Uncertainty quantification of reservoir performance using machine learning algorithms and structured expert judgment

Using commercial numerical reservoir simulators to build a full field reservoir model and simultaneously history match multiple dynamic variables for a highly complex, offshore mature field in Malaysia, had proven to be challenging, manpower intensive, highly expensive, and not very successful. This field includes almost two hundred wells that have been completed in more than 60 different, non-continuous reservoir layers. The field has been producing oil, gas and water for decades. The objective of this article is to demonstrate how Artificial Intelligence (AI) and Machine Learning is used to build a purely data-driven reservoir simulation model that successfully history match all the dynamic variables for all the wells in this field and subsequently used for production forecast. The model has been validated in space and time. The AI and Machine Learning technology that was used to build the dynamic reservoir simulation and modeling is called spatio-temporal learning. Spatio-temporal learning is a machine-learning algorithm specifically developed for data-driven modeling of the physics of fluid flow through porous media. Spatio-temporal learning is used in the context of Deconvolutional Neural Networks. In this article Spatio-temporal Learning and Deconvolutional Neural Networks will be explained. This new technology is the result of more than 20 years of research and development in the application of AI and Machine Learning in reservoir modeling. This technology develops a coupled reservoir and wellbore model that for this particular oil & gas field in Malaysia uses choke setting, well-head pressure and well-head temperature as input and simultaneously history matches Oil production, GOR, WC, reservoir pressure, and water saturation for more than a hundred wells through a completely automated process. Once the data-driven reservoir model is developed and history matched, it is blind validated in space and time in order to establish a reliable and robust reservoir model to be used for decision making purposes and opportunity generation to maximise the field value. The concepts and the methodology of history match of multiple wells, individual offshore platforms, and the entire field will be presented in this article along with the results of blind validation and production forecasting. Results of using this model to perform uncertainty quantification will also be presented. A case study of a highly complex mature field with large number of wells and years of production has been used to be studied and simulated by this data-driven approach. Time, efforts, and resources required for the development of the dynamic reservoir simulation models using AI and Machine Learning is considerably less than time and resources required using the commercial numerical simulators. It is validated that the TDM developed model can make very reasonable prediction of field behavior and production from the existing wells based on modification of operational constraints and can be a prudent complementary tool to conventional numerical simulators for such complex assets.

Structural, stratigraphic, and petrophysical uncertainties result in a wide range of geologic interpretations. For fields with long production and pressure history, 3D-dynamic simulations have been very useful in providing feedback to geologic modelers, which results in improved static models. The Chuchupa Field has produced 1.9 Tscf of dry gas, or approximately 40% of the Original Gas in Place (OGIP). At the time of this study, 3 new horizontal wells were being planned, and new gas sales agreements were being considered. We developed a dynamic workflow to create a range of probabilistic simulation models to forecast dry-gas production under several production scenarios in the Chuchupa field. Recent seismic re-interpretation, a new stratigraphic study and a revision of the petrophysical model resulted in new probabilistic static models for the field. While these static models were being built, a parallel numerical simulation study was conducted to determine the range of OGIP values that could be successfully history-matched. Nine numerical reservoir models were generated by applying pore volume multipliers to the prior-generation reservoir model, yielding a range of OGIP from 3.8 to 6.6 Tscf. We attempted to history match each of these nine models by using an optimization routine to adjust aquifer support, vertical transmissibility across a potential seal, and rock compressibility. The optimization routine proved to be a very useful and efficient tool to attain good quality history matches in short periods of time. Good matches were obtained for models with OGIP ranging from 4.3 to 5.8 Tscf. Based on this information, the geologic modelers revised petrophysical parameters and generated 27 static models. These models encompassed 3 structural interpretations, 3 porosity distributions, and 3 possible positions of gas/water contact (GWC). From experimental design we obtained the P10, P50, and P90 OGIP values of 4.1, 4.7, and 5.3 Tscf respectively. We scaled up and built reservoir simulation models for 8 geologic interpretations to represent the range of OGIP and reservoir geometries. Again, these models were history matched using the optimization routine. The match parameters were static well pressures and the absence of water production. Six out of the eight the models could be satisfactorily history-matched with reasonable adjustments to aquifer strength, vertical transmissibility, and rock compressibility. The OGIP range for these models was 4.1 to 5.6 Tscf. We selected 3 models to forecast future gas production. These models match the P10, P50, and P90 OGIP values determined in the probabilistic static model, and combine the low, mid, and high structures, porosity and Swi distributions, and the range of GWC positions. We also calibrated the various models with historical bottomhole and tubinghead flowing pressures, and coupled the reservoir model with a network consisting of surface lines and equipment; pipelines from two platforms to the onshore sale-point station; and multi-stage compression to 1,215 psia. The model is currently used to evaluate various production and market scenarios.

