电法测井中非均匀地层多参数反演方法研究

Petroleum is a kind of important national resource, and plays an essential role in the national economic development, petroleum exploration and exploitation is a significant strategic task. Electrical well-logging is a major method for the petroleum exploration and exploitation, and has been widely applied in engineering, its basic task is to find out physical parameters and geometric parameters of complicated heterogeneous formation. Because people don't understand the actual formation in advance, the well-logging problem is a multiple parameter inversion problem. Recent studies on the inversion problem for the electrical well-logging are mostly concerned with single parameter identification. However, for the multiple parameter identification, which is more important than the former in the application, the corresponding theoretical study and numerical method are far to achieve effective and perfect degree. For example, we should discuss seriously the following key technological problems: how to construct efficient computational methods when the number of physical parameters is relatively big, how to identify the geometric parameters,and how to identify the geometric parameters and the physical parameters at the same time, which are big challenges for us. Represented by resistivity well-logging and spontaneous potential well-logging, and based on the existing results, this project is going to discuss the inverse problem of the physical parameters and geometric parameters in the electrical well-logging, and establish an effective numerical framework, so as to lay a reliable theoretical foundation in mathematics for the above two kinds of electrical well-logging methods, and provide clues to the effective interpretation for the well-logging data.

石油是重要的国家资源，在国家经济发展中具有非常重要的地位，石油的勘探和开发是一项重要的战略任务。电法测井是石油开发的一个重要方法，在工程中已被广泛应用,其根本任务是探求复杂非均匀地层中的物理参数和几何参数。由于人们事先不了解实际地层的情况，测井所面对的是一个多参数反演问题。目前关于电法测井反问题的研究大多涉及单参数识别，对应用中更为重要的多参数辩识问题，其理论探讨及数值求解还远未达到有效及完善的程度，如物理参数个数较多时，如何构造高效的计算方法；如何同时反演多个几何参数以及同时反演物理参数和几何参数等，都是涉及电法测井的关键技术问题，需要认真进行讨论，具有很大的挑战性。本项目拟以电阻率测井和自然电位测井为代表，力图在有关正问题数学模型的基础上，讨论电法测井中地层物理参数和几何参数的反演问题，研究设计高效的数值计算方法，为两种电法测井方法奠定可靠的数学理论基础，为测井资料的有效解释提供依据。

石油是重要的战略资源，在国家经济发展中具有非常重要的地位，石油的勘探和开发是一项重要的任务。电法测井是石油勘探与开发的一个重要方法，在工程中被广泛应用。 .本项目自2014年1月开始，2016年12月结束。项目以自然电位测井、阵列侧向电阻率测井为代表，研究了与电阻率测井有关的一些重要数学问题：建立了三维自然电位测井的数学模型（包括偏微分方程，交界面条件，发射电极面、测量电极面及绝缘面上的边界条件等），丰富了有关的数学理论，并解决了自然电位测井仪器偏心状态时的数值模拟问题。以阵列侧向电阻率测井为对象，研究了在应用中迫切需要、但在数学处理上尚极不成熟的反演问题，为设计性能更为优良的测井仪器提供了可靠的依据，对应用偏微分方程反问题及相应计算方法的研究做出了贡献。.