Reservoir Modelling of Complex Geological Systems--A Multiple-Point Perspective

Recently, the Ensemble Kalman Filter (EnKF) has emerged as an effective tool for performing continuous updating of petroleum reservoir simulation models. The method is firmly grounded on the theory of Kalman filters and sequential Monte Carlo techniques. The ability of the method to sequentially update the spatial properties in petroleum reservoir models, such as permeability and porosity, by integrating the dynamic production data makes it a very attractive approach. Moreover, the method takes into account the production uncertainty in the reservoir models by using error covariance matrices for the measurement vector (Production and injection rates, Gas-Oil ratio, Steam-Oil ratio, etc.) and the state vector (pressure, saturation, permeability, porosity). Similar to the traditional Kalman filter, the covariance matrices have to be tuned to reflect the uncertainty in the model and the measurements. We consider two unconventional oil reservoir models: 1) highly heterogeneous black-oil reservoir model, and 2) heterogeneous SAGD reservoir model. The results will demonstrate the advantage of using the localized EnKF for effective history matching using ensemble sizes relatively lower than what otherwise would be required with the ordinary EnKF. The results will also show the advantages of using prior knowledge available from the wells (permeability and porosity measurements) to generate initial realizations. One of the main practical advantages of history matching using the EnKF over traditional optimization based approaches is its low computational effort. The computational cost is dominated by Monte Carlo simulation of the ensemble of models only. Thus, significant computational time saving is possible by running each of the ensemble simulations on independent processors in a parallel mode. Moreover, the method can be easily integrated with any commercial reservoir simulation software.

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.

The aim of this work is to present the effectiveness of a fully integrated approach for ensemble-based history matching on a complex real field application. We show that the predictive ability of the ensemble of models is greatly enhanced through an integrated workflow promoting multidisciplinary collaboration between all subsurface disciplines. Consistent integration of geological and engineering understanding within the dynamic data conditioning phase of a reservoir study is a challenging task. The ensemble-based approach offers an efficient solution to this challenge, especially when it is tied in with an appropriate reservoir modeling approach, suitable parameterization and repeatable workflows. All these are key factors to ensure geological consistency while improving the match quality and reliability of the generated reservoir models. One key feature of the ensemble-based method is that it overcomes the typical limitation of the traditional approaches where the number of uncertainty parameters often has to be reduced resulting from practical or algorithm constraints. This is especially important on complex reservoirs, where the subsurface uncertainties cannot be represented in a handful of scalar multipliers while honoring the static and dynamic data measurements. We organize the proposed methodology in four main steps: firstly, an initial ensemble of models able to capture the model uncertainties in all parts of the modeling processes are generated. Next, the match level for different observed data specifying the likelihood error is assigned. Then the uncertainty parameters that should be modified in the history matching process are identified. Finally, we perform a computational intensive step on large-scale computing facilities, where a state-of-art iterative ensemble algorithm, tightly connected with standard geo-modeling tools, is used to consistently update the full set of models. The result is an ensemble of reservoir models where we can quantify both the uncertainty in the production forecast and in the reservoir model parameters. The methodology has been applied on a challenging History Matching problem for a turbiditic channel complex reservoir. We demonstrate the efficiency of the method, by generating an ensemble of reservoir models that offer geologically consistent explanations of the currently measured static and dynamic data. The model forecasts reliability is confirmed through a validation process using dynamic data that have been left out of the history matching process. More importantly, however, is that the proposed workflow, and resulting models provides a good starting point for a more efficient update of the reservoir models as new static and dynamic data become available. With the proposed approach is possible to move from sporadic updates of reservoir models towards frequent model updates when the new data arrive. Utilizing all available data in a consistent manner - when the data are collected - is the key to making more robust reservoir management decisions, especially for complex reservoirs.

