Day 3 Wed, June 07, 2023最新文献

{"title":"AI Grid Design for Fast Reservoir Simulation","authors":"L. Nghiem, C. Dang, N. Nguyen, Chaodong Yang, Jia Luo","doi":"10.2118/214354-ms","DOIUrl":"https://doi.org/10.2118/214354-ms","url":null,"abstract":"\u0000 Reservoir simulators based on physics provide the most accurate method for predicting oil and gas recovery, in particular from waterflood and EOR processes. However, detailed full-field simulation can be computationally demanding. In recent years, there have been attempts in accelerating reservoir simulation by combining simplification of the gridding requirement with data-driven approaches while maintaining the full physics. One such approach is the physics-based data-driven flow network model where 1D or 2D grids connecting the wells are configured and simulated. The parameters of the flow network model are then tuned to match full 3D simulation or field-data. Even though the grid has been simplified, a large number of parameters are needed to reproduce the 3D simulation results.\u0000 In this paper, an approach similar to the flow network model is presented. The main contribution of this paper is the parameterization of the gridding process between the wells such that a minimal number of parameters are needed. Essentially, the grids between the wells are configured to model accurately the flow behavior. The corner-point grid geometry is kept so that current simulators could be used with the proposed method. In this paper, the grid geometry is determined with AI methods for one waterflood run. The grid could be used subsequently for waterflood with widely different injection/production scenarios and even for chemical flood. The ability of the approach to derive the grid from a single waterflood run is another significant contribution of this paper.","PeriodicalId":388039,"journal":{"name":"Day 3 Wed, June 07, 2023","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130086593","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Numerical Investigation of Subsurface Hydrogen Storage: Impact of Cyclic Injection","authors":"H. Zhang, M. Al Kobaisi, M. Arif","doi":"10.2118/214396-ms","DOIUrl":"https://doi.org/10.2118/214396-ms","url":null,"abstract":"\u0000 The use of hydrogen (H2) as a clean fuel has gained enormous interest in recent years. For this purpose, excess H2 can be stored in subsurface geological formations. The underground hydrogen storage (UHS) can help to mitigate the challenges associated with seasonal variability in renewable energy production and provide a reliable source of hydrogen for future utilization. While recent studies showed that repeated hydrogen injection and production in aquifer can result in hydrogen and water cyclic hysteresis, the existing classical trapping models fail to model such phenomena in the context of hydrogen and brine. Moreover, the impact of cyclic hysteretic behavior effect received little or no attention on the reservoir scale and thus still remains poorly understood. This study conducts numerical simulations to analyze the impact of cyclic hysteresis on the efficiency of underground hydrogen storage. The results showed that the cyclic hysteresis effect will result in a shorter lateral migration of the injected H2 and more H2 accumulating in the vicinity of the wellbore due to the poorer hydrogen flow ability and higher critical hydrogen saturation. The accumulated hydrogen will in turn contribute to a higher hydrogen recovery factor and thus improve the efficiency of underground hydrogen storage.","PeriodicalId":388039,"journal":{"name":"Day 3 Wed, June 07, 2023","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129003832","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Massive Geomodel Compression and Rapid Geomodel Generation Using Advanced Autoencoders and Autoregressive Neural Networks","authors":"S. Misra, Jungang Chen, Y. Falola, Polina Churilova, Chung-Kan Huang, Jose F. Delgado","doi":"10.2118/214442-ms","DOIUrl":"https://doi.org/10.2118/214442-ms","url":null,"abstract":"\u0000 The reduction of computational cost when using large geomodels requires low-dimensional representations (transformation or reparameterization) of large geomodels, which need to be computed using fast and robust dimensionality reduction methods. Additionally, to reduce the uncertainty associated with geomodel-based predictions, the probability distribution/density of the subsurface reservoir needs to be accurately estimated as an explicit, intractable quantity for purposes of rapidly generating all possible variability and heterogeneity of the subsurface reservoir. In this paper, we developed and deployed advanced autoencoder-based deep-neural-network architectures for extracting the extremely low-dimensional representations of field geomodels. To that end, the compression and reconstruction efficiencies of vector-quantized variational autoencoders (VQ-VAE) were tested, compared and benchmarked on the task of multi-attribute geomodel compression. Following that, a deep-learning generative model inspired by pixel recurrent network, referred as PixelSNAIL Autoregression, learns not only to estimate the probability density distribution of the low-dimensional representations of large geomodels, but also to make up new latent space samples from the learned prior distributions. To better preserve and reproduce fluvial channels of geomodels, perceptual loss is introduced into the VQ-VAE model as the loss function.