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ECMOR XVII
- Conference date: September 14-17, 2020
- Location: Online Event
- Published: 14 September 2020
21 - 40 of 145 results
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Novel Ensemble Data Assimilation Algorithms Derived from A Class of Generalized Cost Functions
By X. LuoSummaryEnsemble data assimilation algorithms are among the state-of-the-art history matching methods. From an optimization-theoretic point of view, these algorithms can be derived by solving certain stochastic nonlinear-leastsquares problems.
In a broader picture, history matching is essentially an inverse problem, which is often nonlinear and ill-posed, and may not possess any unique solution. To mitigate these noticed issues, in the course of solving an inverse problem, domain knowledge and prior experience are often incorporated into a suitable cost function within a respective optimization problem. This helps to constrain the solution path and promote certain desired properties (e.g., sparsity, smoothness) in the solution. Whereas in the inverse problem theory there is a rich class of inversion algorithms resulting from various choices of cost functions, there are few ensemble data assimilation algorithms which in their practical uses are implemented in a form beyond nonlinear-least-squares.
This work aims to narrow this noticed gap. Specifically, we consider a class of generalized cost functions, and derive a unified formula to construct a corresponding class of novel ensemble data assimilation algorithms, which aim to promote certain desired properties that are chosen by the users, but may not be achieved by using the conventional ensemble-based algorithms.
As an example, we consider a channelized reservoir characterization problem, and formulate history matching as some minimum-average-cost problems with two new cost functions. In one of them, our objective is to restrict the changes of total variations of reservoir models during model updates. While in the other, our goal is instead to curb the modifications of histograms of reservoir models. While these two cost functions may appear unconventional in the context of ensemble data assimilation, the corresponding assimilation algorithms derived from our proposed formula are very similar to the conventional iterative ensemble smoother (IES). As such, our previous experience with the IES can be smoothly transferred into the implementations and applications of these new algorithms. In addition, the experiment results indicate that using either of these two new algorithms leads to better history matching performance, in comparison to the original IES.
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Application of Dynamic Parametrization Algorithm for Non-Intrusive History Matching Approaches
Authors A. Mukhin, M. Elizarev, N. Voskresenskiy and A. KhlyupinSummaryHistory matching generates detailed reservoir description that matches production data and can be used for forecasting and uncertainty estimation. Due to the ill-posedness of the history matching problem, the parametrization of high-dimensional fields in the model (such as permeability and porosity) is widely applied. The common approach of existing parametrization algorithms is to generate a dataset of possible fields realizations (prior models) and then convert this dataset to an orthogonal basis using PCA-based techniques. Model reduction is achieved by truncating the majority of basis components based on energy criteria.
Due to high uncertainty and low quality of real data, the important pattern could be under-represented in the prior dataset and basis components with such structures could be truncated. We present a novel method where omitted components are defined not only by energy criteria but also by objective function sensitivity. In our Adaptive Strategies PCA (AS-PCA) technique we developed and advanced definition of the optimal basis and derived an efficient algorithm for basis recalculation using computational approaches from quantum mechanics. The algorithm requires gradient of an objective function w.r.t latent variables (only at the point of convergence). Then the new basis is obtained by a few linear transformations with negligible computational cost, and optimization continues. The method was tested on history matching of 2D reservoirs and have demonstrated improvements in terms of misfit value and field consistency in comparison with classic PCA parametrization.
However, the applicability of gradient-based methods is constrained by local convergence and high implementation efforts (i.e adjoint technique). To overcome these constraints, we extend adaptive strategies for non-intrusive history matching approaches such as stochastic optimization and ensemble-based algorithms. Numerical gradient approximation is not well-suited for AS-PCA since it is inexact and takes additional simulation time. We developed the regression-based algorithm for gradient estimation using a set of field realizations, represented by an ensemble in ensemble-based methods or a population in evolution-based algorithms. In this study, we demonstrate the theory and examples of adaptive strategies application to history matching using PSO and enKF. The results of history matching with inconsistent prior datasets for 2D gaussian fields and applications to uncertainty quantification will be provided.
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Algebraic Wavefront Parallelization for ILU(0) Smoothing in Reservoir Simulation
By S. GriesSummaryIncomplete factorization methods are an important part of the linear solver strategy in reservoir simulation. It has been shown earlier that the inherited pressure-decoupling effect of (block)-ILU(0) plays an important role for the convergence of efficient linear solvers like System-AMG or CPR. From Black-Oil to coupled geomechanics.
