Single Normal Equation Simulation Research Articles

An integrated approach to lithofacies characterization of a sandstone reservoir using the Single Normal Simulation equation: A Case study

This paper describes a comprehensive approach to improved lithofacies characterization using the simultaneous pre-stack inversion, Bayesian classification, and multiple-point geostatistics. This integrated workflow provides an enhanced lithofacies characterization by reproducing the continuity of geological facies in the meandering-fluvial sandstone reservoir from Upper Assam, India. The simultaneous pre-stack inversion provides the rock elastic properties of the reservoir, such as P- impedance, s-impedance, density, and VP/VS ratio. Next, the probabilistic modeling approach of Baye's theorem is used to integrates seismic elastic properties with well log lithofacies identified from the cross-plot analysis for probability volumes of lithofacies. Finally, the multiple-point geostatistics based on the Single Normal equation Simulation algorithm is used to generate the improved lithofacies model by constraining of the lithofacies probability volumes (soft data) and well logging data (hard data). These results were compared with the Bayesian lithofacies classification and proved that the adopted method had successfully improved the continuation of the reservoir lithofacies by reproducing the lithofacies, hence an improvement in the reservoir characterization.

Seismic Lithofacies Distribution Modeling Using the Single Normal Equation Simulation (SNESIM) Algorithm of Multiple-Point Geostatistics in Upper Assam Basin, India

Recently, multiple-point geostatistical simulation gained much attention for its role in spatial reservoir characterization/modeling in geosciences. Accurate lithofacies modeling is a critical step in the characterization of complex geological reservoirs. In this study, multiple-point facies geostatistics based on the SNESIM algorithm integrated with the seismic modeling technique is used as an efficient reservoir modeling approach for lithofacies modeling of the fluvial Tipam formation in the Upper Assam Basin, India. The Tipam formation acts as a potential reservoir rock in the Upper Assam Basin, India. Due to the basin geological complexity and limitation in seismic resolution, many discontinuities in depositional channels in this fluvial depositional environment have been identified using conventional lithofacies mapping. This study combines three techniques to reproduce continuity of the lithofacies for better reservoir modeling. The first is simultaneous prestack inversion for inverting prestack gathers with angle-dependent wavelets into seismic attributes. A cross-plot of P-impedance and VP/VS ratio from well-log data was used to classify the different reservoir lithofacies such as hydrocarbon sand, brine sand, and shale. The second is the Bayesian approach that incorporates probability density functions (PDFs) of non -parametric statistical classification with seismic attributes for converting the seismic attributes into lithofacies volume and the probability volumes of each type lithofacies. The third technique is multiple-point geostatistical simulation (MPS) using the Single Normal equation Simulation (SNESIM) algorithm applied to training images and probability volumes as constraints for a better lithofacies model. These integrated study results proved that MPS could improve reservoir lithofacies characterization.

Model Selection for Mineral Resource Assessment Considering Geological and Grade Uncertainties: Application of Multiple-Point Geostatistics and a Cluster Analysis to an Iron Deposit

The assessment of mineral resources requires the definition of a geological domain, and the quantitative results obtained should consider geological and grade uncertainties. However, when the available data are limited, it can be difficult to estimate the shape of an ore body owing to the spatial uncertainty. This study describes a methodology for defining geological domains using multiple-point geostatistics and selecting models for realizations using a cluster analysis. Then, the selected realizations were assessed for mineral resources using two-point geostatistics. Of the various multiple-point geostatistics algorithms, the single normal equation simulation was used to generate a realistic ore body, and various cluster algorithms, such as k-means and a density-based spatial clustering of applications with noise, were applied to select a model. Based on the outcomes, a mineral resource assessment that uses a sequential Gaussian simulation was performed, and a reasonable model that reflects the original data well was selected based on the grade statistics of the original data and mineral resource assessment per cluster. This study demonstrates that it is possible to define the ore domain and assess mineral resources while accounting for the uncertainty caused by a lack of spatial information.

