Abstract Steam-assisted gravity drainage (SAGD) is a widely-used method for heavy-oil and bitumen recovery. Analytical SAGD models presented in the literature often overestimate bitumen-production rate substantially. Although bitumen-production rate and steam-oil ratio (SOR) depend significantly on temperature near the steam-chamber edge in SAGD, previous analytical models assumed the injected-steam temperature to uniformly distribute along the edge of a steam chamber. The main objective of this research is to develop the first analytical SAGD model that takes into account temperature variation along the edge of a steam chamber. Local material balance and Darcy’s law are applied to each cross section perpendicular to the edge of a steam chamber. Then, they are coupled with the global material balance for the chamber geometry that is an inverted triangle. New analytical equations are presented for bitumen-production rate and SOR, in addition to associated variables as functions of elevation from the production well, such as oil-flow rate and temperature along a linear chamber edge. Bitumen-production rate and SOR can be calculated for a representative chamber-edge temperature at a certain elevation from the production well. Comparison of the analytical model with numerical simulations shows that bitumen-production rate and SOR can be accurately estimated when the new model is used with the temperature taken from the midpoint of the edge of a steam chamber. The chamber-edge temperature used for the new analytical model that gives accurate results can be up to 100 Kelvin lower than the injected steam temperature for a given operating pressure in the cases tested. The previous assumption of the injected-steam temperature at the chamber edge gives overestimated oil-production rates for SAGD. The constant temperature along the edge of a steam chamber gives Butler’s concave interface of a steam chamber that is detached from the production well. For a chamber to exhibit a linear interface, temperature must vary along the chamber edge, which occurs in reality mainly because of heat losses to the over- and under-burden formations.

中文翻译：

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考虑蒸汽室边缘温度变化的蒸汽辅助重力泄油解析解

摘要 蒸汽辅助重力泄油（SAGD）是一种广泛使用的稠油和沥青回收方法。文献中介绍的分析性 SAGD 模型通常大大高估了沥青生产率。尽管在 SAGD 中，沥青生产率和汽油比 (SOR) 显着取决于蒸汽室边缘附近的温度，但先前的分析模型假设注入的蒸汽温度沿蒸汽室边缘均匀分布。这项研究的主要目标是开发第一个分析 SAGD 模型，该模型考虑了沿蒸汽室边缘的温度变化。局部物质平衡和达西定律适用于垂直于蒸汽室边缘的每个横截面。然后，它们与倒三角形的腔室几何形状的整体材料平衡相结合。除了作为生产井高程函数的相关变量（例如沿线性腔室边缘的油流速率和温度）之外，还提供了用于沥青生产速率和 SOR 的新分析方程。沥青产量和 SOR 可以计算出在距生产井一定高度的代表性室边缘温度。分析模型与数值模拟的比较表明，当使用新模型和取自蒸汽室边缘中点的温度时，可以准确地估计沥青产率和 SOR。在测试的情况下，用于提供准确结果的新分析模型的腔室边缘温度可能比给定操作压力下注入的蒸汽温度低 100 开尔文。先前对腔室边缘注入蒸汽温度的假设给出了对 SAGD 的高估的产油率。沿着蒸汽室边缘的恒定温度使巴特勒的蒸汽室与生产井分离的凹面界面。对于呈现线性界面的腔室，温度必须沿腔室边缘变化，这在现实中主要是由于上覆层和下覆层地层的热损失。先前对腔室边缘注入蒸汽温度的假设给出了对 SAGD 的高估的产油率。沿着蒸汽室边缘的恒定温度使巴特勒的蒸汽室与生产井分离的凹面界面。对于呈现线性界面的腔室，温度必须沿腔室边缘变化，这在现实中主要是由于上覆层和下覆层地层的热损失。先前对腔室边缘注入蒸汽温度的假设给出了对 SAGD 的高估的产油率。沿着蒸汽室边缘的恒定温度使巴特勒的蒸汽室与生产井分离的凹面界面。对于呈现线性界面的腔室，温度必须沿腔室边缘变化，这在现实中主要是由于上覆层和下覆层地层的热损失。