The spatial domain of interpretation in pressure transient and formation testing is constrained by its radius of investigation. A classical descriptor for this radius relies on the time derivative of pressure within a bounded domain becoming time independent. Another approach quantifies the radius of investigation based on the distance at which the pressure change is greater than the characteristic noise or resolution in the measurement system. In this paper, we postulate that the correct measure of radius of investigation is the distance at which the inversion of noisy test data is able to discern an anomaly within a given tolerance. This paper details the design requirements for a testing and measurement system suitable for a given investigation distance, measurement noise, and the confidence requirements for the inferred distance. The approach is demonstrated with two specific models. The first is a formation with a sealing fault in an infinite medium, and the second is a formation with a single-layer boundary vertically displaced from a production probe. With normally distributed random and correlated noise, computed results show that the measure of distance investigated is highly dependent upon the background over which the anomaly is imposed. Although the methodology is illustrated with particular models, the principles are applicable in general.

中文翻译：

---

压力瞬变测试的调查范围

压力瞬变和地层测试中的空间解释受其调查半径的限制。该半径的经典描述符依赖于有界域内压力的时间导数，变得与时间无关。另一种方法根据压力变化大于测量系统中的特征噪声或分辨率的距离来量化调查半径。在本文中，我们假设调查半径的正确度量是噪声测试数据的反演能够在给定容差内辨别异常的距离。本文详细介绍了适用于给定调查距离、测量噪声和推断距离的置信度要求的测试和测量系统的设计要求。该方法通过两个特定模型进行演示。第一种是在无限介质中具有封闭断层的地层，第二种是具有从生产探头垂直位移的单层边界的地层。对于正态分布的随机和相关噪声，计算结果表明所调查的距离度量高度依赖于施加异常的背景。尽管用特定模型说明了该方法，但这些原则是普遍适用的。计算结果表明，所调查的距离度量高度依赖于施加异常的背景。尽管用特定模型说明了该方法，但这些原则是普遍适用的。计算结果表明，所调查的距离度量高度依赖于施加异常的背景。尽管用特定模型说明了该方法，但这些原则是普遍适用的。