**1. Introduction**

As hydrocarbon resource consumption increases, oil and gas development is inevitable in deep-depth onshore and offshore territories. The deep-depth development poses significant challenges during the drilling process because high formation temperature causes failures in current operation designs [1]. First, all drilling facilities need to secure the operational durability of devices in a high-temperature environment, primarily electrical equipment such as logging-while-drilling and measurement-while-drilling tools, motors, and turbines [2]. Additionally, this hostile environment can also impair the performance of drilling fluids. For the appropriate operational design, there have been studies to estimate the temperature of the flowing fluids accurately in the drilling pipe and annulus [3].

The pioneering work to estimate the radial temperature distribution in the reservoir was conducted by Bullard in 1946 [4]. His work was based on a similar diffusivity equation used in a transient well test for obtaining radial pressure, and this approach became one of the major categories to compute the temperature of a reservoir analytically [5]. Edwardson et al. implemented a similar method to Bullard's but modified it to be more practical to use by applying extrapolation in the calculation process [6]. He pointed out that the circulating mud cools down the near-wellbore formation and hypothesized around 10 ft of thermal disturbance.

**Citation:** Jang, M.; Chun, T.S.; An, J. The Transient Thermal Disturbance in Surrounding Formation during Drilling Circulation. *Energies* **2022**, *15*, 8052. https://doi.org/10.3390/ en15218052

Academic Editor: Mofazzal Hossain

Received: 16 October 2022 Accepted: 27 October 2022 Published: 29 October 2022

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Later, there were works estimating the temperature distribution in consideration of more realistic conditions based on numerical methods [2,7–10]. This research illustrated a more sophisticated temperature estimation by dividing domains more and applying each domain's heat and physical properties. At first, the reservoir system was divided into two domains: wellbore and formation [7]. Later, the wellbore was subdivided into the drill pipe and annulus [8], and then it was further divided into multi-grid in the radial direction in the drill pipe [2].

In addition to considering more dividing simulation domains, there have been attempts to improve the accuracy of the temperature calculation. Gorman et al. showed sophisticated radial temperature distributions by implementing the RANS turbulent model, requiring great computing resources [11,12]. In spite of their valuable results, their work did not reveal the temperature at the payzone depth (i.e., near bottom-hole), the most important area in oil drilling. One noteworthy observation in their work is that temperature change by rotating drill pipe is minor because the axial velocity of the drilling fluid is much faster than that of the rotating drill pipe, suppressing the secondary motion induced by the rotating drill pipe [11].

In the transient well test, the temperature has been regarded as a complementary component to identifying reservoir parameters and production rate. However, with the advanced sensing platforms, several thermal applications have been developed using the measured temperature. Not only estimation techniques of production rate, but rate allocation in the multi-payzone system are introduced [13]. Furthermore, flow pattern identification through the real-time temperature data and identification of liquid condensate bank behavior was recently proposed [14].

Drilling mud is injected from the wellhead at an ambient temperature much lower than the deep formation temperature at the initial stage. Although the temperature of the circulating mud increases while it circulates through the deep reservoir, it still stays much lower compared to the deep formation temperature. Cold circulating mud takes heat from the adjacent formation, inducing a cooling effect during drilling operation [8,11]. At the formation surface facing the circulating mud (hereafter, "wellbore wall"), forced convection with a significant heat transfer rate is the dominant heat exchange component between the circulating mud and wellbore wall. On the other hand, although convection can take place in some formation parts containing a porous medium, most heat transfer inside the formation occurs only by conduction [7].

Compared to hydraulic diffusivity, thermal diffusivity is typically so low that thermal transient lasts several years even in a small reservoir with a radius of 50 m [15,16]. As conduction has the lowest heat transfer rate among the heat transfer mechanisms, it is not enough to offset the rapid temperature drop by the circulating mud [17]. Due to the imbalance of heat transfer, a thermal disturbance occurs in the radial direction inside the formation. As a result, the formation starts to cool from the near-wellbore area during the drilling operation. When the drilling operation ends, perforation is initiated after several hours of removing the remaining debris in the wellbore. During the perforation operation, the temperature sensor measures the temperature of reservoir fluids (i.e., hydrocarbon and water) coming into the wellbore. However, the measurement deviates from the actual formation temperature cooled down by circulating mud during drilling and subsequent clean-up operations.

This discrepancy in temperature can significantly degrade the accuracy of the measured temperature as well as the robustness of the thermal applications. Estimation of production rate, one of the applications using the temperature data, requires a high degree of accuracy [13]. Even a slight error in the measured temperature may make the estimated results meaningless. While the cooling effect in the formation by drilling has been mentioned in some previous research works, few papers pay attention to the risk potential of inaccurate temperature measurement [5,7,17]. Furthermore, there has been no specific concept of this thermal disturbance by drilling circulation and its analysis.

In this work, a numerical transient heat transfer model is developed to compute the radial temperature distribution in the drill pipe, annulus, and formation. Using this tool, we introduce the quantified concept of the thermal disturbance, named thermally disturbed radius (TDR), which indicates how long the thermal disturbance occurs radially in the formation (Figure 1). Lastly, through the sensitivity analysis of TDR with various conditions during drilling, we propose operational guidelines to reduce the uncertainty of temperature measurement.

**Figure 1.** Schematic diagram of cooling effect by the circulating mud during drilling.
