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ECMOR XVII
- Conference date: September 14-17, 2020
- Location: Online Event
- Published: 14 September 2020
101 - 120 of 145 results
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The Undrained Split Iterative Coupling Scheme in Fractured Poro-elastic Media
More LessSummaryRecently, solving the coupled flow and mechanics problem received more importance and attention in both academia and industry. This is due to the increasing demand to come up with accurate and efficient models that can simulate the different physical processes involved in unconventional reservoir simulation. Examples of such processes include hydraulic fracturing, CO2 injection and sequestration, sand production, and predicting wellbore stability. Two main coupling schemes to solve the flow problem coupled with geomechanics in an iteratively sequential manner are the fixed-stress split and the undrained split schemes. In the fixed-stress split iterative scheme, a constant volumetric mean total stress is assumed during the flow solve, whereas in the undrained split scheme [4], a constant fluid mass is assumed during the mechanics solve. Both schemes were shown to be convergent in the work of [1] and [4], and an extension of the fixed-stress split iterative scheme to fractured poroelastic media was presented in the work of [2]. In this work, we shall formulate an extension of the undrained split iterative coupling scheme to fractured poro-elastic media, following a similar approach to the one introduced in [2]. In our coupled model, fractures are treated as possibly non-planar interfaces using a lubrication-type system, as described in [3]. Our formulation will be supplemented by a rigorous convergence analysis in which Banach fixed-point contraction results will be derived for the resulting coupled system, establishing the geometric convergence of the scheme, and the uniqueness of the obtained solution. To the best of our knowledge, this is the first time in literature the convergence of the undrained split iterative coupling scheme is established in fractured poro-elastic media.
[1] A. Mikelic, and M. F. Wheeler, “Convergence of Iterative Coupling for Coupled Flow and Geomchanics”. Computational Geomechanics, 17(3), 455–461, 2013.
[2] V. Girault, K. Kumar, and M. F. Wheeler, “Convergence of iterative coupling of geomechanics with flow in a fractured poroelastic medium”. Computational Geosciences, 20 (5), 997–101, 2016.
[3] V. Girault, M. F. Wheeler, B. Ganis, and M. E. Mear: A Lubrication Fracture Model in a Poro-elastic Medium. Mathematical Models and Methods in Applied Sciences, 25 (04), 587–645, 2015.
[4] T. Almani, A. Manea, K. Kumar, and A. H. Dogru, “Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media”. Computational Geomechanics, 2019.
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Adaptive Moment Estimation Framework for Well Placement Optimization
Authors Y. Arouri and M. SayyafzadehSummaryIn this study, we propose the use of a first-order gradient framework, the adaptive moment estimation (Adam), in conjunction with a stochastic gradient approximation, to well location and trajectory optimization problems. The Adam framework allows the incorporation of additional information from previous gradients to calculate variablespecific progression steps. The search direction is a vector composed of a running average of previous gradients that is normalized element-wise by an estimated variance. As a result, this assists the search progression to be adjusted further for each variable and allows a convergence speed-up in problems where the gradient needs to be approximated. The applicability of Adam to well location and trajectory optimization is analysed using two problems involving the PUNQ-S3 benchmark model. The first case is the optimization of four vertical infill wells, leading to a total of eight decision variables. An inter-well constraint is considered to ensure the wells are not located within a minimum distance of each other. The second case is a more complex problem with the optimization of 20 nonconventional wells, resulting in 120 decision variables. A polygon defined by piecewiselinear polynomials was used to represent the reservoir bounds. A distance-based projection method was employed to repair any proposed heel and toe points placed outside the reservoir bounds. The performance of the proposed algorithm is compared against a contemporary first-order framework, steepest descent, and a derivative-free pattern search method, Hooke-Jeeves direct search. The results indicated that the proposed algorithm consistently outperformed both algorithms in terms of optimal value and computational efficiency. This was a consequence of the stochastic nature of the gradient approximation, which allowed the random search of more promising regions. In addition, the proposed algorithm was the least affected by the use of different initial guesses as indicated by the standard deviation.
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Feature Selection for Reservoir Analogues Similarity Ranking As Model-Based Causal Inference
Authors A. Voskresenskiy, N. Bukhanov, Z. Filippova, R. Brandao, V. Segura and E. Vital BrazilSummaryPetroleum geoscience has always been an important part of Earth sciences with a focus on investigating subsurface reservoirs of oil and gas. It is conventional to find teleconnections and long-distance dependencies in climate, environmental and social sciences based on available spatially distributed data across the globe. In the same token, similar attempts in subsurface geoscience face numerous obstacles, including very sparse and confidential datasets, a massive stratigraphic time scale of geological events, and scanty classification of the enormous variety of sedimentological and lithological concepts.
