A General Spatio-Temporal Clustering-Based Non-local Formulation for Multiscale Modeling of Compartmentalized Reservoirs

Representing the reservoir as a network of discrete compartments with neighbor and non-neighbor connections is a fast, yet accurate method for analyzing oil and gas reservoirs. Automatic and rapid detection of coarse-scale compartments with distinct static and dynamic properties is an integral part of such high-level reservoir analysis. In this work, we present a hybrid framework specific to reservoir analysis for an automatic detection of clusters in space using spatial and temporal field data, coupled with a physics-based multiscale modeling approach. In this work a novel hybrid approach is presented in which we couple a physics-based non-local modeling framework with data-driven clustering techniques to provide a fast and accurate multiscale modeling of compartmentalized reservoirs. This research also adds to the literature by presenting a comprehensive work on spatio-temporal clustering for reservoir studies applications that well considers the clustering complexities, the intrinsic sparse and noisy nature of the data, and the interpretability of the outcome. Keywords: Artificial Intelligence; Machine Learning; Spatio-Temporal Clustering; Physics-Based Data-Driven Formulation; Multiscale Modeling

[1]  Sotirios Chatzis,et al.  A Fuzzy Clustering Approach Toward Hidden Markov Random Field Models for Enhanced Spatially Constrained Image Segmentation , 2008, IEEE Transactions on Fuzzy Systems.

[2]  D.K. Bhattacharyya,et al.  An improved sampling-based DBSCAN for large spatial databases , 2004, International Conference on Intelligent Sensing and Information Processing, 2004. Proceedings of.

[3]  E. Gildin,et al.  Reduced Order Modeling In Reservoir Simulation Using the Bilinear Approximation Techniques , 2014 .

[4]  Chaodong Yang,et al.  Reservoir Model Uncertainty Quantification Through Computer-Assisted History Matching , 2007 .

[5]  Mohammad-Reza Alam,et al.  Shape optimization of wave energy converters for broadband directional incident waves , 2018, Ocean Engineering.

[6]  Catherine A. Sugar,et al.  Finding the Number of Clusters in a Dataset , 2003 .

[7]  Eduardo Gildin,et al.  Closed-Loop Reservoir Management: Do we need complex models? , 2011 .

[8]  Insights into the Impact of Water Salinity on Multiphase Flow at the Pore-Scale in Carbonate Formations , 2019, Day 4 Thu, March 21, 2019.

[9]  Arnold Heemink,et al.  Reduced models for linear groundwater flow models using empirical orthogonal functions , 2004 .

[10]  K. alik An efficient k'-means clustering algorithm , 2008 .

[11]  L.J. Durlofsky,et al.  Scale up of heterogeneous three dimensional reservoir descriptions , 1996 .

[12]  Louis J. Durlofsky,et al.  A general method to select representative models for decision making and optimization under uncertainty , 2016, Comput. Geosci..

[13]  Geeta Sikka,et al.  Recent Techniques of Clustering of Time Series Data: A Survey , 2012 .

[14]  H. Tchelepi,et al.  Adaptive Multiscale Finite-Volume Framework for Reservoir Simulation , 2007 .

[15]  G. P. Patil,et al.  Spatially constrained clustering and upper level set scan hotspot detection in surveillance geoinformatics , 2006, Environmental and Ecological Statistics.

[16]  Michael K. Ng,et al.  A fuzzy k-modes algorithm for clustering categorical data , 1999, IEEE Trans. Fuzzy Syst..

[17]  Paul E. Green,et al.  K-modes Clustering , 2001, J. Classif..

[18]  Xiao Han,et al.  A fuzzy k-prototype clustering algorithm for mixed numeric and categorical data , 2012, Knowl. Based Syst..

[19]  S. Chiba,et al.  Dynamic programming algorithm optimization for spoken word recognition , 1978 .

[20]  Xian-Huan Wen,et al.  Upscaling Hydraulic Conductivities in Cross-Bedded Formations , 1998 .

[21]  Aslak Tveito,et al.  An upscaling method for one‐phase flow in heterogeneous reservoirs. A weighted output least squares (WOLS) approach , 1998 .

[22]  Hamdi A. Tchelepi,et al.  K-values based non-equilibrium formulation for upscaling of compositional simulation , 2017 .

