations of Herschel & Bulkley rheological model including the most relevant expressions of pressure drops, valid both for circular and annular sections, are applied in order to determine the three characteristic parameters of a known drilling fluid, having yield pseudoplastic behaviour, and flowing in the drilling hydraulic circuit, starting from field circulation tests. As it is well known, 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 borehole wall or casing and the drill string). In this circuit the drilling mud enters the drill pipe, comes out from the bit, flows up through the annulus up to the surface, where (after a short time for cleaning) it is put back in the circuit. The parameters to be inspected are the yield point, the consistency index k, the flow behaviour index n. By means of at least 3 flow tests at a certain drilling depth, with the bit off bottom, the pump rates and the corresponding 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 nonlinear system of N equations (with N 3) having 3 unknowns (the three parameters of the fluid: n, k and) is solved determining the Herschel & Bulkley rheological parameters. This procedure inspects the most probable solution for each tentative value of the flow behaviour index np, considering the infinite couples of and k satisfying the input value of the stand pipe pressure. Through the computation of the mean square deviation for each of the tentative values of np, the solution tern of the nonlinear system of N equations can be obtained. The computed results are compared to the ones obtained using the readings on the same drilling mud performed on Fann VG 35 viscometer Not always the rheological tern outcoming from the viscometer data exactly fits the equivalent rheological tern found considering the drilling well as viscometer Computed 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, are compared to field stand pipe pressure data. It can be seen that the overall average error between measured and computed SPP (using the Herschel & Bulkley equivalent tern) has drastically reduced to very small values, while the computed SPP using viscometer readings with most of the rheological models today used could lead to large errors, thus misleading an accurate evaluation of the SPP on the rig floor site. This method shows to be useful also to carefully evaluate the annular pressure drop and the corresponding ECD, in order to have the maximum allowable pump rates without fracturing the crossed formations. Besides it could be used to monitor the SPP behaviour for potentially occurring problems in the hydraulic circuit, such as wash out, plugged nozzles, and also in the case of gas kicks in the well. If applied to different drilling depths, the method can usefully inspect the influence of pressure and temperature existing in the well upon the rheology of the mud. This particular characterization is going to be inspected in the forthcoming research stages, which have already been designed to date. Introduction While drilling it is always very important to exactly know the pressure drop within the hydraulic circuit for many reasons. P. 105

The current need of drilling ultradeep wells involves facing new technical problems, especially concerning the effects of high pressure and temperature values. When acting along all the vertical profile of the well, the pressure and temperature effects heavily influence the rheology of the drilling fluids. Some of the main drilling parameters which are involved are cutting lifting and hole cleaning efficiencies (resulting both from the variation of the velocity profile of the fluid flow, and from the variation of the rheological parameters), and - of course - the pressure spatial distribution along the well profile. In order to characterise the real influence of pressure and temperature upon the rheology of the drilling fluids, circulation tests were performed and repeated at different depths inside cased hole (9 5/8" csg at 2973 m) with the 8 1/2" bit off bottom, while making trip (e. g. for the drilling out task of the casing shoe). Complete sets of data are available of circulation tests performed at 2400 m, 1400 m, 800 m and 198 m of the bit depth (while making the POOH trip), obtained by recording the mud flow rate and the corresponding stand pipe pressure (SPP) values. By developing an original numerical procedure able to determine the equivalent rheological tern (n, k and o of any drilling fluid flowing in the well) which fits the observed SPP data in the best way, it has been possible to characterise the rheological curves corresponding to the different testing depths. The processed rheological outputs are finally analysed and matched, pointing out the effects of pressure P and temperature T. The outcoming effects can be remarked with respect to the equivalent viscosity of the considered drilling fluids and to some of the main practical drilling parameters, such as the velocity profile and the pressure spatial distribution along the well profile. Qualitative trends of the field rheological data versus depth have been compared with the results of laboratory studies performed with an Huxley & Bertram HPHT rheometer with OBM systems. Some interesting analogies have been found with the two different approaches and the changes of the rheological parameters vs depth have been discussed also with reference to the mud structure sensitivity to P and T. Introduction The rheological properties of drilling muds under downhole conditions may be very different from those measured at ambient pressures and temperatures at the surface. High temperatures and pressures can influence the rheological properties of the drilling fluids in several way:–Physically: decreases in temperature and increases in pressure both affect the mobility of the systems and lead to an increase of apparent viscosities and viscoelastic relaxation times. The effect of pressure is expected to be greater with oil based systems owing to the oil phase compressibility.–Electrochemically: an increase in temperature augments the ionic activity of any electrolyte, and the solubility of any partially soluble salt that may be present in the mud. This could alter the balance between the interparticle attractive and repulsive forces and so the degree of dispersion and flocculation of the mud systems. Sometimes, this can also deeply affect the emulsion stability of oil based muds. All these phenomena have a profound impact on rheological properties, especially as far as viscoelasticity and thixotropy are concerned.–Chemically: all hydroxides react with clay minerals at temperatures above 90 C. With many kinds of muds, this can result in a change of the structure and therefore also in a change of the mud rheological properties, Because of the large number of variables involved, the behaviour of drilling muds at high temperatures and pressures may be very complicated so that it can be very difficult to get general guidelines for each group of muds (water base muds, oil base muds, etc.) or even for the same type of mud (little differences in the composition can result in considerable differences in the rheological behaviour). P. 115

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: P. 271

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