Multiple-point Geostatistical Research Articles

Multiple-point geostatistical simulation of dykes: application at Sungun porphyry copper system, Iran

Variogram-based methods are not capable of capturing high (>2) order statistics since the variogram measures the relationship between two points at a time only. Multiple-point geostatistics (MPS) has brought new insights into many geological modeling problems. The application of MPS methods has been well documented in realizing complex geological patterns. These methods have often been used in reservoir characterization since their advent in recent decades. The frequent non-linear behaviors of geologic continuity are not limited to reservoirs, but mineral deposits bear complicated formations in many cases. Relying on the power of MPS methods and considering the complexity of geological scenarios in mineral deposits, we have applied MPS in the modeling of mineral deposits. A training image (TI) is produced using geological data from upper horizons of a porphyry copper ore deposit which have been mined out during the previous mining operations. In this study, the SNESIM algorithm has been used. A number of realizations are produced using this multiple-point geostatistical method. Extensive validation steps are performed considering the TI as the reference model. These validations first show that the TI is representative for the domain under study and also illustrates some degrees of similarity between the TI and the realizations. Despite simplifications made to the problem, the application of MPS in mineral deposit modeling still faces many challenges.

Using Multiple-Point Geostatistics for Tracer Test Modeling in a Clay-Drape Environment with Spatially Variable Conductivity and Sorption Coefficient

This study investigates the effect of fine-scale clay drapes on tracer transport. A tracer test was performed in a sandbar deposit consisting of cross-bedded sandy units intercalated with many fine-scale clay drapes. The heterogeneous spatial distribution of the clay drapes causes a spatially variable hydraulic conductivity and sorption coefficient. A fluorescent tracer (sodium naphthionate) was injected in two injection wells and ground water was sampled and analyzed from five pumping wells. To determine (1) whether the fine-scale clay drapes have a significant effect on the measured concentrations and (2) whether application of multiple-point geostatistics can improve interpretation of tracer tests in media with complex geological heterogeneity, this tracer test is analyzed with a local three-dimensional ground-water flow and transport model in which fine-scale sedimentary heterogeneity is modeled using multiple-point geostatistics. To reduce memory needs and calculation time for the multiple-point geostatistical simulation step, this study uses the technique of direct multiple-point geostatistical simulation of edge properties. Instead of simulating pixel values, model cell edge properties indicating the presence of irregularly shaped surfaces are simulated using multiple-point geostatistical simulations. Results of a sensitivity analysis show under which conditions clay drapes have a significant effect on the concentration distribution. Calibration of the model against measured concentrations from the tracer tests reduces the uncertainty on the clay-drape parameters. The calibrated model shows which features of the breakthrough curves can be attributed to the geological heterogeneity of the aquifer and which features are caused by other processes.

Multiple-point geostatistical simulation for post-processing a remotely sensed land cover classification

A post-processing method for increasing the accuracy of a remote sensing classification was developed and tested based on the theory of multiple-point geostatistics. Training images are used to characterise the joint variability and joint continuity of a target spatial pattern, overcoming the limitations of two-point statistical models. Conditional multiple-point simulation (MPS) was applied to a land cover classification derived from a remotely sensed image. Training data were provided in the form of “hard” (land cover labels), and “soft” constraints (class probability surfaces estimated using soft classification). The MPS post-processing method was compared to two alternatives: traditional spatial filtering (also a post-processing method) and the contextual Markov random field (MRF) classifier. The MPS approach increased the accuracy of classification relative to these alternatives, primarily as a result of increasing the accuracy of classification for curvilinear classes. Key advantages of the MPS approach are that, unlike spatial filtering and the MRF classifier, (i) it incorporates a rich model of spatial correlation in the process of smoothing the spectral classification and (ii) it has the advantage of capturing and utilising class-specific spatial training patterns, for example, classes with curvilinear distributions.

Alternative geostatistics tools applied to Morroa aquifer modeling (Sucre-Colombia)

In this paper, stochastic simulations and some multiple-point geostatistical principles are developed using a comparative methodology consisting of two phases. First, a traditional methodology based on variogram concepts called Conditional Stochastic Simulation (CSS) and more specifically the Sequential Indicator Simulation (SISIM) is applied to the aquifer modeling. Secondly, modern algorithm based on multiple-point geostatistics called SNESIM [1] and ζ Model [4] are implemented to integrate information available in the definition of Morroa aquifer facies. The simulations are realized by using algorithms constructed in references [1, 2] and S-Gems software prepared at Stanford University[3]. Results show the convenience of employing training images with soft and hard data conditioning integrated by ζ Model, and CSS for configuring hydrogeological models when barely deficient information is available.

Multiple-point geostatistical simulation using the bunch-pasting direct sampling method

Multiple-point geostatistics has opened a new field of methodologies by which complex geological phenomena have been modeled efficiently. In this study, a modified form of direct sampling (DS) method is introduced which not only keeps the strength of DS simulation technique but also speeds it up by one or two orders of magnitude. While previous methods are based on pasting only one point at a time, here the simulation is done by pasting a bunch of nodes at a time, effectively combining the flexibility of DS with the computational advantages of patch-based methods. This bears the potential of significantly speeding up the DS method. The proposed simulation method can be used with unilateral or random simulation paths. No overlap occurs in the simulation procedure because the bunch takes the shape of the empty space around the simulated nodes. Systematic tests are carried on different training images including both categorical and continuous variables, showing that the realizations preserve the patterns existent in the training image. To illustrate the method, a Matlab implementation of the method is attached to the paper.

