Geological Uncertainty Research Articles

Fast robust optimization using bias correction applied to the mean model

Ensemble methods are remarkably powerful for quantifying geological uncertainty. However, the use of the ensemble of reservoir models for robust optimization (RO) can be computationally demanding. The straightforward computation of the expected net present value (NPV) requires many expensive simulations. To reduce the computational burden without sacrificing accuracy, we present a fast and effective approach that requires only simulation of the mean reservoir model with a bias correction factor. Information from distinct controls and model realizations can be used to estimate bias for different controls. The effectiveness of various bias-correction methods and a linear or quadratic approximation is illustrated by two applications: flow optimization in a one-dimensional model and the drilling-order problem in a synthetic field model. The results show that the approximation of the expected NPV from the mean model is significantly improved by estimating the bias correction factor, and that RO with mean model bias correction is superior to both RO performed using a Taylor series representation of uncertainty and deterministic optimization from a single realization. Use of the bias-corrected mean model to account for model uncertainty allows the application of fairly general optimization methods. In this paper, we apply a nonparametric online learning methodology (learned heuristic search) for efficiently computing an optimal or near-optimal robust drilling sequence on the REEK Field example. This methodology can be used either to optimize a complete drilling sequence or to optimize only the first few wells at a reduced cost by limiting the search depths.

Determination of oil well placement using convolutional neural network coupled with robust optimization under geological uncertainty

This study integrates a convolutional neural network (CNN) within the framework of robust optimization for determining the placement of an oil production well at a petroleum reservoir under geological uncertainty. The proposed algorithm identifies the well location that maximizes the expectation of cumulative oil production of equiprobable realizations. CNN, which inputs near-wellbore permeability and outputs cumulative oil production at a feasible well location, is trained to correlate between petrophysical spatial data and hydrocarbon productivity with several realizations. The trained CNN estimates the productivity at every feasible well location for all given realizations. The approach is tested with application to a set of realizations describing a channelized oil reservoir with an aquifer. The validity of the approach is evaluated by comparing the similarity between the full-physics reservoir simulation (RS) and CNN results for qualified well locations. The most productive well location based on the simulation results is selected as the optimal well placement. The performance of the CNN is also compared with that of an artificial neural network (ANN) for cases with varied numbers of realizations that provide training data with the neural networks. CNN outperforms ANN because of its feature extraction of multi-dimensional data from convolution. A sensitivity analysis is conducted to analyze the effects of the volume of training data on the predictability of the neural networks with k-fold cross-validation. The findings highlight that the integrated approach can be used as an efficient decision-making tool for solving well placement optimization problems with accuracy at an affordable computational cost.

An analytical method for estimating horizontal transition probability matrix of coupled Markov chain for simulating geological uncertainty

Geological uncertainty exists widely in nature, which has a pivotal influence on the deformation and stability of the geotechnical structure. The coupled Markov chain (CMC) model is a widely used method to simulate the variability of strata. However, the difficulty to determine the horizontal transition probability matrix (HTPM), one of the important input parameters for the CMC model, limits its direct application to geotechnical engineering problems. In this study, an analytical method for estimating the HTPM is proposed and the CMC model is enhanced by integrating the analytical HTPM estimation method for simulating geological uncertainty. The validity of the analytical method for the HTPM and the accuracy of the strata simulated by the enhanced CMC model are evaluated through a typical stratum in literature. The results show that the estimated HTPMs are in good agreement with the real values and not sensitive to borehole schemes. The CMC model enhanced by the proposed analytical method for estimating the HTPM is well capable of simulating the strata based on given borehole data.

Managing Uncertainty in Geological Scenarios Using Machine Learning-Based Classification Model on Production Data

