شبیه سازی آماری چندگانه با استفاده از داده های مشروط نامشخص (نرم)

Geostatistical simulation methods have been used to quantify spatial variability of reservoir models since the 80s. In the last two decades, state of the art simulation methods have changed from being based on covariance-based 2-point statistics to multiple-point statistics (MPS), that allow simulation of more realistic Earth-structures. In addition, increasing amounts of geo-information (geophysical, geological, etc.) from multiple sources are being collected. This pose the problem of integration of these different sources of information, such that decisions related to reservoir models can be taken on an as informed base as possible. In principle, though difficult in practice, this can be achieved using computationally expensive Monte Carlo methods. Here we investigate the use of sequential simulation based MPS simulation methods conditional to uncertain (soft) data, as a computational efficient alternative. First, it is demonstrated that current implementations of sequential simulation based on MPS (e.g. SNESIM, ENESIM and Direct Sampling) do not account properly for uncertain conditional information, due to a combination of using only co-located information, and a random simulation path. Then, we suggest two approaches that better account for the available uncertain information. The first make use of a preferential simulation path, where more informed model parameters are visited preferentially to less informed ones. The second approach involves using non co-located uncertain information. For different types of available data, these approaches are demonstrated to produce simulation results similar to those obtained by the general Monte Carlo based approach. These methods allow MPS simulation to condition properly to uncertain (soft) data, and hence provides a computationally attractive approach for integration of information about a reservoir model.