Despite their apparent high dimensionality, spatially distributed reservoir properties can often be compactly (sparsely) described in a properly designed basis. Hence estimation of high-dimensional reservoir flow properties from dynamic performance data, a.k.a. history matching, can be formulated and solved as a sparse reconstruction inverse problem. Recent advances in statistical signal processing, formalized under the compressed sensing paradigm, provide important guidelines on formulating and solving sparse inverse problems, primarily for linear models. Sparse inverse problems have been mainly formulated as a deterministic inverse problem. Given the uncertainty in describing the reservoir properties, even after integration of the dynamic data, it is important to develop a practical sparse Bayesian inversion framework to enable uncertainty quantification. We use sparse geologic dictionaries to compactly represent uncertain reservoir properties and develop a sparse Bayesian approach for effective data integration and uncertainty quantification. In formulating the Bayesian inversion, commonly used Gaussian distributions are not appropriate for representing sparse prior models. Following the results presented by the compressed sensing paradigm, Laplace (or double exponential) probability distributions are appropriate for representing sparse parameters. However, combining Laplace priors with frequently used Gaussian likelihood functions leads to neither Laplace nor Gaussian posterior distributions, thereby complicating the analytical characterization of the posterior distribution. Here, we first express the form of the Maximum A-Posteriori (MAP) estimate for Laplace priors, and then, as a practical approximation, use the Monte-Carlo-based Randomize Maximum Likelihood (RML) method to sample from the derived posterior distribution for uncertainty quantification. The Sparse RML (SpRML) realizations are approximate samples from the posterior distribution and provide a mechanism for assessing the uncertainty in the calibrated reservoir model with a relatively modest computational complexity. We demonstrate the suitability and effectiveness of the proposed SpRML formulation with a synthetic dataset and the model adapted from the PUNQ-S3 benchmark reservoir.

One of the challenges in automatic history matching is to ensure the preservation of the realistic geological features of reservoir models. Realism of the history matched model is vital because of its impact on the flow response and the reliability of the model predictions. The issue is that models with unrealistic geological features can still match history but would fail to deliver reliable predictions. The work tackles the following problems in history matching: (1) identify only realistic geometry of geological bodies in history matching using non-uniform intelligent prior distributions for the uncertain geological parameters; (2) assess uncertainty in the connectivity between permeable geobodies and automatically select the geomodel realisations best matching the production data. The intelligent geological priors and the connectivity measures are incorporated in an automated history matching framework, where adaptive stochastic sampling is used to find multiple history matched models to quantify uncertainty of the reservoir predictions. Use of intelligent priors, also, improves the history matching efficiency by restricting the search only to the geologically realistic models. Connectivity control improves flexibly of the model definition and allows handling uncertainty from multiple stochastic realisations in a more realistic way.

With the growing complexity of land surface models used to represent the terrestrial part of wider Earth system models, the need for sophisticated and robust parameter optimisation techniques is paramount. Quantifying parameter uncertainty is essential for both model development and more accurate projections. History matching is an emerging technique in climate science for uncertainty quantification. Using Gaussian process emulators, history matching allows us to rule out parts of parameter space that lead to model outputs being inconsistent with observations. In this presentation, we assess the power of history matching by comparing results to variational data assimilation, commonly used in land surface models for parameter estimation. Although both approaches have different setups and goals, we can extract posterior parameter distributions from both methods and test the model-data fit of ensembles sampled from these distributions. Using a twin experiment, we test whether we can recover known parameter values. Through variational data assimilation, we closely match the observations. However, the known parameter values are not always contained in the posterior parameter distribution, highlighting the equifinality of the parameter space. In contrast, while more conservative, history matching still gives a reasonably good fit and provides more information about the model structure by allowing for non-Gaussian parameter distributions. Furthermore, the true parameters are contained in the posterior distributions. We then consider history matching's ability to ingest different metrics targeting different physical parts of the model, helping to reduce parameter space further and improve model-data fit. We find the best results when history matching is used with multiple metrics; not only is the model-data fit improved, but we also gain a deeper understanding of the model and how the different parameters constrain different parts of the seasonal cycle. We conclude by discussing the potential of history matching in future studies.