Training image (TI) has a great influence on reservoir modeling as a spatial correlation in the multipoint geostatistics. Unlike the variogram of the two-point geostatistics that is mathematically defined, there is a high degree of geological uncertainty to determine a proper TI. The goal of this study is to develop a classification model for determining the proper geological scenario among plausible TIs by using machine learning methods: (a) support vector machine (SVM), (b) artificial neural network (ANN), and (c) convolutional neural network (CNN). After simulated production data are used to train the classification model, the most possible TI can be selected when the observed production responses are put into the trained model. This study, as far as we know, is the first application of CNN in which production history data are composed as a matrix form for use as an input image. The training data are set to cover various production trends to make the machine learning models more reliable. Therefore, a total of 800 channelized reservoirs were generated from four TIs, which have different channel directions to consider geological uncertainty. We divided them into training, validation, and test sets of 576, 144, and 80, respectively. The input layer comprised 800 production data, i.e., oil production rates and water cuts for eight production wells over 50 time steps, and the output layer consisted of a probability vector for each TI. The SVM and CNN models reasonably reduced the uncertainty in modeling the facies distribution based on the reliable probability for each TI. Even though the ANN and CNN had roughly the same number of parameters, the CNN outperformed the ANN in terms of both validation and test sets. The CNN successfully classified the reference model’s TI with about 95% probability. This is because the CNN can grasp the overall trend of production history. The probabilities of TI from the SVM and CNN were applied to regenerate more reliable reservoir models using the concept of TI rejection and reduced the uncertainty in the geological scenario successfully.

An Introduction of New Simulation and Optimization Software Application for Long-Term Limestone Quarry Production Planning

Long-term limestone quarry production planning is essential to maintain the supply to the cement plant. In which, quarry planners usually attempt to fulfil the complicated calculations, which ensure a consistent supply of raw materials to the cement plant while guaranteeing technical and operational parameters in mining. Traditionally, the calculations are done on a spreadsheet or by trial and error procedure resulting in high additive cost and an increase in product variability. Modern quarry management relies on block models and mathematical algorithms integrated into the software to optimize the long-term limestone quarry production planning. However, this method is potentially sensitive to geological uncertainty in block modelling, resulting in the deviation of the supply production of raw materials. The need for mining intelligently raw material is, therefore, crucial and an increasing issue in the cement industry. In this research, a new simulation and optimization software application called Quarrier is introduced, allowing quarry planners to address the conflicting requirements of long-term limestone quarry production planning while forecasting and mitigating the effects of geological uncertainty on the supply of raw materials for the cement plant. The benefits of this software are demonstrated through a limestone quarry in Vietnam.

System reliability analysis in spatially variable slopes using coupled Markov chain and MARS

The soil heterogeneity has a significant impact on the stability of geotechnical structures. The inherent variability of parameters in one soil type comes from different deposition and tectonic conditions. Furthermore, geological uncertainty could be described by the distribution of varying soil types. Therefore, considering both the inherent variability and geological uncertainty of soil parameters, we introduced a coupled Markov chain (CMC) model to simulate the soil heterogeneity utilizing the field borehole data. Additionally, we initiated an extended Multivariate Adaptive Regression Spline (MARS) model-based Monte Carlo simulation (MCS). This technique is used to overcome the limits of the traditional response surface method that assumed both order and type of polynomials to perform the probabilistic analysis, which occurred in slope reliability evaluation. Our results have shown that the proposed MARS-based MCS approach could effectively conduct the probabilistic analysis with enough accuracy. The comparison of the probabilities of failure obtained by the MARS-based MCS and the other methods suggested that both the robustness and high accuracy of the MARS-based MCS have been discussed in different spatially varied soils. Even though the differences between these three approaches are insignificant, the reliability results obtained by the MARS-based MCS agree better with the results of the direct MCS results. Thus, these calibrated results indicated that the proposed MARS-based MCS could perform the system reliability analysis effectively and accurately.

A framework for adaptive open-pit mining planning under geological uncertainty

Mine planning optimization aims at maximizing the profit obtained from extracting valuable ore. Beyond its theoretical complexity—the open-pit mining problem with capacity constraints reduces to a knapsack problem with precedence constraints, which is NP-hard—practical instances of the problem usually involve a large to very large number of decision variables, typically of the order of millions for large mines. Additionally, any comprehensive approach to mine planning ought to consider the underlying geostatistical uncertainty as only limited information obtained from drill hole samples of the mineral is initially available. In this regard, as blocks are extracted sequentially, information about the ore grades of blocks yet to be extracted changes based on the blocks that have already been mined. Thus, the problem lies in the class of multi-period large scale stochastic optimization problems with decision-dependent information uncertainty. Such problems are exceedingly hard to solve, so approximations are required. This paper presents an adaptive optimization scheme for multi-period production scheduling in open-pit mining under geological uncertainty that allows us to solve practical instances of the problem. Our approach is based on a rolling-horizon adaptive optimization framework that learns from new information that becomes available as blocks are mined. By considering the evolution of geostatistical uncertainty, the proposed optimization framework produces an operational policy that reduces the risk of the production schedule. Our numerical tests with mines of moderate sizes show that our rolling horizon adaptive policy gives consistently better results than a non-adaptive stochastic optimization formulation, for a range of realistic problem instances.

