Production Data Integration into Complex Geologic Facies Models: Exploiting the Behavior of Multiple-Point Statistical Simulation for Effective Data Conditioning

Abstract

Abstract Multiple point statistical (MPS) simulation is a modern pattern-based geostatistical approach for describing and stochastically simulating geologic formations with complex connectivity patterns. In MPS geostatistical simulation, a template containing data patterns around each simulation cell is used to extract and store the local conditional probabilities from a training image (TI). To generate a simulated sample, a random path is generated to sequentially visit all unsampled grid cells and draw conditional samples from the corresponding stored conditional probabilities. The grid-based implementation of MPS simulation offers several advantages for integration of hard and soft data. In the Single Normal Equation SIMulation (SNESIM) implementation of MPS for facies simulation, it has been observed that the integration of soft data can result in many facies realizations that do not provide consistent patterns with the incorporated probability map. This is partly explained by the Markov property that only considers probabilities that are co-located with the simulation node, and hence ignoring spatial information from neighboring cells. In addition to this effect, we show another important mechanism is in play in the SNESIM algorithm that explains the observed behavior. Specifically, at the early stage of the simulation when the first few percentage of the simulation nodes on the random path are visited the local conditioning data are limited and the resulting conditional probabilities that are obtained from the TI are not strictly constrained. Hence the conditional probabilities cover a wide range of values in the range [0,1]. However, after this initial stage, as the simulated data populate more cells in the model grid, they tend to severely constrain the conditional probabilities to assume extreme values of 0 or 1. With these extreme values at the later stages of the simulation the probability values that are included in the soft data (as secondary source of information) tend to be disregarded and the facies types are predominantly determined by the TI. We demonstrate and discuss this behavior of the SNESIM algorithm through several examples and present strategies that can be adopted to compensate for this effect. The presented examples are related to indirect integration of the flow data by first inferring probabilistic information about facies types and using the results as soft data for integration into SNESIM algorithm.