Sequential Gaussian Simulation Research Articles

Integration of rock physics, geostatistics, and Bayesian algorithm to estimate porosity in tight oil reservoirs

The conglomerate reservoirs in the Triassic Baikouquan Formation have been identified as the major target for hydrocarbon exploitation in the Mahu Sag, Junggar Basin, Western China. Nevertheless, conglomerate reservoirs typically have lower porosity than sandstone reservoirs. Therefore, determining sweet spots is critical in reservoir modeling and further hydrocarbon exploitation. To investigate favorable areas and better predict the porosity of the Baikouquan tight oil reservoir, integrated methods were employed, including casting thin sections, scanning electron microscopy (SEM), wireline logs, rock physics template (RPT) modeling, geostatistical simulation, and Bayesian updating. The results showed that pore types consist of microfractures, intercrystal micropores, residual intergranular pores, and dissolution pores. Four rock types (RT) were identified via the built RPT, wherein velocity and porosity had a nonlinear relationship. Afterward, porosity simulation was performed and compared using sequential gaussian simulation (SGS), SGS with collocated cokriging (SGSC), and SGS with Bayesian updating (SGSB). Prior to the simulation, all the data were preprocessed to follow a Gaussian (normal) distribution. The range and azimuth of different RT in variogram modeling were then determined using data from horizontal wells. Consequently, it was revealed that the probability distribution frequency (PDF) of SGS with Bayesian updating was very similar to the hard data, whereas the PDF associated with SGS and SGSC may be biased. Particularly the PDF was too narrow for high values. The cumulative distribution function (CDF) of SGSB also showed a similar trend to the CDF of the input data. The ensemble-averaged (E-type) maps and quantiles maps revealed that SGSB had an advantage over collocated cokriging because it could capture the non-linear relationships between impedance and porosity. This study indicates that Bayesian updating is a reliable technique for incorporating secondary data in the calculation of reservoir properties.

The Best Scenario for Geostatistical Modeling of Porosity in the Sarvak Reservoir in an Iranian Oil Field, Using Electrofacies, Seismic Facies, and Seismic Attributes

Summary The lateral and vertical variations in porosity significantly impact the reservoir quality and the volumetric calculations in heterogeneous reservoirs. With a case study from Iran’s Zagros Basin Sarvak reservoir in the Dezful Embayment, this paper aims to demonstrate an efficient methodology for distributing porosity. Four facies models (based on electrofacies analysis data and seismic facies) with different geostatistical algorithms were used to examine the effect of different facies types on porosity propagation. Both deterministic and stochastic methods are adopted to check the impact of geostatistical algorithms on porosity modeling in the static model. A total of 40 scenarios were run and validated for porosity distribution through a blind test procedure to check the reliability of the models. The study’s findings revealed high correlation values in the blind test data for all porosity realizations linked to seismic facies, ranging from 0.778 to 0.876. In addition, co-kriging to acoustic impedance (AI), as a secondary variable, increases the correlation coefficient in all related cases. Unlike deterministic algorithms, using stochastic methods reduces the uncertainty and causes the porosity model to have an identical histogram compared with the original data. This study introduced a comprehensive workflow for porosity distribution in the studied carbonate Sarvak reservoir, considering the electrofacies, and seismic facies, and applying different geostatistical algorithms. As a result, based on this workflow, simultaneously linking the porosity distribution to seismic facies, co-kriging to AI, and applying the sequential Gaussian simulation (SGS) algorithm result in the best spatial modeling of porosity.

Effects of Reservoir Heterogeneity on CO2 Dissolution Efficiency in Randomly Multilayered Formations

