A two-stage efficient history matching procedure of non-Gaussian fields

The speed and precision of automatic history matching are two critical considerations due to the undetermined character of inverse problems and the nonlinearity of the reservoir flow mechanism. In this work, instead of focusing on faster optimization algorithms, we proposed a two-stage history matching procedure to increase the precision, firstly matching the facies distribution and then adjusting the continuous petrophysical parameters based on the updated facies distribution. This procedure adds local heterogeneity to relatively global trends of property distribution of a formation and in this sense, helps to mitigate the multiplicity instances of the inverse problems. In the first stage, we reconstruct a model parameter vector to describe facies distribution and boundaries by introducing the level set function which better agrees with Gaussian distribution assumption of Bayesian framework. Then, model variables are reparameterized as a linear combination of important models in the initial ensemble by Singular Value Decompostion (SVD) and Simultaneous Perturbation Stochastic Algorithm is applied to solve coefficients of this combination. In the second stage, the posterior facies model is used as prior information to generate the initial unknown petrophysical realizations by commonly used software. Later, local adjustments to continuous petrophysical parameters are carried out to better match the measurements. And, facies inversion of complex reservoirs on upscaled models can greatly reduce simulation time. Field tests on the PUNQ-S3 model revealed that the posterior model produced by the new procedure agrees with reference model much better than the direct history matching to petrophysical parameters, without compromising the speed.