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Numerical reservoir simulation often requires upscaling of fine-scale detailed models and coarse-scale models are necessary to reduce computational time for dynamic evaluations. However, these simplifications may degenerate results due to loss of resolution of the small-scale phenomena, averaging of sub-grid heterogeneity and numerical dispersion, especially in oil fields where miscible gas is injected.
Most of the existing upscaling techniques focus on reproducing the results of a specific geological realization, in a deterministic approach. Nowadays, however, reservoir simulation studies commonly include uncertainty quantifications, which is performed by simulating multiple geological realizations. For that, the use of fine-scale models can be computationally prohibitive and this requires a proper procedure to upscale the coarse-scale simulation models in multiple realizations environment.
In this work, we propose and test an ensemble-level upscaling technique for compositional systems with miscible gas injection. The new approach considers the classical Koval factor, calculated for the fine-scale models, as a guide for selecting representative fine-scale models to train pseudo-functions for the coarse-models. Only a few fine models are simulated (about 1%), and the uncertainty quantification process with coarse-scale models can be significantly improved.
The proposed workflow is guided by ranking the fine-scale models in increasing order of their Koval Factor. We selected representative models and applied a two-step methodology to improve upscaled coarse-scale results for these models. We then propose a consistent procedure to expand the fitted pseudo-functions to all the coarse models, providing an effective ensemble-level upscaling.
The correlation between Koval factor and oil recovery is a useful guide to extrapolate the pseudo-functions obtained for each selected representative model, enabling better coarse-scale simulation results when multiple realizations are considered. This procedure can be applied for continuous miscible gas injection and can be adapted for WAG scheme.
This work was motivated by the lack of practical procedures to improve coarse-scale results at the ensemble-level. With our approach, we can better represent uncertainty quantification using coarse-scale models with reduced computational cost and requiring only a few fine-scale simulation runs.
Foam increases sweep efficiency during gas injection in enhanced oil recovery processes. Surfactant alternating gas (SAG) is the preferred method to inject foam for both operational and injectivity reasons. Dynamic SAG corefloods are unreliable for direct scaleup to the field because of core-scale artifacts. In this study, we report fit and scaleup local-equilibrium (LE) data at very-low injected-liquid fractions in a Bentheimer core for different surfactant concentrations and total superficial velocities.
We fit LE data to an implicit-texture foam model for scaleup to a dynamic foam process on the field scale using fractional-flow theory. We apply different parameter-fitting methods (least-squares fit to entire foam-quality scan and the method of Rossen and Boeije 2015) and compare their fits to data and predictions for scaleup. We also test the implications of complete foam collapse at irreducible water saturation for injectivity.
Each set of data predicts a shock front with sufficient mobility control at the leading edge of the foam bank. Mobility control improves with increasing surfactant concentration. In every case, scaleup injectivity is much better than with coinjection of gas and liquid. The results also illustrate how the foam model without the constraint of foam collapse at irreducible water saturation (Namdar Zanganeh et al. 2014) can greatly underestimate injectivity for strong foams.
For the first time, we examine how the method of fitting the parameters to coreflood data affects the resulting scaleup to field behavior. The method of Rossen and Boeije (2015) does not give a unique parameter fit, but the predicted mobility at the foam front is roughly the same in all cases. However, predicted injectivity does vary somewhat among the parameter fits. Gas injection in a SAG process depends especially on behavior at low injected-water fraction and whether foam collapses at the irreducible water saturation, which may not be apparent from a conventional scan of foam mobility as a function of gas fraction in the injected foam. In two of the five cases examined, this method of fitting the whole scan gives a poor fit for the shock in gas injection in SAG. We also test the sensitivity of the scaleup to the relative permeability krw(Sw) function assumed in the fit to data.
There are many issues involved in scaleup of laboratory data to field performance: reservoir heterogeneity, gravity, interactions between foam and oil, and so on. This study addresses the best way to fit model parameters without oil for a given permeability, an essential first step in scaleup before considering these additional complications.
