Geologically Consistent History Matching for Complex Reservoir Models
Authors: Ma Wei 
Published: October 2018

Abstract
One major goal in reservoir engineering is to improve ultimate recovery factor. In reservoir models with complex geological settings, e.g., river channel reservoir models, the quality of estimation of the patterns of channel connectivity is critical in designing a reservoir development plan to improve ultimate recovery factor. However, geostatistical techniques based on two-point statistics, such as variogram model based methods, are not suitable to reproduce those complex geological connectivity patterns. Moreover, traditional history matching methods have difficulties in estimating and preserving channel connectivity patterns. Recently, multiple point statistics (MPS) methods have been developed to model the complex geological connectivity and generate discrete facies models (e.g., channel facies). In MPS, facies models, e.g., channel models, are sampled based on empirical facies probabilities that are estimated from a geological conceptual model, known as a training image (TI). A training image can be regarded as a databased of spatial structures that contain higher order (higher than 2nd order) multivariate geostatistical information. As a result, MPS can generate facies models that are geologically consistent with the geological features contained in the training image. An advantage of MPS facies simulation is that it is convenient to condition facies models on hard data (e.g., well measurements) and soft data (e.g., seismic data). By taking this advantage, I have developed two MPS based history matching methods, which are able to reproduce geological consistent channel connectivity patterns while matching dynamic flow data. The adapted pilot point method strategically places pilot points in a reservoir model based on both sensitivity and uncertainty information of the model. Then facies type values at the pilot points are estimated and considered as hard data to condition facies simulations. This method enables conditioning MPS facies simulations on flow data, however, it only uses limited information from the reservoir via pilot points that have limited spatial coverage. The second method is a facies probability conditioning method, which infers a facies probability map (the same size as the reservoir model) from flow data and then considers the probability map as soft data to condition the facies simulations. Although this method has a much better coverage of the reservoir model, it suffers from generate facies models that are not consistent with the facies probability map. In this paper, I will show the results from the investigation on this inconsistency issue and explain the reason responsible for the issue: the intrinsic behavior of MPS facies simulation algorithm tends to disregard the facies probability map at the later stage of the simulation. More specifically, the facies patterns in the output of MPS facies simulation are primarily controlled by the first few grid cells along the corresponding random path and the facies simulations at the rest of the grid cells are dominated by the conditional probability estimated from the TI, while the facies probability map has a minimal impact on the outcome. Then, I proposed a new approach for conditioning MPS facies simulations on flow data by ensuring gaining more control on the simulations a t the early grid cells on the random path of a MPS simulation. I will also present numerical experiments to show that this approach leads to generation of more geologically consistent facies connectivity patterns.