Modeling the effect of clay drapes on pumping test response in a cross-bedded aquifer using multiple-point geostatistics

Summary This study investigates whether fine-scale clay drapes can cause an anisotropic pumping test response at a much larger scale. A pumping test was performed in a sandbar deposit consisting of cross-bedded units composed of materials with different grain sizes and hydraulic conductivities. The measured drawdown values in the different observation wells reveal an anisotropic or elliptically-shaped pumping cone. The major axis of the pumping ellipse is parallel with the strike of cm to m-scale clay drapes that are observed in several outcrops. To determine (1) whether this large-scale anisotropy can be the result of fine-scale clay drapes and (2) whether application of multiple-point geostatistics can improve interpretation of pumping tests, this pumping test is analyzed with a local 3D groundwater model in which fine-scale sedimentary heterogeneity is modelled using multiple-point geostatistics. To reduce CPU and RAM demand of the multiple-point geostatistical simulation step, edge properties indicating the presence of irregularly-shaped surfaces are directly simulated. Results show that the anisotropic pumping cone can be attributed to the presence of the clay drapes. Incorporating fine-scale clay drapes results in a better fit between observed and calculated drawdowns. These results thus show that fine-scale clay drapes can cause an anisotropic pumping test response at a much larger scale and that the combined approach of multiple-point geostatistics and cell edge properties is an efficient method for integrating fine-scale features in larger scale models.

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.

Direct Multiple-Point Geostatistical Simulation of Edge Properties for Modeling Thin Irregularly Shaped Surfaces

Thin, irregularly shaped surfaces such as clay drapes often have a major control on flow and transport in heterogeneous porous media. Clay drapes are often complex, curvilinear three-dimensional surfaces and display a very complex spatial distribution. Variogram-based stochastic approaches are also often not able to describe the spatial distribution of clay drapes since complex, curvilinear, continuous, and interconnected structures cannot be characterized using only two-point statistics. Multiple-point geostatistics aims to overcome the limitations of the variogram. The premise of multiple-point geostatistics is to move beyond two-point correlations between variables and to obtain (cross) correlation moments at three or more locations at a time using training images to characterize the patterns of geological heterogeneity. Multiple-point geostatistics can reproduce thin irregularly shaped surfaces such as clay drapes, but this is often computationally very intensive. This paper describes and applies a methodology to simulate thin, irregularly shaped surfaces with a smaller CPU and RAM demand than the conventional multiple-point statistical methods. The proposed method uses edge properties for indicating the presence of thin irregularly shaped surfaces. Instead of pixel values, edge properties indicating the presence of irregularly shaped surfaces are simulated using snesim. This method allows direct simulation of edge properties instead of pixel properties to make it possible to perform multiple-point geostatistical simulations with a larger cell size and thus a smaller computation time and memory demand. This method is particularly valuable for three-dimensional applications of multiple-point geostatistics.

Adapting a texture synthesis algorithm for conditional multiple point geostatistical simulation

Computer vision provides several tools for analyzing and simulating textures. The principles of these techniques are similar to those in multiple-point geostatistics, namely, the reproduction of patterns and consistency in the results from a perceptual point of view, thus, ensuring the reproduction of long range connectivity. The only difference between these techniques and geostatistical simulation accounting for multiple-point statistics is that conditioning is not an issue in computer vision. We present a solution to the problem of conditioning simulated fields while simultaneously honoring multiple-point (pattern) statistics. The proposal is based on a texture synthesis algorithm where a fixed search (causal) pattern is used. Conditioning is achieved by adding a non-causal search neighborhood that modifies the conditional distribution from which the simulated category is drawn, depending on the conditioning information. Results show an excellent reproduction of the features from the training image, while respecting the conditioning information. Some issues related to the data structure and to the computer efficiency are discussed.

History Matching Under Training-Image-Based Geological Model Constraints

SummaryHistory matching forms an integral part of the reservoir modeling workflow process. Despite the existence of many history-matching tools, the integration of production data with seismic and geological continuity data remains a challenge. Geostatistical tools now are routinely employed for integrating large-scale seismic and fine-scale well/core data. A general framework for integrating production data with diverse types of geological/structural data is largely lacking. In this paper, we develop a new method for history matching that can account for production data constraint by prior geological data, such as the presence of channels, fractures, or shale lenses. With multiple-point (MP) geostatistics, prior information about geological patterns is carried by training images from which geological structures are borrowed, then anchored to the subsurface data. A simple Markov chain is proposed to iteratively modify the MP geostatistical realizations until history match. The method is simple and general in the sense that the procedure can be applied to a wide variety of geological environments without requiring a modification of the algorithm. The method does not make assumptions on the flow model. Synthetic cases are used to assess the flexibility of the proposed method.