###### Abstract  
Under different temperatures and pressures, the physical parameters of drilling fluid will change, resulting in inaccurate drilling hydraulic calculations. Aiming to address the problem of the traditional rheological prediction method needing to first determine the rheological model, this paper proposed a method for first predicting the readings of the rheometer and then determining the rheological model. The model established in this paper adopted a parameter-free method, which expands the application range of the model. Rheology experiments were carried out on the three types of oil-based drilling fluids collected at the well site. The model in this paper was verified based on the experimental data. The results showed that, compared with the traditional drilling fluid rheological prediction method, the model established in this paper had a better prediction effect, with an average error of 4.85%, and the average error reduction ranges from 3.8% to 8.3%. The model established in this paper is able to provide theoretical support for accurate hydraulic calculation. HTHP; oil-based drilling fluid; rheology; parameter-free method; managed pressure drilling +
Footnote †: journal: Applied  
time, it was assumed that the temperature and pressure only affected the consistency coefficient of the drilling fluids and the liquidity index had no effect. From this, a simple prediction model of the consistency coefficient was obtained [5]. In 1985, [PERSON] used the Bingham model to carry out an experimental analysis of the rheological properties of reverse-emulsified oil-based drilling fluids under high temperature and pressure and presented a prediction model of the Bingham yield value and plastic viscosity [6]. Since then, many researchers have carried out corresponding research and analysis on the high-temperature and high-pressure rheology of drilling fluid, but most of these studies are based on the Bingham and power-law rheological models recommended by the American Petroleum Institute (API), and the corresponding rheological parameter regression models are obtained through rheological experiment regression. In 1989, [PERSON] carried out an experimental analysis on the high-temperature and high-pressure rheology of mineral-oil-based drilling fluids with different densities and conventional water-in-oil emulsion drilling fluids, mainly analyzing the changes in the plastic viscosity, apparent viscosity, and yield value of drilling fluids with under different temperatures and pressures [7]. In 1990, [PERSON] presented a prediction model for the apparent viscosity of water-in-oil emulsion drilling fluids [8]. In 2009, [PERSON] and others improved the model and further proposed a comprehensive mathematical model for predicting plastic viscosity, yield value, and apparent viscosity [9]. In the same year, [PERSON] and others carried out an experimental study on the ultra-high-temperature and high-pressure rheology of high-temperature water-based drilling fluids and presented a mathematical model for predicting the apparent viscosity of the drilling fluids [10]. In 2010, [PERSON] studied the apparent viscosity and plastic viscosity of water-based drilling fluids and established a model for the variation of apparent viscosity with temperature and pressure [11]. In 2017, [PERSON] conducted research on water-based drilling fluids using a high-pressure, high-temperature (HPHT) Anton Paar MCR-302 compact rheometer, analyzing the effects of pressure on yield stress, apparent viscosity, and the flow behavior index [12]. In 2018, [PERSON] established a model for the apparent viscosity change of oil-based mud based on its characteristics [13]. In 2018, [PERSON] compared the error of different drilling fluid rheological models in predicting the rheological properties of bentonite drilling fluid [14]. In 2021, [PERSON] conducted a study on the thermal stability of drilling fluids under high temperature and pressure [15].