One of the few data-driven workflows widely accepted inside the petroleum industry is the analysis of reservoir analogs in order to estimate missing values in available data and transfer geological assumptions and development strategies from similar reservoirs. Indeed, most of the datasets suffers with a high number of missing parameters compromising the quality of the predictions. Therefore, the similarity ranking of reservoirs and their formations had a few successful implementations recently. To tackle this issue, we propose enhanced feature selection approaches for similarity ranking enabling to perform robust missing values imputation and visual analytics along with discovering insightful causal relationships between reservoir parameters.
Similarity measures for different reservoirs are the primary tool to obtain a ranking of analogs formations. The measure must be constrained for working with categorical and continuous features as key geological parameters (up to 200 parameters in dataset). We conducted several sensitivity analyses of various similarity measures, including a combined approach of Gower function with weighted parameters. The selection of relevant features highly depends on the response feature, which, in our case, is the recovery factor for hydrocarbon reserves. We employed Boruta and SHAP methods for feature selection process based on similarity ranking of reservoir analogs, which allow us to delineate causal relationships between petrophysical parameters across petroleum basins worldwide. Methodology is tested on a few target reservoirs from Middle East region with more than a thousand reservoirs available for ranking.
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Pore-Scale Modeling of Microbial Growth in A Two-Phase Saturated Porous Medium
Authors G. Strobel, B. Hagemann, M. Wirth and L. GanzerSummaryIn the past years, more attention is focusing on microbial engineering in the subsurface. Understanding and modeling the microbial growth and its impact is not only important for microbial enhanced oil recovery but also for future applications such as underground hydrogen storage and underground methanation. However, modeling the coupled processes in porous media is challenging. Especially the growth of microorganisms present in the water phase of a porous medium saturated by two phases can differ from simple batch-reactor observations because the specific surface area between the gas phase and the water phase is much higher.
In order to investigate the behavior of microbes in a porous medium, a 1-D pore-scale model was developed. The model includes the diffusive transport of components in the water phase and the growth and metabolism of methanogenic microbes. Molar balance equations, which include the consumption and production due to the metabolic reaction, are formulated for four chemical components: hydrogen, carbon dioxide, methane and water. The left boundary represents the interface to the gas phase. The microbes, which are defined as an additional immobile component, consume the hydrogen and the carbon dioxide to produce methane and water. The nutrient-limited growth behavior of the microbes is expressed by an adapted double Monod model.
The developed 1-D model was validated by growth experiments performed in microchips, which were build based on real rock samples (CT-scans). To be able to compare the experimental results and the numerical model, the population growth of methanogens in the microchip was interpreted by microscopic analysis. The numerical model is able to predict whether the metabolic reaction becomes diffusion-limited or reaction-limited what depends not only on the Damköhler number of the system but also on the pore scale fluid distribution.
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Testing of Vulkan Visualization for Geo-Models on Mobile Devices and Desktop Systems with Ray Tracing GPUs
Authors M. Mustafin, O. Turar and D. Akhmed-ZakiSummaryThe paper describes development and comparison tests for high performance visualization of geological models on different platforms. It’s motivated by paradigm of ubiquitous computations using distributed systems where any device can potentially act as platform of client interface for the simulator.
Nowadays most of mobile devices have valuable computational resources and thus may be used as platform for scientific computations. So, we present visualization of geological models given in the eclipse format for mobile devices. For rendering we applied standard rasterization pipeline of Vulkan framework with direct coloring of polygons based on numerical values of physical parameters. Such approach leads to necessity of the whole buffer substitution in cases of changing values in new time steps. For this purpose, we implemented double buffering algorithm for vertex buffers used to store color data. To test the performance of visualization comparisons were made based on real time rendering frames per second for geological model differing in cell count.
Also, we implemented and tested geological model visualization performance on advanced desktop stations with leading GPU devices with the implementation of Ray Tracing algorithms. Even though ray tracing algorithm was invented for photorealistic visualization it can show drastic increase of rendering performance due to logarithmic complexity of intersection search algorithms. Because of that it was expected that ray tracing algorithm will show better performance on grid models with high number of cells. In the case of small grids its performance will be lower than performance of rasterization algorithm but its irrelevant due to the overall quickness of such visualization.
Tests shown in the paper mostly confirm that expectations. However, in such comparisons certain additional moments must be considered. Performance of ray tracing algorithm is based on the number of screen fragments or pixels alongside with the number of primitives on the screen. Also, it affects pixel number, or, in other words, percentage of screen, covered by the model. Thus, we show different tests that consider that feature.
