Sequential Gaussian Simulation Method Research Articles

Facies architectural analysis and three-dimensional modeling of Wen79 fault block, Wenliu oilfield, Dongpu depression, China

Wenliu oilfield is one of those typically structural reservoirs in Dongpu depression in China. Wen79 fault block is located in the south of Wenliu oilfield. Nowadays, it has entered the secondary oil recovery stage with a high water cut. Accumulated repository from long-term exploration and production makes the opportunity to fulfill a fine description of Wen79 fault block optimistic. Eight basic lithofacies types (Gt, St, Sp, Sl, Sh, Sr, Fl, Fm) were identified through core observation, and brief description and interpretation were given to each lithofacies. Assemblages of associated facies were arranged into four specified architectural elements (channel fill, proximal overbank, distal overbank, and shallow lake). For the purpose of quantified reservoir physical property characterization, a three-dimensional (3-D) architectural element model was firstly constructed by using the stochastic reservoir modeling technique, truncated Gaussian simulation (TGS). Subsequently, we used the sequential Gaussian simulation (SGS) method to capture probable distributions of reservoir porosity and permeability with the help of facies-controlled method. Meanwhile, non-facies-controlled physical property models were also built for a comparative study. Analysis of both kinds of models indicates that the facies-controlled physical property model is more reliable.

Uncertainty in estimation of coalbed methane resources by geological modelling

This paper presents an uncertainty analysis of coalbed methane resources estimation for a coal seam gas field containing multiple coal seams. Firstly, logs from nine wells and laboratory data from nine coal seams were used to predict the coal thickness, ash content and gas content at nine boreholes. Secondly, the structural models were determined using the well correlation, structural contour and coal seam thicknesses maps from coal mine data by the convergent gridder and sequential Gaussian simulation methods. Then, distributions of coal density and ash content were generated in 3D by using sequential Gaussian simulation based on the well log interpretations. Then, the distributions of gas content for each cell were built by two methods; one is multivariable regression analysis in 3D and the other is sequential Gaussian simulation based on the log interpreted gas content. Finally, coalbed methane resources were estimated based on the cell volume, coal density, net to gross ratio and gas content. In coalbed methane resources estimation, four different density cutoffs were used to define the net to gross ratio of coal in 3D. Results show that the gas contents decreases with increase in depth though with increases of vitrinite reflectance ratio, fixed carbon content and pressure. Calculated gas content from linear multivariate regression by using parameters of ash content, volatile matter content and fixed carbon content and sample's burial depth matches well with laboratory measured values. The total coalbed methane resources estimated are similar by the two geological modelling processes, the multivariable regression analysis in 3D and the sequential Gaussian simulation. It has been found that the effects of coal density cutoffs on coalbed methane resources for different coal seams are different.

Stochastic simulations of calcium contents in sugarcane area

<title>ABSTRACT</title><p>The aim of this study was to quantify and to map the spatial distribution and uncertainty of soil calcium (Ca) content in a sugarcane area by sequential Gaussian and simulated-annealing simulation methods. The study was conducted in the municipality of Guariba, northeast of the São Paulo state. A sampling grid with 206 points separated by a distance of 50 m was established, totaling approximately 42 ha. The calcium contents were evaluated in layer of 0-0.20 m. Techniques of geostatistical estimation, ordinary kriging and stochastic simulations were used. The technique of ordinary kriging does not reproduce satisfactorily the global statistics of the Ca contents. The use of simulation techniques allows reproducing the spatial variability pattern of Ca contents. The techniques of sequential Gaussian simulation and simulated annealing showed significant variations in the contents of Ca in the small scale.</p>

Geostatistical modeling for fine reservoir description of Wei2 block of Weicheng oilfield, Dongpu depression, China