The application of elastic stress simulation for fracture modeling provides a more realistic description of fracture distribution than conventional statistical and geostatistical techniques, allowing the integration of geomechanical data and models into reservoir characterization. The geomechanical prediction of the fracture distribution accounts for the propagation of fracture caused by stress perturbation associated with faults. However, the challenge lies in estimating the past remote stress conditions which induced structural deformation and fracturing, the limited applicability of the elasticity assumption, and the latent uncertainty in the structural geometry of faults. The integration of historical production data and welltest permeability into geomechanical fracture modeling is a practical way to reduce such uncertainty. We propose to combine geostatistical algorithms for history matching with geomechanical elastic simulation model for developing an integrated yet efficient fracture modeling tool. This paper presents an integrated approach to history matching of naturally fractured reservoirs which includes 1) fracture trend prediction through elastic stress simulation, 2) geostatistical population of fracture density based on fracture trend map, 3) fracture permeability modeling integrating fracture density, matrix permeability and welltest permeability, and 4) numerical flow simulation and history matching. All of these implementations are incorporated into a single forward modeling process and iterated in the automatic history matching scheme. To obtain a history match on a reservoir model, we jointly perturb the large-scale fracture trend and local-scale geostatistical fluctuations of fracture densities rather than perturbing permeability calibrated from fractures. This strategy enables us to preserve the geological/geomechanical consistency throughout the history matching process. The geomechanically simulated fracture trend model is calibrated to both production data and geological structure map (faults and horizons) by finding the optimum remote stress condition for elastic stress-field simulation. The latter is achieved by matching the actually observed structural deformation trend with the simulated one. The smaller-scale fluctuation of fracture density is simultaneously history matched through the probability perturbation method of Caers (2003)1,2. The result of synthetic reservoir application is presented.

Summary Reconciling multiscale data for reservoir characterization is a crucial issue, because different data types provide different information about the reservoir architecture and heterogeneity. It is essential that reservoir models preserve small-scale property variations observed in well logs and core measurements and capture the large-scale structure and continuity observed in global measures such as well-test and production data. In this paper, we present a new methodology to directly update fine-scale geostatistically-based reservoir models by combining gradual deformation parameterization for the fine-scale geostatistical model, and an upscaling technique for the coarse-scale flow simulation model. As consequence, both fine- and coarse-scale models are updated by dynamic data during the history matching process. The proposed methodology includes: Perturbation of the fine-scale geostatistical model using the gradual deformation parameterization. Gradual deformation ensures the preservation of the overall geostatistical properties of the fine model. Generation of the coarse-scale flow simulation model by upscaling the fine-scale geostatistical model. Fluid-flow simulation and sensitivity computation of the flow simulation results with respect to the fine-scale parameterization. This sensitivity computation is analytical and takes into account the upscaling process. Direct updating of the fine-scale geostatistical model using classical optimization process. Direct updating ensures consistency between the fine- and coarse-scale models. The accuracy of the proposed methodology was improved by calibrating the flow simulation model. The objective of this calibration is to reduce the error introduced by the upscaling step during the flow simulation. We applied successfully our methodology for fine-scale reservoir characterization process by integrating permanent downhole gauge measurements directly into a 3D-geostatistical model containing about two million gridblocks. This test is designed to highlight several key issues of the proposed methodology: Efficiency of the upscaling step, coupled with gradient-based optimization to speed up history matching. Usefulness of the calibration step for a correct integration of upscaling techniques in history matching. Capability of the methodology for maintaining consistency and coherency between fine-scale and coarse-scale models. Improvement of the reservoir characterization process by integrating dynamic data at both fine geostatistical scale and coarse simulation scale.

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.

In current practice history matching is often performed on upscaled reservoir models without updating the original geological model. Taking into account new production data in an existing model is often problematic because of the lack of appropriate techniques. This problem becomes crucial when using geostatistical models. In such a case, the integration of new static and dynamic constraints requires the modification of an initial realization without destroying the initial history match and the overall geostatistical properties. This paper presents a new methodology based on advanced history matching techniques for updating dynamically 3D stochastic reservoir models to account for new production data. The proposed approach is based on the gradual deformation method. It allows local or global smooth transformations of the model while conserving the overall statistical characteristics. History matching is performed by coupling this method with an optimization process which integrates geostatistical modeling, upscaling, and fluid flow simulation in the same loop. This approach provides great flexibility in history matching various types of production data. In addition, inversion parameters can be selected throughout the entire modeling loop, from the facies spatial distribution, to petrochemical parameters and fluid flow parameters. Finally, local transformations may be performed to account for new wells or to update the reservoir model with new dynamic information. A successful application to a 3D stochastic reservoir model inspired from a real field is presented. The first step was to perform a history match using the production history available from an initial group of production wells. Then, new dynamic information is acquired from infill wells and over one year of additional production data. The heterogeneity distribution is locally modified by gradual deformation to update the model with this new information. The benefit of the proposed approach for improving the model characterization and reducing uncertainty on production forecasts is demonstrated.