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Identification of Critical Operational Uncertainties in Field Development Planning Using Stochastic Gradients
Authors E. Barros, R. Hanea, L. Hustoft, O. Leeuwenburgh and R. FonsecaSummaryThe development of oil and gas fields requires asset teams to make complex decisions in the presence of uncertainties. Studies of reservoir management strategies typically focus exclusively on geological uncertainties by working with an ensemble of reservoir model realizations. However, the development of hydrocarbon reservoirs is often also subject to operational uncertainties such as rig delays or drilling operation delays (which may in turn be related to unpredictable externalities of technical, economical, political or meteorological nature). Production attainment aims to minimize the associated economic risks by employing appropriate mitigation strategies that should ensure that targets are realized.
In this work we use concepts from model-based robust optimization to quantify the impact of operational uncertainties on development strategies. In particular, we employ the stochastic simplex approximate gradient to obtain sensitivities of crucial production metrics with respect to operational factors. The StoSAG gradient has favorable theoretical and computational properties that allow the inclusion in this calculation of for example geological and petrophysical uncertainties. The factors can be sorted based on the associated sensitivity magnitudes to enable a robust ranking and identification of operational parameters with the highest impact on production attainment.
The proposed approach is applied to a synthetic case study including multiple real field development planning aspects. It is demonstrated that results obtained with this approach are able to identify variables with the highest impact on expected loss in production. The analysis for this specific case indicates that planned production start and rig arrival/operational delays are some of the operational uncertainties that are primarily related to a loss of oil production in the short-term production, while factors associated with drilling time are found to have the largest impact in the medium term. The proposed workflow is one element of an integrated approach for robust reservoir development decision maturation.
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The Influence of the Petrophysical Properties’ Heterogeneity on the Well Tests Interpretation Results
Authors R. Khusainov, A. Nekrasov and C. AitovSummaryGeological faults are known to have a considerable impact on the field development and the subsurface gas storage processes. In some cases the geological faults may act as impermeable baffles, that prevent the reservoir fluid’s filtration from one part of the reservoir into another one. That leads to the reservoir compartmentalization and to the pressure/fluid composition difference across the fault plane (in the different reservoir blocks). In the other case, on the contrary, the geological faults may act as the permeable conduits connecting overlaying and underlying formations. That may result in the vertical fluid migration during the reservoir development. Therefore it is necessary to have information about the faults presence in the reservoir to give a reliable production forecast. There are some well testing methods described in the academic literature sources allowing estimate the reservoir properties in the presence of impermeable baffles. It should be noted thought, that the majority of these well testing technics are designed to describe the flow of a weakly compressible or an incompressible fluid. The well testing technics for gas wells are purely researched. But even the presented in available sources methods are based on such severe assumptions as the homogeneity of petrophysical properties, the radial character of the fluid flow, the constant pressure at the well-drainaged zone boundary etc., which can be violated in some real-case situations. This work was aimed to research the influence of the poroperm properties heterogeneity on the results of the gas well tests interpretation in the case of impermeable fault presence near the tested production well. Simulation models of infinite-acting gas-saturated formation with the homogeneous and the heterogeneous property distributions were created using Schlumberger software. Single vertical well was placed in the middle of the modelled reservoir, which produced with a constant gas rate during a specified time interval and then was shut. During the drawdown and the build-up periods the pressure stabilization and the pressure build-up curves were obtained. These curves were processed using classical interpretation technics such as Horner method. The calculated by this way permeability and the distance to the fault plane then were compared with the model parameters. The results of the research show that the heterogeneity may significantly influence the well testing interpretation results.
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The Impact of Numerical Discretisation on the Correct Simulation of CO2 Convective Flow Patterns
Authors M. Awag, S. Ghanbari and E. MackaySummaryThe convective flow patterns induced in CO2 storage processes plays an important role in safe and permanent CO2 storage. However, their development depends on the continuous contact between brine and CO2 ensuring constant CO2 dissolution in brine and removal from contact.
Numerical gridding of such problems, however, implies that the solution is no longer continuous; rather, it is discretised in the spatial domain. Exceptionally, this discretisation may cause the buoyant CO2 and brine to reside in two vertically neighbouring grid blocks without contact. Although this might be physically correct, since this phenomenon disconnects the contact between the two phases, the CO2 dissolution may stop, as supercritical CO2 and brine are no longer in contact. This artefact is important in situations where the direction of CO2 mass transfer caused by different mechanisms are opposite relative to each other. While CO2 migrates upward, the CO2 saturated brine will migrate downward.
We show in this study that, because of the discretisation nature, the simulator may not able to capture the full physics of post-injection CO2 dissolution. A fine grid cross-sectional model was constructed. CO2 was injected followed by long shut-in period allowing CO2 dissolution. A plume was developed after CO2 injection termination. Due to CO2 dissolution the plume-water contact moves gradually upward. However, as soon as it reaches the boundary between two vertical adjacent layers, the dissolution stops, although undissolved CO2 is still present and water underneath is not fully saturated with CO2. The issue was also investigated under different alternative injection configurations, though the same problem was confirmed.
