Optimization-based Framework for Geological Scenario Determination Using Parameterized Training Images

A statistical screening methodology is presented to address uncertainty related to main geological assumptions in green field modeling. The goals are the identification of the entire range of uncertainty on production, learning which are the most impacting geological uncertain inputs and understanding the relationships between geological scenarios and classes of dynamic behavior. The paper presents the methodology and an example application to a green field case study. The method is applied on an ensemble of reservoir models created by combining geological parameters across their range of uncertainty. The ensemble of models is then simulated with a selected development strategy and dynamic responses are grouped in classes of outcome through clustering algorithms. Ensemble responses are visualized on a multidimensional stacking plot, as a function of the geological input, and the most influential parameters are identified by axes sorting on the plot. Geological scenarios are then classified on dynamic responses through classification tree algorithms. Finally, a representative set of models is selected from the geological scenarios. The example study application shows a final oil recovery uncertainty range of 4:1, which is reasonable for a green field in lack of data. Such high range of uncertainty could hardly be found by common risk assessment based on fixed geological assumptions, which often tend to underestimate uncertainty on forecasts. Ensemble outcomes are grouped in four classes by oil recovery, plateau strength, produced water, and breakthrough time. The adoption of such clustering features gives a broad understanding of the reservoir dynamic response. The most influential geological inputs among the examined structural and sedimentological parameters in the example application result to be the fault orientation and channel fraction. This screening result highlights the main drivers of geological uncertainty and is useful for the following scenario classification phase. Classification of the geological scenarios leads to five classes of geological parameter sets, each linked to a main class of dynamic behavior, and finally to five representative models. These five models constitute an effective sampling of the geological uncertainty space which also captures the different types of dynamic response. This paper will contribute to widen the engineering experience on the use of machine learning for risk analysis by presenting an application on a real field case study to explore the relationship between geological uncertainty and reservoir dynamic behavior.

For more than half a century, geostatistics has been developed and has increasingly been used for modeling subsurface heterogeneity. Traditionally, geostatistical simulations are based on a random function model defined according to the specificities of the geological formation under investigation. Unlike traditional geostatistics, multiple‐point (MP) geostatistics avoids the explicit definition of a random function but directly infers the necessary multivariate distributions from training images. This confers on MP geostatistics a potential applicability to any geological environment, provided that there is a training image representative of the geological heterogeneity and that the essential features of this training image can be characterized by statistics defined on a limited point configuration. This paper presents a comprehensive review of MP geostatistics. If the principle of MP geostatistics is straightforward and attractive, its industrial applicability largely depends on the implementation methods. The use of a search tree for storing MP statistics is a great step that made MP geostatistics actually applicable in industry. In the meantime, other methods such as multiple grids and image postprocessing are introduced and allow enhancing the reproduction of patterns observed in training images. Because of the sequential procedure, MP simulations can easily honor local hard data. There are methods available for constraining MP simulations to target global statistics (facies proportions) and also for integrating spatial auxiliary constraints that can tremendously improve the spatial features of MP simulations. Furthermore, both the gradual deformation method and the probability perturbation method are compatible with MP geostatistics and allow integrating hydrodynamic data into MP simulations. More recent developments of MP geostatistics include sequentially simulating patterns instead of points and using different geological scenarios (training images) for dynamic data inversion.

The construction of training images (TIs) depicting the geological prior is one of the most critical step in multiple-point statistics. Geophysical techniques may be used to reduce the uncertainty in the understanding of prior geological scenarios. We developed a methodology to verify the consistency of geophysical data with independently-built TIs. Synthetic geophysical models built from TI scenarios are compared, using multidimensional scaling, with inverted models from field surveys to check if TIs are consistent with geophysical models. Then, the probability of each TI scenario is computed. A cluster analysis enables to determine which parameters used in building the TIs are most impacting the geophysical response. The methodology is tested using ERT to analyze TI scenarios in the Meuse River alluvial aquifer (Belgium)