Carbon dioxide (CO2) dissolution is the secondary trapping mechanism enhancing the long-term security of CO2 in confined geological formations. CO2 injected into a randomly multilayered formation will preferentially migrate along high permeability layers, increasing CO2 dissolution efficiency. In this study, sequential Gaussian simulation is adopted to construct the stratified saline formations, and two-phase flow based on MRST is established to illustrate the spatial mobility and distribution of CO2 migration. The results show that gravity index G and permeability heterogeneity σY2 are the two predominant factors controlling the spatial mobility and distribution of CO2 transports. The CO2 migration shows a totally different spatial mobility under different gravity index and heterogeneity. When the permeability discrepancy is relatively larger, CO2 preferentially migrates along the horizontal layer without accompanying the vertical migration. For the formation controlled by gravity index, CO2 migration is governed by supercritical gaseous characteristics. For the medium gravity index, the upward and lateral flow characteristics of the CO2 plume is determined by gravity index and heterogeneity. When the gravity index is smaller, permeability heterogeneity is the key factor influencing CO2 plume characteristics. Permeability heterogeneity is the decisive factor in determining final CO2 dissolution efficiency. This investigation of CO2 mobility in randomly multilayered reservoirs provides an effective reference for CO2 storage.

Combined synchronous simulation of discrete and continuous variables under high net-to-gross ratio reservoir

The Triassic TIII oil group in the Sangtamu oil field in the Tarim Basin is formed by multiple phases of channels cutting and superimposing one another, and the net-to-gross (NTG) ratio can exceed 90%. Strong heterogeneity exists in the spatial storage and seepage features of the sand body within the channel, causing significant uncertainty in the 3D geological modeling of the reservoir. In order to delicately characterize the reservoir heterogeneity within the channel in its various phases, this paper proposes a facies modeling method based on the deposition process. It includes a strategy of joint synchronous simulation of discrete facies and continuous physical property variables, fused trend body-constrained modeling established by the internal variation characteristics of single-phase channel sand, and an increase in channel phases to meet high NTG ratio reservoir conditions. In this process, the object-based method and sequential gaussian simulation method are both used to simulate step-by-step the 3D geological model of the facies and physical properties of different phase channels, respectively. The results show that 61 small sand bodies compose the results of the established 3D geological model, and the physical simulation results reflect the characteristics of physical changes inside the channel at different phases. The model has been verified by vacuate wells validation with a compliance rate of 97.4%, and the method reduces the model's multiple solutions and uncertainties while offering a new practical method for modeling complex fluvial facies reservoirs.

Risk pre-assessment method for regional drilling engineering based on deep learning and multi-source data

Accurately predicting downhole risk before drilling in new exploration areas is one of the difficulties. Using intelligent algorithms to explore the complex relationship between multi-source data and downhole risk is a hot research topic and frontier in this field. However, due to the small number and uneven distribution of drilled wells in new exploration areas and the lack of sample data related to risk, the training model has insufficient generalization ability, and thus the prediction is not effective. In this paper, a drilling risk profile (depth domain) rich in geological and engineering information is constructed by introducing a quantitative evaluation method for drilling risk of drilled wells, which can provide sufficient risk sample data for model training and thus solve the small sample problem. For the problem of uneven distribution of drilling wells in new exploration areas, the concept of virtual wells and their deployment methods were proposed. Besides, two methods for calculating rock mechanical parameters of virtual wells were proposed, and the accuracy and applicability of the two methods are analyzed. The LSTM deep learning model was optimized to tap the quantitative relationship between drilling risk profiles and multi-source data (e.g., seismic, logging, and rock mechanical parameters). The model was validated to have an average relative error of 9.19%. The quantitative prediction of the drilling risk profile of the virtual well was achieved using the trained LSTM model and the calculation of the relevant parameters of the virtual well. Finally, based on the sequential Gaussian simulation method and the risk distribution of drilled and virtual wells, a regional 3D drilling risk model was constructed. The analysis of real cases shows that the addition of virtual wells can significantly improve the identification of regional drilling risks and the prediction accuracy of pre-drill drilling risks in unexplored areas can be improved by up to 21% compared with the 3D risk model constructed based on drilled wells only.

