Ensemble Kalman Filter for estimation of rock properties in geothermal reservoirs characterized by fractured rocks or fluviatile sediments

控制热液运移的岩石性质在许多地下水流动研究中都很有趣，但对地热储层的评价尤其重要。这个项目的主题是使用集合卡尔曼滤波方法（EnKF）来估计这些属性。孔隙流动的相关物理模型由内部模拟器SHEMAT-Suite提供。与大多数反演方法一样，原始形式的EnKF是基于待估计参数的高斯分布。然而，热液流体流动的关键岩石参数是渗透率，渗透率在储层中往往呈双峰分布。这可能是由沉积储层中河流沉积的多孔性和裂缝性（天然的或工程的）渗透性或夹层叠加造成的。在岩性非均质储层中，热导率也可以观察到类似的双模式分布。对于储层分析，EnKF方法具有决定性的优势，它与参数估计一起提供了估计误差（方差）的度量。然而，小的集合往往低估了这个误差。在本项目中，我们打算通过实施各种新方法来改进EnKF热液参数估计方法，并研究它们的单一和联合效果：(1) Normal Score EnKF用于正态和双峰参数分布之间的转换；(2)定位方法，根据到观测点的距离对滤波函数进行加权；(3)调节协方差矩阵（协方差膨胀）的方法，以减少EnKF中方差的低估。在这里，我们将扩展现有的参数估计方法，并开发新的方法，特别是定位方法。一旦这些方法得到实施，它们将在合成储层模型上进行测试(1)用于结晶EGS储层和含有河流沉积物的沉积储层，以及(2)用于Soultz-sous-Forêts地热试验场的两口井的化学示踪剂浓度时间序列。

The rock properties controlling hydrothermal transport are interesting in many studies of groundwater flow, but are in particular important for the assessment of geothermal reservoirs. The topic of this project is to estimate these properties using the Ensemble Kalman Filter Method (EnKF). The related physical model for porous flow is numerically provided by the in-house simulator SHEMAT-Suite. As most inversion methods, the EnKF in its original form, is based on a Gaussian distribution of the parameters to be estimated. However, the crucial rock parameter for hydrothermal fluid flow is permeability which often has a bi-modal distribution in a reservoir. This may be caused by a superposition of porous and fractured (natural or engineered) permeability or intercalations of fluvial deposits in a sedimentary reservoir. Similar bi-model distribution can be observed for thermal conductivity in lithologically heterogeneous reservoirs. For reservoir analysis, the EnKF method has the decisive advantage that jointly with a parameter estimate it provides also a measure of the error of the estimate (variance). However, small ensembles tend to underestimate this error. In the proposed project we intend to improve the EnKF method for hydrothermal parameter estimation by implementing various new methods and study their single and combined effects: (1) Normal Score EnKF for transformation between normal and bi-modal parameter distributions, (2) localizations methods, to weight the filter function depending on the distance to the observation points, (3) a method for conditioning the covariance matrix (covariance inflation) to reduce the underestimation of the variance in EnKF. Here we will extend existing methods for parameter estimation and develop new approaches, in particular for localization. Once these methods are implemented, they will be tested on synthetic reservoir models (1) for a crystalline EGS reservoir and for a sedimentary reservoir containing fluvial deposits, and (2) on time series of chemical tracer concentration in two wells of the Soultz-sous-Forêts geothermal test site.