Multiple-Point Statistical Simulation of rock fracture network as a key control on the hydrogeology and salinity: a case study from the Qarabagh area, West Azarbayjan Province, Iran

Modeling and characterization of the geometry and distribution of Rock Facture Networks (RFNs) are essential in applications such as hydrogeological or environmental evaluations. It is widely accepted that RFNs are potentially associated with the hydrogeological (thus salinity) characteristics of the surrounding environments. Despite the complexity and inaccessibility of RFNs, stochastic methods provide a functional framework to predict their characteristics in the subsurface. An efficient tool for modeling RFNs is the Discrete Fracture Network (DFN) which also includes a number of geostatistical techniques that consider spatial variability structure. The advantages of these techniques are: realistic results, ease of application, and uncertainty assessments. Multiple-point geostatistics/statistics (MPS) is a modern and effective geostatistical tool for realistically simulating RFNs. In the present study, we modeled the RFNs in a location near the Qarabagh area, in the western Urmia Lake; in this regard, we used the Single Normal Equation Simulation (SNESIM) algorithm of the MPS geostatistical method using Training Images (TIs) instead of variograms. The required datasets and information for this modeling was provided using the field measurements of the fracture orientations and dips, as well as the outcrop photographs. The outcomes of these models can be used in predicting the salinity distribution in the surrounding area . Therefore, through the SNESIM algorithm, TIs obtained from the outcrop photographs, and direct measurements, 100 RFN realizations were generated at each station. These realizations were then averaged to predict the locations with higher and lower fracture probabilities and to assess the general trend of the fracture distributions.

Indicator-based data assimilation with multiple-point statistics for updating an ensemble of models with non-Gaussian parameter distributions

Ground-water flow and the transport of contaminants in groundwater systems are strongly controlled by geologic heterogeneities. Because, the data available to model these subsurface heterogeneities are generally sparse, the observed groundwater flow, piezometric head at well locations, or the concentration profile of solutes provide valuable additional information about these complex subsurface systems. Regardless, there is likely to be considerable uncertainty associated with the predictions of the subsurface heterogeneities. This has motivated the development of several ensemble-based schemes for assimilating flow response data into predictions of subsurface heterogeneities. Most ensemble-based data assimilation methods including ensemble Kalman filter (EnKF) or indicator-based data assimilation (InDA), used for assimilation of dynamic data into geologic models, utilize statistics in the form of covariances calculated using the ensemble of models to perform model updates. These covariance based updates do not preserve the complex spatial characteristics of geologic structures that are better represented using multiple-point statistics. Additionally, in EnKF, the mismatch between the observed and the simulated values are assumed to be linearly related to the parameter updates, and the distribution of the state variable is assumed to be multi-Gaussian. The spatial distribution of the primary variables like facies can be non-Gaussian because of the spatial continuity exhibited by channel facies (sands) and non-channel facies (clay), that have distinctly different properties. Also, the relationship between the mismatch and the parameter updates can be strongly non-linear. In indicator-based data assimilation (InDA) method the indicator transforms of parameter and mismatch variables are used, which affords the treatment of these variables as bi-variate non-Gaussian. Furthermore, in the indicator transformed space, restrictive linear assumption can also be lifted as the indicator transform is invariant under non-linear transformations. However, the updates are still governed by the bivariate interactions between the state variables. A multiple-point extension of InDA is proposed in this paper which utilizes existing multiple-point simulation algorithms like single normal equation simulation (SNESIM) in combination with InDA, to preserve the spatial characteristics of the geologic model while at the same time honor the observed flow or transport response. The proposed method is applied to a synthetic groundwater system with complex channel distributions. The channel features of the final updated ensemble of models is shown to converge towards the reference model and the ensemble flow responses are also shown to match the reference flow response.