With these specific linear systems, this decoupling is a by-product of the row-wise ILU-elimination. However, this also makes ILU sequential in nature, which is a problem on parallel compute hardware.
The parallelization of ILU methods has been a field of active research – and it still is. Various approaches are reported in the literature. All exploit inherited parallelism in the sparse systems to solve. Either by reordering the system accordingly or by setting synchronization points induced by the underlying structure (so-called wavefronts). All of these approaches have certain disadvantages and advantages regarding parallel efficiency and numerical robustness. It depends on the application which approach is best-suited.
Re-ordering approaches affect the elimination order. Hence, they can have significant robustness impacts for AMG in reservoir simulation.
Wavefront parallelizations guarantee equivalence to the sequential method. However, they either require the parallelization structure to be induced by the geometry. This may be challenging in unstructured cases and voids a main advantage of AMG. Or they perform a row-wise data-dependency scan, with a resulting amount of blocking communication.
In this paper, we are going to present a wavefront parallelization for (block-) ILU(0) that does not perform its dependency scan by considering groups of rows. The resulting wavefront setup works analogously to aggregative AMG setups, just with additional constraints. The outcome is a data-dependency graph where one can control the compromise between the frequency of data-exchange and wait-time. The equivalence to the sequential ILU(0) algorithm is still guaranteed.
While this approach can’t compete with the parallelizability of methods like Jacobi-relaxations, it can exploit inherited parallelism with ILU(0) for both OpenMP and MPI. It maintains the numerical properties of the original algorithm. We will demonstrate both with test problems as well as with ones from industrial reservoir simulations.
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Extended Finite Volume Method (XFVM) for Flow Induced Tensile Failure in Fractured Reservoirs
Authors A.A. Habibabadi, R. Deb and P. JennySummaryTensile opening of pre-existing fractures and tensile failure around the fracture tips triggered by fluid injection can lead to permeability increase in a reservoir. Such hydraulically driven fracturing technologies are used in petroleum engineering to achieve enhanced extraction of oil and gas. However, such processes can also lead to increased seismic activity around the reservoir ( Ellsworth 2013 ). Numerical modelling of tensile opening and crack propagation along with shear slip modelling of pre-existing fractures is important to assess advantages and risks of hydro-fracturing.
The main criteria for numerical models of coupled flow and mechanics in fractured reservoirs are accuracy and computational efficiency. For flow, descriptions based on embedded discrete fractures in matrix domains proved to be successful in this regard ( Hajibeygi et al., 2011 ; Lee et al.; 2001 ). In this context, flow induced shear failure and tensile opening can be modelled using an extended finite element method (XFEM) ( Borja, 2008 ) or the recently introduced extended finite volume method (XFVM) ( Deb and Jenny, 2017 , 2020 ). The advantage of XFVM lies in the choice of only one degree of freedom per fracture segment for the displacement ( Deb and Jenny, 2017 ) and that the same conservative method is used for both flow and mechanics.
The current paper deals with an extension of this XFVM framework, such that also crack tip propagation can be simulated. The cohesive stress approach by ( Wells & Sluys, 2001 ) for crack tip propagation was modified and integrated into XFVM. Using the coarse-scale solution of stress field obtained by XFVM at the fracture tips, a fine-scale interpolation is generated. This finescale solution is used to obtain the stress intensity factors (SIF) by an overdeterministic method. The SIF calculation is used to estimate crack growth criterion and direction. An example testcase of tensile failure solution at the crack tips of a single fracture is studied.
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Additive Schwarz Preconditioned Exact Newton Method as a Nonlinear Preconditioner for Multiphase Porous Media Flow
Authors Ø. Klemetsdal, A. Moncorgé, O. Moyner and K. LieSummaryDomain decomposition methods as preconditioners for Krylov methods are widely used for linear problems. There have been recently a growing interest into nonlinear preconditioning methods for Newton’s method applied to porous media flow. In this work, we study a spatial Additive Schwarz Preconditioned Exact Newton (ASPEN) method as a nonlinear preconditioner to the Newton’s method with fully implicit scheme in the context of immiscible and compositional multiphase flow. We first describe the method and how it can be implemented in a reservoir simulation package. We then study the nonlinearities addressed by the different components of the method. We observe that the local fully implicit updates are tackling well all the local nonlinearities and that the global ASPEN updates are tackling well the long range interactions. The combination of the two updates leads to a very competitive algorithm. We illustrate the behavior of the algorithm for conceptual one and two-dimensional cases, as well as realistic three dimensional models. We perform a complexity analysis and demonstrate that the Newton’s method with fully implicit scheme preconditioned by ASPEN is a very robust and scalable alternative to the well-established Newton’s method for fully implicit schemes.
