Application of Markov statistics to modelling lithology distribution in hydrocarbon reservoirs

This paper presents a basic approach to three-dimensional reservoir modelling using Markov chain statistics. The whole study area is divided into many vertical columns with the same size of horizontal section, each of which is assumed to have the same Markov chain characteristics. Markov transition probability matrix and thickness distributions of different lithology groups are set up on the basis of available data. Then random sampling is used to generate a pseudo-lithology sequence and a corresponding thicknesses for each column from the Markov chain and thickness distributions of different lithologies. The solution chosen guarantees the well data are always honoured. The method has been applied to a delta-plain sequence for an oil field in the northern North Sea, i. e. to model channel sand-body distribution there. The results have proved satisfactory, but further work is required to incorporate more geological knowledge