Abstract

The process of pumping water in a formation filled with a more viscous fluid is considered using the simplest model of the interwell space described by a set of parallel pipes. The fluids are assumed to be immiscible with a sharp interface in each pipe. The main task is to recover the parameters of the interwell space from a given displacement characteristic, namely, displacement data for each fluid. An explicit solution of the direct problem is presented for the model under study. It is shown that the problem of medium recovery, which is, in fact, an inverse problem, can be solved up to a one-parameter family. Additionally, a topology is found in which the inverse problem is stable.

中文翻译：

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一组平行管中粘性流体的置换

摘要

使用一组平行管道描述的井间空间的最简单模型，可以考虑在充满粘性流体的地层中抽水的过程。假定流体在每条管道中都没有明显的界面，因此是不混溶的。主要任务是从给定的位移特性（即每种流体的位移数据）恢复井间空间的参数。对于正在研究的模型，提出了直接问题的显式解决方案。结果表明，介质回收问题（实际上是一个反问题）可以解决多达一个参数的族。此外，找到了反问题稳定的拓扑。