Ranking and selecting fault models using flow-indicator fault properties and simple streamline simulations

Fault zones in porous sandstones are commonly divided into two parts: a fault core and a damage zone. Both fault-zone elements could influence subsurface fluid flow and should be incorporated in a geologically realistic model. The fault core can be implemented in the model as a transmissibility multiplier (TM), while the damage zone can be implemented by modifying the grid permeability in the cells adjacent to the model faults. Each of the input parameters used in calculating the TM and damage-zone permeability modification is subject to geological uncertainty. Here an iterative workflow is employed to define probability distribution functions for each of the input parameters, with the result being many fault-model realizations. Here two methods are examined for ranking and selecting the fault-model realizations for further analysis: (i) calculating the flow-indicator fault properties (effective cross-fault transmissibility and effective cross-fault permeability) from the static model; and (ii) employing a simplified flow-based connectivity calculation, returning dynamic measures of model connectivity. The aims are to outline the methodology and workflow used, evaluate the impact of the different input parameters on the results, and examine the results of the static and dynamic approaches to understand how the ranking and selection of models compares between the two. Our results are dependent on the structural model. In a strongly compartmentalized model based on the Gullfaks Field, North Sea, fluid-flow-indicator fault properties are weakly correlated with measures of dynamic behaviour. In particular, models with low fault transmissibility show a much greater range of dynamic behaviour, and are less predictable, than models with high fault transmissibility. In a weakly compartmentalized model with strongly channelized fluvial facies based on the Whitley Bay area in NE England, there was a strong correlation between flow-indicator fault properties and measures of dynamic behaviour. We ascribe these results to the greater complexity of flow paths expected when a highly compartmentalized model contains faults that are likely to be baffles to cross-fault flow. Thematic collection: This article is part of the Fault and top seals collection available at: https://www.lyellcollection.org/cc/fault-and-top-seals-2019

Mixed H∞/Passivity controller design through LMI approach applicable for waterflooding optimization in the presence of geological uncertainty

Waterflooding is one of the most popular techniques which are generally used to increase oil recovery factor in mature reservoirs. A challenging issue in conducting the waterflooding process is how to handle the effects of exiting reservoir uncertainties. To this aim, in this paper an optimization algorithm based on Mixed H∞/passivity controller design is introduced. The presented approach is capable to systematically take into account the unpredicted influences of inherent geological uncertainties on the production regime, while guaranteeing the stability and disturbance attenuation in the closed-loop system. In addition, this technique expresses energy transition between system states and disturbances, which are representatives of the uncertainty effects. In this study, the optimization problem has been formulated such that the gained profit (here, the net present value: npv) is maximized, while dealing with the operational constraints and also the uncertainty impacts. The defined performance index is able to simultaneously achieve the H∞ performance and the passivity property, in the presence of inherent uncertainties. The optimization problem has been solved by Linear Matrix Inequality (LMI) approach. The developed algorithm has been simulated on 10th SPE-model#2 as a well-known case study, by generating hypothetical uncertainty in the permeability grids. The obtained results have shown that the designed controller can appropriately adjust the water injection profile, known as the manipulated variable, to achieve the maximum feasible npv in the presence of uncertainty and operational constraints. Finally, further analysis has been provided to compare the introduced methodology with conventional robust optimization approach.