Time-lapse seismic (4D seismic) has emerged as a critical tool in understanding reservoir dynamics, particularly in complex deep-water turbidite sandstone systems. The application of 4D seismic in the Niger Delta's deep-water turbidite reservoirs has significantly enhanced reservoir management and further development, particularly in modeling waterflood fronts and identifying remaining and/or by-passed oil. This study explored the integration of 4D seismic data into reservoir performance history matching for modeling waterflood fronts and identifying bypassed or remaining oil. Deep-water turbidites are characterized by heterogeneous and high-permeability channel systems, leading to challenges in predicting waterflood efficiency and ultimate recovery. By combining 4D seismic with dynamic reservoir simulation, key insights into saturation changes (remaining oil), reservoir connectivity, and fluid flow pathways were obtained. This workflow involved processing an Ocean-Bottom-Node (OBN) 4D seismic data to extract changes in acoustic impedance, which were linked to saturation and pressure variations. These changes were then incorporated into the reservoir performance history matching to refine the reservoir model, ensuring better alignment with observed production and injection data. The seismic-derived waterflood front tracking enhanced the understanding of the reservoir sweep efficiency and flood front location, highlighting areas with bypassed oil due to intra-reservoir heterogeneities, stratigraphic barriers, sub-seismic faults, or suboptimal well placement. This integrated approach has been used in the Ufoma deepwater oilfield further development as a case study. It did not only improve the accuracy of the existing 3D Earth reservoir models but also supported the optimization of the field development strategy by successfully targeting the remaining oil pockets in the further development project for the reservoir. It also led to improved reservoir characterization and modeling in the Ufoma field reservoir management (i.e., WRFM - History Matching and Prediction) and has proven to be a valuable tool in maximizing hydrocarbon recovery in these complex geological channel sands bodies. This work further demonstrates the efficacy of this integrated approach, leading to improved well placement for maximum oil recovery and optimized field development strategies for the Ufoma oilfield in deepwater Niger-Delta.

Early recognition of porosity and permeability contrasts in a reservoir has economic implications in reservoir management. Reservoir characterization aims at developing a detailed knowledge of the geological heterogeneities that may affect production rates and recovery factors. In the area of reservoir characterization, geological and engineering data have been traditionally inverted separately: a 3-D static reservoir model is established from static data (geology, geophysics and petrophysics) and the parameter distributions in that model are adjusted by history matching with production and other dynamic data. The underlying assumption in this process is that production data correspond to the same model as static data (Floris et al.1; Landa et al.2). This may or may not be the case. Hence, the requirement to first identify separately a model for each type of measurement and to verify that each model is consistent with all the others. Because identification is an inverse problem, with a non-unique solution, it is also desirable to confirm each feature of the reservoir model with different types of measurements3. For some features this is possible with today's technology. For instance, well test analysis can confirm the location of a fault identified from geophysical measurements and vice-versa. Other features, on the other hand, require additional development. The present work looks at the medium-scale architectural elements that have been formed in different depositional environments,, with the objective of reconciling geological and well testing modeling in order to increase the confidence in the evaluation of fault sealing, sandstone bodies geometry and lithofacies distribution. In this approach, the heterogeneities are regarded as geological objects characterized by geometrical parameters as well as by petrophysical properties. Synthetic genetic-type objects are generated by stochastically modeling their external geometries and internal rock-property distribution and their response in a well test is evaluated with the help of a numerical well test simulator. The systematic evaluation of the well testing responses of various geological objects yields a new source of reliable information for reservoir characterization.

