scholarly journals Sequential Assimilation of Tracer Test Data by Ensemble Kalman Filter for Fracture Identification

2009 ◽  
Vol 52 (5) ◽  
pp. 275-282
Author(s):  
Takashi Goda ◽  
Kozo Sato
Keyword(s):  
Kalman Filter ◽  
Test Data ◽  
Ensemble Kalman Filter ◽  
Tracer Test ◽  
Fracture Identification

Dynamic Fracture Characterization From Tracer-Test and Flow-Rate Data With Ensemble Kalman Filter

SPE Journal ◽  
2018 ◽  
Vol 23 (02) ◽  
pp. 449-466 ◽  
Author(s):  
Siavash Hakim Elahi ◽  
Behnam Jafarpour
Keyword(s):  
Kalman Filter ◽  
Hydraulic Conductivity ◽  
Test Data ◽  
Ensemble Kalman Filter ◽  
Tracer Test ◽  
Natural Fracture ◽  
Production Data ◽  
Matrix Properties ◽  
Half Length

Summary Hydraulic fracturing is performed to enable production from low-permeability and organic-rich shale-oil/gas reservoirs by stimulating the rock to increase its permeability. Characterization and imaging of hydraulically induced fractures is critical for accurate prediction of production and of the stimulated reservoir volume (SRV). Recorded tracer concentrations during flowback and historical production data can reveal important information about fracture and matrix properties, including fracture geometry, hydraulic conductivity, and natural-fracture density. However, the complexity and uncertainty in fracture and reservoir descriptions, coupled with data limitations, complicate the estimation of these properties. In this paper, tracer-test and production data are used for dynamic characterization of important parameters of hydraulically fractured reservoirs, including matrix permeability and porosity, planar-fracture half-length and hydraulic conductivity, discrete-fracture-network (DFN) density and conductivity, and fracture-closing (conductivity-decline) rate during production. The ensemble Kalman filter (EnKF) is used to update uncertain model parameters by sequentially assimilating first the tracer-test data and then the production data. The results indicate that the tracer-test and production data have complementary information for estimating fracture half-length and conductivity, with the former being more sensitive to hydraulic conductivity and the latter being more affected by fracture half-length. For characterization of DFN, a stochastic representation is adopted and the parameters of the stochastic model along with matrix and hydraulic-fracture properties are updated. Numerical examples are presented to investigate the sensitivity of the observed production and tracer-test data to fracture and matrix properties and to evaluate the EnKF performance in estimating these parameters.

scholarly journals Coupled and uncoupled hydrogeophysical inversions using ensemble Kalman filter assimilation of ERT-monitored tracer test data

2015 ◽  
Vol 51 (5) ◽  
pp. 3277-3291 ◽  
Author(s):  
Matteo Camporese ◽  
Giorgio Cassiani ◽  
Rita Deiana ◽  
Paolo Salandin ◽  
Andrew Binley
Keyword(s):  
Kalman Filter ◽  
Test Data ◽  
Ensemble Kalman Filter ◽  
Tracer Test

scholarly journals Ensemble Kalman filter versus ensemble smoother for assessing hydraulic conductivity via tracer test data assimilation

2012 ◽  
Vol 9 (11) ◽  
pp. 13083-13115
Author(s):  
E. Crestani ◽  
M. Camporese ◽  
D. Baú ◽  
P. Salandin
Keyword(s):  
Spatial Distribution ◽  
Kalman Filter ◽  
Hydraulic Conductivity ◽  
Ensemble Kalman Filter ◽  
Tracer Test ◽  
State Variables ◽  
Modeling Framework ◽  
Gaussian Probability Density Function ◽  
Flow And Transport ◽  
Ensemble Smoother

Abstract. The significance of estimating the spatial variability of the hydraulic conductivity K in natural aquifers is relevant to the possibility of defining the space and time evolution of a non-reactive plume, since the transport of a solute is mainly controlled by the heterogeneity of K. At the local scale, the spatial distribution of K can be inferred by combining the Lagrangian formulation of the transport with a Kalman filter-based technique and assimilating a sequence of time-lapse concentration C measurements, which, for example, can be evaluated on-site through the application of a geophysical method. The objective of this work is to compare the ensemble Kalman filter (EnKF) and the ensemble smoother (ES) capabilities to retrieve the hydraulic conductivity spatial distribution in a groundwater flow and transport modeling framework. The application refers to a two-dimensional synthetic aquifer in which a tracer test is simulated. Moreover, since Kalman filter-based methods are optimal only if each of the involved variables fit to a Gaussian probability density function (pdf) and since this condition may not be met by some of the flow and transport state variables, issues related to the non-Gaussianity of the variables are analyzed and different transformation of the pdfs are considered in order to evaluate their influence on the performance of the methods. The results show that the EnKF reproduces with good accuracy the hydraulic conductivity field, outperforming the ES regardless of the pdf of the concentrations.

scholarly journals Ensemble Kalman filter versus ensemble smoother for assessing hydraulic conductivity via tracer test data assimilation

2013 ◽  
Vol 17 (4) ◽  
pp. 1517-1531 ◽  
Author(s):  
E. Crestani ◽  
M. Camporese ◽  
D. Baú ◽  
P. Salandin
Keyword(s):  
Spatial Distribution ◽  
Kalman Filter ◽  
Hydraulic Conductivity ◽  
Ensemble Kalman Filter ◽  
Tracer Test ◽  
State Variables ◽  
Modeling Framework ◽  
Gaussian Probability Density Function ◽  
Flow And Transport ◽  
Ensemble Smoother

