Assisted History Matching for Fractured Reservoirs by Use of Hough-Transform-Based Parameterization

SPE Journal ◽  
2015 ◽  
Vol 20 (05) ◽  
pp. 942-961 ◽  
Author(s):  
Le Lu ◽  
Dongxiao Zhang
Keyword(s):  
Hough Transform ◽  
History Matching ◽  
Fractured Reservoirs ◽  
Axial Position ◽  
Model Parameters ◽  
Matching Methods ◽  
Inverse Transform ◽  
Hough Space ◽  
Assisted History Matching ◽  
Matching Techniques

Summary Successful production in fractured reservoirs is significantly dependent on knowledge of the location, orientation, and conductivity of the fractures. Early water breakthrough can be prevented and sweep efficiency can be improved with the help of comprehensive and accurate information of fracture distributions. However, it is a challenge to estimate fracture distributions by conventional-history-matching methods because of the complexity of such reservoirs. Although there has been great progress in assisted-history-matching techniques during the last 2 decades, estimating fracture distributions in fractured reservoirs is still inefficient because of the strong heterogeneity and spatial discontinuity of model parameters. The performance of assisted-history-matching methods, such as the ensemble Kalman filter, can be significantly degraded by the non-Gaussian distributions of the parameters, such as effective permeability and porosity. On the other hand, although the geometric shapes of fractures may be generated properly at the initial step, they are difficult to preserve after updating, which results in geologically unrealistic fracture-distribution maps. In this study, we develop an assisted-history-matching method for fractured reservoirs with a Hough-transform-based parameterization. The facies maps of fractured reservoirs are parameterized into Hough-function fields in a discrete Hough space, whereas each gridblock in the Hough domain represents a fracture defined by its two Cartesian coordinates: angle θ of its normal and ρ of its algebraic distance from the origin in the flow domain. The length and axial position of the fractures are defined by two additional parameters on the same grid. The Hough-function value of each gridblock in the Hough domain is used as the indicator of the existence of the fracture in the facies map. When this parameterization is implemented in assisted history matching, the parameter fields in the Hough space, instead of the facies maps, are updated conditional on the production history. An inverse transform is performed to generate facies maps for the reservoir simulator. Pointwise prior information, such as known fractures discovered from well-log data, as well as the statistics of fracture orientation, can be honored by the inverse transform throughout the history-matching process. Applications and the effectiveness of this method are demonstrated by 2D synthetic-waterflooding examples. The fracture distributions in reference fields are identified by this method, and updated models are capable of providing improved predictions for prolonged periods of production.

Parameters Estimation for Chemical Flooding Modeling Using Ensemble-Based Method

2021 ◽  
Author(s):  
Xindan Wang ◽  
Yin Zhang ◽  
Abhijit Dandekar ◽  
Yudou Wang
Keyword(s):  
Simulation Model ◽  
Oil Recovery ◽  
History Matching ◽  
Simulation Models ◽  
Parameters Estimation ◽  
Model Parameters ◽  
Chemical Flooding ◽  
Multiple Model ◽  
Assisted History Matching ◽  
Matching Techniques

Abstract Chemical flooding has been widely used to enhance oil recovery after conventional waterflooding. However, it is always a challenge to model chemical flooding accurately since many of the model parameters of the chemical flooding cannot be measured accurately in the lab and even some parameters cannot be obtained from the lab. Recently, the ensemble-based assisted history matching techniques have been proven to be efficient and effective in simultaneously estimating multiple model parameters. Therefore, this study validates the effectiveness of the ensemble-based method in estimating model parameters for chemical flooding simulation, and the half-iteration EnKF (HIEnKF) method has been employed to conduct the assisted history matching. In this work, five surfactantpolymer (SP) coreflooding experiments have been first conducted, and the corresponding core scale simulation models have been built to simulate the coreflooding experiments. Then the HIEnKF method has been applied to calibrate the core scale simulation models by assimilating the observed data including cumulative oil production and pressure drop from the corresponding coreflooding experiments. The HIEnKF method has been successively applied to simultaneously estimate multiple model parameters, including porosity and permeability fields, relative permeabilities, polymer viscosity curve, polymer adsorption curve, surfactant interfacial tension (IFT) curve and miscibility function curve, for the SP flooding simulation model. There exists a good agreement between the updated simulation results and observation data, indicating that the updated model parameters are appropriate to characterize the properties of the corresponding porous media and the fluid flow properties in it. At the same time, the effectiveness of the ensemble-based assisted history matching method in chemical enhanced oil recovery (EOR) simulation has been validated. Based on the validated simulation model, numerical simulation tests have been conducted to investigate the influence of injection schemes and operating parameters of SP flooding on the ultimate oil recovery performance. It has been found that the polymer concentration, surfactant concentration and slug size of SP flooding have a significant impact on oil recovery, and these parameters need to be optimized to achieve the maximum economic benefit.