\u0000 The best performing VQ-VAE achieved an excellent reconstruction from the low-dimensional representations, which exhibited structural similarity index measure (SSIM) of 0.87 at a compression ratio of 155. A hierarchical VQ-VAE model achieved extremely high compression ratio of 667 with SSIM of 0.92, which was further extended to a compression ratio of 1250 with SSIM of 0.85. Finally, using the PixelSNAIL based autoregressive recurrent neural network, we were able to rapidly generate thousands of large-scale geomodel realizations to quantify geological uncertainties to help further decision making. Meanwhile, unconditional generation demonstrated very high data augmentation capability to produce new coherent and realistic geomodels with given training dataset.","PeriodicalId":388039,"journal":{"name":"Day 3 Wed, June 07, 2023","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124400610","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Life-Cycle Production Optimization with Nonlinear Constraints Using a Least-Squares Support-Vector Regression Proxy","authors":"A. Almasov, M. Onur","doi":"10.2118/214445-ms","DOIUrl":"https://doi.org/10.2118/214445-ms","url":null,"abstract":"\u0000 In this work, we develop computationally efficient methods for deterministic production optimization under nonlinear constraints using a kernel-based machine learning method where the cost function is the net present value (NPV). We use the least-squares support-vector regression (LSSVR) to maximize the NPV function. To achieve computational efficiency, we generate a set of output values of the NPV and nonlinear constraint functions, which are field liquid production rate (FLPR) and water production rate (FWPR) in this study, by running the high-fidelity simulator for a broad set of input design variables (well controls) and then using the collection of input/output data to train LS-SVR proxy models to replace the high-fidelity simulator to compute NPV and nonlinear constraint functions during iterations of sequential quadratic programming (SQP). To obtain improved (higher) estimated optimal NPV values, we use the existing so-called iterative sampling refinement (ISR) method to update the LSSVR proxy so that the updated proxy remains predictive toward promising regions of search space during the optimization. Direct and indirect ways of constructing LSSVR-based NPVs as well as different combinations of input data, including nonlinear state constraints and/or the bottomhole pressures (BHPs) and water injection rates, are tested as feature space. The results obtained from our proposed LS-SVR-based optimization methods are compared with those obtained from our in-house StoSAG-based line-search SQP programming (LS-SQP-StoSAG) algorithm using directly a high-fidelity simulator to compute the gradients with StoSAG for the Brugge reservoir model. The results show that nonlinear constrained optimization with the LSSVR ISR with SQP is computationally an order of magnitude more efficient than LS-SQP-StoSAG. In addition, the results show that constructing NPV indirectly using the field liquid and water rates for a waterflooding problem where inputs come from LSSVR proxies of the nonlinear state constraints requires significantly fewer training samples than the method constructing NPV directly from the NPVs computed from a high-fidelity simulator. To the best of our knowledge, this is the first study that shows the means of efficient use of a kernel-based machine learning method based on the predictor information alone to perform efficiently life-cycle production optimization with nonlinear state constraints.","PeriodicalId":388039,"journal":{"name":"Day 3 Wed, June 07, 2023","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114404569","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bi-Objective Optimization of Subsurface CO2 Storage with Nonlinear Constraints Using Sequential Quadratic Programming with Stochastic Gradients","authors":"Q. Nguyen, M. Onur, F. Alpak","doi":"10.2118/214363-ms","DOIUrl":"https://doi.org/10.2118/214363-ms","url":null,"abstract":"\u0000 \u0000 \u0000 This study focuses on carbon capture, utilization, and sequestration (CCUS) via the means of nonlinearly constrained production optimization workflow for a CO2-EOR process, in which both the net present value (NPV) and the net present carbon tax credits (NPCTC) are bi-objectively maximized, with the emphasis on the consideration of injection bottomhole pressure (IBHP) constraints on the injectors, in addition to field liquid production rate (FLPR) and field water production rate (FLWR), to ensure the integrity of the formation and to prevent any potential damage during life-cycle injection/production process. The main optimization framework used in this work is a lexicographic method based on line-search sequential quadratic programming (LS-SQP) coupled with stochastic simplex