Characterization of Fracture Length and Conductivity From Tracer Test and Production Data With Ensemble Kalman Filter

2015 ◽  
Author(s):  
Siavash Hakim Elahi* ◽  
Behnam Jafarpour
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Tracer Test ◽  
Production Data ◽  
Fracture Length

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.

A Probabilistic Collocation-Based Kalman Filter for History Matching

SPE Journal ◽  
2011 ◽  
Vol 16 (02) ◽  
pp. 294-306 ◽  
Author(s):  
Lingzao Zeng ◽  
Haibin Chang ◽  
Dongxiao Zhang
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
History Matching ◽  
Initial Conditions ◽  
Collocation Point ◽  
Computational Effort ◽  
Production Data ◽  
Sampling Errors ◽  
Probabilistic Collocation

Summary The ensemble Kalman filter (EnKF) has been used widely for data assimilation. Because the EnKF is a Monte Carlo-based method, a large ensemble size is required to reduce the sampling errors. In this study, a probabilistic collocation-based Kalman filter (PCKF) is developed to adjust the reservoir parameters to honor the production data. It combines the advantages of the EnKF for dynamic data assimilation and the polynomial chaos expansion (PCE) for efficient uncertainty quantification. In this approach, all the system parameters and states and the production data are approximated by the PCE. The PCE coefficients are solved with the probabilistic collocation method (PCM). Collocation realizations are constructed by choosing collocation point sets in the random space. The simulation for each collocation realization is solved forward in time independently by means of an existing deterministic solver, as in the EnKF method. In the analysis step, the needed covariance is approximated by the PCE coefficients. In this study, a square-root filter is employed to update the PCE coefficients. After the analysis, new collocation realizations are constructed. With the parameter collocation realizations as the inputs and the state collocation realizations as initial conditions, respectively, the simulations are forwarded to the next analysis step. Synthetic 2D water/oil examples are used to demonstrate the applicability of the PCKF in history matching. The results are compared with those from the EnKF on the basis of the same analysis. It is shown that the estimations provided by the PCKF are comparable to those obtained from the EnKF. The biggest improvement of the PCKF comes from the leading PCE approximation, with which the computational burden of the PCKF can be greatly reduced by means of a smaller number of simulation runs, and the PCKF outperforms the EnKF for a similar computational effort. When the correlation ratio is much smaller, the PCKF still provides estimations with a better accuracy for a small computational effort.

Quantifying Uncertainty for the PUNQ-S3 Problem in a Bayesian Setting With RML and EnKF

SPE Journal ◽  
2006 ◽  
Vol 11 (04) ◽  
pp. 506-515 ◽  
Author(s):  
Guohua Gao ◽  
Mohammad Zafari ◽  
Albert C. Reynolds
Keyword(s):  
Ensemble Kalman Filter ◽  
Oil Production ◽  
Production Data ◽  
A Posteriori ◽  
Reservoir Performance ◽  
Performance Predictions ◽  
Randomized Maximum Likelihood ◽  
The One ◽  
Probability Density Function Pdf

Summary The well known PUNQ-S3 reservoir model represents a synthetic problem which was formulated to test the ability of various methods and research groups to quantify the uncertainty in the prediction of cumulative oil production. Previous results reported on this project suggest that the randomized maximum likelihood (RML) method gives a biased characterization of the uncertainty. A major objective of this paper is to show that this is incorrect. With a correct implementation of the RML method within a Bayesian framework, we show that RML does an adequate job of sampling the a posteriori distribution for the PUNQ problem. In particular, the true predicted oil production lies within the band of predictions generated with the RML method and is not biased. We also apply the ensemble Kalman Filter (EnKF) method to the PUNQ data set, and show that this method also gives a reasonable quantification of the uncertainty in performance predictions with an uncertainty range similar to the one obtained with RML. Introduction We consider conditioning models to production data in a Bayesian framework and wish to generate a suite (ensemble) of models which represent a correct sampling of the conditional probability density function (pdf). By predicting future reservoir performance with each realization, we obtain a characterization of the uncertainty in predicted performance. Both the rejection algorithm and Markov chain Monte Carlo (MCMC) are theoretically sound sampling procedures, but they are too computationally inefficient for practical applications (Liu and Oliver 2003). Oliver et al. (1996) and Kitanidis (1986) independently proposed the randomized maximum likelihood (RML) method to generate an approximate sampling of the a posteriori pdf. Two different proofs (Oliver 1996; Reynolds et al. 1999) have been presented which show that the RML method samples the posterior probability density function (pdf) correctly if data are linearly related to the model; however, no rigorous theoretical foundation exists for the method when the relation between data and model is nonlinear, which is the case when the data represent production data. Computational results indicate that the RML method generates reasonable characterization of uncertainty for single-phase flow (Oliver et al. 1996; Reynolds et al. 1999; Liu and Oliver 2003). Our first objective is to show that, contrary to a previous claim (Floris 2001), RML gives a reasonable characterization of the uncertainty in predicted performance for the PUNQ-S3 problem; our second objective is to compare the quantification of uncertainty obtained with RML with the one obtained with the ensemble Kalman filter (EnKF). The PUNQ-S3 reservoir represents a synthetic model based on an actual reservoir (Floris et al. 2001; Barker et al. 2001). The problem was set up as a test case to allow various research groups to test their own methodology for the characterization of the uncertainty in reservoir performance predictions given some geologic information on the reservoir, hard data at well gridblocks and some scattered production data from the first 8 years of production. Then participants were asked to predict cumulative oil production for 16.5 years of total production and characterize the uncertainty in this prediction.

Sign in / Sign up

Export Citation Format

Share Document