A New Temperature Field and the Method for Designing Casing in Thermal Horizontal Well
Authors: Xiaoqing Wu , Shiying Luo , Shuzhi Liu 
Published: December 2007

Abstract
It is important for petroleum production and drilling engineers to know the neighboring formation temperature field around a horizontal well in order to determine steam injection parameters and design casing string. The temperature field model and its finite element or finite differential solution in the past were quite complicated so that the calculation in the curved section of the well path was particularly difficult. In this paper, the horizontal wellbore is treated as 3-D pipestring. A new temperature field mathematical model is established and an exact solution to the model is derived with special mathematical methods. The solution is convenient for both theoretical research and calculation of the temperature field in practical use, no matter in vertical, curved or horizontal well path sections. Based on the results, we introduce a method of calculating the casing thermal stress of thermal horizontal well with finite element method. Then, a new method for thermal horizontal well casing string design is developed. Finally, the application of this method in the design of well Lengping-1 is illustrated in this paper.

Introduction
Steam flooding is an effective technique in producing heavy oils, and it is widely used in many countries. If the steam is injected into a reservoir through not a vertical well, but a horizontal, a better result will be achieved. However, the high temperature steam and thermal stress is a very key factor that affects the production of a horizontal well. If a casing string is unreasonably designed, the heat stress from the steam may cause the easing string to be yielded, or even broken. Consequently, the easing string design method is one of the key techniques involved in a horizontal well completion in a heavy oil reservoir. The design technique influences not only the life of oil well, but also the success in developing a heavy oil reservoir by horizontal wells. Thus it can be seen that the reasonable casing string design is of importance in improving production and prolonging the life of a horizontal well.
In the past, when calculating the temperature field in a vertical steam injection well, some researchers assumed that the heat transfer in the wellbore is a one-dimension-steady-state process, and neglected the heat transfer in the vertical direction. In the meantime, when considering the unsteady-state heat transfer from the wellbore (the interface between the cement and the formation) into the formation, they used the Remay dimensionless time function f(t). Thus it can be seen that only the temperatures in the easing and cement can be calculated, while the formation temperatures around the wellbore are unknown. Then, they established a mechanical model used to describe the interaction between the casing string and the cement. Finally, according to the known temperature and the model, they calculated the axial thermal stress of the casing string. In addition, Ref. 3 presented a two-dimension - unsteady-state heat transfer model that described the heat conductivity in vertical and horizontal directions. The model is solved to get the temperature distribution in the formation around a wellbore by means of the numerical differential technique. However, it is very difficult for the model to be used in a horizontal well because the boundary condition treatment of the two-dimension heat transfer in the curved well section is very complicated. Therefore some people usually still use the dimensionless time function f(t) to describe the heat transfer from wellbore into formation. It can easily be seen that the treatment is not accurate.
In this paper, a new temperature field model of a horizontal well is first established. Then, a analytic solution is derived to calculate the temperatures in the easing string and the formation around a horizontal well. In addition, a mechanical model is also developed to describe the interaction among the easing string, the cement and the formation, and to calculate casing string thermal stress.
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