The Wei2 block of Weicheng oilfield is characterized by complicated structure mainly caused by high degree of fault development. Multiple reservoir types are found in this block and the reservoir heterogeneity is severe. The oil and gas reservoirs have already stepped into the stagnant stage of a great water-cut degree together with a rapid production decline rate. Thereby, both stabilizing the oil and gas production and optimizing adjustment for further exploitation make it urgent for geomodelers to build a useful model to predict the inter-well parameters and the distribution of the remaining oil and gas. A three-dimensional geological model established with the help of stochastic modeling technique may provide a perfect window and carrier for fine structure interpretation and reservoir heterogeneity description, compared with a traditional two-dimensional model. Hence, based on stratigraphical layering points, significant surfaces and fault points as well seismic interpretation, an integrated structure model is developed. Using the truncated Gaussian simulation and taking the existing geological maps as references, the sedimentary microfacies model was successfully constructed. Through the use of sequential Gaussian simulation method and the facies-controlled modeling method, the reservoir physical properties are populated. Meanwhile, the comparison between facies-controlled and non-facies-controlled property models indicates that the former is more loyal to previous researching and the representation of heterogeneity is ideal. Finally, the ideas of sample density and reserves fitting are proposed to evaluate the practicability and accuracy of the property models.

Prediction of Essential Amount of Exploration Drilling in Primary Stage of Open Pit Mine Planning

Open pit Mine planning and initial production scheduling of open pit mine are considered as the complicated issues in mining engineering. The high capital investment in mining projects requires more accuracy in preparing base data. A reliable estimation of grade and tonnage of a mineral deposit has a considerable impact on the success of a mining project and initial capital cost prediction. These estimations depend on number of samplestaken from exploration drilling; therefore, it is necessary to determine the proper amount of drilling to reach rational confidence level of grade and tonnage estimation. In this paper, essential amount of drilling for reaching an acceptable confidence level of grade and tonnage estimation has been investigated. Regarding the feasibility, due to multiple sampling and numerous checks, the average mining grade of some declared tonnage is likely to be known within acceptable limits, say ±5%, and verified by standard statistical methods. For this condition, 5 different sampling grids were generated from the geological block model of Sungun copper mine. The grades of Sungun copper mine block model were considered as the actual grade of each block. Then the block model was re-estimatedconcerning different sampling grids. The Sequential Gaussian Simulation method was applied for re-estimating and considering the grade uncertainty of each block.

Improving the accuracy of geological model by using seismic forward and inverse techniques

Abstract Sequential Gaussian simulation method is taken as an example to analyze the characteristics and defects of stochastic simulation methods, and a modeling strategy is proposed that is based on the results of seismic inversion to improve modeling accuracy. Stochastic simulation can only achieve “mathematical reality” by recovery of parameter's macro statistical regularity through examples, and seismic forward model can verify whether the simulation results deviate from the “geological reality”. Seismic forward modeling can verify the reliability of the geological model, and the results of geological modeling constrained by seismic inversion can improve the accuracy of the model to achieve the “geological reality”. For braided river delta, a modeling strategy constrained by seismic inversion results in the condition of “multi-levels” and “multi-conditions” is put forward. For lithofacies modeling, division of lithofacies in single well acts as the first variable; in the stage of exploration and development, lithology probability and lithology body act as the second variable respectively, and then establish facies models. For property modeling, take lithofacies model and the seismic impedance as the first variable and the second variable respectively to create property model, in the condition of horizontal and vertical impedance constraints. The proposed modeling strategy maintains the statistical regularities of input data, keep a better consistency with seismic data, and match with dynamic field production.

Hydrograph Modeling Using SGSim: A Case Study of Behbahan Aquifer, Southwest of Iran

Hydrograph modeling and prediction of groundwater levels are the main concerns of most hydrogeological calculations and water resource management process. The present study is an application of Sequential Gaussian Simulation (SGSim) method for predicting groundwater levels using recorded monthly data (180 months) related to 21 piezometers of Behbahan aquifer, southwest of Iran. To generate realization maps through SGSim method, data were transferred to Gaussian distribution and then simulated 10 times for each month. Then, E_Type maps were produced to obtain hydrograph of interest. Finally, the iterative Box and Jenkins method was used to model the obtained hydrograph. The capability of the resulted ARIMA (0, 1, 1) model was examined by calculating coefficient of determination (R2) and estimated root mean squared error (RMSE). For the obtained model, R2 and RMSE were equal to 0.79 and 1.93, respectively. Drawing on the obtained hydrograph, it can be concluded that there is a significant decrease in groundwater level in the plain for upcoming months.

