## Journal of Central South University

 Vol. 25    No. 6    June 2018

Oil–gas reservoir lithofacies stochastic modeling based on one- to three-dimensional Markov chains

1. School of Mathematics and Statistics, Central South University, Changsha 410012, China;2. Data Center (Beijing), Agricultural Bank of China, Beijing 100161, China;3. Department of Railway Locomotive and Electromechanical Equipment, Shandong Polytechnic,Ji’nan 250104, China

Abstract:Stochastic modeling techniques have been widely applied to oil–gas reservoir lithofacies. Markov chain simulation, however, is still under development, mainly because of the difficulties in reasonably defining conditional probabilities for multi-dimensional Markov chains and determining transition probabilities for horizontal strike and dip directions. The aim of this work is to solve these problems. Firstly, the calculation formulae of conditional probabilities for multi-dimensional Markov chain models are proposed under the full independence and conditional independence assumptions. It is noted that multi-dimensional Markov models based on the conditional independence assumption are reasonable because these models avoid the small-class underestimation problem. Then, the methods for determining transition probabilities are given. The vertical transition probabilities are obtained by computing the transition frequencies from drilling data, while the horizontal transition probabilities are estimated by using well data and the elongation ratios according to Walther’s law. Finally, these models are used to simulate the reservoir lithofacies distribution of Tahe oilfield in China. The results show that the conditional independence method performs better than the full independence counterpart in maintaining the true percentage composition and reproducing lithofacies spatial features.

Key words: independence assumption; Markov chain; reservoir lithofacies; small-class underestimation; transition probability

 中南大学学报（自然科学版） ISSN 1672-7207 CN 43-1426/NZDXZAC 中南大学学报（英文版） ISSN 2095-2899 CN 43-1516/TBJCSTFT