Integration of soft data into multiple-point statistical simulation: re-assessing the probability conditioning method for facies model calibration

Conditioning multiple-point statistical (MPS) facies simulation on dynamic flow data is complicated by the complex relationship between discrete facies distribution and the flow response data. The process can be facilitated by using the probability conditioned method (PCM), in which an ensemble-based data assimilation approach is used to infer, from observed flow data, a facies probability map that can guide conditional simulation from a training image (TI). We discuss important aspects of flow model calibration based on facies probability maps and propose several improvements to the original PCM, including: (1) using a statistically consistent approach for inferring facies probability maps from updated ensemble of continuous hydraulic properties; (2) assigning spatially variable weights to simulation grids based on relative confidence in the information content of observed data; and (3) considering spatial patterns instead of marginal facies probabilities in constructing probability maps. We illustrate that, in simulating categorical facies, the pattern-imitating behavior of MPS can have a significant impact on soft data conditioning. In particular, in the Single Normal Equation SIMulation (SNESIM) algorithm, the initial points that are visited on the random path tend to determine the main global facies connectivity. Once these initial points are populated with simulated values, the conditional probabilities (inferred from the TI) for the subsequent cells on the random path tend to be very close to 0 and 1. Hence, the facies types in the remaining cells are known almost deterministically, making the soft data inconsequential at the later stages of simulation. This behavior suggests that, without compensating for this effect, the facies probability map is not effectively integrated into the SNESIM simulation, an issue that is reflected in the generated realizations. Several numerical experiments are presented and discussed to illustrate this behavior and its impact on soft-data conditioning.

[1]  D. Oliver,et al.  Recent progress on reservoir history matching: a review , 2011 .

[2]  R. Grayson,et al.  Toward capturing hydrologically significant connectivity in spatial patterns , 2001 .

[3]  Behnam Jafarpour,et al.  Reservoir Characterization With the Discrete Cosine Transform , 2009 .

[4]  G. Fogg,et al.  Modeling Spatial Variability with One and Multidimensional Continuous-Lag Markov Chains , 1997 .

[5]  Dean S. Oliver,et al.  History Matching of the PUNQ-S3 Reservoir Model Using the Ensemble Kalman Filter , 2005 .

[6]  Alexandre Boucher,et al.  Applied Geostatistics with SGeMS: A User's Guide , 2009 .

[7]  Dongxiao Zhang,et al.  Efficient Ensemble-Based Closed-Loop Production Optimization , 2009 .

[8]  L. Lake,et al.  A new approach to shale management in field scale simulation models , 1982 .

[9]  Thomas Mejer Hansen,et al.  Multiple-point statistical simulation for hydrogeological models: 3-D training image development and conditioning strategies , 2016 .

[10]  Yoram Rubin,et al.  Strategic placement of localization devices (such as pilot points and anchors) in inverse modeling schemes , 2012 .

[11]  Stephen A. Holditch,et al.  Characterizing average permeability in oil and gas formations , 1992 .

[12]  Timothy C. Coburn,et al.  Geostatistics for Natural Resources Evaluation , 2000, Technometrics.

[13]  Clayton V. Deutsch,et al.  Geostatistical Software Library and User's Guide , 1998 .

[14]  Charles F. Harvey,et al.  When good statistical models of aquifer heterogeneity go bad: A comparison of flow, dispersion, and mass transfer in connected and multivariate Gaussian hydraulic conductivity fields , 2003 .

[15]  B. Jafarpour,et al.  History matching with an ensemble Kalman filter and discrete cosine parameterization , 2008 .

[16]  J. Caers,et al.  The Probability Perturbation Method: A New Look at Bayesian Inverse Modeling , 2006 .

[17]  Jef Caers,et al.  Multiple-point Geostatistics: A Quantitative Vehicle for Integrating Geologic Analogs into Multiple Reservoir Models , 2004 .

[18]  Knud Skou Cordua,et al.  Multiple point statistical simulation using uncertain (soft) conditional data , 2018, Comput. Geosci..

[19]  P. Renard,et al.  Dealing with spatial heterogeneity , 2005 .

