The present trend of drilling deeper wells has increased the importance of estimating the wellbore temperature distribution and its variation with time. The need arises because it has a number of applications, such as: Cementing program design, drilling fluid rheology and design, drill tools planning, estimating mud properties and so on. The current wellbore temperature calculation method is through solving partial differential equation that obtaining the well temperature distribution. This method could obtain the well temperature distribution in different time and position, but the inherent characteristics could not be revealed. We plan to establish the well temperature state space model, and analyze the dynamic characteristics of well temperature according to this method and control theory.

This work presents a study of the thermal behavior of drilling fluid during circulation and shut-in stages. A state space model is developed to calculate wellbore temperature distribution instead of solving partial differential equation. This model is based on wellbore heat transfer mechanism model and control theory. We analyze the dynamic characteristics of well temperature according to the state space model and control theory. Then we analyze how to adjust and control the bottom-hole temperature through operating surface parameters. The performance of the method is illustrated via the simulation of Holmes test well data.

Wellbore temperature distribution profile and its variation with time are obtained according to the state space model. The calculation results shows that the maximum temperature is not appeared in the bottom-hole but appeared in some distance from the bottom-hole. The wellbore temperature will reach steady state in a few of circulation hours, the time to steady state is determined by fluid density, flow rate, specific heat. The bottom-hole temperature decreases as the flow rate or fluid density improving. Besides, we analyze the stability of wellbore heat transfer system according to Lyapunov theorem. The wellbore heat transfer system is steady system without large disturbance. This study can provide theoretical basis for automatic control of wellbore temperature in the future.

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