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ECMOR XVII
- Conference date: September 14-17, 2020
- Location: Online Event
- Published: 14 September 2020
121 - 140 of 145 results
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Machine Learning for Fast EOR Flooding Simulation
Authors B. Samson, C. Marooney, S. Godefroy and S. ShethSummaryMultiple simulator runs are usually a prerequisite for uncertainty and optimization workflows. The requirements that the simulation be both detailed for accuracy, and fast for timely results are in tension: greater model refinement will increase run time. Here we use Machine Learning (ML) to enhance coarser grid models, so that they capture important features in a field development planning which would normally require more refined models, while still giving faster calculation time. We apply this methodology to Enhanced Oil Recovery (EOR), for optimisation workflows aiming to carry out screening evaluations for the most efficient EOR types, optimal configurations of wells and their operation schedules.
A common feature of EOR processes is the formation of a sharp advancing front of the displacing agent (water, polymers, surfactants, etc.) which sweeps the reservoir. Standard accurate numerical modelling of the front would usually need a fine scale grid to capture the front gradients. Without dynamic re-gridding methods, this would require a fine scale grid across the whole reservoir, slowing down the simulations and making it difficult to launch many runs. Our methodology separates the front tracking from the reservoir simulation process, so that the front’s position and topology evolves in parallel with the coarse grid simulation, through modifications using ML-trained correlations. The simulation time of the pre-trained model is then defined by an upscaled coarse grid only, which is fast enough to be used in uncertainty and optimization workflows.
In our example workflow, the ML training is carried out with respect to a representative fine-grid simulation model. The front propagation and deformation learn to be dependent on an array of static (permeabilities, porosity) and dynamic (pressure, saturations, etc.) reservoir properties. These properties become available during the coarse grid simulation where the trained model is applied. The front position is thus adjusted, giving its next time step position. Small-scale geological reservoir features are honoured by refining front position using the same trained model.
This ML assisted coarse grid simulation with accurate front tracking is demonstrated using a range of models with varying degrees of rock heterogeneity. The results show, apart from the speed-up potential, a high degree of fidelity of front tracking using ML enhanced coarse grid workflow compared with the fine-grid model.
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GMRES Based Numerical Simulation of Multicomponent Multiphase Flow in Porous Media on LuNA Fragmented Programming System
Authors N. Kassymbek, B. Matkerim, D. Lebedev, T. Imankulov and D. Akhmed-ZakiSummaryUsing supercomputers can significantly accelerate the solution of problems when using numerical methods. One of these tasks is forecasting oil and gas production at specific oil and gas fields. Modeling of multicomponent multiphase fluid (oil and gas) flow in porous media (in oil reservoirs) is relevant and at the same time complex problem of hydrodynamic simulation. To solve such problems, various methods and schemes are used, some of whom are iterative methods for solving linear systems.
In this paper, we solve the equation system with the Newton-Raphson method, within each iteration of which the algebraic equation system is solved by the generalized minimal residual method (GMRES) with the ILU(0) preconditioner. The application of this problem which is named Newton-ILU(0)-GMRES method is implemented in parallel with MPI and Fragmented Programming (FP) Technology, which is aimed at automation of implementation of numerical applications for multicomputers. As in other numerical methods, in our case is a non-degenerate matrix. Storage of a full matrix with all zero elements leads to huge memory costs. In order to optimize the memory, the format of storage of sparse matrices was chosen – compressed row storage (CSR).
Tested the developed MPI parallel application and fragmented program on the MVS-10P supercomputer of the Interdepartmental Supercomputer Center of the Russian Academy of Sciences. The runtime between the MPI parallel program and the fragmented program in the LuNA system is compared and the results were analyzed. The work was supported by Funding Science committee of Ministry of Education and Science of Kazakhstan, grant no. AP05134651.
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Using SVD Algorithm to Solve Oil Displacement Problem
Authors T. Imankulov, D. Akhmed-Zaki, B. Matkerim and L. ZhumakhanSummarySingular value decomposition (SVD) is one of the powerful methods for matrix computing. The SVD method can be used as a method of extracting patterns from a matrix and as a method of compressing large matrices. This approach can be used to solve hydrodynamic problems for increasing oil recovery of (multiphase flow in anisotropic porous media). There is a known problem in determining the permeability of porous medium. Permeability is one of the important characteristics of the oil reservoir, which greatly affects the flooding of the porous medium and the oil recovery coefficient. Known common methods can determine the value of permeability only in individual sections of the porous medium, while the value in the remaining sections remains unknown.