We present a robust and flexible sequential solution approach in which the flow equation is solved on the original grid, whereas the transport equations are solved with a new dynamic coarsening method that adapts the grid resolution locally to reduce the number of cells as much as possible. The resulting grid is formed by combining precomputed coarse partitions of an underlying fine model. Our approach is flexible and makes very few assumptions on cell geometries and the topology of the grid. To further accelerate the transport step, we combine dynamic coarsening with a local nonlinear solver that permutes the discrete transport equations into an optimal block-triangular form so that these can be solved very efficiently using a nonlinear back-substitution method. Efficiency and utility of the overall approach are assessed through a number of conceptual test cases, including the Olympus field model.
Field-scale representation of highly heterogeneous reservoirs remains a challenge in numerical reservoir simulation. In such reservoirs, detailed geological models are important to properly represent key heterogeneities. However, high computational costs and long simulation run times make these detailed models unfeasible to use in dynamic evaluations. Therefore, the scaling up of geological models is a key step in reservoir-engineering studies to reduce computational time. Scaling up must be carefully performed to maintain integrity; both truncation errors and the smoothing of subgrid heterogeneities can cause significant errors.
This work evaluates the latter—the effect of averaging small-scale heterogeneities in the upscaling process—and proposes a new upscaling technique to overcome the associated limitations. The technique is dependent on splitting the porous media into two levels guided by flow- and storage-capacity analysis and the Lorenz coefficient (LC), both calculated with static properties (permeability and porosity) from a fine-scale reference model. This technique allows the adaptation of a fine highly heterogeneous geological model to a coarse-scale simulation model in a dual-porosity/dual-permeability (DP/DP) approach and represents the main reservoir heterogeneities and possible preferential paths.
The new upscaling technique is applied to different reservoir-simulation models with water injection and immiscible gas injection as recovery methods. In deterministic and probabilistic studies, we show that the resulting coarse-scale dual-permeability models are more accurate and can better reproduce the fine-scale results in different upscaling ratios (URs), without using any simulation results of the reference fine-scale simulation models, as some of the current alternative upscaling methods do.
Rocks are usually not homogeneous, but are made up of multiple components such as mineral grains and pore space. On a larger scale, the bulk properties of rocks will be some weighted combination of the small-scale components. This averaging or upscaling step is needed if we wish to understand the behavior of our laboratory data or extract useful parameters from field data such as logs or seismic measurements. Understanding the boundary constraints is an important factor in this process. The simplest bounds are provided by the constant strain and constant stress limits.
Traditional upscaling methods are dependent on steady-state (SS) concepts of flow, whereas flow simulation itself is used for the calculation of pressure and saturation transients, which can be considered as a sequence of pseudosteady-state (PSS) solutions. In high-contrast or low-permeability systems, neither the SS nor the PSS limits need to be reached within each coarse-cell volume during a simulation timestep, introducing a potentially significant bias into an upscaling or downscaling calculation. We use an asymptotic pressure analysis for transient flow, dependent on the diffusive time of flight, to improve the resolution of these dynamic effects.
We introduce a novel upscaling approach with two major differences from SS upscaling. First, we transition from SS- to PSS-flow solutions. This has been shown to provide identical results to SS upscaling in one dimension, but to have improved localization for upscaling in two and three dimensions. Specifically, there is no longer an explicit dependence upon global pressure boundary conditions. Development of this PSS upscaling approach has also required the introduction of a new transmissibility-weighted pressure-averaging definition instead of the pore-volume (PV) -weighted pressure average used for SS flow. The second difference is in using pressure-transient concepts to identify well-connected subvolumes within a coarse-cell volume. The local source/sink terms during the transient are no longer solely proportional to porosity, as in the PSS limit. Instead, these terms now include a spatial dependence obtained from the asymptotic transient pressure approximation. This dependence is especially important for high-contrast or low-permeability systems. The methodology we have developed is an application of the concepts of the diffusive time of flight and transient drainage volume to obtain source functions that capture both the early- and late-time limits of the transient-flow patterns. Diffuse-source (DS) functions are introduced within each fine cell of a coarse-cell pair, consistent with the transients and with a specified total flux between the coarse cells. The ratio of this flux to the averaged pressure drop is used to obtain the effective transmissibility between the cell pair.