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Analytical Pore Network Approach (APNA) for Rapid Estimation of Capillary Pressure Behaviour in Rock Samples
Authors H. Rabbani, D. Guerillot and T. SeersSummaryCapillary pressure measurements are an integral part of special core analysis (SCAL) to which oil and gas industry greatly rely on. Reservoir engineers implement these macroscopic properties in simulators to determine the amount of hydrocarbons as well as the flowing capacity of fluids in the reservoir. Despite their importance, conventional laboratory techniques used to measure capillary pressure curves of core samples are expensive, tedious, time-consuming and prone to error. Motivated by the importance of capillary pressure measurements in oil and gas industry, here we propose a novel methodology called Analytical Pore Network Approach (APNA) that can provide a reliable forecast of capillary pressure using pore-scale 3D images of reservoir rocks. The proposed approach provides oil and gas companies inexpensive, fast and accurate estimation of capillary pressure data, and reduces the number of required laboratory experiments and facilitates the estimation of such properties from uncored sections of the reservoir (i.e. using drill cuttings).
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Analytical Production Optimization with Modified NPV: Application to 2D Gas-Cone Reservoirs
Authors A. Bizzi, E. Fortaleza and F.P. MuneratoSummaryThis article investigates the analytical and computational optimization of reservoirs in alternate cost and coordinate spaces, by means of a modified NPV function (MNPV). We show that, for reduced systems, undertaking the analysis of reservoirs in these abstract spaces may lead to exact analytical expressions, unattainable under traditional analysis. This, then, may be used to speed up the optimization of large-scale reservoirs.
We demonstrate the concept under a restricted scope, focusing on a simplified case: To undertake the task of maximizing the transient yield of an idealized reservoir. It consists of a single production section of a horizontal well, in the presence of a gas cone. A set of further simplifying assumptions is then applied: For our analysis, the only depletion mechanism present is coning, and the very long 3D reservoir can be considered as composition of a group of 2D models.
Under these restrictions, we present an analytical proof that this modified NPV represents a convex function, for which the local optimization in abstract space generates the optimal global production strategy.
This, coupled to an analysis of monotonicity of the reservoir dynamics, may be used to algebraically demonstrate the existence of diminishing returns from increases in production rate, finally arriving at the most cost effective production strategy for the given system. This is then validated by a series of numerical simulations of the proposed reservoir.
Finally, we discuss similar concepts that may be used for the optimization of more realistic systems, enabling the use of analytical tools in the speeding-up of full-scale reservoir analysis.
The paper’s contributions can be stated in three points:
First, it presents new information on an emerging approach to the optimization of reservoirs. While most tools focus on optimizing the computation of reservoir-related processes, we show that a new approach to the NPV metric itself may lead to promising new results.
Second, it presents a novel, closed-form analytical solution for the optimal production rate of a reservoir with a simplified 2D gas cone.
Finally, it presents an alternate perspective on the role of analytical results in the era of computational reservoir optimization, by proposing a hybrid approach.
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Albite-Anorthite Synergistic Effect on the Performance of Nanofluid Enhanced Oil Recovery
Authors R. Nguele, E.O. Ansah, K. Nchimi Nono and K. SasakiSummaryLarge volumes of oil sit within our reach primarily of the strong capillary forces, which themselves are subsequent to the attraction between the polar ends of the oil and the surface charges of bearing-matrix. Altering these interactions occurring within tiny pore throats or even more, unveiling the extent to which the geochemistry impacts these interactions can invariably improve the production. Therefore, we evaluated the performance of water-based nanofluid for oil production with the respect to the geochemistry.
Alumina-silica nanocomposite (Al/Si-NP), synthesized by plasma-method, was used as primary material. Functionalized by dispersing 0.25 wt.% lyophilized NP into the formation water (TDS=4301 ppm) water under carbon dioxide bubbling. The nanofluid, NF, obtained therefrom, was then used for coreflooding tests, which aim at displacing a dead heavy oil (ρ =0.854 g/cm3) from a waterflooded Berea sandstone. The ionic composition of the effluent fluids was tracked and further used for modeling the geochemical interactions. The latter considered mineral precipitation and dissolution as well as ion adsorption and desorption. Model calculations were performed using the transport algorithm in PHREEQC.