Sequential Gaussian Simulation in the Sungun Cu Porphyry Deposit and Comparing the Stationary Reproduction with Ordinary Kriging

Main aim of this study is stationary (first and second order) reproduction assessment of sequential Gaussian simulation (SGS) compared to ordinary kriging (OK) in the hypogene zone of the Sungun Cu porphyry deposit (NW Iran) based on drillcore data utilizing both SGS and OK. In comparison with OK, geostatistical stochastic simulations are able to assess spatial and uncertain distribution of desired variables. In simulation by SGS method, data were transferred to standard normal and then simulated 10 times (10 realizations were created in this scenario. All of the realizations were honor to histogram and variogram of samples, so all realizations are valid but derived cumulative distribution functions from E-type map and kriging could not reproduce the stationary well.

A geoestatística como ferramenta de estudo da batimetria na vertente continental portuguesa

GEOSTATISTICS AS A TOOL FOR THE STUDY OF BATHYMETRY ON THE PORTUGUESE CONTINENTAL SLOPE. The increasing interest on deep-water resources by the commercial fishing fleet during the last 20 years led the Fisheries Research National Institute (presently INIAP-IPIMAR) to conduct seafloor topography studies, which aimed the identification of potential fishing grounds for deep-water species in the Portuguese continental slope.The present study lies in the scope of the above topography studies. The spatial variability of the seafloor depth from a particular area of the Portuguese continental slope off Figueira da Foz with about 665 sq. m. was investigated. A geostatistical analysis comprising spatial continuity, several estimation methods and its uncertainty was conducted. The sequential gaussian simulation method was applied to evaluate estimation values uncertainty.Residual kriging yielded the lower estimation errors. The higher uncertainty observed in the estimation results obtained by Ordinary Kriging suggests that the geostatistic model to be adopted for the study area should be non-stationary. However its implementation is more straightforward since it has less requirements. Based on the estimation and simulation results two digital maps were constructed for the study area, one on the bathymetry and the other on the trawl fishing uncertainty.

Geologic heterogeneity recognition using discrete wavelet transformation for subsurface flow solute transport simulations

Subsurface flow and solute transport simulations are performed using different scenarios of permeability fields generated from the sequential Gaussian simulation method (SGS), the multiple-point FILTERSIM algorithm and a new multiple-point wavelet-based simulation method (SWS). The SWS method is a multiple-point pattern-based simulation method which uses discrete wavelet transformation for the representation of geologic heterogeneity. For pattern-based simulation, patterns are generated by scanning a training image with a spatial template. The pattern classifications were performed after reducing the dimension of patterns by wavelet decomposition at the suitable scale and by taking only scaling components of wavelet decomposed patterns. The simulation is performed in a sequential manner by finding the best-matched class corresponding to the conditioning data and by randomly sampling a pattern from the best-matched class. The developed method is compared with two other multi-point simulation algorithms, FLTERSIM and SIMPAT. The comparative results revealed that the proposed method is computationally faster than the other two methods while the simulation maps are comparable. Numerical simulations of two flow problems are performed using SGS, SWS and FILTERSIM realizations. The numerical results show a superiority of the SWS method over SGS and FILTERSIM in terms of reproduction of the reference images main features, and agreement with flow and transport results obtained on reference images.

Application of Facies-Controlled Modeling in Physical Property Modeling – A Case of Tuo 128 Block

The foundation and core of the phased modeling non-homogeneous modeling, Shengtuo oilfield geological modeling of the low porosity and permeability reservoir description of the characteristics of data is small, the accuracy is low, uncertainty factors. Using phased stochastic modeling techniques, log interpretation, based on data combined with core analysis, production performance and other known information, the sedimentary facies model as constraints holes, seepage property modeling to reduce the reservoir description is not uncertainty, combined with sequential Gaussian simulation method to establish a geological model of the actual production status of the oil region, the geological basis for the block rational development decisions and improve the effect of oilfield development.