When simulating such problems on large sizes of the computational grid, the matrix of permeability values - Kabs will turn out to be large and sparse. In this regard, the task is to analytically analyze the Kabs matrix, namely, to find the singular values of the Kabs matrix to determine the condition number of the linear operator. The value of the condition number affects the existence of a solution to the original system of the equation and to the accuracy of the solution to solve the oil recovery problem.
This article discusses the application of the SVD algorithm for calculating the eigenvalues/unit values/vectors of a large sparse matrix in oil extraction problems in anisotropic porous media.
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Optimization of CO2 Storage under Geomechanical Risk with Coupled-Physics Models
Authors F. Zheng, A. Jahandideh, B. Jha and B. JafarpourSummaryNumerical flow simulation of CO2 injection into geologic formations that describe the fluid flow, transport, and trapping mechanisms have been used to optimize CO2 storage by improving trapping efficiency and injection strategies. However, CO2 storage in geologic formations can cause geomechanical changes that lead to reservoir expansion, ground surface uplift, and induced seismicity. Such deformations create geomechanical risks associated with CO2 injection, which can compromise the safety and storage capacity of CO2 injection in the field. The geomechanical responses from CO2 sequestration have drawn more attention in recent years due to considerable potential for ground uplifting and induced microseismic activities. An environmental sound and safe approach to CO2 storage must incorporate the geomechanical risks in optimizing the storage performance.
We present an optimization framework for geologic CO2 storage under geomechanical risks, where coupled flow and geomechanical simulation is combined with rock failure criteria, such as Mohr-Coulomb plastic failure, to describe mechanical rock failure risk. Additionally, the outputs from geomechanical simulations are used to quantify the risk associated with the ground surface displacement and plastic strain. A multi-objective optimization is formulated and solved to maximize CO2 storage while minimizing the two forms of geomechanical risks. The optimization decision variables include the location and controls for each injection well. Multiple numerical experiments with increasing complexity, including a field-scale CO2-EOR example, are presented to demonstrate the performance of the proposed framework. The results reveal optimal decisions that are different from those obtained from flow-only simulation that disregard the geomechanical risks associated with CO2 injection. When geomechanical risks are considered, the wells may not necessarily be concentrated in areas with the highest storage capacity because that may lead to rock failure and unacceptable levels of ground surface uplift. Moreover, while surface uplift resulting from each well is highest at the corresponding injection locations, shear failure tends to happen in between the wells and its severity depends on formation properties as well as well configuration and controls. Overall, the observations from this study reveal important differences in optimization results and conclusions when geomechanical risks associated with geologic CO2 storage are considered.
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GPU-Based Parallel Algorithm for Solving Multiphase, Multicomponent Fluid Filtration Problem
Authors T. Imankulov, D. Akhmed-Zaki, B. Daribayev and O. TurarSummaryHydrodynamic modeling of oil reservoir processes is one of the complex problems of fluid mechanics, since underground reservoir processes can be very complex. It is necessary to take into account phase transitions, chemical transformations, temperature effects, and etc. When simulating multiphase, multicomponent liquid filtration, the properties of the phase can vary depending on the composition of temperature and pressure. The oil phase consists of hydrocarbon components that range from the lightest (methane) to the heaviest (bitumen). You can simulate the process of multicomponent filtration, knowing the physical parameters of the pseudo-components (molecular weight, critical pressure, critical temperature, compressibility, density, viscosity, thermal conductivity and specific heat).
Parallel algorithms implemented on graphic processors (GPUs) than on traditional processors (CPUs) are excellently suited to speed up such demanding tasks. In various fields of research, there have been many successful implementations on the GPU, such as medical image analysis and computational fluid dynamics. The GPU achieves high performance by executing more than a thousand threads at the same time, and each of them processes different data sets.
The purpose of this paper is to implement the parallel algorithm on modern graphic processors (GPUs) for numerically solving a multiphase multicomponent fluid filtration problem in porous media, taking into account the number of phases and components. For the numerical solution of the problem, the alternating direction implicit method (ADI) was chosen. ADI is a finite difference numerical method for solving parabolic, hyperbolic and elliptic equations, and it is widely used in the fields of science and technology. In the ADI method, each numerical step is divided into several sub-steps, depending on the spatial dimension of the problem, and systems of linear equations are solved implicitly in one direction, with an explicit scheme in the other direction. In addition, at each sub-stage, the equations have a tridiagonal structure. To solve the tridiagonal system of equations, several parallel algorithms were implemented: cyclic reduction (CR) and parallel cyclic reduction (PCR) methods. And to implement the sequential algorithm, the Thomas implicit method was used.
