Assessing multiple-point statistical facies simulation behavior for effective conditioning on probabilistic data.

*(English)*Zbl 1428.86026Summary: Conditioning multiple-point statistical (MPS) facies simulation on dynamic flow data is complicated by the complex relation between flow responses and facies distribution. One way to incorporate feedback from the flow data into MPS simulation is by constructing (and updating) facies probability maps (soft data) and using the results to constrain the MPS simulation outputs, for example, through Single Normal Equation SIMulation (SNESIM) algorithm and the \(\tau \)-model. The pattern-imitating behavior of MPS simulation (specifically, the SNESIM) has been shown to result in a sizable fraction of facies models that fail to effectively capture the correct location and spatial connectivity represented by the facies probability map. This paper presents two key observations that explains this behavior/outcome: (1) the facies patterns resulting from the SNESIM are primarily controlled by the outcome of the first few grid cells along the corresponding random path (early stages of the simulation); and (2)
the facies outcomes in the remaining grid cells are dominated by extremely confident conditional probabilities extracted from the TI to generate the encoded connectivity patterns in the TI. Hence, the contribution of facies probability map become increasingly inconsequential as the simulation proceeds. This intrinsic property must be accounted for in developing data conditioning methods, especially when training images with large-scale connectivity patterns are considered. Two approaches for addressing this issue include adapting the random path at early stages to the key information in the probability map to properly reflect its impact, or treating high-probability events from the probability map as hard data. Examples are presented to illustrate this behavior, followed by a simple method to improve the effectiveness of integrating facies probability maps (and flow response data) into SNESIM.

##### Keywords:

probability conditioning; conditional simulation; multiple point statistics (MPS); SNESIM algorithm; model calibration; geological facies
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\textit{W. Ma} and \textit{B. Jafarpour}, Math. Geosci. 51, No. 8, 975--998 (2019; Zbl 1428.86026)

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