철광산의 광체 평가를 위한 지구통계학적 복합 모델링

복합 물리탐사(전기비저항, MT)와 지질(시추 자료 및 코어 물성)정보에 대해 지구통계학적 복합해석 기법을 적용하여 3차원 광체 모델링 평가를 수행하였다. 우선, 복합 물리탐사를 통해 시추공 및 그 외의 전체적인 지역에 대한 비저항대 분포를 파악할 수 있었으며, 코어 물성 시험을 통해 연구지역의 자철석(광체)이 코어 내부의 밀도가 높은 전도성 성분(Fe)에 의해 밀도의 증가에 따라 비저항이 감소하는 상관관계를 나타냄을 파악하였다. 3차원 광체 모델링을 수행하기 위해 사용된 자료는 전기비저항 탐사, MT 탐사, 물성 자료와 시추 자료 등이며, 전체 획득 자료 및 시추 자료에서 추출한 광체의 품위 자료를 이용하였다. 본 연구에서는 자료의 복합 해석을 위해 지구통계학적 기법 중에서, 부족한 실제 측정 자료의 평균 및 분산을 잘 재생시키는 실현 값을 통해 지역적으로 변화하는 불균질성을 잘 묘사하는 순차 가우시안 시뮬레이션(sequential Gaussian simulation)을 사용하였다. 획득된 전체 자료와 품위 자료만을 이용하여 도출한 시뮬레이션 결과, 광체가 기존에 연구되어 존재하는 잔광체의 일정 부분에서 유사한 분포를 나타냈으며, 추가적으로 하부 깊은 심도에 대해 광체의 분포 양상을 추정할 수 있었다. Evaluation of three-dimensional ore body modeling has been performed by applying the geostatistical integration technique to multiple geophysical (electrical resistivity, MT) and geological (borehole data, physical properties of core) information. It was available to analyze the resistivity range in borehole and other area through multiple geophysical data. A correlation between resistivity and density from physical properties test of core was also analyzed. In the case study results, the resistivity value of ore body is decreased contrast to increase of the density, which seems to be related to a reason that the ore body (magnetite) includes heavy conductive component (Fe) in itself. Based on the lab test of physical properties in iron mine region, various geophysical, geological and borehole data were used to provide ore body modeling, that is electrical resistivity, MT, physical properties data, borehole data and grade data obtained from borehole data. Of the various geostatistical techniques for the integrated data analysis, in this study, the SGS (sequential Gaussian simulation) method was applied to describe the varying non-homogeneity depending on region through the realization that maintains the mean and variance. With the geostatistical simulation results of geophysical, geological and grade data, the location of residual ore body and ore body which is previously reported was confirmed. In addition, another highly probable region of iron ore bodies was estimated deeper depth in study area through integrated modeling.

Passive seismic velocity tomography and geostatistical simulation on longwall mining panel / Tomografia pasywna pola prędkości i symulacje geostatystyczne w obrębie pola ścianowego

Generally, the accurate determination of the stress in surrounding rock mass of underground mining area has an important role in stability and ground control. In this paper stress redistribution around the longwall face has been studied using passive seismic velocity tomography based on Simultaneous Iterative Reconstructive Technique (SIRT) and Sequential Gaussian Simulation (SGS). The mining-induced microseismic events are used as a passive source. Since such sources are used, the ray coverage is insufficient and in order to resolve this deficiency, the wave velocity is estimated in a denser network and by the SGS method. Consequently the three-dimensional images of wave velocity are created and sliced into the coal seam. To analyze the variations of stress around the panel during the study period, these images are interpreted. Results show that the state of stress redistribution around the longwall panel can be deduced from these velocity images. In addition, movements of the stressed zones, including front and side abutments and the goaf area, along the longwall face are evident. The applied approach illustrated in this paper can be used as a useful method to monitoring the stress changes around the longwall face continuously. This can have significant safety implications and contribute to improvements in operational productivity

Numerical Simulation of Natural Convection in Heterogeneous Porous media for CO2 Geological Storage