The experimental results from coreflood tests showed that Al/Si-NP, injected into a waterflooded sandstone, could displace up to 11% of the oil trapped, which was 10 times higher if no nanofluid as injected. Ionic tracking further revealed that the dissolution of albite along with anorthite weathering; both mechanisms concurred to the logjamming of Al/Si-NF. Furthermore, the geochemical modeling revealed weak and reversible cation exchange between sodium (Na+) and calcium (Ca2+). Also, we found that the pH of the preflush should be mildly basic with for controllable anorthite and albite precipitation plus silica cementation, from which derive Al-Si-NF aggregation. These points were further verified experimentally when the ionic composition was altered accordingly to the geochemical modeling, leading to the conclusion that albite, anorthite and silicate precipitation promotes high recovery, due to high Na+ and K+ ions. Silica cementation was proven to increase formation rock wettability.
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Multiscale Matrix-Fracture Transfer Functions for Naturally Fractured Reservoirs Using an Analytical Discrete Fracture Model
Authors R. Hazlett and R. YounisSummaryFracture matrix transfer functions have long been recognized as tools in modeling naturally fractured reservoirs. If a significant degree of fracturing is present, models involving isolated matrix blocks and matrix block distributions become relevant. However, this methodology captures only the largest fracture sets and treats the matrix blocks as homogeneous, though possibly anisotropic. Herein, we produce the semi-analytic transient baseline solution for depletion for such models. More realistic multi-scale numerical models try to capture below grid scale information and pass it to the larger scale system at some numerical cost. Instead, for below block scale information, we take the semi-analytic solution to the Diffusivity Equation of Hazlett and Babu (2014 , 2018 ) for transient inflow performance of wells of arbitrary trajectory, originally developed for Neumann boundary conditions, and recast it for Dirichlet boundaries. As such, it represents the analytical solution for a matrix block with an arbitrarily complex gathering system surrounded by a constant pressure sink, we take to be the primary fracture system. Instead of using a constant rate internal boundary condition for the gathering system, we segment the well or fracture and force the internal complex fracture feature to be a constant pressure element with net zero flux. In doing so, we create a representative matrix block with any degree of infinite conductivity subscale fractures that impact the overall drainage into the surrounding fracture system. We quantify drainage from each face, capturing the anisotropic effect of internal fractures. We vary the internal fracture structure and delineate sensitivity to fracture spacing and extent of fracturing. This approach also generates the complete transient solution, enabling new well test interpretation for such systems in characterization of block size distributions or extent of below block-scale fracturing. The initial model for fully-penetrating fractures can be further generalized with the 2D distributed source model of Bao et al. (2017) for partially penetrating fractures of arbitrary inclination, as represented by floating, intersecting parallelograms embedded in the matrix block with either infinite or finite conductivity.
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Experimental Evaluation of Sealing Effect of Nano Calcium Carbonate Blocking Agent on Shale Microfracture
More LessSummaryImproving the plugging ability of drilling fluid is an effective way to solve the instability of the wellbore in complex formations. Low porosity, low permeability and micro nano scale fracture developed in shale formation. Traditional large diameter plugging materials can not effectively block micro and nano pores, and drilling fluid filtrate is easy to enter the formation, leading to instability of shaft lining. With the help of GCTS equipment, we carried out the plugging evaluation experiment of nano CaCO3 plugging agent drilling fluid to the shale cores of the long Ma Xi formation in the Sichuan Chongqing formation. It is proposed to evaluate plugging effect by using shale permeability and longitudinal and lateral wave velocity characteristics before and after plugging. The results show that under the same concentration condition, the permeability of core decreases and the acoustic velocity increases with the use of nano CaCO3 plugging agent, which is much better than the effect of base slurry plugging; In the same nano particle material, with the increasing content of the nano CaCO3 plugging agent, the permeability of shale is reduced and the acoustic velocity increases. When the content of nano CaCO3 is 3%, the sealing effect of nanoscale drilling fluid is the best. Through the experimental evaluation study, we provide basic experiment and method support for the optimization of plugging agent for preventing wellbore instability.
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Cube2Vec: Self-Supervised Representation Learning for Sub-Surface Models
Authors P. Lang, T. Adeyemi and R. Schulze-RiegertSummaryMeaningful representations of subsurface structures are essential to downstream machine learning tasks such as classification and regression. While unlabelled data are often abundant, labelling is expensive and for some use cases ill-defined. The ensuing lack of large, labelled datasets makes purely supervised training of models difficult for many tasks.