A comparative analysis of the effect of nanoparticles/surfactant assisted foam injection on the gas mobility control at different heterogeneities

Foam flooding is a popular method for increasing oil recovery in reservoirs with varying levels of heterogeneity. One common foam flooding technique is surfactant-assisted foam flooding (SF), which uses surfactants to create stable foam. However, SF is limited in high-pressure, high-temperature, and high-salinity reservoirs. To overcome these limitations, researchers have proposed a new approach called nanoparticles-assisted foam flooding (NAF), which involves adding nanoparticles to improve surfactant properties. While SF has been shown to improve sweep efficiency in heterogeneous reservoirs, the potential benefits of NAF are not fully understood. In this study, researchers investigated the performance of SF and NAF in controlling gas mobility in reservoirs with different levels of heterogeneity. They defined heterogeneity levels using sequential Gaussian simulation with varying standard deviation values. They also included a gas–water flooding (GW) scenario as a baseline. The results showed that SF effectively delayed breakthroughs and improved recovery factors in highly heterogeneous reservoirs. The researchers also compared normalized values of breakthrough time, breakthrough recovery factor, and recovery factor after 50 years for SF and NAF, which were normalized by corresponding GW results. Simulation results showed that SF and NAF could increase the normalized breakthrough time (SF: 10–17%, NAF: 12–42%), breakthrough recovery factor (SF: 11–20%, NAF: 16–53%), and recovery factor after 50 years (SF: 0–4%, NAF: 0–23%) compared to GW, depending on the heterogeneity level and NP concentration. The benefits of NAF compared to SF and GW were due to a significant decrease in gas mobility and saturation in the topmost layers, which facilitated the piston-wise movement of the front, resulting in higher sweep efficiency and recovery factor.

Uncertainty estimation of regionalised depth–duration–frequency curves in Germany

Abstract. The estimation of rainfall depth–duration–frequency (DDF) curves is necessary for the design of several water systems and protection works. These curves are typically estimated from observed locations, but due to different sources of uncertainties, the risk may be underestimated. Therefore, it becomes crucial to quantify the uncertainty ranges of such curves. For this purpose, the propagation of different uncertainty sources in the regionalisation of the DDF curves for Germany is investigated. Annual extremes are extracted at each location for different durations (from 5 min up to 7 d), and local extreme value analysis is performed according to Koutsoyiannis et al. (1998). Following this analysis, five parameters are obtained for each station, from which four are interpolated using external drift kriging, while one is kept constant over the whole region. Finally, quantiles are derived for each location, duration and given return period. Through a non-parametric bootstrap and geostatistical spatial simulations, the uncertainty is estimated in terms of precision (width of 95 % confidence interval) and accuracy (expected error) for three different components of the regionalisation: (i) local estimation of parameters, (ii) variogram estimation and (iii) spatial estimation of parameters. First, two methods were tested for their suitability in generating multiple equiprobable spatial simulations: sequential Gaussian simulations (SGSs) and simulated annealing (SA) simulations. Between the two, SGS proved to be more accurate and was chosen for the uncertainty estimation from spatial simulations. Next, 100 realisations were run at each component of the regionalisation procedure to investigate their impact on the final regionalisation of parameters and DDF curves, and later combined simulations were performed to propagate the uncertainty from the main components to the final DDF curves. It was found that spatial estimation is the major uncertainty component in the chosen regionalisation procedure, followed by the local estimation of rainfall extremes. In particular, the variogram uncertainty had very little effect on the overall estimation of DDF curves. We conclude that the best way to estimate the total uncertainty consisted of a combination between local resampling and spatial simulations, which resulted in more precise estimation at long observation locations and a decline in precision at unobserved locations according to the distance and density of the observations in the vicinity. Through this combination, the total uncertainty was simulated by 10 000 runs in Germany, and it indicated that, depending on the location and duration level, tolerance ranges from ± 10 %–30 % for low-return periods (lower than 10 years) and from ± 15 %–60 % for high-return periods (higher than 10 years) should be expected, with the very short durations (5 min) being more uncertain than long durations.