[23]  David Castineira,et al.  A Comprehensive Adaptive Forecasting Framework for Optimum Field Development Planning , 2019 .

[24]  Zhexue Huang,et al.  CLUSTERING LARGE DATA SETS WITH MIXED NUMERIC AND CATEGORICAL VALUES , 1997 .

[25]  Hamdi A. Tchelepi,et al.  Multiscale level-set method for accurate modeling of immiscible two-phase flow with deposited thin films on solid surfaces , 2017, J. Comput. Phys..

[26]  Gijs Van Essen,et al.  Reservoir Uncertainty Quantification Using Probabilistic History Matching Workflow , 2014, All Days.

[27]  Tommi S. Jaakkola,et al.  A new approach to analyzing gene expression time series data , 2002, RECOMB '02.

[28]  Andreas Christmann,et al.  Support vector machines , 2008, Data Mining and Knowledge Discovery Handbook.

[29]  R. Manmatha,et al.  Word image matching using dynamic time warping , 2003, 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings..

[30]  Massimiliano Pontil,et al.  Support Vector Machines: Theory and Applications , 2001, Machine Learning and Its Applications.

[31]  Hadi Hajibeygi,et al.  Accurate and Efficient Simulation of Multiphase Flow in a Heterogeneous Reservoir With Error Estimate and Control in the Multiscale Finite-Volume Framework , 2012 .

[32]  J. W. Barker,et al.  A critical review of the use of pseudo-relative permeabilities for upscaling , 1997 .

[33]  Nazish Hoda,et al.  A Robust Iterative Ensemble Smoother Method for Efficient History Matching and Uncertainty Quantification , 2017 .

[34]  Jacquelien M. A. Scherpen,et al.  Balanced Realization and Model Order Reduction for Nonlinear Systems Based on Singular Value Analysis , 2010, SIAM J. Control. Optim..

[35]  M. Muskat The Production Histories of Oil Producing Gas‐Drive Reservoirs , 1945 .

[36]  Joshua Zhexue Huang,et al.  Extensions to the k-Means Algorithm for Clustering Large Data Sets with Categorical Values , 1998, Data Mining and Knowledge Discovery.

[37]  A. Riaz,et al.  Carbon dioxide sequestration in saline formations: Part 2—Review of multiphase flow modeling , 2014 .

[38]  Martin J. Blunt,et al.  Nested gridding and streamline-based simulation for fast reservoir performance prediction , 1999 .

[39]  Jeremy B. Brown,et al.  Using Data-Driven Technologies to Accelerate the Field Development Planning Process for Mature Field Rejuvenation , 2017 .

[40]  John D. Hedengren,et al.  REDUCED ORDER MODELING FOR RESERVOIR INJECTION OPTIMIZATION AND FORECASTING , 2016 .

[41]  George M. Church,et al.  Aligning gene expression time series with time warping algorithms , 2001, Bioinform..

[42]  Guoyin Wang,et al.  An automatic method to determine the number of clusters using decision-theoretic rough set , 2014, Int. J. Approx. Reason..

[43]  Marti A. Hearst Trends & Controversies: Support Vector Machines , 1998, IEEE Intell. Syst..

[44]  Johan A. K. Suykens,et al.  Least Squares Support Vector Machine Classifiers , 1999, Neural Processing Letters.

[45]  Larry S. Davis,et al.  Towards 3-D model-based tracking and recognition of human movement: a multi-view approach , 1995 .

[46]  D. A. Bistrian,et al.  Randomized dynamic mode decomposition for nonintrusive reduced order modelling , 2016, 1611.04884.

[47]  Pierpaolo D'Urso,et al.  A Fuzzy Clustering Model for Multivariate Spatial Time Series , 2010, J. Classif..

[48]  Hamdi A. Tchelepi,et al.  Thermodynamically Consistent Transport Coefficients for Upscaling of Compositional Processes , 2013, ANSS 2013.

[49]  A. Atiya,et al.  Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond , 2005, IEEE Transactions on Neural Networks.

[50]  Mehrdad G. Shirangi History matching production data and uncertainty assessment with an efficient TSVD parameterization algorithm , 2014 .