approximate gradients (StoSAG). We demonstrate the performance of the optimization algorithm and results in a field-scale realistic problem, simulated using a commercial compositional reservoir simulator. Results show that the workflow is capable of solving the single-objective and bi-objective optimization problems computationally efficiently and effectively, especially in handling and honoring nonlinear state constraints imposed onto the problem. Various numerical settings have been experimented with to estimate the Pareto front for the bi-objective optimization problem, showing the trade-off between the two objectives NPV and NPCTC. We also perform a single-objective optimization on the total life-cycle cash flow, which is the aggregated quantity of NPV and NPCTC, and quantify the results to further emphasize the necessity of performing bi-objective production optimization, especially when utilized in conjunction with commercial flow simulators that lack the capability of computing adjoint-based gradients.\u0000","PeriodicalId":388039,"journal":{"name":"Day 3 Wed, June 07, 2023","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124667623","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Comparative Analysis of Convolutional Neural Networks for Seismic Noise Attenuation","authors":"Mrigya Fogat, Samiran Roy, Viviane Ferreira, Satyan Singh","doi":"10.2118/214392-ms","DOIUrl":"https://doi.org/10.2118/214392-ms","url":null,"abstract":"\u0000 Seismic data is an essential source of information often contaminated with disturbing, coherent and random noise. Seismic random noise has degenerative impacts on subsequent seismic processing and data interpretation. Thus, seismic noise attenuation is a key step in seismic processing. Convolutional Neural Networks (CNNs) have proven successful for various image processing tasks in multidisciplinary fields and this paper aims to study the impact of three CNN architectures (autoencoders, denoising CNNs (DnCNN) and residual dense networks (RDN)) on improving the signal to noise ratio of seismic data. The work consists of three steps: Data preparation, model training and model testing. In this study we have used real seismic data to prepare the training dataset we have manually added noise. Most studies on seismic noise attenuation, study only a single kind of noise. However this paper suggests making our approach by exposing the model to many kinds of noises and noise levels such as Guassian noise, Poisson noise, Salt and Pepper and Speckle noise. In this paper we have analysed the performance of three models. Autoencoders: This architecture consists of two parts, the encoders and the decoders. The encoder consists of convolutions on the input image to extract all key information and map it to a latent space with loss of unnecessary data(noise) while the decoder reconstructs the image from the latent space to a seismic image while high signal to noise ratio. DnCNNs: This architecture is a combination of residual learning and batch normalization and mainly consists of three kinds of blocks. The model is trained to predict the residual image, that is the difference between the noisy observation and the latent clean image. RDNs: This architecture comprises of shallow feature extraction net, residual dense blocks (RDBs), dense feature fusion, and lastly up-sampling net. The data prepared as mentioned above is trained on all three CNN models across different noise levels and the performance of these models was compared.\u0000 The model is finally tested on a batch of unseen noisy seismic sections and the performance is measured by an l2 loss namely mean squared error and the improvement in signal to noise ratio.\u0000 The resultant images from all three architectures across different noise levels have drastically improved signal to noise ratio and thus the application of CNN as a denoiser for seismic images proves to be successful. It is important to note that when comparing the difference plots(Noisy image minus the denoised image) we found minimal signal leakage. While the application of CNN for image pre-processing has seen great success in other fields, mathematical denoising techniques such as F-K filter, tao-p filter are still used in oil and gas industry particularly in seismic denoising. After thorough review, this paper studies some of the most successful denoising CNN architectures and its success in seismic denoising.","PeriodicalId":388039,"journal":{"name":"Day 3 Wed, June 07, 2023","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122095514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Improved Hydraulic Fracture Characterization Using Representation Learning","authors":"Aditya Chakravarty, S. Misra","doi":"10.2118/214360-ms","DOIUrl":"https://doi.org/10.2118/214360-ms","url":null,"abstract":"\u0000 Representation learning is a technique for transforming high-dimensional data into lower-dimensional representations that capture meaningful patterns or structures in the data. Uniform manifold approximation and projection (UMAP) enables representation learning that uses a combination of nearest neighbor search and stochastic gradient descent in the low-dimensional graph-based representation to preserve local structure and global distances present in high-dimensional data.