In this paper, to implement parallel algorithms CUDA technology and the OpenCL framework were used. The results of the study showed that the OpenCL framework is promising to use on any GPUs of any devices and get comparable results in terms of calculation time with CUDA. And to calculate parallel algorithms on CUDA, only GPUs from Nvidia are needed.
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Importance of Improving Support Material Removal from Polyjet 3D-Printed Porous Models
Authors S. Lopez Saavedra, S. Ishutov, R. Chalaturnyk and G. Zambrano NarvaezSummaryThe use of 3D printing technology to study physical processes occurring in subsurface porous media is rapidly gaining ground. However, the removal of support material from 3D-printed prototypes represents an obstacle for using such models in laboratory experiments. This study addresses some of the effects of improving support material removal from 3D-printed prototypes and some of the implications of utilizing these enhanced models on investigations of flow through fractures. Two groups of porous models were manufactured utilizing a polyjet 3D printer: 1) cylindrical pore throats specimens and 2) porous models with fractures. Two types of post-processing methods were also tested: 1) a chemical method and 2) a chemical-mechanical method. A Darcy flow experiment was employed to measure absolute permeability on the second group. Experimental results helped correlate testtime to the amount of removed support material and revealed the need for better estimating the required injection pressure to clean out support material from 3D-printed porous models. Permeability measurement was compared to analytical calculations. Results of post-treatment methods highlight the importance of using flushed 3D printed samples when studying physical processes occurring in porous media.
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An Automatic Well Planner for Efficient Well Placement Optimization Under Geological Uncertainty
Authors B.S. Kristoffersen, T. Silva, M. Bellout and C.F. BergSummaryAn Automatic Well Planner (AWP) is developed to efficiently adjust pre-determined well paths to honor near-well model properties and increase overall production. The AWP replicates a modern geo-steering decision-making process, where adjustments to pre-programmed well paths are driven by continuous integration of data obtained from logging-while-drilling and look-ahead technology. This work focuses on combining the AWP into a robust optimization scheme. AWP-determined well trajectories follow reservoir properties in a more realistic manner than common well representations; thus, they deal better with geological uncertainty. Specifically, the AWP creates custom trajectories that consider individual geological near-well conditions of each realization in an ensemble of models. Thus, for each well path calculated by the optimization procedure, the AWP creates one custom trajectory for each geological realization. The expected NPV, computed over the set of trajectories, is then used to assess the performance of the candidate well path.
The core operation of the AWP relies on an artificial neural network for tailoring the trajectory to geological properties. The AWP embeds a geology-based feedback mechanism for the overall well placement search. Commonly, well placement searches are conducted using linear well path representations. Analog to realistic drilling operations, the AWP determines a custom trajectory by moving along such a path in a sequence of steps from the heel to the toe. Subsequent trajectory points are determined by the efficient processing of neighboring geological information through the AWP network.
The proposed scheme is implemented within the open-source optimization framework FieldOpt, which provides a flexible interface for problem parameterization and parallelization. Tests are performed using two derivative-free algorithms: Asynchronous Parallel Pattern Search (APPS) and Particle Swarm Optimization (PSO). Both are applied to the Olympus ensemble. The results show that the AWP improved over a straight-line parametrization in a robust optimization scheme for both APPS and PSO.
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Modeling Transport and Retention: Simultaneous Evaluation of Dispersion and Retention Parameters
More LessSummaryUnderstanding transport and retention in porous media is essential in environmental and industrial processes like aquifer contamination, membrane filtration and water and polymer flooding in oil reservoirs. One of the earliest and most used method to determine transport and retention parameters consists in fitting both tracer and suspension/solution effluent concentrations. However, this method works under the assumption that dispersion coefficients for the suspension/solution and the tracer are equal or the difference between them is negligible. In this article, it is shown that this hypothesis can sometimes lead to misinterpretations. Furthermore, population balance equations for transport and retention are discussed based on the master equations. The obtained system of equations consists of one retention and one population equation for each class of particles. Averaging the aforementioned equations results in a closed system consisting of retention and advection-dispersion-reaction equations. Based on the KT (Kurganov and Tadmor) finite volume method, robust numerical solutions were obtained and applied for solving the inverse problem. Transport and retention parameters are firstly optimized by using the Levenberg-Marquardt algorithm and considering analytical solutions available in the literature (dispersion is neglected). Secondly, the proposed numerical model parameters (including dispersion coefficient) are calculated by setting the parameters obtained in the first step as initial input. Comparisons between analytical and the proposed model confirmed the accuracy of the proposed solutions even when advection is dominant. The aforementioned inverse problem solution was applied for determining fitting parameters for polymer and tracer injection experimental data available in the literature. The results allow concluding that, in general, very similar fitting parameters are obtained when tracer injection experimental data were or not used, suggesting that tracer tests are not necessary. However, in some cases, the results have shown that the polymer dispersion coefficient differs significantly from those obtained for the tracer, suggesting that the same dispersion coefficient used for fitting tracer data would not satisfactorily fit the polymer effluent data. Finally, the simultaneous determination of dispersion and retention coefficients would avoid conducting experimental tests with tracers.