[51]  Jan Dirk Jansen,et al.  Subspace identification of low-order reservoir models* , 2002 .

[52]  Hamdi A. Tchelepi,et al.  K -Values-Based Upscaling of Compositional Simulation , 2019 .

[53]  Michael K. Ng,et al.  A Note on K-modes Clustering , 2003, J. Classif..

[54]  H. Tchelepi,et al.  Multiscale finite-volume formulation for multiphase flow in porous media: black oil formulation of compressible, three-phase flow with gravity , 2008 .

[55]  Lipika Dey,et al.  A k-mean clustering algorithm for mixed numeric and categorical data , 2007, Data Knowl. Eng..

[56]  N. Odling,et al.  Scaling of fracture systems in geological media , 2001 .

[57]  Louis J. Durlofsky,et al.  Coarse scale models of two phase flow in heterogeneous reservoirs: volume averaged equations and their relationship to existing upscaling techniques , 1998 .

[58]  M. A. Cardoso,et al.  Use of Reduced-Order Modeling Procedures for Production Optimization , 2010 .

[59]  M. J. Fetkovich A Simplified Approach to Water Influx Calculations-Finite Aquifer Systems , 1971 .

[60]  Hiroaki Sakoe,et al.  A Dynamic Programming Approach to Continuous Speech Recognition , 1971 .

[61]  Tamás Kalmár-Nagy,et al.  Act-and-wait control of discrete systems with random delays , 2012, 2012 American Control Conference (ACC).

[62]  Patrick Jenny,et al.  Adaptive iterative multiscale finite volume method , 2011, J. Comput. Phys..

[63]  Pejman Tahmasebi,et al.  Rapid Learning-Based and Geologically Consistent History Matching , 2018, Transport in Porous Media.

[64]  Chih-Jen Lin,et al.  A Comparison of Methods for Multi-class Support Vector Machines , 2015 .

[65]  J. A. Hartigan,et al.  A k-means clustering algorithm , 1979 .

[66]  P. Rousseeuw Silhouettes: a graphical aid to the interpretation and validation of cluster analysis , 1987 .

[67]  Louis J. Durlofsky,et al.  Optimization of Nonconventional Well Type, Location, and Trajectory , 2003 .

[68]  Jan Dirk Jansen,et al.  Generation of Low-Order Reservoir Models Using System-Theoretical Concepts , 2004 .

[69]  L. Holden,et al.  Global Upscaling of Permeability in Heterogeneous Reservoirs; The Output Least Squares (OLS) Method , 2000 .

[70]  Anil K. Jain Data clustering: 50 years beyond K-means , 2008, Pattern Recognit. Lett..

[71]  Louis J. Durlofsky,et al.  Development and application of reduced‐order modeling procedures for subsurface flow simulation , 2009 .

[72]  David Castineira,et al.  Application of Flow Diagnostics to Rapid Production Data Integration in Complex Geologic Grids and Dual Permeability Models , 2019 .

[73]  Mingjin Yan,et al.  Methods of Determining the Number of Clusters in a Data Set and a New Clustering Criterion , 2005 .

[74]  Genital occurrence of oral microbiota. , 1978, Acta dermato-venereologica.

[75]  Hamdi A. Tchelepi,et al.  Upscaling of Compositional Flow Simulation based on a non-Equilibrium Formulation , 2012 .

[76]  Tarek Ahmed,et al.  Reservoir Engineering Handbook , 2002 .

[77]  Ying Wah Teh,et al.  Time-series clustering - A decade review , 2015, Inf. Syst..

[78]  Patrick Jenny,et al.  Multiscale finite-volume method for parabolic problems arising from compressible multiphase flow in porous media , 2009, J. Comput. Phys..

[79]  Jonggeun Choe,et al.  Uncertainty Quantification of Channelized Reservoir Using Ensemble Smoother with Selective Measurement Data , 2014 .

[80]  Marco Aurélio Cavalcanti Pacheco,et al.  Uncertainty quantification in reservoir simulation models with polynomial chaos expansions: Smolyak quadrature and regression method approach , 2017 .

[81]  Douglas Steinley,et al.  K-means clustering: a half-century synthesis. , 2006, The British journal of mathematical and statistical psychology.