Three‐dimensional simulation on spatiotemporal variation of salinity in reclaimed saline soil and yield reduction risk assessment

AbstractAmelioration of saline soil to grow crops could increase food production and improve food security. However, the long‐term effects of different methods for ameliorating saline soil still need to be evaluated. In this study (2014–2021), the salinity variations of saline soils under different amelioration methods (T1: salt isolation by a stone layer + cropping; T2: subsurface drainage + cropping; T3: 5‐year cropping; T4: 3‐year cropping; CK: bare land) were monitored using electromagnetic induction. Besides, the long‐term effects of different amelioration methods and yield reduction risk were assessed using the three‐dimensional sequential Gaussian simulation (3D‐SGS). The 3D‐SGS results showed that soil salinity increased during abandonment (2014–2015) and then decreased during reclamation (2016–2021). Salt accumulated in the 0–40 cm soil layer in T3, T4, and CK treatments, while it accumulated in the 40–80 cm soil layer in T1 and T2 treatments. The proportion of high‐risk areas in T1, T2, T3, and T4 treatments reduced after reclamation, but soil salinity only slightly reduced in T3 and T4 treatments, showing a high risk of yield reduction. Besides, the time‐specific regression model had the highest prediction accuracy for soil salinity. Therefore, probabilistic evaluation based on 3D‐SGS is an effective method to evaluate the effectiveness of saline soil amelioration methods, and could help decision‐makers formulate scientific saline soil amelioration plans.

A Multiple Objective Genetic Algorithm Approach for Stochastic Open Pit Production Scheduling Optimisation

ABSTRACT The conventional approach to mine planning is to use a single estimated orebody model as the basis for production scheduling. This approach, however, does not consider grade uncertainties associated with grade estimation. These uncertainties have a significant impact on the net present value (NPV) and can only be accounted for when modelled as part of the production scheduling optimisation problem. In this research, a set of equally probable simulated orebodies generated through Sequential Gaussian Simulation is used as input to a stochastic optimisation model solved with genetic algorithm (GA). Grade variability is considered as part of the stochastic model. The problem definition and resource constraints are formulated and optimised using a specially designed mining-specific GA. This GA is employed to handle partial block processing through a specialised chromosome encoding technique resulting in near-optimal solutions. Two case studies are presented which compare results from the stochastic model solved with GA (SGA) and a Stochastic Mixed Integer Linear Programming (SMILP) model solved with CPLEX. For the second case study, while the SMILP model was at an optimality gap of 101% after 28 days, the SGA model generated an NPV of $10,045 M at 10.16% optimality gap after 1.5 h.

Spatial Data Analytics-Assisted Subsurface Modeling: A Duvernay Case Study

Data analytics facilitate the examination of spatial data sets by using multiple techniques to find and understand patterns to guide decision making. However, standard data analysis tools assume that the data are independent and identically distributed, an assumption that spatial data sets usually do not fulfill. Furthermore, the usual methods neglect spatial continuity and the inherent data paucity that should be considered in the data analytics workflow. We present a new approach that combines data analytics, geostatistics, and optimization techniques to provide an end-to-end workflow to analyze two-dimensional (2D) data sets. The proposed workflow identifies outliers based on their spatial location or distribution, models geological trends using a Gaussian kernel, models the semivariogram, and performs sequential Gaussian simulation applying kriging or cokriging for cosimulation. Moreover, it provides metrics and diagnostic plots to evaluate the goodness of the results at each step. It is also semiautomatic because it leverages the user’s judgment for subsequent operations. For optimization, the workflow uses Bayesian optimization and evolutionary algorithms. We demonstrate the use of the workflow by analyzing 1,152 wells over the Duvernay Formation in Canada. The examples include the simulation of density-porosity as the secondary feature and the cosimulation of total organic content constrained by the former. The proposed workflow helps focus more on interpreting the results than the modeling parameters, reducing workforce time and subjective errors. Moreover, the spatial simulation includes multiple realizations to assess uncertainty and support decision making in data paucity scenarios. Overall, the proposed workflow is a valuable and complementary tool for evaluating uncertainty in mature geospatial data.

Framework of fracture network modeling using conditioned data with sequential Gaussian simulation

The fracture characterization using a geostatistical tool with conditioning data is a computationally efficient tool for subsurface flow and transport applications. The main objective of the paper is to propose a framework of the geostatistical methods to model the fracture network. In the method, we have chosen a neighborhood area to apply the Gaussian Sequential Simulation in order to generate the fracture network in the unknown region. The angle was propagated from the seed where the neighborhood data guide direction. The Poisson procedure is used to distribute initial seeds. The method is applied for geological faults from Central Kazakhstan and for field data from Scotland, UK. The simulation results are compatible with the original fracture network in the flow and transport modeling setting. From the research that has been carried out, it is possible to conclude that the numerical simulation of fracture network is a valuable tool in subsurface flow and transport applications.