An updated geological and dynamic model for a giant Middle East carbonate reservoir was constructed and history matched with the objective of creating an alternative model which is capable of replicating the reservoir production mechanisms and improving predictability, allowing optimizing the field development plan and water injection strategy. Giant Middle East carbonate fields often have long production history and exhibit high reservoir heterogeneity. It is always challenging to get a robust history matched model aligned with geological concepts and dynamic behavior understanding. The objective of this paper is to present an improved and integrated reservoir characterization, modeling and history matching procedure for a giant Lower Cretaceous carbonate reservoir in the Middle East. The applied workflow integrates all available geological data (stratigraphy, depositional facies, and diagenesis), petrophysical data (RCA and minipermeameter data, Petrophysical Group definition, cut-off definition) and the extensive database of dynamic data (long production history, well test, RST, open-hole log saturation over more than 40 years of development drilling, and MICP). The process was initiated with the reservoir review by means of a fully integrated study that allowed having better understanding of the reservoir behavior and production mechanisms. The key heterogeneities (high permeability and intra-dense layers) which control the flow behavior were identified during this process. Geological trend maps were generated to control the distribution of high permeability and intra-dense in the model. Well test data, open-hole logs from development wells and time-lapse saturation logs from observation wells were used to calibrate the trend and permeability log data. A phenomenological model was constructed to test the main factors impacting the production mechanism as identified during the reservoir review. Multiple iterations were performed between the static and dynamic models in a way that allowed a quick and efficient work that is consistent with all disciplines assumptions. Such continuous loop between the dynamic and geological models, with focus on the geological heterogeneities driving the dynamic reservoir behavior, has led to a more robust model capable of replicate the production mechanisms, which represents a major improvement compared to previous model in term of predictability.

This reference is for an abstract only. A full paper was not submitted for this conference. Abstract The Khuff Formation is a major reservoir in Qatar and the rest of the Middle East Gulf region, and contains some of the world's biggest gas reserves. Geologically the carbonate platform system is complex with fine-scaleheterogeneities which impact the static and dynamic reservoir characteristics. These heterogeneities are depositional, stratigraphic and diagenetic in nature and therefore reservoir characterization needs to be an integrated multidisciplinary and multiscale approach. In order to address these issues a large multidisciplinary and multiscale subsurface study has been launched on a large database including fields from across the region. The aim is to better understand the facies distributions, sequence stratigraphic architecture and the regional reservoir development, in order to better characterize dynamically reservoir behavior. Geologically-based fine-scale reservoir characterization is needed in all field optimization projects' and this starts at the appraisal phase of field evaluations, and not just in mature field scenarios. This necessitates an "anticipation" of the kind of field optimization issues that will be eventually needed. It is also important to think of geological reservoir characterization in dynamic terms at the earliest stage possible, but this must always be underpinned by a strong geological framework. This is achieved by calibration of various dynamic data (well tests, production profiles and well interference tests) with the geological understanding, particularly the sedimentological and diagenetic reservoir characterization. The static reservoir model in Khuff reservoirs is highly dependent on the precise type of sedimentary facies, the stratigraphic context and the type of diagenetic overprint, since these control the fine-scale heterogeneity. However, the dynamic reservoir heterogeneity (characterized by the dynamic data available) is particularly sensitive to the diagenetic overprint (i.e. the development of dolomite in grain-supported facies), and it is seen that the fine-scale permeability modeling and 3D permeability architecture is highly diagenetically influenced and fundamental to understanding the dynamic behavior of the field. Moreover the understanding of the 3D permeability architecture(particularly the high permeability zones around the dolomite-limestone transitions) is important for the application of stimulation techniques, such as acidification. The integration of the fine-scale reservoir characterization into the reservoir model is a key step, but governed by the precise objectives of the reservoir model. In particular the resolution of model must be appropriate to the reservoir model objectives (large scale pore volume calculations vs. fine-scale dynamic sensitivity to geological heterogeneity, and adapted if necessary). In-house reservoir-scale modeling tools have been used to model the fine-scale reservoir heterogeneity, and create multiple realizations of the static reservoir properties. Finally these are modeled dynamically to assess the impact of the geological parameters on the production profiles.

