Pejman Tahmasebi

Multiple-point geostatistical modeling based on the cross-correlation functions

An important issue in reservoir modeling is accurate generation of complex structures. The problem is difficult because the connectivity of the flow paths must be preserved. Multiple-point geostatistics is one of the most effective methods that can model the spatial patterns of geological structures, which is based on an informative geological training image that contains the variability, connectivity, and structural properties of a reservoir. Several pixel- and pattern-based methods have been developed in the past. In particular, pattern-based algorithms have become popular due to their ability for honoring the connectivity and geological features of a reservoir. But a shortcoming of such methods is that they require a massive data base, which make them highly memory- and CPU-intensive. In this paper, we propose a novel methodology for which there is no need to construct pattern data base and small data event. A new function for the similarity of the generated pattern and the training image, based on a cross-correlation (CC) function, is proposed that can be used with both categorical and continuous training images. We combine the CC function with an overlap strategy and a new approach, adaptive recursive template splitting along a raster path, in order to develop an algorithm, which we call cross-correlation simulation (CCSIM), for generation of the realizations of a reservoir with accurate conditioning and continuity. The performance of CCSIM is tested for a variety of training images. The results, when compared with those of the previous methods, indicate significant improvement in the CPU and memory requirements.

A hybrid neural networks-fuzzy logic-genetic algorithm for grade estimation

The grade estimation is a quite important and money/time-consuming stage in a mine project, which is considered as a challenge for the geologists and mining engineers due to the structural complexities in mineral ore deposits. To overcome this problem, several artificial intelligence techniques such as Artificial Neural Networks (ANN) and Fuzzy Logic (FL) have recently been employed with various architectures and properties. However, due to the constraints of both methods, they yield the desired results only under the specific circumstances. As an example, one major problem in FL is the difficulty of constructing the membership functions (MFs).Other problems such as architecture and local minima could also be located in ANN designing. Therefore, a new methodology is presented in this paper for grade estimation. This method which is based on ANN and FL is called “Coactive Neuro-Fuzzy Inference System” (CANFIS) which combines two approaches, ANN and FL. The combination of these two artificial intelligence approaches is achieved via the verbal and numerical power of intelligent systems. To improve the performance of this system, a Genetic Algorithm (GA) – as a well-known technique to solve the complex optimization problems – is also employed to optimize the network parameters including learning rate, momentum of the network and the number of MFs for each input. A comparison of these techniques (ANN, Adaptive Neuro-Fuzzy Inference System or ANFIS) with this new method (CANFIS–GA) is also carried out through a case study in Sungun copper deposit, located in East-Azerbaijan, Iran. The results show that CANFIS–GA could be a faster and more accurate alternative to the existing time-consuming methodologies for ore grade estimation and that is, therefore, suggested to be applied for grade estimation in similar problems.

MS-CCSIM

Pattern-based spatial modeling relies on training images as basic modeling component for generating geostatistical realizations. The methodology recognizes that working with the unit of a pattern aids its reproduction, particularly for large systems. In this paper improvements are made, in terms of both the computation time and conditioning, of a pattern-based simulation method that relies on the cross-correlation-based simulation (CCSIM), introduced by Tahmasebi et al. (2012). The extension lies on the use of a multi-scale (MS) representation of the training image along a pattern projection strategy that is markedly different from the traditional multi-grid methods employed in the current methodologies, and proposes acceleration of the method by carrying out most of the computations in the Fourier space. In the proposed multi-scale representation, we transform the high-resolution training image into a pyramid of consecutively up-gridded views of the same image. The pyramid allows for rapid search of the patterns that can be superimposed over a shared overlap area with previously simulated patterns. A second advantage of the multi-scale view lies in data conditioning by means of a new hard data-relocation algorithm and the use of a co-template for looking for conditioning points ahead of the raster path employed in CCSIM. Using synthetic and real-field multi-million cell examples with sparse, as well as dense datasets, we investigate quantitatively how the improved algorithm performs with respect to CCSIM, as well as the traditional MP simulation algorithms. Computational improvement to pattern simulation using multi-scale search.Improved conditioning in raster-path methods using co-template.Multi-million cell real field application in seconds.