We report a modeling and numerical simulation study of density-driven natural convection during geological CO2 storage in heterogeneous formations. We consider an aquifer or depleted oilfield overlain by gaseous CO2, where the water density increases due to CO2 dissolution. The heterogeneity of the aquifer is represented by spatial variations of the permeability, generated using Sequential Gaussian Simulation method. The convective motion of the liquid with dissolved CO2 is investigated. Special attention is paid to instability characteristics of the CO2 concentration profiles, variation of mixing length, and average CO2 mass flux as a function of the heterogeneity characterized by the standard deviation and the correlation length of the log-normal permeability fields. The CO2 concentration profiles show different flow patterns of convective mixing such as gravity fingering, channeling, and dispersive based on the heterogeneity medium of the aquifer. The variation of mixing length with dimensionless time shows three separate regimes such as diffusion, convection, and second diffusion. The average CO2 mass flux at the top boundary decreases quickly at early times then it increases, reaching a constant value at later times for various heterogeneity parameters.

Stochastic modelling of coalbed methane resources: A case study in Southeast Qinshui Basin, China

This paper presents a stochastic analysis of coalbed methane (CBM) resources for a coal seam in southeast Qinshui Basin, China. Log and laboratory data are used to predict the coal thickness, coal ash content and coal gas content. Using reservoir modelling, the distributions of the karst collapse column (KCC), coal seam thickness, coal quality and coal gas content are generated. The convergent interpolation and sequential Gaussian simulation methods are used to model the surface and structure of the coal seam. The structural models are determined by the surface structure and coal seam thickness. Based on the structural models, the coal and KCC are converted to two facies and their distributions are obtained using object modelling. The coal density distributions are simulated based on each facies model using the sequential Gaussian simulation. Finally, different realisations are used to study CBM resources. The results show that the heterogeneities in coal seam thickness and coal quality lead to significant uncertainty in estimating CBM resources. A model with lower heterogeneity gives a greater CBM resource. The distributions of KCC, coal seam thickness, coal quality and gas content are the main sources for uncertainty in CBM resource estimation. The density variogram and top structure contribute less to the uncertainty in CBM resources.

Research on Characteristics and Three-Dimension Geologic Model Building of the Chang2 Reservoir, Yanchang Formation in Zhifang Area, Zhidan Oilfield

Through the reservoir of Chang 2 member in Zhifang area, Zhidan oilfield is typical of low porosity and low permeability reservoir rocks, using casting thin sections, scanning electron microscopy and physical analysis, etc., starting with the reservoir characteristics of Chang2 member, we have understood its causes and characteristics of low permeability. Using sequential indicator simulation and based on the target body method, we established the head of the construction of the reservoir model in Chang 2 member, using the sequential Gaussian simulation method combined with phase control principle, a model of reservoir properties in this area was established, Getting a high quality reservoir and field development and deployment of later development and further adjustments to tap the potential pratical guidance.

Knowledge Engineering Relating to Spatial Web Performance Forecasting with Sequential Gaussian Simulation Method.

Knowledge Engineering Relating to Spatial Web Performance Forecasting with Sequential Gaussian Simulation Method.

Tokat Kazova topraklarının yarayışlı fosfor düzeyinin jeoistatistik tahmin ve simulasyon metodlarıyla modellenmesi ve haritalanması

Determining and mapping the variability of soil properties ensures planning, effective and sustainable management, and monitoring spatial and temporal variability in agricultural areas. The objectives of this study were to model and map available P level of soils using two different geostatistical methods and to interpret differences of results of two methods. Ordinary kriging (OK) and Sequential Gaussian Simulation (SGS) methods were used in mapping. This study was carried out in the Kazova (20,656 ha), largest plain in Tokat and one of the prominent production area of Turkey. Eight hundred soil samples were collected in two depths (0-30 cm and 30-60 cm). Mean available phosphorus of study area were 14.18 mg kg-1 in surface soil and 8.87 mg kg-1 in subsurface soil. Based on maps prepared with ordinary kriging 11.56% of surface soils of Kazova contained low available P, 82.16% and 6.28% of soil had sufficient and excessive available P levels, respectively. Maps of SGS method (mean of 10 simulations) showed that 9.98% of surface soils of Kazova had low available P level. While 86.27% of the surface soil contained sufficient available P and 3.75% of soils was classified as excessive. For the subsoil of Kazova (30-60 cm), dissimilarities between two mapping methods were higher. Different level of available P and location of these levels in the maps prepared with these methods have a potential usage of decision-makers to plan amount of fertilizer and risk modeling.