As the role of reservoir flow simulation increasingly impacts existing operations and field development decisions, it follows that rigor, fitness and consistency should be imposed on the calibration of reservoir flow models to dynamic data through history matching. Although a wealth of history matching techniques exist in the petroleum literature that propose novel algorithms or share case studies, seldom does the content guide the modeler in fit-for-purpose reservoir model calibration for an operating asset. To evaluate the applicability of these diverse techniques against standards required for reservoir management, an internal study was performed to benchmark four assisted history matching (AHM) techniques commonly promoted in the oil and gas industry. The techniques were vetted against a comprehensive suite of modeling requirements for multiple asset classes, integrating a variety of historical dynamic data types through the calibration of reservoir properties that control flow behavior from the field to inter-well scale. The methods benchmarked were: (1) Design of Experiments (DoE)-based, (2) Ensemble Kalman Filter and Ensemble Smoother, (3) Genetic Algorithm and (4) Generalized Travel Time Inversion. This manuscript focuses solely on the DoE-based technique.In order to consistently benchmark the techniques, a set of standards was defined against which each was evaluated to determine its suitability for widespread history matching applications. The standards involve: the capacity to parameterize (and therefore calibrate) a diversity of reservoir flow model attributes, the capacity to integrate different types of dynamic data, the level of independence from the flow simulator and the capability to provide probabilistic outcomes for predictive uncertainty assessment. Of the four techniques, the DoE-based approach uniquely satisfied all requirements. Its history matching workflow has the flexibility to incorporate any form of reservoir model parameter and to assimilate a history matching error metric for any individual or group of historical data types; therefore, benchmarking established DoE-based techniques as unambiguously the most compliant with generic asset modeling requirements. The approach was also identified as the most straightforward, both theoretically and in practical computation, and therefore applicable to the broadest range of practitioners. Perhaps most importantly, the approach demonstrated the capacity for accurate quantification of uncertainty (or non-uniqueness) in reservoir quality resulting from an exhaustive, although approximate, exploration of model parameter space and the associated history matching error metric(s).This manuscript compiles the results and insights gained from benchmarking of the DoE-based techniques through the proposal of a comprehensive assisted history matching workflow. The workflow is designed for generality while providing best practices that guide the modeler in fit-for-purpose application. Limitations of the workflow are also recognized. Key components include: selection and screening of calibration parameters based on statistical significance, development of surrogate models to characterize the relationship between parameters and the simulated historical data being integrated into the reservoir model, use of the surrogate models for exhaustive yet efficient exploration of parameter space to identify (non-unique) history matched models, and (deterministic or probabilistic) discrete reservoir model selection for use in forecast-based decision making. Each step of the AHM workflow is presented from a conceptual and applied perspective, and field applications are provided to demonstrate key concepts. Although the applications presented include two deepwater Gulf of Mexico assets, the workflow and insights provided are developed from benchmarking across a diverse suite of asset types.