[20]  J. Jaime Gómez-Hernández,et al.  ISIM3D: and ANSI-C three-dimensional multiple indicator conditional simulation program , 1990 .

[21]  Andres Alcolea,et al.  Pilot points method incorporating prior information for solving the groundwater flow inverse problem , 2006 .

[22]  A. Journel.  Combining Knowledge from Diverse Sources: An Alternative to Traditional Data Independence Hypotheses , 2002 .

[23]  J. Gómez-Hernández,et al.  To be or not to be multi-Gaussian? A reflection on stochastic hydrogeology , 1998 .

[24]  J. Chilès,et al.  Geostatistics: Modeling Spatial Uncertainty , 1999 .

[25]  Liangping Li,et al.  An approach to handling non-Gaussianity of parameters and state variables in ensemble Kalman filtering , 2011 .

[26]  Steven F. Carle,et al.  CONDITIONAL SIMULATION OF HYDROFACIES ARCHITECTURE: A TRANSITION PROBABILITY/MARKOV APPROACH1 , 1998 .

[27]  D. Stoyan,et al.  Stochastic Geometry and Its Applications , 1989 .

[28]  Ragnar Hauge,et al.  Modeling of Fluvial Reservoirs with Object Models , 1998 .

[29]  Sebastien Strebelle,et al.  Conditional Simulation of Complex Geological Structures Using Multiple-Point Statistics , 2002 .

[30]  Ning Liu,et al.  Automatic History Matching of Geologic Facies , 2004 .

[31]  Philippe Renard,et al.  Blocking Moving Window algorithm: Conditioning multiple‐point simulations to hydrogeological data , 2010 .

[32]  S. Krishnan.  The Tau Model for Data Redundancy and Information Combination in Earth Sciences: Theory and Application , 2008 .

[33]  Behnam Jafarpour.  Wavelet Reconstruction of Geologic Facies From Nonlinear Dynamic Flow Measurements , 2011, IEEE Transactions on Geoscience and Remote Sensing.

[34]  R. M. Srivastava,et al.  Multivariate Geostatistics: Beyond Bivariate Moments , 1993 .

[35]  A. Journel.  Nonparametric estimation of spatial distributions , 1983 .

[36]  Behnam Jafarpour,et al.  A Probability Conditioning Method (PCM) for Nonlinear Flow Data Integration into Multipoint Statistical Facies Simulation , 2011 .

[37]  G. Evensen.  Sampling strategies and square root analysis schemes for the EnKF , 2004 .

[38]  G. Evensen.  Sequential data assimilation with a nonlinear quasi‐geostrophic model using Monte Carlo methods to forecast error statistics , 1994 .

[39]  W. B. Whalley,et al.  The use of fractals and pseudofractals in the analysis of two-dimensional outlines: Review and further exploration , 1989 .

[40]  Jan Law,et al.  A Statistical Approach to the Interstitial Heterogeneity of Sand Reservoirs , 1944 .

[41]  Tor Arne Johansen,et al.  Incorporating 4D Seismic Data in Reservoir Simulation Models Using Ensemble Kalman Filter , 2007 .

[42]  G. Evensen,et al.  Data assimilation and inverse methods in terms of a probabilistic formulation , 1996 .

[43]  L. Lake,et al.  A New Approach to Shale Management in Field-Scale Models , 1984 .

[44]  Andre G. Journel,et al.  Joint simulation of multiple variables with a Markov-type coregionalization model , 1994 .

[45]  Albert C. Reynolds,et al.  A History Matching Procedure for Non-Gaussian Facies Based on ES-MDA , 2015, ANSS 2015.

[46]  Jef Caers,et al.  Geostatistical Reservoir Modelling using Statistical Pattern Recognition , 2001 .

[47]  Clayton V. Deutsch,et al.  Hierarchical Object-Based Geostatistical Modeling of Fluvial Reservoirs , 1996 .

[48]  L. Y. Hu,et al.  Multiple‐point geostatistics for modeling subsurface heterogeneity: A comprehensive review , 2008 .

[49]  Philippe Renard,et al.  Issues in characterizing heterogeneity and connectivity in non-multiGaussian media , 2008 .