Accelerating geostatistical simulations using graphics processing units (GPU)

Geostatistical simulations have become a widely used tool for modeling of oil and gas reservoirs and the assessment of uncertainty. One important current issue is the development of high-resolution models in a reasonable computational time. A possible solution is based on taking advantage of parallel computational strategies. In this paper we present a new methodology that exploits the benefits of graphics processing units (GPUs) along with the master-slave architecture for geostatistical simulations that are based on random paths. The methodology is a hybrid method in which different levels of master and slave processors are used to distribute the computational grid points and to maximize the use of multiple processors utilized in GPU. It avoids conflicts between concurrently simulated grid points, an important issue in high-resolution and efficient simulations. For the sake of comparison, two distinct parallelization methods are implemented, one of which is specific to pattern-based simulations. To illustrate the efficiency of the method, the algorithm for the simulation of pattern is adapted with the GPU. Performance tests are carried out with three large grid sizes. The results are compared with those obtained based on simulations with central processing units (CPU). The comparison indicates that the use of GPUs reduces the computation time by a factor of 26-85.

Simulation of Earth textures by conditional image quilting

Training image-based approaches for stochastic simulations have recently gained attention in surface and subsurface hydrology. This family of methods allows the creation of multiple realizations of a study domain, with a spatial continuity based on a training image (TI) that contains the variability, connectivity, and structural properties deemed realistic. A major drawback of these methods is their computational and/or memory cost, making certain applications challenging. It was found that similar methods, also based on training images or exemplars, have been proposed in computer graphics. One such method, image quilting (IQ), is introduced in this paper and adapted for hydrogeological applications. The main difficulty is that Image Quilting was originally not designed to produce conditional simulations and was restricted to 2-D images. In this paper, the original method developed in computer graphics has been modified to accommodate conditioning data and 3-D problems. This new conditional image quilting method (CIQ) is patch based, does not require constructing a pattern databases, and can be used with both categorical and continuous training images. The main concept is to optimally cut the patches such that they overlap with minimum discontinuity. The optimal cut is determined using a dynamic programming algorithm. Conditioning is accomplished by prior selection of patches that are compatible with the conditioning data. The performance of CIQ is tested for a variety of hydrogeological test cases. The results, when compared with previous multiple-point statistics (MPS) methods, indicate an improvement in CPU time by a factor of at least 50.

Three-Dimensional Stochastic Characterization of Shale SEM Images

Complexity in shale-gas reservoirs lies in the presence of multiscale networks of pores that vary from nanometer to micrometer scale. Scanning electron microscope (SEM) and atomic force microscope imaging are promising tools for a better understanding of such complex microstructures. Obtaining 3D shale images using focused ion beam-SEM for accurate reservoir forecasting and petrophysical assessment is not, however, currently economically feasible. On the other hand, high-quality 2D shale images are widely available. In this paper, a new method based on higher-order statistics of a porous medium (as opposed to the traditional two-point statistics) is proposed in which a single 2D image of a shale sample is used to reconstruct stochastically equiprobable 3D models of the sample. Because some pores may remain undetected in the SEM images, data from other sources, such as the pore-size distribution obtained from nitrogen adsorption data, are integrated with the overall pore network using an object-based technique. The method benefits from a recent algorithm, the cross- correlation-based simulation, by which high-quality, unconditional/conditional realizations of a given sample porous medium are produced. To improve the ultimate 3D model, a novel iterative algorithm is proposed that refines the quality of the realizations significantly. Furthermore, a new histogram matching, which deals with multimodal continuous properties in shale samples, is also proposed. Finally, quantitative comparison is made by computing various statistical and petrophysical properties for the original samples, as well as the reconstructed model.

Multiscale and multiresolution modeling of shales and their flow and morphological properties

The need for more accessible energy resources makes shale formations increasingly important. Characterization of such low-permeability formations is complicated, due to the presence of multiscale features, and defies conventional methods. High-quality 3D imaging may be an ultimate solution for revealing the complexities of such porous media, but acquiring them is costly and time consuming. High-quality 2D images, on the other hand, are widely available. A novel three-step, multiscale, multiresolution reconstruction method is presented that directly uses 2D images in order to develop 3D models of shales. It uses a high-resolution 2D image representing the small-scale features to reproduce the nanopores and their network, a large scale, low-resolution 2D image to create the larger-scale characteristics, and generates stochastic realizations of the porous formation. The method is used to develop a model for a shale system for which the full 3D image is available and its properties can be computed. The predictions of the reconstructed models are in excellent agreement with the data. The method is, however, quite general and can be used for reconstructing models of other important heterogeneous materials and media. Two biological examples and from materials science are also reconstructed to demonstrate the generality of the method.