Summary Accurate characterization of sub-surface oil reservoirs is an essential prerequisite to the design and implementation of enhanced oil recovery (EOR) scenarios. Specifically, in reservoir characterization, integrating static and dynamic data into reservoir models to construct accurate and realistic models has received considerable attention. Unlike most of the conventional geostatistical approaches of integrating data into reservoir models that are based on semi-variograms (two-point statistics) as a measure of spatial connectivity, a complete multiple-point (MP) statistic framework is presented in this paper. In contrast to two-point statistic methods, MP statistics-based methods are capable of reproducing curvilinear geological structures. The algorithm starts with extracting MP statistics from training images (TI) using an optimal spatial template. After collecting different patterns and building the MP histogram, the pattern reproduction process commences. This process begins from data locations and then grows to fill the whole reservoir domain. The algorithm accounts for three main practical issues: uncertainty in geological scenarios, scanning template and non-stationarity. The MP statistics algorithm (growthsim) is capable of integrating data from multiple data sources. Among these data types is dynamic data or flow history. The conventional approach to integrate production information into reservoir models is by iterative perturbation of the reservoir model until the production history of the reservoir is matched. Iterative methods have been applied till date to random fields that are completely characterized by a two-point co-variance function. In contrast, this paper presents a forward modelling approach that investigates history matching within a MP modelling framework. A novel technique implemented in this research is based on the merging of MPs inferred from history matched and geological models. Pattern growth is performed subsequently by sampling from the merged MP histograms. History matched models using the presented approach show an excellent agreement with underlying geological descriptions and match production history.

Summary Energy derived from geothermal systems is essential to the energy transition. Inherent geological and a lack of data requires the use of computer-driven modelling and simulation to aid decision-making. To make sound decisions, many reservoir models that encapsulate different geological scenarios should be analysed such that the impact of geological uncertainty on geothermal energy production can be evaluated adequately. Current geomodelling workflows, however, are too time consuming to build and explore different contrasting geological scenarios at various scales. In this study we used the open-source Rapid Reservoir Modelling (RRM) software to design different geological scenarios of a shallow marine succession hosting a potential geothermal reservoir and analyse how multi-scale geological features impact reservoir flow. RRM allows users to quickly create and explore realistic 3D geological models from intuitive 2D sketches. Models arecreated in minutes while flow diagnostics allow us to analyse fluid-flow behavior in real-time. Models are then imported into commercial reservoir simulation packages to investigate the effect of heterogeneity and scale on geothermal energy production. We show how we can quickly evaluate how different scales of heterogeneity impact geothermal production estimates and which heterogeneities must be represented in reservoir models to obtain reliable results about the possible reservoir behaviours.

A new method for face recognition, landmark model matching, is proposed in this paper. It is based on the concepts of elastic bunch graph matching and active shape model, and optimised with particle swarm optimisation. It is a fully automatic algorithm and can be used for face databases where only one image per person is available. A face is represented by a landmark model consisting of nodes labelled with jets and gray-level profiles. A landmark distribution model is created from a few training images. The model similarity between the landmark distribution model and the deformable landmark model that has to be fitted to the face in the image is maximised by particle swarm optimisation, to find the optimal model to represent the face. Improved results were obtained by this method compared with elastic bunch graph matching without optimisation.

The Traveling Pilot Point method. A novel approach to parameterize the inverse problem for categorical fields

Summary An Automatic Well Planner (AWP) is developed to efficiently adjust pre-determined well paths to honor near-well model properties and increase overall production. The AWP replicates a modern geo-steering decision-making process, where adjustments to pre-programmed well paths are driven by continuous integration of data obtained from logging-while-drilling and look-ahead technology. This work focuses on combining the AWP into a robust optimization scheme. AWP-determined well trajectories follow reservoir properties in a more realistic manner than common well representations; thus, they deal better with geological uncertainty. Specifically, the AWP creates custom trajectories that consider individual geological near-well conditions of each realization in an ensemble of models. Thus, for each well path calculated by the optimization procedure, the AWP creates one custom trajectory for each geological realization. The expected NPV, computed over the set of trajectories, is then used to assess the performance of the candidate well path. The core operation of the AWP relies on an artificial neural network for tailoring the trajectory to geological properties. The AWP embeds a geology-based feedback mechanism for the overall well placement search. Commonly, well placement searches are conducted using linear well path representations. Analog to realistic drilling operations, the AWP determines a custom trajectory by moving along such a path in a sequence of steps from the heel to the toe. Subsequent trajectory points are determined by the efficient processing of neighboring geological information through the AWP network. The proposed scheme is implemented within the open-source optimization framework FieldOpt, which provides a flexible interface for problem parameterization and parallelization. Tests are performed using two derivative-free algorithms: Asynchronous Parallel Pattern Search (APPS) and Particle Swarm Optimization (PSO). Both are applied to the Olympus ensemble. The results show that the AWP improved over a straight-line parametrization in a robust optimization scheme for both APPS and PSO.