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Coupled Forward Simulation of Seismicity: a Stick-Slip Model for Fractures and Transient Geomechanics
More LessSummarySeismic deformation in poroelastic media may be triggered by a variety of physical events including stick-slip frictional instabilities in fracture. While in the context of simulation-aided engineering to mitigate the risks of induced-seismicity, it is sufficient to be able to resolve the onset of seismic slip using quasi-static assumptions, applications involving microseismicity require inertial models throughout the intended operational activity. In this work, we develop a fully-dynamic (inertial), time-adaptive, and coupled numerical model incorporating transient poromechanics and multiphase flow in fractured reservoirs. The model is applied to simultaneously assimilate well-performance and dynamic seismic event sequences, thereby informing about the causal event dynamics. First, we extend the mixed XFEM-EDFM numerical scheme to time-dependent mechanics. A stable and second-order implicit Newark method is developed in time. The pressure-dependent contact forces in fracture are treated using Lagrange multiplier constraints, and a Polynomial Projection Method is developed to stabilize the computation of contact traction. A temporal adaptivity indicators is developed to resolve preseismic triggering and coseismic spontaneous rupture.
The model is validated empirically (for accuracy, consistency, and computational efficiency). Numerical examples are presented to benchmark the proposed dynamic model relative to predictions from a quasi-static approach. In particular, it is demonstrated that computed waveforms can differ to first-order. Furthermore, in simulation test cases with water injection, coseismic rupture and microseismic signals are detected and in-situ stress migration is observed.
We outline implications towards unifying toolchains and workflows for combined geophysical, well completions design, and reservoir performance analysis.
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Turbulent Flow Effects in A Slickwater Fracture Propagation in Permeable Rock
Authors E. Kanin, D. Garagash and A. OsiptsovSummaryThis work is devoted to an analysis of the near-tip region of a hydraulic fracture driven by slickwater in a permeable saturated rock. We consider a steady-state problem of a semi-infinite fracture propagating with constant velocity. The host rock is elastic and homogeneous, and fracture propagates according to linear elastic fracture mechanics. The fluid exchange between the fracture and reservoir is governed by Carter’s law. The distinguishing feature of the model is an account for the transition of the flow regime inside the crack channel from laminar to turbulent moving away from the fracture front. The main objective is to analyse the influence of the leak-off process on the laminar-to-turbulent transition and, thus, potential prominence of turbulent flow effects. Hydraulic fracturing fluid is water with polymeric additives (slickwater). These additives reduce viscous friction resulting in the decrease of energy consumption required for pumping. Compared to water, the slickwater exhibits significantly delayed transition to the turbulent regime described by the maximum drag reduction asymptote ( Virk 1975 ). The system of governing equations, which consists of elasticity equation, propagation condition, the continuity equation for viscous incompressible Newtonian fluid, and Poiseuille’s law modified for the turbulent flow regime, is solved for the fracture aperture and fluid pressure along the fracture as a function of problem parameters. We find out that the leak-off process enhances the turbulent flow effects by shifting the transition between laminar and turbulent flow regimes closer to the fracture front, as compared to the zero-leak-off case ( Lecampion & Zia, 2019 ), resulting in a broader region of the fracture hosting turbulent flow. Consequently, in the permeable reservoir case, the transition to turbulent flow can be realised at a distance from the front smaller than the typical field hydraulic fracture size (10 – 100 meters). We compare the fracture width profiles with the impermeable rock case and reveal that the fracture volume increases when leak-off occurs. We analyse the problem parametric space where five limiting regimes are identified: toughness, laminar-viscosity and -leak-off, turbulent-viscosity and -leak-off. We derive analytical expressions for the fracture width and pressure profiles in the turbulent-leak-off regime while others have been established previously. By comparing the limiting solutions with the general numerical solution, we can define their applicability domains and corresponding solution regime maps. The toughness and turbulent-viscosity regimes approximate the general solution in the near- and far-fields, while the other three limiting cases can emerge in the intermediate field.
