Screening Method Using the Derivative-based Global Sensitivity Indices with Application to Reservoir Simulator

Abstract

Re´sume´-Me´thode de criblage base´e sur les indices de sensibilite´DGSM : application au simulateur de re´servoir -Les simulateurs d'e´coulements en milieux poreux sont utilise´s pour effectuer des pre´visions de la production de gisements pe´troliers. Les mode`les de re´servoir e´tudie´s sont caracte´rise´s par un grand nombre de proprie´te´s qui sont souvent tre`s incertaines. Afin de construire des mode`les pre´dictifs il est donc ne´cessaire de re´duire cette incertitude en se focalisant sur les variables les plus influentes. Les me´thodes d'analyse de sensibilite´permettent de re´soudre ce proble`me, mais sont souvent tre`s couˆteuses en nombre de simulations. Afin de re´duire le nombre d'appels au simulateur des nouveaux indices, nomme´s DGSM (Derivativebased Global Sensitivity Measures) base´s sur la moyenne des de´rive´s partielles, ont e´teí ntroduits. Dans cet article, une version re´vise´e des indices DGSM est propose´e afin d'ame´liorer leur efficacite´et leur convergence dans le cas ou`tre`s peu de simulations peuvent eˆtre effectue´es. L'efficacite´de ces indices est montre´e sur des cas test analytiques ainsi que sur un mode`le synthe´tique de re´servoir.Abstract -Screening Method Using the Derivative-based Global Sensitivity Indices with Application to Reservoir Simulator -Reservoir simulator can involve a large number of uncertain input parameters. Sensitivity analysis can help reservoir engineers focusing on the inputs whose uncertainties have an impact on the model output, which allows reducing the complexity of the model. There are several ways to define the sensitivity indices. A possible quantitative definition is the variancebased sensitivity indices which can quantify the amount of output uncertainty due to the uncertainty of inputs. However, the classical methods to estimate such sensitivity indices in a high-dimensional problem can require a huge number of reservoir model evaluations. Recently, new sensitivity indices based on averaging local derivatives of the model output over the input domain have been introduced. These so-called Derivative-based Global Sensitivity Measures (DGSM) have been proposed to overcome the problem of dimensionality and are linked to total effect indices, which are variance-based sensitivity indices. In this work, we propose a screening method based on revised DGSM indices, which increases the interpretability in some complex cases and has a lower computational cost, as demonstrated by numerical test cases and by an application to a synthetic reservoir test model.

Sensitivity analysis methods in the biomedical sciences

“…The calculation of DGSM indices is typically performed using Monte Carlo, quasi-Monte Carlo or Latin hypercube sampling [172]. The use of Sobol sequences or other lowdiscrepancy number generators may improve the computational efficiency [91].…”

Sensitivity analysis of expensive black-box systems using metamodeling

“…Unfortunately, they generally require a large amount of function evaluations (Kucherenko et al 2009, Touzani andBusby 2014). Using a metamodeling technique, the amount of evaluations can be greatly reduced.…”

Estimation of the Derivative-Based Global Sensitivity Measures Using a Gaussian Process Metamodel

“…As mentioned by [49], the DGSMs are tied with the Morris method [31]. From a synthetic point of view, this method associates to each input parameter x k the empirical mean…”

“…This approach can be tied with the well-known Morris method [31] which considers finite differences instead of the local derivatives: in a way, DGSMs can be viewed as a generalization of the indices obtained with the Morris method [49]. The DGSMs often have the advantage of requiring much less model evaluations than the Sobol' indices [23], especially for high-dimensional problems (many tens of input parameters) or complex models (non linear and interaction effects).…”

“…Various applications have illustrated the use of DGSMs such as an aquatic prey-predator chain [18], a biological system model [21], a flood one [24] or a reservoir simulator [49]. For a screening purpose, it has been proved that the total Sobol' indices are upper bounded up to a constant by the DGSMs, firstly in the case of uniform or normal probability distributions [43], and then in the case of a wider variety of continuous distributions [24].…”