Ensemble-Based Relative Permeability Estimation Using B-Spline Model

Li, Heng; Chen, Shengnan; Yang, Daoyong; Tontiwachwuthikul, Paitoon

doi:10.1007/s11242-010-9587-7

Cited by 28 publications

(8 citation statements)

References 48 publications

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“…The numerical study showed that the inconsistency problem occurs in EnKF results and cannot be resolved by using Confirming EnKF but by Restart EnKF. This finding is consistent with that of Zafari and Reynolds (2007) but different from that of Hendricks Franssen and Kinzelbach (2008) and thus challenges the seemingly consensus opinion that Confirming EnKF has been accepted as a common practice in many studies to alleviate inconsistency (Gu and Oliver, 2006; Krymskaya et al, 2008; Hendricks Franssen and Kinzelbach, 2008; Li et al, 2010; Zagayevskiy et al, 2012; Zhang et al, 2012).…”

supporting

confidence: 63%

Numerical Comparison of Iterative Ensemble Kalman Filters for Unsaturated Flow Inverse Modeling

Song

Shi

et al. 2014

Vadose Zone Journal

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supporting

confidence: 63%

Numerical Comparison of Iterative Ensemble Kalman Filters for Unsaturated Flow Inverse Modeling

Song

Shi

et al. 2014

Vadose Zone Journal

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“…where k is the step size which is determined according to the non-precise linear search. Li et al (2010) also proved that the expectation of stochastic gradients is the real gradients. Therefore, we take the average of several stochastic gradients as the SPSA gradient.…”

Section: Simultaneous Perturbation Stochastic Algorithm (Spsa)mentioning

confidence: 92%

Calibrate complex fracture model for subsurface flow based on Bayesian formulation

Zhang

et al. 2019

Pet. Sci.

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In practical development of unconventional reservoirs, fracture networks are a highly conductive transport media for subsurface fluid flow. Therefore, it is crucial to clearly determine the fracture properties used in production forecast. However, it is different to calibrate the properties of fracture networks because it is an inverse problem with multi-patterns and highcomplexity of fracture distribution and inherent defect of multiplicity of solution. In this paper, in order to solve the problem, the complex fracture model is divided into two sub-systems, namely "Pattern A" and "Pattern B." In addition, the generation method is grouped into two categories. Firstly, we construct each sub-system based on the probability density function of the fracture properties. Secondly, we recombine the sub-systems into an integral complex fracture system. Based on the generation mechanism, the estimation of the complex fracture from dynamic performance and observation data can be solved as an inverse problem. In this study, the Bayesian formulation is used to quantify the uncertainty of fracture properties. To minimize observation data misfit immediately as it occurs, we optimize the updated properties by a simultaneous perturbation stochastic algorithm which requires only two measurements of the loss function. In numerical experiments, we firstly visualize that small-scale fractures significantly contribute to the flow simulation. Then, we demonstrate the suitability and effectiveness of the Bayesian formulation for calibrating the complex fracture model in the following simulation.

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“…In order to estimate absolute and relative permeability by history matching the production data, the state vector of an ensemble member is defined as (Li et al, 2010), …”

Section: Enkf Algorithmmentioning

confidence: 99%

Relative Permeability Estimation from Displacement Experiments Using EnKF Method

Yang

Arhuoma

2010

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The relative permeability is a crucial parameter for accurately evaluating reservoir performance. Two-phase relative permeability curves are normally obtained by either directly or indirectly interpreting the displacement experiment data. As for the direct interpretation, the core samples are assumed to be homogeneous, while the capillary forces are normally neglected. Although the indirect interpreting approach is able to take heterogeneity of the core sample into account, calculating the derivatives of the objective functions through the graphical or numerical methods is prone to considerable errors. In this paper, a new method is developed to calculate the absolute and relative permeability from unsteady-state, two-phase immiscible displacement experiments. The permeability data is determined by history matching the experimentally observed pressure drop, production data and water saturation profiles via the ensemble Kalman filter (EnKF) algorithm. The power-law model is utilized to represent the relative permeability. Both the absolute and relative permeability are calculated simultaneously by assimilating the observed data. The newly developed method is validated using a numerical coreflooding experiment. It has been found that estimations of absolute and relative permeability are improved progressively as more observation data are assimilated. In addition, this method is convenient to be implemented as the derivative of the objective function is not required.

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Ensemble-Based Relative Permeability Estimation Using B-Spline Model

Cited by 28 publications

References 48 publications

Numerical Comparison of Iterative Ensemble Kalman Filters for Unsaturated Flow Inverse Modeling

Numerical Comparison of Iterative Ensemble Kalman Filters for Unsaturated Flow Inverse Modeling

Calibrate complex fracture model for subsurface flow based on Bayesian formulation

Relative Permeability Estimation from Displacement Experiments Using EnKF Method

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