RĂ©sultat de la recherche
A parsimonious parametrization of the Direct Sampling algorithm for multiple-point statistical simulations
Multiple-point statistics algorithms allow modeling spatial variability from training images. Among these techniques, the Direct Sampling (DS) algorithm has advanced capabilities, such as multivariate simulations, treatment of non-stationarity, multi-resolution capabilities, conditioning by inequality or connectivity data. However, finding the right trade-off between computing time and simulation quality requires tuning three main parameters, which can be complicated since simulation time and quality are affected by these parameters in a complex manner. To facilitate the parameter selection, we propose the Direct Sampling Best Candidate (DSBC) parametrization approach. It consists in setting the distance threshold to 0. The two other parameters are kept (the number of neighbors and the scan fraction) as well as all the advantages of DS. We present three test cases that prove that the DSBC approach allows to identify efficiently parameters leading to comparable or better quality and computational time than the standard DS parametrization. We conclude that the DSBC approach could be used as a default mode when using DS, and that the standard parametrization should only be used when the DSBC approach is not sufficient.
Random partitioning and adaptive filters for multiple-point stochastic simulation
Multiple-point geostatistical simulation is used to simulate the spatial structures of geological phenomena. In contrast to conventional two-point variogram based geostatistical methods, the multiple-point approach is capable of simulating complex spatial patterns, shapes, and structures normally observed in geological media. A commonly used pattern based multiple-point geostatistical simulation algorithms is called FILTERSIM. In the conventional FILTERSIM algorithm, the patterns identified in training images are transformed into filter score space using fixed filters that are neither dependent on the training images nor on the characteristics of the patterns extracted from them. In this paper, we introduce two new methods, one for geostatistical simulation and another for conditioning the results. At first, new filters are designed using principal component analysis in such a way to include most structural information specific to the governing training images resulting in the selection of closer patterns in the filter score space. We then propose to combine adaptive filters with an overlap strategy along a raster path and an efficient conditioning method to develop an algorithm for reservoir simulation with high accuracy and continuity. We also combine image quilting with this algorithm to improve connectivity a lot. The proposed method, which we call random partitioning with adaptive filters simulation method, can be used both for continuous and discrete variables. The results of the proposed method show a significant improvement in recovering the expected shapes and structural continuity in the final simulated realizations as compared to those of conventional FILTERSIM algorithm and the algorithm is more than ten times faster than FILTERSIM because of using raster path and using small overlap specially when we use image quilting.
Geological realism in hydrogeological and geophysical inverse modeling: A review
Scientific curiosity,exploration of georesources and environmental concerns are pushing the geoscientific research community toward subsurface investigations of ever-increasing complexity.This review explores various approaches to formulate and solve inverse problems in ways that effectively integrate geological concepts with geophysical and hydrogeological data. Modern geostatistical simulation algorithms can produce multiple subsurface realizations that are in agreement with conceptual geological models and statistical rock physics can be used to map these realizations into physical properties that are sensed by the geophysical or hydrogeological data.The inverse problem consists of finding one or an ensemble of such subsurface realizations that are in agreement with the data.The most general inversion frameworks are presently often computationally intractable when applied to large-scale problems and it is necessary to better understand the implications of simplifying (1) the conceptual geological model (e.g.,using model compression); (2) the physical forward problem (e.g.,using proxy models); and (3) the algorithm used to solve the inverse problem (e.g.,Markov chain Monte Carlo or local optimization methods) to reach practical and robust solutions given today’s computer resources and knowledge. We also highlight the need to not only use geophysical and hydrogeological data for parameter estimation purposes, but also to use them to falsify or corroborate alternative geological scenarios.
Extrapolating the Fractal Characteristics of an Image Using Scale-Invariant Multiple-Point Statistics
The resolution of measurement devices can be insufficient for certain purposes. We propose to stochastically simulate spatial features at scales smaller than the measurement resolution. This is accomplished using multiple-point geostatistical simulation (direct sampling in the present case) to interpolate values at the target scale. These structures are inferred using hypothesis of scale invariance and stationarity on the spatial patterns found at the coarse scale. The proposed multiple-point super-resolution mapping method is able to deal with "both continuous and categorical variables", and can be extended to multivariate problems. The advantages and limitations of the approach are illustrated with examples from satellite imaging.