An Optimum Selection of Simulated Geological Models by Multi-Point Geostatistics and Multi-Criteria Decision-Making Approaches; a Case Study in Sungun Porphyry-Cu deposit, Iran

An accurate modeling of sophisticated geological units has a substantial impact on designing a mine extraction plan. Geostatistical simulation approaches, via defining a variogram model or incorporating a training image (TI), can tackle the construction of various geological units when a sparse pattern of drilling is available. The variogram-based techniques (derived from two-point geostatistics) usually suffer from reproducing complex and non-linear geological units as dyke. However, multipoint geostatistics (MPS) resolves this issue by incorporating a training image from a prior geological information. This work deals with the multi-step Single Normal Equation Simulation (SNESIM) algorithm of dyke structures in the Sungun Porphyry-Cu system, NW Iran. In order to perform a multi-step SNESIM algorithm, the multi-criteria decision-making and MPS approaches are used in a combined form. To this end, two TIs are considered, one for simulating dyke structures in the shallow depth, and two for simulating dyke structures in a deeper depth. In the first step, a TI is produced using geological map, which has been mined out during the previous exploration operations. After producing TI, the 35 realizations are simulated for the shallow depth of deposit in the area under study. To select the best realization (as a TI for the next step) of the simulation results, several statistical criteria are used and the results obtained are compared. To this end, a hybrid multi-criteria decision-making is designed on the basis of a group of statistical criteria. In the next step, the dyke structures in the deeper depth are also simulated by the new TI.

Application of geostatistics in facies modeling of Reservoir-E, \u201cHatch Field\u201d offshore Niger Delta Basin, Nigeria

Lithofacies are very influential in the transmission of fluids within the reservoir. The objective of this study is to use geostatistical techniques of sequential indicator simulation (SISIM) a variogram-based algorithm (VBA), single normal equation simulation (SNESIM) and filter-based simulation (FILTERSIM) of multiple-point geostatistics (MPG) in developing realistic facies model. A reservoir sand package “Reservoir-E” was correlated across five wells in the field. Synthetic seismogram of well HT-1 was generated, and Horizon E picked on seismic section to produce time and depth surfaces of the reservoir. The conditional if statement to generate lithofacies was applied on the extracted volume of shale data within “Reservoir-E,” and the data were inputted in Stanford Geostatistics Modeling Software for facies modeling. The first realization from SISIM was converted to a training image used for MPG. Visually, the MPG algorithm of SNESIM and FILTERSIM produced realization that is substantially better and more realistic than the VBA of SISIM. The magnitude of correlation coefficients of algorithms was carried out using the mean and variance of realizations, the results revealed mean and variance magnitude of correlation coefficients between SISIM and SNESIM with 0.8933 and 0.9637, SISIM and FILTERSIM with 0.8639 and 0.5097 and SNESIM and FILTERSIM with 0.9717 and 0.8603. The results revealed a very good mean and variance magnitude of correlation coefficients between SISIM and SNESIM; good between SISIM and FILTERSIM; and very good mean and variance correlation coefficient between SNESIM and FILTERSIM. The qualitative interpretation of the model built with SNESIM and FILTERSIM clearly detects lithofacies in the field which makes them a better algorithm in facies modeling.

Assessing Multiple-Point Statistical Facies Simulation Behavior for Effective Conditioning on Probabilistic Data

Conditioning multiple-point statistical (MPS) facies simulation on dynamic flow data is complicated by the complex relation between flow responses and facies distribution. One way to incorporate feedback from the flow data into MPS simulation is by constructing (and updating) facies probability maps (soft data) and using the results to constrain the MPS simulation outputs, for example, through Single Normal Equation SIMulation (SNESIM) algorithm and the $$ \tau $$-model. The pattern-imitating behavior of MPS simulation (specifically, the SNESIM) has been shown to result in a sizable fraction of facies models that fail to effectively capture the correct location and spatial connectivity represented by the facies probability map. This paper presents two key observations that explains this behavior/outcome: (1) the facies patterns resulting from the SNESIM are primarily controlled by the outcome of the first few grid cells along the corresponding random path (early stages of the simulation); and (2) the facies outcomes in the remaining grid cells are dominated by extremely confident conditional probabilities extracted from the TI to generate the encoded connectivity patterns in the TI. Hence, the contribution of facies probability map become increasingly inconsequential as the simulation proceeds. This intrinsic property must be accounted for in developing data conditioning methods, especially when training images with large-scale connectivity patterns are considered. Two approaches for addressing this issue include adapting the random path at early stages to the key information in the probability map to properly reflect its impact, or treating high-probability events from the probability map as hard data. Examples are presented to illustrate this behavior, followed by a simple method to improve the effectiveness of integrating facies probability maps (and flow response data) into SNESIM.