A self-supervised deep learning approach is developed which extends a representation learning method for spatially distributed data also referred to as Tile2Vec ( Jean et al., 2019 ) to three dimensions. A metric learning-based loss function uses the overlap between cubes of the subsurface as a proxy for their similarity. This reflects the notion that regions which are close to each other in physical space are on average semantically more similar than regions which are far apart from each other. A three-dimensional convolutional neural network has been trained accordingly on about 100,000 cubes extracted from reservoir simulation models. The resulting model is used to evaluate cubes for their embedding, and the distance to the embedding of other cubes is a direct measure of their similarity in a structural and grid property distribution sense.
The quality of the learned representation model is demonstrated quantitatively for labelled test datasets and empirically for two applications – visual search for similar cubes and the classification of formation sections according to their production potential.
Cube2Vec offers a way to leverage the large quantity of available unlabelled subsurface data to create powerful base models for visual analysis tasks in machine learning.
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On the Robust Value Quantification of Polymer EOR Injection Strategies for Better Decision Making
Authors M. Oguntola and R. LorentzenSummaryOver the last decades several EOR methods have emerged, and corresponding models have been developed and implemented in increasingly more complex simulation tools. In this paper we present methodology and mathematical tools for optimizing and quantifying the value of EOR strategies, such as polymer, smart water or CO2. The developed methodology is demonstrated for polymer injection on medium to highly heterogeneous synthetic reservoir models with different complexity. The purpose of the work is to improve the understanding of the actual benefit of EOR methods, and to provide methodology that quickly allows users to find optimal production strategies that maximize the net present value (NPV).
In this work, the control variables for the optimization problem are polymer concentration and water injection rates for each injecting well, and oil production rates or bottom hole pressures for the producing wells, over the exploration period. Each control variable is constrained with given production limitations. To account for the uncertainty in the reservoir model, an ensemble of geological realizations is considered, and a robust ensemble-based approximate gradient method (EnOpt) is utilized. The gradient is approximated using a sample of control vectors, drawn from a Gaussian multivariate distribution with known mean and covariance. The covariance matrix is defined so that the control variables of the same well is correlated in time. The mean is updated using a preconditioned gradient ascent method with backtracking until an optimum is found.
The presented method is tested on three different synthetic reservoirs: a 2D five-spot field pattern with grid dimension 50×50×1, a 3D field provided by Equinor (the Reek field with dimension 40×64×14), and a 3D field provided by TNO (the OLYMPUS field with dimension 118×118×16). The first two fields have three phases (water, gas, and oil) and the third field has two phases (water and oil). For each case we find the optimal well controls for polymer flooding and then compared with convectional optimized continuous water flooding. The reservoir fluid flow is simulated using the Open Porous Media (OPM) simulator. However, it is worth noting that the optimization method is independent of the reservoir simulator used. Important findings of this study are the feasible control strategies for
polymer EOR methods leading to an increased NPV, and comparison of the economic values for optimized polymer and traditional water flooding for the examples considered.
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Improved Extended Blackoil Formulation for CO2EOR Simulations
Authors T.H. Sandve, O. Sæ vareid and I. AavatsmarkSummaryA well-planned CO2EOR operation can help meet an ever-increasing need for energy and at the same time reduce the total CO2 footprint from the energy production. Good simulation studies are crucial for investment decisions where increased oil recovery is optimized and balanced with permanent CO2 storage. It is common to use a compositional simulator for CO2 injection to accurately calculate the PVT properties of the mixture of oil and CO2. Compositional simulations have significantly increased simulation time compared to blackoil simulations and thus make large simulation studies where many simulations are needed as in the representation of uncertainty and optimization unpractical. Existing extended blackoil formulations often poorly represent the PVT properties of the oil-CO2 mixtures. We therefore present an improved extended blackoil formulation with new process-dependent blackoil properties that depends on the fraction of CO2 in the cell. These properties represent the density and viscosity of the Oil - CO2 mixture more accurately and thus give results closer to the compositional simulator. A fourth component in addition to water, oil and formation gas is used to follow the injected gas. The process-dependent blackoil functions are calculated from numerical slim-tube experiments based on one-dimensional compositional EOS simulations. The same simulations also give estimates on the MMP (minimum-miscibility pressure).
The new extended blackoil model gives results that are closer to compositional simulations compared to existing blackoil formulations. We present examples based on data from the Fifth Comparative Solution Project: Evaluation of Miscible Flood Simulators as well as from CO2 injection on relevant field models.