The artefact can be overcome by the inclusion of mechanisms allowing CO2 to travel across disconnected neighbouring cells. This could be either explicit inclusion of physical diffusion or capillary pressure that smears the front. Interestingly, the problem is exceptional in that grid refinement does not help since it does not create the contact between the two phases residing in vertically neighbouring cells.
Whereas much study has been made of convective mixing effects during CO2 injection, this grid discretisation phenomenon has never previously been identified and reported.
The artefact is important in processes where the direction of mass transfer is different due to phase density differences and dissolution effects, such as during CO2 dissolution in water. This problem affects the calculation of long-term CO2 storage, and the fate of CO2 – does it remain in a supercritical phase or is it dissolved into surrounding aquifer water.
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High-Resolution Hydraulic Fracture Network Modeling on Adaptive PEBI Grids
Authors D. Filippov, B. Vasekin, D. Maksimov, D. Mitrushkin and A. RoshchektaevSummaryHydraulic fracturing is currently the main technology for the development of low permeability reservoirs. As most of them are naturally fractured, hydraulic fracturing operations result in of a system of cracks, known as stimulated reservoir volume (SRV). To increase the efficiency of low permeability reservoirs development, an efficient modeling tool that allows for accurate representation of the flow in the system of intersecting fractures is needed.
There is a number of low-efficiency methods in reservoir simulators for SRV modeling on structured grids. One of them is to represent fracture system using an effective continuum. Application of the Oda algorithm for computing effective permeability allows for correct representation of the flow only in combination with multipoint flux approximation. Dual porosity/permeability model is not applicable for hydraulic fractures because of the high anisotropy associated with them. In contrast, DFM-model provides a higher resolution level of the fluid flow but is computationally more expensive, and hence not widely used. For this problem a good solution is the embedded discrete fracture model (EDFM) which is based on combining two conductive media – pore space and fracture network. As EDFM is mostly used with structured grids, it is usually accompanied by algorithms of local grid refinement for better resolution in fractured regions.
In this paper, we present efficient computational algorithms to calculate flows in reservoir with intersecting fractures on the unstructured PEBI grid with automatic honor of geometric features of fractured system. The computational algorithm is based on the EDFM approach tailored for PEBI grids. The proposed approach is applied to the three-phase isothermal flow problem with phase transitions, gravity and capillary forces (Black Oil).
Special attention is paid to comparison of the flow modeling results on the unstructured PEBI grid using the Oda method for computing effective permeability and the proposed EDFM approach. We demonstrate efficiency of using the unstructured grid for resolving SRV fractures compared with structured grids. Calculation results are given for real fields showing the efficiency of the presented approach for flow simulation of fractured reservoir with hydraulic fracturing treatment.
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Fragmented Algorithm for Construction of Adapted Structured Computational Grids Based on Inverted Beltrami Equation
Authors O. Turar, D. Akhmed-Zaki, G. Khakimzyanov, B. Daribayev and D. LebedevSummaryThe paper describes implementation of Language for Numerical Algorithms (LuNA), which is the system aimed at automatic generation of parallel programs for the large-scale numerical modeling, for construction of structured computational grids adapted to the field of values and gradients. This system is based on operating with data fragments and operation fragments as separate objects with their call and use order and hierarchy.
As any automated system generation of parallel programs may show less efficiency comparing to straight implementation of parallelization for computational programs. But benefit of automatization is in optimization of resource spent for development both in terms of funding in human resources. So, when the time loss of automated program is not too large, i.e. in cases of comparable speed of operation automated approach is counted as effective. Grid construction method is based on solving border problem for inverted Beltrami equation. Adaptation of the grid is managed by control metric that is different from the metric of the space volume where the computations take place. The behavior of such model close to diffuse equation problems considering that metric of the domain is different from flat metric of cartesian grid.
Parallelization is based on algorithm of 3D decomposition for the computational area. The equation is solved on each subdomain of the initial domain using alternating directions implicit (ADI) method in 3D. This parallel algorithm does not exactly parallelize similar ADI method for whole domain. It rather performs adaptation of whole domain as connected patches of lesser domains each of which adapts to control metric and changes border values on each iteration. Correctness of the approach is based on previous research of grid construction method where the correctness such technique for constructing of continuous adapted grids for patched domains are stated. The results and performance of computations on LuNA system were compared with straight parallel algorithm on the same machine.
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Incorporating Uncertainties in A Model-Based Data-Driven Framework Using Transfer Learning
Authors T. Van de Poll, E. Barros, W. Langenkamp and R. FonsecaSummaryModelling and optimization in subsurface applications generally deals with uncertainty. To account for this uncertainty, decision-making workflows use an ensemble of model realizations. This approach leads to a large amount of required full-physics simulations, which can take days to complete.