Integration of soft data into multiple-point statistical simulation: re-assessing the probability conditioning method for facies model calibration

Conditioning multiple-point statistical (MPS) facies simulation on dynamic flow data is complicated by the complex relationship between discrete facies distribution and the flow response data. The process can be facilitated by using the probability conditioned method (PCM), in which an ensemble-based data assimilation approach is used to infer, from observed flow data, a facies probability map that can guide conditional simulation from a training image (TI). We discuss important aspects of flow model calibration based on facies probability maps and propose several improvements to the original PCM, including: (1) using a statistically consistent approach for inferring facies probability maps from updated ensemble of continuous hydraulic properties; (2) assigning spatially variable weights to simulation grids based on relative confidence in the information content of observed data; and (3) considering spatial patterns instead of marginal facies probabilities in constructing probability maps. We illustrate that, in simulating categorical facies, the pattern-imitating behavior of MPS can have a significant impact on soft data conditioning. In particular, in the Single Normal Equation SIMulation (SNESIM) algorithm, the initial points that are visited on the random path tend to determine the main global facies connectivity. Once these initial points are populated with simulated values, the conditional probabilities (inferred from the TI) for the subsequent cells on the random path tend to be very close to 0 and 1. Hence, the facies types in the remaining cells are known almost deterministically, making the soft data inconsequential at the later stages of simulation. This behavior suggests that, without compensating for this effect, the facies probability map is not effectively integrated into the SNESIM simulation, an issue that is reflected in the generated realizations. Several numerical experiments are presented and discussed to illustrate this behavior and its impact on soft-data conditioning.

Nonparametric Geostatistical Simulation of Subsurface Facies: Tools for Validating the Reproduction of, and Uncertainty in, Facies Geometry

Delineation of facies in the subsurface and quantification of uncertainty in their boundaries are significant steps in mineral resource evaluation and reservoir modeling, which impact downstream analyses of a mining or petroleum project. This paper investigates the ability of nonparametric geostatistical simulation algorithms (sequential indicator, single normal equation and filter-based simulation) to construct realizations that reproduce some expected statistical and spatial features, namely facies proportions, boundary regularity, contact relationships and spatial correlation structure, as well as the expected fluctuations of these features across the realizations. The investigation is held through a synthetic case study and a real case study, in which a pluri-Gaussian model is considered as the reference for comparing the simulation results. Sequential indicator simulation and single normal equation simulation based on over-restricted neighborhood implementations yield the poorest results, followed by filter-based simulation, whereas single normal equation simulation with a large neighborhood implementation provides results that are closest to the reference pluri-Gaussian model. However, some biases and inaccurate fluctuations in the realization statistics (facies proportions, indicator direct and cross-variograms) still arise, which can be explained by the use of a single finite-size training image to construct the realizations.

Multiple-point geostatistical simulation for mine evaluation with aeromagnetic data

Multiple-point geostatistical simulation (MPS) was applied to develop 3D ore models matched to surrounding geological information accompanying aeromagnetic data using a training image (TI). Conventional 3D geological models generated from a limited number of boreholes and other geological information may be useful for evaluating the mineral resources around the boreholes, while also bearing uncertainty regarding the evaluation of the ore body over the entire area. Geostatistical analysis accompanying the geophysical interpretation is adopted to reduce the uncertainty of the 3D ore model. Among the geostatistical methods, MPS based on a TI made from available geological information is chosen to simulate the configuration and distribution of the ore body according to the geological structure. The present study proposes a method for reducing the uncertainty of the 3D ore model, applying MPS for mine evaluation to create probabilistic ore models and analysing the correlation between the models and geophysical data. This method was applied to a metal mine located in Korea. Single normal equation simulation (SNESIM) was chosen as the simulation algorithm, and aeromagnetic data were used to support the analysis of simulated models. With comparison/analysis of the probabilistic ore model and geophysical data, the 3D geological model utilising MPS represented the configuration and distribution of the ore body well according to the geological structure. The SNESIM cluster results indicated high reliability for the final interpretation of the 3D models.

