MPS realization selection with an innovative LSTM tool

Abstract Multiple point statistics (MPS) methods are good tools to recreate the spatial heterogeneity of permeability in porous media. On the other hand, a reliable forecast of reservoir performance necessitates a large number of realistic permeability realizations which could be achieved by MPS techniques. However, the cost of numerical simulation on a large number of realizations, especially for screening, optimization or history matching purposes, is completely prohibitive. Emerging techniques in deep learning such as Long Short-Term Memory (LSTM) networks can provide robust proxy models replacing the numerical simulation with reasonable run-time and acceptable predictability. We train LSTM networks using some of realizations as input with a novel implementation. The LSTM network accepts the permeability values in a state of art manner, i.e. accepting the permeability values row by row. The network is trained with reservoir simulation outputs of corresponding MPS-generated realizations. In fact, the output values for training (the labels) are the reservoir simulation outputs for each realization which are obtained by an MPS method. In this way, MPS can be coupled with deep learning to find the realizations having the best match with a reference case. The architecture of the trained LSTM network is illustrated with details. The results show that the trained network is able to find realizations resulting in an adequate match with the reference case. These realizations not only exhibit fairly good prediction in future times of simulation due to MPS-derived permeability heterogeneity within but have an acceptable match with the historical reservoir performance. Our hybrid MPS-LSTM approach allows reducing the uncertainty in reservoir performance prediction. The reason is both meticulous heterogeneity modeling and deep-learning-assisted approach of realization screening. The proposed workflow could be a promising basis for history matching and uncertainty quantification calculation of reservoir.