Multiple Geological Realizations Research Articles

Data-driven analysis of soil consolidation with prefabricated vertical drains considering stratigraphic variation

In coastal cities such as Hong Kong, rapid reclamation using prefabricated vertical drains (PVDs) is preferred as it can accelerate land supply to meet the urgent demand for houses. A robust PVD design relies on the correct identification of permeable soil layers and accurate delineation of their stratigraphic connectivity with surrounding drainage boundaries. The current engineering practice often ignores the physical locations of minor drainage boundaries (e.g., sand lenses) in the subsurface stratigraphy and might lead to a false interpretation of potential drainage and consolidation mechanisms. In this study, a data-driven analysis framework that takes stratigraphic uncertainty into consideration is proposed to investigate the spatiotemporal consolidation of PVD-improved ground using sparse site investigation data often encountered in engineering practice. The method adaptively develops multiple geological cross-sections from limited measurements and prior knowledge that is reflected by a single training image. The resulting multiple geological realizations serve as the input for PVD analysis. The proposed data-driven framework allows for a probabilistic evaluation of soil spatiotemporal behavior in terms of the degree of consolidation and future ground settlement. More importantly, the proposed method accurately predicts the spatial distribution of stratigraphic boundaries with quantified uncertainty, which significantly influences the consolidation mechanism.

Selecting representative geological realizations to model subsurface [formula omitted] storage under uncertainty

Carbon capture and storage (CCS) is one of the quickest and most effective solutions for reducing carbon emissions. The majority of subsurface storage occurs in saline aquifers, for which geological information is lacking which in turn results in geological uncertainty. To evaluate uncertainty in CO2 injection projections, the use of multiple geological realizations (GRs) has been practiced very commonly. In this approach, hundreds or thousands of high-resolution GRs is used that quickly becomes computationally expensive. This issue can be addressed with representative geological realizations (RGRs) that preserve the uncertainty domain of the ensemble GRs. In this study, we propose the use of unsupervised machine learning (UML) frameworks, including dissimilarity measurement, dimensionality reduction, clustering and sampling algorithms ta select a predetermined number of RGRs. We compare the simulation outputs of the RGR sets and the ensemble using the Kolmogorov–Smirnov (KS) test to select the best UML. The UML frameworks and their associated selection processes are evaluated using a saline aquifer with a single CO2 injection well and 200 GRs with varying uncertain petrophysical characteristics. The best UML framework is selected to use only 5% of the GRs while maintaining the uncertainty domain of the ensemble GRs. In addition, the best UML framework is tested using a saline aquifer with three CO2 injection wells and varied GRs. The results show that our proposed UML framework can be used to choose RGRs, capturing the whole uncertainty domain. Our approach leads to a significant reduction in the computational cost associated with scenario testing, decision-making, and development planning for CO2 storage sites under geological uncertainty.

Convolutional – recurrent neural network proxy for robust optimization and closed-loop reservoir management

Production optimization under geological uncertainty is computationally expensive, as a large number of well control schedules must be evaluated over multiple geological realizations. In this work, a convolutional-recurrent neural network (CNN-RNN) proxy model is developed to predict well-by-well oil and water rates, for given time-varying well bottom-hole pressure (BHP) schedules, for each realization in an ensemble. This capability enables the estimation of the objective function and nonlinear constraint values required for robust optimization. The proxy model represents an extension of a recently developed long short-term memory (LSTM) RNN proxy designed to predict well rates for a single geomodel. A CNN is introduced here to processes permeability realizations, and this provides the initial states for the RNN. The CNN-RNN proxy is trained using simulation results for 300 different sets of BHP schedules and permeability realizations. We demonstrate proxy accuracy for oil-water flow through multiple realizations of 3D multi-Gaussian permeability models. The proxy is then incorporated into a closed-loop reservoir management (CLRM) workflow, where it is used with particle swarm optimization and a filter-based method for nonlinear constraint satisfaction. History matching is achieved using an adjoint-gradient-based procedure. The proxy model is shown to perform well in this setting for five different (synthetic) ‘true’ models. Improved net present value along with constraint satisfaction and uncertainty reduction are observed with CLRM. For the robust production optimization steps, the proxy provides O(100) runtime speedup over simulation-based optimization.