The application of pressure-transient concepts has allowed us to develop completely local upscaling and downscaling calculations. A characteristic time is determined for which a well-connected subvolume for each coarse-cell pair is sufficiently close to PSS. This enables us to distinguish between well-connected and weakly connected pay while upscaling. Unlike SS upscaling calculations, which explicitly impose flow on the boundaries of an upscaling region and implicitly couple the local problem to a global flow field, these calculations are completely local. The methodology is tested on SPE10 (Christie and Blunt 2001) with permeability variations over eight orders of magnitude, making it a high-contrast example. We also test the method on a low-net/gross onshore tight gas reservoir consisting of thin fluvial channels undergoing primary depletion. The comparisons of performance prediction with fine-scale numerical simulation and SS upscaling demonstrate the accuracy of the proposed approach.
NOTE: Supplement available in Supporting Information section.
Direct numerical simulation at the pore scale on three-dimensional (3D) digital volumes obtained by highresolution x-ray computed tomography (CT) images is a powerful tool for helping predict petrophysical properties. However, obtaining sufficiently high resolution and large field-of-view 3D CT images that capture multiscale heterogeneities in a single image is often not possible. Thus, methods for integrating and upscaling properties from multiple scales at various resolutions to plug scale are necessary. The methodology and results for upscaling capillary-dominated, two-phase flow in rocks based on multiscale CT images using trends are presented and discussed in this paper.
He, Xupeng (King Abdullah University of Science and Technology) | Santoso, Ryan (King Abdullah University of Science and Technology) | Hoteit, Hussein (King Abdullah University of Science and Technology)
Modeling fluid flow in fractured media is of importance in many disciplines, including subsurface water management and petroleum reservoir engineering. Detailed geological characterization of a fractured reservoir is commonly described by a discrete-fracture model (DFM), in which the fractures and rock-matrix are explicitly represented by unstructured grid elements. Traditional static-based and flow-based upscaling methods used to generate equivalent-continuum models from DFM suffer from low accuracy and high computational cost, respectively. This work introduces a new deep-learning technique based on neural networks to accelerate upscaling of discrete-fracture models.
The objective of this work is to automate the process of permeability upscaling from detailed discrete-fracture characterizations. We build an "image-to-value" model to map the nonlinear relationship between high-resolution DFM images, provided as input, and the equivalent-continuum model (output), which comprises the predicted equivalent permeability of each grid-block. The proposed upscaling workflow incorporates the generation of the training datasets, design of the neural network architecture, and the validation process. The implemented deep neural networks consist of 20 layers including 18 hidden layers. Good quality input data and suitable network structure are crucial to obtaining a successful trained model. Therefore, high-resolution simulations were used to generate the training set. A training-validating process is conducted to update of training data and to optimize the network architecture until the trained model reaches an accuracy exceeding 95%.
We first verify the deep learning-based (DL-based) approach by applying it to a set of single rotating fractures with known analytical solutions. We then demonstrate it on a synthetic DFM including connected and disconnected fractures, and on a DFM from an actual outcrop. We compare the method performance to reference fully-resolved solutions and to an advanced flow-based upscaling method, referred to as a multi-boundary fracture upscaling method. In the tested cases, simulation results show that the DL-based method is computational more efficiency than the flow-based method by two orders of magnitude without significant loss of accuracy.
This work demonstrates the potential of a physics-based DL approach for the upscaling of high-resolution images of fractured media. The proposed DL approach is more accurate than the static-based upscaling methods and more efficient than the flow-based upscaling methods, and therefore, has the potential to be used to improve the computational performance of CPU-intensive upscaling methods.
The PDF file of this paper is in Russian.
