In the oil production industry, it is of significance to measure and predict the form of multi-phase flow and gas flow that are present within petroleum production and processing pipelines. One component which has received little attention is the characteristics of bubbly flow around production pipelines. Rising bubble behavior in a wellbore changes with various factors, of which temperature leading to variations of liquids properties is one of the important factors. Herein, using an improved drag coefficient model to investigate bubble rising behavior at different temperatures is considered to calculate bubble flow velocities for drilling design, operation and wellbore pressure control. Firstly, a series of simulated laboratory experiments were conducted at 5–100 °C in four Newtonian fluids to obtain liquid properties and bubble parameters, such as bubbles shape, terminal velocity and trajectory. Then, compared with terminal velocities obtained by using the drag coefficients models C_D = 0.95, which was considered to be constant by many literature at high Reynolds region (Re > 135), the modified drag coefficient model C_D = 1.227 yielded better satisfactory prediction results for bubbles terminal rising velocity. Additionally, a new correlation using Reynolds number, Eötvös number, Weber number is proposed to predict bubble terminal velocity at low Reynolds number (Re < 135) based on experimental data and the Schiller–Naumann model. The results showed excellent agreement with the experimental data, with standard error of 5.32%.

中文翻译：

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使用修正阻力系数的静态牛顿流体中单气泡上升与温度的关系的实验研究

在石油生产行业中，重要的是测量和预测石油生产和加工管道中存在的多相流和气流的形式。很少受到关注的一个组件是生产管道周围的气泡流特征。井眼中气泡的上升行为随各种因素而变化，其中导致液体性质变化的温度是重要因素之一。这里，考虑使用改进的阻力系数模型来研究在不同温度下的气泡上升行为，以计算用于钻探设计，操作和井眼压力控制的气泡流速。首先，在5–100°C的温度下，在四种牛顿流体中进行了一系列模拟实验室实验，以获取液体性质和气泡参数，例如气泡的形状，终极速度和轨迹。然后，与使用阻力系数模型获得的最终速度进行比较C _D  = 0.95，许多文献认为在高雷诺兹区域（Re> 135）是恒定的，修改后的阻力系数模型C _D  = 1.227产生了更好的气泡末端上升速度的令人满意的预测结果。此外，基于实验数据和席勒-瑙曼模型，提出了使用雷诺数，Eötvös数，韦伯数的新相关性，以预测低雷诺数（Re <135）下的气泡终极速度。结果与实验数据吻合良好，标准误为5.32％。