Development of 3D Geological Model and Analysis of the Uncertainty in a Tight Oil Reservoir in the Halfaya Oil Field

A geological model was built for the Sadi reservoir, located at the Halfaya oil field. It is regarded as one of the most significant oilfields in Iraq. The study includes several steps, the most essential of which was importing well logs from six oil wells to the Interactive Petrophysics software for conducting interpretation and analysis to calculate the petrophysical properties such as permeability, porosity, shale volume, water saturation, and NTG and then importing maps and the well tops to the Petrel software to build the 3D-Geological model and to calculate the value of the original oil in place. Three geological surfaces were produced for all Sadi units based on well-top data and the top Sadi structural map. The reservoir has been divided into 85 sublayers in the vertical direction and 170*143 grid cells in the x-y direction, totalling 2,066,350 grid cells. The Sequential Gaussian Simulation technique is used to fill 3D grid cells with property values in locations far from wells after upscaling the well log data, then distributed across all reservoir zones. The standard original oil in place has been calculated, uncertainty evaluation was used to obtain more accurate results. Model Risk Analysis employs Monte Carlo Simulation to generate the pessimistic, most likely, and optimistic reserve values (P90, P50, and P10). The uncertainty was affected by the oil formation volume factor, oil depth, petrophysical model (porosity, water saturation, and NTG), and reservoir geometric structure (horizons and zones).

Inversion of seismic data to modeling the Interval Velocity in an Oilfield of SW Iran

Seismic velocity is considered the best attribute related to formation pressure changes. Integrating seismic attributes and well-logging data through seismic inversion predicts the reservoir characteristics across the field with the highest accuracy. This study especially presents seismic velocity for the whole south Azadegan Field in SW Iran for carbonate formations. The considered dataset includes 3D seismic data, vertical seismic profiling (VSP), logging data of 23 wells, and geological information. Here, we estimated the interval velocity using post-stack migration velocity, seismic inversion, and the relationship between the acoustic impedance (AI) model and the sonic log to predict formation pressure. As a result, the correlation coefficient of 0.71 and a high inversion accuracy (8.76% relative error) is concluded. The actual and predicted P-wave (Vp) correlation coefficient is calculated as 0.74 and all sevens as 0.79 using an AI seismic attribute. Thus, the estimated Vp agrees with the original well-log values. Inverted AI cubes in the deeper formations of the field are about 8000-15000 [(m/s)*(g/cm3)], which could be referred to as calcareous formations. The correlation of the Vp cube resulting from the Sequential Gaussian simulation (SGS) considering co-kriging with the AI, with the initial velocity cube using the inverse distance weighted (IDW) method being 0.54 is more than the same method applied with interval migration velocity trend in co-kriging. The anisotropy of the final Vp cube for the vertical variogram range is 96m, and for major and minor directions is 11850 m.

Machine learning-based inversion for acoustic impedance with large synthetic training data: Workflow and data characterization

Where wells are sparse or training data are difficult to label with high-quality wireline-derived impedance logs, machine learning (ML)-based inversion of acoustic impedance typically depends on small training data sets, leading to biased prediction. We have advanced a novel workflow that applies large synthetic seismic training data to reduce facies-related bias. Using a geologically realistic model as the truth model, we randomly select sparse seed wells to perform sequential Gaussian simulation (SGS) for impedance models of the same geometry and simulate facies variability. We implement random forest regression on 30 features extracted from the synthetic volume. We observe that more seed wells tend to reduce facies-induced bias by sampling more types of facies, resulting in a better prediction. We then focus on the responses of SGS models to facies changes, the number of seed wells necessary for a useful synthetic model, and how much a synthetic model can help ML-based inversion. We observe that the SGS synthetic training model outperforms well-direct training in general. For modeled clastic shore-zone systems in Miocene Gulf of Mexico, two or more seed wells are necessary for a significant reduction of root-mean-square error and outliners, and improvement of facies imaging. In a field-data test, we apply a similar workflow to quantitatively predict acoustic impedance, which is then converted to a sand-volume map at a high-frequency sequence (10–100 m), revealing detailed facies and sandstone patterns. Such results are valuable in many geologic and engineering applications, such as hydrocarbon and CO2 reservoir prospecting, reserve estimation, simulation, etc.