Statistical prediction of waterflooding performance by K-means clustering and empirical modeling

Statistical prediction is often required in reservoir simulation to quantify production uncertainty or assess potential risks. Most existing uncertainty quantification procedures aim to decompose the input random field to independent random variables, and may suffer from the curse of dimensionality if the correlation scale is small compared to the domain size. In this work, we develop and test a new approach, K-means clustering assisted empirical modeling, for efficiently estimating waterflooding performance for multiple geological realizations. This method performs single-phase flow simulations in a large number of realizations, and uses K-means clustering to select only a few representatives, on which the two-phase flow simulations are implemented. The empirical models are then adopted to describe the relation between the single-phase solutions and the two-phase solutions using these representatives. Finally, the two-phase solutions in all realizations can be predicted using the empirical models readily. The method is applied to both 2D and 3D synthetic models and is shown to perform well in the P10, P50 and P90 of production rates, as well as the probability distributions as illustrated by cumulative density functions. It is able to capture the ensemble statistics of the Monte Carlo simulation results with a large number of realizations, and the computational cost is significantly reduced.

An artificial intelligence method for improving upscaling in complex reservoirs

The upscaling of geological properties is a fundamental requirement to construct a suitable simulation model since the geological model typically contains millions of cells, which makes it computationally difficult to simulate it on such a scale. The process consists of a scale transfer that adapts the petrophysical properties of a high-resolution grid to a coarser grid. Nevertheless, this is not a trivial operation, especially for absolute permeability, which is a non-additive property. One of the most reliable methods is to perform a flow simulation on fine-scale cells that correspond to the coarse block and derive the single permeability value that reflects the same flow value. Still, this is a very time-consuming method and depends on the imposed boundary conditions. This work aims to take advantage of recent advances in artificial intelligence to produce results with similar or better quality of flow-based methods, and more adaptive. It handles models with multiple geological realizations by employing machine learning to capture patterns from a subset of scenarios and use it to generalize for all others. The methodology is divided into two stages — local and global. In the first one, a deep neural network is trained with a fraction of geological realizations using the flow-based results as a reference. In the second stage, clustering analysis is employed along with a neural network optimization to learn an adjustment procedure for the coarse simulation model concerning the cumulative field production predicted by the fine model simulation. Afterward, the trained network performs the upscaling of remaining realizations, but more efficiently in terms of computational time and providing better output in terms of production and injection. The method was applied to a benchmark model and the experimental results demonstrate that the local technique was capable of reproducing very similar values to the flow-based upscaling using only one scenario in training and at the global stage the coarse model was improved even further matching the field oil production forecast of the fine model. Different scenarios were used for training and testing and the results were consistent showing no bias towards a specific configuration and capability of generalization to different scenarios. Ultimately, the proposed artificial intelligence approach performed an accurate upscaling, surpassing the reference approach with forecast production similar to the fine model, and also fast to compute when considering multiple geological realizations, since it reduces the required numerical simulations to a fraction of the total.

Fast Optimization of Injector Selection for Waterflood, CO2-EOR and Storage Using an Innovative Machine Learning Framework

Optimal injector selection is a key oilfield development endeavor that can be computationally costly. Methods proposed in the literature to reduce the number of function evaluations are often designed for pattern level analysis and do not scale easily to full field analysis. These methods are rarely applied to both water and miscible gas floods with carbon storage objectives; reservoir management decision making under geological uncertainty is also relatively underexplored. In this work, several innovations are proposed to efficiently determine the optimal injector location under geological uncertainty. A geomodel ensemble is prepared in order to capture the range of geological uncertainty. In these models, the reservoir is divided into multiple well regions that are delineated through spatial clustering. Streamline simulation results are used to train a meta-learner proxy. A posterior sampling algorithm evaluates injector locations across multiple geological realizations. The proposed methodology was applied to a producing field in Asia. The proxy predicted optimal injector locations for water and CO2 EOR and storage floods within several seconds (94–98% R2 scores). Blind tests with geomodels not used in training yielded accuracies greater than 90% (R2 scores). Posterior sampling selected optimal injection locations within minutes compared to hours using numerical simulation. This methodology enabled the rapid evaluation of injector well location for a variety of flood projects. This will aid reservoir managers to rapidly make field development decisions for field scale injection and storage projects under geological uncertainty.

