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 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 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

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.

Simultaneous identification of contaminant source location, initial contaminant concentration, horizontal and vertical hydraulic conductivity in a three-dimensional coastal aquifer via ensemble Kalman filter 

2021 ◽  
Author(s):  
Arezou Dodangeh ◽  
Mohammad Mahdi Rajabi ◽  
Marwan Fahs
Keyword(s):  
Kalman Filter ◽  
Hydraulic Conductivity ◽  
Coastal Aquifers ◽  
Ensemble Kalman Filter ◽  
Coastal Aquifer ◽  
Three Dimensional ◽  
Source Location ◽  
Contaminant Concentration ◽  
Contaminant Source ◽  
Vertical Hydraulic Conductivity

<p>In coastal aquifers, we face the problem of salt water intrusion, which creates a complex flow field. Many of these coastal aquifers are also exposed to contaminants from various sources. In addition, in many cases there is no information about the characteristics of the aquifer. Simultaneous identification of the contaminant source and coastal aquifer characteristics can be a challenging issue. Much work has been done to identify the contaminant source, but in the complex velocity field of coastal aquifer, no one has resolved this issue yet. We want to address that in a three-dimensional artificial coastal aquifer.</p><p>To achieve this goal, we have developed a method in which the contaminant source can be identified and the characteristics of the aquifer can be estimated by using information obtained from observation wells. First, by assuming the input parameters required to simulate the contaminant transfer to the aquifer, this three-dimensional coastal aquifer that is affected by various phenomena such as seawater intrusion, tides, shore slope, rain, discharge and injection wells, is simulated and the time series of the output parameters including head, salinity and contaminant concentration are estimated. In the next step, with the aim of performing inverse modeling, random values ​​are added to the time series of outputs obtained at specific points (points belonging to observation wells) in order to rebuilt the initial conditions of the problem to achieve the desired unknowns (contaminant source and aquifer characteristics). The unknowns estimated in this study are the contaminant source location (x, y, z), the initial contaminant concentration, the horizontal and vertical hydraulic conductivity of the aquifer. SEAWAT model in GMS software environment has been used to solve the equations of flow and contaminant transfer and simulate a three-dimensional coastal aquifer. Next, for reverse modeling, one of the Bayesian Filters subset (ensemble Kalman filter) has been used in the Python programming language environment. Also, to reduce the code run time, the neural network model is designed and trained for the SEAWAT model.</p><p>This method is able to meet the main purpose of the study, namely estimating the value ​​of unknown input parameters, including the contaminant source location, the initial contaminant concentration, the horizontal and vertical hydraulic conductivity of the aquifer. In addition, that makes it possible to achieve a three-dimensional numerical model of the coastal aquifer that can be used as a benchmark to examine more accurately the impact of different phenomena simultaneously. In conclusion, we have developed an algorithm which can be used in the world's coastal aquifers to identify the contaminant source and estimate its characteristics.</p><p> </p><p>Key words: coastal aquifer, seawater intrusion, contaminants, groundwater, flow field, parameter estimation, ensemble kalman filter</p>

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