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A Location-Based Multiple Point Statistics Method: Modeling the Reservoir With Non-Stationary Characteristics

Abstract

The two-point geostatistics and the new development of multiple point statistics (MPS) (Yin et al., 2009; Strebelle and Journel, 2001; Strebelle, 2002; Liu Y et al., 2004; Caers and Zhang, 2004; Ezequiel and González, 2008; Arpat and Caers, 2007)are well developed based on the basic assumption that reservoir statistical properties do not change with the location, which is called as statistical properties of ‘stationary’. However, in the delta reservoir, sedimentary type changes in different positions, the model is not accepted as fluvial one with MPS based on the theory of stationary hypothesis (Caers and Zhang, 2004). The above issue, which is the so called statistical property of ‘non-stationary’, is a difficult problem in MPS. In this paper, based on the phenomenon of reservoir sedimentary patterns varying with location, a new MPS method for modeling non-stationary geological phenomenon is proposed. The method firstly scan data event and its center position information in training image at the same time. Then, the choice of the most matching data event is constrain using the data event matching and the closest distance between data events center points. Thirdly, taking local integral replacement of data events to represent the depositional mode so as to achieve better reproduction of spatial and temporal variation of non-stationary data and describe reservoir geological characteristics. Because the distance is calculated with the relative central position, training images can be differently scaled with the simulation region, which avoid the problem faced by the distanced-based mps method(Hu et al, 2013). The whole scanning training image can avoid the data events clustering and all sedimentary patterns to equal consideration. Giving weights on distance function can be moderately characterization of reservoir heterogeneity in various directions. This method is compared with the traditional Snesim method using a synthesized 3-D training image of Poyang Lake and a reservoir model of Shengli oilfield in China. The results indicated that the new method can better reproduce the non-stationary characteristics than the traditional one, and is more suitable for the simulation of delta-front deposits.. These results demonstrated the new method is a powerful tool to model reservoir with non-stationary characteristics.