The model has been implemented in the Flow simulator. The Flow simulator is developed as part of the open porous media (OPM) project. The Flow simulator is an openly developed and free reservoir simulator that is capable of simulating industry relevant reservoir models with similar single and parallel performance as commercial simulators.
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Well Location Optimisation by using Surface-Based Modelling and Dynamic Mesh Optimisation
Authors P. Salinas, C. Jacquemyn, C. Heaney, C. Pain and M. JacksonSummaryPredictions of production obtained by numerical simulation often depend on grid resolution as fine resolution is required to resolve key aspects of flow. Moreover, the controls on flow can depend on well location in a model. In some cases, it may be key to capture coning or cusping; in others, it might be the location of specific high permeability thief zones or low permeability flow barriers. Thus, models with a suitable grid resolution for one particular set of well locations may fail to properly capture key aspects of flow if the wells are moved. During well optimisation, it is impossible to predict a-priori which well locations will be tested in a given model. Thus, it is unlikely to know a-priori if the grid resolution is suitable for all possible locations tested during a well optimisation procedure on a single model, and the problem is even more profound if well optimisation is tested over a range of different models.
Here, we report an optimisation methodology based on Dynamic Mesh Optimisation (DMO). DMO will produce optimised meshes for a given model, set of well locations, pressure (and other key fields) distribution and timelevel. Grid-free Surface-Based Modelling (SBM) models are automatically generated in which well trajectories are introduced (also not constrained by a mesh), respected by DMO. For the optimization of the well location a Genetic Algorithm (GA) approach is used, more specifically the open-source software package DEAP. DMO ensures that all the models automatically generated and simulated in the optimisation process are modelled with an equivalent mesh resolution without user interaction, in this way, the local pressure drawdown and associated physical effects (such as coning or cusping) can be properly captured if they appear in any of the many scenarios that are studied. We demonstrate that the method has wide application in reservoir-scale models of oil and gas fields, and regional models of groundwater resources.
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Geoengineering Tool for Field Development: A Decision-Making Tool for Deviated Well Placement
Authors S. Bouquet and A. FornelSummaryThe developed geoengineering tool aims at improving the decision-making of deviated well positions to increase mature field production. It is based on statistical and visual analysis of oil field features. The main advantage of this method is its reservoir-engineer focus and that no additional flow simulations are needed unlike most of iterative optimization algorithms requiring thousands of simulations. Moreover, this methodology is not constrained by a well geometry, but proposes well placements and trajectories which are the most interesting considering the studied oil field features. For deviated wells, the drilling is not constrained by a fixed direction (horizontal or vertical), its direction is function of available resources (non-communicating oil-rich layers or disconnected oil-rich areas). In practice, this kind of wells are difficult to position manually by reservoir engineer. Here, we use information from field features and their classification to define a profitable well trajectory to maximize the oil production.
The field features are either static (e.g. anisotropy) or dynamic reservoir characteristics, e.g. mobile oil thickness, time-of-flight… To facilitate their analyses, an automatic, statistical analysis is performed on these features by unsupervised classification of the grid cells. A 3D-grid of classes indices, depending on the combination of the features, is obtained. This grid allows to identify the areas of interest for production. A specific visualization of potential field production capacities is proposed by defining and calculating geobodies. They are defined by groups of connected cells with the most interesting features. While these connections are hardly viewable in 3D, the geobody calculation allows to display the areas of interest and their compartmentalization.
The geobody with the highest quality index should be the first area-to-be-drained. The proposed trajectory will start at the cell with the highest quality index in this geobody. The quality indexes are calculated using a movering-average method. The trajectory is calculated with a Dijkstra algorithm, weighted by the quality indexes of cells and geobodies and constrained by a maximum well length.
This methodology was first applied on a synthetic case then on a real field case of North Africa, for which a standard reservoir engineer study had already been performed. The geoengineering tool results were compared to the reservoir engineering study results. This tool allowed to identify the high potential areas and proposed a well trajectory and placement with the most promising features according to the field constraints, improving the oil production while limiting the computational cost.
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Comparison Between Algebraic Multigrid and Multilevel Multiscale Methods for Reservoir Simulation
Authors H. Nilsen, A. Moncorge, K. Bao, O. Møyner, K. Lie and A. BrodtkorbSummaryMultiscale methods for solving strongly heterogenous systems in reservoirs have a long history from the early ideas used on incompressible flow to the newly released version in commercial simulation. Much effort has been put into making the MsFV method work for fully unstructured multiphase problems. The MsRSB version is a newly developed version, which tackles most of the "real" world problems. It is to our knowledge, the only multiscale method that has been released in a commercial simulator. You can alternatively see the method as a variant of smoothed aggregation or as an iterative approach to AMG with energy minimizing basis functions. This will be discussed in detail.