Resource and Grade Control Model Updating for Underground Mining Production Settings

A key requirement for the mining industry is the characterization of the spatial distribution of geometallurgical properties of the ore and waste in a mineral deposit. Due to geological uncertainty, resource models are crude representations of reality, and their value for forecasting is limited. Information collected during the production process is therefore of high value in the mining production chain. Models for mine planning are usually based on exploration information from an initial phase of the mineral extraction process. The integration of data with different supports into the resource or grade control model allows for continuous updating and is able to provide estimates that are more accurate locally. In this paper, an updating algorithm is presented that integrates two types of sensor information: sensors characterizing the exposed mine face, and sensors installed in the conveyor belt. The impact of the updating algorithm is analysed through a case study based on information collected from Reiche-Zeche, a silver–lead–zinc underground mine in Freiberg, Germany. The algorithm is implemented for several scenarios of a grade control model. Each scenario represents a different level of conditioning information prior to extraction: no conditioning information, conditioning information at the periphery of the mining panel, and conditioning information at the periphery and from boreholes intersecting the mining panel. Analysis is performed to compare the improvement obtained by updating for the different scenarios. It becomes obvious that the level of conditioning information before mining does not influence the updating performance after two or three updating steps. The learning effect of the updating algorithm kicks in very quickly and overwrites the conditioning information.

Implementation of Geostatistical Algorithms

The state of nature is uncertain. Andre G. Journel championed the concept that we must quantify our uncertainty, then make a risk-qualified decision. The theory for this concept applied to the earth sciences was developed by Andre and others over the past four decades. Theory is unquestionably important, but the implementation of theory in algorithms and practical workflows has always been an essential aspect of geostatistics. This motivated the geostatistical software library and other computer codes. The effort remains unfinished. The workflows for the quantification of geological uncertainty and risk-qualified decision making are achievable to a select few who are comfortable bending arcane software to their will. The routine calculation of probabilistic resources and risk qualified decision making requires a clarity of vision or, as Andre was fond of saying, an understanding of the essence. The essential steps required for constructing numerical models that effectively quantify our state of nature have emerged. The concepts for risk-qualified decision making are clear. Practitioners have technical solutions to quantify and manage geological risk, thus reducing the lost opportunity cost of low-quality geological models and inferior decisions

Direct forecasting of global and spatial model parameters from dynamic data

Direct forecasting has recently been proposed as a method for uncertainty quantification in non-linear inverse problems. The method directly forecasts a desired future response without the need for full model inversion. The method has been successfully applied to a range of subsurface field cases, such as groundwater, shallow and deep geothermal and oil/gas predictions. In this paper, we extend the framework of direct forecasting to do what it was avoided to do in the first place: model inversion. The idea is simple: replace the prediction variables with the model variables. Two challenges now occur: the model dimensions, in subsurface realm at least, are much higher than data variables. This is the case in the paper where we consider dynamic data and high-dimensional spatial models for geological structure and properties. Secondly, the regression applied in the original method, being a linear regression of prediction variables on transformed data, is unlikely to lead to models that match field observations. We address these challenges first by adding a variable selection method (through global sensitivity analysis) for the model space. More specifically, we select those model components that are most sensitive to data variables only. The linear assumption is mitigated by a sequential updating of sensitive model variables. We illustrate our method on a Libyan oil reservoir with complex geological uncertainty involving structural, petrophysical and fluid model parameters.

Developing the 3D geological model for Crossrail 2, London, UK

A 3D geological model, referred to as the Project Stratigraphic Model, has been developed for Crossrail 2, a proposed £30 bn railway linking Surrey and Hertfordshire via 27 km long tunnels through London. The British Geological Survey 1:50 000 scale 3D model of the London Basin was adopted as the initial baseline. Over 1000 boreholes were collated, together with information from existing publications, such as tunnel face excavation records, to review and develop the Project Stratigraphic Model. Digital tools such as ArcGIS and Leapfrog Works facilitated the efficient development, interrogation and dissemination of the c. 40 km 2 model and helped to communicate geological uncertainty. The Project Stratigraphic Model was a key tool in identifying geological hazards along the route, designing the vertical alignment, informing early design decisions for the proposed structures and estimating third-party building foundation depths for obstruction risk assessments. Further refinement of the model will continue into future design and construction stages, including the addition of project-specific ground investigation, geotechnical parameters and construction data, and will provide an invaluable geotechnical risk management tool for the project. Thematic collection: This article is part of the Ground models in engineering geology and hydrogeology collection available at: https://www.lyellcollection.org/cc/Ground-models-in-engineering-geology-and-hydrogeology