3D geo-cellular modeling for Oligocene reservoirs: a marginal field in offshore Vietnam

This study focuses on constructing a 3D geo-cellular model by using well-log data and other geological information to enable a deep investigation of the reservoir characteristics and estimation of the hydrocarbon potential in the clastic reservoir of the marginal field in offshore Vietnam. In this study, Petrel software was adopted for geostatistical modeling. First, a sequential indicator simulation (SIS) was adopted for facies modeling. Next, sequential Gaussian simulation (SGS) and co-kriging approaches were utilized for petrophysical modeling. Furthermore, the results of the petrophysical models were verified by a quality control process before determining the in-place oil for each reservoir in the field. Multiple geological realizations were generated to reduce the geological uncertainty of the model assessment for the facies and porosity model. The most consistent one would then be the best candidate for further evaluation. The porosity distribution ranged from 9 to 22%. The original oil place of clastic reservoirs in the marginal field was 50.28 MMbbl. Ultimately, this research found that the marginal field could be considered a potential candidate for future oil and gas development in offshore Vietnam.

BHPSO combined with statistical net hydrocarbon thickness map for well placement optimization under uncertainty

Investments in oil and gas projects are driven by critical field development decisions including well placement, which often significantly affect the projects’ economics. Due to their typically high cost and inherently insufficient data (especially in greenfields, or fields in their early stage of development), managing uncertainty is critical when optimizing a field development plan. The use of a single deterministic base case for hydrocarbon, both in place assessment and production forecasting is often misleading and leads to sub-optimal decisions. Consequently, robust field development plans require multiple geological realizations covering the range of uncertainty in reservoir properties and encompassing both multiple geological concepts and geostatistical properties distribution. Typically, an objective function such as the average net present value (NPV) or the average cumulative oil production (COP) is optimized in order to select an optimal development scenario. Nevertheless, such an assessment can be computationally prohibitive, especially when using optimization methods require hundreds, often thousands of costly simulations over a single realization, a number that significantly increases when multiple realizations are involved. This study proposes a new method for well placement optimization under uncertainty, building on map-based evolutionary optimization technique: the black hole particle swarm optimization (BHPSO). The statistical net hydrocarbon thickness (SNHCT) map is introduced to guide the BHPSO algorithm; and hence, pragmatically account for uncertainty in the process of well placement optimization. We optimize well placement on the realization corresponding to the minimum difference between its NHCT map and the SNHCT map. The SNHCT combines the average and the P90 NHCT maps; hence, assuring that the selected sweet spots for well placement are statistically the best with regard to the multiple subsurface realizations. The method is applied on the Olympus benchmark case and results are compared to two scenario reduction methods: RMfinder and k-means-k-medoids Clustering. Results show superior performance over the two methods in terms of optimality of the result and the required computational load.

Integrated modelling framework for enhancement history matching in fluvial channel sandstone reservoirs

Abstract Modelling lithofacies and petrophysical properties are the challenging processes at the beginning of exploration and production of hydrocarbon reservoirs. However, the limited amount of well data and core data are the main issues facing conventional modelling processes. In this study, Artificial Neural Network (ANN), Sequential Gaussian Simulation (SGS), Co-kriging and object-based modelling (OBM) were integrated as the enhancement framework for lithofacies and petrophysical properties modelling in the fluvial channel sandstone reservoir. In the OBM, multiple fluvial channels were generated in the lithofacies model. The result of this model represented all the characteristic of the fluvial channel reservoir. The model was then distributed with channels, crevasse, and leeves depositional facies with background shale. Multiple geological realizations were made and cross-validation to select the most suitable lithofacies distribution. This model was cross-validated by modelling the porosity and permeability properties using Sequential Gaussian Simulation. Thereafter, the modelling process continued with Artificial Neural Network. Petrophysical properties (mainly porosity and permeability) were predicted by training various seismic attributes and well log data using the ANN. Applying the co-kriging algorithm, the predicted ANN model was integrated with OBM simulated lithofacies model to preserve the fluvial features of the geological system. To achieve full field history matching, the final geological model was upscaled to serve as input data in dynamic history matching. An excellent and nearly perfect history matching with a least mismatch was obtained between the measurement and simulated bottom hole pressure from well test and production history. The results indicated that an efficient integrated workflow of ANN and other geostatistical approaches are imperative to attaining an excellent history matching.

A framework for assisted history matching and robust optimization of low salinity waterflooding under geological uncertainties