To make this process more computationally efficient, we seek ways of replacing an ensemble of full-physics simulation models with an ensemble of fast data-driven models. Training a single data-driven model of a particular realization of the full-physics model requires a significant amount of full-physics simulations. As a consequence, the straightforward approach of training a data-driven model for each realization independently, to form an ensemble of models, would require an infeasible amount of full-physics simulations. The total computational cost would significantly exceed the effort necessary to perform any state-of-the-art decision-making workflow directly on an ensemble of full-physics models.
In this work, we developed a framework using concepts of transfer learning from the machine learning (ML) community to create an ensemble of data-driven (ML) models in a computationally efficient way. Transfer learning enables the generation of ML models using a limited amount of training samples (i.e., full-physics simulations) per realization through the utilization of information obtained as a result of the training of a base ML model built on one full-physics model realization. Hence, it dramatically accelerates the training process of the next ML models, enabling the feasible generation of an ensemble of ML models based on an ensemble of full physics models.
Our results show that the same prediction accuracy as training with 500 samples (i.e., 500 full-physics simulations minimum number required to achieve an acceptable prediction accuracy in our experiments) per realization can be achieved using as few as 20 training samples per model realization, thereby reducing the computational effort by a factor 25. Our results also confirm the robustness of the approach to different base ML models.
We conclude that transfer learning techniques are an effective approach to incorporate uncertainty within a model based data-driven framework, which can be used to make computationally demanding workflows more practical.
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Improving the Predictive Ability of A Geomechanical Model Using Neural Networks (Deep Learning)
Authors N. Zakharenko, A. Gula, A. Bochkarev and Y. OvcharenkoSummaryWith the growth of hydrocarbon consumption and depletion of developed fields, the task of extracting hard recovering oil reserves becomes actual. To solve this problem, modern drilling methods are used, such as the drilling of directional and horizontal multi-lateral wells. Also methods for increasing oil recovery are used, such as multi-hydraulic fracturing. In the first case, it is important to avoid possible complications during drilling associated with absorption and collapse of the borehole walls. In the second one for successful hydraulic fracturing, it is necessary to understand stress field distribution in the formation, for selecting successful fracture initiation point and determining injection volumes. These problems could be solved with three dimensional geomechanical modeling.
One of the main input for geomechanical model is well logs. In common, the required volume of surveys is partially absent in wells selected for modeling. In this paper, effective tool for log data recovery was considered - deep learning neural network.
A number of mathematical approaches was observed:
• One-hot coding
Each layer has its own unique lithology, strength and elastic properties. One-hot-coding allows to convert categorical data “reservoir name” into a digital format that is convenient for neural network. It allows automatically find out a unique property correspondence for each individual layer.
• Construction of additional features
Using mathematical transformations of input data allows better processing of peak curve values, increasing model prediction accuracy.
• Residual connections, regularization of weights and dropping
These methods were used to solve the problem of damped gradient in a multilayer neural network model.
• Hyper parameters automatically configuring and callbacks
They allow for more sensitive tuning of network hyper parameters, and save weights of the model with the best validation result.
• Optimizer observation
Usually, the SGD optimizer is used - Stochastic gradient descent optimizer. In this neural network, more efficient optimizers such as ADAM and RMSPROP were tested and used.
• Ensemble models
It is another technique for increasing neural networks predictive ability. Ensemble models use an average value of neural networks results with different architectures, for example, LSTM and fully connected network. To sum up, listed approaches allowed us to obtain a high-precision tool for solving the regression problem. It significantly surpasses methods of multi-regression, which are usually used to restore data in geomechanics and allows to get a complete set of data for high-quality 3D geomechanical modeling.
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Assessment of Interaction Between Natural and Tecnogenic Fractures During Multi-Stage Fracturing
Authors A. Gula, A. Bochkarev, A. Vishnivetskiy, A. Glazyrina and R. NikitinSummaryPurpose of this work is approbation of geomechanical approach for modeling of natural fracture network and integration with hydraulic simulator to account effect of interaction technogenic and natural fractures. Challenges of modern oil and gas recoveries requires effective technologies for exploitation, which in turn has led to the massive applying of horizontal wellbores and technologies of multistage fracturing. As well as development modern methods for modeling, which allows to give a reservoir more detailed characterization.
Modeling of multistage fracturing is a complex process that requires an understanding of the mechanical behavior of the formation, fractures and faults. Fractures formed during the hydraulic fracturing change the stress field around it, this effect is called the shadow stress effect. Natural fractures or faults may have an effect on production rates, in particular, on connectivity of the reservoir. If stress shadow effect of the hydraulic fracturing is taken into account, then can be additionally taken into account the reactivated natural fractures with induced stresses as well. Development of natural fractures is based on a geomechanical paleostress inversion that uses observation data such as seismic or well logging data. Iterative process of modeling allows constrain results within parameters of fracture mechanics. Behavior of hydraulic fracture growth and interaction with natural factors defines by geomechacnical model.