Abstract. Estimating the spatial variability of hydraulic conductivity K in natural aquifers is important for predicting the transport of dissolved compounds. Especially in the nonreactive case, the plume evolution is mainly controlled by the heterogeneity of K. At the local scale, the spatial distribution of K can be inferred by combining the Lagrangian formulation of the transport with a Kalman-filter-based technique and assimilating a sequence of time-lapse concentration C measurements, which, for example, can be evaluated on site through the application of a geophysical method. The objective of this work is to compare the ensemble Kalman filter (EnKF) and the ensemble smoother (ES) capabilities to retrieve the hydraulic conductivity spatial distribution in a groundwater flow and transport modeling framework. The application refers to a two-dimensional synthetic aquifer in which a tracer test is simulated. Moreover, since Kalman-filter-based methods are optimal only if each of the involved variables fit to a Gaussian probability density function (pdf) and since this condition may not be met by some of the flow and transport state variables, issues related to the non-Gaussianity of the variables are analyzed and different transformation of the pdfs are considered in order to evaluate their influence on the performance of the methods. The results show that the EnKF reproduces with good accuracy the hydraulic conductivity field, outperforming the ES regardless of the pdf of the concentrations.

Ensemble Kalman Filter for Out of Sequence Measurement Tracking

2012 ◽  
Vol 132 (10) ◽  
pp. 1617-1625
Author(s):  
Sirichai Pornsarayouth ◽  
Masaki Yamakita
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter

Data assimilation with the weighted ensemble Kalman filter

2010 ◽  
Author(s):  
Nicolas Papadakis ◽  
Etienne Mémin ◽  
Anne Cuzol ◽  
Nicolas Gengembre
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter

scholarly journals Assimilation of D-InSAR snow depth data by an ensemble Kalman filter

2021 ◽  
Vol 14 (6) ◽  
Author(s):  
Jinming Yang ◽  
Chengzhi Li
Keyword(s):  
Remote Sensing ◽  
Kalman Filter ◽  
Water Resource ◽  
Ensemble Kalman Filter ◽  
Snow Depth ◽  
Resource Assessment ◽  
Measured Data ◽  
Hydrological Process ◽  
Depth Data ◽  
Water Resource Assessment

AbstractSnow depth mirrors regional climate change and is a vital parameter for medium- and long-term numerical climate prediction, numerical simulation of land-surface hydrological process, and water resource assessment. However, the quality of the available snow depth products retrieved from remote sensing is inevitably affected by cloud and mountain shadow, and the spatiotemporal resolution of the snow depth data cannot meet the need of hydrological research and decision-making assistance. Therefore, a method to enhance the accuracy of snow depth data is urgently required. In the present study, three kinds of snow depth data which included the D-InSAR data retrieved from the remote sensing images of Sentinel-1 synthetic aperture radar, the automatically measured data using ultrasonic snow depth detectors, and the manually measured data were assimilated based on ensemble Kalman filter. The assimilated snow depth data were spatiotemporally consecutive and integrated. Under the constraint of the measured data, the accuracy of the assimilated snow depth data was higher and met the need of subsequent research. The development of ultrasonic snow depth detector and the application of D-InSAR technology in snow depth inversion had greatly alleviated the insufficiency of snow depth data in types and quantity. At the same time, the assimilation of multi-source snow depth data by ensemble Kalman filter also provides high-precision data to support remote sensing hydrological research, water resource assessment, and snow disaster prevention and control program.

scholarly journals Assimilation of Dynamic Combined Finite Discrete Element Methods Using the Ensemble Kalman Filter

2021 ◽  
Vol 11 (7) ◽  
pp. 2898
Author(s):  
Humberto C. Godinez ◽  
Esteban Rougier
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Failure Modes ◽  
Split Hopkinson Pressure Bar ◽  
Peak Stress ◽  
Discrete Element ◽  
Material Behavior ◽  
Model Parameters ◽  
Hopkinson Pressure Bar ◽  
Parameter Values

Simulation of fracture initiation, propagation, and arrest is a problem of interest for many applications in the scientific community. There are a number of numerical methods used for this purpose, and among the most widely accepted is the combined finite-discrete element method (FDEM). To model fracture with FDEM, material behavior is described by specifying a combination of elastic properties, strengths (in the normal and tangential directions), and energy dissipated in failure modes I and II, which are modeled by incorporating a parameterized softening curve defining a post-peak stress-displacement relationship unique to each material. In this work, we implement a data assimilation method to estimate key model parameter values with the objective of improving the calibration processes for FDEM fracture simulations. Specifically, we implement the ensemble Kalman filter assimilation method to the Hybrid Optimization Software Suite (HOSS), a FDEM-based code which was developed for the simulation of fracture and fragmentation behavior. We present a set of assimilation experiments to match the numerical results obtained for a Split Hopkinson Pressure Bar (SHPB) model with experimental observations for granite. We achieved this by calibrating a subset of model parameters. The results show a steady convergence of the assimilated parameter values towards observed time/stress curves from the SHPB observations. In particular, both tensile and shear strengths seem to be converging faster than the other parameters considered.

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