Shared micromobility services are experiencing rapid growth, particularly in addressing last‐mile transportation needs. The most crucial questions focus on identifying the determinants of user behavior and the factors driving demand for micromobility vehicles. Investigating this topic is thus essential for meeting the demand of micromobility vehicles, ensuring their dynamic and flexible deployment, and optimizing overall system planning. In this study, demand forecasting was performed using a shared electric scooter (e‐scooter) dataset and by comparing 19 distinct machine learning (ML) and deep learning (DL) algorithms, including traditional ML algorithms, neural network–based (NN) models , ANN and metaheuristic hybrid models, and ensemble models. Algorithm performance, evaluated using R 2 and RMSE metrics, shows that boosting and hybrid models significantly outperform traditional algorithms. In this study, the algorithms were compared not only with RMSE and R 2 but also with their running times. Our analysis reveals that GRU, ANN–Grid–Search, ANN–Bayesian, ANN–Randomize–Search, ANN‐PSO, and ANN‐GA models achieve the highest performance, though this performance is inversely related to their computational cost. When the running time is included in the analysis, the GRU algorithm ranks best (RMSE: 0.945248, R 2 : 0.174226, runtime: 6.1), followed by ANN‐GA and ANN‐PSO models. These findings will help e‐scooter providers plan effectively and make informed investment decisions.

Reservoir characterization is a crucial aspect of the oil and gas industry, providing insights into the properties and potential productivity of hydrocarbon reservoirs. Advanced geological modeling techniques have significantly enhanced the accuracy and efficiency of reservoir characterization. These techniques integrate diverse datasets and sophisticated algorithms to create detailed subsurface models that inform exploration, development, and production strategies. One of the primary techniques in advanced geological modeling is seismic interpretation, which involves the analysis of seismic data to map subsurface structures. High-resolution 3D seismic surveys provide detailed images of the subsurface, allowing geologists to identify faults, fractures, and stratigraphic features with greater precision. The integration of seismic inversion techniques converts seismic reflection data into quantitative rock property estimates, such as porosity and fluid saturation, further refining the reservoir model. Geostatistical modeling is another critical technique that improves reservoir characterization. By utilizing statistical methods to analyze spatial variability, geostatistics generates multiple realizations of reservoir properties, capturing the inherent uncertainty and heterogeneity of the subsurface. Techniques such as kriging, co-kriging, and sequential Gaussian simulation are commonly used to interpolate and extrapolate data from well logs and seismic surveys, creating probabilistic models that guide decision-making under uncertainty. Petrophysical analysis plays a significant role in enhancing geological models. Well logs, core samples, and laboratory measurements provide direct information about rock and fluid properties. Petrophysical models are developed to correlate these properties with depth and other geological features. Advances in machine learning and data analytics have further refined petrophysical interpretation by enabling the integration of large datasets and the identification of complex patterns that traditional methods might miss. Another advanced technique is the use of reservoir simulation, which models the flow of fluids within the reservoir over time. Reservoir simulators incorporate geological models, petrophysical data, and production history to predict future reservoir performance under different production scenarios. This dynamic modeling is essential for optimizing recovery strategies, enhancing field development plans, and managing reservoir performance. Multi-scale modeling approaches have also become increasingly important. These approaches integrate data and models across different spatial and temporal scales, from pore-scale petrophysical properties to basin-scale geological structures. By capturing the interactions between processes occurring at different scales, multi-scale models provide a more comprehensive understanding of reservoir behavior and improve the accuracy of predictions. The integration of machine learning and artificial intelligence (AI) has revolutionized reservoir characterization. Machine learning algorithms can process vast amounts of data from various sources, such as seismic surveys, well logs, production data, and geological maps, to identify patterns and relationships that enhance the understanding of reservoir properties. AI-driven techniques, including neural networks and support vector machines, are increasingly used for tasks such as facies classification, porosity prediction, and fracture detection, leading to more accurate and efficient reservoir models. The application of big data analytics in geological modeling has enabled the handling and analysis of massive datasets that were previously unmanageable. Advanced data analytics tools facilitate the integration, processing, and visualization of complex datasets, enhancing the ability to derive actionable insights and improve decision-making in reservoir management. Keywords: Techniques, Reservoir Characterization, Advanced, Geological Modeling, Oil, Gas, Industries

This paper presents real time road traffic state estimation framework together with its evaluation. To evaluate the framework, a three-layer Artificial Neural Network model is proposed and used to estimate complete link traffic state. The inputs to the ANN model include probe vehicle's position, time stamps and speeds. To model the arterial road network the microscopic simulation SUMO is used to generate aggregated speed and FCD export files which are used in the training and evaluation of the ANN model. Besides, real A-GPS data gathered using A-GPS mobile phone on a moving vehicle on the sample roads is used to evaluate the ANN model. The performance of the ANN model is evaluated using the performance indicators RMSE and MPAE and on average the MPAE is less than 1.2%. The trained ANN model is also used to estimate the sample road link speeds and compared with ground truth speed (aggregate edge states) on a 10-minute interval for 1hr. The estimation accuracy using MAE and estimation availability indicated that reliable link speed estimation can be generated and used to indicate real-time urban road traffic condition.