Drivers and barriers for taking account of geological uncertainty in decision making for groundwater protection

The geological conceptual model is considered a major source of uncertainty in groundwater modelling and well capture zone delineation. However, how to account for it in groundwater policy and management remains largely unresolved. We explore the drivers and barriers to account for geological conceptual uncertainty in groundwater protection amongst decision makers and stakeholders in an agricultural groundwater catchment in Denmark. Using a groundwater model, we analyze the impact of alternative geological conceptual models on capture zone delineation. A focus area, which covers multiple modelled capture zones, is defined and considered for groundwater protection. Model uncertainty and focus area are discussed at two workshops, one with local and national stakeholders and another with local farmers. The drivers to account for model uncertainty include: i) safer drinking water protection by considering a larger area for protection than identified from a single geological model; and ii) stability over time of management plans. The main barrier is the additional cost to the stakeholders for the protection of a larger area. We conclude that integration of geological uncertainty in groundwater protection plans may be improved through: i) better communication between the research community and the national water authority; ii) more constraining guidelines regarding the estimation of geological uncertainty; and iii) the development of a framework ensuring knowledge transfer to the local water authorities and detailing how to integrate uncertainty in management plans.

Accuracy of fully coupled and sequential approaches for modeling hydro- and geomechanical processes

Subsurface flow and geomechanics are often modeled with sequential approaches. This can be computationally beneficial compared with fully coupled schemes, while it requires usually compromises in numerical accuracy, at least when the sequential scheme is non-iterative. We discuss the influence of the choice of scheme on the numerical accuracy and the expected computational effort based on a comparison of a fully coupled scheme, a scheme employing a one-way coupling, and an iterative scheme using a fixed-stress split for two subsurface injection scenarios. All these schemes were implemented in the numerical simulator DuMux. This study identifies conditions of problem settings where differences due to the choice of the model approach are as important as differences in geologic features. It is shown that in particular transient and multiphase flow, effects can be causing significant deviations between non-iterative and iterative sequential schemes, which might be in the same order of magnitude as geologic uncertainty. An iterated fixed-stress split has the same numerical accuracy as a fully coupled scheme but only for a certain number of iterations which might use up the computational advantage of solving two smaller systems of equations rather than a big monolithical one.

The role of geophysics in enhancing mine planning decision-making in small-scale mining.

Small-scale mining usually operates under high geological uncertainty conditions. This turns mine planning into a complex and sometimes inaccurate task, resulting in low productivity and substantial variability in the quantity and quality of the mineral products. This research demonstrates how the application of a novel methodology that relies on traditional and low-cost geophysical methods can contribute to mine planning in small-scale mining. A combination of resistivity and induced polarization methods is applied to enhance mine planning decision-making in three small-scale mining operations. This approach allows for the acquisition of new data regarding local geological settings, supporting geological modelling and enhancing decision-making processes for mine planning in a timely and low-cost fashion. The results indicate time savings of up to 77% and cost reductions of up to 94% as compared with conventional methods, contributing to more effective mine planning and, ultimately, improving sustainability in small-scale mining.

Method of Distributions for Quantification of Geologic Uncertainty in Flow Simulations

AbstractProbabilistic models of subsurface flow and transport are required for risk assessment and reliable decision making under uncertainty. These applications require accurate estimates of confidence intervals, which generally cannot be ascertained with statistical moments such as mean (unbiased estimate) and variance (a measure of uncertainty) of a quantity of interest (QoI). The method of distributions provides this information by computing either the probability density function or the cumulative distribution function (CDF‐) of the QoI. The standard method can be orders of magnitude faster than Monte Carlo simulations (MCS) but is applicable to stationary, mildly to moderately heterogeneous porous media in which the coefficient of variation of input parameters (e.g., log‐conductivity) is below four. Our CDF‐random domain decomposition (RDD) framework alleviates these limitations by combining the method of distributions and RDD; it also accounts for uncertainty in the geologic makeup of a subsurface environment. For a given realization of the geological map, we derive a deterministic equation for the conditional CDF of hydraulic head of steady single‐phase flow. The solutions of this equation are then averaged over realizations of the geological map‐ to compute the hydraulic head CDF. Our numerical experiments reveal that the CDF‐RDD method remains accurate for two‐dimensional flow in a porous medium composed of two heterogeneous hydrofacies, a setting in which the original CDF method fails. For the same accuracy, the CDF‐RDD method is an order of magnitude faster than MCS.