scholarly journals Gaussian Processes Proxy Model with Latent Variable Models and Variogram-Based Sensitivity Analysis for Assisted History Matching

Energies ◽  
2020 ◽  
Vol 13 (17) ◽  
pp. 4290
Author(s):  
Dongmei Zhang ◽  
Yuyang Zhang ◽  
Bohou Jiang ◽  
Xinwei Jiang ◽  
Zhijiang Kang
Keyword(s):  
Sensitivity Analysis ◽  
Gaussian Processes ◽  
Latent Variable ◽  
History Matching ◽  
Latent Variable Models ◽  
High Dimensional ◽  
Model Parameters ◽  
Variable Model ◽  
Assisted History Matching ◽  
Proxy Models

Reservoir history matching is a well-known inverse problem for production prediction where enormous uncertain reservoir parameters of a reservoir numerical model are optimized by minimizing the misfit between the simulated and history production data. Gaussian Process (GP) has shown promising performance for assisted history matching due to the efficient nonparametric and nonlinear model with few model parameters to be tuned automatically. Recently introduced Gaussian Processes proxy models and Variogram Analysis of Response Surface-based sensitivity analysis (GP-VARS) uses forward and inverse Gaussian Processes (GP) based proxy models with the VARS-based sensitivity analysis to optimize the high-dimensional reservoir parameters. However, the inverse GP solution (GPIS) in GP-VARS are unsatisfactory especially for enormous reservoir parameters where the mapping from low-dimensional misfits to high-dimensional uncertain reservoir parameters could be poorly modeled by GP. To improve the performance of GP-VARS, in this paper we propose the Gaussian Processes proxy models with Latent Variable Models and VARS-based sensitivity analysis (GPLVM-VARS) where Gaussian Processes Latent Variable Model (GPLVM)-based inverse solution (GPLVMIS) instead of GP-based GPIS is provided with the inputs and outputs of GPIS reversed. The experimental results demonstrate the effectiveness of the proposed GPLVM-VARS in terms of accuracy and complexity. The source code of the proposed GPLVM-VARS is available at https://github.com/XinweiJiang/GPLVM-VARS.

Multiscale-Network Structure Inversion of Fractured Media Based on a Hierarchical-Parameterization and Data-Driven Evolutionary-Optimization Method

SPE Journal ◽  
2020 ◽  
Vol 25 (05) ◽  
pp. 2729-2748
Author(s):  
Xiaopeng Ma ◽  
Kai Zhang ◽  
Chuanjin Yao ◽  
Liming Zhang ◽  
Jian Wang ◽  
...  
Keyword(s):  
Network Structure ◽  
Inverse Modeling ◽  
History Matching ◽  
Fractured Reservoirs ◽  
Fracture Network ◽  
Fractured Media ◽  
Naturally Fractured Reservoirs ◽  
Data Driven ◽  
Model Parameters ◽  
Parameterization Method

Summary Efficient identification and characterization of fracture networks are crucial for the exploitation of fractured media such as naturally fractured reservoirs. Using the information obtained from borehole logs, core images, and outcrops, fracture geometries can be roughly estimated. However, this estimation always has uncertainty, which can be decreased using inverse modeling. Following the Bayes framework, a common practice for inverse modeling is to sample from the posterior distribution of uncertain parameters, given the observational data. However, a challenge for fractured reservoirs is that the fractures often occur on different scales, and these fractures form an irregular network structure that is difficult to model and predict. In this work, a multiscale-parameterization method is developed to model the fracture network. Based on this parameterization method, we present a novel history-matching approach using a data-driven evolutionary algorithm to explore the Bayesian posterior space and decrease the uncertainties of the model parameters. Empirical studies on hypothetical and outcrop-based cases demonstrate that the proposed method can model and estimate the complex multiscale-fracture network on a limited computational budget.