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History Matching with Generative Adversarial Networks
Authors S. Mohd Razak and B. JafarpourSummaryConditioning reservoir models with complex non-Gaussian spatial patterns on nonlinear production data is complicated by the need to preserve the expected geological features to maintain solution plausibility. Generative adversarial networks (GANs) have recently been proposed as a promising approach for low-dimensional representation of complex high-dimensional images. It has also been adopted for low-rank parameterization of complex geologic models to facilitate data integration and uncertainty quantification workflows. A challenging aspect in adopting parametric methods for history matching is the ease of data conditioning. While conditional GAN (CGAN) has been developed for conditioning on image labels, reservoir engineering applications require conditioning on nonlinear flow data, which is a far more complex problem.
We present two approaches for generating flow-conditioned models with complex spatial patterns using GAN. The first method is through CGAN, whereby a production response label is used as an auxiliary input when training CGAN. The label is derived from clustering the flow responses of the prior model realizations. The underlying assumption of this approach is that CGAN can learn the association between the spatial features corresponding to the production responses within each cluster. An alternative method that involves two steps is also presented, where in the first step a neighborhood selection algorithm identifies the subset of relevant flow responses around the observed data (using the training models). The second step employs GAN to generate conditional models based on the realizations selected in the first step. In this case, GAN is not required to learn the relation between production responses and spatial patterns. Instead, it is tasked to learn the patterns that are involved in the selected realizations. This approach allows for exploring the spatial variability in the conditional realizations, which can be critical for decision-making.
We present several examples, including non-Gaussian prior models with linear and non-linear forward models, to evaluate the performance of the two methods in generating flow-conditioned models. The results show that the generated conditional models preserve geologic realism and can reproduce the field production data within a specified error. An important advantage of GAN for data conditioning is that it automatically honors the geological feasibility constraint, which is not trivial to accomplish using existing low-dimensional parameterization methods. Moreover, it achieves this performance even when very few latent variables (parameters) are used, which is desirable for uncertainty quantification. We present and discuss the important properties of GAN for data conditioning with several examples with increasing complexity.
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Adaptive Mesh Refinement for Thermal-Reactive Flow and Transport on Unstructured Grids
Authors E. Jones, S. De Hoop and D. VoskovSummaryA coupled description of flow and thermal-reactive transport is spanning a wide range of scales in space and time, which often introduces a significant complexity for the modelling of such processes. Subsurface reservoir heterogeneity with complex multi-scale features increases the modelling complexity even further. Traditional Algebraic Multiscale techniques are usually focused on the accuracy of the pressure solution and often ignore the transport. Improving the transport solution can however be quite significant for the performance of the simulation, especially in complex applications related to thermal-compositional flow. The use of an Adaptive Mesh Refinement enables the grid to adapt dynamically during the simulation, which facilitates the efficient use of computational resources. This is especially important in applications with reactive flow and transport where the region requires high-resolution calculations as often localized in space. In this work, the aim is to develop an Adaptive Mesh Refinement framework for general-purpose reservoir simulation. The approach uses a multi-level connection list and can be applied to fully unstructured grids. The adaptivity of the grid in the developed framework is based on a hierarchical approach. First, the fine-scale model is constructed, which accurately approximates all reservoir heterogeneity. Next, a global flow-based upscaling is applied, where an unstructured partitioning of the original grid is created. Once the full hierarchy of levels is constructed, the simulation is started at the coarsest grid. Grid space refinement criteria can be developed specifically for a particular application of interest. The multi-level connectivity lists are redefined at each timestep and used as an input for the next. The developed Adaptive Mesh Refinement framework was implemented in Delft Advanced Research Terra Simulator which uses the Operator-Based Linearization technique. The performance of the proposed approach is illustrated for several applications, including hydrocarbon production, geothermal energy extraction and subsurface storage.
