Global weak solutions for a compressible gas-liquid model with well-formation interaction
Global weak solutions for a compressible gas-liquid model with well-formation interaction
复制标题
DOI：
10.1016/j.jde.2011.07.013
复制
发表时间：
2011-10
影响因子：
2.4
通讯作者：
S. Evje
中科院分区：
文献类型：
--
作者：
S. Evje
本工作的目的是探索一种可压缩气液模型，用于模拟井流过程。我们通过允许气井和地层（周围的储层）之间的气体流动来建立井-储相互作用模型。在石油工程的背景下，天然气的流入以及随后上升到井顶的膨胀（所谓的气涌）是各种井作业的主要关注点。在初始数据的正则性和控制井与地层间气体流动的速率函数的适当假设下，得到了一个全局存在性结果。通过对初始数据施加更多的规则性，也可以获得唯一性。关键的估计是得到适当的气体和液体质量的下界和上界。为此，我们引入了原始模型的转换版本，该版本非常便于对原始模型进行分析。特别是，在对转换后的模型进行分析时，表示井-地层相互作用的附加项可以通过先前用于单相Navier-Stokes模型的论点的自然扩展来处理。分析保证了当初始状态为真正的气液混合物时，不会出现向单相区域的过渡。
The objective of this work is to explore a compressible gas-liquid model designed for modeling of well flow processes. We build into the model well-reservoir interaction by allowing flow of gas between well and formation (surrounding reservoir). Inflow of gas and subsequent expansion of gas as it ascends towards the top of the well (a so-called gas kick) represents a major concern for various well operations in the context of petroleum engineering. We obtain a global existence result under suitable assumptions on the regularity of initial data and the rate function that controls the flow of gas between well and formation. Uniqueness is also obtained by imposing more regularity on the initial data. The key estimates are to obtain appropriate lower and upper bounds on the gas and liquid masses. For that purpose we introduce a transformed version of the original model that is highly convenient for analysis of the original model. In particular, in the analysis of the transformed model additional terms, representing well-formation interaction, can be treated by natural extensions of arguments that previously have been employed for the single-phase Navier–Stokes model. The analysis ensures that transition to single-phase regions do not appear when the initial state is a true gas-liquid mixture.