\u0000 We introduce a new technique in representation learning, where high-dimensional data is transformed into a lower-dimensional, graph-based representation using UMAP. Our method, which combines nearest neighbor search and stochastic gradient descent, effectively captures meaningful patterns and structures in the data, preserving local and global distances. In this paper, we demonstrate our expertise by utilizing unsupervised representation learning on accelerometer and hydrophone signals recorded during a fracture propagation experiment at the Sanford Underground Research Facility in South Dakota.\u0000 Our UMAP-based representation executes a five-step process, including distance formulation, connection probability calculation, and low-dimensional projection using force-directed optimization. Our analysis shows that the short-time Fourier Transform of signals recorded by a single channel of the 3D accelerometer is the best feature extraction technique for representation learning. For the first time, we have successfully identified the distinct fracture planes corresponding to each micro-earthquake location using accelerometer and hydrophone data from an intermediate-scale hydraulic stimulation experiment. Our results from the EGS Collab project show the accuracy of this method in identifying fracture planes and hypocenter locations using signals from both accelerometers and hydrophones. Our findings demonstrate the superiority of UMAP as a powerful tool for understanding the underlying structure of seismic signals in hydraulic fracturing.","PeriodicalId":388039,"journal":{"name":"Day 3 Wed, June 07, 2023","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120949086","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An Intrusive Hybrid-Analytics and Modelling with Deep-Learning for Efficient and Accurate Predictions of Hole-Cleaning Process during Wellbore Drilling Simulations","authors":"Mandar V. Tabib, P. Nivlet, Knut Steinar, J. O. Skogestad, Roar Nybø, A. Rasheed","doi":"10.2118/214369-ms","DOIUrl":"https://doi.org/10.2118/214369-ms","url":null,"abstract":"\u0000 The paper aims at demonstrating a novel intrusive hybrid-analytics and modelling (HAM) that combines physics-based model and machine learning (ML) for predicting key variables in the monitoring of hole cleaning during drilling, and more specifically monitoring pressure/Equivalent Circulating Density (ECD) and cuttings volume fraction.\u0000 Currently, for predicting the spatial-temporal evolution of circulating mud in real-time in the annulus during drilling and potentially anticipating hole cleaning issues, a low-resolution physics-based 1D model is utilized that solves multi-phase flow equations. This model is computationally efficient but susceptible to discrepancies with actual observations. These errors could be a result of numerical issues, unmodelled physics in the model, or inaccurate input to the model. Here, machine learning is used to learn the pattern in residuals between the low-resolution model and a higher fidelity calculation, as well as measurements. The results show that the inclusion of machine learning models for correcting the low-fidelity cutting transport model has helped to improve the accuracy of low-fidelity model in predicting pressure and cutting volume fractions : which are key variables for monitoring hole cleaning. The machine learning models (ANN and LSTM models) have shown good performance in learning and correcting various errors associated with the 1D model, like (a) the numerical errors, (i.e. the error resulting from coarser and finer time-scales for the cuttings volume fraction along the well), and (b) the error due to physics (i.e. the difference in predictions between hi-fidelity model and low-fidelity model for pressure), and (c) the error between measurements and predictions of low-fidelity model. The conclusion of the work is that the intrusive HAM approach combining deep-learning with physics-based approach has the potential to provide a robust and efficient replacement of unknown parts of complex physics in mathematical models for drilling. Future work may involve using this HAM-in-drilling approach in conjunction with an anomaly detection algorithm to enable real-time decision when an anomaly occurs.","PeriodicalId":388039,"journal":{"name":"Day 3 Wed, June 07, 2023","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115339773","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Well Performance Metrics Suitable for Automated Monitoring","authors":"A. Shchipanov, G. Namazova, K. Muradov","doi":"10.2118/214425-ms","DOIUrl":"https://doi.org/10.2118/214425-ms","url":null,"abstract":"\u0000 Automated well operations is a rapidly growing area with recent progress in automated drilling extending now into automated well monitoring and control during production operations. In reservoir engineering, although the industry continues to guide decision making processes mainly based on physics-based models and simulations, the focus of further developments of the industrial workflows has shifted towards hybrid solutions incorporating machine learning and big data analytics. Development of such solutions requires new approaches to integrate the reservoir physics into the workflows suitable for machine learning and big data analytics.