Geologic heterogeneity representation using high‐order spatial cumulants for subsurface flow and transport simulations

The effects of geological heterogeneity representation on the hydraulic properties of two‐dimensional flow and transport simulations are studied using various stochastic simulation algorithms. An alternative multiple‐point method (HOSIM) on the basis of high‐order spatial cumulants and Legendre polynomials is used and compared to the multiple‐point FilterSIM method, and the sequential Gaussian simulation (SGS) method. Conditional realizations of a fluvial reservoir system are generated by HOSIM, FilterSIM, and SGS methods. Then, the simulated hydraulic permeability fields (K) are used in a numerical groundwater flow and solute transport models. Numerical results showed that the HOSIM method created greater connectivity in the reservoir/aquifer (channel) network than FilterSIM and SGS realizations. The numerical simulations show that in a reservoir/aquifer system with a strongly connected network of high‐K materials, the Gaussian and FilterSIM approaches are not as effective as HOSIM in reproducing this behavior. The simulations showed a good agreement between HOSIM realizations and the exhaustive reference image.

Role of correlation structures of permeability field on residual trapping mechanisms and buoyancy-driven CO2 migration

Previous research suggests that for many geological CO2 sequestration reservoirs, up to 60% of the injected CO2 will be trapped by capillary forces (irreducible saturation), a mechanism termed residual CO2 trapping. More specifically, our recent models of ongoing field tests of geological sequestration suggest that residual CO2 trapping can be maximized if the CO2 plume rises a greater distance due to buoyancy (i.e., injection at the deepest part of a thick reservoir) and sweeps a larger area before coming in contact with low permeability caprock. Although this strategy maximizes the residual CO2 trapping in theory because CO2 plume contacts more pore spaces, it also increases the probability that upwelling- CO2 may come into contact with faults or other leakage pathways. Geological heterogeneity seems to play greater role with respect to residual CO2 trapping potential. To help clarify what processes and properties will maximize residual CO2 trapping and minimize CO2-buoyant flow, we conducted a systematic analysis of permeability (k) fields and its correlation structures. The k fields served as primary parameterization of a numerical model describing CO2 migration during a 100-year simulation period. We compared various permutations of two-dimensional conceptual models, including homogeneous, random, homogenous with low-k lens, and anisotropically-correlated k fields. Using a Sequential Gaussian Simulation method, for most of models, we generated 10 realizations in each model permutation. In each simulation, the amount of mobile-, residual-, and aqueous-trapped CO2 was calculated and the spatial distribution of the CO2 plume was quantified using the first and second spatial moments. Both homogeneous and random simulation results suggest that the amount of residual trapped CO2 increases as the effective k increases. These results imply that the overall velocity distribution, which governs the sweeping area of the CO2 plume, is a critical factor for residual CO2 trapping. However, as overall velocity (or k field) increases, we observed that the CO2 plume reaches the caprock more quickly. In simulations of anisotropically correlated k fields with specific correlation length ratios of 25 m×10 m,50 m×10 m, and 100 m×10 m in x (horizontal) and z (vertical) directions, respectively, the CO2 migration distance due to buoyancy force is shorter as the horizontal correlation length becomes greater. In addition, as the horizontal correlation length becomes greater, residual trapping increases because the CO2 plume spreads farther laterally, sweeping a larger area. In sum, results of this analysis suggest that heterogeneous k fields with greater anisotropic correlation ratios tend to maximize residual trapping and minimize buoyancy-driven CO2 migration. Our findings also suggest that k correlation structures, especially anisotropic media with specific ratios of correlation lengths, can strongly impact CO2 trapping mechanisms by controlling velocity and tortuosity, which in turn determines the sweeping area of CO2 plumes.