SummaryAssisted history matching (AHM) of a channelized reservoir is still a very-challenging task because it is very difficult to gradually deform the discrete facies in an automated fashion, while preserving geological realism. In this paper, a pluri-principal-component-analysis (PCA) method, which supports PCA with a pluri-Gaussian model, is proposed to reconstruct geological and reservoir models with multiple facies. PCA extracts the major geological features from a large collection of training channelized models and generates gridblock-based properties and real-valued (i.e., noninteger-valued) facies. The real-valued facies are mapped to discrete facies indicators according to rock-type rules (RTRs) that determine the fraction of each facies and neighboring connections between different facies. Pluri-PCA preserves the main (or principal) features of both geological and geostatistical characteristics of the prior models. A new method is also proposed to automatically build the RTRs with an ensemble of training realizations. An AHM work flow is developed by integrating pluri-PCA with a derivative-free optimization algorithm. This work flow is validated on a synthetic model with four facies types and a real-field channelized model with three facies types, and it is applied to update both the facies model and the reservoir model by conditioning to production data and/or hard data. The models generated by pluri-PCA preserve the major geological/geostatistical descriptions of the original training models. This has great potential for practical applications in large-scale history matching and uncertainty quantification.

CO2 cyclic stimulation (huff and puff) is a method for increasing well productivity after primary and secondary production. In this work, we study the feasibility and estimated enhanced oil recovery of CO2 huff and puff for light oil low-pressure and low-permeability reservoirs using numerical simulation supported by experimental and field test data. We performed CO2 huff and puff numerical modeling to (1) understand the effect of operational and geological parameters on incremental oil recovery and (2) also history match a huff and puff pilot test. The reservoir model is based on available geologic data and experimental PVT data in depleted oil reservoirs similar to those in the Appalachian Basin. The previous huff and puff operations in the Appalachian basin have been used in a wide range of operational parameters such as CO2 injected mass and CO2 cycles. Simulation results in this study, using a pseudomiscible approach in a black oil model, show that the injection rate and the mixing parameter are the main parameters affecting incremental oil recovery. There is a nonlinear relationship between CO2 injected mass (beyond 200 MT) and incremental recovery. Also, permeability heterogeneity can significantly affect CO2 huff and puff performance and should be accounted in the model. In addition to the parametric study, numerical simulations focusing on matching primary production data and pressure data from the CO2 injection period during a huff and puff pilot test in a depleted oil reservoir were performed with sensitivity to uncertain parameters. Homogenous and composite single wellbore models were built for the history match. Uncertain parameters include the permeability of each zone and relative permeability relationships. Simulation results of the matched model show the importance of considering bottom hole pressure during huff and puff as a matching parameter to evaluate the model’s uncertain parameters (such as permeability) accurately. A comparison of the oil–water relative permeability of the matched model with the core-flood experimental data, using a Clinton sandstone core, is also discussed.

Generative deep learning is becoming a widely used approach in geological modelling, especially in problems that involve optimization processes under uncertainty like history matching. The basic idea of reservoir modelling and history matching by generative deep learning is to train some kind of reservoir generator and provide optimization under different constraints. There are different approaches that have been developed to utilize various modifications of Generative Adversarial Networks or Variational Autoencoders to implement reservoir generators, but most of them have "conventional" convolution neural networks, hence all data have to be regular (rectangular) in structure. This should be recognized as a limitation. In this work, we introduce a novel approach of reservoir modelling with Variational Autoencoders based on graph convolutions as opposed to "conventional" convolutions. In our approach reservoir model is considered as a graph, i.e., not a structured data type. Graph convolutions can deal with these data types, and connection with Variational Autoencoders provides us with the capability to generate initially unstructured reservoirs. Variational Autoencoders (VAE) demonstrate the ability to implicitly parameterize geological representations into a latent space of reduced dimensionality and provide ways to uncertainty quantification and production profiling among various geological concepts. In the first part, we introduce the motivation to Graph Variational Autoencoders (GVAE) as opposed to conventional Generative Deep learning models. The rest of the paper is dedicated to experiments on a synthetic dataset with two different geological scenarios. We show that trained GVAE performs the generation of reservoir models with reliable geology. A latent space structure between Encoder and Decoder of GVAE is represented, and interpretation considering geology under investigation is performed. Finally, we show how latent space can help to estimate the uncertainty of production and an optimization workflow under well data constraints.