Reconstruction of 3D porous media using multiple-point statistics based on a 3D training image

To date many methods of constructing porous media have been proposed. Among them, the multiple-point statistics (MPS) method has a unique advantage in reconstructing 3D pore space because it can reproduce pore space of long-range connectivity. The Single Normal Equation Simulation (SNESIM) is one of most commonly used algorithms of MPS. In the SNESIM algorithm, the selection of training image is vital because it contains the basic pore structure patterns. In the previous reconstructions of 3D porous media using SNESIM, a 2D slice was usually employed as the training image. However, it is difficult for a 2D slice to contain complex 3D pore space geometry and topology patterns. In this paper, a 3D training image is used in order to provide more realistic 3D pore structure features. Besides, a multi-grid search template is applied for the purpose of capturing the pore structures of different scales and speeding up the reconstruction process. Two sandstone cores are taken as test examples and the 3D porous media are reconstructed. The two-point correlation function, pore network structure parameters and absolute permeability are applied as the evaluation indexes to validate the accuracy of the reconstructed models. The comparison result shows that the reconstructed models are in good agreement with the real model obtained by X-ray computed tomography scanning in the pore throat geometry and topology and transport property, which justifies the reliability of the proposed method.

Assessing flow paths in a karst aquifer based on multiple dye tracing tests using stochastic simulation and the MODFLOW-CFP code

Karst systems show high spatial variability of hydraulic parameters over small distances and this makes their modeling a difficult task with several uncertainties. Interconnections of fractures have a major role on the transport of groundwater, but many of the stochastic methods in use do not have the capability to reproduce these complex structures. A methodology is presented for the quantification of tortuosity using the single normal equation simulation (SNESIM) algorithm and a groundwater flow model. A training image was produced based on the statistical parameters of fractures and then used in the simulation process. The SNESIM algorithm was used to generate 75 realizations of the four classes of fractures in a karst aquifer in Iran. The results from six dye tracing tests were used to assign hydraulic conductivity values to each class of fractures. In the next step, the MODFLOW-CFP and MODPATH codes were consecutively implemented to compute the groundwater flow paths. The 9,000 flow paths obtained from the MODPATH code were further analyzed to calculate the tortuosity factor. Finally, the hydraulic conductivity values calculated from the dye tracing experiments were refined using the actual flow paths of groundwater. The key outcomes of this research are: (1) a methodology for the quantification of tortuosity; (2) hydraulic conductivities, that are incorrectly estimated (biased low) with empirical equations that assume Darcian (laminar) flow with parallel rather than tortuous streamlines; and (3) an understanding of the scale-dependence and non-normal distributions of tortuosity.

Combining a connected-component labeling algorithm with FILTERSIM to simulate continuous discrete fracture networks

Because modeling the flow of gas and oil in fractured media is increasingly important, multipoint geostatistics approaches, such as single normal equation simulation and FILTERSIM, have become a focus of research in the simulation of sedimentary faces. However, there are problems when these methods are applied to the simulation of discrete fracture networks (DFNs). The biggest problem is that the generated fractures are discontinuous, behaving as separated and isolated points. This paper proposes an improved approach we call CCL-FILTERSIM, which combines FILTERSIM with a run-based, connected-component labeling algorithm to generate more continuous fractures. This paper focuses on the continuity of the simulated fracture network and adopts the scan of the training image, classification of the patterns, and the sequential simulation proposed by FILTERSIM. The principle innovation of the CCL-FILTERSIM approach is the choice of data pattern. Only patterns that form better continuous object patterns are chosen. This is realized by a connected-component labeling algorithm that calculates the connected runs of selected patterns and chooses the pattern with the least runs. Some cases are presented to compare realizations from CCL-FILTERSIM and FILTERSIM, which show that CCL-FILTERSIM yields more continuous objects than FILTERSIM. The DFNs generated by this method provide better conditions for subsequent fluid flow research.

