マルコフ連鎖モンテカルロ法を利用したトレーサー試験からフラクチャーの物理パラメータを推定する方法

抄録

A tracer test is a powerful experiment to identify fractures in underground reservoirs, which significantly affect fluid flow in a porous medium. The complex variable boundary element method (CVBEM) is capable of simulating time-series of the tracer concentration at a producer when the physical properties of the medium and the tracer injection plan are given. Several studies have proposed inversion procedures to identify physical parameters of a fracture in a homogeneous porous medium, using such as the genetic algorithm (GA) or the ensemble Kalman filter (EnKF) combined with iterative computations of CVBEM. The present paper proposes, for this inversion problem, a Markov chain Monte Carlo (MCMC) algorithm, which enables us to obtain a posterior probability density function (PDF) as well as an optimum value for each model parameter that characterizes the fracture. The proposed algorithm is performed to twin experiments that confirm whether properties of a synthetically-assumed fracture are reproduced from time-series of tracer concentration at a producer, which CVBEM has computed in advance. A clustering result of the K-means, which is applied to the samples obtained by MCMC, provides candidate solutions corresponding to local maximums of the posterior PDF. The candidate solutions are ranked by the posterior PDF at the centroid of each cluster. Especially in the case of the two-directional tracer test, in which two pairs of injector and producer are located, the optimum parameter set that maximizes the posterior PDF successfully reproduces both the fracture properties and the concentration curves.