In this paper, we demonstrate the results of a numerical evaluation of multistage fracturing influence in the change of the stress field. The stress field, modified during the stimulation, was used to assess the critical stress fractures, which allows increasing the stimulated reservoir volume due to reactivated natural fractures. Such fractures do not need to be fixed, since they are formed by sliding along the plane of failure with small changes in the stress field and give an additional contribution to the total area of induced fractures. Resulted assessment give understanding of failure mechanics and stress regime for maximizing stimulated volume of the reservoir.
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Studying the Effects of Heterogeneity on Dissolution Processes Using Operator Based Linearization and High-Resolution LiDAR Data
Authors S. De Hoop, D. Voskov and G. BertottiSummaryGrowing demand for cleaner energy sources has led to the comprehensive investigation of high-enthalpy carbonate reservoirs. These reservoirs are often chemically and mechanically altered and hence contain a large uncertainty in the spatial distribution of the reservoir parameters. The resulting discontinuity features commonly include complex fracture networks, large inter-connected cave systems, and other flow barriers/conduits. Several conceptual models exist for simulation of such systems; however, the main driving forces behind the resulting geometry are not fully understood which complicates quantitative predictions. To improve the reservoir characterization of these complex reservoirs, high-resolution LiDAR datasets from several outcrops were acquired. Statistical analysis is performed on the geometry of the resulting cave networks. Several geometrical parameters are deduced from the LiDAR surveys which are then correlated with the possible physical processes involved. The effect of the heterogeneity of the porous media and fracture network is studied extensively using the newly developed reactive transport module in the Delft Advanced Research Terra Simulator (DARTS) framework. DARTS uses the Operator Based Linearization approach which transfers the governing nonlinear Partial Differential Equations into a linearized operator-form where the Jacobian is constructed as a product of a matrix of derivatives with respect to state variables and discretization operators. The state-dependent operators are only evaluated adaptively at vertices of the mesh introduced in the parameter-space. The continuous representation of state-dependent operators as well as their derivatives is achieved by using a multi-linear interpolation in parameter-space which significantly improves simulation performance. We extend the reactive transport module for both kinetic and equilibrium reactions which allows for more complex chemical interactions in the simulation framework. Linking the processes of wormholes creation with the aid of numerical simulations and the measured manifestation of the discontinuity networks will substantially improve the reservoir modeling process and subsequent uncertainty quantification.
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Modelling Porosity and Permeability Alteration during CO2 WAG Injection in Carbonate Oil Reservoirs
Authors A. Ribeiro, L. Guimarães and E. MackaySummaryThe alternate injection of CO2 gas and water (CO2 WAG) adds more complexity to the development of carbonate oil reservoirs. First, the switching between water and gas cycles causes oscillations in the pressure and flow rate because of variable fluid mobilities. Second, gravity segregation can occur since the CO2 is less dense than water (and oil) under most reservoir conditions. Moreover, since the injected fluids are generally cooler than the initial reservoir temperature, heat exchange is constantly happening because the injected fluids (especially water) extract heat from the reservoir rock as they propagate from cooler to warmer regions. These changes in temperature disturb the flow behaviour not only by modifying the physical properties of the fluids, such as densities and viscosities, but also by enhancing calcite dissolution and subsequent pore space alterations.
In this work, we simulate multiphase flow coupled with heat exchange and mineral reactions to model the porosity and permeability changes during CO2 WAG injection in carbonate oil reservoirs. A multilayered model of a limestone reservoir is initialised with 500 bar to calculate calcite volume changes in a more reactive environment comparable with the Brazilian pre-salt, as compared to reported (carbonate) field cases and simulations. Porosity changes are derived from volume change of calcite at each time step, while permeability is updated following the formulation of Carman-Kozeny. Dissolution zones around the injectors are calculated as well as their impact on permeability and injectivity increase. Special considerations are made regarding the mass of calcite that can potentially precipitate in the production system (i.e. scale management).
This contibution extends the knowledge about the impacts of calcite dissolution and re-precipitation on CO2 WAG operations in deep carbonate reservoirs. The novelty lies on the investigation of the effects of cross-flow between layers and gravity segregation on the scale deposition. Moreover, this model extends our previous work on twodimensional simulation by including the vertical heterogeneity. We show how reactions proceed in layer of different properties and what are the risks of scale deposition at well perforations for a given vertical profile of initial porosity and permeability.