Streamline-based assisted and automatic history matching techniques have shown great potential in reconciling high resolution geologic models to production data. However, a major drawback of these approaches has been incompressibility or slight compressibility assumptions that have limited applications to two-phase water-oil displacements only. We propose an approach to history matching three-phase flow using a novel compressible streamline formulation and streamline-derived analytic sensitivities. First, we utilize a generalized streamline model to account for compressible flow by introducing an 'effective density' of total fluids along streamlines. Second, we analytically compute parameter sensitivities that define the relationship between the reservoir properties and the production response, viz. water-cut and gas/oil ratio (GOR). These sensitivities are an integral part of history matching, and streamline models permit efficient computation of these sensitivities through a single flow simulation. We calibrate geologic models to production data by matching the water-cut and gas/oil ratio using our previously proposed generalized travel time inversion (GTTI) technique. For field applications, however, the highly non-monotonic profile of the gas/oil ratio data often presents a challenge to this technique. In this work we present a transformation of the field production data that makes it more amenable to GTTI. Further, we generalize the approach to incorporate bottom-hole flowing pressure during three-phase history matching. We examine the practical feasibility of the method using a field-scale synthetic example (SPE-9 comparative study) and a field application. Recently Ensemble Kalman Filtering (EnKF) has gained increased attention for history matching and continuous reservoir model updating using data from permanent downhole sensors. It is a sequential Monte-Carlo approach that works with an ensemble of reservoir models. Specifically, the method utilizes cross-covariances between measurements and model parameters estimated from the ensemble. For practical field applications, the ensemble size needs to be kept small for computational efficiency. However, this leads to poor approximations of the cross-covariance matrix, resulting in loss of geologic realism. Specifically, the updated parameter field tends to become scattered with a loss of connectivities of extreme values such as high permeability channels and low permeability barriers, which are of special significance during reservoir characterization. We propose a novel approach to overcome this limitation of the EnKF through a 'covariance localization' method that utilizes sensitivities that quantify the influence of model parameters on the observed data. These sensitivities are used in the EnKF to modify the cross-covariance matrix in order to reduce unwanted influences of distant observation points on model parameter updates. The key to the success of the sensitivity-based covariance-localization is its close link to the underlying physics of flow compared to a simple distance-dependent covariance function as used in the past. This flow-relevant conditioning leads to an efficient and robust approach for history matching and continuous reservoir model updating, avoiding much of the problems in traditional EnKF associated with instabilities, parameter overshoots and loss of geologic continuity. We illustrate the power and utility of our approach using both synthetic and field applications.

Probabilistic production forecasting at Tengiz is largely driven by reservoir uncertainty. Reservoir uncertainty is most effectively synthesized and quantified through simulation modeling. Early in the construction of a new Tengiz dynamic model, fundamental reservoir uncertainties were identified and evaluated. This allowed for model ‘building blocks’ to be developed with different characterizations to encompass key uncertainties. Key uncertainties, which can significantly impact future production under primary depletion and sour gas injection, have been described. These include typical uncertainties such as porosity, irreducible water saturation, hydrocarbon fluid properties, oil-water contact levels, rock compressibility, geologic baffles, and relative permeability. Unique uncertainties specific to Tengiz include geometry and density of the natural fractures, and reservoir heterogeneity. Considerable production history and a large reservoir surveillance database provided input for rigorously characterizing and subsequently validating the range of each uncertainty. After ranges were established, appropriate model realizations were created. A wide range of reservoir models were obtained by selecting combinations of high/mid/low realizations for each uncertainty. Using experimental design (ED), reservoir simulations were conducted to test uncertainty ranges against field history. A quantitative history match and statistical analysis were developed to objectively judge the appropriateness of uncertainty values. Uncertainties with the largest overall impact on the history match are: fracture density, platform horizontal permeability, compressibility, and platform heterogeneity. This case study demonstrates how analysis of reservoir uncertainties can be: (1) captured in static and dynamic reservoir models and (2) validated through ED and quantitative history matching. This study employs state-of-the-art technologies to evaluate model uncertainties of a giant carbonate reservoir undergoing both depletion and miscible gas drives. The range of reservoir models subsequently developed will be of great value in creating robust probabilistic reservoir forecasts to optimize field operation and future development.

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.

History matching is an important part of reservoir numerical simulation research and the basis for predicting oilfield development performance. At present, integrated smoother and ensemble Kalman filter methods are the mainstream methods of history matching. However, these data assimilation algorithms need to be based on Gaussian assumptions and cannot guarantee the geological authenticity of the modified model. Therefore, to achieve end-to-end processing of dynamic data to modify the reservoir model, while ensuring that the distribution of data does not need to be restricted by Gaussian distribution, this paper proposes the use of the deep conditional generative adversarial network (CGAN) method for automatic reservoir history matching for the first time. The mapping relationship between static geological reservoir parameters and dynamic production data is found through the training generative network, which reduces the uncertainty of the reservoir model obtained by automatic history matching and explains parallel offline processing. The numerical simulation results show that the prediction results on the 2D two-phase flow model are consistent with the results of the proposed deep conditional generative adversarial network method.