Accelerated Bayesian inference-based history matching of petroleum reservoirs using polynomial chaos expansions

Abstract In reservoir simulations, model parameters such as porosity and permeability are often uncertain and therefore better estimates of these parameters are obtained by matching the simulation predictions with the production history. Bayesian inference provides a convenient way of estimating parameters of a mathematical model, starting from a probable range of parameter values and knowing the production history. Bayesian inference techniques for history matching require computationally expensive Monte Carlo simulations, which limit their use in petroleum reservoir engineering. To overcome this limitation, we perform accelerated Bayesian inference based history matching by employing polynomial chaos (PC) expansions to represent random variables and stochastic processes. As a substitute to computationally expensive Monte Carlo simulations, we use a stochastic technique based on PC expansions for propagation of uncertainty from model parameters to model predictions. The PC expansions of the stochastic variables are obtained using relatively few deterministic simulations, which are then used to calculate the probability density of the model predictions. These results are used along with the measured data to obtain a better estimate (posterior distribution) of the model parameters using the Bayes rule. We demonstrate this method for history matching using an example case of SPE1CASE2 problem of SPEs Comparative Solution Projects. We estimate the porosity and permeability of the reservoir from limited and noisy production data.

Bayesian updating via bootstrap filtering combined with data-driven polynomial chaos expansions: methodology and application to history matching for carbon dioxide storage in geological formations

Computational Geosciences ◽

10.1007/s10596-013-9350-6 ◽

2013 ◽

Vol 17 (4) ◽

pp. 671-687 ◽

Cited By ~ 24

Author(s):

Sergey Oladyshkin ◽

Holger Class ◽

Wolfgang Nowak

Keyword(s):

Carbon Dioxide ◽

History Matching ◽

Polynomial Chaos ◽

Bayesian Updating ◽

Data Driven ◽

Carbon Dioxide Storage ◽

Polynomial Chaos Expansions ◽

Geological Formations

SURROGATE MODELING FOR STOCHASTIC DYNAMICAL SYSTEMS BY COMBINING NONLINEAR AUTOREGRESSIVE WITH EXOGENOUS INPUT MODELS AND POLYNOMIAL CHAOS EXPANSIONS

International Journal for Uncertainty Quantification ◽

10.1615/int.j.uncertaintyquantification.2016016603 ◽

2016 ◽

Vol 6 (4) ◽

pp. 313-339 ◽

Cited By ~ 20

Author(s):

Chu V. Mai ◽

Minas D. Spiridonakos ◽

Eleni N. Chatzi ◽

Bruno Sudret

Keyword(s):

Dynamical Systems ◽

Polynomial Chaos ◽

Surrogate Modeling ◽

Stochastic Dynamical Systems ◽

Polynomial Chaos Expansions ◽

Nonlinear Autoregressive

Extending bluff-and-fix estimates for polynomial chaos expansions

Journal of Computational Science ◽

10.1016/j.jocs.2020.101287 ◽

2021 ◽

pp. 101287

Author(s):

Laura Lyman ◽

Gianluca Iaccarino

Keyword(s):

Polynomial Chaos ◽

Polynomial Chaos Expansions

Subsampled Gauss Quadrature Nodes for Estimating Polynomial Chaos Expansions

SIAM/ASA Journal on Uncertainty Quantification ◽

10.1137/130913511 ◽

2014 ◽

Vol 2 (1) ◽

pp. 423-443 ◽

Cited By ~ 18

Author(s):

Gary Tang ◽

Gianluca Iaccarino

Keyword(s):

Polynomial Chaos ◽

Gauss Quadrature ◽

Polynomial Chaos Expansions

Modeling of Stochastic EMC Problems with Anisotropic Polynomial Chaos Expansions

IEEE Electromagnetic Compatibility Magazine ◽

10.1109/memc.2021.9477236 ◽

2021 ◽

Vol 10 (2) ◽

pp. 70-79

Author(s):

Theodoros Zygiridis ◽

Georgios Kommatas ◽

Aristeides Papadopoulos ◽

Nikolaos Kantartzis

Keyword(s):

Polynomial Chaos ◽

Polynomial Chaos Expansions

A preconditioning approach for improved estimation of sparse polynomial chaos expansions

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2018.08.005 ◽

2018 ◽

Vol 342 ◽

pp. 474-489 ◽

Cited By ~ 2

Author(s):

Negin Alemazkoor ◽

Hadi Meidani

Keyword(s):

Polynomial Chaos ◽

Sparse Polynomial ◽

Polynomial Chaos Expansions

ASSISTED HISTORY MATCHING FOR PETROLEUM RESERVOIRS IN THE SOCIAL COMPUTING ERA

American Journal of Applied Sciences ◽

10.3844/ajassp.2013.901.916 ◽

2013 ◽

Vol 10 (8) ◽

pp. 901-916 ◽

Cited By ~ 3

Author(s):

Cancelliere

Keyword(s):

History Matching ◽

Social Computing ◽

Petroleum Reservoirs ◽

The Social ◽

Assisted History Matching

Multi-model polynomial chaos surrogate dictionary for Bayesian inference in elasticity problems

Probabilistic Engineering Mechanics ◽

10.1016/j.probengmech.2016.08.004 ◽

2016 ◽

Vol 46 ◽

pp. 107-119 ◽

Cited By ~ 4

Author(s):

Andres A. Contreras ◽

Olivier P. Le Maître ◽

Wilkins Aquino ◽

Omar M. Knio

Keyword(s):

Bayesian Inference ◽

Polynomial Chaos ◽

Elasticity Problems

mumpce_py: A Python Implementation of the Method of Uncertainty Minimization Using Polynomial Chaos Expansions

Journal of Research of the National Institute of Standards and Technology ◽

10.6028/jres.122.039 ◽

2017 ◽

Vol 122 ◽

Cited By ~ 2

Author(s):

David A. Sheen

Keyword(s):

Measurement Uncertainty ◽

First Principles ◽

Polynomial Chaos ◽

Software Tool ◽

Physical Models ◽

Physical Parameters ◽

Experimental Measurements ◽

Uncertainty Minimization ◽

Polynomial Chaos Expansions ◽

Parameter Values

The Method of Uncertainty Minimization using Polynomial Chaos Expansions (MUM-PCE) was developed as a software tool to constrain physical models against experimental measurements. These models contain parameters that cannot be easily determined from first principles and so must be measured, and some which cannot even be easily measured. In such cases, the models are validated and tuned against a set of global experiments which may depend on the underlying physical parameters in a complex way. The measurement uncertainty will affect the uncertainty in the parameter values.