Uncertainty assessment of spatiotemporal distribution and variation in regional soil heavy metals based on spatiotemporal sequential Gaussian simulation

Revealing the spatiotemporal (ST) distribution and changes in regional soil heavy metals is significant to soil pollution control and management. However, most of the ST analysis models in the existing studies ignore the uncertainty of ST changes in soil heavy metals, making their results unreliable. In this study, using soil Pb collected from 2016 to 2019 in a mining city in China as case data, an ST sequential Gaussian simulation (STSGS) is proposed to reveal the ST distribution and variation in heavy metals in regional soils and their uncertainties. Firstly, the ST variogram was analysed and fitted using a theoretical variogram model integrating the experimental variations at the ST scale. Secondly, 500 simulation realisations with random access path were generated by the ST Kriging method. Considering the obtained 500 simulation realisations, a series of ST analysis methods was proposed and employed to reveal the ST distribution and changes with uncertainty assessment of regional soil heavy metals. The main results are as follows. (1) For the whole study region, soil Pb content initially increased and then decreased from 2016 to 2019. The average probability of soil Pb exceeding 90 mg/kg was 0.121, 0.214, 0.312 and 0.291 in 2016, 2017, 2018 and 2019, respectively, whereas the average probability of always exceeding 90 mg/kg in the 4 years was only 0.032. (2) From 2016 to 2019, the area proportions of the increase and decrease of soil Pb content in the study area were 87.2% and 12.8%, respectively. However, according to the standardised statistic, only 0.161% and 8.72% of the total areas were determined to have a significant decrease and increase in soil Pb content from 2016 to 2019. (3) From 2016 to 2019, the areas with a greater than 0.6 probability of soil Pb concentration decreasing by more than 5 mg/kg and increasing by more than 20, 40 and 80 mg/kg accounted for 4.96%, 32.2%, 11.5% and only 1.91% of the total study region, respectively. The incremental high-probability areas were primarily those where Pb pollution was already serious. Finally, the advantages of the proposed STSGS method were summarised.

3D geostatistical modelling of a tailings storage facility: Resource potential and environmental implications

The management of mine tailings presents a global challenge. Re-mining of tailings to recover remaining metals and other valuable constituents could play a crucial role in reducing the volume of stored tailings. To assess the resource potential of tailings storage facilities, 3D resource models must be constructed. This is not straightforward owing to the heterogeneous nature of tailings. In this case study, modelling of the Davidschacht tailings deposit was performed using universal sequential Gaussian simulation, to account for the strong trends and heterogeneity in chemical distribution. The tonnages of the valuable elements were estimated with reasonable certainty, confirming that relatively few drill holes are required for robust resource estimates of tailings storage facilities. Zinc is the most abundant valuable metal (∼5,170±517 t), followed by Pb (∼2,060±206 t), Cu (∼550±66 t) and In (∼11±1 t), while the toxic elements As and Cd are present in tonnages of ∼8,350±585 t and ∼47±4 t, respectively, with errors given for 95 % confidence levels. Despite the In tonnage being low compared to the other elements, its in situ value is around half that of Cu and Pb, demonstrating the importance of high value by-products for re-mining potential. Although tailings deposits typically have lower grades than primary ore deposits, and the quantities of recoverable valuable elements may be even lower due to current technological limitations, re-mining of TSFs may help to diversify raw materials supply chains and should also be considered for rehabilitation purposes. Geostatistical modelling, particularly universal kriging-based simulation, has been proven to produce robust tonnage estimates of tailings storage facilities and should be adopted in industry to reduce the technical and financial uncertainties associated with re-mining.