An Adaptive Ensemble Smoother With Multiple Data Assimilation for Assisted History Matching

SPE Journal ◽  
2016 ◽  
Vol 21 (06) ◽  
pp. 2195-2207 ◽  
Author(s):  
Duc H. Le ◽  
Alexandre A. Emerick ◽  
Albert C. Reynolds
Keyword(s):  
Data Assimilation ◽  
History Matching ◽  
Extreme Values ◽  
Model Parameters ◽  
Negative Effects ◽  
Vertical Permeability ◽  
Multiple Data ◽  
Ensemble Smoother ◽  
Assisted History Matching ◽  
Three Phase Flow

Summary Recently, Emerick and Reynolds (2012) introduced the ensemble smoother with multiple data assimilations (ES-MDA) for assisted history matching. With computational examples, they demonstrated that ES-MDA provides both a better data match and a better quantification of uncertainty than is obtained with the ensemble Kalman filter (EnKF). However, similar to EnKF, ES-MDA can experience near ensemble collapse and results in too many extreme values of rock-property fields for complex problems. These negative effects can be avoided by a judicious choice of the ES-MDA inflation factors, but, before this work, the optimal inflation factors could only be determined by trial and error. Here, we provide two automatic procedures for choosing the inflation factor for the next data-assimilation step adaptively as the history match proceeds. Both methods are motivated by knowledge of regularization procedures—the first is intuitive and heuristical; the second is motivated by existing theory on the regularization of least-squares inverse problems. We illustrate that the adaptive ES-MDA algorithms are superior to the original ES-MDA algorithm by history matching three-phase-flow production data for a complicated synthetic problem in which the reservoir-model parameters include the porosity, horizontal and vertical permeability fields, depths of the initial fluid contacts, and the parameters of power-law permeability curves.

History Matching of Naturally Fractured Reservoirs Using a Deep Sparse Autoencoder

SPE Journal ◽  
2021 ◽  
pp. 1-22
Author(s):  
Kai Zhang ◽  
Jinding Zhang ◽  
Xiaopeng Ma ◽  
Chuanjin Yao ◽  
Liming Zhang ◽  
...  
Keyword(s):  
Dimensionality Reduction ◽  
Latent Variables ◽  
History Matching ◽  
Reduction Method ◽  
Fractured Reservoirs ◽  
Fracture Network ◽  
Naturally Fractured Reservoirs ◽  
Model Parameters ◽  
Sparse Autoencoder ◽  
Dimensionality Reduction Method

Summary Although researchers have applied many methods to history matching, such as Monte Carlo methods, ensemble-based methods, and optimization algorithms, history matching fractured reservoirs is still challenging. The key challenges are effectively representing the fracture network and coping with large amounts of reservoir-model parameters. With increasing numbers of fractures, the dimension becomes larger, resulting in heavy computational work in the inversion of fractures. This paper proposes a new characterization method for the multiscale fracture network, and a powerful dimensionality-reduction method by means of an autoencoder for model parameters. The characterization method of the fracture network is dependent on the length, orientation, and position of fractures, including large-scale and small-scale fractures. To significantly reduce the dimension of parameters, the deep sparse autoencoder (DSAE) transforms the input to the low-dimensional latent variables through encoding and decoding. Integrated with the greedy layer-wise algorithm, we set up a DSAE and then take the latent variables as optimization variables. The performance of the DSAE with fewer activating nodes is excellent because it reduces the redundant information of the input and avoids overfitting. Then, we adopt the ensemble smoother (ES) with multiple data assimilation (ES-MDA) to solve this minimization problem. We test our proposed method in three synthetic reservoir history-matching problems, compared with the no-dimensionality-reduction method and the principal-component analysis (PCA). The numerical results show that the characterization method integrated with the DSAE could simplify the fracture network, preserve the distribution of fractures during the update, and improve the quality of history matching naturally fractured reservoirs.

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