Reservoir Geostatistical Estimates of Imprecise Information Using Fuzzy-Kriging Approach
Reservoir Geostatistical Estimates of Imprecise Information Using Fuzzy-Kriging Approach
复制标题
使用模糊克里格方法对不精确信息进行储层地质统计估计
DOI：
10.2118/190051-pa
复制
发表时间：
2020
影响因子：
2.1
通讯作者：
S. Cassidy
中科院分区：
文献类型：
--
作者：
Xiaoxi Zhao;A. Popa;I. Ershaghi;F. Aminzadeh;Yuanjun Li;S. Cassidy
本文提出了一种储层性质的地质统计学估计方法，以处理观测和建模中的不确定性。给定地质区域中的某些已知测井数据，克里格方法用于从估计的随机函数估计或预测非采样位置处的空间现象。该方法假设数据是准确和精确的，并且随机函数是从已知数据集的彻底描述性分析中生成的。关于经典克里格法中考虑的假设，假设空间数据包含一定量的不精确性是现实的，主要是因为测量误差，并且缺乏适当评估唯一随机函数模型的信息。提出了一种用于储层性质的地质统计估计的方法，以处理观测和建模中的不确定性。常规的，或经典的，克里格和模糊逻辑方法的组合。因此，不精确的输入数据和变差函数参数的模糊逻辑理论的基础上建模，而预测和方差计算的克立格分析的特征在于隶属函数。最后，提出了一种求解约束模糊非线性方程组的优化方法。所提出的方法得到实施，并开发了一个用户友好的集成工具，使用户能够创建一个网格结构的基础上的输入数据，进行统计分析，并运行模糊克里格的各种问题。我们使用该工具运行了一个测试用例，使用SPE 10（SPE比较解决方案项目，型号II 2000）孔隙率数据。使用模糊克里格方法，生成具有上限值和下限值的两个地图。与真实数据相比，上限图倾向于更好地包括较高的值，而下限图倾向于更好地包括较低的值部分。此外，一个案例研究已经进行了使用测量的岩心渗透率数据在非均质油藏，以证明该技术的可行性。
This paper presents a methodology for the geostatistical estimation of reservoir properties to handle uncertainties in observation and modeling. Given certain known well-log data in a geological region, the Kriging methodology is used to estimate or predict spatial phenomena at nonsampled locations from the estimated random function. The approach assumes that the data are accurate and precise, and the random function is generated from a thorough descriptive analysis of the known data set. Regarding the assumptions considered in classic Kriging, it is realistic to assume that spatial data contain a certain amount of imprecision, mostly because of measurement errors, and information is lacking to properly assess a unique random-function model. A methodology is presented for the geostatistical estimation of reservoir properties to handle uncertainties in observation and modeling. A combination of regular, or classic, Kriging and the fuzzy-logic method is proposed. As such, imprecise input data and variogram parameters are modeled on the basis of fuzzy-logic theory, while the predictions and variances are computed from Kriging analysis characterized by membership functions. Last, an optimization method is included to solve the constrained fuzzy-nonlinear-equation system. The proposed methodology was implemented, and a user-friendly integrated tool was developed, which enables the user to create a grid structure on the basis of the input data, conduct statistical analysis, and run fuzzy Kriging for various problems. We used the tool to run a test case using the SPE 10 (SPE Comparative Solution Project, Model-II 2000) porosity data. With the fuzzy-Kriging methodology, two maps are generated with upper-bound values and lower-bound values. Compared with true data, the upper-bound map trends to include higher values better, while the lower-bound map trends to include lower-value parts better. In addition, a case study has been conducted using measured core-permeability data in a heterogeneous reservoir to demonstrate the viability of the technology.