Low Salinity Waterflood (LSW) is an emerging Enhanced Oil Recovery (EOR) method that is simple to implement and has been shown to yield a substantial increase in oil recovery over conventional waterflood, especially in oil-wet sandstone reservoirs. The major mechanism for increased oil recovery is a wettability change from oil-wet to water-wet, which is induced by ion exchange between the injected fluid and the clay surface.This paper presents a framework for field scale modeling, assisted history match, and robust optimization of LSW under geological uncertainties that has rarely been discussed in the past. To handle this complex recovery process, a comprehensive ion-exchange model has been implemented, fully coupled with geochemistry specially designed for the modeling of LSW physical phenomena in an EOS reservoir simulator. This model is capable of accounting for the critical role of the properties, quantity, and distributions of clay minerals.A systematic study was performed to evaluate the critical effects of geology on large scale LSW performance. Numerous geostatistical realizations of a five-spot LSW pattern were generated to evaluate the effect of clay on LSW. The numerical simulation results indicate that LSW's performance depends critically on the reservoir geological characteristics. Based on the integrated modeling approach presented in this paper, multiple geological realizations can be automatically generated from a big-loop approach that is needed for fast and accurate HM and optimization of LSW. The key parameters for successful field scale LSW HM include: clay distribution/quantity associated with different facies, relative permeability modification, wettability alteration thresholds, reservoir minerals, geochemical reactions, and operating conditions. More importantly, LSW HM by tuning reservoir parameters may only lead to poor prediction results, while the integrated modeling approach provides much better forecasting results to true history data.Finally, a new concept for LSW robust optimization under geological uncertainty is introduced and demonstrated with reservoir simulation. As there are uncertainties associated with the geological modeling of the clay distribution, this paper shows how robust optimization can be applied to reduce uncertainties in the LSW optimization through well placement.

Multilevel Field Development Optimization Under Uncertainty Using a Sequence of Upscaled Models

The robust optimization of reservoir performance under geological uncertainty typically requires the simulation of multiple geological realizations at each iteration of the optimization run. This results in high computational expense, particularly when simulation models are highly resolved and many realizations are employed to characterize geological uncertainty. In recent work we introduced a multilevel optimization procedure that uses a sequence of upscaled models to accelerate field development optimization. The core optimizer is a particle swarm optimization–mesh adaptive direct search (PSO–MADS) hybrid technique. Coarse-scale models are constructed from the fine-grid geological characterization using an accurate global transmissibility upscaling procedure. In this paper we extend the multilevel framework to enable efficient optimization under uncertainty. New treatments include the use of a sample validation procedure for realization selection and the use of the standalone MADS optimizer (rather than PSO–MADS) after the first optimization stage. Numerical results are presented for two example systems, and for each case optimization over both ten and 100 realizations is performed. For ten-realization cases we achieve comparable results, and speedups of a factor of 10 or more, relative to the conventional single-level optimization procedure. Speedups are estimated to be even more substantial for 100 realization cases, for which conventional optimization is not practical. We also investigate the application of a multilevel Monte Carlo approach as an alternative to our proposed techniques for optimization under uncertainty. Although this method is faster than the conventional approach, it is not as efficient as the multilevel procedures developed in this work.

Ensemble level upscaling for compositional flow simulation

Uncertainty quantification is typically accomplished by simulating multiple geological realizations, which can be very expensive computationally if the flow process is complicated and the models are highly resolved. Upscaling procedures can be applied to reduce computational demands, though it is essential that the resulting coarse-model predictions correspond to reference fine-scale solutions. In this work, we develop an ensemble level upscaling (EnLU) procedure for compositional systems, which enables the efficient generation of multiple coarse models for use in uncertainty quantification. We apply a newly developed global compositional upscaling method to provide coarse-scale parameters and functions for selected realizations. This global upscaling entails transmissibility and relative permeability upscaling, along with the computation of a-factors to capture component fluxes. Additional features include near-well upscaling for all coarse parameters and functions, and iteration on the a-factors, which is shown to improve accuracy. In the EnLU framework, this global upscaling is applied for only a few selected realizations. For 90 % or more of the realizations, upscaled functions are assigned statistically based on quickly computed flow and permeability attributes. A sequential Gaussian co-simulation procedure is incorporated to provide coarse models that honor the spatial correlation structure of the upscaled properties. The resulting EnLU procedure is applied for multiple realizations of two-dimensional models, for both Gaussian and channelized permeability fields. Results demonstrate that EnLU provides P10, P50, and P90 results for phase and component production rates that are in close agreement with reference fine-scale results. Less accuracy is observed in realization-by-realization comparisons, though the models are still much more accurate than those generated using standard coarsening procedures.