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High Performance Framework for Modelling of Complex Subsurface Flow and Transport Applications
Authors M. Khait, D. Voskov and R. ZaydullinSummaryNumerical modelling of multiphase multicomponent flow coupled with mass and energy transport in porous media is crucially important for many applications including oil recovery, carbon storage and geothermal. To deliver robust simulation results, a fully or adaptive implicit method is usually employed, creating a highly nonlinear system of equations. It is then solved with the Newton-Raphson method, which requires a linearization procedure to assemble a Jacobian matrix. Operator Based Linearization (OBL) approach allows detaching property computations from the linearization stage by using piece-wise multilinear approximations of state-dependent operators related to complex physics. The values of operators used for interpolation are computed adaptively in the parameter-space domain, which is uniformly discretized with the desired accuracy. As the result, the simulation performance does not depend on the cost of property computations, making it possible to use expensive equation-of-state formulations (e.g., fugacity-activity thermodynamic models) or even black-box chemical packages (e.g., PHREEQC) for an accurate representation of governing physics without penalizing runtime. On the other hand, the implementation of the simulation framework is significantly simplified, which allows improving the simulation performance further by executing the complete simulation loop on GPU architecture. The integrated open-source framework Delft Advanced Research Terra Simulator (DARTS) is built around the OBL concept and provides a flexible, modular and computationally efficient modelling package. In this work, we evaluate the computational performance of DARTS for various subsurface applications of practical interests on both CPU and GPU platforms. We provide a detailed performance comparison of particular workflow pieces composing Jacobian assembly and linear system solution, including both stages of Constrained Pressure Residual solver.
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Compositional Modelling of Petroleum Reservoirs and Subsurface CO2 Storage with the MUFITS Simulator
By A. AfanasyevSummaryWe present recent extensions of the academic reservoir simulator MUFITS (www.mufits.imec.msu.ru) for modelling multicomponent flows in porous media. The extended simulator capabilities include a new fluid properties module for the compositional and thermal reservoir simulations in which a cubic equations of state (EoS) is used for prediction the PVT properties. Besides the standard three-parameter EoS, e.g. Peng-Robinson or Soave-Redlich-Kwong EoS with the volume correction, the simulator is supplemented with a built-in library of coefficients for a more general cubic EoS proposed by Brusilovskii (2002 ) which allows for improved prediction of phase compositions and densities without the volume-shifts. Unlike some other codes, MUFITS allows for compositional modelling of thermal processes in porous media. The phase enthalpies are predicted with EoS supplemented by the correlations of Passut & Danner (1972 ) for the ideal-gas enthalpy. In order to simplify the simulator usage, an extended library of hydrocarbons, carbon dioxide, nitrogen, water, and other components is built into the simulator, and additional components can be characterized and loaded into the library.
The standard iterative algorithms for the calculation of phase equilibria can stall near the critical condition, if two phases are almost identical, or in the case of multi-phase equilibria, e.g. VLL-equilibria. To model the fluid transport at such conditions, the simulator is supplemented with another thermal module which utilises our new method SDPE (Simplex Decomposition for Phase Equilibria) for the fluid properties prediction. The SPDE method is based on the decomposition of phase diagram into the simplices, i.e. multidimensional tetrahedra. At constant pressure and temperature, the space of total concentrations is triangulated, i.e. divided into simplices. The thermophysical parameters are approximated by linear functions in each simplex, and any boundary between equilibria of different type must be the boundary between two simplices. Thus, the set of simplices is a triangulated look-up table for the properties of multiphase fluid. Consequently, SPDE is a non-iterative method, what results in accelerated prediction of the fluid properties. We demonstrate the method applications for modelling the flows of simple 3-component hydrocarbon mixtures and the CO2-H2O-NaCl mixture in the problems of CO2 storage.
We acknowledge the funding from Russian Science Foundation under grant # 19-71-10051.
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Engineering Design of Neural Network Architectures for Estimation of Inter-Well Connectivity and Production Performance
Authors J. Yu, A. Jahandideh and B. JafarpourSummaryAdvances in machine learning and data science have given rise to a new set of tools and methods for developing efficient fit-for-purpose proxy models. Two major difficulties in adopting these methods are (i) the lack of physical constraints and domain insight in the design and construction of these models, and (ii) their limited interpretability, which can seriously impede their broader application to scientific domains, including reservoir engineering. In this paper, neural network architectures are designed based on simple reservoir engineering insights to characterize inter-well connectivity and well production performance under different operational conditions.