Clustering algorithm is a crucial step before to analysis object's feature in image applications. The adapt DB-PSO patterns clustering algorithms (ADPCA) combined the particle swarm optimization (PSO) clustering algorithm and adapt DB_index measuring methodology to efficiently decide the real number of clusters, cluster centers, and then to recognize the correct catalog even if there are exiting some cases in various shapes, multi-dimension, real life training patterns and image datasets. In general, the PSO is adapted for dealing complex and global optimization problems. The population-based evolutional PSO learning algorithm with the self-adapt mathematic index can fit the data vibration to perform the real criterion of homogeneity of neighboring pixels in many image vision and understanding cases. Owing to the purpose of generating automatic clustering algorithms, the specific fitness function contains the DB_validity measure to significantly improve resolutions of spatial information among the given training patterns. The computation of image DB_index is delivered to retrieve the specific objects by evaluating the characters of given patterns. The novel ADPCA actually indicate the homogeneity region of interesting pictures and eliminate small pieces of elements by the supports of DB index measure, which can be used to dynamically compute the maximal similarity and small difference of the discussed image patterns. Several artificial datasets include the three-dimensional dataset with five spherical clusters, two-dimensional patterns with three different sizes circles, one Chtree Fractal image patterns, one real life IRIS data and one grey level image data, which are given as training patterns to demonstrate the adaptation and efficiency of the ADPCA learning method. It presents that ADPCA determine the correct clustering number and suitable cluster position in different data clustering examples. Two image segmentation applications also show that ADPCA can achieve correct detection of subjects. In conclusion, several simulations compared with the traditional k-means algorithm demonstrate the great results of ADPCA learning machine.

Abstract: This paper presents a novel approach utilizing Particle Swarm Optimization (PSO) for enhancing the efficiency of solar-powered electric vehicle (EV) charging systems. With the increasing adoption of EVs and the imperative to transition towards renewable energy sources, optimizing the utilization of solar power for charging becomes crucial. The proposed system integrates photovoltaic (PV) panels to harness solar energy, providing a sustainable and renewable power source for EV charging. The key innovation lies in the application of PSO, a nature-inspired optimization algorithm, to dynamically adjust charging parameters based on real-time environmental conditions, grid electricity prices, and EV battery requirements. PSO offers a robust and efficient method for solving optimization problems by simulating the behavior of swarms in nature. In the context of solar-powered EV charging, the PSO algorithm iteratively adjusts charging rates and schedules to maximize solar energy utilization, minimize charging costs, and ensure optimal battery health. The integration of PSO optimization with solarpowered EV charging represents a promising step towards achieving sustainable and intelligent transportation solutions. Future research directions may include further optimization refinements, scalability studies, and real-world deployment to validate the practicality and effectiveness of the proposed approach in diverse environments and usage scenarios.