Many recent developments in generating history matched reservoir models that approximately characterize subsurface uncertainty are associated with the ensemble smoother (ES) method. It is much better suited for practical history matching applications because it does not require updating of the dynamical variables and thus the frequent simulation restarts required by ensemble kalman filter (EnKF) are avoided. However, the performance of original single update scheme of ES is poor for strongly nonlinear problems and therefore iterations may be needed. Several iterative forms of ES were proposed in the past few years, most of which combine ideas from random maximum likelihood (RML) and ensemble-based techniques. Unlike previous implementations, we pose the history matching problem as a full nonlinear least squares optimization problem and classical Levenberg-Marquardt (LM) algorithm is used as the optimization solver. By showing the that solution of the linearized least squares subproblems arising from each iteration has similar structure to that of standard ES update equation, we propose to use ES as the linear least squares solver to avoid the expensive adjoint calculation. In this way, the proposed algorithm can be considered as an iterative ES and the regularization parameter can be updated following the standard LM rule. Furthermore, because it is casted as an optimization problem, it is straightforward to extend it to robust nonlinear least squares method that can automatically estimate the measurement noise level and reduce the effect of outliers in the data that is essential for field applications. Two synthetic reservoir models are used to showcase the effectiveness and robustness of the newly developed algorithm.

An increasing number of field development projects include rigorous uncertainty quantification workflows based on parameterized subsurface uncertainties. Reservoir model calibration workflows for reservoir simulation models including historical production data, also called history matching, deliver non-unique solutions and remain technically challenging. In addition, the validation process of the reservoir simulation model often introduces a break of the conceptual connection to the geological model. This raises questions on how to quantify the deviation between the calibrated simulation model and the original geological model. Workflow designs for history matching require scalable and efficient optimization techniques to address project needs. Derivative-free techniques like Markov Chain Monte Carlo (MCMC) are used for optimization and uncertainty quantification. Adjoint techniques derive analytical sensitivities directly from the flow equations. For history matching those sensitivities are efficiently used for property updates on grid block level. Both techniques have different characteristics and support alternative history matching strategies like global vs. local, stochastic vs. deterministic. In this work both techniques will be applied in an integrated workflow design to the Norne field. The Norne field is a North Sea oil-and-gas reservoir with approximately 30 wells, with one third being used for WAG injection for pressure support. Field data was previously released by Statoil and made available for a public benchmark study (NTNU Norway) testing history matching techniques including production and time-lapsed seismic data. We focus on well production data for history matching. MCMC is used for global parameter updates and uncertainty quantification in a Bayesian context. An implementation of an adjoint technique is applied for analytical sensitivity calculations and local parameter adjustments of rock properties. History matching results are presented for field wide and well-by-well production data. Consistency checks between updated and original geological model are presented for rock property distribution maps. Geostatistical measures including spatial correlations are used to quantify deviations between updated and original geological model. In conclusion scalability and performance efficiency of the practical workflow implementation is discussed with a perspective of a consistent feedback loop from history matching to geological modeling.

The aim of the study is to condition stochastic generated realizations on well test data in order to improve simulation of fades and petrophysics in fluvial reservoirs. First we have used the pressure data to estimate the shortest distance from the well to a possible channel boundary and thereby simulate the channel structures. The well test also provides the permeability average in the part of the channel intersected by the well. Together with core/log data and general knowledge of the reservoir this have been used to simulate permeability. These permeability realizations is input to a numerical flow simulator and compared with experimental results of the well test.