So far, most work on comparing MsRSB with AMG methods has been on qualitative performance measures like iteration number rather than on pure runtime on fair code implementation. We discuss the theoretical performance and show the practical performance for our implementation. Here, we compare performance of pure AMG, standard two-level MsRSB with pure AMG as coarse solver, as well as a new truly multilevel MsRSB scheme. Our implementation uses the DUNE-ISTL framework. To limit the scope of the discussion we restrict our assessment to AMG with aggregation and smoothed aggregation and the MsRSB method. These three methods are closely related and are primarily distinguished in a preconditioner setting by the coarsening factors used, and the degree of smoothing applied to the basis. We also compare with other state-of-the-art AMG implementations, but do not investigate combinations of them with the MSRB method. For the MsRSB method, we also discuss practical considerations in different parallelization regimes including domain decomposition using MPI, shared memory using OpenMP, and GPU acceleration with CUDA.
All comparisons will focus on the setting in which many similar systems should be solved, e.g. during a large-scale, multiphase flow simulation. That is, our emphasis is on the performance of updating a preconditioner and on the apply time for the preconditioner relative to the convergence rate. Performance of the solvers will be tested for pure parabolic/elliptic problems that either arise as part of a sequential splitting procedure or as a pseudo-elliptic preconditioner/solver as a part of a CPR preconditioner for a multiphase system, for which block ILU0 is used as the outer smoother.
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Modeling of Water-Induced Fracture Growth Pressure Using Poroelastic Approach
Authors P. Kabanova and E. ShelSummaryOne of the main factors affecting the efficiency of hydrocarbon production during the field development is waterflooding pattern used for the formation pressure maintenance. It is common practice when production wells that have been worked for depletion are converted to the injection. However, since hydraulic fracturing was previously performed on the majority of production wells, the injection under high pressure can cause risks associated with spontaneous fracture growth. This can lead to the water breakthrough and decreasing of production efficiency. The purpose of this work is modeling of fracture growth pressure on the injection well using poroelasticity approach.
Thus, a physico-mathematical model of the problem for determining the pressure at which the fracture will grow on the injection well is built. Solving a problem involves sequential finding of the pressure field in a development element using Laplace equation, and then the stress field using an equilibrium equation. The solutions were obtained by usage of analytical and numerical approaches including Fourier transform and finite-difference scheme. Verification of the obtained solution was carried out by validating the model on a finite element solution. The criterion of fracture growth was also derived, according to which the fracture propagation occurs when the minimum horizontal stress at the tip of the fracture is exceeded.
The influence of the parameters of the reservoir and the development on the value of the critical pressure was evaluated, namely, it was shown that an increase of Biot coefficient leads to an increase of fracture growth pressure and an increase of Poisson’s ratio decreases the critical pressure.
It was found that an increase of the distance between the wells in the line leads to the decrease of the pressure at which water-induced fracture starts to grow, while an increase in the distance in a row along the vertical increases this pressure.
It should be pointed out that the most common way to control the growth of water-induced fractures is combined hydrodynamic and geomechanical modeling, but this method is very time consuming and computationally expensive. In this connection, a quick method for estimating the fracture initiation pressure was proposed. The presented model can be used to control the growth of water-induced fracture, namely, to determine the regimes of fracture growth, to regulate the waterflood regimes (pressure and flow control), and to optimize the field development system without using combined hydrodynamic and full geomechanical modeling.
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Analysis of Low Salinity and Polymer Synergies in a Dynamic Pore-Scale Network Simulator
Authors E. David, S. McDougall and A. BoujelbenSummaryIt has been postulated that combining different EOR techniques might yield a synergistic behaviour that could result in additional oil recovery beyond that obtained from each EOR technique applied separately. This has been investigated in recent experimental work (Alagic et al., 2010; Mohammadi and Jerauld, 2012 ; Shiran and Skauge, 2013 ; Pettersen and Skauge, 2016), where both polymer and surfactant solutions have been reported to be more efficient in a low salinity environment. We have investigated a number of different injection protocols using a pore-scale dynamic simulator that combines both low salinity brine (LS) and polymer injection.
Four synergistic combinations have been considered: (i) LS brine and polymer injected simultaneously at the start of the simulation (secondary mode), (ii) LS brine and polymer injected simultaneously following high salinity (HS) water breakthrough, (iii) LS brine injected initially, followed by simultaneous LS brine/polymer injection after LS breakthrough, and (iv) LS brine injected initially followed by polymer injection after LS water breakthrough.