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A Semi-Analytical Solution of Dimethyl Ether Enhanced Water Flooding
Authors P. Soleimani, M. Chahardowli and M. SimjooSummaryDimethyl Ether Enhanced Water Flooding (DEW) is a promising water-soluble solvent-based EOR method. In this paper, we developed a semi-analytical solution to describe a one-dimensional (1D) DEW process that considers the effect of Dimethyl Ether (DME) partition coefficient. The 1D flow equations of DEW process were presented by Buckley-Leveret methodology in a linearized form to generate a series of fractional flow curves during oil displacement by DEW. The premise of the study was that once the DME-water solution is injected into the reservoir and comes in contact with oil, DME molecules partition into the oleic phase, which mobilizes waterflood residual oil as a consequence of oil swelling and oil viscosity reduction effects. The dependence of these effects on the DME partition coefficient significantly affects the oil- water fractional flow curve. Accordingly, results showed that there are two shock fronts during DEW process which are related to water and DME advancement. We also obtained the velocity of DME shock front as a function of DME partition coefficient that enables us to describe the fractional flow solution of the DEW process. As to the results, when the DME partition coefficient increases, the distance between water and DME fractional flow curves increases mainly due to the mobility enhancement of the oleic phase as a result of higher partitioning of DME into the oil. In addition, model results showed that increase of the DME partition coefficient up to 10 improved the ultimate oil recovery to as much as 15% of the OIIP on top of water flooding for the case of a heavy crude oil with a viscosity of 20 cp. As to the results, increase of the DME partition coefficient accelerates the oil recovery rate as well.
At the end, this paper provided a semi-analytical solution based on the fractional flow theory to describe DEW process with the emphasis on the partitioning effect..
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Efficient Adjoint-Based Well-Placement Optimization Using Flow Diagnostics Proxies
Authors S. Krogstad and H. Møll NilsenSummaryOptimizing placement and trajectory of wells is a computationally demanding, and hence time-consuming task due to the high number of simulations typically required to achieve a local optimum. In this work, we combine three remedies for speeding up the workflow; firstly, we employ a flow-diagnostics (see [1] ) proxy for the objective e.g., net-present-value; secondly, we implement an efficient adjoint for computing approximate sensitivities with respect to the placement/trajectory parameters (as suggested in [2] ); and finally, we include a version of the generalized reduced gradient (GRG) method (see [3] ) for efficient constraints handling of the control optimization problem.
The suggested flow diagnostic proxy is based on a single (or a few) pressure solutions for the given scenario and the solution of several inter-well time-of-flight and steady-state tracer equations, typically achieved in a few seconds for a reservoir model of medium size. Although the proxy may not be a particularly good approximation of the full reservoir simulation response, we find that for the cases considered, the correlation is very good and hence the proxy is suitable for use in an optimization loop. The adjoint simulation providing control gradients and placement sensitivities is of similar computational complexity as the forward model (a few seconds). The version of the GRG used here amounts to treating all individual well constraints (e.g., bhp and rates) as control variables and update only those that are active for a given control step. This means that individual well constraints can be enforced within the flow diagnostics computations, and hence every iteration becomes feasible without sacrificing gradient information.
We present numerical experiments illustrating the efficiency and performance of the approach for well-placement problems involving trajectories and simulation models of realistic complexity. The suggested placements are evaluated using full simulations. We conclude by discussing the limitations and possible enhancements of the methodology.
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Fluid-Rock Geomechanical Interactions: Micro-Mechanics and Fractured Reservoirs
By G. CouplesSummaryMicro-mechanics models of the process interactions, occurring between a rock framework and its contained pore fluids, provide phenomenological understanding of bulk behaviour. When fluid pressure is increased, the rock+fluid system is induced to expand, but real-world constraints normally inhibit this. As a consequence, stress components increase, and the rock experiences an increase intensive energy in both the fluid and solid components. Applying this understanding to fractured rock, the increased pressure tends to cause fractures to close, an opposite behaviour to the rule usually adopted. Conversely, when pressures are lowered, the rock loses energy, and stresses diminish, with opportunities for fractures to open, or blocks to move. The observed flow response of a fractured reservoir is explained as follows. During production of a well, the nearby rock mass is unloaded, allowing shifts between fracture-bounded blocks, enhancing bulk fluid flow. During near-well rock mass relaxation, the distant response is similar to what happens during drilling, where rocks move (slightly) towards the reduced-energy region. A ‘ring’ of high-strain-energy rock forms, like a horizontal, circular(ish) arch, reducing the potential flow paths from the far-field to the well area. Thus, a well initially produces at a high rate, and then a sharp decline is observed as the pore fluids in the protected region are depleted. The process described cannot be correctly simulated at present, because existing simulators are based on continuum laws (and extensions of them) that are not valid. The ‘law of effective stress’ used in geomechanics is physically wrong, further degrading the value of present simulations. Using approximate models of fractured-rock behaviour, recognising that those models lack correct fluid effects, some strategies emerge for consideration. By judicious use of depletion locations and timings, the responses noted here could be deliberately provoked to cause a new arrangement of flow paths and isolations to be induced.