Direct simulation of non-additive properties on unstructured grids
Uncertainties related to permeability heterogeneity can be estimated using geostatistical simulation methods. Usually, these methods are applied on regular grids with cells of constant size, whereas unstructured grids are more flexible to honor geological structures and offer local refinements for fluid-flow simulations. However, cells of different sizes require to account for the support dependency of permeability statistics (support effect). This paper presents a novel workflow based on the power averaging technique. The averaging exponent đťś” is estimated using a response surface calibrated from numerical upscaling experiments. Using spectral turning bands, permeability is simulated on points in each unstructured cell, and later averaged with a local value of đťś” that depends on the cell size and shape. The method is illustrated on a synthetic case. The simulation of a tracer experiment is used to compare this novel geostatistical simulation method with a conventional approach based on a fine scale Cartesian grid. The results show the consistency of both the simulated permeability fields and the tracer breakthrough curves. The computational cost is much lower than the conventional approach based on a pressure-solver upscaling.
Geothermal state of the deep Western Alpine Molasse Basin, France-Switzerland
Over the last few years the Western Alpine Molasse Basin (WAMB) has been attracting large institutional, industrial and scientific interest to evaluate the feasibility of geothermal energy production. However, the thermal state of the basin, which is instrumental to the development of such geothermal projects, has remained to date poorly known. Here, we compile and correct temperature measurements (mostly bottom hole temperature) from 26 existing well data mostly acquired during former hydrocarbon exploration in the basin. These data suggest that the average geothermal gradient of the WAMB is around 25–30 °C/km. We further use these data to build the first well data-driven 3D geostatistical temperature model of the whole basin and generate probabilistic maps of isotherms at 70 and 140 °C. This model highlights a number of positive and negative thermal anomalies that are interpreted in the context of heat advection caused by fluid circulation along faults and/or karst systems. This study confirms that the WAMB has a great potential for low-enthalpy geothermal resources and presents a typology of advection-dominated potential targets.
3D multiple-point statistics simulation using 2D training images
One of the main issues in the application of multiple-point statistics (MPS) to the simulation of three-dimensional (3D) blocks is the lack of a suitable 3D training image. In this work, we compare three methods of overcoming this issue using information coming from bidimensional (20) training images. One approach is based on the aggregation of probabilities. The other approaches are novel. One relies on merging the lists obtained using the impala algorithm from diverse 2D training images, creating a list of compatible data events that is then used for the MPS simulation. The other (s2Dcd) is based on sequential simulations of 2D slices constrained by the conditioning data computed at the previous simulation steps. These three methods are tested on the reproduction of two 3D images that are used as references, and on a real case study where two training images of sedimentary structures are considered. The tests show that it is possible to obtain 3D MPS simulations with at least two 2D training images. The simulations obtained, in particular those obtained with the s2Dcd method, are close to the references, according to a number of comparison criteria. The CPU time required to simulate with the method s2Dcd is from two to four orders of magnitude smaller than the one required by a MPS simulation performed using a 3D training image, while the results obtained are comparable. This computational efficiency and the possibility of using MPS for 3D simulation without the need for a 3D training image facilitates the inclusion of MPS in Monte Carlo, uncertainty evaluation, and stochastic inverse problems frameworks.
Oil production uncertainty assessment by predicting reservoir production curves and confidence intervals from arbitrary proxy responses
Underground fluid flow in hydrocarbon reservoirs (or aquifers) is difficult to predict accurately due to geological and petrophysical uncertainties. To quantify that uncertainty, several spatial statistical methods are often used to generate an ensemble of subsurface models representing and sampling these uncertainties. However, to predict the uncertainties in terms of flow responses, one needs to run a forward flow simulator (often multiphase flow in transient state) on every model of this ensemble and this generally entails intractable computational costs. Approximate solutions (flow proxies) can help addressing this challenge but introduce physical simplifications whose impact on the uncertainty quantification is difficult to characterize. This paper proposes a workflow to assess the dynamic reservoir behavior uncertainties from an input ensemble of realizations sampling geological and geophysical uncertainties. Analytical reservoir production curves are estimated from proxy distances computed between all ensemble members and from a few accurate flow responses computed on a subset of the ensemble. A randomization process accounting for proxy quality and for model selection is used to assess confidence intervals about reservoir production quantile curves. The process can use both static and dynamic proxies and also permits to compare their efficiency. A case study on a real turbiditic reservoir shows the applicability of the method, and highlights the value of even a simple proxy to increase the confidence about future reservoir production.
Constraining distance-based multipoint simulations to proportions and trends
In the last years, the use of training images to represent spatial variability has emerged as a viable concept. Among the possible algorithms dealing with training images, those using distances between patterns have been successful for applications to subsurface modeling and earth surface observation. However, one limitation of these algorithms is that they do not provide a precise control on the local proportion of each category in the output simulations. We present a distance perturbation strategy that addresses this issue. During the simulation, the distance to a candidate value is penalized if it does not result in proportions that tend to a target given by the user. The method is illustrated on applications to remote sensing and pore-scale modeling. These examples show that the approach offers increased user control on the simulation by allowing to easily impose trends or proportions that differ from the proportions in the training image.