TY - JOUR

T1 - Uncertainty quantification in reservoir simulation models with polynomial chaos expansions

T2 - Smolyak quadrature and regression method approach

AU - Camacho, Alejandra

AU - Talavera, Alvaro

AU - Emerick, Alexandre A.

AU - Pacheco, Marco A.C.

AU - Zanni, João

PY - 2017/1/1

Y1 - 2017/1/1

N2 - The use of PCE enables the representation of the outcome of a given model as a polynomial, created by a function basis that depends on the probability distribution of the input variables and beyond that, the estimation of statistical properties such as the mean, standard deviation, percentiles and more rigorously, the entire probability distribution. In oil reservoir management, it is of great importance to determine the influence the parameters have in the behavior of the model response. In high dimensional problems the estimation of the expansion coefficients has a high computational cost due to the existence of an exponentially increasing relationship between the number of variables and the number of coefficients. Adding the inherent cost of simulating a real reservoir model, finding efficient solutions becomes absolutely necessary. The Smolyak or sparse quadrature is proposed, as well as the regression approach with experimental design, to approximate the expansion coefficients dealing with high dimensional cost. The accuracy of these techniques will be tested in a reservoir simulation model composed of eleven uncertain parameters, and results will be compared to traditional Monte Carlo Simulation.

AB - The use of PCE enables the representation of the outcome of a given model as a polynomial, created by a function basis that depends on the probability distribution of the input variables and beyond that, the estimation of statistical properties such as the mean, standard deviation, percentiles and more rigorously, the entire probability distribution. In oil reservoir management, it is of great importance to determine the influence the parameters have in the behavior of the model response. In high dimensional problems the estimation of the expansion coefficients has a high computational cost due to the existence of an exponentially increasing relationship between the number of variables and the number of coefficients. Adding the inherent cost of simulating a real reservoir model, finding efficient solutions becomes absolutely necessary. The Smolyak or sparse quadrature is proposed, as well as the regression approach with experimental design, to approximate the expansion coefficients dealing with high dimensional cost. The accuracy of these techniques will be tested in a reservoir simulation model composed of eleven uncertain parameters, and results will be compared to traditional Monte Carlo Simulation.

KW - Experimental design

KW - Polynomial chaos expansions

KW - Quadratures

KW - Regression approach

KW - Reservoir simulation

KW - Smolyak

KW - Uncertainty

KW - Experimental design

KW - Polynomial chaos expansions

KW - Quadratures

KW - Regression approach

KW - Reservoir simulation

KW - Smolyak

KW - Uncertainty

UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85016388745&origin=inward

UR - https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=85016388745&origin=inward

U2 - 10.1016/j.petrol.2017.03.046

DO - 10.1016/j.petrol.2017.03.046

M3 - Article in a journal

VL - 153

SP - 203

EP - 211

JO - Journal of Petroleum Science and Engineering

JF - Journal of Petroleum Science and Engineering

SN - 0920-4105

ER -