\u0000 In this paper, we apply and test new metrics for permanent well monitoring developed based on time-lapse pressure transient analysis, called PTA-metrics. These metrics, inheriting reservoir mechanics gained from PTA, remain comparatively simple and suitable for automated workflows. The metrics have been tested on real well data from sandstone and carbonate fields, including slanted injection and horizontal production and injection wells. The testing has confirmed its capabilities in well monitoring separating reservoir from well-reservoir connection contributions to well performance. Application of the metrics enables on-the-fly well monitoring and alarming on well performance issues highlighting the issue origin: either a reservoir or a well-reservoir connection. At the same time, the testing also revealed that reliable application of the metrics depends on the patterns developed by time-lapse pressure transient responses and their Bourdet derivatives. It was shown that the PTA-metrics give reliable results for stable patterns, while change in the pattern may reduce their reliability. The paper concludes with a discussion of ways for application of the metrics in every-day well and reservoir monitoring practice as well as their integration in automated data interpretation workflows developed in the industry.","PeriodicalId":388039,"journal":{"name":"Day 3 Wed, June 07, 2023","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115706356","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Effective Relative Permeabilities Based on Momentum Equations with Brinkmann Terms and Viscous Coupling","authors":"Yangyang Qiao, P. Andersen, Sadegh Ahmadpour","doi":"10.2118/214388-ms","DOIUrl":"https://doi.org/10.2118/214388-ms","url":null,"abstract":"The relative permeability expresses the mobility reduction factor when a fluid flows through a porous medium in presence of another fluid and appears in Darcy's law for multiphase flow. In this work, we replace Darcy's law with more general momentum equations accounting for fluid-rock interaction (flow resistance), fluid-fluid interaction (drag) and Brinkmann terms responding to gradients in fluid interstitial velocities. By coupling the momentum equations with phase transport equations, we study two important flow processes: forced imbibition (core flooding) and counter-current spontaneous imbibition. In the former a constant water injection rate is applied, and capillary forces neglected, while in the latter, capillary forces drive the process, and the total flux is zero. Our aim is to understand what relative permeabilities result from these systems and flow configurations.\u0000 From previous work, when using momentum equations without Brinkmann terms, unique saturation dependent relative permeabilities are obtained for the two flow modes that depend on the flow mode. Now, with Brinkmann terms included the relative permeabilities depend on local spatial derivatives of interstitial velocity and pressure. Local relative permeabilities are calculated for both phases utilizing the ratio of phase Darcy velocity and phase pressure gradient. In addition, we utilize the JBN method for forced imbibition to calculate relative permeabilities from pressure drop and average saturation. Both flow setups are parameterized with literature data and sensitivity analysis is performed.\u0000 During core flooding, Brinkmann terms give a flatter saturation profile and higher front saturation. The saturation profile shape changes with time. Local water relative permeabilities are reduced, while they are slightly raised for oil. The saturation range where relative permeabilities can be evaluated locally is raised and made narrower with increased Brinkmann terms. JBN relative permeabilities deviate from the local values: the trends in curves and saturation range are the same but more pronounced as they incorporate average measurements including the strong impact at the inlet. Brinkmann effects vanish after sufficient distance traveled resulting in the unique saturation functions as a limit. Unsteady state relative permeabilities (based on transient data from single phase injection) differ from steady state relative permeabilities (based on steady state data from co-injection of two fluids) because the Brinkmann terms are zero at steady state. During spontaneous imbibition, higher effect from the Brinkmann terms caused oil relative permeabilities to decrease at low water saturations and slightly increase at high saturations, while water relative permeability was only slightly reduced. The net effect was a delay of the imbibition profile. Local relative permeabilities approached the unique saturation functions without Brinkmann terms deeper in the system because phase velocities","PeriodicalId":388039,"journal":{"name":"Day 3 Wed, June 07, 2023","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125396184","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}