Lithofacies and electrofacies models for Mishrif Formation in West Qurna oilfield, Southern Iraq by deterministic and stochastic methods (comparison and analyzing)

In this study, the researchers attempted to build models that are more accurate by using lithofacies data along the field. Using a wider field area and extended data from both electrofacies and lithofacies could provide an accurate model of the reservoir description that will be useful for future field developments. The stochastic and deterministic models were presented to build the facies model as the basis for the construction, comparison, and selection of the more accurate model of the Mishrif Formation in the West Qurna oilfield/Iraq. The results obtained from this study indicated that the Sequential Gaussian indicator simulation algorithm offered a more accurate stochastic model between lithofacies data extracted from 20 wells and electrofacies from 75 wells, while the Truncated Gaussian simulation algorithm has a better match than others for the distribution percentage of lithofacies and electrofacies. The stochastic model shows that Mishrif Formation consists of approximately 35–40% as carbonates, 32–35% as shale, and 28–30% as coarse sand, Dolomite, and other materials according to the SISIM and GTSIM, while the deterministic by the kriging algorithm referred to as 62%, 24%, and 14%, respectively. The best variogram that gives the best results indicated that the direction of facies distribution is mainly South-North with an inclination to North-West.

A novel geostatistical index of uncertainty for short-term mining plan

ABSTRACT The uncertainty associated with geostatistical estimates is as important in a model as the estimated value itself. This uncertainty is commonly assessed through different scenarios obtained by geostatistical simulation methods. Although the applications of geostatistical simulation methods have grown significantly in recent decades in long-term modeling, the same improvement has not occurred in medium- and short-term modeling. This study presents the “geological-operational risk indicator,” which comprises: (1) the uncertainty of geological contacts, determined by the variance of the sequential indicator simulation; and (2) the continuity of grades, obtained by sequential Gaussian simulation for variability of grades in relation to the economic or operational limit of that variable. The proposed index is applied to five grade variables of a short-term model of the Capitão do Mato iron mine in Brazil. The results are satisfactory and advance the concept of a geological risk indicator that is appropriate for medium- and short-term operations. This novel indicator helps to predict and manage in advance the uncertainties associated with mining plans.

Numerical Simulation of Carbon Dioxide–Nitrogen Mixture Dissolution in Water-Saturated Porous Media: Considering Cross-Diffusion Effects

The possibility of impure carbon dioxide (CO2) sequestration can reduce the cost of these projects and facilitate their widespread adoption. Despite this, there are a limited number of studies that address impure CO2 sequestration aspects. In this study, we examine the convection–diffusion process of the CO2–nitrogen (N2) mixture dissolution in water-saturated porous media through numerical simulations. Cross-diffusion values, as the missing parameters in previous studies, are considered here to see the impact of N2 impurity on dissolution trapping in more realistic conditions. Homogeneous porous media are used to examine this impact without side effects from the heterogeneity, and then simulations are extended to heterogeneous porous media, which are a good representative of the real fields. Heterogeneity in the permeability field is generated with sequential Gaussian simulation. Using the averaged dissolved CO2 and dissolution fluxes for each case, we could determine the onset of different dissolution regimes and behaviors of dissolution fluxes in CO2–N2 mixture dissolution processes. The results show that there is a notable difference between the pure cases and impure cases. Additionally, a failure to recognize the changes in the diffusion matrix and cross-diffusion effects can result in significant errors in the dissolution process. At lower temperatures, the N2 impurity decreases the amount and flux of CO2 dissolution; however, at higher temperatures, sequestrating the CO2–N2 mixture would be a more reasonable choice due to enhancing the dissolution behavior and lowering the project costs. The results of the heterogeneous cases indicate that heterogeneity, in most cases, reduces the averaged dissolved CO2, and dissolution flux and impedes the onset of convection. We believe that the results of this study set a basis for future studies regarding the CO2–N2 mixture sequestration in saline aquifers.

Analysis of the Lost Circulation Problem

The well-known “lost circulation” problem refers to the uncontrolled flow of whole mud into a formation. In order to address the problem related to the paucity of available data, in the present study, a model is introduced for the lost-circulation risk sample profile of a drilled well. The model is built taking into account effective data (the Block L). Then, using a three-dimensional geological modeling software, relying on the variation function and sequential Gaussian simulation method, a three-dimensional block lost-circulation risk model is introduced able to provide relevant information for regional analyses.