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 193895, “Multilevel Strategies and Geological Parameterizations for History Matching Complex Reservoir Models,” by Yimin Liu, SPE, and Louis J. Durlofsky, SPE, Stanford University, prepared for the 2019 SPE Reservoir Simulation Conference, Galveston, Texas, 10–11 April. The paper has not been peer reviewed. The complete paper explores the use of multilevel derivative-free optimization for history matching, with model properties described using principal component analysis (PCA) -based parameterization techniques. The parameterizations applied are optimization-based PCA (O-PCA) and convolutional-neural-network-based PCA (CNN-PCA). Mesh adaptive direct search (MADS), a pattern search method that parallelizes naturally, is used for the optimizations required to generate posterior models. The use of PCA-based parameterization reduces considerably the number of variables that must be determined during history matching, but the optimization problem can still be computationally demanding. The multilevel strategy addresses this issue by reducing the number of simulations that must be performed at each MADS iteration. History-matching results demonstrate that substantial uncertainty reduction is achieved in all cases considered and that the multilevel strategy is effective in reducing the number of simulations required. Overview Parameterization has two key advantages in history matching: Far fewer parameters must be determined, which simplifies greatly the minimization in some cases. Posterior (history-matched) geomodels will be consistent with the geological scenario or training image for which the parameterization was constructed. PCA is the foundation for many geological-dimension-reduction parameterization methods. PCA is based on the eigen-decomposition of the prior geomodel covariance matrix and, thus, honors only two-point spatial statistics. History-matching algorithms largely can be classified as either optimization-based or ensemble-based procedures. Optimization-based algorithms generate one history-matched model at a time, while ensemble-based algorithms update a large set of models simultaneously. The resulting ensemble of posterior models is used to quantify uncertainty. In this study, only optimization-based history matching is considered, though the parameterizations applied also can be used with ensemble-based methods. Optimization-based history-matching algorithms can be classified further into gradient-based and derivative-free optimization (DFO) methods. Gradient-based algorithms often are combined with adjoint procedures that provide the required gradient efficiently. Unlike adjoint-based procedures, DFO algorithms (which are considered in this work) are nonintrusive. They treat the reservoir simulator as a so-called “black box,” and, as a result, they are much easier to implement and can be applied with any simulator. In this study, MADS, a pattern-search DFO, is applied for history matching. In pattern-search (or stencil-based) algorithms, the number of simulations required at each iteration scales with the number of parameters to be determined. Because the latter typically is much smaller than the number of grid-blocks in the model, geological parameterization leads to large computational savings when a pattern search, or other DFO, is used for history matching. The performance of DFO for history matching with non-Gaussian models, a primary topic in the complete paper, has not been studied extensively. The authors devise a multilevel strategy, applicable for PCA-based parameterization methods, to further reduce the computational cost of history matching using DFO. A multilevel strategy lends itself naturally to PCA-based parameterizations because the PCA representation can be ordered from the most-important to the least-important principal component. Thus, PCA parameters can be determined sequentially, level by level, in groups, rather than all at once.

Quantifying geological uncertainty for flow and transport modeling in multi-modal heterogeneous formations

The phase diversity (PD) algorithm is an image-based co-phasing error detection method for segmented mirror synthetic aperture optical systems. Particle swarm optimization (PSO) is suitable for PD for its fast convergence speed and simple structure. However, with the increase of the numbers of subapertures, optimization of cost function formed by the PD algorithm becomes a high-dimension non-linear optimization problem, which would lead PSO to result in a premature solution. Regarding the problem above, this paper presented a modified PSO in the PD algorithm to co-phase the segmented primary mirror, which overcame drawbacks of the traditional PSO, such as premature convergence and deactivation of particles, and enhanced the dig ability of the algorithm. Vast simulation results show that the modified PSO in the PD algorithm can effectively restore the segmented primary mirror, reducing the peak-to-valley (PV) value to 0.0012λ and the root mean square error to 0.0007λ, and raising the Strehl ratio to over 0.999. A comparison was also conducted to show that the modified PSO has advantages over two existing algorithms in higher accuracy and faster convergence speed.

Metaheuristic algorithms have emerged as powerful optimization techniques capable of efficiently exploring complex solution spaces to find near-optimal solutions. This paper provides a comprehensive review and comparative analysis of several widely used metaheuristic algorithms, including genetic algorithms (GA), particle swarm optimization (PSO), firefly algorithm (FA), grey wolf optimizer (GWO), squirrel search algorithm (SSA), flying fox optimization algorithm (FFO). The comparative analysis encompasses various performance metrics, such as convergence speed, solution quality, robustness, scalability, and applicability across diverse problem domains. The study investigates the strengths and weaknesses of each algorithm through empirical evaluations of benchmark problems, highlighting their suitability for different optimization scenarios. Additionally, the impact of parameter tuning on algorithm performance is discussed, emphasizing the need for careful parameter selection to achieve optimal results.

The importance of Distributed Generators (DGs) in the operation of electric power distribution systems both technically and economically has grown significantly in recent times. This is primarily due to the continuous rise in electricity demand which is increasingly challenging to meet with the energy generation. As a result, DGs provide more efficient alternatives for delivering quality energy close to consumption sites. This study modelled a typified Nigerian power distribution network by integrating renewable DG units based on solar Photovoltaics (PV) capacity factors. The study aimed to determine the optimal DG sizing and location using Particle Swarm Optimization (PSO) to enhance network performance. Three optimization scenarios were explored: minimizing total cost with loss, minimizing total cost with voltage stability index and minimizing total cost and loss with voltage stability index. These scenarios considered constraints such as voltage limits, DG power injection, power balance and power flow. The results obtained indicated that the third scenario which focused on minimizing total cost and loss while improving voltage stability yielded the best network performance. It resulted in significant loss reduction, voltage stability improvement and cost savings compared to the other two and the base scenarios.