Enhancing multiple‐point geostatistical modeling: 2. Iterative simulation and multiple distance function

This series addresses a fundamental issue in multiple-point statistical (MPS) simulation for generation of realizations of large-scale porous media. Past methods suffer from the fact that they generate discontinuities and patchiness in the realizations that, in turn, affect their flow and transport properties. Part I of this series addressed certain aspects of this fundamental issue, and proposed two ways of improving of one such MPS method, namely, the cross correlation-based simulation (CCSIM) method that was proposed by the authors. In the present paper, a new algorithm is proposed to further improve the quality of the realizations. The method utilizes the realizations generated by the algorithm introduced in Part I, iteratively removes any possible remaining discontinuities in them, and addresses the problem with honoring hard (quantitative) data, using an error map. The map represents the differences between the patterns in the training image (TI) and the current iteration of a realization. The resulting iterative CCSIM—the iCCSIM algorithm—utilizes a random path and the error map to identify the locations in the current realization in the iteration process that need further “repairing;” that is, those locations at which discontinuities may still exist. The computational time of the new iterative algorithm is considerably lower than one in which every cell of the simulation grid is visited in order to repair the discontinuities. Furthermore, several efficient distance functions are introduced by which one extracts effectively key information from the TIs. To increase the quality of the realizations and extracting the maximum amount of information from the TIs, the distance functions can be used simultaneously. The performance of the iCCSIM algorithm is studied using very complex 2-D and 3-D examples, including those that are process-based. Comparison is made between the quality and accuracy of the results with those generated by the original CCSIM algorithm, which demonstrates the superior performance of the iCCSIM.

Enhancing multiple‐point geostatistical modeling: 1. Graph theory and pattern adjustment

In recent years, higher-order geostatistical methods have been used for modeling of a wide variety of large-scale porous media, such as groundwater aquifers and oil reservoirs. Their popularity stems from their ability to account for qualitative data and the great flexibility that they offer for conditioning the models to hard (quantitative) data, which endow them with the capability for generating realistic realizations of porous formations with very complex channels, as well as features that are mainly a barrier to fluid flow. One group of such models consists of pattern-based methods that use a set of data points for generating stochastic realizations by which the large-scale structure and highly-connected features are reproduced accurately. The cross correlation-based simulation (CCSIM) algorithm, proposed previously by the authors, is a member of this group that has been shown to be capable of simulating multimillion cell models in a matter of a few CPU seconds. The method is, however, sensitive to patterns specifications, such as boundaries and the number of replicates. In this paper the original CCSIM algorithm is reconsidered and two significant improvements are proposed for accurately reproducing large-scale patterns of heterogeneities in porous media. First, an effective boundary-correction method based on the graph theory is presented by which one identifies the optimal cutting path/surface for removing the patchiness and discontinuities in the realization of a porous medium. Next, a new pattern adjustment method is proposed that automatically transfers the features in a pattern to one that seamlessly matches the surrounding patterns. The original CCSIM algorithm is then combined with the two methods and is tested using various complex two- and three-dimensional examples. It should, however, be emphasized that the methods that we propose in this paper are applicable to other pattern-based geostatistical simulation methods.

Geostatistical Simulation and Reconstruction of Porous Media by a Cross-Correlation Function and Integration of Hard and Soft Data

A new method is proposed for geostatistical simulation and reconstruction of porous media by integrating hard (quantitative) and soft (qualitative) data with a newly developed method of reconstruction. The reconstruction method is based on a cross-correlation function that we recently proposed and contains global multiple-point information about the porous medium under study, which is referred to cross-correlation-based simulation (CCSIM). The porous medium to be reconstructed is represented by a reference image (RI). Some of the information contained in the RI is represented by a training image (TI). In unconditional simulation, only the TI is used to reconstruct the RI, without honoring any particular data. If some soft data, such as a seismic image, and hard data are also available, they are integrated with the TI and conditional CCSIM method in order to reconstruct the RI, by honoring the hard data exactly. To illustrate the method, several two- and three-dimensional porous media are simulated and reconstructed, and the results are compared with those provided by the RI, as well as those generated by the traditional two-point geostatistical simulation, namely the co-sequential Gaussian simulation. To quantify the accuracy of the simulations and reconstruction, several statistical properties of the porous media, such as their porosity distribution, variograms, and long-range connectivity, as well as two-phase flow of oil and water through them, are computed. Excellent agreement is demonstrated between the results computed with the simulated model and those obtained with the RI.