A positive synergy was observed when LS brine and polymer were injected simultaneously in both secondary and tertiary modes, with the combined effect yielding significant increases in oil recovery. The mixture of polymer and LS brine was found to cause capillary fingers to thicken and swell, allowing the LS brine to access more of the pore space as a consequence of the higher viscous forces induced by the polymer. In secondary mode, the mixture of polymer and LS brine was observed to stabilise the water fingers and shifted the flow regime from viscous/capillary fingering to stable displacement. Moreover, results suggest that this synergistic LS/polymer effect is sensitive to a range of rock/fluid parameters, such as wettability, viscosity ratio, and capillary number.
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Conditioning Surface-Based Geological Models to Well Data Using Neural Networks
Authors Z. Titus, C. Pain, C. Jacquemyn, P. Salinas, C. Heaney and M. JacksonSummaryGenerating representative reservoir models that accurately describe the spatial distribution of geological heterogeneities is crucial for reliable predictions of historic and future reservoir performance. Surface-based geological models (SBGMs) have been shown to better capture complex reservoir architecture than grid-based methods; however, conditioning such models to well data can be challenging because it is an ill-posed inverse problem with spatially distributed parameters.
Here, we propose the use of deep Convolutional Neural Networks (CNNs) to generate geologically plausible SBGMs that honour well data. Deep CNNs have previously demonstrated capability in learning representative features of spatially correlated data for large scale and highly non-linear geophysical systems similar to those encountered in subsurface reservoirs.
In the work reported here, a CNN is trained to learn the relationship between parameterised inputs to SBGM, the resulting geometry and heterogeneity distribution, and the mis-match between model surfaces and well data. We show that the trained CNN can generate a range of geologically plausible models that honour well data. The method is demonstrated for a 2D example model, representing a shallow marine reservoir and a 3D extension of the model that captures typical heterogeneities encountered in the subsurface such as parasequences, clinoforms and facies boundaries. These test cases highlight the improvement in reservoir characterisation for realistic geological cases.
We present here a method of generating geologically consistent reservoir models that match well data. The developed method will allow the generation of new high-fidelity realizations of subsurface geology conditioned to information at wells, which is the most direct observational data that can be acquired.
Technical Contributions
- – The use of surface-based modelling to describe even complex geological features compared to grid-based modelling significantly decreases the computational expense of training the network as there are fewer parameters to optimize.
- – Conditioning geological models to well data is a challenging ill-posed inverse problem in reservoir characterisation. The use of neural networks presents another approach for generating geologically plausible models that are calibrated with observed well data and can be extended to object-based modelling.
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Modified Peaceman Correction for Improved Calculation of Polymer Injectivity in Coarse Grid Numerical Simulations
Authors I. Tai, A. Muggeridge and M.A. GiddinsSummaryAn improved method for calculating the injectivity of non-Newtonian polymers in finite volume, numerical simulation is presented. Non-Newtonian rheologies can significantly impact the performance of a polymer flood. This is especially important in the near wellbore region and at the start of injection. In the near well bore region velocities and shear rates are at a maximum and change rapidly with distance from the well. These effects are expected to be highest at the beginning of a polymer flood due to the near-wellbore region being saturated with more viscous oil.
An analytical method for calculating the modified Peaceman pressure equivalent radius when the well block contains only polymer solution is derived and then extended to the case when the well block contains both oil and polymer solution (as occurs at early time). This is done using fractional flow theory to derive well pseudo relative permeability functions. The approach is validated by comparing the results from fine grid radial and coarse grid Cartesian simulation models. The importance of the correction is demonstrated by simulating polymer injection into a realistic field scale model of a viscous oil field.
The modified Peaceman radius, combined with well pseudo relative permeabilities, significantly reduces the error when calculating the bottomhole flowing pressure in wells injecting a shear-thinning polymer solution. In the field scale simulation, with injection pressure constrained by the fracture pressure of the rock, our results show that polymer injection can be a viable technique for enhanced oil recovery in this reservoir. The new method leads to higher well injectivity and more optimistic prediction of polymer flood performance, compared to the standard Peaceman calculation used by most reservoir simulators, where non-Newtonian behaviour in the well block is unaccounted for.
This paper provides a simple and accurate method to capture the impact of shear thinning behaviour on polymer injectivity. The method will improve estimations of injectivity in reservoir simulations of shear thinning polymer solutions.
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