Temperature and Pressure Effects on Drilling Fluid Rheology and ECD in Very Deep Wells
Authors: Rommetveit R. , Bjorkevoll K.S. 
Published: December 2007

Abstract
The rheological properties of drilling fluids are usually approximated to be independent of pressure and temperature. In many cases this is a good approximation. For shallow wells the temperature changes are not so large, and hence the rheological variations with temperature are small. Also, many wells have a large gap between pore pressure and fracture pressure, so errors in the estimation of the dynamic circulation pressure have no consequences for well integrity or kick probability.
However, for wells with small margins between pore and fracture pressure, careful evaluations and analysis of the effects of temperature and pressure on wellbore hydraulics and kick probability is needed. This was a lesson from the serious well-control problems in many North Sea wells in general, and in the Saga 2/4-14 well in Norway in particular. Today wells of this type are planned and drilled around the world, for example in the North Sea, South-East Asia and also in South America.
In this paper the effects of pressure and temperature are discussed and described for typical HPHT wells. Laboratory measurements show that rheology is very pressure and temperature dependent. The practical implications of these observations are illustrated through a series of calculations with an advanced pressure and temperature simulator.

Introduction
The rheological properties of a drilling mud at HPHT conditions are in some cases measured prior to the drilling of a HPHT section. Still, a more general knowledge of the pressure and temperature dependence of HPHT muds can be very useful when HPHT data are not available, e.g. at an early stage of planning. In the latter case the effects of HPHT dependent rheology can be studied through correlation based models.
Several studies of the HPF rheology of water based and oil based drilling fluids have been presented in earlier papers, e.g. in Refs. [2–5]. Some of these, Refs. [3–5], include mathematical expressions that are to some extent theoretically motivated, and reproduce observed pressure and temperature dependence of one or more rheological parameters like e.g. viscosity, plastic viscosity or yield stress. The mathematical expressions include a multiplicative factor than can be written on the form
where A, B, and C are independent of pressure (p) and temperature (T), but depend on the composition of the drilling fluid. The three constants are also different for different rheological parameters since pressure and temperature dependence of shear stress can be very different at low and high shear rates.
The cited references present fits of the two parameters of the Casson and Bingham plastic models, to their p, T models. It could be attempting to determine p, T behaviour of the parameters of the more accurate three parameter models like the Hurschel-Bulkley or Robertson-Stiff models. The problem is that the parameters of the three parameter models depend on pressure and temperature in a less regular way than the parameters of two parameter models (see Figures in [4]). One reason for this is that the different parameters of three parameter models are correlated, such that it is not possible to extract the precise pressure and temperature dependence of each parameter due to measurement uncertainties. For the present work a slightly different procedure has been selected. Shear stress has been multiplied by a factor that depends on pressure, temperature, and shear rate.
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