Integration of soft data into multiple-point statistical simulation: re-assessing the probability conditioning method for facies model calibration

Conditioning multiple-point statistical (MPS) facies simulation on dynamic flow data is complicated by the complex relationship between discrete facies distribution and the flow response data. The process can be facilitated by using the probability conditioned method (PCM), in which an ensemble-based data assimilation approach is used to infer, from observed flow data, a facies probability map that can guide conditional simulation from a training image (TI). We discuss important aspects of flow model calibration based on facies probability maps and propose several improvements to the original PCM, including: (1) using a statistically consistent approach for inferring facies probability maps from updated ensemble of continuous hydraulic properties; (2) assigning spatially variable weights to simulation grids based on relative confidence in the information content of observed data; and (3) considering spatial patterns instead of marginal facies probabilities in constructing probability maps. We illustrate that, in simulating categorical facies, the pattern-imitating behavior of MPS can have a significant impact on soft data conditioning. In particular, in the Single Normal Equation SIMulation (SNESIM) algorithm, the initial points that are visited on the random path tend to determine the main global facies connectivity. Once these initial points are populated with simulated values, the conditional probabilities (inferred from the TI) for the subsequent cells on the random path tend to be very close to 0 and 1. Hence, the facies types in the remaining cells are known almost deterministically, making the soft data inconsequential at the later stages of simulation. This behavior suggests that, without compensating for this effect, the facies probability map is not effectively integrated into the SNESIM simulation, an issue that is reflected in the generated realizations. Several numerical experiments are presented and discussed to illustrate this behavior and its impact on soft-data conditioning.