Approximate Bayesian inference of seismic velocity and pore-pressure uncertainty with basin modeling, rock physics, and imaging constraints

We have introduced a methodology for quantifying seismic velocity and pore-pressure uncertainty that incorporates information regarding the geologic history of a basin, rock physics, well log, drilling, and seismic data. In particular, our approach relies on linking velocity models to the basin modeling outputs of porosity, mineral volume fractions, and pore pressure through rock-physics models. We account for geologic uncertainty by defining prior probability distributions on lithology-specific porosity compaction model parameters, permeability-porosity model parameters, and heat-flow boundary condition. Monte Carlo basin simulations are performed by sampling the prior uncertainty space. We perform probabilistic calibration of the basin model outputs by defining data likelihood distributions to represent well data uncertainty. Rock physics modeling transforms the basin modeling outputs to give us multiple velocity realizations used to perform multiple depth migrations. We have developed an approximate Bayesian inference framework that uses migration velocity analysis in conjunction with well data for updating velocity and basin modeling uncertainty. We apply our methodology in 2D to a real field case from the Gulf of Mexico; our methodology allows for building a geologic and physical model space for velocity and pore-pressure prediction with reduced uncertainty.

A Classification-Based Surrogate-Assisted Multiobjective Evolutionary Algorithm for Production Optimization under Geological Uncertainty

Summary Multiobjective optimization (MOO) is a popular procedure for waterflooding optimization under geological uncertainty that maximizes the expectation of net present value (NPV) over all possible uncertainty models and minimizes the variance simultaneously. However, the optimization process involves a large number of decision variables, and the problem is computationally expensive. Surrogate-assisted evolutionary algorithms (SAEAs), which have proved to be an effective way to solve expensive problems, design computationally inexpensive functions to approximate each objective function. On the basis of characterization, we have designed an efficient multiobjective evolutionary algorithm (MOEA) to effectively deal with computationally expensive simulation-based optimization problems. The uniqueness of this algorithm is that it incorporates a Pareto-rank-learning scheme with surrogate-assisted infill criterion. The first is to introduce a multiclass error-correcting output codes (ECOC) model that directly predicts the dominance relationship between candidate solutions and prescreens, and the second is to train a radial-basis function (RBF) network that predicts the objective functions of prescreened solutions to calculate the hypervolume (HV) improvement that maintains convergence and diversity. Compared with typical surrogate-based methods, the developed method provides a classifier first that can enhance the accuracy in high dimensions and reduce computational complexity. To the best of our knowledge, the proposed method compares with state-of-the-art surrogate frameworks for multiobjective production-optimization problems. In this paper, the proposed approach is applied to two 200D benchmark problems and two synthetic reservoir models. The results show that the proposed method can achieve more comprehensive and efficient reservoir management (RM) with a higher convergence speed compared with traditional MOEAs and surrogate-assisted optimization methods.

A stochastic particle swarm based model for long term production planning of open pit mines considering the geological uncertainty

Long term production planning (LTPP) plays a critical role to achieve success of a mining operation. LTPP, as an optimization problem, aims to maximize the net present value (NPV) of a mine subject to a set of constraints. One of the main reasons for not achieving production targets is the uncertainty of the LTPP's inputs. Geological uncertainty as the main sources of uncertainty is considered in this research. In this regard, a set of equiprobable scenarios of orebody and derived two new block model called “risk block model” and “EType” were used as inputs. Then, a stochastic integer programming (SIP) model was developed to integrate the geological uncertainty. Finally, a PSO-based algorithm was developed to solve the SIP model. Four different strategies were developed, according to the population topology and how to use the risk block model. Population topology defines the subset of particles that effect on each particle. Implementation the proposed approach on a large scale mine demonstrate its performance to develop a unique schedule considering geological uncertainties with maximum NPV and minimum risk of not achieving production targets. Investigations show that Gbest based PSO is more susceptible to trap in local optima. Multiple risk based strategies are able to generate better solutions, however, single risk based strategies are good practices when companies are looking for flexible or specific risk based designs.