Uncertainty assessment of spatially distributed nitrate reduction potential in groundwater using multiple geological realizations

Spatially distributed nitrate reduction potential in groundwater was estimated for the clay till dominated Norsminde fjord catchment in Denmark using the distributed hydrological model MIKE SHE. The nitrate transport was simulated using particle tracking and nitrate was assumed to be instantaneously reduced at the redox interface. Spatially distributed depths of the redox interface were estimated based on the spatial patterns in groundwater recharge and sediment redox capacity. Uncertainty of the estimated nitrate reduction due to geological uncertainty was assessed using multiple geological realizations. The geological realizations were generated using the geostatistical software TProGS and either conditioned based on borehole data only or soft conditioned based on both borehole data and geophysical data. Finally an upscaling of the predicted nitrate reduction was done in order to evaluate the change in uncertainty with increasing scale. The study showed that the uncertainty (one standard deviation) of the estimated nitrate reduction potential (in percentage of nitrate input) on the original 100 m model scale was 25% if only using borehole data and 19% if combining the borehole data with geophysical data. The uncertainty on the model predictions decreased with increasing aggregation scale. The decrease in uncertainty was most apparent the first 500 m, where after the uncertainty started to level off. This scale corresponded well to the mean length of the sand units within the clay till. It is concluded that using geophysical data in combination with borehole data in generation of geological realizations can help decrease uncertainty on the estimated nitrate reduction and that the predictive capability of distributed models is constrained by the spatial resolution of key data such as geology.

Optimization of Production Performance in a CO2 Flooding Reservoir Under Uncertainty

Abstract CO2 flooding has gained momentum in the oil and gas industry and might be suitable for approximately 80% of oil reservoirs worldwide based on the oil recovery criteria alone. In addition to miscibility, production performance needs to be optimized to achieve higher sweep efficiency and oil recovery. Although many techniques have been made available for production optimization in the upstream oil and gas industry, it is still a challenging task to optimize production performance in the presence of physical and/or financial uncertainties. In this paper, a new technique is developed to optimize production performance in a CO2 flooding reservoir under uncertainty. More specifically, potential uncertainties influencing production performance are analyzed and assessed by using the geostatistical technique. This enables us to integrate the available information within a unified and consistent framework and to generate multiple geological realizations accounting for uncertainty and spatial variability. Subsequently, the net present value (NPV) is selected as the objective function to be optimized by using the genetic algorithm, while well rates of the injectors and the flowing bottomhole pressure for the producers are chosen as the controlling variables. In addition, corresponding modifications have been made to accelerate the convergence speed of the genetic algorithm. A field case is used to demonstrate the procedures of the newly developed technique and the optimized results show that the oil recovery and the NPV can be increased by 6.4% and 9.2%, respectively. It is also found that the genetic algorithm is a powerful and reliable search method to optimize production performance of reservoirs with complex structures. Introduction CO2 flooding is considered as a promising and practical enhanced oil recovery (EOR) process because it not only increases oil recovery, but also reduces greenhouse gas emissions by sequestrating CO2 in the depleted reservoirs. In practice, CO2 flooding performance can be greatly affected by the reservoir heterogeneity, which can severely reduce the sweep efficiency, result in early CO2 breakthrough at the producers, and thus, leave a large amount of bypassed oil in the reservoir(1). Therefore, it is of fundamental and practical importance to optimize production performance of a CO2 flooding reservoir.

Ensemble-Level Upscaling for Efficient Estimation of Fine-Scale Production Statistics

Summary Upscaling is often needed in reservoir simulation to coarsen highly detailed geological descriptions. Most existing upscaling procedures aim to reproduce fine-scale results for a particular geological model (realization). In this work, we develop and test a new approach, ensemble-level upscaling, for efficiently generating up-scaled two-phase flow parameters (e.g., upscaled relative permeabilities) for multiple geological realizations. The ensemble-level upscaling approach aims to achieve agreement between the fine-and coarse-scale flow models at the ensemble level, rather than realization-by-realization agreement, as is the intent of existing upscaling techniques. For this purpose, flow-based upscaling calculations are combined with a statistical procedure based on a cluster analysis. This approach allows us to compute numerically the upscaled two-phase flow functions for only a small fraction of the coarse blocks. For the majority of blocks, these functions are estimated statistically on the basis of single-phase velocity information (attributes), determined when the upscaled single-phase parameters are calculated. The procedure is designed to maintain close correspondence between the cumulative distribution functions (CDFs) for the numerically computed and statistically estimated two-phase flow functions. We apply the method to 2D synthetic models of multiple realizations for uncertainty quantification. Models with different geological heterogeneity and fluid-mobility ratios are considered. It is shown that the method consistently corrects the biases evident in primitive coarse-scale predictions and can capture the ensemble statistics (e.g., P50, P10, P90) of the fine-scale results almost as accurately as the full flow-based upscaling procedures but with much less computational effort. The overall approach is flexible and can be used with any combination of upscaling procedures.