Mixed‐point geostatistical simulation: A combination of two‐ and multiple‐point geostatistics

AbstractMultiple‐point‐based geostatistical methods are used to model complex geological structures. However, a training image containing the characteristic patterns of the Earth model has to be provided. If no training image is available, two‐point (i.e., covariance‐based) geostatistical methods are typically applied instead because these methods provide fewer constraints on the Earth model. This study is motivated by the case where 1‐D vertical training images are available through borehole logs, whereas little or no information about horizontal dependencies exists. This problem is solved by developing theory that makes it possible to combine information from multiple‐ and two‐point geostatistics for different directions, leading to a mixed‐point geostatistical model. An example of combining information from the multiple‐point‐based single normal equation simulation algorithm and two‐point‐based sequential indicator simulation algorithm is provided. The mixed‐point geostatistical model is used for conditional sequential simulation based on vertical training images from five borehole logs and a range parameter describing the horizontal dependencies.

Utilizing spatial association analysis to determine the number of multiple grids for multiple-point statistics

Scale selection is a fundamental issue of spatial analysis. Based on spatial association analysis, this paper proposes a quantitative method for estimating the scale, which is represented using the minimal number of multiple grids in a single normal equation simulation. First, the largest scale structural information that a data template can consider for the finest grid is computed using the distance between the central cell and the border of the data template. The maximum distance at which cells are associated with each other in the training image is then analyzed using join count statistics. Finally, the minimal number of multiple grids is estimated based on the criterion that the data template used on the largest grid should account for the maximum distance between associated cells. The proposed method is validated using two- and three-dimensional experiments. The results show that increasing the number of multiple grids does not significantly improve the simulation quality when the number of multiple grids used is larger than that estimated. A sensitivity analysis demonstrates that the proposed method adapts to the configuration of the data template, the geometric structure of the target surface objects, and a re-scaled training image if it adequately represents the large-scale structural information of the target surface objects.

Pattern density function for reconstruction of three-dimensional porous media from a single two-dimensional image.

Three-dimensional (3D) structures are useful for studying the spatial structures and physical properties of porous media. A 3D structure can be reconstructed from a single two-dimensional (2D) training image (TI) by using mathematical modeling methods. Among many reconstruction algorithms, an optimal-based algorithm was developed and has strong stability. However, this type of algorithm generally uses an autocorrelation function (which is unable to accurately describe the morphological features of porous media) as its objective function. This has negatively affected further research on porous media. To accurately reconstruct 3D porous media, a pattern density function is proposed in this paper, which is based on a random variable employed to characterize image patterns. In addition, the paper proposes an original optimal-based algorithm called the pattern density function simulation; this algorithm uses a pattern density function as its objective function, and adopts a multiple-grid system. Meanwhile, to address the key point of algorithm reconstruction speed, we propose the use of neighborhood statistics, the adjacent grid and reversed phase method, and a simplified temperature-controlled mechanism. The pattern density function is a high-order statistical function; thus, when all grids in the reconstruction results converge in the objective functions, the morphological features and statistical properties of the reconstruction results will be consistent with those of the TI. The experiments include 2D reconstruction using one artificial structure, and 3D reconstruction using battery materials and cores. Hierarchical simulated annealing and single normal equation simulation are employed as the comparison algorithms. The autocorrelation function, linear path function, and pore network model are used as the quantitative measures. Comprehensive tests show that 3D porous media can be reconstructed accurately from a single 2D training image by using the method proposed in this paper.

