About the Use of Quality Indicators to Reduce Information Loss When Performing Upscaling

Abstract

-Hydrocarbon reservoirs are characterized by the spatial distributions of petrophysical properties. These spatial characteristics are usually derived from well data and seismic information. To study a reservoir, the engineers build a fine geological model, also called a geostatistical model, to represent the field. The purpose is to capture as well as possible the peculiarities and heterogeneity of the true reservoir. At this stage, performing a flow simulation with such detailed geological models is just too time-demanding. Therefore, a possibility consists of upscaling the geological model to an upscaled mesh, thus resulting in a coarse reservoir model for which fluid flow can be numerically simulated in a reasonable amount of time. The coarse grid blocks of this reservoir model are attributed equivalent petrophysical properties related to the properties populating the fine grid blocks. These properties are upscaled, and so they do not capture all of the details of the fine model. In this paper, we investigate the potential of various numerical and easy to compute criteria, which help evaluate the information loss due to the upscaling process. Our final purpose is to provide and access the reliability of quality indicators, which make it possible to evaluate the quality of the upscaled reservoir model. The potential of this systematic and integrated study is illustrated with two types of numerical experiments based upon the SPE10 case. First, we apply different upscaling methods to determine coarse reservoir models. Quality indicators are computed for each of them so that we identify the most suitable upscaling methods. Then, the upscaled models are input to flow simulators to check the accuracy of our quality estimations. Second, we also investigate the influence of coarsening and try to determine from the computed quality indicators the coarse cell size above which too much information is lost.Re´sume´-À propos de l'utilisation d'indicateurs de qualite´afin de re´duire la perte d'information lors d'un upscaling -Les re´servoirs pe´troliers sont caracte´rise´s par une distribution spatiale de proprie´te´s pe´trophysiques. Ces caracte´ristiques spatiales sont ge´ne´ralement de´rive´es de donne´es de puits et sismiques. Les inge´nieurs construisent alors un mode`le ge´ologique fin, aussi appeleḿ ode`le ge´ostatistique, pour repre´senter le champ. Le but est de capturer aussi bien que possible les particularite´s et l'he´te´roge´ne´ite´du re´servoir. À ce stade, re´aliser une simulation d'e´coulement avec ces mode`les ge´ologiques aussi de´taille´s est trop couˆteux en temps de calcul. Par conse´quent, une possibilite´consiste a`« upscaler » le mode`le ge´ologique sur une grille grossie`re, afin d'obtenir un mode`le de re´servoir grossier pour lequel l'e´coulement peut eˆtre simule´nume´riquement dans un laps de temps raisonnable. On attribue alors des proprie´te´s pe´trophysiques e´quivalentes aux cellules de la grille grossie`re. Meˆme si ces donne´es e´quivalentes sont obtenues a`partir des proprie´t...

A priori error estimation of upscaled coarse grids for water‐flooding process

“…Preux [17] also showed that ILIv ¼ 1 when there is no information loss while ILIv ¼ 0 corresponds to a too strong upscaling process in which too much information is lost.…”

“…In this section, the existing error prediction criteria including ILIr and ILIv information loss indices of Preux, [17] and QQ plot of Sablok and Aziz [16] will be briefly described. Preux [17] defined the data range indicator, ILIr, and the variance indicator, ILIv, as follows:…”

“…[17] Qi and Hesketh [15] proposed two indices, ILIa and ILIb, to quantify the information loss in the permeability field of the coarse grid with respect to the fine-scale model. They employed these two indices to predict the performance of a "REV grid method" [18] compared to conventional upscaling methods.…”

“…Preux, [17] similar to Qi and Hesketh, [15] introduced two information loss indices, ILIr and ILIv, to measure the quality of the coarse-scale model prior to any fluid-flow simulation. They investigated the performance of these indices compared to other criteria, e.g.…”

Selecting an Appropriate Upscaled Reservoir Model Based on Connectivity Analysis

“…However, selecting the most suitable technique is far from straightforward. To date, distinct criteria [2][3][4][5][6] have been proposed to quantify the information loss due to upscaling so that the quality of an upscaled model can be estimated without performing any fluid flow simulation. For instance, it was recommended to define the information loss from the ratio of the number of fine cells to the number of coarse cells or from the comparison of the histograms of the studied property at the fine and coarse scales.…”