Coarsening of computational spatial grids is one of the main ways to reduce the cost of computing resources in geological and hydrodynamic modeling of hydrocarbon reservoirs. The procedure of overriding reservoir properties in an upsized cell of the computational grid is called upscaling (averaging). The quality of this procedure is determined by degree of prognostic capability decreasing of applied models. The traditional way for determining the average value as the arithmetic mean is not always applicable in practice, since it does not take into account the spatial heterogeneity of the averaged values distribution. In this paper, we consider the case of a reservoir with formation reservoir properties (permeability and porosity) values close to power functions of the spatial variable. Proximity of reservoir properties to power function indicates to a fractal inhomogeneity of the porous medium. The power-law upscaling procedure is proposed for this case. An initial-boundary-value problem for a one-dimensional fractal model of unsteady-state filtration is considered. The identification procedure of fractal quantities of this model is proposed and investigated. The proposed methods tested on data from one of the fields in Western Siberia. A comparative analysis with the arithmetic mean method is performed on permeability data. The proposed techniques have a potential for use in reservoir engineering and monitoring.
Укрупнение расчетных сеток по пространственным переменным является одним из основных способов снижения затрат на вычислительные ресурсы при геолого-гидродинамическом моделировании месторождений углеводородов. Процедура переопределения коллекторских свойств в укрупненной ячейке расчетной сетки называется апскейлингом. Качество этой процедуры определяется степенью снижения прогнозных способностей используемых моделей. Традиционно используемый метод определения среднего значения как среднего арифметического не всегда применим на практике, так как не учитывает пространственной неоднородности распределения усредняемых величин. В статье рассмотрен пласт, фильтрационно-емкостные параметры (пористость и проницаемость) которого, близкими к значениям степенных функций в зависимости от пространственной координаты, что соответствует фрактальной неоднородности пористой среды. Для данного случая предложена процедура апскейлинга, которая учитывает степенной закон изменения пористости и проницаемости в пространстве. Рассмотрена начально-краевая задача для одномерной модели нестационарной фильтрации в условиях фильтрационно-емкостных свойств (ФЕС), соответствующих среде с фрактальными свойствами. Предложена и исследована процедура идентификации величин, учитывающих фрактальную неоднородность среды, из условия минимума меры близости решения этой задачи к решению задачи с фактическими ФЕС. Апробация предложенной методики проведена на промысловых данных одного из месторождений Западной Сибири. Выполнено сравнение с результатами, полученными при использовании стандартного метода определения проницаемости как среднего арифметического в усредняемой области. Показано, что предложенная методика позволяет повысить качество геолого-гидродинамического моделирования за счет учета фрактальной неоднородности пласта, что имеет большой потенциал применения при проектировании и мониторинге разработки месторождений.
Bio-mediated soil improvements phenomena have been observed though various experimental tests and investigations that the shear strength of microbial-mediated soils can be improved using the process of bio-chemical cementation. In the modern geotechnical community, this phenomenon is expected to become the focus of innovative technologies for use in next-generation soil improvement technologies. Also, the bio-chemical cementation is also observed in a natural environment. Thus, the microbially induced cementation in geo-materials is of interest from an engineering viewpoint because there is a possibility that this is applied artificially to natural environments. In contrast, predicting technique for microbially induced structural evolution of inner soil is still to be investigated in practice because we may not be able to change certain parameters easily with respect to the microbial activity. In this work, the authors attempt to bring a new perspective to the field of bio-mediated soil improvement technology, drawing on mathematical modelling and simulation techniques in order to understand the mechanism of microstructural formation and predict the future state of the soil. The mathematical model in microscale space is formulated by reaction-diffusion system where the metabolic reactions of microorganism are considered. Whereas, the mechanical behavior in macroscale space is calculated by a homogenization technique.
Over the last century, various numerical and experimental methodologies for soil improvement have been investigated (DeJong, et al., 2006). In these investigations the soil improvement technologies have been developed experimentally and empirically from several viewpoints such as geotechnical engineering, geomechanics, chemodynamics, and microbiology (Alvarez and Steinbach, 2009). In particular, the microbiological viewpoint has attracted attention, and microorganisms have been used in soil improvement technique (Whiffin, et al., 2007). This approach has been considered to be friendly more than traditional engineering technique in natural environments because some microorganisms in a natural environment can be used for soil improvement (DeJong, et al., 2006).