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Using Machine Learning Methods for Oil Recovery Prediction
Authors B. Daribayev, D. Akhmed-Zaki, T. Imankulov, Y. Nurakhov and Y. KenzhebekSummaryIn recent years, machine learning methods have been widely used in various fields of science for big data processing. The application of machine learning in the oil industry is also actively expanding. To solve oil recovery problems, it is necessary to use geological models of reservoir fields. With increasing of the reservoir model complexity (size), the computing time also increases. Therefore, it takes longer to predict oil recovery. There are two approaches to solve this problem. The first approach is to develop an effective parallel algorithm taking into account the heterogeneity of computing systems. Many scientists from all over the world are developing parallel algorithms in this field. In particular, we have written many scientific papers. The disadvantage of using this approach is that when you change the initial data for the oil recovery prediction, you need to make calculations on supercomputers every time, which takes a lot of time and resources. The second approach is to use machine learning methods, which is the purpose of this paper.
This paper discusses approaches to using effective machine learning methods for oil recovery prediction. To train the system, we used historical data from the oil field and synthetic data obtained from surrogate models based on two wells (injection and production). Synthetic data were generated based on mathematical models (oil displacement models, enhanced oil recovery models) by varying the different geological parameters. This problem belongs to the “supervised learning” - type of machine learning. Supervised learning requires a complete set of marked data for training the model at all stages of its construction. When implementing the algorithm, we considered machine learning methods for solving the regression and classification problems.
As a result, it was discovered that compared to traditional computational experiments on a regular grid, calculations using machine learning methods are more productive.
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Higher Resolution Hybrid Unstructured Spectral Finite-volume Methods For Flow In Porous Media
Authors Y. Xie and M. EdwardsSummaryNovel higher resolution hybrid spectral finite-volume methods are presented and coupled with the control-volume distributed multi-point flux approximation (CVD-MPFA) for flow in porous media including fractures and gravity. The spectral-volume is the primal cell which is sub-divided into sub-cell control-volumes, the sub-cells are then used to develop an efficient strategy for reconstruction of both a higher resolution approximation of the convective transport flux and Darcy flux approximation on sub-cell interfaces. The new method extends the first order structured grid hybrid method of [Lee et al] to a higher resolution spectral formulation on unstructured grids. The novel hybrid spectral-volume method presented involves reconstruction of both the convection variable(s) and the Darcy-flux. First the pressure equation is solved on a primal coarse grid using the CVD-MPFA method. Each coarse primal cell is subdivided into sub-cells following the spectral-volume method. Darcy-fluxes are then reconstructed on the sub-cell control-volume faces from using the course primal cell solution. For the convective transport equation approximation, each sub-cell is assigned a degree of freedom for saturation and/or concentration and a higher resolution hybrid sub-cell control-volume transport approximation is efficiently reconstructed over each spectral-volume. The fine scale saturation field is then updated via the new hybrid reconstructed finite volume approximations over the sub-cell control-volumes.
Performance comparisons are presented for tracer and two-phase flow problems, including fracture and gravity problems on unstructured meshes. Comparisons between the standard lower-order and higher resolution hybrid CVD-MPFA methods and the new higher resolution hybrid spectral-volume method demonstrate both the improved resolution of flow fields achieved by the standard higher resolution method, and the extra fine flow field resolution achieved by the spectral-volume method, while the spectral-volume method is also shown to be considerably more efficient.
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Quasi-K-Orthogonal Grid Generation for Quasi-Positive CVD-MPFA
Authors S. Manzoor, M. Edwards and A. DogruSummaryA novel Quasi K-orthogonal grid generation method is presented, where the grid is designed to ensure that linear control-volume distributed multi-point flux approximation (CVD-MPFA) methods retain a discrete quasi positive approximation. The quasi K-orthogonal grid generation method improves grid quality and method stability with respect to flux approximation in the presence of strongly anisotropic full-tensor permeability fields.
K-orthogonal grid generation is only possible for relatively low anisotropy ratios. Quasi K-orthogonal grid generation involves satisfying the K-orthogonal condition approximately, resulting in practical grids that place less demand on an approximation with respect to stability conditions, and therefore improve grid quality with respect to flux approximation in the presence of anisotropic permeability fields. The standard two-point flux approximation (TPFA) requires strict K-orthogonality for consistency, consequently CVD-MPFA schemes which are consistent on non k-orthogonal meshes are still required as the grids are only approximately K-orthogonal in such cases. The grid generation employed enables Delaunay grid generation principles to be employed in a locally transformed system according to local permeability tensor variation. The resulting method has great flexibility for handling complex geometries and can handle jumps in permeability tensor principal axes orientation and jumps in coefficients and details will be presented.