Two different approaches are presented for construction of a neural network proxy model. The first approach takes a global view by representing all well connections in a fully connected neural network to allow any injector to be connected to a producer. The resulting network is a highly redundant description as many of the included connections are not plausible. To systematically eliminate unrealistic connections, l1-norm regularization is adopted to sparsify the network topology (connections) during the training stage. The resulting sparse structure characterizes the inter-well connectivity and defines a network topology that is supported by the training data. In the second approach, a local view is taken in building the proxy model. In this case, each producer is assumed to be supported by very few surrounding injection wells and likely to have weak connections with distant wells. However, inter-well connectivity in complex large-scale reservoirs is not just a function of distance and rather difficult to determine. Therefore, we use a series of randomly sized neighborhoods around each producer to include different number of injectors in the local networks. The variability in the neighborhood size reflects the prior uncertainty about the potential connectivity between wells at different distances. This approach results in many local neural networks (several local networks per each producer) that can be aggregated into a single large neural network model with pre-defined topological structure to represent possible connections. The training is then used to estimate the weights in the resulting architecture.
The methods are applied to predict inter-well connectivity and oil production in a large-scale mature field that undergoes water flooding. Examination of the estimated connectivity parameters inside the neural network shows that the retrieved inter-well connectivity map is consistent with the existing geological features. The results suggest that even simple engineering insights can lead to noticeable improvement in the performance of neural networks.
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Stochastic Closed-Loop Reservoir Management under Uncertain Predictions and Development Plans
Authors A. Jahandideh and B. JafarpourSummaryOilfield development projects involve significant investments and critical investment decisions that can have direct impact on economic performance of the asset over its life cycle. Standard closed-loop management approaches combine field performance optimization and model updating to base development decisions based on the most current predictions of the future performance. A practical flaw of this approach is that in predicting the future performance of the reservoir, it considers development and operation strategies as decision variables. While within a modeling study this assumption seems reasonable, field development is a complex and involved process and several external and unanticipated factors may render development plans unpredictable. Given the uncertain nature of field development practices, a more realistic approach is to view future development and operations as uncertain variables, or at least consider multiple development options to hedge against changes in development plans.
We present a closed-loop stochastic reservoir management framework that accounts for the uncertainty in geologic and future operation scenarios. In this approach, the development decision for the current stage (e.g., well locations and control settings) are modeled as optimization decision variables while future development and operation plans and geologic reservoir description are considered as uncertain variables. The uncertainty in future operation and development variables is incorporated through drilling scenario trees, probabilistic well placement, and future control assignments, while geologic uncertainty is represented through an ensemble of reservoir models with different reservoir properties. We implement the workflow in a closed-loop format, consisting of dynamic model updating followed by optimization of current decision variable, where updatable decision variables (those that are not irreversible) are adjusted after each model updating stage. That is, if after model updating at the current time step a field development stage is reached, the decision variables consist of the locations of the new wells and the future controls of all existing and new wells. On the other hand, when a field development stage is not reached immediately following a current model updating step, only future well controls of existing wells are optimized. Several numerical experiments are presented to demonstrate the new workflow and its implementation. Comparison between the proposed stochastic field development optimization approach with the conventional closed-loop field development optimization formulations shows that treating future development and operation variables as uncertain parameters results in a more robust solution that is not sensitive to alternative development scenarios, even those that are not included in the problem formulation.
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History Matching under Uncertain Geologic Scenarios with Variational Autoencoders
Authors A. Jiang and B. JafarpourSummaryInference of high-resolution reservoir models from limited production data leads to ill-posed inverse problems. Parameterization methods are used to reduce the number of unknowns while maintaining the salient connectivity features of the reservoir model. Existing parameterization methods, such as principle component analysis (PCA), are not suitable for capturing complex non-Gaussian connectivity patterns that are exhibited in certain geological formation such as fluvial systems. Recent advances in machine learning have given rise to new approaches for dimensionality reduction that can be applied for parameterization of reservoir models in history matching. Many conventional parameterization techniques exhibit strong sensitivity to diversity in the geologic features (e.g., when multiple scenarios are used to account for prior uncertainty). One potential advantage of the new techniques is their ability to learn complex and diverse patterns, which leads to robustness against geologic uncertainty. We present variational autoencoders (VAEs) as a special form of convolutional neural networks for parametrization of history matching problems under multiple geologic scenarios.
Autoencoders have achieved great performance in data compression by taking advantage of the power of convolutional neural networks for detecting local spatial patterns. We present VAEs as an effective parameterization approach for complex spatial models with non-Gaussian statistics. These methods project complex spatial models to a low-dimensional latent space, where a small number of latent variables with simple probability density functions (e.g., Gaussian) approximate the original models. The latent space variables are used to update the reservoir model during history matching. We evaluate the dimensionality reduction power of VAEs and use them with stochastic gradient-based inversion methods to perform history matching. We present history matching results when the training data is based on a single geologic scenario and when multiple geologic scenarios lead to very diverse features in the training data. Comparison between the performance of VAE and PCA shows that the former offers important advantages over PCA. The performance difference between the two methods become more significant when multiple geologic scenarios are present. We present several examples to demonstrate the implementation of VAE and its important properties in comparison to PCA.
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