Stochastic simulation of the Fox kimberlitic diamond pipe, Ekati mine, Northwest Territories, Canada

$�=A5<B< Multiple-point simulation (MPS) methods have been developed over the last decade as a means of reproducing complex geological patterns while generating stochastic simulations. Some geological spatial configurations are complex, such as the spatial geometries and patterns of diamondbearing kimberlite pipes and their internal facies controlling diamond quality and distribution. Two MPS methods were tested for modelling the geology of a diamond pipe located at the Ekati mine, NT, Canada. These are the single normal equation simulation algorithm SNESIM, which captures different patterns from a training image (TI), and the filter simulation algorithm FILTERSIM, which classifies the patterns founded on the TI. Both methods were tested in the stochastic simulation of a four-category geology model: crater, diatreme, xenoliths, and host rock. Soft information about the location of host rock was also used. The validation of the simulation results shows a reasonable reproduction of the geometry and data proportions for all geological units considered; the validation of spatial statistics, however, shows that although simulated realizations from both methods reasonably reproduce the fourth-order spatial statistics of the TI, they do not reproduce well the same spatial statistics of the available data (when this differs from the TI). An interesting observation is that SNESIM better imitated the shape of the pipe, while FILTERSIM yielded a better reproduction of the xenolith bodies.

A Stochastic Algorithm for Generating Realistic Virtual Interstitial Cell of Cajal Networks.

Interstitial cells of Cajal (ICC) play a central role in coordinating normal gastrointestinal (GI) motility. Depletion of ICC numbers and network integrity contributes to major functional GI motility disorders. However, the mechanisms relating ICC structure to GI function and dysfunction remains unclear, partly because there is a lack of large-scale ICC network imaging data across a spectrum of depletion levels to guide models. Experimental imaging of these large-scale networks remains challenging because of technical constraints, and hence, we propose the generation of realistic virtual ICC networks in silico using the single normal equation simulation (SNESIM) algorithm. ICC network imaging data obtained from wild-type (normal) and 5-HT2B serotonin receptor knockout (depleted ICC) mice were used to inform the algorithm, and the virtual networks generated were assessed using ICC network structural metrics and biophysically-based computational modeling. When the virtual networks were compared to the original networks, there was less than 10% error for four out of five structural metrics and all four functional measures. The SNESIM algorithm was then modified to enable the generation of ICC networks across a spectrum of depletion levels, and as a proof-of-concept, virtual networks were successfully generated with a range of structural and functional properties. The SNESIM and modified SNESIM algorithms, therefore, offer an alternative strategy for obtaining the large-scale ICC network imaging data across a spectrum of depletion levels. These models can be applied to accurately inform the physiological consequences of ICC depletion.

GPU-accelerated 3D reconstruction of porous media using multiple-point statistics

It is very important for the study of predicting fluid transport properties or mechanisms of fluid flow in porous media that the characteristics of porous media can be extracted in relatively smaller scales and then are copied in a larger or even arbitrary region to reconstruct virtual 3D porous media that have similar structures with the real porous media. One of multiple-point statistics (MPS) method, the single normal equation simulation algorithm (SNESIM), has been widely used in reconstructing 3D porous media recently. However, owing to its large CPU cost and rigid memory demand, the application of SNESIM has been limited in some cases. To overcome this disadvantage, parallelization of SNESIM is performed on the compute unified device architecture (CUDA) kernels in the graphic processing unit (GPU) to reconstruct each node on simulation grids, combined with choosing the optimal size of data templates based on the entropy calculation towards the training image (TI) to acquire high-quality reconstruction with a low CPU cost; meanwhile, the integration of hard data and soft data is also included in the processing of CUDA kernels to improve the accuracy. Representative elementary volumes (REVs) for porosity, variogram, and entropy are analyzed to guarantee that the scale of observation is large enough and parameters of concern are constant. This parallel GPU-version 3D porous media reconstruction only requires relatively small size memory and benefits from the tremendous calculating power given by CUDA kernels to shorten the CPU time, showing its high efficiency for the reconstruction of porous media.