基于数据分布域变换与贝叶斯神经网络的渗透率预测及不确定性估计

Permeability prediction and uncertainty quantification base on Bayesian neural network and data distribution domain transformation

渗透率是储层评价和油气藏开发的关键参数.传统测井方法与常规机器学习方法估算的渗透率都是固定值.但由于测井数据本身存在噪声,渗透率的预测结果可能受到噪声的影响出现测量性的随机误差(即任意不确定性);同时,当测试数据与训练数据存在差异时,机器学习模型在预测渗透率时可能出现模型参数的不确定性(即认知不确定性).为实现渗透率的准确预测并量化两种不确定性对结果的影响,本文提出基于数据分布域变换和贝叶斯神经网络同时实现渗透率预测及其不确定性的估计.提出方法主要包括两个部分:一部分是不同域数据分布的相互转换,另一部分是基于贝叶斯理论的神经网络渗透率建模预测和不确定性估计.由于贝叶斯神经网络存在数据分布的假设,当标签的概率分布与网络的分布保持一致时,贝叶斯神经网络可以更好的学习到数据之间的关系.因此通过寻找一个函数将一个原始域的渗透率标签转换为目标域的与渗透率有关的变量(我们称为目标域渗透率),使得该变量符合贝叶斯神经网络的分布假设.我们使用贝叶斯神经网络预测目标域渗透率以及任意不确定性和认知不确定性.随后,通过分布域的逆变换,我们将目标域渗透率还原回原始域渗透率.应用本文方法到某油田的18口井的测井数据中,使用16口井的数据进行训练,2口井进行测试.测试井的预测渗透率与真实渗透率基本一致.同时,任意不确定性的预测结果提供了渗透率预测值受到的测井数据噪声影响的位置.认知不确定的预测结果说明数据量少的位置具有更高的认知不确定性.我们提出的这一流程不仅显示了在储层表征方面的巨大潜力,同时可以降低测井解释时的风险.

Permeability is a key parameter for reservoir evaluation and reservoir development.The permeability estimated by traditional logging methods and conventional machine learning methods is a fixed value.However,due to the noise in the logging data itself,the prediction results of permeability may be affected by the noise,resulting in random measurement errors(ie,arbitrary uncertainty).At the same time,when there are differences between test data and training data,the machine learning model may have the uncertainty of model parameters(i.e.cognitive uncertainty)in predicting permeability.In order to realize the accurate prediction of permeability and quantify the impact of two uncertainties on the results,this paper proposes to realize the prediction of permeability and the estimation of its uncertainty simultaneously based on data distribution domain transformation and Bayesian neural network.The proposed method mainly includes two parts:one is the mutual transformation of data distribution in different domains,and the other is the neural network permeability modeling,prediction and uncertainty estimation based on Bayesian theory.Due to the assumption of data distribution in Bayesian neural network,Bayesian neural network can better learn the relationship between data when the probability distribution of label is consistent with the distribution of network.Therefore,by looking for a function,the permeability label of an original domain is transformed into the permeability related variable of the target domain(we call it the permeability of the target domain),so that the variable conforms to the distribution assumption of Bayesian neural network.We use Bayesian neural network to predict target domain penetration,as well as arbitrary uncertainty and cognitive uncertainty.Then,based on the inverse transformation of distribution domain,we restore the permeability of target domain back to the permeability of original domain.This method is applied to the logging data of 18 wells in an oil field.The data of 16 wells are used for training and 2 wells are tested.The predicted permeability of the test well is basically consistent with the real permeability.At the same time,the prediction results with arbitrary uncertainty provide the location where the permeability prediction value is affected by the noise of logging data.The prediction results of cognitive uncertainty show that the location with less data has higher cognitive uncertainty.The proposed process not only shows great potential in reservoir characterization,but also reduces the risk of logging interpretation.