Results are presented that demonstrate the benefit of the quasi K-orthogonal grid generator. Highly challenging cases involving strong full-tensor permeability fields are tested, where CVD-MPFA schemes exceed their stability limits and yield solutions with spurious oscillations when using conventional grids. In contrast when employing the new quasi K-orthogonal grids, the CVD-MPFA schemes yield well resolved solutions that are free of visible spurious oscillations.
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Physics-Based Data-Driven Model for Production Forecast
Authors A. Blinovs, M. Khait and D. VoskovSummaryA physics-based data-driven model is proposed in this study for the forecasting of secondary oil recovery. The model fully relies on production data and does not directly requires any in-depth knowledge of the reservoir geology or governing physics. In the proposed approach, we utilise Delft Advanced Reservoir Terra Simulator (DARTS) as a base for data-driven simulation. DARTS uses an Operator-Based Linearization technique which exploits an abstract interpretation of physics benefiting computational performance for a forward simulation. The proposed strategy was evaluated first on the two synthetic data ensembles and showed good prediction accuracy for a significantly reduced model size. Besides, the data-driven proxy methodology was compared with an advanced flow-based upscaling technique and demonstrated an improved accuracy for both ensembles. Besides, the proposed data-driven approach was examined on two realistic data sets. For the first case, the methodology demonstrates advanced predictive performance for training based on synthetic data generated from a high-fidelity simulation model with imposed random noise. To check the robustness of the proposed methodology, the control parameters for a forecast period were significantly changed in comparison to the training period. The data-driven model still manages to predict the forecast production quite close to the reference high-fidelity results. However, the training performed on another data set based on historical production from a real brownfield was not fully successful. We relate a bigger error in both training and forecast period for this model to poor data quality. The training procedure for this model led to a moderate accuracy in history matching for a long production period, where general production trends have resembled true data and water breakthrough time was restored in nearly all wells. However, there are still periods of poor accuracy, especially where shark peaks and falls are experienced.
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Hydro-Mechanical Coupling for Flow Diagnostics: A Fast Screening Method to Assess Geomechanics on Flow Field Distributions
Authors L. Gutierrez Sosa, S. Geiger and F. DosterSummaryHydro-mechanical coupling is imperative when the stress disturbances induced by production/injection processes affect the reservoir performance. However, the application of coupled hydro-mechanical models in actual full-field studies is still limited, mainly because of the high computational cost. Despite the existence of simplified coupling strategies (one-way coupling and loose coupling) that reduce the computational cost, numerical simulations remain challenging because of the significant computing time required to simulate coupled processes in complex and heterogeneous reservoir models. With the appropriate extension, flow diagnostics could also be used to screen and assess the impact of hydro-mechanical processes on reservoir performance so as to select a smaller number of models for detailed, and computationally costly, fully coupled hydro-mechanical simulations.
We hence present an approach that allows us to extend the existing flow diagnostics to account for geomechanical effects without increasing the computational overhead significantly. Flow diagnostics approximate the dynamic reservoir behaviour in seconds by computing the time of flight and steady-state tracer distributions directly on the reservoir grid. Hence, the extended flow diagnostics simulations complement full-physics simulations for estimating reservoir connectivity, fluid-fronts distributions, fluid displacement efficiency and well allocation factors under geomechanical effect.
The acceleration of the proposed hydro-mechanical coupling is achieved by: 1) the representation of the dynamic behaviour through the use of flow diagnostics simulations ( Møyner et al., 2014 ); 2) the formulation of the hydro-mechanical problem to account for steady-state conditions based on poro-elastic theory (Coussy, 1994, 2004 ); 3) a sequential stress-flow coupling using stress-dependent permeability as a coupling term. This coupling strategy ensures stability and fast convergence of the hydro-mechanical solution using a stress-fixed split strategy ( Kim et al., 2011a , 2011b ) and yields a significant reduction of the CPU time.
Two cases studies were analysed based on the SPE 10 Model ( Christie and Blunt, 2001 ) in which the effect of a 5-spot injection pattern subjected to a gravity load is studied, and the effect of mechanical heterogeneity is considered. These examples demonstrate the application of the proposed methodology to assess geomechanical impact in highly heterogeneous formations and the importance of not only account for petrophysical heterogeneities when assessing reservoir performance but also for the heterogeneity of mechanical properties as these alter the petrophysical properties when stress-sensitive reservoirs are produced.
Geomechanically informed flow diagnostics account for coupled hydro-mechanical effects that can alter the performance of stress-sensitive reservoirs during production.
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